tri, hexa->tetra',\n '2d' : 'force a 2D mesh by removing the z coordinates - assumes a 3D mesh'\n ' in the xy plane',\n 'save-per-mat': 'extract cells by material id and save them into'\n ' separate mesh files with a name based on filename_out and the id'\n ' numbers (preserves original mesh vertices)',\n\n 'remesh' : \"\"\"when given, remesh the given mesh using tetgen.\n The options can be the following, separated by spaces, in this order: 1.\n \"r\" causes remeshing of the mesh volume - if not present the mesh surface\n is extracted and used for the volume mesh generation. 2.\n \"q[/]\" (required) - the two numbers after \"q\" are a maximum\n radius-edge ratio bound and a minimum dihedral angle bound. 3. \"a\"\n (optional) - the number imposes a maximum volume constraint on all\n tetrahedra. 4. O[<0-9>/<0-7>] - the two numbers correspond to a mesh\n optimization level and a choice of optimizing operations. 5. \"V\"\n (optional) - if present, mesh statistics are printed. Consult the tetgen\n documentation for details.\"\"\",\n}\n\ndef _parse_val_or_vec(option, name, parser):\n if option is not None:\n try:\n try:\n option = float(option)\n except ValueError:\n option = [float(ii) for ii in option.split(',')]\n option = nm.array(option, dtype=nm.float64, ndmin=1)\n except:\n output('bad %s! (%s)' % (name, option))\n parser.print_help()\n sys.exit(1)\n\n return option\n\ndef main():\n parser = ArgumentParser(description=__doc__,\n formatter_class=RawDescriptionHelpFormatter)\n parser.add_argument('-s', '--scale', metavar='scale',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='scale',\n default=None, help=helps['scale'])\n parser.add_argument('-c', '--center', metavar='center',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='center',\n default=None, help=helps['center'])\n parser.add_argument('-r', '--refine', metavar='level',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", type=int, dest='refine',\n default=0, help=helps['refine'])\n parser.add_argument('-f', '--format', metavar='format',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", type=str, dest='format',\n default=None, help=helps['format'])\n parser.add_argument('-l', '--list', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='list', help=helps['list'])\n parser.add_argument('-m', '--merge', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='merge', help=helps['merge'])\n parser.add_argument('-t', '--tri-tetra', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='tri_tetra', help=helps['tri-tetra'])\n parser.add_argument('-2', '--2d', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='force_2d', help=helps['2d'])\n parser.add_argument('--save-per-mat', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='save_per_mat', help=helps['save-per-mat'])\n parser.add_argument('--remesh', metavar='options',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='remesh',\n default=None, help=helps['remesh'])\n parser.add_argument('filename_in')\n parser.add_argument('filename_out')\n options = parser.parse_args()\n\n if options.list:\n output('Supported readable mesh formats:')\n output('--------------------------------')\n output_mesh_formats('r')\n output('')\n output('Supported writable mesh formats:')\n output('--------------------------------')\n output_mesh_formats('w')\n sys.exit(0)\n\n scale = _parse_val_or_vec(options.scale, 'scale', parser)\n center = _parse_val_or_vec(options.center, 'center', parser)\n\n filename_in = options.filename_in\n filename_out = options.filename_out\n\n if options.remesh:\n import tempfile\n import shlex\n import subprocess\n\n dirname = tempfile.mkdtemp()\n\n is_surface = options.remesh.startswith('q')\n if is_surface:\n mesh = Mesh.from_file(filename_in)\n domain = FEDomain(mesh.name, mesh)\n region = domain.create_region('surf', 'vertices of surface',\n 'facet')\n surf_mesh = Mesh.from_region(region, mesh,\n localize=True, is_surface=True)\n\n filename = op.join(dirname, 'surf.mesh')\n surf_mesh.write(filename, io='auto')\n\n else:\n import shutil\n\n shutil.copy(filename_in, dirname)\n filename = op.join(dirname, op.basename(filename_in))\n\n qopts = ''.join(options.remesh.split()) # Remove spaces.\n command = 'tetgen -BFENkACp%s %s' % (qopts, filename)\n args = shlex.split(command)\n subprocess.call(args)\n\n root, ext = op.splitext(filename)\n mesh = Mesh.from_file(root + '.1.vtk')\n\n remove_files(dirname)\n\n else:\n mesh = Mesh.from_file(filename_in)\n\n if options.force_2d:\n data = list(mesh._get_io_data())\n data[0] = data[0][:, :2]\n mesh = Mesh.from_data(mesh.name, *data)\n\n if scale is not None:\n if len(scale) == 1:\n tr = nm.eye(mesh.dim, dtype=nm.float64) * scale\n elif len(scale) == mesh.dim:\n tr = nm.diag(scale)\n else:\n raise ValueError('bad scale! (%s)' % scale)\n mesh.transform_coors(tr)\n\n if center is not None:\n cc = 0.5 * mesh.get_bounding_box().sum(0)\n shift = center - cc\n tr = nm.c_[nm.eye(mesh.dim, dtype=nm.float64), shift[:, None]]\n mesh.transform_coors(tr)\n\n if options.refine > 0:\n domain = FEDomain(mesh.name, mesh)\n output('initial mesh: %d nodes %d elements'\n % (domain.shape.n_nod, domain.shape.n_el))\n\n for ii in range(options.refine):\n output('refine %d...' % ii)\n domain = domain.refine()\n output('... %d nodes %d elements'\n % (domain.shape.n_nod, domain.shape.n_el))\n\n mesh = domain.mesh\n\n if options.tri_tetra > 0:\n conns = None\n for k, new_desc in [('3_8', '3_4'), ('2_4', '2_3')]:\n if k in mesh.descs:\n conns = mesh.get_conn(k)\n break\n\n if conns is not None:\n nelo = conns.shape[0]\n output('initial mesh: %d elements' % nelo)\n\n new_conns = elems_q2t(conns)\n nn = new_conns.shape[0] // nelo\n new_cgroups = nm.repeat(mesh.cmesh.cell_groups, nn)\n\n output('new mesh: %d elements' % new_conns.shape[0])\n mesh = Mesh.from_data(mesh.name, mesh.coors,\n mesh.cmesh.vertex_groups,\n [new_conns], [new_cgroups], [new_desc])\n\n if options.merge:\n desc = mesh.descs[0]\n coor, ngroups, conns = fix_double_nodes(mesh.coors,\n mesh.cmesh.vertex_groups,\n mesh.get_conn(desc), 1e-9)\n mesh = Mesh.from_data(mesh.name + '_merged',\n coor, ngroups,\n [conns], [mesh.cmesh.cell_groups], [desc])\n\n if options.save_per_mat:\n desc = mesh.descs[0]\n conns, cgroups = mesh.get_conn(desc), mesh.cmesh.cell_groups\n coors, ngroups = mesh.coors, mesh.cmesh.vertex_groups\n mat_ids = nm.unique(cgroups)\n\n for mat_id in mat_ids:\n idxs = nm.where(cgroups == mat_id)[0]\n imesh = Mesh.from_data(mesh.name + '_matid_%d' % mat_id,\n coors, ngroups,\n [conns[idxs]], [cgroups[idxs]], [desc])\n\n fbase, fext = op.splitext(filename_out)\n ifilename_out = '%s_matid_%d%s' % (fbase, mat_id, fext)\n io = MeshIO.for_format(ifilename_out, format=options.format,\n writable=True)\n output('writing %s...' % ifilename_out)\n imesh.write(ifilename_out, io=io)\n output('...done')\n\n io = MeshIO.for_format(filename_out, format=options.format,\n writable=True)\n\n cell_types = ', '.join(supported_cell_types[io.format])\n "},"completion":{"kind":"string","value":"output('writing [%s] %s...' % (cell_types, filename_out))"},"api":{"kind":"string","value":"sfepy.base.base.output"}}},{"rowIdx":25,"cells":{"prompt":{"kind":"string","value":"#!/usr/bin/env python\n\"\"\"\nConvert a mesh file from one SfePy-supported format to another.\n\nExamples::\n\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s2.5\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 -c 0\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.mesh --remesh='q2/0 a1e-8 O9/7 V'\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new2.mesh --remesh='rq2/0 a1e-8 O9/7 V'\n\"\"\"\nfrom __future__ import absolute_import\nimport sys\nimport os.path as op\nfrom six.moves import range\nsys.path.append('.')\n\nfrom argparse import ArgumentParser, RawDescriptionHelpFormatter\nfrom sfepy.base.base import nm, output\nfrom sfepy.base.ioutils import remove_files\nfrom sfepy.discrete.fem import Mesh, FEDomain\nfrom sfepy.discrete.fem.meshio import (output_mesh_formats, MeshIO,\n supported_cell_types)\nfrom sfepy.discrete.fem.mesh import fix_double_nodes\nfrom sfepy.mesh.mesh_tools import elems_q2t\n\nhelps = {\n 'scale' : 'scale factor (float or comma-separated list for each axis)'\n ' [default: %(default)s]',\n 'center' : 'center of the output mesh (0 for origin or'\n ' comma-separated list for each axis) applied after scaling'\n ' [default: %(default)s]',\n 'refine' : 'uniform refinement level [default: %(default)s]',\n 'format' : 'output mesh format (overrides filename_out extension)',\n 'list' : 'list supported readable/writable output mesh formats',\n 'merge' : 'remove duplicate vertices',\n 'tri-tetra' : 'convert elements: quad->tri, hexa->tetra',\n '2d' : 'force a 2D mesh by removing the z coordinates - assumes a 3D mesh'\n ' in the xy plane',\n 'save-per-mat': 'extract cells by material id and save them into'\n ' separate mesh files with a name based on filename_out and the id'\n ' numbers (preserves original mesh vertices)',\n\n 'remesh' : \"\"\"when given, remesh the given mesh using tetgen.\n The options can be the following, separated by spaces, in this order: 1.\n \"r\" causes remeshing of the mesh volume - if not present the mesh surface\n is extracted and used for the volume mesh generation. 2.\n \"q[/]\" (required) - the two numbers after \"q\" are a maximum\n radius-edge ratio bound and a minimum dihedral angle bound. 3. \"a\"\n (optional) - the number imposes a maximum volume constraint on all\n tetrahedra. 4. O[<0-9>/<0-7>] - the two numbers correspond to a mesh\n optimization level and a choice of optimizing operations. 5. \"V\"\n (optional) - if present, mesh statistics are printed. Consult the tetgen\n documentation for details.\"\"\",\n}\n\ndef _parse_val_or_vec(option, name, parser):\n if option is not None:\n try:\n try:\n option = float(option)\n except ValueError:\n option = [float(ii) for ii in option.split(',')]\n option = nm.array(option, dtype=nm.float64, ndmin=1)\n except:\n output('bad %s! (%s)' % (name, option))\n parser.print_help()\n sys.exit(1)\n\n return option\n\ndef main():\n parser = ArgumentParser(description=__doc__,\n formatter_class=RawDescriptionHelpFormatter)\n parser.add_argument('-s', '--scale', metavar='scale',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='scale',\n default=None, help=helps['scale'])\n parser.add_argument('-c', '--center', metavar='center',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='center',\n default=None, help=helps['center'])\n parser.add_argument('-r', '--refine', metavar='level',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", type=int, dest='refine',\n default=0, help=helps['refine'])\n parser.add_argument('-f', '--format', metavar='format',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", type=str, dest='format',\n default=None, help=helps['format'])\n parser.add_argument('-l', '--list', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='list', help=helps['list'])\n parser.add_argument('-m', '--merge', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='merge', help=helps['merge'])\n parser.add_argument('-t', '--tri-tetra', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='tri_tetra', help=helps['tri-tetra'])\n parser.add_argument('-2', '--2d', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='force_2d', help=helps['2d'])\n parser.add_argument('--save-per-mat', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='save_per_mat', help=helps['save-per-mat'])\n parser.add_argument('--remesh', metavar='options',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='remesh',\n default=None, help=helps['remesh'])\n parser.add_argument('filename_in')\n parser.add_argument('filename_out')\n options = parser.parse_args()\n\n if options.list:\n output('Supported readable mesh formats:')\n output('--------------------------------')\n output_mesh_formats('r')\n output('')\n output('Supported writable mesh formats:')\n output('--------------------------------')\n output_mesh_formats('w')\n sys.exit(0)\n\n scale = _parse_val_or_vec(options.scale, 'scale', parser)\n center = _parse_val_or_vec(options.center, 'center', parser)\n\n filename_in = options.filename_in\n filename_out = options.filename_out\n\n if options.remesh:\n import tempfile\n import shlex\n import subprocess\n\n dirname = tempfile.mkdtemp()\n\n is_surface = options.remesh.startswith('q')\n if is_surface:\n mesh = Mesh.from_file(filename_in)\n domain = FEDomain(mesh.name, mesh)\n region = domain.create_region('surf', 'vertices of surface',\n 'facet')\n surf_mesh = Mesh.from_region(region, mesh,\n localize=True, is_surface=True)\n\n filename = op.join(dirname, 'surf.mesh')\n surf_mesh.write(filename, io='auto')\n\n else:\n import shutil\n\n shutil.copy(filename_in, dirname)\n filename = op.join(dirname, op.basename(filename_in))\n\n qopts = ''.join(options.remesh.split()) # Remove spaces.\n command = 'tetgen -BFENkACp%s %s' % (qopts, filename)\n args = shlex.split(command)\n subprocess.call(args)\n\n root, ext = op.splitext(filename)\n mesh = Mesh.from_file(root + '.1.vtk')\n\n remove_files(dirname)\n\n else:\n mesh = Mesh.from_file(filename_in)\n\n if options.force_2d:\n data = list(mesh._get_io_data())\n data[0] = data[0][:, :2]\n mesh = Mesh.from_data(mesh.name, *data)\n\n if scale is not None:\n if len(scale) == 1:\n tr = nm.eye(mesh.dim, dtype=nm.float64) * scale\n elif len(scale) == mesh.dim:\n tr = nm.diag(scale)\n else:\n raise ValueError('bad scale! (%s)' % scale)\n mesh.transform_coors(tr)\n\n if center is not None:\n cc = 0.5 * mesh.get_bounding_box().sum(0)\n shift = center - cc\n tr = nm.c_[nm.eye(mesh.dim, dtype=nm.float64), shift[:, None]]\n mesh.transform_coors(tr)\n\n if options.refine > 0:\n domain = FEDomain(mesh.name, mesh)\n output('initial mesh: %d nodes %d elements'\n % (domain.shape.n_nod, domain.shape.n_el))\n\n for ii in range(options.refine):\n output('refine %d...' % ii)\n domain = domain.refine()\n output('... %d nodes %d elements'\n % (domain.shape.n_nod, domain.shape.n_el))\n\n mesh = domain.mesh\n\n if options.tri_tetra > 0:\n conns = None\n for k, new_desc in [('3_8', '3_4'), ('2_4', '2_3')]:\n if k in mesh.descs:\n conns = mesh.get_conn(k)\n break\n\n if conns is not None:\n nelo = conns.shape[0]\n output('initial mesh: %d elements' % nelo)\n\n new_conns = elems_q2t(conns)\n nn = new_conns.shape[0] // nelo\n new_cgroups = nm.repeat(mesh.cmesh.cell_groups, nn)\n\n output('new mesh: %d elements' % new_conns.shape[0])\n mesh = Mesh.from_data(mesh.name, mesh.coors,\n mesh.cmesh.vertex_groups,\n [new_conns], [new_cgroups], [new_desc])\n\n if options.merge:\n desc = mesh.descs[0]\n coor, ngroups, conns = fix_double_nodes(mesh.coors,\n mesh.cmesh.vertex_groups,\n mesh.get_conn(desc), 1e-9)\n mesh = Mesh.from_data(mesh.name + '_merged',\n coor, ngroups,\n [conns], [mesh.cmesh.cell_groups], [desc])\n\n if options.save_per_mat:\n desc = mesh.descs[0]\n conns, cgroups = mesh.get_conn(desc), mesh.cmesh.cell_groups\n coors, ngroups = mesh.coors, mesh.cmesh.vertex_groups\n mat_ids = nm.unique(cgroups)\n\n for mat_id in mat_ids:\n idxs = nm.where(cgroups == mat_id)[0]\n imesh = Mesh.from_data(mesh.name + '_matid_%d' % mat_id,\n coors, ngroups,\n [conns[idxs]], [cgroups[idxs]], [desc])\n\n fbase, fext = op.splitext(filename_out)\n ifilename_out = '%s_matid_%d%s' % (fbase, mat_id, fext)\n io = MeshIO.for_format(ifilename_out, format=options.format,\n writable=True)\n output('writing %s...' % ifilename_out)\n imesh.write(ifilename_out, io=io)\n output('...done')\n\n io = MeshIO.for_format(filename_out, format=options.format,\n writable=True)\n\n cell_types = ', '.join(supported_cell_types[io.format])\n output('writing [%s] %s...' % (cell_types, filename_out))\n mesh.write(filename_out, io=io)\n "},"completion":{"kind":"string","value":"output('...done')"},"api":{"kind":"string","value":"sfepy.base.base.output"}}},{"rowIdx":26,"cells":{"prompt":{"kind":"string","value":"#!/usr/bin/env python\n\"\"\"\nConvert a mesh file from one SfePy-supported format to another.\n\nExamples::\n\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s2.5\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 -c 0\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.mesh --remesh='q2/0 a1e-8 O9/7 V'\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new2.mesh --remesh='rq2/0 a1e-8 O9/7 V'\n\"\"\"\nfrom __future__ import absolute_import\nimport sys\nimport os.path as op\nfrom six.moves import range\nsys.path.append('.')\n\nfrom argparse import ArgumentParser, RawDescriptionHelpFormatter\nfrom sfepy.base.base import nm, output\nfrom sfepy.base.ioutils import remove_files\nfrom sfepy.discrete.fem import Mesh, FEDomain\nfrom sfepy.discrete.fem.meshio import (output_mesh_formats, MeshIO,\n supported_cell_types)\nfrom sfepy.discrete.fem.mesh import fix_double_nodes\nfrom sfepy.mesh.mesh_tools import elems_q2t\n\nhelps = {\n 'scale' : 'scale factor (float or comma-separated list for each axis)'\n ' [default: %(default)s]',\n 'center' : 'center of the output mesh (0 for origin or'\n ' comma-separated list for each axis) applied after scaling'\n ' [default: %(default)s]',\n 'refine' : 'uniform refinement level [default: %(default)s]',\n 'format' : 'output mesh format (overrides filename_out extension)',\n 'list' : 'list supported readable/writable output mesh formats',\n 'merge' : 'remove duplicate vertices',\n 'tri-tetra' : 'convert elements: quad->tri, hexa->tetra',\n '2d' : 'force a 2D mesh by removing the z coordinates - assumes a 3D mesh'\n ' in the xy plane',\n 'save-per-mat': 'extract cells by material id and save them into'\n ' separate mesh files with a name based on filename_out and the id'\n ' numbers (preserves original mesh vertices)',\n\n 'remesh' : \"\"\"when given, remesh the given mesh using tetgen.\n The options can be the following, separated by spaces, in this order: 1.\n \"r\" causes remeshing of the mesh volume - if not present the mesh surface\n is extracted and used for the volume mesh generation. 2.\n \"q[/]\" (required) - the two numbers after \"q\" are a maximum\n radius-edge ratio bound and a minimum dihedral angle bound. 3. \"a\"\n (optional) - the number imposes a maximum volume constraint on all\n tetrahedra. 4. O[<0-9>/<0-7>] - the two numbers correspond to a mesh\n optimization level and a choice of optimizing operations. 5. \"V\"\n (optional) - if present, mesh statistics are printed. Consult the tetgen\n documentation for details.\"\"\",\n}\n\ndef _parse_val_or_vec(option, name, parser):\n if option is not None:\n try:\n try:\n option = float(option)\n except ValueError:\n option = [float(ii) for ii in option.split(',')]\n option = nm.array(option, dtype=nm.float64, ndmin=1)\n except:\n output('bad %s! (%s)' % (name, option))\n parser.print_help()\n sys.exit(1)\n\n return option\n\ndef main():\n parser = ArgumentParser(description=__doc__,\n formatter_class=RawDescriptionHelpFormatter)\n parser.add_argument('-s', '--scale', metavar='scale',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='scale',\n default=None, help=helps['scale'])\n parser.add_argument('-c', '--center', metavar='center',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='center',\n default=None, help=helps['center'])\n parser.add_argument('-r', '--refine', metavar='level',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", type=int, dest='refine',\n default=0, help=helps['refine'])\n parser.add_argument('-f', '--format', metavar='format',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", type=str, dest='format',\n default=None, help=helps['format'])\n parser.add_argument('-l', '--list', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='list', help=helps['list'])\n parser.add_argument('-m', '--merge', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='merge', help=helps['merge'])\n parser.add_argument('-t', '--tri-tetra', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='tri_tetra', help=helps['tri-tetra'])\n parser.add_argument('-2', '--2d', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='force_2d', help=helps['2d'])\n parser.add_argument('--save-per-mat', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='save_per_mat', help=helps['save-per-mat'])\n parser.add_argument('--remesh', metavar='options',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='remesh',\n default=None, help=helps['remesh'])\n parser.add_argument('filename_in')\n parser.add_argument('filename_out')\n options = parser.parse_args()\n\n if options.list:\n "},"completion":{"kind":"string","value":"output('Supported readable mesh formats:')"},"api":{"kind":"string","value":"sfepy.base.base.output"}}},{"rowIdx":27,"cells":{"prompt":{"kind":"string","value":"#!/usr/bin/env python\n\"\"\"\nConvert a mesh file from one SfePy-supported format to another.\n\nExamples::\n\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s2.5\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 -c 0\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.mesh --remesh='q2/0 a1e-8 O9/7 V'\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new2.mesh --remesh='rq2/0 a1e-8 O9/7 V'\n\"\"\"\nfrom __future__ import absolute_import\nimport sys\nimport os.path as op\nfrom six.moves import range\nsys.path.append('.')\n\nfrom argparse import ArgumentParser, RawDescriptionHelpFormatter\nfrom sfepy.base.base import nm, output\nfrom sfepy.base.ioutils import remove_files\nfrom sfepy.discrete.fem import Mesh, FEDomain\nfrom sfepy.discrete.fem.meshio import (output_mesh_formats, MeshIO,\n supported_cell_types)\nfrom sfepy.discrete.fem.mesh import fix_double_nodes\nfrom sfepy.mesh.mesh_tools import elems_q2t\n\nhelps = {\n 'scale' : 'scale factor (float or comma-separated list for each axis)'\n ' [default: %(default)s]',\n 'center' : 'center of the output mesh (0 for origin or'\n ' comma-separated list for each axis) applied after scaling'\n ' [default: %(default)s]',\n 'refine' : 'uniform refinement level [default: %(default)s]',\n 'format' : 'output mesh format (overrides filename_out extension)',\n 'list' : 'list supported readable/writable output mesh formats',\n 'merge' : 'remove duplicate vertices',\n 'tri-tetra' : 'convert elements: quad->tri, hexa->tetra',\n '2d' : 'force a 2D mesh by removing the z coordinates - assumes a 3D mesh'\n ' in the xy plane',\n 'save-per-mat': 'extract cells by material id and save them into'\n ' separate mesh files with a name based on filename_out and the id'\n ' numbers (preserves original mesh vertices)',\n\n 'remesh' : \"\"\"when given, remesh the given mesh using tetgen.\n The options can be the following, separated by spaces, in this order: 1.\n \"r\" causes remeshing of the mesh volume - if not present the mesh surface\n is extracted and used for the volume mesh generation. 2.\n \"q[/]\" (required) - the two numbers after \"q\" are a maximum\n radius-edge ratio bound and a minimum dihedral angle bound. 3. \"a\"\n (optional) - the number imposes a maximum volume constraint on all\n tetrahedra. 4. O[<0-9>/<0-7>] - the two numbers correspond to a mesh\n optimization level and a choice of optimizing operations. 5. \"V\"\n (optional) - if present, mesh statistics are printed. Consult the tetgen\n documentation for details.\"\"\",\n}\n\ndef _parse_val_or_vec(option, name, parser):\n if option is not None:\n try:\n try:\n option = float(option)\n except ValueError:\n option = [float(ii) for ii in option.split(',')]\n option = nm.array(option, dtype=nm.float64, ndmin=1)\n except:\n output('bad %s! (%s)' % (name, option))\n parser.print_help()\n sys.exit(1)\n\n return option\n\ndef main():\n parser = ArgumentParser(description=__doc__,\n formatter_class=RawDescriptionHelpFormatter)\n parser.add_argument('-s', '--scale', metavar='scale',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='scale',\n default=None, help=helps['scale'])\n parser.add_argument('-c', '--center', metavar='center',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='center',\n default=None, help=helps['center'])\n parser.add_argument('-r', '--refine', metavar='level',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", type=int, dest='refine',\n default=0, help=helps['refine'])\n parser.add_argument('-f', '--format', metavar='format',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", type=str, dest='format',\n default=None, help=helps['format'])\n parser.add_argument('-l', '--list', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='list', help=helps['list'])\n parser.add_argument('-m', '--merge', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='merge', help=helps['merge'])\n parser.add_argument('-t', '--tri-tetra', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='tri_tetra', help=helps['tri-tetra'])\n parser.add_argument('-2', '--2d', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='force_2d', help=helps['2d'])\n parser.add_argument('--save-per-mat', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='save_per_mat', help=helps['save-per-mat'])\n parser.add_argument('--remesh', metavar='options',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='remesh',\n default=None, help=helps['remesh'])\n parser.add_argument('filename_in')\n parser.add_argument('filename_out')\n options = parser.parse_args()\n\n if options.list:\n output('Supported readable mesh formats:')\n "},"completion":{"kind":"string","value":"output('--------------------------------')"},"api":{"kind":"string","value":"sfepy.base.base.output"}}},{"rowIdx":28,"cells":{"prompt":{"kind":"string","value":"#!/usr/bin/env python\n\"\"\"\nConvert a mesh file from one SfePy-supported format to another.\n\nExamples::\n\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s2.5\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 -c 0\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.mesh --remesh='q2/0 a1e-8 O9/7 V'\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new2.mesh --remesh='rq2/0 a1e-8 O9/7 V'\n\"\"\"\nfrom __future__ import absolute_import\nimport sys\nimport os.path as op\nfrom six.moves import range\nsys.path.append('.')\n\nfrom argparse import ArgumentParser, RawDescriptionHelpFormatter\nfrom sfepy.base.base import nm, output\nfrom sfepy.base.ioutils import remove_files\nfrom sfepy.discrete.fem import Mesh, FEDomain\nfrom sfepy.discrete.fem.meshio import (output_mesh_formats, MeshIO,\n supported_cell_types)\nfrom sfepy.discrete.fem.mesh import fix_double_nodes\nfrom sfepy.mesh.mesh_tools import elems_q2t\n\nhelps = {\n 'scale' : 'scale factor (float or comma-separated list for each axis)'\n ' [default: %(default)s]',\n 'center' : 'center of the output mesh (0 for origin or'\n ' comma-separated list for each axis) applied after scaling'\n ' [default: %(default)s]',\n 'refine' : 'uniform refinement level [default: %(default)s]',\n 'format' : 'output mesh format (overrides filename_out extension)',\n 'list' : 'list supported readable/writable output mesh formats',\n 'merge' : 'remove duplicate vertices',\n 'tri-tetra' : 'convert elements: quad->tri, hexa->tetra',\n '2d' : 'force a 2D mesh by removing the z coordinates - assumes a 3D mesh'\n ' in the xy plane',\n 'save-per-mat': 'extract cells by material id and save them into'\n ' separate mesh files with a name based on filename_out and the id'\n ' numbers (preserves original mesh vertices)',\n\n 'remesh' : \"\"\"when given, remesh the given mesh using tetgen.\n The options can be the following, separated by spaces, in this order: 1.\n \"r\" causes remeshing of the mesh volume - if not present the mesh surface\n is extracted and used for the volume mesh generation. 2.\n \"q[/]\" (required) - the two numbers after \"q\" are a maximum\n radius-edge ratio bound and a minimum dihedral angle bound. 3. \"a\"\n (optional) - the number imposes a maximum volume constraint on all\n tetrahedra. 4. O[<0-9>/<0-7>] - the two numbers correspond to a mesh\n optimization level and a choice of optimizing operations. 5. \"V\"\n (optional) - if present, mesh statistics are printed. Consult the tetgen\n documentation for details.\"\"\",\n}\n\ndef _parse_val_or_vec(option, name, parser):\n if option is not None:\n try:\n try:\n option = float(option)\n except ValueError:\n option = [float(ii) for ii in option.split(',')]\n option = nm.array(option, dtype=nm.float64, ndmin=1)\n except:\n output('bad %s! (%s)' % (name, option))\n parser.print_help()\n sys.exit(1)\n\n return option\n\ndef main():\n parser = ArgumentParser(description=__doc__,\n formatter_class=RawDescriptionHelpFormatter)\n parser.add_argument('-s', '--scale', metavar='scale',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='scale',\n default=None, help=helps['scale'])\n parser.add_argument('-c', '--center', metavar='center',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='center',\n default=None, help=helps['center'])\n parser.add_argument('-r', '--refine', metavar='level',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", type=int, dest='refine',\n default=0, help=helps['refine'])\n parser.add_argument('-f', '--format', metavar='format',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", type=str, dest='format',\n default=None, help=helps['format'])\n parser.add_argument('-l', '--list', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='list', help=helps['list'])\n parser.add_argument('-m', '--merge', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='merge', help=helps['merge'])\n parser.add_argument('-t', '--tri-tetra', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='tri_tetra', help=helps['tri-tetra'])\n parser.add_argument('-2', '--2d', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='force_2d', help=helps['2d'])\n parser.add_argument('--save-per-mat', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='save_per_mat', help=helps['save-per-mat'])\n parser.add_argument('--remesh', metavar='options',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='remesh',\n default=None, help=helps['remesh'])\n parser.add_argument('filename_in')\n parser.add_argument('filename_out')\n options = parser.parse_args()\n\n if options.list:\n output('Supported readable mesh formats:')\n output('--------------------------------')\n "},"completion":{"kind":"string","value":"output_mesh_formats('r')"},"api":{"kind":"string","value":"sfepy.discrete.fem.meshio.output_mesh_formats"}}},{"rowIdx":29,"cells":{"prompt":{"kind":"string","value":"#!/usr/bin/env python\n\"\"\"\nConvert a mesh file from one SfePy-supported format to another.\n\nExamples::\n\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s2.5\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 -c 0\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.mesh --remesh='q2/0 a1e-8 O9/7 V'\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new2.mesh --remesh='rq2/0 a1e-8 O9/7 V'\n\"\"\"\nfrom __future__ import absolute_import\nimport sys\nimport os.path as op\nfrom six.moves import range\nsys.path.append('.')\n\nfrom argparse import ArgumentParser, RawDescriptionHelpFormatter\nfrom sfepy.base.base import nm, output\nfrom sfepy.base.ioutils import remove_files\nfrom sfepy.discrete.fem import Mesh, FEDomain\nfrom sfepy.discrete.fem.meshio import (output_mesh_formats, MeshIO,\n supported_cell_types)\nfrom sfepy.discrete.fem.mesh import fix_double_nodes\nfrom sfepy.mesh.mesh_tools import elems_q2t\n\nhelps = {\n 'scale' : 'scale factor (float or comma-separated list for each axis)'\n ' [default: %(default)s]',\n 'center' : 'center of the output mesh (0 for origin or'\n ' comma-separated list for each axis) applied after scaling'\n ' [default: %(default)s]',\n 'refine' : 'uniform refinement level [default: %(default)s]',\n 'format' : 'output mesh format (overrides filename_out extension)',\n 'list' : 'list supported readable/writable output mesh formats',\n 'merge' : 'remove duplicate vertices',\n 'tri-tetra' : 'convert elements: quad->tri, hexa->tetra',\n '2d' : 'force a 2D mesh by removing the z coordinates - assumes a 3D mesh'\n ' in the xy plane',\n 'save-per-mat': 'extract cells by material id and save them into'\n ' separate mesh files with a name based on filename_out and the id'\n ' numbers (preserves original mesh vertices)',\n\n 'remesh' : \"\"\"when given, remesh the given mesh using tetgen.\n The options can be the following, separated by spaces, in this order: 1.\n \"r\" causes remeshing of the mesh volume - if not present the mesh surface\n is extracted and used for the volume mesh generation. 2.\n \"q[/]\" (required) - the two numbers after \"q\" are a maximum\n radius-edge ratio bound and a minimum dihedral angle bound. 3. \"a\"\n (optional) - the number imposes a maximum volume constraint on all\n tetrahedra. 4. O[<0-9>/<0-7>] - the two numbers correspond to a mesh\n optimization level and a choice of optimizing operations. 5. \"V\"\n (optional) - if present, mesh statistics are printed. Consult the tetgen\n documentation for details.\"\"\",\n}\n\ndef _parse_val_or_vec(option, name, parser):\n if option is not None:\n try:\n try:\n option = float(option)\n except ValueError:\n option = [float(ii) for ii in option.split(',')]\n option = nm.array(option, dtype=nm.float64, ndmin=1)\n except:\n output('bad %s! (%s)' % (name, option))\n parser.print_help()\n sys.exit(1)\n\n return option\n\ndef main():\n parser = ArgumentParser(description=__doc__,\n formatter_class=RawDescriptionHelpFormatter)\n parser.add_argument('-s', '--scale', metavar='scale',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='scale',\n default=None, help=helps['scale'])\n parser.add_argument('-c', '--center', metavar='center',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='center',\n default=None, help=helps['center'])\n parser.add_argument('-r', '--refine', metavar='level',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", type=int, dest='refine',\n default=0, help=helps['refine'])\n parser.add_argument('-f', '--format', metavar='format',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", type=str, dest='format',\n default=None, help=helps['format'])\n parser.add_argument('-l', '--list', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='list', help=helps['list'])\n parser.add_argument('-m', '--merge', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='merge', help=helps['merge'])\n parser.add_argument('-t', '--tri-tetra', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='tri_tetra', help=helps['tri-tetra'])\n parser.add_argument('-2', '--2d', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='force_2d', help=helps['2d'])\n parser.add_argument('--save-per-mat', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='save_per_mat', help=helps['save-per-mat'])\n parser.add_argument('--remesh', metavar='options',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='remesh',\n default=None, help=helps['remesh'])\n parser.add_argument('filename_in')\n parser.add_argument('filename_out')\n options = parser.parse_args()\n\n if options.list:\n output('Supported readable mesh formats:')\n output('--------------------------------')\n output_mesh_formats('r')\n "},"completion":{"kind":"string","value":"output('')"},"api":{"kind":"string","value":"sfepy.base.base.output"}}},{"rowIdx":30,"cells":{"prompt":{"kind":"string","value":"#!/usr/bin/env python\n\"\"\"\nConvert a mesh file from one SfePy-supported format to another.\n\nExamples::\n\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s2.5\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 -c 0\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.mesh --remesh='q2/0 a1e-8 O9/7 V'\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new2.mesh --remesh='rq2/0 a1e-8 O9/7 V'\n\"\"\"\nfrom __future__ import absolute_import\nimport sys\nimport os.path as op\nfrom six.moves import range\nsys.path.append('.')\n\nfrom argparse import ArgumentParser, RawDescriptionHelpFormatter\nfrom sfepy.base.base import nm, output\nfrom sfepy.base.ioutils import remove_files\nfrom sfepy.discrete.fem import Mesh, FEDomain\nfrom sfepy.discrete.fem.meshio import (output_mesh_formats, MeshIO,\n supported_cell_types)\nfrom sfepy.discrete.fem.mesh import fix_double_nodes\nfrom sfepy.mesh.mesh_tools import elems_q2t\n\nhelps = {\n 'scale' : 'scale factor (float or comma-separated list for each axis)'\n ' [default: %(default)s]',\n 'center' : 'center of the output mesh (0 for origin or'\n ' comma-separated list for each axis) applied after scaling'\n ' [default: %(default)s]',\n 'refine' : 'uniform refinement level [default: %(default)s]',\n 'format' : 'output mesh format (overrides filename_out extension)',\n 'list' : 'list supported readable/writable output mesh formats',\n 'merge' : 'remove duplicate vertices',\n 'tri-tetra' : 'convert elements: quad->tri, hexa->tetra',\n '2d' : 'force a 2D mesh by removing the z coordinates - assumes a 3D mesh'\n ' in the xy plane',\n 'save-per-mat': 'extract cells by material id and save them into'\n ' separate mesh files with a name based on filename_out and the id'\n ' numbers (preserves original mesh vertices)',\n\n 'remesh' : \"\"\"when given, remesh the given mesh using tetgen.\n The options can be the following, separated by spaces, in this order: 1.\n \"r\" causes remeshing of the mesh volume - if not present the mesh surface\n is extracted and used for the volume mesh generation. 2.\n \"q[/]\" (required) - the two numbers after \"q\" are a maximum\n radius-edge ratio bound and a minimum dihedral angle bound. 3. \"a\"\n (optional) - the number imposes a maximum volume constraint on all\n tetrahedra. 4. O[<0-9>/<0-7>] - the two numbers correspond to a mesh\n optimization level and a choice of optimizing operations. 5. \"V\"\n (optional) - if present, mesh statistics are printed. Consult the tetgen\n documentation for details.\"\"\",\n}\n\ndef _parse_val_or_vec(option, name, parser):\n if option is not None:\n try:\n try:\n option = float(option)\n except ValueError:\n option = [float(ii) for ii in option.split(',')]\n option = nm.array(option, dtype=nm.float64, ndmin=1)\n except:\n output('bad %s! (%s)' % (name, option))\n parser.print_help()\n sys.exit(1)\n\n return option\n\ndef main():\n parser = ArgumentParser(description=__doc__,\n formatter_class=RawDescriptionHelpFormatter)\n parser.add_argument('-s', '--scale', metavar='scale',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='scale',\n default=None, help=helps['scale'])\n parser.add_argument('-c', '--center', metavar='center',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='center',\n default=None, help=helps['center'])\n parser.add_argument('-r', '--refine', metavar='level',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", type=int, dest='refine',\n default=0, help=helps['refine'])\n parser.add_argument('-f', '--format', metavar='format',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", type=str, dest='format',\n default=None, help=helps['format'])\n parser.add_argument('-l', '--list', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='list', help=helps['list'])\n parser.add_argument('-m', '--merge', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='merge', help=helps['merge'])\n parser.add_argument('-t', '--tri-tetra', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='tri_tetra', help=helps['tri-tetra'])\n parser.add_argument('-2', '--2d', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='force_2d', help=helps['2d'])\n parser.add_argument('--save-per-mat', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='save_per_mat', help=helps['save-per-mat'])\n parser.add_argument('--remesh', metavar='options',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='remesh',\n default=None, help=helps['remesh'])\n parser.add_argument('filename_in')\n parser.add_argument('filename_out')\n options = parser.parse_args()\n\n if options.list:\n output('Supported readable mesh formats:')\n output('--------------------------------')\n output_mesh_formats('r')\n output('')\n "},"completion":{"kind":"string","value":"output('Supported writable mesh formats:')"},"api":{"kind":"string","value":"sfepy.base.base.output"}}},{"rowIdx":31,"cells":{"prompt":{"kind":"string","value":"#!/usr/bin/env python\n\"\"\"\nConvert a mesh file from one SfePy-supported format to another.\n\nExamples::\n\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s2.5\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 -c 0\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.mesh --remesh='q2/0 a1e-8 O9/7 V'\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new2.mesh --remesh='rq2/0 a1e-8 O9/7 V'\n\"\"\"\nfrom __future__ import absolute_import\nimport sys\nimport os.path as op\nfrom six.moves import range\nsys.path.append('.')\n\nfrom argparse import ArgumentParser, RawDescriptionHelpFormatter\nfrom sfepy.base.base import nm, output\nfrom sfepy.base.ioutils import remove_files\nfrom sfepy.discrete.fem import Mesh, FEDomain\nfrom sfepy.discrete.fem.meshio import (output_mesh_formats, MeshIO,\n supported_cell_types)\nfrom sfepy.discrete.fem.mesh import fix_double_nodes\nfrom sfepy.mesh.mesh_tools import elems_q2t\n\nhelps = {\n 'scale' : 'scale factor (float or comma-separated list for each axis)'\n ' [default: %(default)s]',\n 'center' : 'center of the output mesh (0 for origin or'\n ' comma-separated list for each axis) applied after scaling'\n ' [default: %(default)s]',\n 'refine' : 'uniform refinement level [default: %(default)s]',\n 'format' : 'output mesh format (overrides filename_out extension)',\n 'list' : 'list supported readable/writable output mesh formats',\n 'merge' : 'remove duplicate vertices',\n 'tri-tetra' : 'convert elements: quad->tri, hexa->tetra',\n '2d' : 'force a 2D mesh by removing the z coordinates - assumes a 3D mesh'\n ' in the xy plane',\n 'save-per-mat': 'extract cells by material id and save them into'\n ' separate mesh files with a name based on filename_out and the id'\n ' numbers (preserves original mesh vertices)',\n\n 'remesh' : \"\"\"when given, remesh the given mesh using tetgen.\n The options can be the following, separated by spaces, in this order: 1.\n \"r\" causes remeshing of the mesh volume - if not present the mesh surface\n is extracted and used for the volume mesh generation. 2.\n \"q[/]\" (required) - the two numbers after \"q\" are a maximum\n radius-edge ratio bound and a minimum dihedral angle bound. 3. \"a\"\n (optional) - the number imposes a maximum volume constraint on all\n tetrahedra. 4. O[<0-9>/<0-7>] - the two numbers correspond to a mesh\n optimization level and a choice of optimizing operations. 5. \"V\"\n (optional) - if present, mesh statistics are printed. Consult the tetgen\n documentation for details.\"\"\",\n}\n\ndef _parse_val_or_vec(option, name, parser):\n if option is not None:\n try:\n try:\n option = float(option)\n except ValueError:\n option = [float(ii) for ii in option.split(',')]\n option = nm.array(option, dtype=nm.float64, ndmin=1)\n except:\n output('bad %s! (%s)' % (name, option))\n parser.print_help()\n sys.exit(1)\n\n return option\n\ndef main():\n parser = ArgumentParser(description=__doc__,\n formatter_class=RawDescriptionHelpFormatter)\n parser.add_argument('-s', '--scale', metavar='scale',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='scale',\n default=None, help=helps['scale'])\n parser.add_argument('-c', '--center', metavar='center',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='center',\n default=None, help=helps['center'])\n parser.add_argument('-r', '--refine', metavar='level',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", type=int, dest='refine',\n default=0, help=helps['refine'])\n parser.add_argument('-f', '--format', metavar='format',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", type=str, dest='format',\n default=None, help=helps['format'])\n parser.add_argument('-l', '--list', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='list', help=helps['list'])\n parser.add_argument('-m', '--merge', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='merge', help=helps['merge'])\n parser.add_argument('-t', '--tri-tetra', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='tri_tetra', help=helps['tri-tetra'])\n parser.add_argument('-2', '--2d', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='force_2d', help=helps['2d'])\n parser.add_argument('--save-per-mat', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='save_per_mat', help=helps['save-per-mat'])\n parser.add_argument('--remesh', metavar='options',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='remesh',\n default=None, help=helps['remesh'])\n parser.add_argument('filename_in')\n parser.add_argument('filename_out')\n options = parser.parse_args()\n\n if options.list:\n output('Supported readable mesh formats:')\n output('--------------------------------')\n output_mesh_formats('r')\n output('')\n output('Supported writable mesh formats:')\n "},"completion":{"kind":"string","value":"output('--------------------------------')"},"api":{"kind":"string","value":"sfepy.base.base.output"}}},{"rowIdx":32,"cells":{"prompt":{"kind":"string","value":"#!/usr/bin/env python\n\"\"\"\nConvert a mesh file from one SfePy-supported format to another.\n\nExamples::\n\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s2.5\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 -c 0\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.mesh --remesh='q2/0 a1e-8 O9/7 V'\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new2.mesh --remesh='rq2/0 a1e-8 O9/7 V'\n\"\"\"\nfrom __future__ import absolute_import\nimport sys\nimport os.path as op\nfrom six.moves import range\nsys.path.append('.')\n\nfrom argparse import ArgumentParser, RawDescriptionHelpFormatter\nfrom sfepy.base.base import nm, output\nfrom sfepy.base.ioutils import remove_files\nfrom sfepy.discrete.fem import Mesh, FEDomain\nfrom sfepy.discrete.fem.meshio import (output_mesh_formats, MeshIO,\n supported_cell_types)\nfrom sfepy.discrete.fem.mesh import fix_double_nodes\nfrom sfepy.mesh.mesh_tools import elems_q2t\n\nhelps = {\n 'scale' : 'scale factor (float or comma-separated list for each axis)'\n ' [default: %(default)s]',\n 'center' : 'center of the output mesh (0 for origin or'\n ' comma-separated list for each axis) applied after scaling'\n ' [default: %(default)s]',\n 'refine' : 'uniform refinement level [default: %(default)s]',\n 'format' : 'output mesh format (overrides filename_out extension)',\n 'list' : 'list supported readable/writable output mesh formats',\n 'merge' : 'remove duplicate vertices',\n 'tri-tetra' : 'convert elements: quad->tri, hexa->tetra',\n '2d' : 'force a 2D mesh by removing the z coordinates - assumes a 3D mesh'\n ' in the xy plane',\n 'save-per-mat': 'extract cells by material id and save them into'\n ' separate mesh files with a name based on filename_out and the id'\n ' numbers (preserves original mesh vertices)',\n\n 'remesh' : \"\"\"when given, remesh the given mesh using tetgen.\n The options can be the following, separated by spaces, in this order: 1.\n \"r\" causes remeshing of the mesh volume - if not present the mesh surface\n is extracted and used for the volume mesh generation. 2.\n \"q[/]\" (required) - the two numbers after \"q\" are a maximum\n radius-edge ratio bound and a minimum dihedral angle bound. 3. \"a\"\n (optional) - the number imposes a maximum volume constraint on all\n tetrahedra. 4. O[<0-9>/<0-7>] - the two numbers correspond to a mesh\n optimization level and a choice of optimizing operations. 5. \"V\"\n (optional) - if present, mesh statistics are printed. Consult the tetgen\n documentation for details.\"\"\",\n}\n\ndef _parse_val_or_vec(option, name, parser):\n if option is not None:\n try:\n try:\n option = float(option)\n except ValueError:\n option = [float(ii) for ii in option.split(',')]\n option = nm.array(option, dtype=nm.float64, ndmin=1)\n except:\n output('bad %s! (%s)' % (name, option))\n parser.print_help()\n sys.exit(1)\n\n return option\n\ndef main():\n parser = ArgumentParser(description=__doc__,\n formatter_class=RawDescriptionHelpFormatter)\n parser.add_argument('-s', '--scale', metavar='scale',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='scale',\n default=None, help=helps['scale'])\n parser.add_argument('-c', '--center', metavar='center',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='center',\n default=None, help=helps['center'])\n parser.add_argument('-r', '--refine', metavar='level',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", type=int, dest='refine',\n default=0, help=helps['refine'])\n parser.add_argument('-f', '--format', metavar='format',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", type=str, dest='format',\n default=None, help=helps['format'])\n parser.add_argument('-l', '--list', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='list', help=helps['list'])\n parser.add_argument('-m', '--merge', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='merge', help=helps['merge'])\n parser.add_argument('-t', '--tri-tetra', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='tri_tetra', help=helps['tri-tetra'])\n parser.add_argument('-2', '--2d', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='force_2d', help=helps['2d'])\n parser.add_argument('--save-per-mat', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='save_per_mat', help=helps['save-per-mat'])\n parser.add_argument('--remesh', metavar='options',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='remesh',\n default=None, help=helps['remesh'])\n parser.add_argument('filename_in')\n parser.add_argument('filename_out')\n options = parser.parse_args()\n\n if options.list:\n output('Supported readable mesh formats:')\n output('--------------------------------')\n output_mesh_formats('r')\n output('')\n output('Supported writable mesh formats:')\n output('--------------------------------')\n "},"completion":{"kind":"string","value":"output_mesh_formats('w')"},"api":{"kind":"string","value":"sfepy.discrete.fem.meshio.output_mesh_formats"}}},{"rowIdx":33,"cells":{"prompt":{"kind":"string","value":"#!/usr/bin/env python\n\"\"\"\nConvert a mesh file from one SfePy-supported format to another.\n\nExamples::\n\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s2.5\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 -c 0\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.mesh --remesh='q2/0 a1e-8 O9/7 V'\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new2.mesh --remesh='rq2/0 a1e-8 O9/7 V'\n\"\"\"\nfrom __future__ import absolute_import\nimport sys\nimport os.path as op\nfrom six.moves import range\nsys.path.append('.')\n\nfrom argparse import ArgumentParser, RawDescriptionHelpFormatter\nfrom sfepy.base.base import nm, output\nfrom sfepy.base.ioutils import remove_files\nfrom sfepy.discrete.fem import Mesh, FEDomain\nfrom sfepy.discrete.fem.meshio import (output_mesh_formats, MeshIO,\n supported_cell_types)\nfrom sfepy.discrete.fem.mesh import fix_double_nodes\nfrom sfepy.mesh.mesh_tools import elems_q2t\n\nhelps = {\n 'scale' : 'scale factor (float or comma-separated list for each axis)'\n ' [default: %(default)s]',\n 'center' : 'center of the output mesh (0 for origin or'\n ' comma-separated list for each axis) applied after scaling'\n ' [default: %(default)s]',\n 'refine' : 'uniform refinement level [default: %(default)s]',\n 'format' : 'output mesh format (overrides filename_out extension)',\n 'list' : 'list supported readable/writable output mesh formats',\n 'merge' : 'remove duplicate vertices',\n 'tri-tetra' : 'convert elements: quad->tri, hexa->tetra',\n '2d' : 'force a 2D mesh by removing the z coordinates - assumes a 3D mesh'\n ' in the xy plane',\n 'save-per-mat': 'extract cells by material id and save them into'\n ' separate mesh files with a name based on filename_out and the id'\n ' numbers (preserves original mesh vertices)',\n\n 'remesh' : \"\"\"when given, remesh the given mesh using tetgen.\n The options can be the following, separated by spaces, in this order: 1.\n \"r\" causes remeshing of the mesh volume - if not present the mesh surface\n is extracted and used for the volume mesh generation. 2.\n \"q[/]\" (required) - the two numbers after \"q\" are a maximum\n radius-edge ratio bound and a minimum dihedral angle bound. 3. \"a\"\n (optional) - the number imposes a maximum volume constraint on all\n tetrahedra. 4. O[<0-9>/<0-7>] - the two numbers correspond to a mesh\n optimization level and a choice of optimizing operations. 5. \"V\"\n (optional) - if present, mesh statistics are printed. Consult the tetgen\n documentation for details.\"\"\",\n}\n\ndef _parse_val_or_vec(option, name, parser):\n if option is not None:\n try:\n try:\n option = float(option)\n except ValueError:\n option = [float(ii) for ii in option.split(',')]\n option = nm.array(option, dtype=nm.float64, ndmin=1)\n except:\n output('bad %s! (%s)' % (name, option))\n parser.print_help()\n sys.exit(1)\n\n return option\n\ndef main():\n parser = ArgumentParser(description=__doc__,\n formatter_class=RawDescriptionHelpFormatter)\n parser.add_argument('-s', '--scale', metavar='scale',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='scale',\n default=None, help=helps['scale'])\n parser.add_argument('-c', '--center', metavar='center',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='center',\n default=None, help=helps['center'])\n parser.add_argument('-r', '--refine', metavar='level',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", type=int, dest='refine',\n default=0, help=helps['refine'])\n parser.add_argument('-f', '--format', metavar='format',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", type=str, dest='format',\n default=None, help=helps['format'])\n parser.add_argument('-l', '--list', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='list', help=helps['list'])\n parser.add_argument('-m', '--merge', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='merge', help=helps['merge'])\n parser.add_argument('-t', '--tri-tetra', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='tri_tetra', help=helps['tri-tetra'])\n parser.add_argument('-2', '--2d', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='force_2d', help=helps['2d'])\n parser.add_argument('--save-per-mat', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='save_per_mat', help=helps['save-per-mat'])\n parser.add_argument('--remesh', metavar='options',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='remesh',\n default=None, help=helps['remesh'])\n parser.add_argument('filename_in')\n parser.add_argument('filename_out')\n options = parser.parse_args()\n\n if options.list:\n output('Supported readable mesh formats:')\n output('--------------------------------')\n output_mesh_formats('r')\n output('')\n output('Supported writable mesh formats:')\n output('--------------------------------')\n output_mesh_formats('w')\n sys.exit(0)\n\n scale = _parse_val_or_vec(options.scale, 'scale', parser)\n center = _parse_val_or_vec(options.center, 'center', parser)\n\n filename_in = options.filename_in\n filename_out = options.filename_out\n\n if options.remesh:\n import tempfile\n import shlex\n import subprocess\n\n dirname = tempfile.mkdtemp()\n\n is_surface = options.remesh.startswith('q')\n if is_surface:\n mesh = Mesh.from_file(filename_in)\n domain = FEDomain(mesh.name, mesh)\n region = domain.create_region('surf', 'vertices of surface',\n 'facet')\n surf_mesh = Mesh.from_region(region, mesh,\n localize=True, is_surface=True)\n\n filename = op.join(dirname, 'surf.mesh')\n surf_mesh.write(filename, io='auto')\n\n else:\n import shutil\n\n shutil.copy(filename_in, dirname)\n filename = op.join(dirname, op.basename(filename_in))\n\n qopts = ''.join(options.remesh.split()) # Remove spaces.\n command = 'tetgen -BFENkACp%s %s' % (qopts, filename)\n args = shlex.split(command)\n subprocess.call(args)\n\n root, ext = op.splitext(filename)\n mesh = "},"completion":{"kind":"string","value":"Mesh.from_file(root + '.1.vtk')"},"api":{"kind":"string","value":"sfepy.discrete.fem.Mesh.from_file"}}},{"rowIdx":34,"cells":{"prompt":{"kind":"string","value":"#!/usr/bin/env python\n\"\"\"\nConvert a mesh file from one SfePy-supported format to another.\n\nExamples::\n\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s2.5\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 -c 0\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.mesh --remesh='q2/0 a1e-8 O9/7 V'\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new2.mesh --remesh='rq2/0 a1e-8 O9/7 V'\n\"\"\"\nfrom __future__ import absolute_import\nimport sys\nimport os.path as op\nfrom six.moves import range\nsys.path.append('.')\n\nfrom argparse import ArgumentParser, RawDescriptionHelpFormatter\nfrom sfepy.base.base import nm, output\nfrom sfepy.base.ioutils import remove_files\nfrom sfepy.discrete.fem import Mesh, FEDomain\nfrom sfepy.discrete.fem.meshio import (output_mesh_formats, MeshIO,\n supported_cell_types)\nfrom sfepy.discrete.fem.mesh import fix_double_nodes\nfrom sfepy.mesh.mesh_tools import elems_q2t\n\nhelps = {\n 'scale' : 'scale factor (float or comma-separated list for each axis)'\n ' [default: %(default)s]',\n 'center' : 'center of the output mesh (0 for origin or'\n ' comma-separated list for each axis) applied after scaling'\n ' [default: %(default)s]',\n 'refine' : 'uniform refinement level [default: %(default)s]',\n 'format' : 'output mesh format (overrides filename_out extension)',\n 'list' : 'list supported readable/writable output mesh formats',\n 'merge' : 'remove duplicate vertices',\n 'tri-tetra' : 'convert elements: quad->tri, hexa->tetra',\n '2d' : 'force a 2D mesh by removing the z coordinates - assumes a 3D mesh'\n ' in the xy plane',\n 'save-per-mat': 'extract cells by material id and save them into'\n ' separate mesh files with a name based on filename_out and the id'\n ' numbers (preserves original mesh vertices)',\n\n 'remesh' : \"\"\"when given, remesh the given mesh using tetgen.\n The options can be the following, separated by spaces, in this order: 1.\n \"r\" causes remeshing of the mesh volume - if not present the mesh surface\n is extracted and used for the volume mesh generation. 2.\n \"q[/]\" (required) - the two numbers after \"q\" are a maximum\n radius-edge ratio bound and a minimum dihedral angle bound. 3. \"a\"\n (optional) - the number imposes a maximum volume constraint on all\n tetrahedra. 4. O[<0-9>/<0-7>] - the two numbers correspond to a mesh\n optimization level and a choice of optimizing operations. 5. \"V\"\n (optional) - if present, mesh statistics are printed. Consult the tetgen\n documentation for details.\"\"\",\n}\n\ndef _parse_val_or_vec(option, name, parser):\n if option is not None:\n try:\n try:\n option = float(option)\n except ValueError:\n option = [float(ii) for ii in option.split(',')]\n option = nm.array(option, dtype=nm.float64, ndmin=1)\n except:\n output('bad %s! (%s)' % (name, option))\n parser.print_help()\n sys.exit(1)\n\n return option\n\ndef main():\n parser = ArgumentParser(description=__doc__,\n formatter_class=RawDescriptionHelpFormatter)\n parser.add_argument('-s', '--scale', metavar='scale',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='scale',\n default=None, help=helps['scale'])\n parser.add_argument('-c', '--center', metavar='center',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='center',\n default=None, help=helps['center'])\n parser.add_argument('-r', '--refine', metavar='level',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", type=int, dest='refine',\n default=0, help=helps['refine'])\n parser.add_argument('-f', '--format', metavar='format',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", type=str, dest='format',\n default=None, help=helps['format'])\n parser.add_argument('-l', '--list', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='list', help=helps['list'])\n parser.add_argument('-m', '--merge', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='merge', help=helps['merge'])\n parser.add_argument('-t', '--tri-tetra', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='tri_tetra', help=helps['tri-tetra'])\n parser.add_argument('-2', '--2d', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='force_2d', help=helps['2d'])\n parser.add_argument('--save-per-mat', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='save_per_mat', help=helps['save-per-mat'])\n parser.add_argument('--remesh', metavar='options',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='remesh',\n default=None, help=helps['remesh'])\n parser.add_argument('filename_in')\n parser.add_argument('filename_out')\n options = parser.parse_args()\n\n if options.list:\n output('Supported readable mesh formats:')\n output('--------------------------------')\n output_mesh_formats('r')\n output('')\n output('Supported writable mesh formats:')\n output('--------------------------------')\n output_mesh_formats('w')\n sys.exit(0)\n\n scale = _parse_val_or_vec(options.scale, 'scale', parser)\n center = _parse_val_or_vec(options.center, 'center', parser)\n\n filename_in = options.filename_in\n filename_out = options.filename_out\n\n if options.remesh:\n import tempfile\n import shlex\n import subprocess\n\n dirname = tempfile.mkdtemp()\n\n is_surface = options.remesh.startswith('q')\n if is_surface:\n mesh = Mesh.from_file(filename_in)\n domain = FEDomain(mesh.name, mesh)\n region = domain.create_region('surf', 'vertices of surface',\n 'facet')\n surf_mesh = Mesh.from_region(region, mesh,\n localize=True, is_surface=True)\n\n filename = op.join(dirname, 'surf.mesh')\n surf_mesh.write(filename, io='auto')\n\n else:\n import shutil\n\n shutil.copy(filename_in, dirname)\n filename = op.join(dirname, op.basename(filename_in))\n\n qopts = ''.join(options.remesh.split()) # Remove spaces.\n command = 'tetgen -BFENkACp%s %s' % (qopts, filename)\n args = shlex.split(command)\n subprocess.call(args)\n\n root, ext = op.splitext(filename)\n mesh = Mesh.from_file(root + '.1.vtk')\n\n "},"completion":{"kind":"string","value":"remove_files(dirname)"},"api":{"kind":"string","value":"sfepy.base.ioutils.remove_files"}}},{"rowIdx":35,"cells":{"prompt":{"kind":"string","value":"#!/usr/bin/env python\n\"\"\"\nConvert a mesh file from one SfePy-supported format to another.\n\nExamples::\n\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s2.5\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 -c 0\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.mesh --remesh='q2/0 a1e-8 O9/7 V'\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new2.mesh --remesh='rq2/0 a1e-8 O9/7 V'\n\"\"\"\nfrom __future__ import absolute_import\nimport sys\nimport os.path as op\nfrom six.moves import range\nsys.path.append('.')\n\nfrom argparse import ArgumentParser, RawDescriptionHelpFormatter\nfrom sfepy.base.base import nm, output\nfrom sfepy.base.ioutils import remove_files\nfrom sfepy.discrete.fem import Mesh, FEDomain\nfrom sfepy.discrete.fem.meshio import (output_mesh_formats, MeshIO,\n supported_cell_types)\nfrom sfepy.discrete.fem.mesh import fix_double_nodes\nfrom sfepy.mesh.mesh_tools import elems_q2t\n\nhelps = {\n 'scale' : 'scale factor (float or comma-separated list for each axis)'\n ' [default: %(default)s]',\n 'center' : 'center of the output mesh (0 for origin or'\n ' comma-separated list for each axis) applied after scaling'\n ' [default: %(default)s]',\n 'refine' : 'uniform refinement level [default: %(default)s]',\n 'format' : 'output mesh format (overrides filename_out extension)',\n 'list' : 'list supported readable/writable output mesh formats',\n 'merge' : 'remove duplicate vertices',\n 'tri-tetra' : 'convert elements: quad->tri, hexa->tetra',\n '2d' : 'force a 2D mesh by removing the z coordinates - assumes a 3D mesh'\n ' in the xy plane',\n 'save-per-mat': 'extract cells by material id and save them into'\n ' separate mesh files with a name based on filename_out and the id'\n ' numbers (preserves original mesh vertices)',\n\n 'remesh' : \"\"\"when given, remesh the given mesh using tetgen.\n The options can be the following, separated by spaces, in this order: 1.\n \"r\" causes remeshing of the mesh volume - if not present the mesh surface\n is extracted and used for the volume mesh generation. 2.\n \"q[/]\" (required) - the two numbers after \"q\" are a maximum\n radius-edge ratio bound and a minimum dihedral angle bound. 3. \"a\"\n (optional) - the number imposes a maximum volume constraint on all\n tetrahedra. 4. O[<0-9>/<0-7>] - the two numbers correspond to a mesh\n optimization level and a choice of optimizing operations. 5. \"V\"\n (optional) - if present, mesh statistics are printed. Consult the tetgen\n documentation for details.\"\"\",\n}\n\ndef _parse_val_or_vec(option, name, parser):\n if option is not None:\n try:\n try:\n option = float(option)\n except ValueError:\n option = [float(ii) for ii in option.split(',')]\n option = nm.array(option, dtype=nm.float64, ndmin=1)\n except:\n output('bad %s! (%s)' % (name, option))\n parser.print_help()\n sys.exit(1)\n\n return option\n\ndef main():\n parser = ArgumentParser(description=__doc__,\n formatter_class=RawDescriptionHelpFormatter)\n parser.add_argument('-s', '--scale', metavar='scale',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='scale',\n default=None, help=helps['scale'])\n parser.add_argument('-c', '--center', metavar='center',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='center',\n default=None, help=helps['center'])\n parser.add_argument('-r', '--refine', metavar='level',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", type=int, dest='refine',\n default=0, help=helps['refine'])\n parser.add_argument('-f', '--format', metavar='format',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", type=str, dest='format',\n default=None, help=helps['format'])\n parser.add_argument('-l', '--list', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='list', help=helps['list'])\n parser.add_argument('-m', '--merge', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='merge', help=helps['merge'])\n parser.add_argument('-t', '--tri-tetra', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='tri_tetra', help=helps['tri-tetra'])\n parser.add_argument('-2', '--2d', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='force_2d', help=helps['2d'])\n parser.add_argument('--save-per-mat', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='save_per_mat', help=helps['save-per-mat'])\n parser.add_argument('--remesh', metavar='options',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='remesh',\n default=None, help=helps['remesh'])\n parser.add_argument('filename_in')\n parser.add_argument('filename_out')\n options = parser.parse_args()\n\n if options.list:\n output('Supported readable mesh formats:')\n output('--------------------------------')\n output_mesh_formats('r')\n output('')\n output('Supported writable mesh formats:')\n output('--------------------------------')\n output_mesh_formats('w')\n sys.exit(0)\n\n scale = _parse_val_or_vec(options.scale, 'scale', parser)\n center = _parse_val_or_vec(options.center, 'center', parser)\n\n filename_in = options.filename_in\n filename_out = options.filename_out\n\n if options.remesh:\n import tempfile\n import shlex\n import subprocess\n\n dirname = tempfile.mkdtemp()\n\n is_surface = options.remesh.startswith('q')\n if is_surface:\n mesh = Mesh.from_file(filename_in)\n domain = FEDomain(mesh.name, mesh)\n region = domain.create_region('surf', 'vertices of surface',\n 'facet')\n surf_mesh = Mesh.from_region(region, mesh,\n localize=True, is_surface=True)\n\n filename = op.join(dirname, 'surf.mesh')\n surf_mesh.write(filename, io='auto')\n\n else:\n import shutil\n\n shutil.copy(filename_in, dirname)\n filename = op.join(dirname, op.basename(filename_in))\n\n qopts = ''.join(options.remesh.split()) # Remove spaces.\n command = 'tetgen -BFENkACp%s %s' % (qopts, filename)\n args = shlex.split(command)\n subprocess.call(args)\n\n root, ext = op.splitext(filename)\n mesh = Mesh.from_file(root + '.1.vtk')\n\n remove_files(dirname)\n\n else:\n mesh = "},"completion":{"kind":"string","value":"Mesh.from_file(filename_in)"},"api":{"kind":"string","value":"sfepy.discrete.fem.Mesh.from_file"}}},{"rowIdx":36,"cells":{"prompt":{"kind":"string","value":"#!/usr/bin/env python\n\"\"\"\nConvert a mesh file from one SfePy-supported format to another.\n\nExamples::\n\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s2.5\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 -c 0\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.mesh --remesh='q2/0 a1e-8 O9/7 V'\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new2.mesh --remesh='rq2/0 a1e-8 O9/7 V'\n\"\"\"\nfrom __future__ import absolute_import\nimport sys\nimport os.path as op\nfrom six.moves import range\nsys.path.append('.')\n\nfrom argparse import ArgumentParser, RawDescriptionHelpFormatter\nfrom sfepy.base.base import nm, output\nfrom sfepy.base.ioutils import remove_files\nfrom sfepy.discrete.fem import Mesh, FEDomain\nfrom sfepy.discrete.fem.meshio import (output_mesh_formats, MeshIO,\n supported_cell_types)\nfrom sfepy.discrete.fem.mesh import fix_double_nodes\nfrom sfepy.mesh.mesh_tools import elems_q2t\n\nhelps = {\n 'scale' : 'scale factor (float or comma-separated list for each axis)'\n ' [default: %(default)s]',\n 'center' : 'center of the output mesh (0 for origin or'\n ' comma-separated list for each axis) applied after scaling'\n ' [default: %(default)s]',\n 'refine' : 'uniform refinement level [default: %(default)s]',\n 'format' : 'output mesh format (overrides filename_out extension)',\n 'list' : 'list supported readable/writable output mesh formats',\n 'merge' : 'remove duplicate vertices',\n 'tri-tetra' : 'convert elements: quad->tri, hexa->tetra',\n '2d' : 'force a 2D mesh by removing the z coordinates - assumes a 3D mesh'\n ' in the xy plane',\n 'save-per-mat': 'extract cells by material id and save them into'\n ' separate mesh files with a name based on filename_out and the id'\n ' numbers (preserves original mesh vertices)',\n\n 'remesh' : \"\"\"when given, remesh the given mesh using tetgen.\n The options can be the following, separated by spaces, in this order: 1.\n \"r\" causes remeshing of the mesh volume - if not present the mesh surface\n is extracted and used for the volume mesh generation. 2.\n \"q[/]\" (required) - the two numbers after \"q\" are a maximum\n radius-edge ratio bound and a minimum dihedral angle bound. 3. \"a\"\n (optional) - the number imposes a maximum volume constraint on all\n tetrahedra. 4. O[<0-9>/<0-7>] - the two numbers correspond to a mesh\n optimization level and a choice of optimizing operations. 5. \"V\"\n (optional) - if present, mesh statistics are printed. Consult the tetgen\n documentation for details.\"\"\",\n}\n\ndef _parse_val_or_vec(option, name, parser):\n if option is not None:\n try:\n try:\n option = float(option)\n except ValueError:\n option = [float(ii) for ii in option.split(',')]\n option = nm.array(option, dtype=nm.float64, ndmin=1)\n except:\n output('bad %s! (%s)' % (name, option))\n parser.print_help()\n sys.exit(1)\n\n return option\n\ndef main():\n parser = ArgumentParser(description=__doc__,\n formatter_class=RawDescriptionHelpFormatter)\n parser.add_argument('-s', '--scale', metavar='scale',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='scale',\n default=None, help=helps['scale'])\n parser.add_argument('-c', '--center', metavar='center',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='center',\n default=None, help=helps['center'])\n parser.add_argument('-r', '--refine', metavar='level',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", type=int, dest='refine',\n default=0, help=helps['refine'])\n parser.add_argument('-f', '--format', metavar='format',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", type=str, dest='format',\n default=None, help=helps['format'])\n parser.add_argument('-l', '--list', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='list', help=helps['list'])\n parser.add_argument('-m', '--merge', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='merge', help=helps['merge'])\n parser.add_argument('-t', '--tri-tetra', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='tri_tetra', help=helps['tri-tetra'])\n parser.add_argument('-2', '--2d', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='force_2d', help=helps['2d'])\n parser.add_argument('--save-per-mat', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='save_per_mat', help=helps['save-per-mat'])\n parser.add_argument('--remesh', metavar='options',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='remesh',\n default=None, help=helps['remesh'])\n parser.add_argument('filename_in')\n parser.add_argument('filename_out')\n options = parser.parse_args()\n\n if options.list:\n output('Supported readable mesh formats:')\n output('--------------------------------')\n output_mesh_formats('r')\n output('')\n output('Supported writable mesh formats:')\n output('--------------------------------')\n output_mesh_formats('w')\n sys.exit(0)\n\n scale = _parse_val_or_vec(options.scale, 'scale', parser)\n center = _parse_val_or_vec(options.center, 'center', parser)\n\n filename_in = options.filename_in\n filename_out = options.filename_out\n\n if options.remesh:\n import tempfile\n import shlex\n import subprocess\n\n dirname = tempfile.mkdtemp()\n\n is_surface = options.remesh.startswith('q')\n if is_surface:\n mesh = Mesh.from_file(filename_in)\n domain = FEDomain(mesh.name, mesh)\n region = domain.create_region('surf', 'vertices of surface',\n 'facet')\n surf_mesh = Mesh.from_region(region, mesh,\n localize=True, is_surface=True)\n\n filename = op.join(dirname, 'surf.mesh')\n surf_mesh.write(filename, io='auto')\n\n else:\n import shutil\n\n shutil.copy(filename_in, dirname)\n filename = op.join(dirname, op.basename(filename_in))\n\n qopts = ''.join(options.remesh.split()) # Remove spaces.\n command = 'tetgen -BFENkACp%s %s' % (qopts, filename)\n args = shlex.split(command)\n subprocess.call(args)\n\n root, ext = op.splitext(filename)\n mesh = Mesh.from_file(root + '.1.vtk')\n\n remove_files(dirname)\n\n else:\n mesh = Mesh.from_file(filename_in)\n\n if options.force_2d:\n data = list(mesh._get_io_data())\n data[0] = data[0][:, :2]\n mesh = "},"completion":{"kind":"string","value":"Mesh.from_data(mesh.name, *data)"},"api":{"kind":"string","value":"sfepy.discrete.fem.Mesh.from_data"}}},{"rowIdx":37,"cells":{"prompt":{"kind":"string","value":"#!/usr/bin/env python\n\"\"\"\nConvert a mesh file from one SfePy-supported format to another.\n\nExamples::\n\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s2.5\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 -c 0\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.mesh --remesh='q2/0 a1e-8 O9/7 V'\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new2.mesh --remesh='rq2/0 a1e-8 O9/7 V'\n\"\"\"\nfrom __future__ import absolute_import\nimport sys\nimport os.path as op\nfrom six.moves import range\nsys.path.append('.')\n\nfrom argparse import ArgumentParser, RawDescriptionHelpFormatter\nfrom sfepy.base.base import nm, output\nfrom sfepy.base.ioutils import remove_files\nfrom sfepy.discrete.fem import Mesh, FEDomain\nfrom sfepy.discrete.fem.meshio import (output_mesh_formats, MeshIO,\n supported_cell_types)\nfrom sfepy.discrete.fem.mesh import fix_double_nodes\nfrom sfepy.mesh.mesh_tools import elems_q2t\n\nhelps = {\n 'scale' : 'scale factor (float or comma-separated list for each axis)'\n ' [default: %(default)s]',\n 'center' : 'center of the output mesh (0 for origin or'\n ' comma-separated list for each axis) applied after scaling'\n ' [default: %(default)s]',\n 'refine' : 'uniform refinement level [default: %(default)s]',\n 'format' : 'output mesh format (overrides filename_out extension)',\n 'list' : 'list supported readable/writable output mesh formats',\n 'merge' : 'remove duplicate vertices',\n 'tri-tetra' : 'convert elements: quad->tri, hexa->tetra',\n '2d' : 'force a 2D mesh by removing the z coordinates - assumes a 3D mesh'\n ' in the xy plane',\n 'save-per-mat': 'extract cells by material id and save them into'\n ' separate mesh files with a name based on filename_out and the id'\n ' numbers (preserves original mesh vertices)',\n\n 'remesh' : \"\"\"when given, remesh the given mesh using tetgen.\n The options can be the following, separated by spaces, in this order: 1.\n \"r\" causes remeshing of the mesh volume - if not present the mesh surface\n is extracted and used for the volume mesh generation. 2.\n \"q[/]\" (required) - the two numbers after \"q\" are a maximum\n radius-edge ratio bound and a minimum dihedral angle bound. 3. \"a\"\n (optional) - the number imposes a maximum volume constraint on all\n tetrahedra. 4. O[<0-9>/<0-7>] - the two numbers correspond to a mesh\n optimization level and a choice of optimizing operations. 5. \"V\"\n (optional) - if present, mesh statistics are printed. Consult the tetgen\n documentation for details.\"\"\",\n}\n\ndef _parse_val_or_vec(option, name, parser):\n if option is not None:\n try:\n try:\n option = float(option)\n except ValueError:\n option = [float(ii) for ii in option.split(',')]\n option = nm.array(option, dtype=nm.float64, ndmin=1)\n except:\n output('bad %s! (%s)' % (name, option))\n parser.print_help()\n sys.exit(1)\n\n return option\n\ndef main():\n parser = ArgumentParser(description=__doc__,\n formatter_class=RawDescriptionHelpFormatter)\n parser.add_argument('-s', '--scale', metavar='scale',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='scale',\n default=None, help=helps['scale'])\n parser.add_argument('-c', '--center', metavar='center',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='center',\n default=None, help=helps['center'])\n parser.add_argument('-r', '--refine', metavar='level',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", type=int, dest='refine',\n default=0, help=helps['refine'])\n parser.add_argument('-f', '--format', metavar='format',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", type=str, dest='format',\n default=None, help=helps['format'])\n parser.add_argument('-l', '--list', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='list', help=helps['list'])\n parser.add_argument('-m', '--merge', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='merge', help=helps['merge'])\n parser.add_argument('-t', '--tri-tetra', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='tri_tetra', help=helps['tri-tetra'])\n parser.add_argument('-2', '--2d', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='force_2d', help=helps['2d'])\n parser.add_argument('--save-per-mat', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='save_per_mat', help=helps['save-per-mat'])\n parser.add_argument('--remesh', metavar='options',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='remesh',\n default=None, help=helps['remesh'])\n parser.add_argument('filename_in')\n parser.add_argument('filename_out')\n options = parser.parse_args()\n\n if options.list:\n output('Supported readable mesh formats:')\n output('--------------------------------')\n output_mesh_formats('r')\n output('')\n output('Supported writable mesh formats:')\n output('--------------------------------')\n output_mesh_formats('w')\n sys.exit(0)\n\n scale = _parse_val_or_vec(options.scale, 'scale', parser)\n center = _parse_val_or_vec(options.center, 'center', parser)\n\n filename_in = options.filename_in\n filename_out = options.filename_out\n\n if options.remesh:\n import tempfile\n import shlex\n import subprocess\n\n dirname = tempfile.mkdtemp()\n\n is_surface = options.remesh.startswith('q')\n if is_surface:\n mesh = Mesh.from_file(filename_in)\n domain = FEDomain(mesh.name, mesh)\n region = domain.create_region('surf', 'vertices of surface',\n 'facet')\n surf_mesh = Mesh.from_region(region, mesh,\n localize=True, is_surface=True)\n\n filename = op.join(dirname, 'surf.mesh')\n surf_mesh.write(filename, io='auto')\n\n else:\n import shutil\n\n shutil.copy(filename_in, dirname)\n filename = op.join(dirname, op.basename(filename_in))\n\n qopts = ''.join(options.remesh.split()) # Remove spaces.\n command = 'tetgen -BFENkACp%s %s' % (qopts, filename)\n args = shlex.split(command)\n subprocess.call(args)\n\n root, ext = op.splitext(filename)\n mesh = Mesh.from_file(root + '.1.vtk')\n\n remove_files(dirname)\n\n else:\n mesh = Mesh.from_file(filename_in)\n\n if options.force_2d:\n data = list(mesh._get_io_data())\n data[0] = data[0][:, :2]\n mesh = Mesh.from_data(mesh.name, *data)\n\n if scale is not None:\n if len(scale) == 1:\n tr = nm.eye(mesh.dim, dtype=nm.float64) * scale\n elif len(scale) == mesh.dim:\n tr = nm.diag(scale)\n else:\n raise ValueError('bad scale! (%s)' % scale)\n mesh.transform_coors(tr)\n\n if center is not None:\n cc = 0.5 * mesh.get_bounding_box().sum(0)\n shift = center - cc\n tr = nm.c_[nm.eye(mesh.dim, dtype=nm.float64), shift[:, None]]\n mesh.transform_coors(tr)\n\n if options.refine > 0:\n domain = "},"completion":{"kind":"string","value":"FEDomain(mesh.name, mesh)"},"api":{"kind":"string","value":"sfepy.discrete.fem.FEDomain"}}},{"rowIdx":38,"cells":{"prompt":{"kind":"string","value":"#!/usr/bin/env python\n\"\"\"\nConvert a mesh file from one SfePy-supported format to another.\n\nExamples::\n\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s2.5\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 -c 0\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.mesh --remesh='q2/0 a1e-8 O9/7 V'\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new2.mesh --remesh='rq2/0 a1e-8 O9/7 V'\n\"\"\"\nfrom __future__ import absolute_import\nimport sys\nimport os.path as op\nfrom six.moves import range\nsys.path.append('.')\n\nfrom argparse import ArgumentParser, RawDescriptionHelpFormatter\nfrom sfepy.base.base import nm, output\nfrom sfepy.base.ioutils import remove_files\nfrom sfepy.discrete.fem import Mesh, FEDomain\nfrom sfepy.discrete.fem.meshio import (output_mesh_formats, MeshIO,\n supported_cell_types)\nfrom sfepy.discrete.fem.mesh import fix_double_nodes\nfrom sfepy.mesh.mesh_tools import elems_q2t\n\nhelps = {\n 'scale' : 'scale factor (float or comma-separated list for each axis)'\n ' [default: %(default)s]',\n 'center' : 'center of the output mesh (0 for origin or'\n ' comma-separated list for each axis) applied after scaling'\n ' [default: %(default)s]',\n 'refine' : 'uniform refinement level [default: %(default)s]',\n 'format' : 'output mesh format (overrides filename_out extension)',\n 'list' : 'list supported readable/writable output mesh formats',\n 'merge' : 'remove duplicate vertices',\n 'tri-tetra' : 'convert elements: quad->tri, hexa->tetra',\n '2d' : 'force a 2D mesh by removing the z coordinates - assumes a 3D mesh'\n ' in the xy plane',\n 'save-per-mat': 'extract cells by material id and save them into'\n ' separate mesh files with a name based on filename_out and the id'\n ' numbers (preserves original mesh vertices)',\n\n 'remesh' : \"\"\"when given, remesh the given mesh using tetgen.\n The options can be the following, separated by spaces, in this order: 1.\n \"r\" causes remeshing of the mesh volume - if not present the mesh surface\n is extracted and used for the volume mesh generation. 2.\n \"q[/]\" (required) - the two numbers after \"q\" are a maximum\n radius-edge ratio bound and a minimum dihedral angle bound. 3. \"a\"\n (optional) - the number imposes a maximum volume constraint on all\n tetrahedra. 4. O[<0-9>/<0-7>] - the two numbers correspond to a mesh\n optimization level and a choice of optimizing operations. 5. \"V\"\n (optional) - if present, mesh statistics are printed. Consult the tetgen\n documentation for details.\"\"\",\n}\n\ndef _parse_val_or_vec(option, name, parser):\n if option is not None:\n try:\n try:\n option = float(option)\n except ValueError:\n option = [float(ii) for ii in option.split(',')]\n option = nm.array(option, dtype=nm.float64, ndmin=1)\n except:\n output('bad %s! (%s)' % (name, option))\n parser.print_help()\n sys.exit(1)\n\n return option\n\ndef main():\n parser = ArgumentParser(description=__doc__,\n formatter_class=RawDescriptionHelpFormatter)\n parser.add_argument('-s', '--scale', metavar='scale',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='scale',\n default=None, help=helps['scale'])\n parser.add_argument('-c', '--center', metavar='center',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='center',\n default=None, help=helps['center'])\n parser.add_argument('-r', '--refine', metavar='level',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", type=int, dest='refine',\n default=0, help=helps['refine'])\n parser.add_argument('-f', '--format', metavar='format',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", type=str, dest='format',\n default=None, help=helps['format'])\n parser.add_argument('-l', '--list', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='list', help=helps['list'])\n parser.add_argument('-m', '--merge', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='merge', help=helps['merge'])\n parser.add_argument('-t', '--tri-tetra', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='tri_tetra', help=helps['tri-tetra'])\n parser.add_argument('-2', '--2d', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='force_2d', help=helps['2d'])\n parser.add_argument('--save-per-mat', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='save_per_mat', help=helps['save-per-mat'])\n parser.add_argument('--remesh', metavar='options',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='remesh',\n default=None, help=helps['remesh'])\n parser.add_argument('filename_in')\n parser.add_argument('filename_out')\n options = parser.parse_args()\n\n if options.list:\n output('Supported readable mesh formats:')\n output('--------------------------------')\n output_mesh_formats('r')\n output('')\n output('Supported writable mesh formats:')\n output('--------------------------------')\n output_mesh_formats('w')\n sys.exit(0)\n\n scale = _parse_val_or_vec(options.scale, 'scale', parser)\n center = _parse_val_or_vec(options.center, 'center', parser)\n\n filename_in = options.filename_in\n filename_out = options.filename_out\n\n if options.remesh:\n import tempfile\n import shlex\n import subprocess\n\n dirname = tempfile.mkdtemp()\n\n is_surface = options.remesh.startswith('q')\n if is_surface:\n mesh = Mesh.from_file(filename_in)\n domain = FEDomain(mesh.name, mesh)\n region = domain.create_region('surf', 'vertices of surface',\n 'facet')\n surf_mesh = Mesh.from_region(region, mesh,\n localize=True, is_surface=True)\n\n filename = op.join(dirname, 'surf.mesh')\n surf_mesh.write(filename, io='auto')\n\n else:\n import shutil\n\n shutil.copy(filename_in, dirname)\n filename = op.join(dirname, op.basename(filename_in))\n\n qopts = ''.join(options.remesh.split()) # Remove spaces.\n command = 'tetgen -BFENkACp%s %s' % (qopts, filename)\n args = shlex.split(command)\n subprocess.call(args)\n\n root, ext = op.splitext(filename)\n mesh = Mesh.from_file(root + '.1.vtk')\n\n remove_files(dirname)\n\n else:\n mesh = Mesh.from_file(filename_in)\n\n if options.force_2d:\n data = list(mesh._get_io_data())\n data[0] = data[0][:, :2]\n mesh = Mesh.from_data(mesh.name, *data)\n\n if scale is not None:\n if len(scale) == 1:\n tr = nm.eye(mesh.dim, dtype=nm.float64) * scale\n elif len(scale) == mesh.dim:\n tr = nm.diag(scale)\n else:\n raise ValueError('bad scale! (%s)' % scale)\n mesh.transform_coors(tr)\n\n if center is not None:\n cc = 0.5 * mesh.get_bounding_box().sum(0)\n shift = center - cc\n tr = nm.c_[nm.eye(mesh.dim, dtype=nm.float64), shift[:, None]]\n mesh.transform_coors(tr)\n\n if options.refine > 0:\n domain = FEDomain(mesh.name, mesh)\n output('initial mesh: %d nodes %d elements'\n % (domain.shape.n_nod, domain.shape.n_el))\n\n for ii in range(options.refine):\n output('refine %d...' % ii)\n domain = domain.refine()\n output('... %d nodes %d elements'\n % (domain.shape.n_nod, domain.shape.n_el))\n\n mesh = domain.mesh\n\n if options.tri_tetra > 0:\n conns = None\n for k, new_desc in [('3_8', '3_4'), ('2_4', '2_3')]:\n if k in mesh.descs:\n conns = mesh.get_conn(k)\n break\n\n if conns is not None:\n nelo = conns.shape[0]\n output('initial mesh: %d elements' % nelo)\n\n new_conns = elems_q2t(conns)\n nn = new_conns.shape[0] // nelo\n new_cgroups = nm.repeat(mesh.cmesh.cell_groups, nn)\n\n output('new mesh: %d elements' % new_conns.shape[0])\n mesh = Mesh.from_data(mesh.name, mesh.coors,\n mesh.cmesh.vertex_groups,\n [new_conns], [new_cgroups], [new_desc])\n\n if options.merge:\n desc = mesh.descs[0]\n coor, ngroups, conns = fix_double_nodes(mesh.coors,\n mesh.cmesh.vertex_groups,\n mesh.get_conn(desc), 1e-9)\n mesh = Mesh.from_data(mesh.name + '_merged',\n coor, ngroups,\n [conns], [mesh.cmesh.cell_groups], [desc])\n\n if options.save_per_mat:\n desc = mesh.descs[0]\n conns, cgroups = mesh.get_conn(desc), mesh.cmesh.cell_groups\n coors, ngroups = mesh.coors, mesh.cmesh.vertex_groups\n mat_ids = "},"completion":{"kind":"string","value":"nm.unique(cgroups)"},"api":{"kind":"string","value":"sfepy.base.base.nm.unique"}}},{"rowIdx":39,"cells":{"prompt":{"kind":"string","value":"#!/usr/bin/env python\n\"\"\"\nConvert a mesh file from one SfePy-supported format to another.\n\nExamples::\n\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s2.5\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 -c 0\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.mesh --remesh='q2/0 a1e-8 O9/7 V'\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new2.mesh --remesh='rq2/0 a1e-8 O9/7 V'\n\"\"\"\nfrom __future__ import absolute_import\nimport sys\nimport os.path as op\nfrom six.moves import range\nsys.path.append('.')\n\nfrom argparse import ArgumentParser, RawDescriptionHelpFormatter\nfrom sfepy.base.base import nm, output\nfrom sfepy.base.ioutils import remove_files\nfrom sfepy.discrete.fem import Mesh, FEDomain\nfrom sfepy.discrete.fem.meshio import (output_mesh_formats, MeshIO,\n supported_cell_types)\nfrom sfepy.discrete.fem.mesh import fix_double_nodes\nfrom sfepy.mesh.mesh_tools import elems_q2t\n\nhelps = {\n 'scale' : 'scale factor (float or comma-separated list for each axis)'\n ' [default: %(default)s]',\n 'center' : 'center of the output mesh (0 for origin or'\n ' comma-separated list for each axis) applied after scaling'\n ' [default: %(default)s]',\n 'refine' : 'uniform refinement level [default: %(default)s]',\n 'format' : 'output mesh format (overrides filename_out extension)',\n 'list' : 'list supported readable/writable output mesh formats',\n 'merge' : 'remove duplicate vertices',\n 'tri-tetra' : 'convert elements: quad->tri, hexa->tetra',\n '2d' : 'force a 2D mesh by removing the z coordinates - assumes a 3D mesh'\n ' in the xy plane',\n 'save-per-mat': 'extract cells by material id and save them into'\n ' separate mesh files with a name based on filename_out and the id'\n ' numbers (preserves original mesh vertices)',\n\n 'remesh' : \"\"\"when given, remesh the given mesh using tetgen.\n The options can be the following, separated by spaces, in this order: 1.\n \"r\" causes remeshing of the mesh volume - if not present the mesh surface\n is extracted and used for the volume mesh generation. 2.\n \"q[/]\" (required) - the two numbers after \"q\" are a maximum\n radius-edge ratio bound and a minimum dihedral angle bound. 3. \"a\"\n (optional) - the number imposes a maximum volume constraint on all\n tetrahedra. 4. O[<0-9>/<0-7>] - the two numbers correspond to a mesh\n optimization level and a choice of optimizing operations. 5. \"V\"\n (optional) - if present, mesh statistics are printed. Consult the tetgen\n documentation for details.\"\"\",\n}\n\ndef _parse_val_or_vec(option, name, parser):\n if option is not None:\n try:\n try:\n option = float(option)\n except ValueError:\n option = [float(ii) for ii in option.split(',')]\n option = "},"completion":{"kind":"string","value":"nm.array(option, dtype=nm.float64, ndmin=1)"},"api":{"kind":"string","value":"sfepy.base.base.nm.array"}}},{"rowIdx":40,"cells":{"prompt":{"kind":"string","value":"#!/usr/bin/env python\n\"\"\"\nConvert a mesh file from one SfePy-supported format to another.\n\nExamples::\n\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s2.5\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 -c 0\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.mesh --remesh='q2/0 a1e-8 O9/7 V'\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new2.mesh --remesh='rq2/0 a1e-8 O9/7 V'\n\"\"\"\nfrom __future__ import absolute_import\nimport sys\nimport os.path as op\nfrom six.moves import range\nsys.path.append('.')\n\nfrom argparse import ArgumentParser, RawDescriptionHelpFormatter\nfrom sfepy.base.base import nm, output\nfrom sfepy.base.ioutils import remove_files\nfrom sfepy.discrete.fem import Mesh, FEDomain\nfrom sfepy.discrete.fem.meshio import (output_mesh_formats, MeshIO,\n supported_cell_types)\nfrom sfepy.discrete.fem.mesh import fix_double_nodes\nfrom sfepy.mesh.mesh_tools import elems_q2t\n\nhelps = {\n 'scale' : 'scale factor (float or comma-separated list for each axis)'\n ' [default: %(default)s]',\n 'center' : 'center of the output mesh (0 for origin or'\n ' comma-separated list for each axis) applied after scaling'\n ' [default: %(default)s]',\n 'refine' : 'uniform refinement level [default: %(default)s]',\n 'format' : 'output mesh format (overrides filename_out extension)',\n 'list' : 'list supported readable/writable output mesh formats',\n 'merge' : 'remove duplicate vertices',\n 'tri-tetra' : 'convert elements: quad->tri, hexa->tetra',\n '2d' : 'force a 2D mesh by removing the z coordinates - assumes a 3D mesh'\n ' in the xy plane',\n 'save-per-mat': 'extract cells by material id and save them into'\n ' separate mesh files with a name based on filename_out and the id'\n ' numbers (preserves original mesh vertices)',\n\n 'remesh' : \"\"\"when given, remesh the given mesh using tetgen.\n The options can be the following, separated by spaces, in this order: 1.\n \"r\" causes remeshing of the mesh volume - if not present the mesh surface\n is extracted and used for the volume mesh generation. 2.\n \"q[/]\" (required) - the two numbers after \"q\" are a maximum\n radius-edge ratio bound and a minimum dihedral angle bound. 3. \"a\"\n (optional) - the number imposes a maximum volume constraint on all\n tetrahedra. 4. O[<0-9>/<0-7>] - the two numbers correspond to a mesh\n optimization level and a choice of optimizing operations. 5. \"V\"\n (optional) - if present, mesh statistics are printed. Consult the tetgen\n documentation for details.\"\"\",\n}\n\ndef _parse_val_or_vec(option, name, parser):\n if option is not None:\n try:\n try:\n option = float(option)\n except ValueError:\n option = [float(ii) for ii in option.split(',')]\n option = nm.array(option, dtype=nm.float64, ndmin=1)\n except:\n output('bad %s! (%s)' % (name, option))\n parser.print_help()\n sys.exit(1)\n\n return option\n\ndef main():\n parser = ArgumentParser(description=__doc__,\n formatter_class=RawDescriptionHelpFormatter)\n parser.add_argument('-s', '--scale', metavar='scale',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='scale',\n default=None, help=helps['scale'])\n parser.add_argument('-c', '--center', metavar='center',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='center',\n default=None, help=helps['center'])\n parser.add_argument('-r', '--refine', metavar='level',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", type=int, dest='refine',\n default=0, help=helps['refine'])\n parser.add_argument('-f', '--format', metavar='format',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", type=str, dest='format',\n default=None, help=helps['format'])\n parser.add_argument('-l', '--list', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='list', help=helps['list'])\n parser.add_argument('-m', '--merge', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='merge', help=helps['merge'])\n parser.add_argument('-t', '--tri-tetra', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='tri_tetra', help=helps['tri-tetra'])\n parser.add_argument('-2', '--2d', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='force_2d', help=helps['2d'])\n parser.add_argument('--save-per-mat', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='save_per_mat', help=helps['save-per-mat'])\n parser.add_argument('--remesh', metavar='options',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='remesh',\n default=None, help=helps['remesh'])\n parser.add_argument('filename_in')\n parser.add_argument('filename_out')\n options = parser.parse_args()\n\n if options.list:\n output('Supported readable mesh formats:')\n output('--------------------------------')\n output_mesh_formats('r')\n output('')\n output('Supported writable mesh formats:')\n output('--------------------------------')\n output_mesh_formats('w')\n sys.exit(0)\n\n scale = _parse_val_or_vec(options.scale, 'scale', parser)\n center = _parse_val_or_vec(options.center, 'center', parser)\n\n filename_in = options.filename_in\n filename_out = options.filename_out\n\n if options.remesh:\n import tempfile\n import shlex\n import subprocess\n\n dirname = tempfile.mkdtemp()\n\n is_surface = options.remesh.startswith('q')\n if is_surface:\n mesh = "},"completion":{"kind":"string","value":"Mesh.from_file(filename_in)"},"api":{"kind":"string","value":"sfepy.discrete.fem.Mesh.from_file"}}},{"rowIdx":41,"cells":{"prompt":{"kind":"string","value":"#!/usr/bin/env python\n\"\"\"\nConvert a mesh file from one SfePy-supported format to another.\n\nExamples::\n\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s2.5\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 -c 0\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.mesh --remesh='q2/0 a1e-8 O9/7 V'\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new2.mesh --remesh='rq2/0 a1e-8 O9/7 V'\n\"\"\"\nfrom __future__ import absolute_import\nimport sys\nimport os.path as op\nfrom six.moves import range\nsys.path.append('.')\n\nfrom argparse import ArgumentParser, RawDescriptionHelpFormatter\nfrom sfepy.base.base import nm, output\nfrom sfepy.base.ioutils import remove_files\nfrom sfepy.discrete.fem import Mesh, FEDomain\nfrom sfepy.discrete.fem.meshio import (output_mesh_formats, MeshIO,\n supported_cell_types)\nfrom sfepy.discrete.fem.mesh import fix_double_nodes\nfrom sfepy.mesh.mesh_tools import elems_q2t\n\nhelps = {\n 'scale' : 'scale factor (float or comma-separated list for each axis)'\n ' [default: %(default)s]',\n 'center' : 'center of the output mesh (0 for origin or'\n ' comma-separated list for each axis) applied after scaling'\n ' [default: %(default)s]',\n 'refine' : 'uniform refinement level [default: %(default)s]',\n 'format' : 'output mesh format (overrides filename_out extension)',\n 'list' : 'list supported readable/writable output mesh formats',\n 'merge' : 'remove duplicate vertices',\n 'tri-tetra' : 'convert elements: quad->tri, hexa->tetra',\n '2d' : 'force a 2D mesh by removing the z coordinates - assumes a 3D mesh'\n ' in the xy plane',\n 'save-per-mat': 'extract cells by material id and save them into'\n ' separate mesh files with a name based on filename_out and the id'\n ' numbers (preserves original mesh vertices)',\n\n 'remesh' : \"\"\"when given, remesh the given mesh using tetgen.\n The options can be the following, separated by spaces, in this order: 1.\n \"r\" causes remeshing of the mesh volume - if not present the mesh surface\n is extracted and used for the volume mesh generation. 2.\n \"q[/]\" (required) - the two numbers after \"q\" are a maximum\n radius-edge ratio bound and a minimum dihedral angle bound. 3. \"a\"\n (optional) - the number imposes a maximum volume constraint on all\n tetrahedra. 4. O[<0-9>/<0-7>] - the two numbers correspond to a mesh\n optimization level and a choice of optimizing operations. 5. \"V\"\n (optional) - if present, mesh statistics are printed. Consult the tetgen\n documentation for details.\"\"\",\n}\n\ndef _parse_val_or_vec(option, name, parser):\n if option is not None:\n try:\n try:\n option = float(option)\n except ValueError:\n option = [float(ii) for ii in option.split(',')]\n option = nm.array(option, dtype=nm.float64, ndmin=1)\n except:\n output('bad %s! (%s)' % (name, option))\n parser.print_help()\n sys.exit(1)\n\n return option\n\ndef main():\n parser = ArgumentParser(description=__doc__,\n formatter_class=RawDescriptionHelpFormatter)\n parser.add_argument('-s', '--scale', metavar='scale',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='scale',\n default=None, help=helps['scale'])\n parser.add_argument('-c', '--center', metavar='center',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='center',\n default=None, help=helps['center'])\n parser.add_argument('-r', '--refine', metavar='level',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", type=int, dest='refine',\n default=0, help=helps['refine'])\n parser.add_argument('-f', '--format', metavar='format',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", type=str, dest='format',\n default=None, help=helps['format'])\n parser.add_argument('-l', '--list', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='list', help=helps['list'])\n parser.add_argument('-m', '--merge', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='merge', help=helps['merge'])\n parser.add_argument('-t', '--tri-tetra', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='tri_tetra', help=helps['tri-tetra'])\n parser.add_argument('-2', '--2d', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='force_2d', help=helps['2d'])\n parser.add_argument('--save-per-mat', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='save_per_mat', help=helps['save-per-mat'])\n parser.add_argument('--remesh', metavar='options',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='remesh',\n default=None, help=helps['remesh'])\n parser.add_argument('filename_in')\n parser.add_argument('filename_out')\n options = parser.parse_args()\n\n if options.list:\n output('Supported readable mesh formats:')\n output('--------------------------------')\n output_mesh_formats('r')\n output('')\n output('Supported writable mesh formats:')\n output('--------------------------------')\n output_mesh_formats('w')\n sys.exit(0)\n\n scale = _parse_val_or_vec(options.scale, 'scale', parser)\n center = _parse_val_or_vec(options.center, 'center', parser)\n\n filename_in = options.filename_in\n filename_out = options.filename_out\n\n if options.remesh:\n import tempfile\n import shlex\n import subprocess\n\n dirname = tempfile.mkdtemp()\n\n is_surface = options.remesh.startswith('q')\n if is_surface:\n mesh = Mesh.from_file(filename_in)\n domain = "},"completion":{"kind":"string","value":"FEDomain(mesh.name, mesh)"},"api":{"kind":"string","value":"sfepy.discrete.fem.FEDomain"}}},{"rowIdx":42,"cells":{"prompt":{"kind":"string","value":"#!/usr/bin/env python\n\"\"\"\nConvert a mesh file from one SfePy-supported format to another.\n\nExamples::\n\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s2.5\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 -c 0\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.mesh --remesh='q2/0 a1e-8 O9/7 V'\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new2.mesh --remesh='rq2/0 a1e-8 O9/7 V'\n\"\"\"\nfrom __future__ import absolute_import\nimport sys\nimport os.path as op\nfrom six.moves import range\nsys.path.append('.')\n\nfrom argparse import ArgumentParser, RawDescriptionHelpFormatter\nfrom sfepy.base.base import nm, output\nfrom sfepy.base.ioutils import remove_files\nfrom sfepy.discrete.fem import Mesh, FEDomain\nfrom sfepy.discrete.fem.meshio import (output_mesh_formats, MeshIO,\n supported_cell_types)\nfrom sfepy.discrete.fem.mesh import fix_double_nodes\nfrom sfepy.mesh.mesh_tools import elems_q2t\n\nhelps = {\n 'scale' : 'scale factor (float or comma-separated list for each axis)'\n ' [default: %(default)s]',\n 'center' : 'center of the output mesh (0 for origin or'\n ' comma-separated list for each axis) applied after scaling'\n ' [default: %(default)s]',\n 'refine' : 'uniform refinement level [default: %(default)s]',\n 'format' : 'output mesh format (overrides filename_out extension)',\n 'list' : 'list supported readable/writable output mesh formats',\n 'merge' : 'remove duplicate vertices',\n 'tri-tetra' : 'convert elements: quad->tri, hexa->tetra',\n '2d' : 'force a 2D mesh by removing the z coordinates - assumes a 3D mesh'\n ' in the xy plane',\n 'save-per-mat': 'extract cells by material id and save them into'\n ' separate mesh files with a name based on filename_out and the id'\n ' numbers (preserves original mesh vertices)',\n\n 'remesh' : \"\"\"when given, remesh the given mesh using tetgen.\n The options can be the following, separated by spaces, in this order: 1.\n \"r\" causes remeshing of the mesh volume - if not present the mesh surface\n is extracted and used for the volume mesh generation. 2.\n \"q[/]\" (required) - the two numbers after \"q\" are a maximum\n radius-edge ratio bound and a minimum dihedral angle bound. 3. \"a\"\n (optional) - the number imposes a maximum volume constraint on all\n tetrahedra. 4. O[<0-9>/<0-7>] - the two numbers correspond to a mesh\n optimization level and a choice of optimizing operations. 5. \"V\"\n (optional) - if present, mesh statistics are printed. Consult the tetgen\n documentation for details.\"\"\",\n}\n\ndef _parse_val_or_vec(option, name, parser):\n if option is not None:\n try:\n try:\n option = float(option)\n except ValueError:\n option = [float(ii) for ii in option.split(',')]\n option = nm.array(option, dtype=nm.float64, ndmin=1)\n except:\n output('bad %s! (%s)' % (name, option))\n parser.print_help()\n sys.exit(1)\n\n return option\n\ndef main():\n parser = ArgumentParser(description=__doc__,\n formatter_class=RawDescriptionHelpFormatter)\n parser.add_argument('-s', '--scale', metavar='scale',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='scale',\n default=None, help=helps['scale'])\n parser.add_argument('-c', '--center', metavar='center',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='center',\n default=None, help=helps['center'])\n parser.add_argument('-r', '--refine', metavar='level',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", type=int, dest='refine',\n default=0, help=helps['refine'])\n parser.add_argument('-f', '--format', metavar='format',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", type=str, dest='format',\n default=None, help=helps['format'])\n parser.add_argument('-l', '--list', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='list', help=helps['list'])\n parser.add_argument('-m', '--merge', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='merge', help=helps['merge'])\n parser.add_argument('-t', '--tri-tetra', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='tri_tetra', help=helps['tri-tetra'])\n parser.add_argument('-2', '--2d', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='force_2d', help=helps['2d'])\n parser.add_argument('--save-per-mat', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='save_per_mat', help=helps['save-per-mat'])\n parser.add_argument('--remesh', metavar='options',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='remesh',\n default=None, help=helps['remesh'])\n parser.add_argument('filename_in')\n parser.add_argument('filename_out')\n options = parser.parse_args()\n\n if options.list:\n output('Supported readable mesh formats:')\n output('--------------------------------')\n output_mesh_formats('r')\n output('')\n output('Supported writable mesh formats:')\n output('--------------------------------')\n output_mesh_formats('w')\n sys.exit(0)\n\n scale = _parse_val_or_vec(options.scale, 'scale', parser)\n center = _parse_val_or_vec(options.center, 'center', parser)\n\n filename_in = options.filename_in\n filename_out = options.filename_out\n\n if options.remesh:\n import tempfile\n import shlex\n import subprocess\n\n dirname = tempfile.mkdtemp()\n\n is_surface = options.remesh.startswith('q')\n if is_surface:\n mesh = Mesh.from_file(filename_in)\n domain = FEDomain(mesh.name, mesh)\n region = domain.create_region('surf', 'vertices of surface',\n 'facet')\n surf_mesh = Mesh.from_region(region, mesh,\n localize=True, is_surface=True)\n\n filename = op.join(dirname, 'surf.mesh')\n surf_mesh.write(filename, io='auto')\n\n else:\n import shutil\n\n shutil.copy(filename_in, dirname)\n filename = op.join(dirname, op.basename(filename_in))\n\n qopts = ''.join(options.remesh.split()) # Remove spaces.\n command = 'tetgen -BFENkACp%s %s' % (qopts, filename)\n args = shlex.split(command)\n subprocess.call(args)\n\n root, ext = op.splitext(filename)\n mesh = Mesh.from_file(root + '.1.vtk')\n\n remove_files(dirname)\n\n else:\n mesh = Mesh.from_file(filename_in)\n\n if options.force_2d:\n data = list(mesh._get_io_data())\n data[0] = data[0][:, :2]\n mesh = Mesh.from_data(mesh.name, *data)\n\n if scale is not None:\n if len(scale) == 1:\n tr = nm.eye(mesh.dim, dtype=nm.float64) * scale\n elif len(scale) == mesh.dim:\n tr = nm.diag(scale)\n else:\n raise ValueError('bad scale! (%s)' % scale)\n mesh.transform_coors(tr)\n\n if center is not None:\n cc = 0.5 * mesh.get_bounding_box().sum(0)\n shift = center - cc\n tr = nm.c_[nm.eye(mesh.dim, dtype=nm.float64), shift[:, None]]\n mesh.transform_coors(tr)\n\n if options.refine > 0:\n domain = FEDomain(mesh.name, mesh)\n output('initial mesh: %d nodes %d elements'\n % (domain.shape.n_nod, domain.shape.n_el))\n\n for ii in range(options.refine):\n "},"completion":{"kind":"string","value":"output('refine %d...' % ii)"},"api":{"kind":"string","value":"sfepy.base.base.output"}}},{"rowIdx":43,"cells":{"prompt":{"kind":"string","value":"#!/usr/bin/env python\n\"\"\"\nConvert a mesh file from one SfePy-supported format to another.\n\nExamples::\n\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s2.5\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 -c 0\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.mesh --remesh='q2/0 a1e-8 O9/7 V'\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new2.mesh --remesh='rq2/0 a1e-8 O9/7 V'\n\"\"\"\nfrom __future__ import absolute_import\nimport sys\nimport os.path as op\nfrom six.moves import range\nsys.path.append('.')\n\nfrom argparse import ArgumentParser, RawDescriptionHelpFormatter\nfrom sfepy.base.base import nm, output\nfrom sfepy.base.ioutils import remove_files\nfrom sfepy.discrete.fem import Mesh, FEDomain\nfrom sfepy.discrete.fem.meshio import (output_mesh_formats, MeshIO,\n supported_cell_types)\nfrom sfepy.discrete.fem.mesh import fix_double_nodes\nfrom sfepy.mesh.mesh_tools import elems_q2t\n\nhelps = {\n 'scale' : 'scale factor (float or comma-separated list for each axis)'\n ' [default: %(default)s]',\n 'center' : 'center of the output mesh (0 for origin or'\n ' comma-separated list for each axis) applied after scaling'\n ' [default: %(default)s]',\n 'refine' : 'uniform refinement level [default: %(default)s]',\n 'format' : 'output mesh format (overrides filename_out extension)',\n 'list' : 'list supported readable/writable output mesh formats',\n 'merge' : 'remove duplicate vertices',\n 'tri-tetra' : 'convert elements: quad->tri, hexa->tetra',\n '2d' : 'force a 2D mesh by removing the z coordinates - assumes a 3D mesh'\n ' in the xy plane',\n 'save-per-mat': 'extract cells by material id and save them into'\n ' separate mesh files with a name based on filename_out and the id'\n ' numbers (preserves original mesh vertices)',\n\n 'remesh' : \"\"\"when given, remesh the given mesh using tetgen.\n The options can be the following, separated by spaces, in this order: 1.\n \"r\" causes remeshing of the mesh volume - if not present the mesh surface\n is extracted and used for the volume mesh generation. 2.\n \"q[/]\" (required) - the two numbers after \"q\" are a maximum\n radius-edge ratio bound and a minimum dihedral angle bound. 3. \"a\"\n (optional) - the number imposes a maximum volume constraint on all\n tetrahedra. 4. O[<0-9>/<0-7>] - the two numbers correspond to a mesh\n optimization level and a choice of optimizing operations. 5. \"V\"\n (optional) - if present, mesh statistics are printed. Consult the tetgen\n documentation for details.\"\"\",\n}\n\ndef _parse_val_or_vec(option, name, parser):\n if option is not None:\n try:\n try:\n option = float(option)\n except ValueError:\n option = [float(ii) for ii in option.split(',')]\n option = nm.array(option, dtype=nm.float64, ndmin=1)\n except:\n output('bad %s! (%s)' % (name, option))\n parser.print_help()\n sys.exit(1)\n\n return option\n\ndef main():\n parser = ArgumentParser(description=__doc__,\n formatter_class=RawDescriptionHelpFormatter)\n parser.add_argument('-s', '--scale', metavar='scale',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='scale',\n default=None, help=helps['scale'])\n parser.add_argument('-c', '--center', metavar='center',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='center',\n default=None, help=helps['center'])\n parser.add_argument('-r', '--refine', metavar='level',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", type=int, dest='refine',\n default=0, help=helps['refine'])\n parser.add_argument('-f', '--format', metavar='format',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", type=str, dest='format',\n default=None, help=helps['format'])\n parser.add_argument('-l', '--list', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='list', help=helps['list'])\n parser.add_argument('-m', '--merge', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='merge', help=helps['merge'])\n parser.add_argument('-t', '--tri-tetra', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='tri_tetra', help=helps['tri-tetra'])\n parser.add_argument('-2', '--2d', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='force_2d', help=helps['2d'])\n parser.add_argument('--save-per-mat', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='save_per_mat', help=helps['save-per-mat'])\n parser.add_argument('--remesh', metavar='options',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='remesh',\n default=None, help=helps['remesh'])\n parser.add_argument('filename_in')\n parser.add_argument('filename_out')\n options = parser.parse_args()\n\n if options.list:\n output('Supported readable mesh formats:')\n output('--------------------------------')\n output_mesh_formats('r')\n output('')\n output('Supported writable mesh formats:')\n output('--------------------------------')\n output_mesh_formats('w')\n sys.exit(0)\n\n scale = _parse_val_or_vec(options.scale, 'scale', parser)\n center = _parse_val_or_vec(options.center, 'center', parser)\n\n filename_in = options.filename_in\n filename_out = options.filename_out\n\n if options.remesh:\n import tempfile\n import shlex\n import subprocess\n\n dirname = tempfile.mkdtemp()\n\n is_surface = options.remesh.startswith('q')\n if is_surface:\n mesh = Mesh.from_file(filename_in)\n domain = FEDomain(mesh.name, mesh)\n region = domain.create_region('surf', 'vertices of surface',\n 'facet')\n surf_mesh = Mesh.from_region(region, mesh,\n localize=True, is_surface=True)\n\n filename = op.join(dirname, 'surf.mesh')\n surf_mesh.write(filename, io='auto')\n\n else:\n import shutil\n\n shutil.copy(filename_in, dirname)\n filename = op.join(dirname, op.basename(filename_in))\n\n qopts = ''.join(options.remesh.split()) # Remove spaces.\n command = 'tetgen -BFENkACp%s %s' % (qopts, filename)\n args = shlex.split(command)\n subprocess.call(args)\n\n root, ext = op.splitext(filename)\n mesh = Mesh.from_file(root + '.1.vtk')\n\n remove_files(dirname)\n\n else:\n mesh = Mesh.from_file(filename_in)\n\n if options.force_2d:\n data = list(mesh._get_io_data())\n data[0] = data[0][:, :2]\n mesh = Mesh.from_data(mesh.name, *data)\n\n if scale is not None:\n if len(scale) == 1:\n tr = nm.eye(mesh.dim, dtype=nm.float64) * scale\n elif len(scale) == mesh.dim:\n tr = nm.diag(scale)\n else:\n raise ValueError('bad scale! (%s)' % scale)\n mesh.transform_coors(tr)\n\n if center is not None:\n cc = 0.5 * mesh.get_bounding_box().sum(0)\n shift = center - cc\n tr = nm.c_[nm.eye(mesh.dim, dtype=nm.float64), shift[:, None]]\n mesh.transform_coors(tr)\n\n if options.refine > 0:\n domain = FEDomain(mesh.name, mesh)\n output('initial mesh: %d nodes %d elements'\n % (domain.shape.n_nod, domain.shape.n_el))\n\n for ii in range(options.refine):\n output('refine %d...' % ii)\n domain = domain.refine()\n output('... %d nodes %d elements'\n % (domain.shape.n_nod, domain.shape.n_el))\n\n mesh = domain.mesh\n\n if options.tri_tetra > 0:\n conns = None\n for k, new_desc in [('3_8', '3_4'), ('2_4', '2_3')]:\n if k in mesh.descs:\n conns = mesh.get_conn(k)\n break\n\n if conns is not None:\n nelo = conns.shape[0]\n "},"completion":{"kind":"string","value":"output('initial mesh: %d elements' % nelo)"},"api":{"kind":"string","value":"sfepy.base.base.output"}}},{"rowIdx":44,"cells":{"prompt":{"kind":"string","value":"#!/usr/bin/env python\n\"\"\"\nConvert a mesh file from one SfePy-supported format to another.\n\nExamples::\n\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s2.5\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 -c 0\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.mesh --remesh='q2/0 a1e-8 O9/7 V'\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new2.mesh --remesh='rq2/0 a1e-8 O9/7 V'\n\"\"\"\nfrom __future__ import absolute_import\nimport sys\nimport os.path as op\nfrom six.moves import range\nsys.path.append('.')\n\nfrom argparse import ArgumentParser, RawDescriptionHelpFormatter\nfrom sfepy.base.base import nm, output\nfrom sfepy.base.ioutils import remove_files\nfrom sfepy.discrete.fem import Mesh, FEDomain\nfrom sfepy.discrete.fem.meshio import (output_mesh_formats, MeshIO,\n supported_cell_types)\nfrom sfepy.discrete.fem.mesh import fix_double_nodes\nfrom sfepy.mesh.mesh_tools import elems_q2t\n\nhelps = {\n 'scale' : 'scale factor (float or comma-separated list for each axis)'\n ' [default: %(default)s]',\n 'center' : 'center of the output mesh (0 for origin or'\n ' comma-separated list for each axis) applied after scaling'\n ' [default: %(default)s]',\n 'refine' : 'uniform refinement level [default: %(default)s]',\n 'format' : 'output mesh format (overrides filename_out extension)',\n 'list' : 'list supported readable/writable output mesh formats',\n 'merge' : 'remove duplicate vertices',\n 'tri-tetra' : 'convert elements: quad->tri, hexa->tetra',\n '2d' : 'force a 2D mesh by removing the z coordinates - assumes a 3D mesh'\n ' in the xy plane',\n 'save-per-mat': 'extract cells by material id and save them into'\n ' separate mesh files with a name based on filename_out and the id'\n ' numbers (preserves original mesh vertices)',\n\n 'remesh' : \"\"\"when given, remesh the given mesh using tetgen.\n The options can be the following, separated by spaces, in this order: 1.\n \"r\" causes remeshing of the mesh volume - if not present the mesh surface\n is extracted and used for the volume mesh generation. 2.\n \"q[/]\" (required) - the two numbers after \"q\" are a maximum\n radius-edge ratio bound and a minimum dihedral angle bound. 3. \"a\"\n (optional) - the number imposes a maximum volume constraint on all\n tetrahedra. 4. O[<0-9>/<0-7>] - the two numbers correspond to a mesh\n optimization level and a choice of optimizing operations. 5. \"V\"\n (optional) - if present, mesh statistics are printed. Consult the tetgen\n documentation for details.\"\"\",\n}\n\ndef _parse_val_or_vec(option, name, parser):\n if option is not None:\n try:\n try:\n option = float(option)\n except ValueError:\n option = [float(ii) for ii in option.split(',')]\n option = nm.array(option, dtype=nm.float64, ndmin=1)\n except:\n output('bad %s! (%s)' % (name, option))\n parser.print_help()\n sys.exit(1)\n\n return option\n\ndef main():\n parser = ArgumentParser(description=__doc__,\n formatter_class=RawDescriptionHelpFormatter)\n parser.add_argument('-s', '--scale', metavar='scale',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='scale',\n default=None, help=helps['scale'])\n parser.add_argument('-c', '--center', metavar='center',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='center',\n default=None, help=helps['center'])\n parser.add_argument('-r', '--refine', metavar='level',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", type=int, dest='refine',\n default=0, help=helps['refine'])\n parser.add_argument('-f', '--format', metavar='format',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", type=str, dest='format',\n default=None, help=helps['format'])\n parser.add_argument('-l', '--list', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='list', help=helps['list'])\n parser.add_argument('-m', '--merge', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='merge', help=helps['merge'])\n parser.add_argument('-t', '--tri-tetra', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='tri_tetra', help=helps['tri-tetra'])\n parser.add_argument('-2', '--2d', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='force_2d', help=helps['2d'])\n parser.add_argument('--save-per-mat', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='save_per_mat', help=helps['save-per-mat'])\n parser.add_argument('--remesh', metavar='options',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='remesh',\n default=None, help=helps['remesh'])\n parser.add_argument('filename_in')\n parser.add_argument('filename_out')\n options = parser.parse_args()\n\n if options.list:\n output('Supported readable mesh formats:')\n output('--------------------------------')\n output_mesh_formats('r')\n output('')\n output('Supported writable mesh formats:')\n output('--------------------------------')\n output_mesh_formats('w')\n sys.exit(0)\n\n scale = _parse_val_or_vec(options.scale, 'scale', parser)\n center = _parse_val_or_vec(options.center, 'center', parser)\n\n filename_in = options.filename_in\n filename_out = options.filename_out\n\n if options.remesh:\n import tempfile\n import shlex\n import subprocess\n\n dirname = tempfile.mkdtemp()\n\n is_surface = options.remesh.startswith('q')\n if is_surface:\n mesh = Mesh.from_file(filename_in)\n domain = FEDomain(mesh.name, mesh)\n region = domain.create_region('surf', 'vertices of surface',\n 'facet')\n surf_mesh = Mesh.from_region(region, mesh,\n localize=True, is_surface=True)\n\n filename = op.join(dirname, 'surf.mesh')\n surf_mesh.write(filename, io='auto')\n\n else:\n import shutil\n\n shutil.copy(filename_in, dirname)\n filename = op.join(dirname, op.basename(filename_in))\n\n qopts = ''.join(options.remesh.split()) # Remove spaces.\n command = 'tetgen -BFENkACp%s %s' % (qopts, filename)\n args = shlex.split(command)\n subprocess.call(args)\n\n root, ext = op.splitext(filename)\n mesh = Mesh.from_file(root + '.1.vtk')\n\n remove_files(dirname)\n\n else:\n mesh = Mesh.from_file(filename_in)\n\n if options.force_2d:\n data = list(mesh._get_io_data())\n data[0] = data[0][:, :2]\n mesh = Mesh.from_data(mesh.name, *data)\n\n if scale is not None:\n if len(scale) == 1:\n tr = nm.eye(mesh.dim, dtype=nm.float64) * scale\n elif len(scale) == mesh.dim:\n tr = nm.diag(scale)\n else:\n raise ValueError('bad scale! (%s)' % scale)\n mesh.transform_coors(tr)\n\n if center is not None:\n cc = 0.5 * mesh.get_bounding_box().sum(0)\n shift = center - cc\n tr = nm.c_[nm.eye(mesh.dim, dtype=nm.float64), shift[:, None]]\n mesh.transform_coors(tr)\n\n if options.refine > 0:\n domain = FEDomain(mesh.name, mesh)\n output('initial mesh: %d nodes %d elements'\n % (domain.shape.n_nod, domain.shape.n_el))\n\n for ii in range(options.refine):\n output('refine %d...' % ii)\n domain = domain.refine()\n output('... %d nodes %d elements'\n % (domain.shape.n_nod, domain.shape.n_el))\n\n mesh = domain.mesh\n\n if options.tri_tetra > 0:\n conns = None\n for k, new_desc in [('3_8', '3_4'), ('2_4', '2_3')]:\n if k in mesh.descs:\n conns = mesh.get_conn(k)\n break\n\n if conns is not None:\n nelo = conns.shape[0]\n output('initial mesh: %d elements' % nelo)\n\n new_conns = "},"completion":{"kind":"string","value":"elems_q2t(conns)"},"api":{"kind":"string","value":"sfepy.mesh.mesh_tools.elems_q2t"}}},{"rowIdx":45,"cells":{"prompt":{"kind":"string","value":"#!/usr/bin/env python\n\"\"\"\nConvert a mesh file from one SfePy-supported format to another.\n\nExamples::\n\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s2.5\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 -c 0\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.mesh --remesh='q2/0 a1e-8 O9/7 V'\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new2.mesh --remesh='rq2/0 a1e-8 O9/7 V'\n\"\"\"\nfrom __future__ import absolute_import\nimport sys\nimport os.path as op\nfrom six.moves import range\nsys.path.append('.')\n\nfrom argparse import ArgumentParser, RawDescriptionHelpFormatter\nfrom sfepy.base.base import nm, output\nfrom sfepy.base.ioutils import remove_files\nfrom sfepy.discrete.fem import Mesh, FEDomain\nfrom sfepy.discrete.fem.meshio import (output_mesh_formats, MeshIO,\n supported_cell_types)\nfrom sfepy.discrete.fem.mesh import fix_double_nodes\nfrom sfepy.mesh.mesh_tools import elems_q2t\n\nhelps = {\n 'scale' : 'scale factor (float or comma-separated list for each axis)'\n ' [default: %(default)s]',\n 'center' : 'center of the output mesh (0 for origin or'\n ' comma-separated list for each axis) applied after scaling'\n ' [default: %(default)s]',\n 'refine' : 'uniform refinement level [default: %(default)s]',\n 'format' : 'output mesh format (overrides filename_out extension)',\n 'list' : 'list supported readable/writable output mesh formats',\n 'merge' : 'remove duplicate vertices',\n 'tri-tetra' : 'convert elements: quad->tri, hexa->tetra',\n '2d' : 'force a 2D mesh by removing the z coordinates - assumes a 3D mesh'\n ' in the xy plane',\n 'save-per-mat': 'extract cells by material id and save them into'\n ' separate mesh files with a name based on filename_out and the id'\n ' numbers (preserves original mesh vertices)',\n\n 'remesh' : \"\"\"when given, remesh the given mesh using tetgen.\n The options can be the following, separated by spaces, in this order: 1.\n \"r\" causes remeshing of the mesh volume - if not present the mesh surface\n is extracted and used for the volume mesh generation. 2.\n \"q[/]\" (required) - the two numbers after \"q\" are a maximum\n radius-edge ratio bound and a minimum dihedral angle bound. 3. \"a\"\n (optional) - the number imposes a maximum volume constraint on all\n tetrahedra. 4. O[<0-9>/<0-7>] - the two numbers correspond to a mesh\n optimization level and a choice of optimizing operations. 5. \"V\"\n (optional) - if present, mesh statistics are printed. Consult the tetgen\n documentation for details.\"\"\",\n}\n\ndef _parse_val_or_vec(option, name, parser):\n if option is not None:\n try:\n try:\n option = float(option)\n except ValueError:\n option = [float(ii) for ii in option.split(',')]\n option = nm.array(option, dtype=nm.float64, ndmin=1)\n except:\n output('bad %s! (%s)' % (name, option))\n parser.print_help()\n sys.exit(1)\n\n return option\n\ndef main():\n parser = ArgumentParser(description=__doc__,\n formatter_class=RawDescriptionHelpFormatter)\n parser.add_argument('-s', '--scale', metavar='scale',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='scale',\n default=None, help=helps['scale'])\n parser.add_argument('-c', '--center', metavar='center',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='center',\n default=None, help=helps['center'])\n parser.add_argument('-r', '--refine', metavar='level',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", type=int, dest='refine',\n default=0, help=helps['refine'])\n parser.add_argument('-f', '--format', metavar='format',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", type=str, dest='format',\n default=None, help=helps['format'])\n parser.add_argument('-l', '--list', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='list', help=helps['list'])\n parser.add_argument('-m', '--merge', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='merge', help=helps['merge'])\n parser.add_argument('-t', '--tri-tetra', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='tri_tetra', help=helps['tri-tetra'])\n parser.add_argument('-2', '--2d', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='force_2d', help=helps['2d'])\n parser.add_argument('--save-per-mat', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='save_per_mat', help=helps['save-per-mat'])\n parser.add_argument('--remesh', metavar='options',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='remesh',\n default=None, help=helps['remesh'])\n parser.add_argument('filename_in')\n parser.add_argument('filename_out')\n options = parser.parse_args()\n\n if options.list:\n output('Supported readable mesh formats:')\n output('--------------------------------')\n output_mesh_formats('r')\n output('')\n output('Supported writable mesh formats:')\n output('--------------------------------')\n output_mesh_formats('w')\n sys.exit(0)\n\n scale = _parse_val_or_vec(options.scale, 'scale', parser)\n center = _parse_val_or_vec(options.center, 'center', parser)\n\n filename_in = options.filename_in\n filename_out = options.filename_out\n\n if options.remesh:\n import tempfile\n import shlex\n import subprocess\n\n dirname = tempfile.mkdtemp()\n\n is_surface = options.remesh.startswith('q')\n if is_surface:\n mesh = Mesh.from_file(filename_in)\n domain = FEDomain(mesh.name, mesh)\n region = domain.create_region('surf', 'vertices of surface',\n 'facet')\n surf_mesh = Mesh.from_region(region, mesh,\n localize=True, is_surface=True)\n\n filename = op.join(dirname, 'surf.mesh')\n surf_mesh.write(filename, io='auto')\n\n else:\n import shutil\n\n shutil.copy(filename_in, dirname)\n filename = op.join(dirname, op.basename(filename_in))\n\n qopts = ''.join(options.remesh.split()) # Remove spaces.\n command = 'tetgen -BFENkACp%s %s' % (qopts, filename)\n args = shlex.split(command)\n subprocess.call(args)\n\n root, ext = op.splitext(filename)\n mesh = Mesh.from_file(root + '.1.vtk')\n\n remove_files(dirname)\n\n else:\n mesh = Mesh.from_file(filename_in)\n\n if options.force_2d:\n data = list(mesh._get_io_data())\n data[0] = data[0][:, :2]\n mesh = Mesh.from_data(mesh.name, *data)\n\n if scale is not None:\n if len(scale) == 1:\n tr = nm.eye(mesh.dim, dtype=nm.float64) * scale\n elif len(scale) == mesh.dim:\n tr = nm.diag(scale)\n else:\n raise ValueError('bad scale! (%s)' % scale)\n mesh.transform_coors(tr)\n\n if center is not None:\n cc = 0.5 * mesh.get_bounding_box().sum(0)\n shift = center - cc\n tr = nm.c_[nm.eye(mesh.dim, dtype=nm.float64), shift[:, None]]\n mesh.transform_coors(tr)\n\n if options.refine > 0:\n domain = FEDomain(mesh.name, mesh)\n output('initial mesh: %d nodes %d elements'\n % (domain.shape.n_nod, domain.shape.n_el))\n\n for ii in range(options.refine):\n output('refine %d...' % ii)\n domain = domain.refine()\n output('... %d nodes %d elements'\n % (domain.shape.n_nod, domain.shape.n_el))\n\n mesh = domain.mesh\n\n if options.tri_tetra > 0:\n conns = None\n for k, new_desc in [('3_8', '3_4'), ('2_4', '2_3')]:\n if k in mesh.descs:\n conns = mesh.get_conn(k)\n break\n\n if conns is not None:\n nelo = conns.shape[0]\n output('initial mesh: %d elements' % nelo)\n\n new_conns = elems_q2t(conns)\n nn = new_conns.shape[0] // nelo\n new_cgroups = "},"completion":{"kind":"string","value":"nm.repeat(mesh.cmesh.cell_groups, nn)"},"api":{"kind":"string","value":"sfepy.base.base.nm.repeat"}}},{"rowIdx":46,"cells":{"prompt":{"kind":"string","value":"#!/usr/bin/env python\n\"\"\"\nConvert a mesh file from one SfePy-supported format to another.\n\nExamples::\n\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s2.5\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 -c 0\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.mesh --remesh='q2/0 a1e-8 O9/7 V'\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new2.mesh --remesh='rq2/0 a1e-8 O9/7 V'\n\"\"\"\nfrom __future__ import absolute_import\nimport sys\nimport os.path as op\nfrom six.moves import range\nsys.path.append('.')\n\nfrom argparse import ArgumentParser, RawDescriptionHelpFormatter\nfrom sfepy.base.base import nm, output\nfrom sfepy.base.ioutils import remove_files\nfrom sfepy.discrete.fem import Mesh, FEDomain\nfrom sfepy.discrete.fem.meshio import (output_mesh_formats, MeshIO,\n supported_cell_types)\nfrom sfepy.discrete.fem.mesh import fix_double_nodes\nfrom sfepy.mesh.mesh_tools import elems_q2t\n\nhelps = {\n 'scale' : 'scale factor (float or comma-separated list for each axis)'\n ' [default: %(default)s]',\n 'center' : 'center of the output mesh (0 for origin or'\n ' comma-separated list for each axis) applied after scaling'\n ' [default: %(default)s]',\n 'refine' : 'uniform refinement level [default: %(default)s]',\n 'format' : 'output mesh format (overrides filename_out extension)',\n 'list' : 'list supported readable/writable output mesh formats',\n 'merge' : 'remove duplicate vertices',\n 'tri-tetra' : 'convert elements: quad->tri, hexa->tetra',\n '2d' : 'force a 2D mesh by removing the z coordinates - assumes a 3D mesh'\n ' in the xy plane',\n 'save-per-mat': 'extract cells by material id and save them into'\n ' separate mesh files with a name based on filename_out and the id'\n ' numbers (preserves original mesh vertices)',\n\n 'remesh' : \"\"\"when given, remesh the given mesh using tetgen.\n The options can be the following, separated by spaces, in this order: 1.\n \"r\" causes remeshing of the mesh volume - if not present the mesh surface\n is extracted and used for the volume mesh generation. 2.\n \"q[/]\" (required) - the two numbers after \"q\" are a maximum\n radius-edge ratio bound and a minimum dihedral angle bound. 3. \"a\"\n (optional) - the number imposes a maximum volume constraint on all\n tetrahedra. 4. O[<0-9>/<0-7>] - the two numbers correspond to a mesh\n optimization level and a choice of optimizing operations. 5. \"V\"\n (optional) - if present, mesh statistics are printed. Consult the tetgen\n documentation for details.\"\"\",\n}\n\ndef _parse_val_or_vec(option, name, parser):\n if option is not None:\n try:\n try:\n option = float(option)\n except ValueError:\n option = [float(ii) for ii in option.split(',')]\n option = nm.array(option, dtype=nm.float64, ndmin=1)\n except:\n output('bad %s! (%s)' % (name, option))\n parser.print_help()\n sys.exit(1)\n\n return option\n\ndef main():\n parser = ArgumentParser(description=__doc__,\n formatter_class=RawDescriptionHelpFormatter)\n parser.add_argument('-s', '--scale', metavar='scale',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='scale',\n default=None, help=helps['scale'])\n parser.add_argument('-c', '--center', metavar='center',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='center',\n default=None, help=helps['center'])\n parser.add_argument('-r', '--refine', metavar='level',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", type=int, dest='refine',\n default=0, help=helps['refine'])\n parser.add_argument('-f', '--format', metavar='format',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", type=str, dest='format',\n default=None, help=helps['format'])\n parser.add_argument('-l', '--list', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='list', help=helps['list'])\n parser.add_argument('-m', '--merge', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='merge', help=helps['merge'])\n parser.add_argument('-t', '--tri-tetra', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='tri_tetra', help=helps['tri-tetra'])\n parser.add_argument('-2', '--2d', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='force_2d', help=helps['2d'])\n parser.add_argument('--save-per-mat', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='save_per_mat', help=helps['save-per-mat'])\n parser.add_argument('--remesh', metavar='options',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='remesh',\n default=None, help=helps['remesh'])\n parser.add_argument('filename_in')\n parser.add_argument('filename_out')\n options = parser.parse_args()\n\n if options.list:\n output('Supported readable mesh formats:')\n output('--------------------------------')\n output_mesh_formats('r')\n output('')\n output('Supported writable mesh formats:')\n output('--------------------------------')\n output_mesh_formats('w')\n sys.exit(0)\n\n scale = _parse_val_or_vec(options.scale, 'scale', parser)\n center = _parse_val_or_vec(options.center, 'center', parser)\n\n filename_in = options.filename_in\n filename_out = options.filename_out\n\n if options.remesh:\n import tempfile\n import shlex\n import subprocess\n\n dirname = tempfile.mkdtemp()\n\n is_surface = options.remesh.startswith('q')\n if is_surface:\n mesh = Mesh.from_file(filename_in)\n domain = FEDomain(mesh.name, mesh)\n region = domain.create_region('surf', 'vertices of surface',\n 'facet')\n surf_mesh = Mesh.from_region(region, mesh,\n localize=True, is_surface=True)\n\n filename = op.join(dirname, 'surf.mesh')\n surf_mesh.write(filename, io='auto')\n\n else:\n import shutil\n\n shutil.copy(filename_in, dirname)\n filename = op.join(dirname, op.basename(filename_in))\n\n qopts = ''.join(options.remesh.split()) # Remove spaces.\n command = 'tetgen -BFENkACp%s %s' % (qopts, filename)\n args = shlex.split(command)\n subprocess.call(args)\n\n root, ext = op.splitext(filename)\n mesh = Mesh.from_file(root + '.1.vtk')\n\n remove_files(dirname)\n\n else:\n mesh = Mesh.from_file(filename_in)\n\n if options.force_2d:\n data = list(mesh._get_io_data())\n data[0] = data[0][:, :2]\n mesh = Mesh.from_data(mesh.name, *data)\n\n if scale is not None:\n if len(scale) == 1:\n tr = nm.eye(mesh.dim, dtype=nm.float64) * scale\n elif len(scale) == mesh.dim:\n tr = nm.diag(scale)\n else:\n raise ValueError('bad scale! (%s)' % scale)\n mesh.transform_coors(tr)\n\n if center is not None:\n cc = 0.5 * mesh.get_bounding_box().sum(0)\n shift = center - cc\n tr = nm.c_[nm.eye(mesh.dim, dtype=nm.float64), shift[:, None]]\n mesh.transform_coors(tr)\n\n if options.refine > 0:\n domain = FEDomain(mesh.name, mesh)\n output('initial mesh: %d nodes %d elements'\n % (domain.shape.n_nod, domain.shape.n_el))\n\n for ii in range(options.refine):\n output('refine %d...' % ii)\n domain = domain.refine()\n output('... %d nodes %d elements'\n % (domain.shape.n_nod, domain.shape.n_el))\n\n mesh = domain.mesh\n\n if options.tri_tetra > 0:\n conns = None\n for k, new_desc in [('3_8', '3_4'), ('2_4', '2_3')]:\n if k in mesh.descs:\n conns = mesh.get_conn(k)\n break\n\n if conns is not None:\n nelo = conns.shape[0]\n output('initial mesh: %d elements' % nelo)\n\n new_conns = elems_q2t(conns)\n nn = new_conns.shape[0] // nelo\n new_cgroups = nm.repeat(mesh.cmesh.cell_groups, nn)\n\n "},"completion":{"kind":"string","value":"output('new mesh: %d elements' % new_conns.shape[0])"},"api":{"kind":"string","value":"sfepy.base.base.output"}}},{"rowIdx":47,"cells":{"prompt":{"kind":"string","value":"#!/usr/bin/env python\n\"\"\"\nConvert a mesh file from one SfePy-supported format to another.\n\nExamples::\n\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s2.5\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 -c 0\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.mesh --remesh='q2/0 a1e-8 O9/7 V'\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new2.mesh --remesh='rq2/0 a1e-8 O9/7 V'\n\"\"\"\nfrom __future__ import absolute_import\nimport sys\nimport os.path as op\nfrom six.moves import range\nsys.path.append('.')\n\nfrom argparse import ArgumentParser, RawDescriptionHelpFormatter\nfrom sfepy.base.base import nm, output\nfrom sfepy.base.ioutils import remove_files\nfrom sfepy.discrete.fem import Mesh, FEDomain\nfrom sfepy.discrete.fem.meshio import (output_mesh_formats, MeshIO,\n supported_cell_types)\nfrom sfepy.discrete.fem.mesh import fix_double_nodes\nfrom sfepy.mesh.mesh_tools import elems_q2t\n\nhelps = {\n 'scale' : 'scale factor (float or comma-separated list for each axis)'\n ' [default: %(default)s]',\n 'center' : 'center of the output mesh (0 for origin or'\n ' comma-separated list for each axis) applied after scaling'\n ' [default: %(default)s]',\n 'refine' : 'uniform refinement level [default: %(default)s]',\n 'format' : 'output mesh format (overrides filename_out extension)',\n 'list' : 'list supported readable/writable output mesh formats',\n 'merge' : 'remove duplicate vertices',\n 'tri-tetra' : 'convert elements: quad->tri, hexa->tetra',\n '2d' : 'force a 2D mesh by removing the z coordinates - assumes a 3D mesh'\n ' in the xy plane',\n 'save-per-mat': 'extract cells by material id and save them into'\n ' separate mesh files with a name based on filename_out and the id'\n ' numbers (preserves original mesh vertices)',\n\n 'remesh' : \"\"\"when given, remesh the given mesh using tetgen.\n The options can be the following, separated by spaces, in this order: 1.\n \"r\" causes remeshing of the mesh volume - if not present the mesh surface\n is extracted and used for the volume mesh generation. 2.\n \"q[/]\" (required) - the two numbers after \"q\" are a maximum\n radius-edge ratio bound and a minimum dihedral angle bound. 3. \"a\"\n (optional) - the number imposes a maximum volume constraint on all\n tetrahedra. 4. O[<0-9>/<0-7>] - the two numbers correspond to a mesh\n optimization level and a choice of optimizing operations. 5. \"V\"\n (optional) - if present, mesh statistics are printed. Consult the tetgen\n documentation for details.\"\"\",\n}\n\ndef _parse_val_or_vec(option, name, parser):\n if option is not None:\n try:\n try:\n option = float(option)\n except ValueError:\n option = [float(ii) for ii in option.split(',')]\n option = nm.array(option, dtype=nm.float64, ndmin=1)\n except:\n output('bad %s! (%s)' % (name, option))\n parser.print_help()\n sys.exit(1)\n\n return option\n\ndef main():\n parser = ArgumentParser(description=__doc__,\n formatter_class=RawDescriptionHelpFormatter)\n parser.add_argument('-s', '--scale', metavar='scale',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='scale',\n default=None, help=helps['scale'])\n parser.add_argument('-c', '--center', metavar='center',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='center',\n default=None, help=helps['center'])\n parser.add_argument('-r', '--refine', metavar='level',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", type=int, dest='refine',\n default=0, help=helps['refine'])\n parser.add_argument('-f', '--format', metavar='format',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", type=str, dest='format',\n default=None, help=helps['format'])\n parser.add_argument('-l', '--list', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='list', help=helps['list'])\n parser.add_argument('-m', '--merge', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='merge', help=helps['merge'])\n parser.add_argument('-t', '--tri-tetra', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='tri_tetra', help=helps['tri-tetra'])\n parser.add_argument('-2', '--2d', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='force_2d', help=helps['2d'])\n parser.add_argument('--save-per-mat', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='save_per_mat', help=helps['save-per-mat'])\n parser.add_argument('--remesh', metavar='options',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='remesh',\n default=None, help=helps['remesh'])\n parser.add_argument('filename_in')\n parser.add_argument('filename_out')\n options = parser.parse_args()\n\n if options.list:\n output('Supported readable mesh formats:')\n output('--------------------------------')\n output_mesh_formats('r')\n output('')\n output('Supported writable mesh formats:')\n output('--------------------------------')\n output_mesh_formats('w')\n sys.exit(0)\n\n scale = _parse_val_or_vec(options.scale, 'scale', parser)\n center = _parse_val_or_vec(options.center, 'center', parser)\n\n filename_in = options.filename_in\n filename_out = options.filename_out\n\n if options.remesh:\n import tempfile\n import shlex\n import subprocess\n\n dirname = tempfile.mkdtemp()\n\n is_surface = options.remesh.startswith('q')\n if is_surface:\n mesh = Mesh.from_file(filename_in)\n domain = FEDomain(mesh.name, mesh)\n region = domain.create_region('surf', 'vertices of surface',\n 'facet')\n surf_mesh = Mesh.from_region(region, mesh,\n localize=True, is_surface=True)\n\n filename = op.join(dirname, 'surf.mesh')\n surf_mesh.write(filename, io='auto')\n\n else:\n import shutil\n\n shutil.copy(filename_in, dirname)\n filename = op.join(dirname, op.basename(filename_in))\n\n qopts = ''.join(options.remesh.split()) # Remove spaces.\n command = 'tetgen -BFENkACp%s %s' % (qopts, filename)\n args = shlex.split(command)\n subprocess.call(args)\n\n root, ext = op.splitext(filename)\n mesh = Mesh.from_file(root + '.1.vtk')\n\n remove_files(dirname)\n\n else:\n mesh = Mesh.from_file(filename_in)\n\n if options.force_2d:\n data = list(mesh._get_io_data())\n data[0] = data[0][:, :2]\n mesh = Mesh.from_data(mesh.name, *data)\n\n if scale is not None:\n if len(scale) == 1:\n tr = nm.eye(mesh.dim, dtype=nm.float64) * scale\n elif len(scale) == mesh.dim:\n tr = nm.diag(scale)\n else:\n raise ValueError('bad scale! (%s)' % scale)\n mesh.transform_coors(tr)\n\n if center is not None:\n cc = 0.5 * mesh.get_bounding_box().sum(0)\n shift = center - cc\n tr = nm.c_[nm.eye(mesh.dim, dtype=nm.float64), shift[:, None]]\n mesh.transform_coors(tr)\n\n if options.refine > 0:\n domain = FEDomain(mesh.name, mesh)\n output('initial mesh: %d nodes %d elements'\n % (domain.shape.n_nod, domain.shape.n_el))\n\n for ii in range(options.refine):\n output('refine %d...' % ii)\n domain = domain.refine()\n output('... %d nodes %d elements'\n % (domain.shape.n_nod, domain.shape.n_el))\n\n mesh = domain.mesh\n\n if options.tri_tetra > 0:\n conns = None\n for k, new_desc in [('3_8', '3_4'), ('2_4', '2_3')]:\n if k in mesh.descs:\n conns = mesh.get_conn(k)\n break\n\n if conns is not None:\n nelo = conns.shape[0]\n output('initial mesh: %d elements' % nelo)\n\n new_conns = elems_q2t(conns)\n nn = new_conns.shape[0] // nelo\n new_cgroups = nm.repeat(mesh.cmesh.cell_groups, nn)\n\n output('new mesh: %d elements' % new_conns.shape[0])\n mesh = Mesh.from_data(mesh.name, mesh.coors,\n mesh.cmesh.vertex_groups,\n [new_conns], [new_cgroups], [new_desc])\n\n if options.merge:\n desc = mesh.descs[0]\n coor, ngroups, conns = fix_double_nodes(mesh.coors,\n mesh.cmesh.vertex_groups,\n mesh.get_conn(desc), 1e-9)\n mesh = Mesh.from_data(mesh.name + '_merged',\n coor, ngroups,\n [conns], [mesh.cmesh.cell_groups], [desc])\n\n if options.save_per_mat:\n desc = mesh.descs[0]\n conns, cgroups = mesh.get_conn(desc), mesh.cmesh.cell_groups\n coors, ngroups = mesh.coors, mesh.cmesh.vertex_groups\n mat_ids = nm.unique(cgroups)\n\n for mat_id in mat_ids:\n idxs = nm.where(cgroups == mat_id)[0]\n imesh = Mesh.from_data(mesh.name + '_matid_%d' % mat_id,\n coors, ngroups,\n [conns[idxs]], [cgroups[idxs]], [desc])\n\n fbase, fext = op.splitext(filename_out)\n ifilename_out = '%s_matid_%d%s' % (fbase, mat_id, fext)\n io = MeshIO.for_format(ifilename_out, format=options.format,\n writable=True)\n "},"completion":{"kind":"string","value":"output('writing %s...' % ifilename_out)"},"api":{"kind":"string","value":"sfepy.base.base.output"}}},{"rowIdx":48,"cells":{"prompt":{"kind":"string","value":"#!/usr/bin/env python\n\"\"\"\nConvert a mesh file from one SfePy-supported format to another.\n\nExamples::\n\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s2.5\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 -c 0\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.mesh --remesh='q2/0 a1e-8 O9/7 V'\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new2.mesh --remesh='rq2/0 a1e-8 O9/7 V'\n\"\"\"\nfrom __future__ import absolute_import\nimport sys\nimport os.path as op\nfrom six.moves import range\nsys.path.append('.')\n\nfrom argparse import ArgumentParser, RawDescriptionHelpFormatter\nfrom sfepy.base.base import nm, output\nfrom sfepy.base.ioutils import remove_files\nfrom sfepy.discrete.fem import Mesh, FEDomain\nfrom sfepy.discrete.fem.meshio import (output_mesh_formats, MeshIO,\n supported_cell_types)\nfrom sfepy.discrete.fem.mesh import fix_double_nodes\nfrom sfepy.mesh.mesh_tools import elems_q2t\n\nhelps = {\n 'scale' : 'scale factor (float or comma-separated list for each axis)'\n ' [default: %(default)s]',\n 'center' : 'center of the output mesh (0 for origin or'\n ' comma-separated list for each axis) applied after scaling'\n ' [default: %(default)s]',\n 'refine' : 'uniform refinement level [default: %(default)s]',\n 'format' : 'output mesh format (overrides filename_out extension)',\n 'list' : 'list supported readable/writable output mesh formats',\n 'merge' : 'remove duplicate vertices',\n 'tri-tetra' : 'convert elements: quad->tri, hexa->tetra',\n '2d' : 'force a 2D mesh by removing the z coordinates - assumes a 3D mesh'\n ' in the xy plane',\n 'save-per-mat': 'extract cells by material id and save them into'\n ' separate mesh files with a name based on filename_out and the id'\n ' numbers (preserves original mesh vertices)',\n\n 'remesh' : \"\"\"when given, remesh the given mesh using tetgen.\n The options can be the following, separated by spaces, in this order: 1.\n \"r\" causes remeshing of the mesh volume - if not present the mesh surface\n is extracted and used for the volume mesh generation. 2.\n \"q[/]\" (required) - the two numbers after \"q\" are a maximum\n radius-edge ratio bound and a minimum dihedral angle bound. 3. \"a\"\n (optional) - the number imposes a maximum volume constraint on all\n tetrahedra. 4. O[<0-9>/<0-7>] - the two numbers correspond to a mesh\n optimization level and a choice of optimizing operations. 5. \"V\"\n (optional) - if present, mesh statistics are printed. Consult the tetgen\n documentation for details.\"\"\",\n}\n\ndef _parse_val_or_vec(option, name, parser):\n if option is not None:\n try:\n try:\n option = float(option)\n except ValueError:\n option = [float(ii) for ii in option.split(',')]\n option = nm.array(option, dtype=nm.float64, ndmin=1)\n except:\n output('bad %s! (%s)' % (name, option))\n parser.print_help()\n sys.exit(1)\n\n return option\n\ndef main():\n parser = ArgumentParser(description=__doc__,\n formatter_class=RawDescriptionHelpFormatter)\n parser.add_argument('-s', '--scale', metavar='scale',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='scale',\n default=None, help=helps['scale'])\n parser.add_argument('-c', '--center', metavar='center',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='center',\n default=None, help=helps['center'])\n parser.add_argument('-r', '--refine', metavar='level',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", type=int, dest='refine',\n default=0, help=helps['refine'])\n parser.add_argument('-f', '--format', metavar='format',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", type=str, dest='format',\n default=None, help=helps['format'])\n parser.add_argument('-l', '--list', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='list', help=helps['list'])\n parser.add_argument('-m', '--merge', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='merge', help=helps['merge'])\n parser.add_argument('-t', '--tri-tetra', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='tri_tetra', help=helps['tri-tetra'])\n parser.add_argument('-2', '--2d', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='force_2d', help=helps['2d'])\n parser.add_argument('--save-per-mat', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='save_per_mat', help=helps['save-per-mat'])\n parser.add_argument('--remesh', metavar='options',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='remesh',\n default=None, help=helps['remesh'])\n parser.add_argument('filename_in')\n parser.add_argument('filename_out')\n options = parser.parse_args()\n\n if options.list:\n output('Supported readable mesh formats:')\n output('--------------------------------')\n output_mesh_formats('r')\n output('')\n output('Supported writable mesh formats:')\n output('--------------------------------')\n output_mesh_formats('w')\n sys.exit(0)\n\n scale = _parse_val_or_vec(options.scale, 'scale', parser)\n center = _parse_val_or_vec(options.center, 'center', parser)\n\n filename_in = options.filename_in\n filename_out = options.filename_out\n\n if options.remesh:\n import tempfile\n import shlex\n import subprocess\n\n dirname = tempfile.mkdtemp()\n\n is_surface = options.remesh.startswith('q')\n if is_surface:\n mesh = Mesh.from_file(filename_in)\n domain = FEDomain(mesh.name, mesh)\n region = domain.create_region('surf', 'vertices of surface',\n 'facet')\n surf_mesh = Mesh.from_region(region, mesh,\n localize=True, is_surface=True)\n\n filename = op.join(dirname, 'surf.mesh')\n surf_mesh.write(filename, io='auto')\n\n else:\n import shutil\n\n shutil.copy(filename_in, dirname)\n filename = op.join(dirname, op.basename(filename_in))\n\n qopts = ''.join(options.remesh.split()) # Remove spaces.\n command = 'tetgen -BFENkACp%s %s' % (qopts, filename)\n args = shlex.split(command)\n subprocess.call(args)\n\n root, ext = op.splitext(filename)\n mesh = Mesh.from_file(root + '.1.vtk')\n\n remove_files(dirname)\n\n else:\n mesh = Mesh.from_file(filename_in)\n\n if options.force_2d:\n data = list(mesh._get_io_data())\n data[0] = data[0][:, :2]\n mesh = Mesh.from_data(mesh.name, *data)\n\n if scale is not None:\n if len(scale) == 1:\n tr = nm.eye(mesh.dim, dtype=nm.float64) * scale\n elif len(scale) == mesh.dim:\n tr = nm.diag(scale)\n else:\n raise ValueError('bad scale! (%s)' % scale)\n mesh.transform_coors(tr)\n\n if center is not None:\n cc = 0.5 * mesh.get_bounding_box().sum(0)\n shift = center - cc\n tr = nm.c_[nm.eye(mesh.dim, dtype=nm.float64), shift[:, None]]\n mesh.transform_coors(tr)\n\n if options.refine > 0:\n domain = FEDomain(mesh.name, mesh)\n output('initial mesh: %d nodes %d elements'\n % (domain.shape.n_nod, domain.shape.n_el))\n\n for ii in range(options.refine):\n output('refine %d...' % ii)\n domain = domain.refine()\n output('... %d nodes %d elements'\n % (domain.shape.n_nod, domain.shape.n_el))\n\n mesh = domain.mesh\n\n if options.tri_tetra > 0:\n conns = None\n for k, new_desc in [('3_8', '3_4'), ('2_4', '2_3')]:\n if k in mesh.descs:\n conns = mesh.get_conn(k)\n break\n\n if conns is not None:\n nelo = conns.shape[0]\n output('initial mesh: %d elements' % nelo)\n\n new_conns = elems_q2t(conns)\n nn = new_conns.shape[0] // nelo\n new_cgroups = nm.repeat(mesh.cmesh.cell_groups, nn)\n\n output('new mesh: %d elements' % new_conns.shape[0])\n mesh = Mesh.from_data(mesh.name, mesh.coors,\n mesh.cmesh.vertex_groups,\n [new_conns], [new_cgroups], [new_desc])\n\n if options.merge:\n desc = mesh.descs[0]\n coor, ngroups, conns = fix_double_nodes(mesh.coors,\n mesh.cmesh.vertex_groups,\n mesh.get_conn(desc), 1e-9)\n mesh = Mesh.from_data(mesh.name + '_merged',\n coor, ngroups,\n [conns], [mesh.cmesh.cell_groups], [desc])\n\n if options.save_per_mat:\n desc = mesh.descs[0]\n conns, cgroups = mesh.get_conn(desc), mesh.cmesh.cell_groups\n coors, ngroups = mesh.coors, mesh.cmesh.vertex_groups\n mat_ids = nm.unique(cgroups)\n\n for mat_id in mat_ids:\n idxs = nm.where(cgroups == mat_id)[0]\n imesh = Mesh.from_data(mesh.name + '_matid_%d' % mat_id,\n coors, ngroups,\n [conns[idxs]], [cgroups[idxs]], [desc])\n\n fbase, fext = op.splitext(filename_out)\n ifilename_out = '%s_matid_%d%s' % (fbase, mat_id, fext)\n io = MeshIO.for_format(ifilename_out, format=options.format,\n writable=True)\n output('writing %s...' % ifilename_out)\n imesh.write(ifilename_out, io=io)\n "},"completion":{"kind":"string","value":"output('...done')"},"api":{"kind":"string","value":"sfepy.base.base.output"}}},{"rowIdx":49,"cells":{"prompt":{"kind":"string","value":"#!/usr/bin/env python\n\"\"\"\nConvert a mesh file from one SfePy-supported format to another.\n\nExamples::\n\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s2.5\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 -c 0\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.mesh --remesh='q2/0 a1e-8 O9/7 V'\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new2.mesh --remesh='rq2/0 a1e-8 O9/7 V'\n\"\"\"\nfrom __future__ import absolute_import\nimport sys\nimport os.path as op\nfrom six.moves import range\nsys.path.append('.')\n\nfrom argparse import ArgumentParser, RawDescriptionHelpFormatter\nfrom sfepy.base.base import nm, output\nfrom sfepy.base.ioutils import remove_files\nfrom sfepy.discrete.fem import Mesh, FEDomain\nfrom sfepy.discrete.fem.meshio import (output_mesh_formats, MeshIO,\n supported_cell_types)\nfrom sfepy.discrete.fem.mesh import fix_double_nodes\nfrom sfepy.mesh.mesh_tools import elems_q2t\n\nhelps = {\n 'scale' : 'scale factor (float or comma-separated list for each axis)'\n ' [default: %(default)s]',\n 'center' : 'center of the output mesh (0 for origin or'\n ' comma-separated list for each axis) applied after scaling'\n ' [default: %(default)s]',\n 'refine' : 'uniform refinement level [default: %(default)s]',\n 'format' : 'output mesh format (overrides filename_out extension)',\n 'list' : 'list supported readable/writable output mesh formats',\n 'merge' : 'remove duplicate vertices',\n 'tri-tetra' : 'convert elements: quad->tri, hexa->tetra',\n '2d' : 'force a 2D mesh by removing the z coordinates - assumes a 3D mesh'\n ' in the xy plane',\n 'save-per-mat': 'extract cells by material id and save them into'\n ' separate mesh files with a name based on filename_out and the id'\n ' numbers (preserves original mesh vertices)',\n\n 'remesh' : \"\"\"when given, remesh the given mesh using tetgen.\n The options can be the following, separated by spaces, in this order: 1.\n \"r\" causes remeshing of the mesh volume - if not present the mesh surface\n is extracted and used for the volume mesh generation. 2.\n \"q[/]\" (required) - the two numbers after \"q\" are a maximum\n radius-edge ratio bound and a minimum dihedral angle bound. 3. \"a\"\n (optional) - the number imposes a maximum volume constraint on all\n tetrahedra. 4. O[<0-9>/<0-7>] - the two numbers correspond to a mesh\n optimization level and a choice of optimizing operations. 5. \"V\"\n (optional) - if present, mesh statistics are printed. Consult the tetgen\n documentation for details.\"\"\",\n}\n\ndef _parse_val_or_vec(option, name, parser):\n if option is not None:\n try:\n try:\n option = float(option)\n except ValueError:\n option = [float(ii) for ii in option.split(',')]\n option = nm.array(option, dtype=nm.float64, ndmin=1)\n except:\n "},"completion":{"kind":"string","value":"output('bad %s! (%s)' % (name, option))"},"api":{"kind":"string","value":"sfepy.base.base.output"}}},{"rowIdx":50,"cells":{"prompt":{"kind":"string","value":"#!/usr/bin/env python\n\"\"\"\nConvert a mesh file from one SfePy-supported format to another.\n\nExamples::\n\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s2.5\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 -c 0\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.mesh --remesh='q2/0 a1e-8 O9/7 V'\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new2.mesh --remesh='rq2/0 a1e-8 O9/7 V'\n\"\"\"\nfrom __future__ import absolute_import\nimport sys\nimport os.path as op\nfrom six.moves import range\nsys.path.append('.')\n\nfrom argparse import ArgumentParser, RawDescriptionHelpFormatter\nfrom sfepy.base.base import nm, output\nfrom sfepy.base.ioutils import remove_files\nfrom sfepy.discrete.fem import Mesh, FEDomain\nfrom sfepy.discrete.fem.meshio import (output_mesh_formats, MeshIO,\n supported_cell_types)\nfrom sfepy.discrete.fem.mesh import fix_double_nodes\nfrom sfepy.mesh.mesh_tools import elems_q2t\n\nhelps = {\n 'scale' : 'scale factor (float or comma-separated list for each axis)'\n ' [default: %(default)s]',\n 'center' : 'center of the output mesh (0 for origin or'\n ' comma-separated list for each axis) applied after scaling'\n ' [default: %(default)s]',\n 'refine' : 'uniform refinement level [default: %(default)s]',\n 'format' : 'output mesh format (overrides filename_out extension)',\n 'list' : 'list supported readable/writable output mesh formats',\n 'merge' : 'remove duplicate vertices',\n 'tri-tetra' : 'convert elements: quad->tri, hexa->tetra',\n '2d' : 'force a 2D mesh by removing the z coordinates - assumes a 3D mesh'\n ' in the xy plane',\n 'save-per-mat': 'extract cells by material id and save them into'\n ' separate mesh files with a name based on filename_out and the id'\n ' numbers (preserves original mesh vertices)',\n\n 'remesh' : \"\"\"when given, remesh the given mesh using tetgen.\n The options can be the following, separated by spaces, in this order: 1.\n \"r\" causes remeshing of the mesh volume - if not present the mesh surface\n is extracted and used for the volume mesh generation. 2.\n \"q[/]\" (required) - the two numbers after \"q\" are a maximum\n radius-edge ratio bound and a minimum dihedral angle bound. 3. \"a\"\n (optional) - the number imposes a maximum volume constraint on all\n tetrahedra. 4. O[<0-9>/<0-7>] - the two numbers correspond to a mesh\n optimization level and a choice of optimizing operations. 5. \"V\"\n (optional) - if present, mesh statistics are printed. Consult the tetgen\n documentation for details.\"\"\",\n}\n\ndef _parse_val_or_vec(option, name, parser):\n if option is not None:\n try:\n try:\n option = float(option)\n except ValueError:\n option = [float(ii) for ii in option.split(',')]\n option = nm.array(option, dtype=nm.float64, ndmin=1)\n except:\n output('bad %s! (%s)' % (name, option))\n parser.print_help()\n sys.exit(1)\n\n return option\n\ndef main():\n parser = ArgumentParser(description=__doc__,\n formatter_class=RawDescriptionHelpFormatter)\n parser.add_argument('-s', '--scale', metavar='scale',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='scale',\n default=None, help=helps['scale'])\n parser.add_argument('-c', '--center', metavar='center',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='center',\n default=None, help=helps['center'])\n parser.add_argument('-r', '--refine', metavar='level',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", type=int, dest='refine',\n default=0, help=helps['refine'])\n parser.add_argument('-f', '--format', metavar='format',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", type=str, dest='format',\n default=None, help=helps['format'])\n parser.add_argument('-l', '--list', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='list', help=helps['list'])\n parser.add_argument('-m', '--merge', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='merge', help=helps['merge'])\n parser.add_argument('-t', '--tri-tetra', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='tri_tetra', help=helps['tri-tetra'])\n parser.add_argument('-2', '--2d', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='force_2d', help=helps['2d'])\n parser.add_argument('--save-per-mat', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='save_per_mat', help=helps['save-per-mat'])\n parser.add_argument('--remesh', metavar='options',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='remesh',\n default=None, help=helps['remesh'])\n parser.add_argument('filename_in')\n parser.add_argument('filename_out')\n options = parser.parse_args()\n\n if options.list:\n output('Supported readable mesh formats:')\n output('--------------------------------')\n output_mesh_formats('r')\n output('')\n output('Supported writable mesh formats:')\n output('--------------------------------')\n output_mesh_formats('w')\n sys.exit(0)\n\n scale = _parse_val_or_vec(options.scale, 'scale', parser)\n center = _parse_val_or_vec(options.center, 'center', parser)\n\n filename_in = options.filename_in\n filename_out = options.filename_out\n\n if options.remesh:\n import tempfile\n import shlex\n import subprocess\n\n dirname = tempfile.mkdtemp()\n\n is_surface = options.remesh.startswith('q')\n if is_surface:\n mesh = Mesh.from_file(filename_in)\n domain = FEDomain(mesh.name, mesh)\n region = domain.create_region('surf', 'vertices of surface',\n 'facet')\n surf_mesh = Mesh.from_region(region, mesh,\n localize=True, is_surface=True)\n\n filename = op.join(dirname, 'surf.mesh')\n surf_mesh.write(filename, io='auto')\n\n else:\n import shutil\n\n shutil.copy(filename_in, dirname)\n filename = op.join(dirname, op.basename(filename_in))\n\n qopts = ''.join(options.remesh.split()) # Remove spaces.\n command = 'tetgen -BFENkACp%s %s' % (qopts, filename)\n args = shlex.split(command)\n subprocess.call(args)\n\n root, ext = op.splitext(filename)\n mesh = Mesh.from_file(root + '.1.vtk')\n\n remove_files(dirname)\n\n else:\n mesh = Mesh.from_file(filename_in)\n\n if options.force_2d:\n data = list(mesh._get_io_data())\n data[0] = data[0][:, :2]\n mesh = Mesh.from_data(mesh.name, *data)\n\n if scale is not None:\n if len(scale) == 1:\n tr = "},"completion":{"kind":"string","value":"nm.eye(mesh.dim, dtype=nm.float64)"},"api":{"kind":"string","value":"sfepy.base.base.nm.eye"}}},{"rowIdx":51,"cells":{"prompt":{"kind":"string","value":"#!/usr/bin/env python\n\"\"\"\nConvert a mesh file from one SfePy-supported format to another.\n\nExamples::\n\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s2.5\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 -c 0\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.mesh --remesh='q2/0 a1e-8 O9/7 V'\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new2.mesh --remesh='rq2/0 a1e-8 O9/7 V'\n\"\"\"\nfrom __future__ import absolute_import\nimport sys\nimport os.path as op\nfrom six.moves import range\nsys.path.append('.')\n\nfrom argparse import ArgumentParser, RawDescriptionHelpFormatter\nfrom sfepy.base.base import nm, output\nfrom sfepy.base.ioutils import remove_files\nfrom sfepy.discrete.fem import Mesh, FEDomain\nfrom sfepy.discrete.fem.meshio import (output_mesh_formats, MeshIO,\n supported_cell_types)\nfrom sfepy.discrete.fem.mesh import fix_double_nodes\nfrom sfepy.mesh.mesh_tools import elems_q2t\n\nhelps = {\n 'scale' : 'scale factor (float or comma-separated list for each axis)'\n ' [default: %(default)s]',\n 'center' : 'center of the output mesh (0 for origin or'\n ' comma-separated list for each axis) applied after scaling'\n ' [default: %(default)s]',\n 'refine' : 'uniform refinement level [default: %(default)s]',\n 'format' : 'output mesh format (overrides filename_out extension)',\n 'list' : 'list supported readable/writable output mesh formats',\n 'merge' : 'remove duplicate vertices',\n 'tri-tetra' : 'convert elements: quad->tri, hexa->tetra',\n '2d' : 'force a 2D mesh by removing the z coordinates - assumes a 3D mesh'\n ' in the xy plane',\n 'save-per-mat': 'extract cells by material id and save them into'\n ' separate mesh files with a name based on filename_out and the id'\n ' numbers (preserves original mesh vertices)',\n\n 'remesh' : \"\"\"when given, remesh the given mesh using tetgen.\n The options can be the following, separated by spaces, in this order: 1.\n \"r\" causes remeshing of the mesh volume - if not present the mesh surface\n is extracted and used for the volume mesh generation. 2.\n \"q[/]\" (required) - the two numbers after \"q\" are a maximum\n radius-edge ratio bound and a minimum dihedral angle bound. 3. \"a\"\n (optional) - the number imposes a maximum volume constraint on all\n tetrahedra. 4. O[<0-9>/<0-7>] - the two numbers correspond to a mesh\n optimization level and a choice of optimizing operations. 5. \"V\"\n (optional) - if present, mesh statistics are printed. Consult the tetgen\n documentation for details.\"\"\",\n}\n\ndef _parse_val_or_vec(option, name, parser):\n if option is not None:\n try:\n try:\n option = float(option)\n except ValueError:\n option = [float(ii) for ii in option.split(',')]\n option = nm.array(option, dtype=nm.float64, ndmin=1)\n except:\n output('bad %s! (%s)' % (name, option))\n parser.print_help()\n sys.exit(1)\n\n return option\n\ndef main():\n parser = ArgumentParser(description=__doc__,\n formatter_class=RawDescriptionHelpFormatter)\n parser.add_argument('-s', '--scale', metavar='scale',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='scale',\n default=None, help=helps['scale'])\n parser.add_argument('-c', '--center', metavar='center',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='center',\n default=None, help=helps['center'])\n parser.add_argument('-r', '--refine', metavar='level',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", type=int, dest='refine',\n default=0, help=helps['refine'])\n parser.add_argument('-f', '--format', metavar='format',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", type=str, dest='format',\n default=None, help=helps['format'])\n parser.add_argument('-l', '--list', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='list', help=helps['list'])\n parser.add_argument('-m', '--merge', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='merge', help=helps['merge'])\n parser.add_argument('-t', '--tri-tetra', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='tri_tetra', help=helps['tri-tetra'])\n parser.add_argument('-2', '--2d', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='force_2d', help=helps['2d'])\n parser.add_argument('--save-per-mat', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='save_per_mat', help=helps['save-per-mat'])\n parser.add_argument('--remesh', metavar='options',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='remesh',\n default=None, help=helps['remesh'])\n parser.add_argument('filename_in')\n parser.add_argument('filename_out')\n options = parser.parse_args()\n\n if options.list:\n output('Supported readable mesh formats:')\n output('--------------------------------')\n output_mesh_formats('r')\n output('')\n output('Supported writable mesh formats:')\n output('--------------------------------')\n output_mesh_formats('w')\n sys.exit(0)\n\n scale = _parse_val_or_vec(options.scale, 'scale', parser)\n center = _parse_val_or_vec(options.center, 'center', parser)\n\n filename_in = options.filename_in\n filename_out = options.filename_out\n\n if options.remesh:\n import tempfile\n import shlex\n import subprocess\n\n dirname = tempfile.mkdtemp()\n\n is_surface = options.remesh.startswith('q')\n if is_surface:\n mesh = Mesh.from_file(filename_in)\n domain = FEDomain(mesh.name, mesh)\n region = domain.create_region('surf', 'vertices of surface',\n 'facet')\n surf_mesh = Mesh.from_region(region, mesh,\n localize=True, is_surface=True)\n\n filename = op.join(dirname, 'surf.mesh')\n surf_mesh.write(filename, io='auto')\n\n else:\n import shutil\n\n shutil.copy(filename_in, dirname)\n filename = op.join(dirname, op.basename(filename_in))\n\n qopts = ''.join(options.remesh.split()) # Remove spaces.\n command = 'tetgen -BFENkACp%s %s' % (qopts, filename)\n args = shlex.split(command)\n subprocess.call(args)\n\n root, ext = op.splitext(filename)\n mesh = Mesh.from_file(root + '.1.vtk')\n\n remove_files(dirname)\n\n else:\n mesh = Mesh.from_file(filename_in)\n\n if options.force_2d:\n data = list(mesh._get_io_data())\n data[0] = data[0][:, :2]\n mesh = Mesh.from_data(mesh.name, *data)\n\n if scale is not None:\n if len(scale) == 1:\n tr = nm.eye(mesh.dim, dtype=nm.float64) * scale\n elif len(scale) == mesh.dim:\n tr = "},"completion":{"kind":"string","value":"nm.diag(scale)"},"api":{"kind":"string","value":"sfepy.base.base.nm.diag"}}},{"rowIdx":52,"cells":{"prompt":{"kind":"string","value":"#!/usr/bin/env python\n\"\"\"\nConvert a mesh file from one SfePy-supported format to another.\n\nExamples::\n\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s2.5\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 -c 0\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.mesh --remesh='q2/0 a1e-8 O9/7 V'\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new2.mesh --remesh='rq2/0 a1e-8 O9/7 V'\n\"\"\"\nfrom __future__ import absolute_import\nimport sys\nimport os.path as op\nfrom six.moves import range\nsys.path.append('.')\n\nfrom argparse import ArgumentParser, RawDescriptionHelpFormatter\nfrom sfepy.base.base import nm, output\nfrom sfepy.base.ioutils import remove_files\nfrom sfepy.discrete.fem import Mesh, FEDomain\nfrom sfepy.discrete.fem.meshio import (output_mesh_formats, MeshIO,\n supported_cell_types)\nfrom sfepy.discrete.fem.mesh import fix_double_nodes\nfrom sfepy.mesh.mesh_tools import elems_q2t\n\nhelps = {\n 'scale' : 'scale factor (float or comma-separated list for each axis)'\n ' [default: %(default)s]',\n 'center' : 'center of the output mesh (0 for origin or'\n ' comma-separated list for each axis) applied after scaling'\n ' [default: %(default)s]',\n 'refine' : 'uniform refinement level [default: %(default)s]',\n 'format' : 'output mesh format (overrides filename_out extension)',\n 'list' : 'list supported readable/writable output mesh formats',\n 'merge' : 'remove duplicate vertices',\n 'tri-tetra' : 'convert elements: quad->tri, hexa->tetra',\n '2d' : 'force a 2D mesh by removing the z coordinates - assumes a 3D mesh'\n ' in the xy plane',\n 'save-per-mat': 'extract cells by material id and save them into'\n ' separate mesh files with a name based on filename_out and the id'\n ' numbers (preserves original mesh vertices)',\n\n 'remesh' : \"\"\"when given, remesh the given mesh using tetgen.\n The options can be the following, separated by spaces, in this order: 1.\n \"r\" causes remeshing of the mesh volume - if not present the mesh surface\n is extracted and used for the volume mesh generation. 2.\n \"q[/]\" (required) - the two numbers after \"q\" are a maximum\n radius-edge ratio bound and a minimum dihedral angle bound. 3. \"a\"\n (optional) - the number imposes a maximum volume constraint on all\n tetrahedra. 4. O[<0-9>/<0-7>] - the two numbers correspond to a mesh\n optimization level and a choice of optimizing operations. 5. \"V\"\n (optional) - if present, mesh statistics are printed. Consult the tetgen\n documentation for details.\"\"\",\n}\n\ndef _parse_val_or_vec(option, name, parser):\n if option is not None:\n try:\n try:\n option = float(option)\n except ValueError:\n option = [float(ii) for ii in option.split(',')]\n option = nm.array(option, dtype=nm.float64, ndmin=1)\n except:\n output('bad %s! (%s)' % (name, option))\n parser.print_help()\n sys.exit(1)\n\n return option\n\ndef main():\n parser = ArgumentParser(description=__doc__,\n formatter_class=RawDescriptionHelpFormatter)\n parser.add_argument('-s', '--scale', metavar='scale',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='scale',\n default=None, help=helps['scale'])\n parser.add_argument('-c', '--center', metavar='center',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='center',\n default=None, help=helps['center'])\n parser.add_argument('-r', '--refine', metavar='level',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", type=int, dest='refine',\n default=0, help=helps['refine'])\n parser.add_argument('-f', '--format', metavar='format',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", type=str, dest='format',\n default=None, help=helps['format'])\n parser.add_argument('-l', '--list', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='list', help=helps['list'])\n parser.add_argument('-m', '--merge', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='merge', help=helps['merge'])\n parser.add_argument('-t', '--tri-tetra', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='tri_tetra', help=helps['tri-tetra'])\n parser.add_argument('-2', '--2d', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='force_2d', help=helps['2d'])\n parser.add_argument('--save-per-mat', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='save_per_mat', help=helps['save-per-mat'])\n parser.add_argument('--remesh', metavar='options',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='remesh',\n default=None, help=helps['remesh'])\n parser.add_argument('filename_in')\n parser.add_argument('filename_out')\n options = parser.parse_args()\n\n if options.list:\n output('Supported readable mesh formats:')\n output('--------------------------------')\n output_mesh_formats('r')\n output('')\n output('Supported writable mesh formats:')\n output('--------------------------------')\n output_mesh_formats('w')\n sys.exit(0)\n\n scale = _parse_val_or_vec(options.scale, 'scale', parser)\n center = _parse_val_or_vec(options.center, 'center', parser)\n\n filename_in = options.filename_in\n filename_out = options.filename_out\n\n if options.remesh:\n import tempfile\n import shlex\n import subprocess\n\n dirname = tempfile.mkdtemp()\n\n is_surface = options.remesh.startswith('q')\n if is_surface:\n mesh = Mesh.from_file(filename_in)\n domain = FEDomain(mesh.name, mesh)\n region = domain.create_region('surf', 'vertices of surface',\n 'facet')\n surf_mesh = Mesh.from_region(region, mesh,\n localize=True, is_surface=True)\n\n filename = op.join(dirname, 'surf.mesh')\n surf_mesh.write(filename, io='auto')\n\n else:\n import shutil\n\n shutil.copy(filename_in, dirname)\n filename = op.join(dirname, op.basename(filename_in))\n\n qopts = ''.join(options.remesh.split()) # Remove spaces.\n command = 'tetgen -BFENkACp%s %s' % (qopts, filename)\n args = shlex.split(command)\n subprocess.call(args)\n\n root, ext = op.splitext(filename)\n mesh = Mesh.from_file(root + '.1.vtk')\n\n remove_files(dirname)\n\n else:\n mesh = Mesh.from_file(filename_in)\n\n if options.force_2d:\n data = list(mesh._get_io_data())\n data[0] = data[0][:, :2]\n mesh = Mesh.from_data(mesh.name, *data)\n\n if scale is not None:\n if len(scale) == 1:\n tr = nm.eye(mesh.dim, dtype=nm.float64) * scale\n elif len(scale) == mesh.dim:\n tr = nm.diag(scale)\n else:\n raise ValueError('bad scale! (%s)' % scale)\n mesh.transform_coors(tr)\n\n if center is not None:\n cc = 0.5 * mesh.get_bounding_box().sum(0)\n shift = center - cc\n tr = nm.c_["},"completion":{"kind":"string","value":"nm.eye(mesh.dim, dtype=nm.float64)"},"api":{"kind":"string","value":"sfepy.base.base.nm.eye"}}},{"rowIdx":53,"cells":{"prompt":{"kind":"string","value":"#!/usr/bin/env python\n\"\"\"\nConvert a mesh file from one SfePy-supported format to another.\n\nExamples::\n\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s2.5\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 -c 0\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.mesh --remesh='q2/0 a1e-8 O9/7 V'\n $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new2.mesh --remesh='rq2/0 a1e-8 O9/7 V'\n\"\"\"\nfrom __future__ import absolute_import\nimport sys\nimport os.path as op\nfrom six.moves import range\nsys.path.append('.')\n\nfrom argparse import ArgumentParser, RawDescriptionHelpFormatter\nfrom sfepy.base.base import nm, output\nfrom sfepy.base.ioutils import remove_files\nfrom sfepy.discrete.fem import Mesh, FEDomain\nfrom sfepy.discrete.fem.meshio import (output_mesh_formats, MeshIO,\n supported_cell_types)\nfrom sfepy.discrete.fem.mesh import fix_double_nodes\nfrom sfepy.mesh.mesh_tools import elems_q2t\n\nhelps = {\n 'scale' : 'scale factor (float or comma-separated list for each axis)'\n ' [default: %(default)s]',\n 'center' : 'center of the output mesh (0 for origin or'\n ' comma-separated list for each axis) applied after scaling'\n ' [default: %(default)s]',\n 'refine' : 'uniform refinement level [default: %(default)s]',\n 'format' : 'output mesh format (overrides filename_out extension)',\n 'list' : 'list supported readable/writable output mesh formats',\n 'merge' : 'remove duplicate vertices',\n 'tri-tetra' : 'convert elements: quad->tri, hexa->tetra',\n '2d' : 'force a 2D mesh by removing the z coordinates - assumes a 3D mesh'\n ' in the xy plane',\n 'save-per-mat': 'extract cells by material id and save them into'\n ' separate mesh files with a name based on filename_out and the id'\n ' numbers (preserves original mesh vertices)',\n\n 'remesh' : \"\"\"when given, remesh the given mesh using tetgen.\n The options can be the following, separated by spaces, in this order: 1.\n \"r\" causes remeshing of the mesh volume - if not present the mesh surface\n is extracted and used for the volume mesh generation. 2.\n \"q[/]\" (required) - the two numbers after \"q\" are a maximum\n radius-edge ratio bound and a minimum dihedral angle bound. 3. \"a\"\n (optional) - the number imposes a maximum volume constraint on all\n tetrahedra. 4. O[<0-9>/<0-7>] - the two numbers correspond to a mesh\n optimization level and a choice of optimizing operations. 5. \"V\"\n (optional) - if present, mesh statistics are printed. Consult the tetgen\n documentation for details.\"\"\",\n}\n\ndef _parse_val_or_vec(option, name, parser):\n if option is not None:\n try:\n try:\n option = float(option)\n except ValueError:\n option = [float(ii) for ii in option.split(',')]\n option = nm.array(option, dtype=nm.float64, ndmin=1)\n except:\n output('bad %s! (%s)' % (name, option))\n parser.print_help()\n sys.exit(1)\n\n return option\n\ndef main():\n parser = ArgumentParser(description=__doc__,\n formatter_class=RawDescriptionHelpFormatter)\n parser.add_argument('-s', '--scale', metavar='scale',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='scale',\n default=None, help=helps['scale'])\n parser.add_argument('-c', '--center', metavar='center',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='center',\n default=None, help=helps['center'])\n parser.add_argument('-r', '--refine', metavar='level',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", type=int, dest='refine',\n default=0, help=helps['refine'])\n parser.add_argument('-f', '--format', metavar='format',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", type=str, dest='format',\n default=None, help=helps['format'])\n parser.add_argument('-l', '--list', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='list', help=helps['list'])\n parser.add_argument('-m', '--merge', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='merge', help=helps['merge'])\n parser.add_argument('-t', '--tri-tetra', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='tri_tetra', help=helps['tri-tetra'])\n parser.add_argument('-2', '--2d', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='force_2d', help=helps['2d'])\n parser.add_argument('--save-per-mat', action="https://huggingface.co/datasets/luna-code/sfepy/store_true",\n dest='save_per_mat', help=helps['save-per-mat'])\n parser.add_argument('--remesh', metavar='options',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='remesh',\n default=None, help=helps['remesh'])\n parser.add_argument('filename_in')\n parser.add_argument('filename_out')\n options = parser.parse_args()\n\n if options.list:\n output('Supported readable mesh formats:')\n output('--------------------------------')\n output_mesh_formats('r')\n output('')\n output('Supported writable mesh formats:')\n output('--------------------------------')\n output_mesh_formats('w')\n sys.exit(0)\n\n scale = _parse_val_or_vec(options.scale, 'scale', parser)\n center = _parse_val_or_vec(options.center, 'center', parser)\n\n filename_in = options.filename_in\n filename_out = options.filename_out\n\n if options.remesh:\n import tempfile\n import shlex\n import subprocess\n\n dirname = tempfile.mkdtemp()\n\n is_surface = options.remesh.startswith('q')\n if is_surface:\n mesh = Mesh.from_file(filename_in)\n domain = FEDomain(mesh.name, mesh)\n region = domain.create_region('surf', 'vertices of surface',\n 'facet')\n surf_mesh = Mesh.from_region(region, mesh,\n localize=True, is_surface=True)\n\n filename = op.join(dirname, 'surf.mesh')\n surf_mesh.write(filename, io='auto')\n\n else:\n import shutil\n\n shutil.copy(filename_in, dirname)\n filename = op.join(dirname, op.basename(filename_in))\n\n qopts = ''.join(options.remesh.split()) # Remove spaces.\n command = 'tetgen -BFENkACp%s %s' % (qopts, filename)\n args = shlex.split(command)\n subprocess.call(args)\n\n root, ext = op.splitext(filename)\n mesh = Mesh.from_file(root + '.1.vtk')\n\n remove_files(dirname)\n\n else:\n mesh = Mesh.from_file(filename_in)\n\n if options.force_2d:\n data = list(mesh._get_io_data())\n data[0] = data[0][:, :2]\n mesh = Mesh.from_data(mesh.name, *data)\n\n if scale is not None:\n if len(scale) == 1:\n tr = nm.eye(mesh.dim, dtype=nm.float64) * scale\n elif len(scale) == mesh.dim:\n tr = nm.diag(scale)\n else:\n raise ValueError('bad scale! (%s)' % scale)\n mesh.transform_coors(tr)\n\n if center is not None:\n cc = 0.5 * mesh.get_bounding_box().sum(0)\n shift = center - cc\n tr = nm.c_[nm.eye(mesh.dim, dtype=nm.float64), shift[:, None]]\n mesh.transform_coors(tr)\n\n if options.refine > 0:\n domain = FEDomain(mesh.name, mesh)\n output('initial mesh: %d nodes %d elements'\n % (domain.shape.n_nod, domain.shape.n_el))\n\n for ii in range(options.refine):\n output('refine %d...' % ii)\n domain = domain.refine()\n output('... %d nodes %d elements'\n % (domain.shape.n_nod, domain.shape.n_el))\n\n mesh = domain.mesh\n\n if options.tri_tetra > 0:\n conns = None\n for k, new_desc in [('3_8', '3_4'), ('2_4', '2_3')]:\n if k in mesh.descs:\n conns = mesh.get_conn(k)\n break\n\n if conns is not None:\n nelo = conns.shape[0]\n output('initial mesh: %d elements' % nelo)\n\n new_conns = elems_q2t(conns)\n nn = new_conns.shape[0] // nelo\n new_cgroups = nm.repeat(mesh.cmesh.cell_groups, nn)\n\n output('new mesh: %d elements' % new_conns.shape[0])\n mesh = Mesh.from_data(mesh.name, mesh.coors,\n mesh.cmesh.vertex_groups,\n [new_conns], [new_cgroups], [new_desc])\n\n if options.merge:\n desc = mesh.descs[0]\n coor, ngroups, conns = fix_double_nodes(mesh.coors,\n mesh.cmesh.vertex_groups,\n mesh.get_conn(desc), 1e-9)\n mesh = Mesh.from_data(mesh.name + '_merged',\n coor, ngroups,\n [conns], [mesh.cmesh.cell_groups], [desc])\n\n if options.save_per_mat:\n desc = mesh.descs[0]\n conns, cgroups = mesh.get_conn(desc), mesh.cmesh.cell_groups\n coors, ngroups = mesh.coors, mesh.cmesh.vertex_groups\n mat_ids = nm.unique(cgroups)\n\n for mat_id in mat_ids:\n idxs = "},"completion":{"kind":"string","value":"nm.where(cgroups == mat_id)"},"api":{"kind":"string","value":"sfepy.base.base.nm.where"}}},{"rowIdx":54,"cells":{"prompt":{"kind":"string","value":"# This example implements macroscopic homogenized model of Biot-Darcy-Brinkman model of flow in deformable\r\n# double porous media.\r\n# The mathematical model is described in:\r\n#\r\n#., ., .\r\n#The Biot-Darcy-Brinkman model of flow in deformable double porous media; homogenization and numerical modelling.\r\n# Computers and Mathematics with applications, 78(9):3044-3066, 2019,\r\n# https://doi.org/10.1016/j.camwa.2019.04.004\r\n#\r\n# Run simulation:\r\n#\r\n# ./simple.py example_perfusion_BDB/perf_BDB_mac.py\r\n#\r\n# The results are stored in `example_perfusion_BDB/results/macro` directory.\r\n#\r\n\r\nimport numpy as nm\r\nfrom sfepy.homogenization.micmac import get_homog_coefs_linear\r\nfrom sfepy.homogenization.utils import define_box_regions\r\nfrom sfepy.discrete.fem.mesh import Mesh\r\nimport os.path as osp\r\n\r\n\r\nmaterial_cache = {}\r\ndata_dir = 'example_perfusion_BDB'\r\n\r\n\r\ndef coefs2qp(coefs, nqp):\r\n out = {}\r\n for k, v in coefs.items():\r\n if type(v) not in [nm.ndarray, float]:\r\n continue\r\n\r\n if type(v) is nm.ndarray:\r\n if len(v.shape) >= 3:\r\n out[k] = v\r\n\r\n out[k] = nm.tile(v, (nqp, 1, 1))\r\n\r\n return out\r\n\r\n# Get raw homogenized coefficients, recalculate them if necessary\r\ndef get_raw_coefs(problem):\r\n if 'raw_coefs' not in material_cache:\r\n micro_filename = material_cache['meso_filename']\r\n coefs_filename = 'coefs_meso'\r\n coefs_filename = osp.join(problem.conf.options.get('output_dir', '.'),\r\n coefs_filename) + '.h5'\r\n coefs = get_homog_coefs_linear(0, 0, None,\r\n micro_filename=micro_filename, coefs_filename=coefs_filename)\r\n coefs['B'] = coefs['B'][:, nm.newaxis]\r\n material_cache['raw_coefs'] = coefs\r\n return material_cache['raw_coefs']\r\n\r\n#Get homogenized coefficients in quadrature points\r\ndef get_homog(coors,pb, mode, **kwargs):\r\n if not (mode == 'qp'):\r\n return\r\n nqp = coors.shape[0]\r\n\r\n coefs=get_raw_coefs(pb)\r\n for k in coefs.keys():\r\n v = coefs[k]\r\n if type(v) is nm.ndarray:\r\n if len(v.shape) == 0:\r\n coefs[k] = v.reshape((1, 1))\r\n elif len(v.shape) == 1:\r\n coefs[k] = v[:, nm.newaxis]\r\n elif isinstance(v, float):\r\n coefs[k] = nm.array([[v]])\r\n\r\n out = coefs2qp(coefs, nqp)\r\n\r\n return out\r\n\r\n#Definition of dirichlet boundary conditions\r\ndef get_ebc( coors, amplitude, cg1, cg2,const=False):\r\n \"\"\"\r\n Define the essential boundary conditions as a function of coordinates\r\n `coors` of region nodes.\r\n \"\"\"\r\n y = coors[:, 1] - cg1\r\n z = coors[:, 2] - cg2\r\n\r\n val = amplitude*((cg1**2 - (abs(y)**2))+(cg2**2 - (abs(z)**2)))\r\n if const:\r\n val=nm.ones_like(y) *amplitude\r\n\r\n return val\r\n\r\n#Returns value of \\phi_c\\bar{w}^{mes} as a material function\r\ndef get_ebc_mat( coors,pb, mode, amplitude, cg1, cg2,konst=False):\r\n if mode == 'qp':\r\n val = get_ebc( coors, amplitude, cg1, cg2,konst)\r\n phic = get_raw_coefs(pb)['vol'][\"fraction_Zc\"]\r\n v_w1 = val[:, nm.newaxis, nm.newaxis]\r\n return {'val': v_w1*phic}\r\n\r\n#Definition of boundary conditions for numerical example at http://sfepy.org/sfepy_examples/example_perfusion_BDB/\r\ndef define_bc(cg1,cg2, val_in=1e2, val_out=1e2):\r\n\r\n funs = {\r\n 'w_in': (lambda ts, coor, bc, problem, **kwargs:\r\n get_ebc( coor, val_in, cg1, cg2),),\r\n 'w_out': (lambda ts, coor, bc, problem, **kwargs:\r\n get_ebc( coor, val_out, cg1, cg2),),\r\n 'w_in_mat': (lambda ts,coor, problem, mode=None, **kwargs:\r\n get_ebc_mat( coor, problem, mode, val_in,\r\n cg1, cg2),),\r\n 'w_out_mat': (lambda ts,coor, problem, mode=None, **kwargs:\r\n get_ebc_mat( coor, problem, mode, val_out,\r\n cg1, cg2),),\r\n }\r\n mats = {\r\n 'w_in': 'w_in_mat',\r\n 'w_out': 'w_out_mat',\r\n }\r\n\r\n ebcs = {\r\n 'fix_u_in': ('In', {'u.all': 0.0}),\r\n 'fix_u_out': ('Out', {'u.all': 0.0}),\r\n 'w_in': ('In', {'w.0': 'w_in','w.[1,2]': 0.0}),\r\n 'w_out': ('Out', {'w.0': 'w_out','w.[1,2]': 0.0}),\r\n 'wB_dirichlet':('Bottom',{'w.2' :0.0,'u.2':0.0}),\r\n 'WT_dirichlet':('Top',{'w.2' :0.0,'u.2':0.0}),\r\n 'wN_dirichlet':('Near',{'w.1' :0.0,'u.1':0.0}),\r\n 'wF_dirichlet':('Far',{'w.1' :0.0,'u.1':0.0}),\r\n }\r\n lcbcs = {\r\n 'imv': ('Omega', {'ls.all' : None}, None, 'integral_mean_value')\r\n }\r\n return ebcs, funs, mats, lcbcs\r\n\r\n\r\n#Definition of macroscopic problem\r\ndef define(filename_mesh=None,cg1=None, cg2=None):\r\n\r\n if filename_mesh is None:\r\n filename_mesh = osp.join(data_dir, 'macro_perf.vtk')\r\n cg1, cg2 = 0.0015, 0.0015 # y and z coordinates of center of gravity\r\n\r\n mesh = "},"completion":{"kind":"string","value":"Mesh.from_file(filename_mesh)"},"api":{"kind":"string","value":"sfepy.discrete.fem.mesh.Mesh.from_file"}}},{"rowIdx":55,"cells":{"prompt":{"kind":"string","value":"# This example implements macroscopic homogenized model of Biot-Darcy-Brinkman model of flow in deformable\r\n# double porous media.\r\n# The mathematical model is described in:\r\n#\r\n#., ., .\r\n#The Biot-Darcy-Brinkman model of flow in deformable double porous media; homogenization and numerical modelling.\r\n# Computers and Mathematics with applications, 78(9):3044-3066, 2019,\r\n# https://doi.org/10.1016/j.camwa.2019.04.004\r\n#\r\n# Run simulation:\r\n#\r\n# ./simple.py example_perfusion_BDB/perf_BDB_mac.py\r\n#\r\n# The results are stored in `example_perfusion_BDB/results/macro` directory.\r\n#\r\n\r\nimport numpy as nm\r\nfrom sfepy.homogenization.micmac import get_homog_coefs_linear\r\nfrom sfepy.homogenization.utils import define_box_regions\r\nfrom sfepy.discrete.fem.mesh import Mesh\r\nimport os.path as osp\r\n\r\n\r\nmaterial_cache = {}\r\ndata_dir = 'example_perfusion_BDB'\r\n\r\n\r\ndef coefs2qp(coefs, nqp):\r\n out = {}\r\n for k, v in coefs.items():\r\n if type(v) not in [nm.ndarray, float]:\r\n continue\r\n\r\n if type(v) is nm.ndarray:\r\n if len(v.shape) >= 3:\r\n out[k] = v\r\n\r\n out[k] = nm.tile(v, (nqp, 1, 1))\r\n\r\n return out\r\n\r\n# Get raw homogenized coefficients, recalculate them if necessary\r\ndef get_raw_coefs(problem):\r\n if 'raw_coefs' not in material_cache:\r\n micro_filename = material_cache['meso_filename']\r\n coefs_filename = 'coefs_meso'\r\n coefs_filename = osp.join(problem.conf.options.get('output_dir', '.'),\r\n coefs_filename) + '.h5'\r\n coefs = get_homog_coefs_linear(0, 0, None,\r\n micro_filename=micro_filename, coefs_filename=coefs_filename)\r\n coefs['B'] = coefs['B'][:, nm.newaxis]\r\n material_cache['raw_coefs'] = coefs\r\n return material_cache['raw_coefs']\r\n\r\n#Get homogenized coefficients in quadrature points\r\ndef get_homog(coors,pb, mode, **kwargs):\r\n if not (mode == 'qp'):\r\n return\r\n nqp = coors.shape[0]\r\n\r\n coefs=get_raw_coefs(pb)\r\n for k in coefs.keys():\r\n v = coefs[k]\r\n if type(v) is nm.ndarray:\r\n if len(v.shape) == 0:\r\n coefs[k] = v.reshape((1, 1))\r\n elif len(v.shape) == 1:\r\n coefs[k] = v[:, nm.newaxis]\r\n elif isinstance(v, float):\r\n coefs[k] = nm.array([[v]])\r\n\r\n out = coefs2qp(coefs, nqp)\r\n\r\n return out\r\n\r\n#Definition of dirichlet boundary conditions\r\ndef get_ebc( coors, amplitude, cg1, cg2,const=False):\r\n \"\"\"\r\n Define the essential boundary conditions as a function of coordinates\r\n `coors` of region nodes.\r\n \"\"\"\r\n y = coors[:, 1] - cg1\r\n z = coors[:, 2] - cg2\r\n\r\n val = amplitude*((cg1**2 - (abs(y)**2))+(cg2**2 - (abs(z)**2)))\r\n if const:\r\n val=nm.ones_like(y) *amplitude\r\n\r\n return val\r\n\r\n#Returns value of \\phi_c\\bar{w}^{mes} as a material function\r\ndef get_ebc_mat( coors,pb, mode, amplitude, cg1, cg2,konst=False):\r\n if mode == 'qp':\r\n val = get_ebc( coors, amplitude, cg1, cg2,konst)\r\n phic = get_raw_coefs(pb)['vol'][\"fraction_Zc\"]\r\n v_w1 = val[:, nm.newaxis, nm.newaxis]\r\n return {'val': v_w1*phic}\r\n\r\n#Definition of boundary conditions for numerical example at http://sfepy.org/sfepy_examples/example_perfusion_BDB/\r\ndef define_bc(cg1,cg2, val_in=1e2, val_out=1e2):\r\n\r\n funs = {\r\n 'w_in': (lambda ts, coor, bc, problem, **kwargs:\r\n get_ebc( coor, val_in, cg1, cg2),),\r\n 'w_out': (lambda ts, coor, bc, problem, **kwargs:\r\n get_ebc( coor, val_out, cg1, cg2),),\r\n 'w_in_mat': (lambda ts,coor, problem, mode=None, **kwargs:\r\n get_ebc_mat( coor, problem, mode, val_in,\r\n cg1, cg2),),\r\n 'w_out_mat': (lambda ts,coor, problem, mode=None, **kwargs:\r\n get_ebc_mat( coor, problem, mode, val_out,\r\n cg1, cg2),),\r\n }\r\n mats = {\r\n 'w_in': 'w_in_mat',\r\n 'w_out': 'w_out_mat',\r\n }\r\n\r\n ebcs = {\r\n 'fix_u_in': ('In', {'u.all': 0.0}),\r\n 'fix_u_out': ('Out', {'u.all': 0.0}),\r\n 'w_in': ('In', {'w.0': 'w_in','w.[1,2]': 0.0}),\r\n 'w_out': ('Out', {'w.0': 'w_out','w.[1,2]': 0.0}),\r\n 'wB_dirichlet':('Bottom',{'w.2' :0.0,'u.2':0.0}),\r\n 'WT_dirichlet':('Top',{'w.2' :0.0,'u.2':0.0}),\r\n 'wN_dirichlet':('Near',{'w.1' :0.0,'u.1':0.0}),\r\n 'wF_dirichlet':('Far',{'w.1' :0.0,'u.1':0.0}),\r\n }\r\n lcbcs = {\r\n 'imv': ('Omega', {'ls.all' : None}, None, 'integral_mean_value')\r\n }\r\n return ebcs, funs, mats, lcbcs\r\n\r\n\r\n#Definition of macroscopic problem\r\ndef define(filename_mesh=None,cg1=None, cg2=None):\r\n\r\n if filename_mesh is None:\r\n filename_mesh = osp.join(data_dir, 'macro_perf.vtk')\r\n cg1, cg2 = 0.0015, 0.0015 # y and z coordinates of center of gravity\r\n\r\n mesh = Mesh.from_file(filename_mesh)\r\n poroela_mezo_file = osp.join(data_dir,'perf_BDB_mes.py')\r\n material_cache['meso_filename']=poroela_mezo_file\r\n\r\n bbox = mesh.get_bounding_box()\r\n regions = "},"completion":{"kind":"string","value":"define_box_regions(mesh.dim, bbox[0], bbox[1], eps=1e-6)"},"api":{"kind":"string","value":"sfepy.homogenization.utils.define_box_regions"}}},{"rowIdx":56,"cells":{"prompt":{"kind":"string","value":"#!/usr/bin/env python\n\"\"\"\nDispersion analysis of a heterogeneous finite scale periodic cell.\n\nThe periodic cell mesh has to contain two subdomains Y1 (with the cell ids 1),\nY2 (with the cell ids 2), so that different material properties can be defined\nin each of the subdomains (see ``--pars`` option). The command line parameters\ncan be given in any consistent unit set, for example the basic SI units. The\n``--unit-multipliers`` option can be used to rescale the input units to ones\nmore suitable to the simulation, for example to prevent having different\nmatrix blocks with large differences of matrix entries magnitudes. The results\nare then in the rescaled units.\n\nUsage Examples\n--------------\n\nDefault material parameters, a square periodic cell with a spherical inclusion,\nlogs also standard pressure dilatation and shear waves, no eigenvectors::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only\n\nAs above, with custom eigenvalue solver parameters, and different number of\neigenvalues, mesh size and units used in the calculation::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --solver-conf=\"kind='eig.scipy', method='eigsh', tol=1e-10, maxiter=1000, which='LM', sigma=0\" --log-std-waves -n 5 --range=0,640,101 --mode=omega --unit-multipliers=1e-6,1e-2,1e-3 --mesh-size=1e-2 --eigs-only\n\nDefault material parameters, a square periodic cell with a square inclusion,\nand a very small mesh to allow comparing the omega and kappa modes (full matrix\nsolver required!)::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf=\"kind='eig.scipy', method='eigh'\" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf=\"kind='eig.qevp', method='companion', mode='inverted', solver={kind='eig.scipy', method='eig'}\" --log-std-waves -n 500 --range=0,4000000,1001 --mesh-size=1e-2 --mode=kappa --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/kappa\n\nView/compare the resulting logs::\n\n python script/plot_logs.py output/omega/frequencies.txt --no-legends -g 1 -o mode-omega.png\n python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends -o mode-kappa.png\n python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends --swap-axes -o mode-kappa-t.png\n\nIn contrast to the heterogeneous square periodic cell, a homogeneous\nsquare periodic cell (the region Y2 is empty)::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_1m.mesh --solver-conf=\"kind='eig.scipy', method='eigh'\" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega-h\n\n python script/plot_logs.py output/omega-h/frequencies.txt --no-legends -g 1 -o mode-omega-h.png\n\nUse the Brillouin stepper::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves -n=60 --eigs-only --no-legends --stepper=brillouin\n\n python script/plot_logs.py output/frequencies.txt -g 0 --rc=\"'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4\" -o brillouin-stepper-kappas.png\n\n python script/plot_logs.py output/frequencies.txt -g 1 --no-legends --rc=\"'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4\" -o brillouin-stepper-omegas.png\n\nAdditional arguments can be passed to the problem configuration's\n:func:`define()` function using the ``--define-kwargs`` option. In this file,\nonly the mesh vertex separation parameter `mesh_eps` can be used::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only --define-kwargs=\"mesh_eps=1e-10\" --save-regions\n\"\"\"\nfrom __future__ import absolute_import\nimport os\nimport sys\nsys.path.append('.')\nimport gc\nfrom copy import copy\nfrom argparse import ArgumentParser, RawDescriptionHelpFormatter\n\nimport numpy as nm\nimport matplotlib.pyplot as plt\n\nfrom sfepy.base.base import import_file, output, Struct\nfrom sfepy.base.conf import dict_from_string, ProblemConf\nfrom sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options\nfrom sfepy.base.log import Log\nfrom sfepy.discrete.fem import MeshIO\nfrom sfepy.mechanics.matcoefs import stiffness_from_youngpoisson as stiffness\nimport sfepy.mechanics.matcoefs as mc\nfrom sfepy.mechanics.units import apply_unit_multipliers\nimport sfepy.discrete.fem.periodic as per\nfrom sfepy.discrete.fem.meshio import convert_complex_output\nfrom sfepy.homogenization.utils import define_box_regions\nfrom sfepy.discrete import Problem\nfrom sfepy.mechanics.tensors import get_von_mises_stress\nfrom sfepy.solvers import Solver\nfrom sfepy.solvers.ts import get_print_info, TimeStepper\nfrom sfepy.linalg.utils import output_array_stats, max_diff_csr\n\ndef apply_units(pars, unit_multipliers):\n new_pars = apply_unit_multipliers(pars,\n ['stress', 'one', 'density',\n 'stress', 'one' ,'density'],\n unit_multipliers)\n return new_pars\n\ndef compute_von_mises(out, pb, state, extend=False, wmag=None, wdir=None):\n \"\"\"\n Calculate the von Mises stress.\n \"\"\"\n stress = pb.evaluate('ev_cauchy_stress.i.Omega(m.D, u)', mode='el_avg')\n\n vms = get_von_mises_stress(stress.squeeze())\n vms.shape = (vms.shape[0], 1, 1, 1)\n out['von_mises_stress'] = Struct(name='output_data', mode='cell',\n data=vms)\n\n return out\n\ndef define(filename_mesh, pars, approx_order, refinement_level, solver_conf,\n plane='strain', post_process=False, mesh_eps=1e-8):\n io = "},"completion":{"kind":"string","value":"MeshIO.any_from_filename(filename_mesh)"},"api":{"kind":"string","value":"sfepy.discrete.fem.MeshIO.any_from_filename"}}},{"rowIdx":57,"cells":{"prompt":{"kind":"string","value":"#!/usr/bin/env python\n\"\"\"\nDispersion analysis of a heterogeneous finite scale periodic cell.\n\nThe periodic cell mesh has to contain two subdomains Y1 (with the cell ids 1),\nY2 (with the cell ids 2), so that different material properties can be defined\nin each of the subdomains (see ``--pars`` option). The command line parameters\ncan be given in any consistent unit set, for example the basic SI units. The\n``--unit-multipliers`` option can be used to rescale the input units to ones\nmore suitable to the simulation, for example to prevent having different\nmatrix blocks with large differences of matrix entries magnitudes. The results\nare then in the rescaled units.\n\nUsage Examples\n--------------\n\nDefault material parameters, a square periodic cell with a spherical inclusion,\nlogs also standard pressure dilatation and shear waves, no eigenvectors::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only\n\nAs above, with custom eigenvalue solver parameters, and different number of\neigenvalues, mesh size and units used in the calculation::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --solver-conf=\"kind='eig.scipy', method='eigsh', tol=1e-10, maxiter=1000, which='LM', sigma=0\" --log-std-waves -n 5 --range=0,640,101 --mode=omega --unit-multipliers=1e-6,1e-2,1e-3 --mesh-size=1e-2 --eigs-only\n\nDefault material parameters, a square periodic cell with a square inclusion,\nand a very small mesh to allow comparing the omega and kappa modes (full matrix\nsolver required!)::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf=\"kind='eig.scipy', method='eigh'\" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf=\"kind='eig.qevp', method='companion', mode='inverted', solver={kind='eig.scipy', method='eig'}\" --log-std-waves -n 500 --range=0,4000000,1001 --mesh-size=1e-2 --mode=kappa --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/kappa\n\nView/compare the resulting logs::\n\n python script/plot_logs.py output/omega/frequencies.txt --no-legends -g 1 -o mode-omega.png\n python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends -o mode-kappa.png\n python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends --swap-axes -o mode-kappa-t.png\n\nIn contrast to the heterogeneous square periodic cell, a homogeneous\nsquare periodic cell (the region Y2 is empty)::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_1m.mesh --solver-conf=\"kind='eig.scipy', method='eigh'\" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega-h\n\n python script/plot_logs.py output/omega-h/frequencies.txt --no-legends -g 1 -o mode-omega-h.png\n\nUse the Brillouin stepper::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves -n=60 --eigs-only --no-legends --stepper=brillouin\n\n python script/plot_logs.py output/frequencies.txt -g 0 --rc=\"'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4\" -o brillouin-stepper-kappas.png\n\n python script/plot_logs.py output/frequencies.txt -g 1 --no-legends --rc=\"'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4\" -o brillouin-stepper-omegas.png\n\nAdditional arguments can be passed to the problem configuration's\n:func:`define()` function using the ``--define-kwargs`` option. In this file,\nonly the mesh vertex separation parameter `mesh_eps` can be used::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only --define-kwargs=\"mesh_eps=1e-10\" --save-regions\n\"\"\"\nfrom __future__ import absolute_import\nimport os\nimport sys\nsys.path.append('.')\nimport gc\nfrom copy import copy\nfrom argparse import ArgumentParser, RawDescriptionHelpFormatter\n\nimport numpy as nm\nimport matplotlib.pyplot as plt\n\nfrom sfepy.base.base import import_file, output, Struct\nfrom sfepy.base.conf import dict_from_string, ProblemConf\nfrom sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options\nfrom sfepy.base.log import Log\nfrom sfepy.discrete.fem import MeshIO\nfrom sfepy.mechanics.matcoefs import stiffness_from_youngpoisson as stiffness\nimport sfepy.mechanics.matcoefs as mc\nfrom sfepy.mechanics.units import apply_unit_multipliers\nimport sfepy.discrete.fem.periodic as per\nfrom sfepy.discrete.fem.meshio import convert_complex_output\nfrom sfepy.homogenization.utils import define_box_regions\nfrom sfepy.discrete import Problem\nfrom sfepy.mechanics.tensors import get_von_mises_stress\nfrom sfepy.solvers import Solver\nfrom sfepy.solvers.ts import get_print_info, TimeStepper\nfrom sfepy.linalg.utils import output_array_stats, max_diff_csr\n\ndef apply_units(pars, unit_multipliers):\n new_pars = apply_unit_multipliers(pars,\n ['stress', 'one', 'density',\n 'stress', 'one' ,'density'],\n unit_multipliers)\n return new_pars\n\ndef compute_von_mises(out, pb, state, extend=False, wmag=None, wdir=None):\n \"\"\"\n Calculate the von Mises stress.\n \"\"\"\n stress = pb.evaluate('ev_cauchy_stress.i.Omega(m.D, u)', mode='el_avg')\n\n vms = get_von_mises_stress(stress.squeeze())\n vms.shape = (vms.shape[0], 1, 1, 1)\n out['von_mises_stress'] = Struct(name='output_data', mode='cell',\n data=vms)\n\n return out\n\ndef define(filename_mesh, pars, approx_order, refinement_level, solver_conf,\n plane='strain', post_process=False, mesh_eps=1e-8):\n io = MeshIO.any_from_filename(filename_mesh)\n bbox = io.read_bounding_box()\n dim = bbox.shape[1]\n\n options = {\n 'absolute_mesh_path' : True,\n 'refinement_level' : refinement_level,\n 'allow_empty_regions' : True,\n 'post_process_hook' : 'compute_von_mises' if post_process else None,\n }\n\n fields = {\n 'displacement': ('complex', dim, 'Omega', approx_order),\n }\n\n young1, poisson1, density1, young2, poisson2, density2 = pars\n materials = {\n 'm' : ({\n 'D' : {'Y1' : stiffness(dim, young=young1, poisson=poisson1,\n plane=plane),\n 'Y2' : stiffness(dim, young=young2, poisson=poisson2,\n plane=plane)},\n 'density' : {'Y1' : density1, 'Y2' : density2},\n },),\n 'wave' : 'get_wdir',\n }\n\n variables = {\n 'u' : ('unknown field', 'displacement', 0),\n 'v' : ('test field', 'displacement', 'u'),\n }\n\n regions = {\n 'Omega' : 'all',\n 'Y1': 'cells of group 1',\n 'Y2': 'cells of group 2',\n }\n regions.update(define_box_regions(dim,\n bbox[0], bbox[1], mesh_eps))\n\n ebcs = {\n }\n\n if dim == 3:\n epbcs = {\n 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},\n 'match_x_plane'),\n 'periodic_y' : (['Near', 'Far'], {'u.all' : 'u.all'},\n 'match_y_plane'),\n 'periodic_z' : (['Top', 'Bottom'], {'u.all' : 'u.all'},\n 'match_z_plane'),\n }\n else:\n epbcs = {\n 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},\n 'match_y_line'),\n 'periodic_y' : (['Bottom', 'Top'], {'u.all' : 'u.all'},\n 'match_x_line'),\n }\n\n "},"completion":{"kind":"string","value":"per.set_accuracy(mesh_eps)"},"api":{"kind":"string","value":"sfepy.discrete.fem.periodic.set_accuracy"}}},{"rowIdx":58,"cells":{"prompt":{"kind":"string","value":"#!/usr/bin/env python\n\"\"\"\nDispersion analysis of a heterogeneous finite scale periodic cell.\n\nThe periodic cell mesh has to contain two subdomains Y1 (with the cell ids 1),\nY2 (with the cell ids 2), so that different material properties can be defined\nin each of the subdomains (see ``--pars`` option). The command line parameters\ncan be given in any consistent unit set, for example the basic SI units. The\n``--unit-multipliers`` option can be used to rescale the input units to ones\nmore suitable to the simulation, for example to prevent having different\nmatrix blocks with large differences of matrix entries magnitudes. The results\nare then in the rescaled units.\n\nUsage Examples\n--------------\n\nDefault material parameters, a square periodic cell with a spherical inclusion,\nlogs also standard pressure dilatation and shear waves, no eigenvectors::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only\n\nAs above, with custom eigenvalue solver parameters, and different number of\neigenvalues, mesh size and units used in the calculation::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --solver-conf=\"kind='eig.scipy', method='eigsh', tol=1e-10, maxiter=1000, which='LM', sigma=0\" --log-std-waves -n 5 --range=0,640,101 --mode=omega --unit-multipliers=1e-6,1e-2,1e-3 --mesh-size=1e-2 --eigs-only\n\nDefault material parameters, a square periodic cell with a square inclusion,\nand a very small mesh to allow comparing the omega and kappa modes (full matrix\nsolver required!)::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf=\"kind='eig.scipy', method='eigh'\" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf=\"kind='eig.qevp', method='companion', mode='inverted', solver={kind='eig.scipy', method='eig'}\" --log-std-waves -n 500 --range=0,4000000,1001 --mesh-size=1e-2 --mode=kappa --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/kappa\n\nView/compare the resulting logs::\n\n python script/plot_logs.py output/omega/frequencies.txt --no-legends -g 1 -o mode-omega.png\n python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends -o mode-kappa.png\n python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends --swap-axes -o mode-kappa-t.png\n\nIn contrast to the heterogeneous square periodic cell, a homogeneous\nsquare periodic cell (the region Y2 is empty)::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_1m.mesh --solver-conf=\"kind='eig.scipy', method='eigh'\" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega-h\n\n python script/plot_logs.py output/omega-h/frequencies.txt --no-legends -g 1 -o mode-omega-h.png\n\nUse the Brillouin stepper::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves -n=60 --eigs-only --no-legends --stepper=brillouin\n\n python script/plot_logs.py output/frequencies.txt -g 0 --rc=\"'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4\" -o brillouin-stepper-kappas.png\n\n python script/plot_logs.py output/frequencies.txt -g 1 --no-legends --rc=\"'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4\" -o brillouin-stepper-omegas.png\n\nAdditional arguments can be passed to the problem configuration's\n:func:`define()` function using the ``--define-kwargs`` option. In this file,\nonly the mesh vertex separation parameter `mesh_eps` can be used::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only --define-kwargs=\"mesh_eps=1e-10\" --save-regions\n\"\"\"\nfrom __future__ import absolute_import\nimport os\nimport sys\nsys.path.append('.')\nimport gc\nfrom copy import copy\nfrom argparse import ArgumentParser, RawDescriptionHelpFormatter\n\nimport numpy as nm\nimport matplotlib.pyplot as plt\n\nfrom sfepy.base.base import import_file, output, Struct\nfrom sfepy.base.conf import dict_from_string, ProblemConf\nfrom sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options\nfrom sfepy.base.log import Log\nfrom sfepy.discrete.fem import MeshIO\nfrom sfepy.mechanics.matcoefs import stiffness_from_youngpoisson as stiffness\nimport sfepy.mechanics.matcoefs as mc\nfrom sfepy.mechanics.units import apply_unit_multipliers\nimport sfepy.discrete.fem.periodic as per\nfrom sfepy.discrete.fem.meshio import convert_complex_output\nfrom sfepy.homogenization.utils import define_box_regions\nfrom sfepy.discrete import Problem\nfrom sfepy.mechanics.tensors import get_von_mises_stress\nfrom sfepy.solvers import Solver\nfrom sfepy.solvers.ts import get_print_info, TimeStepper\nfrom sfepy.linalg.utils import output_array_stats, max_diff_csr\n\ndef apply_units(pars, unit_multipliers):\n new_pars = apply_unit_multipliers(pars,\n ['stress', 'one', 'density',\n 'stress', 'one' ,'density'],\n unit_multipliers)\n return new_pars\n\ndef compute_von_mises(out, pb, state, extend=False, wmag=None, wdir=None):\n \"\"\"\n Calculate the von Mises stress.\n \"\"\"\n stress = pb.evaluate('ev_cauchy_stress.i.Omega(m.D, u)', mode='el_avg')\n\n vms = get_von_mises_stress(stress.squeeze())\n vms.shape = (vms.shape[0], 1, 1, 1)\n out['von_mises_stress'] = Struct(name='output_data', mode='cell',\n data=vms)\n\n return out\n\ndef define(filename_mesh, pars, approx_order, refinement_level, solver_conf,\n plane='strain', post_process=False, mesh_eps=1e-8):\n io = MeshIO.any_from_filename(filename_mesh)\n bbox = io.read_bounding_box()\n dim = bbox.shape[1]\n\n options = {\n 'absolute_mesh_path' : True,\n 'refinement_level' : refinement_level,\n 'allow_empty_regions' : True,\n 'post_process_hook' : 'compute_von_mises' if post_process else None,\n }\n\n fields = {\n 'displacement': ('complex', dim, 'Omega', approx_order),\n }\n\n young1, poisson1, density1, young2, poisson2, density2 = pars\n materials = {\n 'm' : ({\n 'D' : {'Y1' : stiffness(dim, young=young1, poisson=poisson1,\n plane=plane),\n 'Y2' : stiffness(dim, young=young2, poisson=poisson2,\n plane=plane)},\n 'density' : {'Y1' : density1, 'Y2' : density2},\n },),\n 'wave' : 'get_wdir',\n }\n\n variables = {\n 'u' : ('unknown field', 'displacement', 0),\n 'v' : ('test field', 'displacement', 'u'),\n }\n\n regions = {\n 'Omega' : 'all',\n 'Y1': 'cells of group 1',\n 'Y2': 'cells of group 2',\n }\n regions.update(define_box_regions(dim,\n bbox[0], bbox[1], mesh_eps))\n\n ebcs = {\n }\n\n if dim == 3:\n epbcs = {\n 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},\n 'match_x_plane'),\n 'periodic_y' : (['Near', 'Far'], {'u.all' : 'u.all'},\n 'match_y_plane'),\n 'periodic_z' : (['Top', 'Bottom'], {'u.all' : 'u.all'},\n 'match_z_plane'),\n }\n else:\n epbcs = {\n 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},\n 'match_y_line'),\n 'periodic_y' : (['Bottom', 'Top'], {'u.all' : 'u.all'},\n 'match_x_line'),\n }\n\n per.set_accuracy(mesh_eps)\n functions = {\n 'match_x_plane' : (per.match_x_plane,),\n 'match_y_plane' : (per.match_y_plane,),\n 'match_z_plane' : (per.match_z_plane,),\n 'match_x_line' : (per.match_x_line,),\n 'match_y_line' : (per.match_y_line,),\n 'get_wdir' : (get_wdir,),\n }\n\n integrals = {\n 'i' : 2 * approx_order,\n }\n\n equations = {\n 'K' : 'dw_lin_elastic.i.Omega(m.D, v, u)',\n 'S' : 'dw_elastic_wave.i.Omega(m.D, wave.vec, v, u)',\n 'R' : \"\"\"1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, u, v)\n - 1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, v, u)\"\"\",\n 'M' : 'dw_volume_dot.i.Omega(m.density, v, u)',\n }\n\n solver_0 = solver_conf.copy()\n solver_0['name'] = 'eig'\n\n return locals()\n\ndef get_wdir(ts, coors, mode=None,\n equations=None, term=None, problem=None, wdir=None, **kwargs):\n if mode == 'special':\n return {'vec' : wdir}\n\ndef set_wave_dir(pb, wdir):\n materials = pb.get_materials()\n wave_mat = materials['wave']\n wave_mat.set_extra_args(wdir=wdir)\n\ndef save_materials(output_dir, pb, options):\n stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n young, poisson = mc.youngpoisson_from_stiffness(stiffness,\n plane=options.plane)\n density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n\n out = {}\n out['young'] = Struct(name='young', mode='cell',\n data=young[..., None, None])\n out['poisson'] = Struct(name='poisson', mode='cell',\n data=poisson[..., None, None])\n out['density'] = "},"completion":{"kind":"string","value":"Struct(name='density', mode='cell', data=density)"},"api":{"kind":"string","value":"sfepy.base.base.Struct"}}},{"rowIdx":59,"cells":{"prompt":{"kind":"string","value":"#!/usr/bin/env python\n\"\"\"\nDispersion analysis of a heterogeneous finite scale periodic cell.\n\nThe periodic cell mesh has to contain two subdomains Y1 (with the cell ids 1),\nY2 (with the cell ids 2), so that different material properties can be defined\nin each of the subdomains (see ``--pars`` option). The command line parameters\ncan be given in any consistent unit set, for example the basic SI units. The\n``--unit-multipliers`` option can be used to rescale the input units to ones\nmore suitable to the simulation, for example to prevent having different\nmatrix blocks with large differences of matrix entries magnitudes. The results\nare then in the rescaled units.\n\nUsage Examples\n--------------\n\nDefault material parameters, a square periodic cell with a spherical inclusion,\nlogs also standard pressure dilatation and shear waves, no eigenvectors::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only\n\nAs above, with custom eigenvalue solver parameters, and different number of\neigenvalues, mesh size and units used in the calculation::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --solver-conf=\"kind='eig.scipy', method='eigsh', tol=1e-10, maxiter=1000, which='LM', sigma=0\" --log-std-waves -n 5 --range=0,640,101 --mode=omega --unit-multipliers=1e-6,1e-2,1e-3 --mesh-size=1e-2 --eigs-only\n\nDefault material parameters, a square periodic cell with a square inclusion,\nand a very small mesh to allow comparing the omega and kappa modes (full matrix\nsolver required!)::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf=\"kind='eig.scipy', method='eigh'\" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf=\"kind='eig.qevp', method='companion', mode='inverted', solver={kind='eig.scipy', method='eig'}\" --log-std-waves -n 500 --range=0,4000000,1001 --mesh-size=1e-2 --mode=kappa --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/kappa\n\nView/compare the resulting logs::\n\n python script/plot_logs.py output/omega/frequencies.txt --no-legends -g 1 -o mode-omega.png\n python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends -o mode-kappa.png\n python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends --swap-axes -o mode-kappa-t.png\n\nIn contrast to the heterogeneous square periodic cell, a homogeneous\nsquare periodic cell (the region Y2 is empty)::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_1m.mesh --solver-conf=\"kind='eig.scipy', method='eigh'\" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega-h\n\n python script/plot_logs.py output/omega-h/frequencies.txt --no-legends -g 1 -o mode-omega-h.png\n\nUse the Brillouin stepper::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves -n=60 --eigs-only --no-legends --stepper=brillouin\n\n python script/plot_logs.py output/frequencies.txt -g 0 --rc=\"'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4\" -o brillouin-stepper-kappas.png\n\n python script/plot_logs.py output/frequencies.txt -g 1 --no-legends --rc=\"'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4\" -o brillouin-stepper-omegas.png\n\nAdditional arguments can be passed to the problem configuration's\n:func:`define()` function using the ``--define-kwargs`` option. In this file,\nonly the mesh vertex separation parameter `mesh_eps` can be used::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only --define-kwargs=\"mesh_eps=1e-10\" --save-regions\n\"\"\"\nfrom __future__ import absolute_import\nimport os\nimport sys\nsys.path.append('.')\nimport gc\nfrom copy import copy\nfrom argparse import ArgumentParser, RawDescriptionHelpFormatter\n\nimport numpy as nm\nimport matplotlib.pyplot as plt\n\nfrom sfepy.base.base import import_file, output, Struct\nfrom sfepy.base.conf import dict_from_string, ProblemConf\nfrom sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options\nfrom sfepy.base.log import Log\nfrom sfepy.discrete.fem import MeshIO\nfrom sfepy.mechanics.matcoefs import stiffness_from_youngpoisson as stiffness\nimport sfepy.mechanics.matcoefs as mc\nfrom sfepy.mechanics.units import apply_unit_multipliers\nimport sfepy.discrete.fem.periodic as per\nfrom sfepy.discrete.fem.meshio import convert_complex_output\nfrom sfepy.homogenization.utils import define_box_regions\nfrom sfepy.discrete import Problem\nfrom sfepy.mechanics.tensors import get_von_mises_stress\nfrom sfepy.solvers import Solver\nfrom sfepy.solvers.ts import get_print_info, TimeStepper\nfrom sfepy.linalg.utils import output_array_stats, max_diff_csr\n\ndef apply_units(pars, unit_multipliers):\n new_pars = apply_unit_multipliers(pars,\n ['stress', 'one', 'density',\n 'stress', 'one' ,'density'],\n unit_multipliers)\n return new_pars\n\ndef compute_von_mises(out, pb, state, extend=False, wmag=None, wdir=None):\n \"\"\"\n Calculate the von Mises stress.\n \"\"\"\n stress = pb.evaluate('ev_cauchy_stress.i.Omega(m.D, u)', mode='el_avg')\n\n vms = get_von_mises_stress(stress.squeeze())\n vms.shape = (vms.shape[0], 1, 1, 1)\n out['von_mises_stress'] = Struct(name='output_data', mode='cell',\n data=vms)\n\n return out\n\ndef define(filename_mesh, pars, approx_order, refinement_level, solver_conf,\n plane='strain', post_process=False, mesh_eps=1e-8):\n io = MeshIO.any_from_filename(filename_mesh)\n bbox = io.read_bounding_box()\n dim = bbox.shape[1]\n\n options = {\n 'absolute_mesh_path' : True,\n 'refinement_level' : refinement_level,\n 'allow_empty_regions' : True,\n 'post_process_hook' : 'compute_von_mises' if post_process else None,\n }\n\n fields = {\n 'displacement': ('complex', dim, 'Omega', approx_order),\n }\n\n young1, poisson1, density1, young2, poisson2, density2 = pars\n materials = {\n 'm' : ({\n 'D' : {'Y1' : stiffness(dim, young=young1, poisson=poisson1,\n plane=plane),\n 'Y2' : stiffness(dim, young=young2, poisson=poisson2,\n plane=plane)},\n 'density' : {'Y1' : density1, 'Y2' : density2},\n },),\n 'wave' : 'get_wdir',\n }\n\n variables = {\n 'u' : ('unknown field', 'displacement', 0),\n 'v' : ('test field', 'displacement', 'u'),\n }\n\n regions = {\n 'Omega' : 'all',\n 'Y1': 'cells of group 1',\n 'Y2': 'cells of group 2',\n }\n regions.update(define_box_regions(dim,\n bbox[0], bbox[1], mesh_eps))\n\n ebcs = {\n }\n\n if dim == 3:\n epbcs = {\n 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},\n 'match_x_plane'),\n 'periodic_y' : (['Near', 'Far'], {'u.all' : 'u.all'},\n 'match_y_plane'),\n 'periodic_z' : (['Top', 'Bottom'], {'u.all' : 'u.all'},\n 'match_z_plane'),\n }\n else:\n epbcs = {\n 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},\n 'match_y_line'),\n 'periodic_y' : (['Bottom', 'Top'], {'u.all' : 'u.all'},\n 'match_x_line'),\n }\n\n per.set_accuracy(mesh_eps)\n functions = {\n 'match_x_plane' : (per.match_x_plane,),\n 'match_y_plane' : (per.match_y_plane,),\n 'match_z_plane' : (per.match_z_plane,),\n 'match_x_line' : (per.match_x_line,),\n 'match_y_line' : (per.match_y_line,),\n 'get_wdir' : (get_wdir,),\n }\n\n integrals = {\n 'i' : 2 * approx_order,\n }\n\n equations = {\n 'K' : 'dw_lin_elastic.i.Omega(m.D, v, u)',\n 'S' : 'dw_elastic_wave.i.Omega(m.D, wave.vec, v, u)',\n 'R' : \"\"\"1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, u, v)\n - 1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, v, u)\"\"\",\n 'M' : 'dw_volume_dot.i.Omega(m.density, v, u)',\n }\n\n solver_0 = solver_conf.copy()\n solver_0['name'] = 'eig'\n\n return locals()\n\ndef get_wdir(ts, coors, mode=None,\n equations=None, term=None, problem=None, wdir=None, **kwargs):\n if mode == 'special':\n return {'vec' : wdir}\n\ndef set_wave_dir(pb, wdir):\n materials = pb.get_materials()\n wave_mat = materials['wave']\n wave_mat.set_extra_args(wdir=wdir)\n\ndef save_materials(output_dir, pb, options):\n stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n young, poisson = mc.youngpoisson_from_stiffness(stiffness,\n plane=options.plane)\n density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n\n out = {}\n out['young'] = Struct(name='young', mode='cell',\n data=young[..., None, None])\n out['poisson'] = Struct(name='poisson', mode='cell',\n data=poisson[..., None, None])\n out['density'] = Struct(name='density', mode='cell', data=density)\n materials_filename = os.path.join(output_dir, 'materials.vtk')\n pb.save_state(materials_filename, out=out)\n\ndef get_std_wave_fun(pb, options):\n stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n young, poisson = mc.youngpoisson_from_stiffness(stiffness,\n plane=options.plane)\n density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n\n lam, mu = mc.lame_from_youngpoisson(young, poisson,\n plane=options.plane)\n alam = nm.average(lam)\n amu = nm.average(mu)\n adensity = nm.average(density)\n\n cp = nm.sqrt((alam + 2.0 * amu) / adensity)\n cs = nm.sqrt(amu / adensity)\n "},"completion":{"kind":"string","value":"output('average p-wave speed:', cp)"},"api":{"kind":"string","value":"sfepy.base.base.output"}}},{"rowIdx":60,"cells":{"prompt":{"kind":"string","value":"#!/usr/bin/env python\n\"\"\"\nDispersion analysis of a heterogeneous finite scale periodic cell.\n\nThe periodic cell mesh has to contain two subdomains Y1 (with the cell ids 1),\nY2 (with the cell ids 2), so that different material properties can be defined\nin each of the subdomains (see ``--pars`` option). The command line parameters\ncan be given in any consistent unit set, for example the basic SI units. The\n``--unit-multipliers`` option can be used to rescale the input units to ones\nmore suitable to the simulation, for example to prevent having different\nmatrix blocks with large differences of matrix entries magnitudes. The results\nare then in the rescaled units.\n\nUsage Examples\n--------------\n\nDefault material parameters, a square periodic cell with a spherical inclusion,\nlogs also standard pressure dilatation and shear waves, no eigenvectors::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only\n\nAs above, with custom eigenvalue solver parameters, and different number of\neigenvalues, mesh size and units used in the calculation::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --solver-conf=\"kind='eig.scipy', method='eigsh', tol=1e-10, maxiter=1000, which='LM', sigma=0\" --log-std-waves -n 5 --range=0,640,101 --mode=omega --unit-multipliers=1e-6,1e-2,1e-3 --mesh-size=1e-2 --eigs-only\n\nDefault material parameters, a square periodic cell with a square inclusion,\nand a very small mesh to allow comparing the omega and kappa modes (full matrix\nsolver required!)::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf=\"kind='eig.scipy', method='eigh'\" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf=\"kind='eig.qevp', method='companion', mode='inverted', solver={kind='eig.scipy', method='eig'}\" --log-std-waves -n 500 --range=0,4000000,1001 --mesh-size=1e-2 --mode=kappa --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/kappa\n\nView/compare the resulting logs::\n\n python script/plot_logs.py output/omega/frequencies.txt --no-legends -g 1 -o mode-omega.png\n python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends -o mode-kappa.png\n python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends --swap-axes -o mode-kappa-t.png\n\nIn contrast to the heterogeneous square periodic cell, a homogeneous\nsquare periodic cell (the region Y2 is empty)::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_1m.mesh --solver-conf=\"kind='eig.scipy', method='eigh'\" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega-h\n\n python script/plot_logs.py output/omega-h/frequencies.txt --no-legends -g 1 -o mode-omega-h.png\n\nUse the Brillouin stepper::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves -n=60 --eigs-only --no-legends --stepper=brillouin\n\n python script/plot_logs.py output/frequencies.txt -g 0 --rc=\"'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4\" -o brillouin-stepper-kappas.png\n\n python script/plot_logs.py output/frequencies.txt -g 1 --no-legends --rc=\"'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4\" -o brillouin-stepper-omegas.png\n\nAdditional arguments can be passed to the problem configuration's\n:func:`define()` function using the ``--define-kwargs`` option. In this file,\nonly the mesh vertex separation parameter `mesh_eps` can be used::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only --define-kwargs=\"mesh_eps=1e-10\" --save-regions\n\"\"\"\nfrom __future__ import absolute_import\nimport os\nimport sys\nsys.path.append('.')\nimport gc\nfrom copy import copy\nfrom argparse import ArgumentParser, RawDescriptionHelpFormatter\n\nimport numpy as nm\nimport matplotlib.pyplot as plt\n\nfrom sfepy.base.base import import_file, output, Struct\nfrom sfepy.base.conf import dict_from_string, ProblemConf\nfrom sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options\nfrom sfepy.base.log import Log\nfrom sfepy.discrete.fem import MeshIO\nfrom sfepy.mechanics.matcoefs import stiffness_from_youngpoisson as stiffness\nimport sfepy.mechanics.matcoefs as mc\nfrom sfepy.mechanics.units import apply_unit_multipliers\nimport sfepy.discrete.fem.periodic as per\nfrom sfepy.discrete.fem.meshio import convert_complex_output\nfrom sfepy.homogenization.utils import define_box_regions\nfrom sfepy.discrete import Problem\nfrom sfepy.mechanics.tensors import get_von_mises_stress\nfrom sfepy.solvers import Solver\nfrom sfepy.solvers.ts import get_print_info, TimeStepper\nfrom sfepy.linalg.utils import output_array_stats, max_diff_csr\n\ndef apply_units(pars, unit_multipliers):\n new_pars = apply_unit_multipliers(pars,\n ['stress', 'one', 'density',\n 'stress', 'one' ,'density'],\n unit_multipliers)\n return new_pars\n\ndef compute_von_mises(out, pb, state, extend=False, wmag=None, wdir=None):\n \"\"\"\n Calculate the von Mises stress.\n \"\"\"\n stress = pb.evaluate('ev_cauchy_stress.i.Omega(m.D, u)', mode='el_avg')\n\n vms = get_von_mises_stress(stress.squeeze())\n vms.shape = (vms.shape[0], 1, 1, 1)\n out['von_mises_stress'] = Struct(name='output_data', mode='cell',\n data=vms)\n\n return out\n\ndef define(filename_mesh, pars, approx_order, refinement_level, solver_conf,\n plane='strain', post_process=False, mesh_eps=1e-8):\n io = MeshIO.any_from_filename(filename_mesh)\n bbox = io.read_bounding_box()\n dim = bbox.shape[1]\n\n options = {\n 'absolute_mesh_path' : True,\n 'refinement_level' : refinement_level,\n 'allow_empty_regions' : True,\n 'post_process_hook' : 'compute_von_mises' if post_process else None,\n }\n\n fields = {\n 'displacement': ('complex', dim, 'Omega', approx_order),\n }\n\n young1, poisson1, density1, young2, poisson2, density2 = pars\n materials = {\n 'm' : ({\n 'D' : {'Y1' : stiffness(dim, young=young1, poisson=poisson1,\n plane=plane),\n 'Y2' : stiffness(dim, young=young2, poisson=poisson2,\n plane=plane)},\n 'density' : {'Y1' : density1, 'Y2' : density2},\n },),\n 'wave' : 'get_wdir',\n }\n\n variables = {\n 'u' : ('unknown field', 'displacement', 0),\n 'v' : ('test field', 'displacement', 'u'),\n }\n\n regions = {\n 'Omega' : 'all',\n 'Y1': 'cells of group 1',\n 'Y2': 'cells of group 2',\n }\n regions.update(define_box_regions(dim,\n bbox[0], bbox[1], mesh_eps))\n\n ebcs = {\n }\n\n if dim == 3:\n epbcs = {\n 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},\n 'match_x_plane'),\n 'periodic_y' : (['Near', 'Far'], {'u.all' : 'u.all'},\n 'match_y_plane'),\n 'periodic_z' : (['Top', 'Bottom'], {'u.all' : 'u.all'},\n 'match_z_plane'),\n }\n else:\n epbcs = {\n 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},\n 'match_y_line'),\n 'periodic_y' : (['Bottom', 'Top'], {'u.all' : 'u.all'},\n 'match_x_line'),\n }\n\n per.set_accuracy(mesh_eps)\n functions = {\n 'match_x_plane' : (per.match_x_plane,),\n 'match_y_plane' : (per.match_y_plane,),\n 'match_z_plane' : (per.match_z_plane,),\n 'match_x_line' : (per.match_x_line,),\n 'match_y_line' : (per.match_y_line,),\n 'get_wdir' : (get_wdir,),\n }\n\n integrals = {\n 'i' : 2 * approx_order,\n }\n\n equations = {\n 'K' : 'dw_lin_elastic.i.Omega(m.D, v, u)',\n 'S' : 'dw_elastic_wave.i.Omega(m.D, wave.vec, v, u)',\n 'R' : \"\"\"1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, u, v)\n - 1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, v, u)\"\"\",\n 'M' : 'dw_volume_dot.i.Omega(m.density, v, u)',\n }\n\n solver_0 = solver_conf.copy()\n solver_0['name'] = 'eig'\n\n return locals()\n\ndef get_wdir(ts, coors, mode=None,\n equations=None, term=None, problem=None, wdir=None, **kwargs):\n if mode == 'special':\n return {'vec' : wdir}\n\ndef set_wave_dir(pb, wdir):\n materials = pb.get_materials()\n wave_mat = materials['wave']\n wave_mat.set_extra_args(wdir=wdir)\n\ndef save_materials(output_dir, pb, options):\n stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n young, poisson = mc.youngpoisson_from_stiffness(stiffness,\n plane=options.plane)\n density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n\n out = {}\n out['young'] = Struct(name='young', mode='cell',\n data=young[..., None, None])\n out['poisson'] = Struct(name='poisson', mode='cell',\n data=poisson[..., None, None])\n out['density'] = Struct(name='density', mode='cell', data=density)\n materials_filename = os.path.join(output_dir, 'materials.vtk')\n pb.save_state(materials_filename, out=out)\n\ndef get_std_wave_fun(pb, options):\n stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n young, poisson = mc.youngpoisson_from_stiffness(stiffness,\n plane=options.plane)\n density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n\n lam, mu = mc.lame_from_youngpoisson(young, poisson,\n plane=options.plane)\n alam = nm.average(lam)\n amu = nm.average(mu)\n adensity = nm.average(density)\n\n cp = nm.sqrt((alam + 2.0 * amu) / adensity)\n cs = nm.sqrt(amu / adensity)\n output('average p-wave speed:', cp)\n "},"completion":{"kind":"string","value":"output('average shear wave speed:', cs)"},"api":{"kind":"string","value":"sfepy.base.base.output"}}},{"rowIdx":61,"cells":{"prompt":{"kind":"string","value":"#!/usr/bin/env python\n\"\"\"\nDispersion analysis of a heterogeneous finite scale periodic cell.\n\nThe periodic cell mesh has to contain two subdomains Y1 (with the cell ids 1),\nY2 (with the cell ids 2), so that different material properties can be defined\nin each of the subdomains (see ``--pars`` option). The command line parameters\ncan be given in any consistent unit set, for example the basic SI units. The\n``--unit-multipliers`` option can be used to rescale the input units to ones\nmore suitable to the simulation, for example to prevent having different\nmatrix blocks with large differences of matrix entries magnitudes. The results\nare then in the rescaled units.\n\nUsage Examples\n--------------\n\nDefault material parameters, a square periodic cell with a spherical inclusion,\nlogs also standard pressure dilatation and shear waves, no eigenvectors::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only\n\nAs above, with custom eigenvalue solver parameters, and different number of\neigenvalues, mesh size and units used in the calculation::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --solver-conf=\"kind='eig.scipy', method='eigsh', tol=1e-10, maxiter=1000, which='LM', sigma=0\" --log-std-waves -n 5 --range=0,640,101 --mode=omega --unit-multipliers=1e-6,1e-2,1e-3 --mesh-size=1e-2 --eigs-only\n\nDefault material parameters, a square periodic cell with a square inclusion,\nand a very small mesh to allow comparing the omega and kappa modes (full matrix\nsolver required!)::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf=\"kind='eig.scipy', method='eigh'\" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf=\"kind='eig.qevp', method='companion', mode='inverted', solver={kind='eig.scipy', method='eig'}\" --log-std-waves -n 500 --range=0,4000000,1001 --mesh-size=1e-2 --mode=kappa --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/kappa\n\nView/compare the resulting logs::\n\n python script/plot_logs.py output/omega/frequencies.txt --no-legends -g 1 -o mode-omega.png\n python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends -o mode-kappa.png\n python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends --swap-axes -o mode-kappa-t.png\n\nIn contrast to the heterogeneous square periodic cell, a homogeneous\nsquare periodic cell (the region Y2 is empty)::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_1m.mesh --solver-conf=\"kind='eig.scipy', method='eigh'\" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega-h\n\n python script/plot_logs.py output/omega-h/frequencies.txt --no-legends -g 1 -o mode-omega-h.png\n\nUse the Brillouin stepper::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves -n=60 --eigs-only --no-legends --stepper=brillouin\n\n python script/plot_logs.py output/frequencies.txt -g 0 --rc=\"'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4\" -o brillouin-stepper-kappas.png\n\n python script/plot_logs.py output/frequencies.txt -g 1 --no-legends --rc=\"'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4\" -o brillouin-stepper-omegas.png\n\nAdditional arguments can be passed to the problem configuration's\n:func:`define()` function using the ``--define-kwargs`` option. In this file,\nonly the mesh vertex separation parameter `mesh_eps` can be used::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only --define-kwargs=\"mesh_eps=1e-10\" --save-regions\n\"\"\"\nfrom __future__ import absolute_import\nimport os\nimport sys\nsys.path.append('.')\nimport gc\nfrom copy import copy\nfrom argparse import ArgumentParser, RawDescriptionHelpFormatter\n\nimport numpy as nm\nimport matplotlib.pyplot as plt\n\nfrom sfepy.base.base import import_file, output, Struct\nfrom sfepy.base.conf import dict_from_string, ProblemConf\nfrom sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options\nfrom sfepy.base.log import Log\nfrom sfepy.discrete.fem import MeshIO\nfrom sfepy.mechanics.matcoefs import stiffness_from_youngpoisson as stiffness\nimport sfepy.mechanics.matcoefs as mc\nfrom sfepy.mechanics.units import apply_unit_multipliers\nimport sfepy.discrete.fem.periodic as per\nfrom sfepy.discrete.fem.meshio import convert_complex_output\nfrom sfepy.homogenization.utils import define_box_regions\nfrom sfepy.discrete import Problem\nfrom sfepy.mechanics.tensors import get_von_mises_stress\nfrom sfepy.solvers import Solver\nfrom sfepy.solvers.ts import get_print_info, TimeStepper\nfrom sfepy.linalg.utils import output_array_stats, max_diff_csr\n\ndef apply_units(pars, unit_multipliers):\n new_pars = apply_unit_multipliers(pars,\n ['stress', 'one', 'density',\n 'stress', 'one' ,'density'],\n unit_multipliers)\n return new_pars\n\ndef compute_von_mises(out, pb, state, extend=False, wmag=None, wdir=None):\n \"\"\"\n Calculate the von Mises stress.\n \"\"\"\n stress = pb.evaluate('ev_cauchy_stress.i.Omega(m.D, u)', mode='el_avg')\n\n vms = get_von_mises_stress(stress.squeeze())\n vms.shape = (vms.shape[0], 1, 1, 1)\n out['von_mises_stress'] = Struct(name='output_data', mode='cell',\n data=vms)\n\n return out\n\ndef define(filename_mesh, pars, approx_order, refinement_level, solver_conf,\n plane='strain', post_process=False, mesh_eps=1e-8):\n io = MeshIO.any_from_filename(filename_mesh)\n bbox = io.read_bounding_box()\n dim = bbox.shape[1]\n\n options = {\n 'absolute_mesh_path' : True,\n 'refinement_level' : refinement_level,\n 'allow_empty_regions' : True,\n 'post_process_hook' : 'compute_von_mises' if post_process else None,\n }\n\n fields = {\n 'displacement': ('complex', dim, 'Omega', approx_order),\n }\n\n young1, poisson1, density1, young2, poisson2, density2 = pars\n materials = {\n 'm' : ({\n 'D' : {'Y1' : stiffness(dim, young=young1, poisson=poisson1,\n plane=plane),\n 'Y2' : stiffness(dim, young=young2, poisson=poisson2,\n plane=plane)},\n 'density' : {'Y1' : density1, 'Y2' : density2},\n },),\n 'wave' : 'get_wdir',\n }\n\n variables = {\n 'u' : ('unknown field', 'displacement', 0),\n 'v' : ('test field', 'displacement', 'u'),\n }\n\n regions = {\n 'Omega' : 'all',\n 'Y1': 'cells of group 1',\n 'Y2': 'cells of group 2',\n }\n regions.update(define_box_regions(dim,\n bbox[0], bbox[1], mesh_eps))\n\n ebcs = {\n }\n\n if dim == 3:\n epbcs = {\n 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},\n 'match_x_plane'),\n 'periodic_y' : (['Near', 'Far'], {'u.all' : 'u.all'},\n 'match_y_plane'),\n 'periodic_z' : (['Top', 'Bottom'], {'u.all' : 'u.all'},\n 'match_z_plane'),\n }\n else:\n epbcs = {\n 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},\n 'match_y_line'),\n 'periodic_y' : (['Bottom', 'Top'], {'u.all' : 'u.all'},\n 'match_x_line'),\n }\n\n per.set_accuracy(mesh_eps)\n functions = {\n 'match_x_plane' : (per.match_x_plane,),\n 'match_y_plane' : (per.match_y_plane,),\n 'match_z_plane' : (per.match_z_plane,),\n 'match_x_line' : (per.match_x_line,),\n 'match_y_line' : (per.match_y_line,),\n 'get_wdir' : (get_wdir,),\n }\n\n integrals = {\n 'i' : 2 * approx_order,\n }\n\n equations = {\n 'K' : 'dw_lin_elastic.i.Omega(m.D, v, u)',\n 'S' : 'dw_elastic_wave.i.Omega(m.D, wave.vec, v, u)',\n 'R' : \"\"\"1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, u, v)\n - 1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, v, u)\"\"\",\n 'M' : 'dw_volume_dot.i.Omega(m.density, v, u)',\n }\n\n solver_0 = solver_conf.copy()\n solver_0['name'] = 'eig'\n\n return locals()\n\ndef get_wdir(ts, coors, mode=None,\n equations=None, term=None, problem=None, wdir=None, **kwargs):\n if mode == 'special':\n return {'vec' : wdir}\n\ndef set_wave_dir(pb, wdir):\n materials = pb.get_materials()\n wave_mat = materials['wave']\n wave_mat.set_extra_args(wdir=wdir)\n\ndef save_materials(output_dir, pb, options):\n stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n young, poisson = mc.youngpoisson_from_stiffness(stiffness,\n plane=options.plane)\n density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n\n out = {}\n out['young'] = Struct(name='young', mode='cell',\n data=young[..., None, None])\n out['poisson'] = Struct(name='poisson', mode='cell',\n data=poisson[..., None, None])\n out['density'] = Struct(name='density', mode='cell', data=density)\n materials_filename = os.path.join(output_dir, 'materials.vtk')\n pb.save_state(materials_filename, out=out)\n\ndef get_std_wave_fun(pb, options):\n stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n young, poisson = mc.youngpoisson_from_stiffness(stiffness,\n plane=options.plane)\n density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n\n lam, mu = mc.lame_from_youngpoisson(young, poisson,\n plane=options.plane)\n alam = nm.average(lam)\n amu = nm.average(mu)\n adensity = nm.average(density)\n\n cp = nm.sqrt((alam + 2.0 * amu) / adensity)\n cs = nm.sqrt(amu / adensity)\n output('average p-wave speed:', cp)\n output('average shear wave speed:', cs)\n\n log_names = [r'$\\omega_p$', r'$\\omega_s$']\n log_plot_kwargs = [{'ls' : '--', 'color' : 'k'},\n {'ls' : '--', 'color' : 'gray'}]\n\n if options.mode == 'omega':\n fun = lambda wmag, wdir: (cp * wmag, cs * wmag)\n\n else:\n fun = lambda wmag, wdir: (wmag / cp, wmag / cs)\n\n return fun, log_names, log_plot_kwargs\n\ndef get_stepper(rng, pb, options):\n if options.stepper == 'linear':\n stepper = TimeStepper(rng[0], rng[1], dt=None, n_step=rng[2])\n return stepper\n\n bbox = pb.domain.mesh.get_bounding_box()\n\n bzone = 2.0 * nm.pi / (bbox[1] - bbox[0])\n\n num = rng[2] // 3\n\n class BrillouinStepper(Struct):\n \"\"\"\n Step over 1. Brillouin zone in xy plane.\n \"\"\"\n def __init__(self, t0, t1, dt=None, n_step=None, step=None, **kwargs):\n Struct.__init__(self, t0=t0, t1=t1, dt=dt, n_step=n_step, step=step)\n\n self.n_digit, self.format, self.suffix = get_print_info(self.n_step)\n\n def __iter__(self):\n ts = TimeStepper(0, bzone[0], dt=None, n_step=num)\n for ii, val in ts:\n yield ii, val, nm.array([1.0, 0.0])\n if ii == (num-2): break\n\n ts = TimeStepper(0, bzone[1], dt=None, n_step=num)\n for ii, k1 in ts:\n wdir = nm.array([bzone[0], k1])\n val = nm.linalg.norm(wdir)\n wdir = wdir / val\n yield num + ii, val, wdir\n if ii == (num-2): break\n\n wdir = nm.array([bzone[0], bzone[1]])\n val = nm.linalg.norm(wdir)\n wdir = wdir / val\n ts = TimeStepper(0, 1, dt=None, n_step=num)\n for ii, _ in ts:\n yield 2 * num + ii, val * (1.0 - float(ii)/(num-1)), wdir\n\n stepper = BrillouinStepper(0, 1, n_step=rng[2])\n\n return stepper\n\ndef save_eigenvectors(filename, svecs, wmag, wdir, pb):\n if svecs is None: return\n\n variables = pb.get_variables()\n # Make full eigenvectors (add DOFs fixed by boundary conditions).\n vecs = nm.empty((variables.di.ptr[-1], svecs.shape[1]),\n dtype=svecs.dtype)\n for ii in range(svecs.shape[1]):\n vecs[:, ii] = variables.make_full_vec(svecs[:, ii])\n\n # Save the eigenvectors.\n out = {}\n state = pb.create_state()\n\n pp_name = pb.conf.options.get('post_process_hook')\n pp = getattr(pb.conf.funmod, pp_name if pp_name is not None else '',\n lambda out, *args, **kwargs: out)\n\n for ii in range(svecs.shape[1]):\n state.set_full(vecs[:, ii])\n aux = state.create_output_dict()\n aux2 = {}\n pp(aux2, pb, state, wmag=wmag, wdir=wdir)\n aux.update(convert_complex_output(aux2))\n out.update({key + '%03d' % ii : aux[key] for key in aux})\n\n pb.save_state(filename, out=out)\n\ndef assemble_matrices(define, mod, pars, set_wave_dir, options, wdir=None):\n \"\"\"\n Assemble the blocks of dispersion eigenvalue problem matrices.\n \"\"\"\n define_dict = define(filename_mesh=options.mesh_filename,\n pars=pars,\n approx_order=options.order,\n refinement_level=options.refine,\n solver_conf=options.solver_conf,\n plane=options.plane,\n post_process=options.post_process,\n **options.define_kwargs)\n\n conf = "},"completion":{"kind":"string","value":"ProblemConf.from_dict(define_dict, mod)"},"api":{"kind":"string","value":"sfepy.base.conf.ProblemConf.from_dict"}}},{"rowIdx":62,"cells":{"prompt":{"kind":"string","value":"#!/usr/bin/env python\n\"\"\"\nDispersion analysis of a heterogeneous finite scale periodic cell.\n\nThe periodic cell mesh has to contain two subdomains Y1 (with the cell ids 1),\nY2 (with the cell ids 2), so that different material properties can be defined\nin each of the subdomains (see ``--pars`` option). The command line parameters\ncan be given in any consistent unit set, for example the basic SI units. The\n``--unit-multipliers`` option can be used to rescale the input units to ones\nmore suitable to the simulation, for example to prevent having different\nmatrix blocks with large differences of matrix entries magnitudes. The results\nare then in the rescaled units.\n\nUsage Examples\n--------------\n\nDefault material parameters, a square periodic cell with a spherical inclusion,\nlogs also standard pressure dilatation and shear waves, no eigenvectors::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only\n\nAs above, with custom eigenvalue solver parameters, and different number of\neigenvalues, mesh size and units used in the calculation::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --solver-conf=\"kind='eig.scipy', method='eigsh', tol=1e-10, maxiter=1000, which='LM', sigma=0\" --log-std-waves -n 5 --range=0,640,101 --mode=omega --unit-multipliers=1e-6,1e-2,1e-3 --mesh-size=1e-2 --eigs-only\n\nDefault material parameters, a square periodic cell with a square inclusion,\nand a very small mesh to allow comparing the omega and kappa modes (full matrix\nsolver required!)::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf=\"kind='eig.scipy', method='eigh'\" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf=\"kind='eig.qevp', method='companion', mode='inverted', solver={kind='eig.scipy', method='eig'}\" --log-std-waves -n 500 --range=0,4000000,1001 --mesh-size=1e-2 --mode=kappa --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/kappa\n\nView/compare the resulting logs::\n\n python script/plot_logs.py output/omega/frequencies.txt --no-legends -g 1 -o mode-omega.png\n python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends -o mode-kappa.png\n python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends --swap-axes -o mode-kappa-t.png\n\nIn contrast to the heterogeneous square periodic cell, a homogeneous\nsquare periodic cell (the region Y2 is empty)::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_1m.mesh --solver-conf=\"kind='eig.scipy', method='eigh'\" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega-h\n\n python script/plot_logs.py output/omega-h/frequencies.txt --no-legends -g 1 -o mode-omega-h.png\n\nUse the Brillouin stepper::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves -n=60 --eigs-only --no-legends --stepper=brillouin\n\n python script/plot_logs.py output/frequencies.txt -g 0 --rc=\"'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4\" -o brillouin-stepper-kappas.png\n\n python script/plot_logs.py output/frequencies.txt -g 1 --no-legends --rc=\"'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4\" -o brillouin-stepper-omegas.png\n\nAdditional arguments can be passed to the problem configuration's\n:func:`define()` function using the ``--define-kwargs`` option. In this file,\nonly the mesh vertex separation parameter `mesh_eps` can be used::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only --define-kwargs=\"mesh_eps=1e-10\" --save-regions\n\"\"\"\nfrom __future__ import absolute_import\nimport os\nimport sys\nsys.path.append('.')\nimport gc\nfrom copy import copy\nfrom argparse import ArgumentParser, RawDescriptionHelpFormatter\n\nimport numpy as nm\nimport matplotlib.pyplot as plt\n\nfrom sfepy.base.base import import_file, output, Struct\nfrom sfepy.base.conf import dict_from_string, ProblemConf\nfrom sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options\nfrom sfepy.base.log import Log\nfrom sfepy.discrete.fem import MeshIO\nfrom sfepy.mechanics.matcoefs import stiffness_from_youngpoisson as stiffness\nimport sfepy.mechanics.matcoefs as mc\nfrom sfepy.mechanics.units import apply_unit_multipliers\nimport sfepy.discrete.fem.periodic as per\nfrom sfepy.discrete.fem.meshio import convert_complex_output\nfrom sfepy.homogenization.utils import define_box_regions\nfrom sfepy.discrete import Problem\nfrom sfepy.mechanics.tensors import get_von_mises_stress\nfrom sfepy.solvers import Solver\nfrom sfepy.solvers.ts import get_print_info, TimeStepper\nfrom sfepy.linalg.utils import output_array_stats, max_diff_csr\n\ndef apply_units(pars, unit_multipliers):\n new_pars = apply_unit_multipliers(pars,\n ['stress', 'one', 'density',\n 'stress', 'one' ,'density'],\n unit_multipliers)\n return new_pars\n\ndef compute_von_mises(out, pb, state, extend=False, wmag=None, wdir=None):\n \"\"\"\n Calculate the von Mises stress.\n \"\"\"\n stress = pb.evaluate('ev_cauchy_stress.i.Omega(m.D, u)', mode='el_avg')\n\n vms = get_von_mises_stress(stress.squeeze())\n vms.shape = (vms.shape[0], 1, 1, 1)\n out['von_mises_stress'] = Struct(name='output_data', mode='cell',\n data=vms)\n\n return out\n\ndef define(filename_mesh, pars, approx_order, refinement_level, solver_conf,\n plane='strain', post_process=False, mesh_eps=1e-8):\n io = MeshIO.any_from_filename(filename_mesh)\n bbox = io.read_bounding_box()\n dim = bbox.shape[1]\n\n options = {\n 'absolute_mesh_path' : True,\n 'refinement_level' : refinement_level,\n 'allow_empty_regions' : True,\n 'post_process_hook' : 'compute_von_mises' if post_process else None,\n }\n\n fields = {\n 'displacement': ('complex', dim, 'Omega', approx_order),\n }\n\n young1, poisson1, density1, young2, poisson2, density2 = pars\n materials = {\n 'm' : ({\n 'D' : {'Y1' : stiffness(dim, young=young1, poisson=poisson1,\n plane=plane),\n 'Y2' : stiffness(dim, young=young2, poisson=poisson2,\n plane=plane)},\n 'density' : {'Y1' : density1, 'Y2' : density2},\n },),\n 'wave' : 'get_wdir',\n }\n\n variables = {\n 'u' : ('unknown field', 'displacement', 0),\n 'v' : ('test field', 'displacement', 'u'),\n }\n\n regions = {\n 'Omega' : 'all',\n 'Y1': 'cells of group 1',\n 'Y2': 'cells of group 2',\n }\n regions.update(define_box_regions(dim,\n bbox[0], bbox[1], mesh_eps))\n\n ebcs = {\n }\n\n if dim == 3:\n epbcs = {\n 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},\n 'match_x_plane'),\n 'periodic_y' : (['Near', 'Far'], {'u.all' : 'u.all'},\n 'match_y_plane'),\n 'periodic_z' : (['Top', 'Bottom'], {'u.all' : 'u.all'},\n 'match_z_plane'),\n }\n else:\n epbcs = {\n 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},\n 'match_y_line'),\n 'periodic_y' : (['Bottom', 'Top'], {'u.all' : 'u.all'},\n 'match_x_line'),\n }\n\n per.set_accuracy(mesh_eps)\n functions = {\n 'match_x_plane' : (per.match_x_plane,),\n 'match_y_plane' : (per.match_y_plane,),\n 'match_z_plane' : (per.match_z_plane,),\n 'match_x_line' : (per.match_x_line,),\n 'match_y_line' : (per.match_y_line,),\n 'get_wdir' : (get_wdir,),\n }\n\n integrals = {\n 'i' : 2 * approx_order,\n }\n\n equations = {\n 'K' : 'dw_lin_elastic.i.Omega(m.D, v, u)',\n 'S' : 'dw_elastic_wave.i.Omega(m.D, wave.vec, v, u)',\n 'R' : \"\"\"1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, u, v)\n - 1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, v, u)\"\"\",\n 'M' : 'dw_volume_dot.i.Omega(m.density, v, u)',\n }\n\n solver_0 = solver_conf.copy()\n solver_0['name'] = 'eig'\n\n return locals()\n\ndef get_wdir(ts, coors, mode=None,\n equations=None, term=None, problem=None, wdir=None, **kwargs):\n if mode == 'special':\n return {'vec' : wdir}\n\ndef set_wave_dir(pb, wdir):\n materials = pb.get_materials()\n wave_mat = materials['wave']\n wave_mat.set_extra_args(wdir=wdir)\n\ndef save_materials(output_dir, pb, options):\n stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n young, poisson = mc.youngpoisson_from_stiffness(stiffness,\n plane=options.plane)\n density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n\n out = {}\n out['young'] = Struct(name='young', mode='cell',\n data=young[..., None, None])\n out['poisson'] = Struct(name='poisson', mode='cell',\n data=poisson[..., None, None])\n out['density'] = Struct(name='density', mode='cell', data=density)\n materials_filename = os.path.join(output_dir, 'materials.vtk')\n pb.save_state(materials_filename, out=out)\n\ndef get_std_wave_fun(pb, options):\n stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n young, poisson = mc.youngpoisson_from_stiffness(stiffness,\n plane=options.plane)\n density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n\n lam, mu = mc.lame_from_youngpoisson(young, poisson,\n plane=options.plane)\n alam = nm.average(lam)\n amu = nm.average(mu)\n adensity = nm.average(density)\n\n cp = nm.sqrt((alam + 2.0 * amu) / adensity)\n cs = nm.sqrt(amu / adensity)\n output('average p-wave speed:', cp)\n output('average shear wave speed:', cs)\n\n log_names = [r'$\\omega_p$', r'$\\omega_s$']\n log_plot_kwargs = [{'ls' : '--', 'color' : 'k'},\n {'ls' : '--', 'color' : 'gray'}]\n\n if options.mode == 'omega':\n fun = lambda wmag, wdir: (cp * wmag, cs * wmag)\n\n else:\n fun = lambda wmag, wdir: (wmag / cp, wmag / cs)\n\n return fun, log_names, log_plot_kwargs\n\ndef get_stepper(rng, pb, options):\n if options.stepper == 'linear':\n stepper = TimeStepper(rng[0], rng[1], dt=None, n_step=rng[2])\n return stepper\n\n bbox = pb.domain.mesh.get_bounding_box()\n\n bzone = 2.0 * nm.pi / (bbox[1] - bbox[0])\n\n num = rng[2] // 3\n\n class BrillouinStepper(Struct):\n \"\"\"\n Step over 1. Brillouin zone in xy plane.\n \"\"\"\n def __init__(self, t0, t1, dt=None, n_step=None, step=None, **kwargs):\n Struct.__init__(self, t0=t0, t1=t1, dt=dt, n_step=n_step, step=step)\n\n self.n_digit, self.format, self.suffix = get_print_info(self.n_step)\n\n def __iter__(self):\n ts = TimeStepper(0, bzone[0], dt=None, n_step=num)\n for ii, val in ts:\n yield ii, val, nm.array([1.0, 0.0])\n if ii == (num-2): break\n\n ts = TimeStepper(0, bzone[1], dt=None, n_step=num)\n for ii, k1 in ts:\n wdir = nm.array([bzone[0], k1])\n val = nm.linalg.norm(wdir)\n wdir = wdir / val\n yield num + ii, val, wdir\n if ii == (num-2): break\n\n wdir = nm.array([bzone[0], bzone[1]])\n val = nm.linalg.norm(wdir)\n wdir = wdir / val\n ts = TimeStepper(0, 1, dt=None, n_step=num)\n for ii, _ in ts:\n yield 2 * num + ii, val * (1.0 - float(ii)/(num-1)), wdir\n\n stepper = BrillouinStepper(0, 1, n_step=rng[2])\n\n return stepper\n\ndef save_eigenvectors(filename, svecs, wmag, wdir, pb):\n if svecs is None: return\n\n variables = pb.get_variables()\n # Make full eigenvectors (add DOFs fixed by boundary conditions).\n vecs = nm.empty((variables.di.ptr[-1], svecs.shape[1]),\n dtype=svecs.dtype)\n for ii in range(svecs.shape[1]):\n vecs[:, ii] = variables.make_full_vec(svecs[:, ii])\n\n # Save the eigenvectors.\n out = {}\n state = pb.create_state()\n\n pp_name = pb.conf.options.get('post_process_hook')\n pp = getattr(pb.conf.funmod, pp_name if pp_name is not None else '',\n lambda out, *args, **kwargs: out)\n\n for ii in range(svecs.shape[1]):\n state.set_full(vecs[:, ii])\n aux = state.create_output_dict()\n aux2 = {}\n pp(aux2, pb, state, wmag=wmag, wdir=wdir)\n aux.update(convert_complex_output(aux2))\n out.update({key + '%03d' % ii : aux[key] for key in aux})\n\n pb.save_state(filename, out=out)\n\ndef assemble_matrices(define, mod, pars, set_wave_dir, options, wdir=None):\n \"\"\"\n Assemble the blocks of dispersion eigenvalue problem matrices.\n \"\"\"\n define_dict = define(filename_mesh=options.mesh_filename,\n pars=pars,\n approx_order=options.order,\n refinement_level=options.refine,\n solver_conf=options.solver_conf,\n plane=options.plane,\n post_process=options.post_process,\n **options.define_kwargs)\n\n conf = ProblemConf.from_dict(define_dict, mod)\n\n pb = "},"completion":{"kind":"string","value":"Problem.from_conf(conf)"},"api":{"kind":"string","value":"sfepy.discrete.Problem.from_conf"}}},{"rowIdx":63,"cells":{"prompt":{"kind":"string","value":"#!/usr/bin/env python\n\"\"\"\nDispersion analysis of a heterogeneous finite scale periodic cell.\n\nThe periodic cell mesh has to contain two subdomains Y1 (with the cell ids 1),\nY2 (with the cell ids 2), so that different material properties can be defined\nin each of the subdomains (see ``--pars`` option). The command line parameters\ncan be given in any consistent unit set, for example the basic SI units. The\n``--unit-multipliers`` option can be used to rescale the input units to ones\nmore suitable to the simulation, for example to prevent having different\nmatrix blocks with large differences of matrix entries magnitudes. The results\nare then in the rescaled units.\n\nUsage Examples\n--------------\n\nDefault material parameters, a square periodic cell with a spherical inclusion,\nlogs also standard pressure dilatation and shear waves, no eigenvectors::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only\n\nAs above, with custom eigenvalue solver parameters, and different number of\neigenvalues, mesh size and units used in the calculation::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --solver-conf=\"kind='eig.scipy', method='eigsh', tol=1e-10, maxiter=1000, which='LM', sigma=0\" --log-std-waves -n 5 --range=0,640,101 --mode=omega --unit-multipliers=1e-6,1e-2,1e-3 --mesh-size=1e-2 --eigs-only\n\nDefault material parameters, a square periodic cell with a square inclusion,\nand a very small mesh to allow comparing the omega and kappa modes (full matrix\nsolver required!)::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf=\"kind='eig.scipy', method='eigh'\" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf=\"kind='eig.qevp', method='companion', mode='inverted', solver={kind='eig.scipy', method='eig'}\" --log-std-waves -n 500 --range=0,4000000,1001 --mesh-size=1e-2 --mode=kappa --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/kappa\n\nView/compare the resulting logs::\n\n python script/plot_logs.py output/omega/frequencies.txt --no-legends -g 1 -o mode-omega.png\n python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends -o mode-kappa.png\n python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends --swap-axes -o mode-kappa-t.png\n\nIn contrast to the heterogeneous square periodic cell, a homogeneous\nsquare periodic cell (the region Y2 is empty)::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_1m.mesh --solver-conf=\"kind='eig.scipy', method='eigh'\" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega-h\n\n python script/plot_logs.py output/omega-h/frequencies.txt --no-legends -g 1 -o mode-omega-h.png\n\nUse the Brillouin stepper::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves -n=60 --eigs-only --no-legends --stepper=brillouin\n\n python script/plot_logs.py output/frequencies.txt -g 0 --rc=\"'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4\" -o brillouin-stepper-kappas.png\n\n python script/plot_logs.py output/frequencies.txt -g 1 --no-legends --rc=\"'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4\" -o brillouin-stepper-omegas.png\n\nAdditional arguments can be passed to the problem configuration's\n:func:`define()` function using the ``--define-kwargs`` option. In this file,\nonly the mesh vertex separation parameter `mesh_eps` can be used::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only --define-kwargs=\"mesh_eps=1e-10\" --save-regions\n\"\"\"\nfrom __future__ import absolute_import\nimport os\nimport sys\nsys.path.append('.')\nimport gc\nfrom copy import copy\nfrom argparse import ArgumentParser, RawDescriptionHelpFormatter\n\nimport numpy as nm\nimport matplotlib.pyplot as plt\n\nfrom sfepy.base.base import import_file, output, Struct\nfrom sfepy.base.conf import dict_from_string, ProblemConf\nfrom sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options\nfrom sfepy.base.log import Log\nfrom sfepy.discrete.fem import MeshIO\nfrom sfepy.mechanics.matcoefs import stiffness_from_youngpoisson as stiffness\nimport sfepy.mechanics.matcoefs as mc\nfrom sfepy.mechanics.units import apply_unit_multipliers\nimport sfepy.discrete.fem.periodic as per\nfrom sfepy.discrete.fem.meshio import convert_complex_output\nfrom sfepy.homogenization.utils import define_box_regions\nfrom sfepy.discrete import Problem\nfrom sfepy.mechanics.tensors import get_von_mises_stress\nfrom sfepy.solvers import Solver\nfrom sfepy.solvers.ts import get_print_info, TimeStepper\nfrom sfepy.linalg.utils import output_array_stats, max_diff_csr\n\ndef apply_units(pars, unit_multipliers):\n new_pars = apply_unit_multipliers(pars,\n ['stress', 'one', 'density',\n 'stress', 'one' ,'density'],\n unit_multipliers)\n return new_pars\n\ndef compute_von_mises(out, pb, state, extend=False, wmag=None, wdir=None):\n \"\"\"\n Calculate the von Mises stress.\n \"\"\"\n stress = pb.evaluate('ev_cauchy_stress.i.Omega(m.D, u)', mode='el_avg')\n\n vms = get_von_mises_stress(stress.squeeze())\n vms.shape = (vms.shape[0], 1, 1, 1)\n out['von_mises_stress'] = Struct(name='output_data', mode='cell',\n data=vms)\n\n return out\n\ndef define(filename_mesh, pars, approx_order, refinement_level, solver_conf,\n plane='strain', post_process=False, mesh_eps=1e-8):\n io = MeshIO.any_from_filename(filename_mesh)\n bbox = io.read_bounding_box()\n dim = bbox.shape[1]\n\n options = {\n 'absolute_mesh_path' : True,\n 'refinement_level' : refinement_level,\n 'allow_empty_regions' : True,\n 'post_process_hook' : 'compute_von_mises' if post_process else None,\n }\n\n fields = {\n 'displacement': ('complex', dim, 'Omega', approx_order),\n }\n\n young1, poisson1, density1, young2, poisson2, density2 = pars\n materials = {\n 'm' : ({\n 'D' : {'Y1' : stiffness(dim, young=young1, poisson=poisson1,\n plane=plane),\n 'Y2' : stiffness(dim, young=young2, poisson=poisson2,\n plane=plane)},\n 'density' : {'Y1' : density1, 'Y2' : density2},\n },),\n 'wave' : 'get_wdir',\n }\n\n variables = {\n 'u' : ('unknown field', 'displacement', 0),\n 'v' : ('test field', 'displacement', 'u'),\n }\n\n regions = {\n 'Omega' : 'all',\n 'Y1': 'cells of group 1',\n 'Y2': 'cells of group 2',\n }\n regions.update(define_box_regions(dim,\n bbox[0], bbox[1], mesh_eps))\n\n ebcs = {\n }\n\n if dim == 3:\n epbcs = {\n 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},\n 'match_x_plane'),\n 'periodic_y' : (['Near', 'Far'], {'u.all' : 'u.all'},\n 'match_y_plane'),\n 'periodic_z' : (['Top', 'Bottom'], {'u.all' : 'u.all'},\n 'match_z_plane'),\n }\n else:\n epbcs = {\n 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},\n 'match_y_line'),\n 'periodic_y' : (['Bottom', 'Top'], {'u.all' : 'u.all'},\n 'match_x_line'),\n }\n\n per.set_accuracy(mesh_eps)\n functions = {\n 'match_x_plane' : (per.match_x_plane,),\n 'match_y_plane' : (per.match_y_plane,),\n 'match_z_plane' : (per.match_z_plane,),\n 'match_x_line' : (per.match_x_line,),\n 'match_y_line' : (per.match_y_line,),\n 'get_wdir' : (get_wdir,),\n }\n\n integrals = {\n 'i' : 2 * approx_order,\n }\n\n equations = {\n 'K' : 'dw_lin_elastic.i.Omega(m.D, v, u)',\n 'S' : 'dw_elastic_wave.i.Omega(m.D, wave.vec, v, u)',\n 'R' : \"\"\"1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, u, v)\n - 1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, v, u)\"\"\",\n 'M' : 'dw_volume_dot.i.Omega(m.density, v, u)',\n }\n\n solver_0 = solver_conf.copy()\n solver_0['name'] = 'eig'\n\n return locals()\n\ndef get_wdir(ts, coors, mode=None,\n equations=None, term=None, problem=None, wdir=None, **kwargs):\n if mode == 'special':\n return {'vec' : wdir}\n\ndef set_wave_dir(pb, wdir):\n materials = pb.get_materials()\n wave_mat = materials['wave']\n wave_mat.set_extra_args(wdir=wdir)\n\ndef save_materials(output_dir, pb, options):\n stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n young, poisson = mc.youngpoisson_from_stiffness(stiffness,\n plane=options.plane)\n density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n\n out = {}\n out['young'] = Struct(name='young', mode='cell',\n data=young[..., None, None])\n out['poisson'] = Struct(name='poisson', mode='cell',\n data=poisson[..., None, None])\n out['density'] = Struct(name='density', mode='cell', data=density)\n materials_filename = os.path.join(output_dir, 'materials.vtk')\n pb.save_state(materials_filename, out=out)\n\ndef get_std_wave_fun(pb, options):\n stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n young, poisson = mc.youngpoisson_from_stiffness(stiffness,\n plane=options.plane)\n density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n\n lam, mu = mc.lame_from_youngpoisson(young, poisson,\n plane=options.plane)\n alam = nm.average(lam)\n amu = nm.average(mu)\n adensity = nm.average(density)\n\n cp = nm.sqrt((alam + 2.0 * amu) / adensity)\n cs = nm.sqrt(amu / adensity)\n output('average p-wave speed:', cp)\n output('average shear wave speed:', cs)\n\n log_names = [r'$\\omega_p$', r'$\\omega_s$']\n log_plot_kwargs = [{'ls' : '--', 'color' : 'k'},\n {'ls' : '--', 'color' : 'gray'}]\n\n if options.mode == 'omega':\n fun = lambda wmag, wdir: (cp * wmag, cs * wmag)\n\n else:\n fun = lambda wmag, wdir: (wmag / cp, wmag / cs)\n\n return fun, log_names, log_plot_kwargs\n\ndef get_stepper(rng, pb, options):\n if options.stepper == 'linear':\n stepper = TimeStepper(rng[0], rng[1], dt=None, n_step=rng[2])\n return stepper\n\n bbox = pb.domain.mesh.get_bounding_box()\n\n bzone = 2.0 * nm.pi / (bbox[1] - bbox[0])\n\n num = rng[2] // 3\n\n class BrillouinStepper(Struct):\n \"\"\"\n Step over 1. Brillouin zone in xy plane.\n \"\"\"\n def __init__(self, t0, t1, dt=None, n_step=None, step=None, **kwargs):\n Struct.__init__(self, t0=t0, t1=t1, dt=dt, n_step=n_step, step=step)\n\n self.n_digit, self.format, self.suffix = get_print_info(self.n_step)\n\n def __iter__(self):\n ts = TimeStepper(0, bzone[0], dt=None, n_step=num)\n for ii, val in ts:\n yield ii, val, nm.array([1.0, 0.0])\n if ii == (num-2): break\n\n ts = TimeStepper(0, bzone[1], dt=None, n_step=num)\n for ii, k1 in ts:\n wdir = nm.array([bzone[0], k1])\n val = nm.linalg.norm(wdir)\n wdir = wdir / val\n yield num + ii, val, wdir\n if ii == (num-2): break\n\n wdir = nm.array([bzone[0], bzone[1]])\n val = nm.linalg.norm(wdir)\n wdir = wdir / val\n ts = TimeStepper(0, 1, dt=None, n_step=num)\n for ii, _ in ts:\n yield 2 * num + ii, val * (1.0 - float(ii)/(num-1)), wdir\n\n stepper = BrillouinStepper(0, 1, n_step=rng[2])\n\n return stepper\n\ndef save_eigenvectors(filename, svecs, wmag, wdir, pb):\n if svecs is None: return\n\n variables = pb.get_variables()\n # Make full eigenvectors (add DOFs fixed by boundary conditions).\n vecs = nm.empty((variables.di.ptr[-1], svecs.shape[1]),\n dtype=svecs.dtype)\n for ii in range(svecs.shape[1]):\n vecs[:, ii] = variables.make_full_vec(svecs[:, ii])\n\n # Save the eigenvectors.\n out = {}\n state = pb.create_state()\n\n pp_name = pb.conf.options.get('post_process_hook')\n pp = getattr(pb.conf.funmod, pp_name if pp_name is not None else '',\n lambda out, *args, **kwargs: out)\n\n for ii in range(svecs.shape[1]):\n state.set_full(vecs[:, ii])\n aux = state.create_output_dict()\n aux2 = {}\n pp(aux2, pb, state, wmag=wmag, wdir=wdir)\n aux.update(convert_complex_output(aux2))\n out.update({key + '%03d' % ii : aux[key] for key in aux})\n\n pb.save_state(filename, out=out)\n\ndef assemble_matrices(define, mod, pars, set_wave_dir, options, wdir=None):\n \"\"\"\n Assemble the blocks of dispersion eigenvalue problem matrices.\n \"\"\"\n define_dict = define(filename_mesh=options.mesh_filename,\n pars=pars,\n approx_order=options.order,\n refinement_level=options.refine,\n solver_conf=options.solver_conf,\n plane=options.plane,\n post_process=options.post_process,\n **options.define_kwargs)\n\n conf = ProblemConf.from_dict(define_dict, mod)\n\n pb = Problem.from_conf(conf)\n pb.dispersion_options = options\n pb.set_output_dir(options.output_dir)\n dim = pb.domain.shape.dim\n\n # Set the normalized wave vector direction to the material(s).\n if wdir is None:\n wdir = nm.asarray(options.wave_dir[:dim], dtype=nm.float64)\n wdir = wdir / nm.linalg.norm(wdir)\n set_wave_dir(pb, wdir)\n\n bbox = pb.domain.mesh.get_bounding_box()\n size = (bbox[1] - bbox[0]).max()\n scaling0 = apply_unit_multipliers([1.0], ['length'],\n options.unit_multipliers)[0]\n scaling = scaling0\n if options.mesh_size is not None:\n scaling *= options.mesh_size / size\n "},"completion":{"kind":"string","value":"output('scaling factor of periodic cell mesh coordinates:', scaling)"},"api":{"kind":"string","value":"sfepy.base.base.output"}}},{"rowIdx":64,"cells":{"prompt":{"kind":"string","value":"#!/usr/bin/env python\n\"\"\"\nDispersion analysis of a heterogeneous finite scale periodic cell.\n\nThe periodic cell mesh has to contain two subdomains Y1 (with the cell ids 1),\nY2 (with the cell ids 2), so that different material properties can be defined\nin each of the subdomains (see ``--pars`` option). The command line parameters\ncan be given in any consistent unit set, for example the basic SI units. The\n``--unit-multipliers`` option can be used to rescale the input units to ones\nmore suitable to the simulation, for example to prevent having different\nmatrix blocks with large differences of matrix entries magnitudes. The results\nare then in the rescaled units.\n\nUsage Examples\n--------------\n\nDefault material parameters, a square periodic cell with a spherical inclusion,\nlogs also standard pressure dilatation and shear waves, no eigenvectors::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only\n\nAs above, with custom eigenvalue solver parameters, and different number of\neigenvalues, mesh size and units used in the calculation::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --solver-conf=\"kind='eig.scipy', method='eigsh', tol=1e-10, maxiter=1000, which='LM', sigma=0\" --log-std-waves -n 5 --range=0,640,101 --mode=omega --unit-multipliers=1e-6,1e-2,1e-3 --mesh-size=1e-2 --eigs-only\n\nDefault material parameters, a square periodic cell with a square inclusion,\nand a very small mesh to allow comparing the omega and kappa modes (full matrix\nsolver required!)::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf=\"kind='eig.scipy', method='eigh'\" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf=\"kind='eig.qevp', method='companion', mode='inverted', solver={kind='eig.scipy', method='eig'}\" --log-std-waves -n 500 --range=0,4000000,1001 --mesh-size=1e-2 --mode=kappa --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/kappa\n\nView/compare the resulting logs::\n\n python script/plot_logs.py output/omega/frequencies.txt --no-legends -g 1 -o mode-omega.png\n python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends -o mode-kappa.png\n python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends --swap-axes -o mode-kappa-t.png\n\nIn contrast to the heterogeneous square periodic cell, a homogeneous\nsquare periodic cell (the region Y2 is empty)::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_1m.mesh --solver-conf=\"kind='eig.scipy', method='eigh'\" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega-h\n\n python script/plot_logs.py output/omega-h/frequencies.txt --no-legends -g 1 -o mode-omega-h.png\n\nUse the Brillouin stepper::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves -n=60 --eigs-only --no-legends --stepper=brillouin\n\n python script/plot_logs.py output/frequencies.txt -g 0 --rc=\"'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4\" -o brillouin-stepper-kappas.png\n\n python script/plot_logs.py output/frequencies.txt -g 1 --no-legends --rc=\"'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4\" -o brillouin-stepper-omegas.png\n\nAdditional arguments can be passed to the problem configuration's\n:func:`define()` function using the ``--define-kwargs`` option. In this file,\nonly the mesh vertex separation parameter `mesh_eps` can be used::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only --define-kwargs=\"mesh_eps=1e-10\" --save-regions\n\"\"\"\nfrom __future__ import absolute_import\nimport os\nimport sys\nsys.path.append('.')\nimport gc\nfrom copy import copy\nfrom argparse import ArgumentParser, RawDescriptionHelpFormatter\n\nimport numpy as nm\nimport matplotlib.pyplot as plt\n\nfrom sfepy.base.base import import_file, output, Struct\nfrom sfepy.base.conf import dict_from_string, ProblemConf\nfrom sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options\nfrom sfepy.base.log import Log\nfrom sfepy.discrete.fem import MeshIO\nfrom sfepy.mechanics.matcoefs import stiffness_from_youngpoisson as stiffness\nimport sfepy.mechanics.matcoefs as mc\nfrom sfepy.mechanics.units import apply_unit_multipliers\nimport sfepy.discrete.fem.periodic as per\nfrom sfepy.discrete.fem.meshio import convert_complex_output\nfrom sfepy.homogenization.utils import define_box_regions\nfrom sfepy.discrete import Problem\nfrom sfepy.mechanics.tensors import get_von_mises_stress\nfrom sfepy.solvers import Solver\nfrom sfepy.solvers.ts import get_print_info, TimeStepper\nfrom sfepy.linalg.utils import output_array_stats, max_diff_csr\n\ndef apply_units(pars, unit_multipliers):\n new_pars = apply_unit_multipliers(pars,\n ['stress', 'one', 'density',\n 'stress', 'one' ,'density'],\n unit_multipliers)\n return new_pars\n\ndef compute_von_mises(out, pb, state, extend=False, wmag=None, wdir=None):\n \"\"\"\n Calculate the von Mises stress.\n \"\"\"\n stress = pb.evaluate('ev_cauchy_stress.i.Omega(m.D, u)', mode='el_avg')\n\n vms = get_von_mises_stress(stress.squeeze())\n vms.shape = (vms.shape[0], 1, 1, 1)\n out['von_mises_stress'] = Struct(name='output_data', mode='cell',\n data=vms)\n\n return out\n\ndef define(filename_mesh, pars, approx_order, refinement_level, solver_conf,\n plane='strain', post_process=False, mesh_eps=1e-8):\n io = MeshIO.any_from_filename(filename_mesh)\n bbox = io.read_bounding_box()\n dim = bbox.shape[1]\n\n options = {\n 'absolute_mesh_path' : True,\n 'refinement_level' : refinement_level,\n 'allow_empty_regions' : True,\n 'post_process_hook' : 'compute_von_mises' if post_process else None,\n }\n\n fields = {\n 'displacement': ('complex', dim, 'Omega', approx_order),\n }\n\n young1, poisson1, density1, young2, poisson2, density2 = pars\n materials = {\n 'm' : ({\n 'D' : {'Y1' : stiffness(dim, young=young1, poisson=poisson1,\n plane=plane),\n 'Y2' : stiffness(dim, young=young2, poisson=poisson2,\n plane=plane)},\n 'density' : {'Y1' : density1, 'Y2' : density2},\n },),\n 'wave' : 'get_wdir',\n }\n\n variables = {\n 'u' : ('unknown field', 'displacement', 0),\n 'v' : ('test field', 'displacement', 'u'),\n }\n\n regions = {\n 'Omega' : 'all',\n 'Y1': 'cells of group 1',\n 'Y2': 'cells of group 2',\n }\n regions.update(define_box_regions(dim,\n bbox[0], bbox[1], mesh_eps))\n\n ebcs = {\n }\n\n if dim == 3:\n epbcs = {\n 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},\n 'match_x_plane'),\n 'periodic_y' : (['Near', 'Far'], {'u.all' : 'u.all'},\n 'match_y_plane'),\n 'periodic_z' : (['Top', 'Bottom'], {'u.all' : 'u.all'},\n 'match_z_plane'),\n }\n else:\n epbcs = {\n 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},\n 'match_y_line'),\n 'periodic_y' : (['Bottom', 'Top'], {'u.all' : 'u.all'},\n 'match_x_line'),\n }\n\n per.set_accuracy(mesh_eps)\n functions = {\n 'match_x_plane' : (per.match_x_plane,),\n 'match_y_plane' : (per.match_y_plane,),\n 'match_z_plane' : (per.match_z_plane,),\n 'match_x_line' : (per.match_x_line,),\n 'match_y_line' : (per.match_y_line,),\n 'get_wdir' : (get_wdir,),\n }\n\n integrals = {\n 'i' : 2 * approx_order,\n }\n\n equations = {\n 'K' : 'dw_lin_elastic.i.Omega(m.D, v, u)',\n 'S' : 'dw_elastic_wave.i.Omega(m.D, wave.vec, v, u)',\n 'R' : \"\"\"1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, u, v)\n - 1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, v, u)\"\"\",\n 'M' : 'dw_volume_dot.i.Omega(m.density, v, u)',\n }\n\n solver_0 = solver_conf.copy()\n solver_0['name'] = 'eig'\n\n return locals()\n\ndef get_wdir(ts, coors, mode=None,\n equations=None, term=None, problem=None, wdir=None, **kwargs):\n if mode == 'special':\n return {'vec' : wdir}\n\ndef set_wave_dir(pb, wdir):\n materials = pb.get_materials()\n wave_mat = materials['wave']\n wave_mat.set_extra_args(wdir=wdir)\n\ndef save_materials(output_dir, pb, options):\n stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n young, poisson = mc.youngpoisson_from_stiffness(stiffness,\n plane=options.plane)\n density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n\n out = {}\n out['young'] = Struct(name='young', mode='cell',\n data=young[..., None, None])\n out['poisson'] = Struct(name='poisson', mode='cell',\n data=poisson[..., None, None])\n out['density'] = Struct(name='density', mode='cell', data=density)\n materials_filename = os.path.join(output_dir, 'materials.vtk')\n pb.save_state(materials_filename, out=out)\n\ndef get_std_wave_fun(pb, options):\n stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n young, poisson = mc.youngpoisson_from_stiffness(stiffness,\n plane=options.plane)\n density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n\n lam, mu = mc.lame_from_youngpoisson(young, poisson,\n plane=options.plane)\n alam = nm.average(lam)\n amu = nm.average(mu)\n adensity = nm.average(density)\n\n cp = nm.sqrt((alam + 2.0 * amu) / adensity)\n cs = nm.sqrt(amu / adensity)\n output('average p-wave speed:', cp)\n output('average shear wave speed:', cs)\n\n log_names = [r'$\\omega_p$', r'$\\omega_s$']\n log_plot_kwargs = [{'ls' : '--', 'color' : 'k'},\n {'ls' : '--', 'color' : 'gray'}]\n\n if options.mode == 'omega':\n fun = lambda wmag, wdir: (cp * wmag, cs * wmag)\n\n else:\n fun = lambda wmag, wdir: (wmag / cp, wmag / cs)\n\n return fun, log_names, log_plot_kwargs\n\ndef get_stepper(rng, pb, options):\n if options.stepper == 'linear':\n stepper = TimeStepper(rng[0], rng[1], dt=None, n_step=rng[2])\n return stepper\n\n bbox = pb.domain.mesh.get_bounding_box()\n\n bzone = 2.0 * nm.pi / (bbox[1] - bbox[0])\n\n num = rng[2] // 3\n\n class BrillouinStepper(Struct):\n \"\"\"\n Step over 1. Brillouin zone in xy plane.\n \"\"\"\n def __init__(self, t0, t1, dt=None, n_step=None, step=None, **kwargs):\n Struct.__init__(self, t0=t0, t1=t1, dt=dt, n_step=n_step, step=step)\n\n self.n_digit, self.format, self.suffix = get_print_info(self.n_step)\n\n def __iter__(self):\n ts = TimeStepper(0, bzone[0], dt=None, n_step=num)\n for ii, val in ts:\n yield ii, val, nm.array([1.0, 0.0])\n if ii == (num-2): break\n\n ts = TimeStepper(0, bzone[1], dt=None, n_step=num)\n for ii, k1 in ts:\n wdir = nm.array([bzone[0], k1])\n val = nm.linalg.norm(wdir)\n wdir = wdir / val\n yield num + ii, val, wdir\n if ii == (num-2): break\n\n wdir = nm.array([bzone[0], bzone[1]])\n val = nm.linalg.norm(wdir)\n wdir = wdir / val\n ts = TimeStepper(0, 1, dt=None, n_step=num)\n for ii, _ in ts:\n yield 2 * num + ii, val * (1.0 - float(ii)/(num-1)), wdir\n\n stepper = BrillouinStepper(0, 1, n_step=rng[2])\n\n return stepper\n\ndef save_eigenvectors(filename, svecs, wmag, wdir, pb):\n if svecs is None: return\n\n variables = pb.get_variables()\n # Make full eigenvectors (add DOFs fixed by boundary conditions).\n vecs = nm.empty((variables.di.ptr[-1], svecs.shape[1]),\n dtype=svecs.dtype)\n for ii in range(svecs.shape[1]):\n vecs[:, ii] = variables.make_full_vec(svecs[:, ii])\n\n # Save the eigenvectors.\n out = {}\n state = pb.create_state()\n\n pp_name = pb.conf.options.get('post_process_hook')\n pp = getattr(pb.conf.funmod, pp_name if pp_name is not None else '',\n lambda out, *args, **kwargs: out)\n\n for ii in range(svecs.shape[1]):\n state.set_full(vecs[:, ii])\n aux = state.create_output_dict()\n aux2 = {}\n pp(aux2, pb, state, wmag=wmag, wdir=wdir)\n aux.update(convert_complex_output(aux2))\n out.update({key + '%03d' % ii : aux[key] for key in aux})\n\n pb.save_state(filename, out=out)\n\ndef assemble_matrices(define, mod, pars, set_wave_dir, options, wdir=None):\n \"\"\"\n Assemble the blocks of dispersion eigenvalue problem matrices.\n \"\"\"\n define_dict = define(filename_mesh=options.mesh_filename,\n pars=pars,\n approx_order=options.order,\n refinement_level=options.refine,\n solver_conf=options.solver_conf,\n plane=options.plane,\n post_process=options.post_process,\n **options.define_kwargs)\n\n conf = ProblemConf.from_dict(define_dict, mod)\n\n pb = Problem.from_conf(conf)\n pb.dispersion_options = options\n pb.set_output_dir(options.output_dir)\n dim = pb.domain.shape.dim\n\n # Set the normalized wave vector direction to the material(s).\n if wdir is None:\n wdir = nm.asarray(options.wave_dir[:dim], dtype=nm.float64)\n wdir = wdir / nm.linalg.norm(wdir)\n set_wave_dir(pb, wdir)\n\n bbox = pb.domain.mesh.get_bounding_box()\n size = (bbox[1] - bbox[0]).max()\n scaling0 = apply_unit_multipliers([1.0], ['length'],\n options.unit_multipliers)[0]\n scaling = scaling0\n if options.mesh_size is not None:\n scaling *= options.mesh_size / size\n output('scaling factor of periodic cell mesh coordinates:', scaling)\n "},"completion":{"kind":"string","value":"output('new mesh size with applied unit multipliers:', scaling * size)"},"api":{"kind":"string","value":"sfepy.base.base.output"}}},{"rowIdx":65,"cells":{"prompt":{"kind":"string","value":"#!/usr/bin/env python\n\"\"\"\nDispersion analysis of a heterogeneous finite scale periodic cell.\n\nThe periodic cell mesh has to contain two subdomains Y1 (with the cell ids 1),\nY2 (with the cell ids 2), so that different material properties can be defined\nin each of the subdomains (see ``--pars`` option). The command line parameters\ncan be given in any consistent unit set, for example the basic SI units. The\n``--unit-multipliers`` option can be used to rescale the input units to ones\nmore suitable to the simulation, for example to prevent having different\nmatrix blocks with large differences of matrix entries magnitudes. The results\nare then in the rescaled units.\n\nUsage Examples\n--------------\n\nDefault material parameters, a square periodic cell with a spherical inclusion,\nlogs also standard pressure dilatation and shear waves, no eigenvectors::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only\n\nAs above, with custom eigenvalue solver parameters, and different number of\neigenvalues, mesh size and units used in the calculation::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --solver-conf=\"kind='eig.scipy', method='eigsh', tol=1e-10, maxiter=1000, which='LM', sigma=0\" --log-std-waves -n 5 --range=0,640,101 --mode=omega --unit-multipliers=1e-6,1e-2,1e-3 --mesh-size=1e-2 --eigs-only\n\nDefault material parameters, a square periodic cell with a square inclusion,\nand a very small mesh to allow comparing the omega and kappa modes (full matrix\nsolver required!)::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf=\"kind='eig.scipy', method='eigh'\" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf=\"kind='eig.qevp', method='companion', mode='inverted', solver={kind='eig.scipy', method='eig'}\" --log-std-waves -n 500 --range=0,4000000,1001 --mesh-size=1e-2 --mode=kappa --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/kappa\n\nView/compare the resulting logs::\n\n python script/plot_logs.py output/omega/frequencies.txt --no-legends -g 1 -o mode-omega.png\n python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends -o mode-kappa.png\n python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends --swap-axes -o mode-kappa-t.png\n\nIn contrast to the heterogeneous square periodic cell, a homogeneous\nsquare periodic cell (the region Y2 is empty)::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_1m.mesh --solver-conf=\"kind='eig.scipy', method='eigh'\" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega-h\n\n python script/plot_logs.py output/omega-h/frequencies.txt --no-legends -g 1 -o mode-omega-h.png\n\nUse the Brillouin stepper::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves -n=60 --eigs-only --no-legends --stepper=brillouin\n\n python script/plot_logs.py output/frequencies.txt -g 0 --rc=\"'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4\" -o brillouin-stepper-kappas.png\n\n python script/plot_logs.py output/frequencies.txt -g 1 --no-legends --rc=\"'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4\" -o brillouin-stepper-omegas.png\n\nAdditional arguments can be passed to the problem configuration's\n:func:`define()` function using the ``--define-kwargs`` option. In this file,\nonly the mesh vertex separation parameter `mesh_eps` can be used::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only --define-kwargs=\"mesh_eps=1e-10\" --save-regions\n\"\"\"\nfrom __future__ import absolute_import\nimport os\nimport sys\nsys.path.append('.')\nimport gc\nfrom copy import copy\nfrom argparse import ArgumentParser, RawDescriptionHelpFormatter\n\nimport numpy as nm\nimport matplotlib.pyplot as plt\n\nfrom sfepy.base.base import import_file, output, Struct\nfrom sfepy.base.conf import dict_from_string, ProblemConf\nfrom sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options\nfrom sfepy.base.log import Log\nfrom sfepy.discrete.fem import MeshIO\nfrom sfepy.mechanics.matcoefs import stiffness_from_youngpoisson as stiffness\nimport sfepy.mechanics.matcoefs as mc\nfrom sfepy.mechanics.units import apply_unit_multipliers\nimport sfepy.discrete.fem.periodic as per\nfrom sfepy.discrete.fem.meshio import convert_complex_output\nfrom sfepy.homogenization.utils import define_box_regions\nfrom sfepy.discrete import Problem\nfrom sfepy.mechanics.tensors import get_von_mises_stress\nfrom sfepy.solvers import Solver\nfrom sfepy.solvers.ts import get_print_info, TimeStepper\nfrom sfepy.linalg.utils import output_array_stats, max_diff_csr\n\ndef apply_units(pars, unit_multipliers):\n new_pars = apply_unit_multipliers(pars,\n ['stress', 'one', 'density',\n 'stress', 'one' ,'density'],\n unit_multipliers)\n return new_pars\n\ndef compute_von_mises(out, pb, state, extend=False, wmag=None, wdir=None):\n \"\"\"\n Calculate the von Mises stress.\n \"\"\"\n stress = pb.evaluate('ev_cauchy_stress.i.Omega(m.D, u)', mode='el_avg')\n\n vms = get_von_mises_stress(stress.squeeze())\n vms.shape = (vms.shape[0], 1, 1, 1)\n out['von_mises_stress'] = Struct(name='output_data', mode='cell',\n data=vms)\n\n return out\n\ndef define(filename_mesh, pars, approx_order, refinement_level, solver_conf,\n plane='strain', post_process=False, mesh_eps=1e-8):\n io = MeshIO.any_from_filename(filename_mesh)\n bbox = io.read_bounding_box()\n dim = bbox.shape[1]\n\n options = {\n 'absolute_mesh_path' : True,\n 'refinement_level' : refinement_level,\n 'allow_empty_regions' : True,\n 'post_process_hook' : 'compute_von_mises' if post_process else None,\n }\n\n fields = {\n 'displacement': ('complex', dim, 'Omega', approx_order),\n }\n\n young1, poisson1, density1, young2, poisson2, density2 = pars\n materials = {\n 'm' : ({\n 'D' : {'Y1' : stiffness(dim, young=young1, poisson=poisson1,\n plane=plane),\n 'Y2' : stiffness(dim, young=young2, poisson=poisson2,\n plane=plane)},\n 'density' : {'Y1' : density1, 'Y2' : density2},\n },),\n 'wave' : 'get_wdir',\n }\n\n variables = {\n 'u' : ('unknown field', 'displacement', 0),\n 'v' : ('test field', 'displacement', 'u'),\n }\n\n regions = {\n 'Omega' : 'all',\n 'Y1': 'cells of group 1',\n 'Y2': 'cells of group 2',\n }\n regions.update(define_box_regions(dim,\n bbox[0], bbox[1], mesh_eps))\n\n ebcs = {\n }\n\n if dim == 3:\n epbcs = {\n 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},\n 'match_x_plane'),\n 'periodic_y' : (['Near', 'Far'], {'u.all' : 'u.all'},\n 'match_y_plane'),\n 'periodic_z' : (['Top', 'Bottom'], {'u.all' : 'u.all'},\n 'match_z_plane'),\n }\n else:\n epbcs = {\n 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},\n 'match_y_line'),\n 'periodic_y' : (['Bottom', 'Top'], {'u.all' : 'u.all'},\n 'match_x_line'),\n }\n\n per.set_accuracy(mesh_eps)\n functions = {\n 'match_x_plane' : (per.match_x_plane,),\n 'match_y_plane' : (per.match_y_plane,),\n 'match_z_plane' : (per.match_z_plane,),\n 'match_x_line' : (per.match_x_line,),\n 'match_y_line' : (per.match_y_line,),\n 'get_wdir' : (get_wdir,),\n }\n\n integrals = {\n 'i' : 2 * approx_order,\n }\n\n equations = {\n 'K' : 'dw_lin_elastic.i.Omega(m.D, v, u)',\n 'S' : 'dw_elastic_wave.i.Omega(m.D, wave.vec, v, u)',\n 'R' : \"\"\"1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, u, v)\n - 1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, v, u)\"\"\",\n 'M' : 'dw_volume_dot.i.Omega(m.density, v, u)',\n }\n\n solver_0 = solver_conf.copy()\n solver_0['name'] = 'eig'\n\n return locals()\n\ndef get_wdir(ts, coors, mode=None,\n equations=None, term=None, problem=None, wdir=None, **kwargs):\n if mode == 'special':\n return {'vec' : wdir}\n\ndef set_wave_dir(pb, wdir):\n materials = pb.get_materials()\n wave_mat = materials['wave']\n wave_mat.set_extra_args(wdir=wdir)\n\ndef save_materials(output_dir, pb, options):\n stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n young, poisson = mc.youngpoisson_from_stiffness(stiffness,\n plane=options.plane)\n density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n\n out = {}\n out['young'] = Struct(name='young', mode='cell',\n data=young[..., None, None])\n out['poisson'] = Struct(name='poisson', mode='cell',\n data=poisson[..., None, None])\n out['density'] = Struct(name='density', mode='cell', data=density)\n materials_filename = os.path.join(output_dir, 'materials.vtk')\n pb.save_state(materials_filename, out=out)\n\ndef get_std_wave_fun(pb, options):\n stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n young, poisson = mc.youngpoisson_from_stiffness(stiffness,\n plane=options.plane)\n density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n\n lam, mu = mc.lame_from_youngpoisson(young, poisson,\n plane=options.plane)\n alam = nm.average(lam)\n amu = nm.average(mu)\n adensity = nm.average(density)\n\n cp = nm.sqrt((alam + 2.0 * amu) / adensity)\n cs = nm.sqrt(amu / adensity)\n output('average p-wave speed:', cp)\n output('average shear wave speed:', cs)\n\n log_names = [r'$\\omega_p$', r'$\\omega_s$']\n log_plot_kwargs = [{'ls' : '--', 'color' : 'k'},\n {'ls' : '--', 'color' : 'gray'}]\n\n if options.mode == 'omega':\n fun = lambda wmag, wdir: (cp * wmag, cs * wmag)\n\n else:\n fun = lambda wmag, wdir: (wmag / cp, wmag / cs)\n\n return fun, log_names, log_plot_kwargs\n\ndef get_stepper(rng, pb, options):\n if options.stepper == 'linear':\n stepper = TimeStepper(rng[0], rng[1], dt=None, n_step=rng[2])\n return stepper\n\n bbox = pb.domain.mesh.get_bounding_box()\n\n bzone = 2.0 * nm.pi / (bbox[1] - bbox[0])\n\n num = rng[2] // 3\n\n class BrillouinStepper(Struct):\n \"\"\"\n Step over 1. Brillouin zone in xy plane.\n \"\"\"\n def __init__(self, t0, t1, dt=None, n_step=None, step=None, **kwargs):\n Struct.__init__(self, t0=t0, t1=t1, dt=dt, n_step=n_step, step=step)\n\n self.n_digit, self.format, self.suffix = get_print_info(self.n_step)\n\n def __iter__(self):\n ts = TimeStepper(0, bzone[0], dt=None, n_step=num)\n for ii, val in ts:\n yield ii, val, nm.array([1.0, 0.0])\n if ii == (num-2): break\n\n ts = TimeStepper(0, bzone[1], dt=None, n_step=num)\n for ii, k1 in ts:\n wdir = nm.array([bzone[0], k1])\n val = nm.linalg.norm(wdir)\n wdir = wdir / val\n yield num + ii, val, wdir\n if ii == (num-2): break\n\n wdir = nm.array([bzone[0], bzone[1]])\n val = nm.linalg.norm(wdir)\n wdir = wdir / val\n ts = TimeStepper(0, 1, dt=None, n_step=num)\n for ii, _ in ts:\n yield 2 * num + ii, val * (1.0 - float(ii)/(num-1)), wdir\n\n stepper = BrillouinStepper(0, 1, n_step=rng[2])\n\n return stepper\n\ndef save_eigenvectors(filename, svecs, wmag, wdir, pb):\n if svecs is None: return\n\n variables = pb.get_variables()\n # Make full eigenvectors (add DOFs fixed by boundary conditions).\n vecs = nm.empty((variables.di.ptr[-1], svecs.shape[1]),\n dtype=svecs.dtype)\n for ii in range(svecs.shape[1]):\n vecs[:, ii] = variables.make_full_vec(svecs[:, ii])\n\n # Save the eigenvectors.\n out = {}\n state = pb.create_state()\n\n pp_name = pb.conf.options.get('post_process_hook')\n pp = getattr(pb.conf.funmod, pp_name if pp_name is not None else '',\n lambda out, *args, **kwargs: out)\n\n for ii in range(svecs.shape[1]):\n state.set_full(vecs[:, ii])\n aux = state.create_output_dict()\n aux2 = {}\n pp(aux2, pb, state, wmag=wmag, wdir=wdir)\n aux.update(convert_complex_output(aux2))\n out.update({key + '%03d' % ii : aux[key] for key in aux})\n\n pb.save_state(filename, out=out)\n\ndef assemble_matrices(define, mod, pars, set_wave_dir, options, wdir=None):\n \"\"\"\n Assemble the blocks of dispersion eigenvalue problem matrices.\n \"\"\"\n define_dict = define(filename_mesh=options.mesh_filename,\n pars=pars,\n approx_order=options.order,\n refinement_level=options.refine,\n solver_conf=options.solver_conf,\n plane=options.plane,\n post_process=options.post_process,\n **options.define_kwargs)\n\n conf = ProblemConf.from_dict(define_dict, mod)\n\n pb = Problem.from_conf(conf)\n pb.dispersion_options = options\n pb.set_output_dir(options.output_dir)\n dim = pb.domain.shape.dim\n\n # Set the normalized wave vector direction to the material(s).\n if wdir is None:\n wdir = nm.asarray(options.wave_dir[:dim], dtype=nm.float64)\n wdir = wdir / nm.linalg.norm(wdir)\n set_wave_dir(pb, wdir)\n\n bbox = pb.domain.mesh.get_bounding_box()\n size = (bbox[1] - bbox[0]).max()\n scaling0 = apply_unit_multipliers([1.0], ['length'],\n options.unit_multipliers)[0]\n scaling = scaling0\n if options.mesh_size is not None:\n scaling *= options.mesh_size / size\n output('scaling factor of periodic cell mesh coordinates:', scaling)\n output('new mesh size with applied unit multipliers:', scaling * size)\n pb.domain.mesh.coors[:] *= scaling\n pb.set_mesh_coors(pb.domain.mesh.coors, update_fields=True)\n\n bzone = 2.0 * nm.pi / (scaling * size)\n "},"completion":{"kind":"string","value":"output('1. Brillouin zone size:', bzone * scaling0)"},"api":{"kind":"string","value":"sfepy.base.base.output"}}},{"rowIdx":66,"cells":{"prompt":{"kind":"string","value":"#!/usr/bin/env python\n\"\"\"\nDispersion analysis of a heterogeneous finite scale periodic cell.\n\nThe periodic cell mesh has to contain two subdomains Y1 (with the cell ids 1),\nY2 (with the cell ids 2), so that different material properties can be defined\nin each of the subdomains (see ``--pars`` option). The command line parameters\ncan be given in any consistent unit set, for example the basic SI units. The\n``--unit-multipliers`` option can be used to rescale the input units to ones\nmore suitable to the simulation, for example to prevent having different\nmatrix blocks with large differences of matrix entries magnitudes. The results\nare then in the rescaled units.\n\nUsage Examples\n--------------\n\nDefault material parameters, a square periodic cell with a spherical inclusion,\nlogs also standard pressure dilatation and shear waves, no eigenvectors::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only\n\nAs above, with custom eigenvalue solver parameters, and different number of\neigenvalues, mesh size and units used in the calculation::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --solver-conf=\"kind='eig.scipy', method='eigsh', tol=1e-10, maxiter=1000, which='LM', sigma=0\" --log-std-waves -n 5 --range=0,640,101 --mode=omega --unit-multipliers=1e-6,1e-2,1e-3 --mesh-size=1e-2 --eigs-only\n\nDefault material parameters, a square periodic cell with a square inclusion,\nand a very small mesh to allow comparing the omega and kappa modes (full matrix\nsolver required!)::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf=\"kind='eig.scipy', method='eigh'\" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf=\"kind='eig.qevp', method='companion', mode='inverted', solver={kind='eig.scipy', method='eig'}\" --log-std-waves -n 500 --range=0,4000000,1001 --mesh-size=1e-2 --mode=kappa --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/kappa\n\nView/compare the resulting logs::\n\n python script/plot_logs.py output/omega/frequencies.txt --no-legends -g 1 -o mode-omega.png\n python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends -o mode-kappa.png\n python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends --swap-axes -o mode-kappa-t.png\n\nIn contrast to the heterogeneous square periodic cell, a homogeneous\nsquare periodic cell (the region Y2 is empty)::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_1m.mesh --solver-conf=\"kind='eig.scipy', method='eigh'\" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega-h\n\n python script/plot_logs.py output/omega-h/frequencies.txt --no-legends -g 1 -o mode-omega-h.png\n\nUse the Brillouin stepper::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves -n=60 --eigs-only --no-legends --stepper=brillouin\n\n python script/plot_logs.py output/frequencies.txt -g 0 --rc=\"'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4\" -o brillouin-stepper-kappas.png\n\n python script/plot_logs.py output/frequencies.txt -g 1 --no-legends --rc=\"'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4\" -o brillouin-stepper-omegas.png\n\nAdditional arguments can be passed to the problem configuration's\n:func:`define()` function using the ``--define-kwargs`` option. In this file,\nonly the mesh vertex separation parameter `mesh_eps` can be used::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only --define-kwargs=\"mesh_eps=1e-10\" --save-regions\n\"\"\"\nfrom __future__ import absolute_import\nimport os\nimport sys\nsys.path.append('.')\nimport gc\nfrom copy import copy\nfrom argparse import ArgumentParser, RawDescriptionHelpFormatter\n\nimport numpy as nm\nimport matplotlib.pyplot as plt\n\nfrom sfepy.base.base import import_file, output, Struct\nfrom sfepy.base.conf import dict_from_string, ProblemConf\nfrom sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options\nfrom sfepy.base.log import Log\nfrom sfepy.discrete.fem import MeshIO\nfrom sfepy.mechanics.matcoefs import stiffness_from_youngpoisson as stiffness\nimport sfepy.mechanics.matcoefs as mc\nfrom sfepy.mechanics.units import apply_unit_multipliers\nimport sfepy.discrete.fem.periodic as per\nfrom sfepy.discrete.fem.meshio import convert_complex_output\nfrom sfepy.homogenization.utils import define_box_regions\nfrom sfepy.discrete import Problem\nfrom sfepy.mechanics.tensors import get_von_mises_stress\nfrom sfepy.solvers import Solver\nfrom sfepy.solvers.ts import get_print_info, TimeStepper\nfrom sfepy.linalg.utils import output_array_stats, max_diff_csr\n\ndef apply_units(pars, unit_multipliers):\n new_pars = apply_unit_multipliers(pars,\n ['stress', 'one', 'density',\n 'stress', 'one' ,'density'],\n unit_multipliers)\n return new_pars\n\ndef compute_von_mises(out, pb, state, extend=False, wmag=None, wdir=None):\n \"\"\"\n Calculate the von Mises stress.\n \"\"\"\n stress = pb.evaluate('ev_cauchy_stress.i.Omega(m.D, u)', mode='el_avg')\n\n vms = get_von_mises_stress(stress.squeeze())\n vms.shape = (vms.shape[0], 1, 1, 1)\n out['von_mises_stress'] = Struct(name='output_data', mode='cell',\n data=vms)\n\n return out\n\ndef define(filename_mesh, pars, approx_order, refinement_level, solver_conf,\n plane='strain', post_process=False, mesh_eps=1e-8):\n io = MeshIO.any_from_filename(filename_mesh)\n bbox = io.read_bounding_box()\n dim = bbox.shape[1]\n\n options = {\n 'absolute_mesh_path' : True,\n 'refinement_level' : refinement_level,\n 'allow_empty_regions' : True,\n 'post_process_hook' : 'compute_von_mises' if post_process else None,\n }\n\n fields = {\n 'displacement': ('complex', dim, 'Omega', approx_order),\n }\n\n young1, poisson1, density1, young2, poisson2, density2 = pars\n materials = {\n 'm' : ({\n 'D' : {'Y1' : stiffness(dim, young=young1, poisson=poisson1,\n plane=plane),\n 'Y2' : stiffness(dim, young=young2, poisson=poisson2,\n plane=plane)},\n 'density' : {'Y1' : density1, 'Y2' : density2},\n },),\n 'wave' : 'get_wdir',\n }\n\n variables = {\n 'u' : ('unknown field', 'displacement', 0),\n 'v' : ('test field', 'displacement', 'u'),\n }\n\n regions = {\n 'Omega' : 'all',\n 'Y1': 'cells of group 1',\n 'Y2': 'cells of group 2',\n }\n regions.update(define_box_regions(dim,\n bbox[0], bbox[1], mesh_eps))\n\n ebcs = {\n }\n\n if dim == 3:\n epbcs = {\n 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},\n 'match_x_plane'),\n 'periodic_y' : (['Near', 'Far'], {'u.all' : 'u.all'},\n 'match_y_plane'),\n 'periodic_z' : (['Top', 'Bottom'], {'u.all' : 'u.all'},\n 'match_z_plane'),\n }\n else:\n epbcs = {\n 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},\n 'match_y_line'),\n 'periodic_y' : (['Bottom', 'Top'], {'u.all' : 'u.all'},\n 'match_x_line'),\n }\n\n per.set_accuracy(mesh_eps)\n functions = {\n 'match_x_plane' : (per.match_x_plane,),\n 'match_y_plane' : (per.match_y_plane,),\n 'match_z_plane' : (per.match_z_plane,),\n 'match_x_line' : (per.match_x_line,),\n 'match_y_line' : (per.match_y_line,),\n 'get_wdir' : (get_wdir,),\n }\n\n integrals = {\n 'i' : 2 * approx_order,\n }\n\n equations = {\n 'K' : 'dw_lin_elastic.i.Omega(m.D, v, u)',\n 'S' : 'dw_elastic_wave.i.Omega(m.D, wave.vec, v, u)',\n 'R' : \"\"\"1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, u, v)\n - 1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, v, u)\"\"\",\n 'M' : 'dw_volume_dot.i.Omega(m.density, v, u)',\n }\n\n solver_0 = solver_conf.copy()\n solver_0['name'] = 'eig'\n\n return locals()\n\ndef get_wdir(ts, coors, mode=None,\n equations=None, term=None, problem=None, wdir=None, **kwargs):\n if mode == 'special':\n return {'vec' : wdir}\n\ndef set_wave_dir(pb, wdir):\n materials = pb.get_materials()\n wave_mat = materials['wave']\n wave_mat.set_extra_args(wdir=wdir)\n\ndef save_materials(output_dir, pb, options):\n stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n young, poisson = mc.youngpoisson_from_stiffness(stiffness,\n plane=options.plane)\n density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n\n out = {}\n out['young'] = Struct(name='young', mode='cell',\n data=young[..., None, None])\n out['poisson'] = Struct(name='poisson', mode='cell',\n data=poisson[..., None, None])\n out['density'] = Struct(name='density', mode='cell', data=density)\n materials_filename = os.path.join(output_dir, 'materials.vtk')\n pb.save_state(materials_filename, out=out)\n\ndef get_std_wave_fun(pb, options):\n stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n young, poisson = mc.youngpoisson_from_stiffness(stiffness,\n plane=options.plane)\n density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n\n lam, mu = mc.lame_from_youngpoisson(young, poisson,\n plane=options.plane)\n alam = nm.average(lam)\n amu = nm.average(mu)\n adensity = nm.average(density)\n\n cp = nm.sqrt((alam + 2.0 * amu) / adensity)\n cs = nm.sqrt(amu / adensity)\n output('average p-wave speed:', cp)\n output('average shear wave speed:', cs)\n\n log_names = [r'$\\omega_p$', r'$\\omega_s$']\n log_plot_kwargs = [{'ls' : '--', 'color' : 'k'},\n {'ls' : '--', 'color' : 'gray'}]\n\n if options.mode == 'omega':\n fun = lambda wmag, wdir: (cp * wmag, cs * wmag)\n\n else:\n fun = lambda wmag, wdir: (wmag / cp, wmag / cs)\n\n return fun, log_names, log_plot_kwargs\n\ndef get_stepper(rng, pb, options):\n if options.stepper == 'linear':\n stepper = TimeStepper(rng[0], rng[1], dt=None, n_step=rng[2])\n return stepper\n\n bbox = pb.domain.mesh.get_bounding_box()\n\n bzone = 2.0 * nm.pi / (bbox[1] - bbox[0])\n\n num = rng[2] // 3\n\n class BrillouinStepper(Struct):\n \"\"\"\n Step over 1. Brillouin zone in xy plane.\n \"\"\"\n def __init__(self, t0, t1, dt=None, n_step=None, step=None, **kwargs):\n Struct.__init__(self, t0=t0, t1=t1, dt=dt, n_step=n_step, step=step)\n\n self.n_digit, self.format, self.suffix = get_print_info(self.n_step)\n\n def __iter__(self):\n ts = TimeStepper(0, bzone[0], dt=None, n_step=num)\n for ii, val in ts:\n yield ii, val, nm.array([1.0, 0.0])\n if ii == (num-2): break\n\n ts = TimeStepper(0, bzone[1], dt=None, n_step=num)\n for ii, k1 in ts:\n wdir = nm.array([bzone[0], k1])\n val = nm.linalg.norm(wdir)\n wdir = wdir / val\n yield num + ii, val, wdir\n if ii == (num-2): break\n\n wdir = nm.array([bzone[0], bzone[1]])\n val = nm.linalg.norm(wdir)\n wdir = wdir / val\n ts = TimeStepper(0, 1, dt=None, n_step=num)\n for ii, _ in ts:\n yield 2 * num + ii, val * (1.0 - float(ii)/(num-1)), wdir\n\n stepper = BrillouinStepper(0, 1, n_step=rng[2])\n\n return stepper\n\ndef save_eigenvectors(filename, svecs, wmag, wdir, pb):\n if svecs is None: return\n\n variables = pb.get_variables()\n # Make full eigenvectors (add DOFs fixed by boundary conditions).\n vecs = nm.empty((variables.di.ptr[-1], svecs.shape[1]),\n dtype=svecs.dtype)\n for ii in range(svecs.shape[1]):\n vecs[:, ii] = variables.make_full_vec(svecs[:, ii])\n\n # Save the eigenvectors.\n out = {}\n state = pb.create_state()\n\n pp_name = pb.conf.options.get('post_process_hook')\n pp = getattr(pb.conf.funmod, pp_name if pp_name is not None else '',\n lambda out, *args, **kwargs: out)\n\n for ii in range(svecs.shape[1]):\n state.set_full(vecs[:, ii])\n aux = state.create_output_dict()\n aux2 = {}\n pp(aux2, pb, state, wmag=wmag, wdir=wdir)\n aux.update(convert_complex_output(aux2))\n out.update({key + '%03d' % ii : aux[key] for key in aux})\n\n pb.save_state(filename, out=out)\n\ndef assemble_matrices(define, mod, pars, set_wave_dir, options, wdir=None):\n \"\"\"\n Assemble the blocks of dispersion eigenvalue problem matrices.\n \"\"\"\n define_dict = define(filename_mesh=options.mesh_filename,\n pars=pars,\n approx_order=options.order,\n refinement_level=options.refine,\n solver_conf=options.solver_conf,\n plane=options.plane,\n post_process=options.post_process,\n **options.define_kwargs)\n\n conf = ProblemConf.from_dict(define_dict, mod)\n\n pb = Problem.from_conf(conf)\n pb.dispersion_options = options\n pb.set_output_dir(options.output_dir)\n dim = pb.domain.shape.dim\n\n # Set the normalized wave vector direction to the material(s).\n if wdir is None:\n wdir = nm.asarray(options.wave_dir[:dim], dtype=nm.float64)\n wdir = wdir / nm.linalg.norm(wdir)\n set_wave_dir(pb, wdir)\n\n bbox = pb.domain.mesh.get_bounding_box()\n size = (bbox[1] - bbox[0]).max()\n scaling0 = apply_unit_multipliers([1.0], ['length'],\n options.unit_multipliers)[0]\n scaling = scaling0\n if options.mesh_size is not None:\n scaling *= options.mesh_size / size\n output('scaling factor of periodic cell mesh coordinates:', scaling)\n output('new mesh size with applied unit multipliers:', scaling * size)\n pb.domain.mesh.coors[:] *= scaling\n pb.set_mesh_coors(pb.domain.mesh.coors, update_fields=True)\n\n bzone = 2.0 * nm.pi / (scaling * size)\n output('1. Brillouin zone size:', bzone * scaling0)\n "},"completion":{"kind":"string","value":"output('1. Brillouin zone size with applied unit multipliers:', bzone)"},"api":{"kind":"string","value":"sfepy.base.base.output"}}},{"rowIdx":67,"cells":{"prompt":{"kind":"string","value":"#!/usr/bin/env python\n\"\"\"\nDispersion analysis of a heterogeneous finite scale periodic cell.\n\nThe periodic cell mesh has to contain two subdomains Y1 (with the cell ids 1),\nY2 (with the cell ids 2), so that different material properties can be defined\nin each of the subdomains (see ``--pars`` option). The command line parameters\ncan be given in any consistent unit set, for example the basic SI units. The\n``--unit-multipliers`` option can be used to rescale the input units to ones\nmore suitable to the simulation, for example to prevent having different\nmatrix blocks with large differences of matrix entries magnitudes. The results\nare then in the rescaled units.\n\nUsage Examples\n--------------\n\nDefault material parameters, a square periodic cell with a spherical inclusion,\nlogs also standard pressure dilatation and shear waves, no eigenvectors::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only\n\nAs above, with custom eigenvalue solver parameters, and different number of\neigenvalues, mesh size and units used in the calculation::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --solver-conf=\"kind='eig.scipy', method='eigsh', tol=1e-10, maxiter=1000, which='LM', sigma=0\" --log-std-waves -n 5 --range=0,640,101 --mode=omega --unit-multipliers=1e-6,1e-2,1e-3 --mesh-size=1e-2 --eigs-only\n\nDefault material parameters, a square periodic cell with a square inclusion,\nand a very small mesh to allow comparing the omega and kappa modes (full matrix\nsolver required!)::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf=\"kind='eig.scipy', method='eigh'\" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf=\"kind='eig.qevp', method='companion', mode='inverted', solver={kind='eig.scipy', method='eig'}\" --log-std-waves -n 500 --range=0,4000000,1001 --mesh-size=1e-2 --mode=kappa --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/kappa\n\nView/compare the resulting logs::\n\n python script/plot_logs.py output/omega/frequencies.txt --no-legends -g 1 -o mode-omega.png\n python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends -o mode-kappa.png\n python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends --swap-axes -o mode-kappa-t.png\n\nIn contrast to the heterogeneous square periodic cell, a homogeneous\nsquare periodic cell (the region Y2 is empty)::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_1m.mesh --solver-conf=\"kind='eig.scipy', method='eigh'\" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega-h\n\n python script/plot_logs.py output/omega-h/frequencies.txt --no-legends -g 1 -o mode-omega-h.png\n\nUse the Brillouin stepper::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves -n=60 --eigs-only --no-legends --stepper=brillouin\n\n python script/plot_logs.py output/frequencies.txt -g 0 --rc=\"'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4\" -o brillouin-stepper-kappas.png\n\n python script/plot_logs.py output/frequencies.txt -g 1 --no-legends --rc=\"'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4\" -o brillouin-stepper-omegas.png\n\nAdditional arguments can be passed to the problem configuration's\n:func:`define()` function using the ``--define-kwargs`` option. In this file,\nonly the mesh vertex separation parameter `mesh_eps` can be used::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only --define-kwargs=\"mesh_eps=1e-10\" --save-regions\n\"\"\"\nfrom __future__ import absolute_import\nimport os\nimport sys\nsys.path.append('.')\nimport gc\nfrom copy import copy\nfrom argparse import ArgumentParser, RawDescriptionHelpFormatter\n\nimport numpy as nm\nimport matplotlib.pyplot as plt\n\nfrom sfepy.base.base import import_file, output, Struct\nfrom sfepy.base.conf import dict_from_string, ProblemConf\nfrom sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options\nfrom sfepy.base.log import Log\nfrom sfepy.discrete.fem import MeshIO\nfrom sfepy.mechanics.matcoefs import stiffness_from_youngpoisson as stiffness\nimport sfepy.mechanics.matcoefs as mc\nfrom sfepy.mechanics.units import apply_unit_multipliers\nimport sfepy.discrete.fem.periodic as per\nfrom sfepy.discrete.fem.meshio import convert_complex_output\nfrom sfepy.homogenization.utils import define_box_regions\nfrom sfepy.discrete import Problem\nfrom sfepy.mechanics.tensors import get_von_mises_stress\nfrom sfepy.solvers import Solver\nfrom sfepy.solvers.ts import get_print_info, TimeStepper\nfrom sfepy.linalg.utils import output_array_stats, max_diff_csr\n\ndef apply_units(pars, unit_multipliers):\n new_pars = apply_unit_multipliers(pars,\n ['stress', 'one', 'density',\n 'stress', 'one' ,'density'],\n unit_multipliers)\n return new_pars\n\ndef compute_von_mises(out, pb, state, extend=False, wmag=None, wdir=None):\n \"\"\"\n Calculate the von Mises stress.\n \"\"\"\n stress = pb.evaluate('ev_cauchy_stress.i.Omega(m.D, u)', mode='el_avg')\n\n vms = get_von_mises_stress(stress.squeeze())\n vms.shape = (vms.shape[0], 1, 1, 1)\n out['von_mises_stress'] = Struct(name='output_data', mode='cell',\n data=vms)\n\n return out\n\ndef define(filename_mesh, pars, approx_order, refinement_level, solver_conf,\n plane='strain', post_process=False, mesh_eps=1e-8):\n io = MeshIO.any_from_filename(filename_mesh)\n bbox = io.read_bounding_box()\n dim = bbox.shape[1]\n\n options = {\n 'absolute_mesh_path' : True,\n 'refinement_level' : refinement_level,\n 'allow_empty_regions' : True,\n 'post_process_hook' : 'compute_von_mises' if post_process else None,\n }\n\n fields = {\n 'displacement': ('complex', dim, 'Omega', approx_order),\n }\n\n young1, poisson1, density1, young2, poisson2, density2 = pars\n materials = {\n 'm' : ({\n 'D' : {'Y1' : stiffness(dim, young=young1, poisson=poisson1,\n plane=plane),\n 'Y2' : stiffness(dim, young=young2, poisson=poisson2,\n plane=plane)},\n 'density' : {'Y1' : density1, 'Y2' : density2},\n },),\n 'wave' : 'get_wdir',\n }\n\n variables = {\n 'u' : ('unknown field', 'displacement', 0),\n 'v' : ('test field', 'displacement', 'u'),\n }\n\n regions = {\n 'Omega' : 'all',\n 'Y1': 'cells of group 1',\n 'Y2': 'cells of group 2',\n }\n regions.update(define_box_regions(dim,\n bbox[0], bbox[1], mesh_eps))\n\n ebcs = {\n }\n\n if dim == 3:\n epbcs = {\n 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},\n 'match_x_plane'),\n 'periodic_y' : (['Near', 'Far'], {'u.all' : 'u.all'},\n 'match_y_plane'),\n 'periodic_z' : (['Top', 'Bottom'], {'u.all' : 'u.all'},\n 'match_z_plane'),\n }\n else:\n epbcs = {\n 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},\n 'match_y_line'),\n 'periodic_y' : (['Bottom', 'Top'], {'u.all' : 'u.all'},\n 'match_x_line'),\n }\n\n per.set_accuracy(mesh_eps)\n functions = {\n 'match_x_plane' : (per.match_x_plane,),\n 'match_y_plane' : (per.match_y_plane,),\n 'match_z_plane' : (per.match_z_plane,),\n 'match_x_line' : (per.match_x_line,),\n 'match_y_line' : (per.match_y_line,),\n 'get_wdir' : (get_wdir,),\n }\n\n integrals = {\n 'i' : 2 * approx_order,\n }\n\n equations = {\n 'K' : 'dw_lin_elastic.i.Omega(m.D, v, u)',\n 'S' : 'dw_elastic_wave.i.Omega(m.D, wave.vec, v, u)',\n 'R' : \"\"\"1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, u, v)\n - 1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, v, u)\"\"\",\n 'M' : 'dw_volume_dot.i.Omega(m.density, v, u)',\n }\n\n solver_0 = solver_conf.copy()\n solver_0['name'] = 'eig'\n\n return locals()\n\ndef get_wdir(ts, coors, mode=None,\n equations=None, term=None, problem=None, wdir=None, **kwargs):\n if mode == 'special':\n return {'vec' : wdir}\n\ndef set_wave_dir(pb, wdir):\n materials = pb.get_materials()\n wave_mat = materials['wave']\n wave_mat.set_extra_args(wdir=wdir)\n\ndef save_materials(output_dir, pb, options):\n stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n young, poisson = mc.youngpoisson_from_stiffness(stiffness,\n plane=options.plane)\n density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n\n out = {}\n out['young'] = Struct(name='young', mode='cell',\n data=young[..., None, None])\n out['poisson'] = Struct(name='poisson', mode='cell',\n data=poisson[..., None, None])\n out['density'] = Struct(name='density', mode='cell', data=density)\n materials_filename = os.path.join(output_dir, 'materials.vtk')\n pb.save_state(materials_filename, out=out)\n\ndef get_std_wave_fun(pb, options):\n stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n young, poisson = mc.youngpoisson_from_stiffness(stiffness,\n plane=options.plane)\n density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n\n lam, mu = mc.lame_from_youngpoisson(young, poisson,\n plane=options.plane)\n alam = nm.average(lam)\n amu = nm.average(mu)\n adensity = nm.average(density)\n\n cp = nm.sqrt((alam + 2.0 * amu) / adensity)\n cs = nm.sqrt(amu / adensity)\n output('average p-wave speed:', cp)\n output('average shear wave speed:', cs)\n\n log_names = [r'$\\omega_p$', r'$\\omega_s$']\n log_plot_kwargs = [{'ls' : '--', 'color' : 'k'},\n {'ls' : '--', 'color' : 'gray'}]\n\n if options.mode == 'omega':\n fun = lambda wmag, wdir: (cp * wmag, cs * wmag)\n\n else:\n fun = lambda wmag, wdir: (wmag / cp, wmag / cs)\n\n return fun, log_names, log_plot_kwargs\n\ndef get_stepper(rng, pb, options):\n if options.stepper == 'linear':\n stepper = TimeStepper(rng[0], rng[1], dt=None, n_step=rng[2])\n return stepper\n\n bbox = pb.domain.mesh.get_bounding_box()\n\n bzone = 2.0 * nm.pi / (bbox[1] - bbox[0])\n\n num = rng[2] // 3\n\n class BrillouinStepper(Struct):\n \"\"\"\n Step over 1. Brillouin zone in xy plane.\n \"\"\"\n def __init__(self, t0, t1, dt=None, n_step=None, step=None, **kwargs):\n Struct.__init__(self, t0=t0, t1=t1, dt=dt, n_step=n_step, step=step)\n\n self.n_digit, self.format, self.suffix = get_print_info(self.n_step)\n\n def __iter__(self):\n ts = TimeStepper(0, bzone[0], dt=None, n_step=num)\n for ii, val in ts:\n yield ii, val, nm.array([1.0, 0.0])\n if ii == (num-2): break\n\n ts = TimeStepper(0, bzone[1], dt=None, n_step=num)\n for ii, k1 in ts:\n wdir = nm.array([bzone[0], k1])\n val = nm.linalg.norm(wdir)\n wdir = wdir / val\n yield num + ii, val, wdir\n if ii == (num-2): break\n\n wdir = nm.array([bzone[0], bzone[1]])\n val = nm.linalg.norm(wdir)\n wdir = wdir / val\n ts = TimeStepper(0, 1, dt=None, n_step=num)\n for ii, _ in ts:\n yield 2 * num + ii, val * (1.0 - float(ii)/(num-1)), wdir\n\n stepper = BrillouinStepper(0, 1, n_step=rng[2])\n\n return stepper\n\ndef save_eigenvectors(filename, svecs, wmag, wdir, pb):\n if svecs is None: return\n\n variables = pb.get_variables()\n # Make full eigenvectors (add DOFs fixed by boundary conditions).\n vecs = nm.empty((variables.di.ptr[-1], svecs.shape[1]),\n dtype=svecs.dtype)\n for ii in range(svecs.shape[1]):\n vecs[:, ii] = variables.make_full_vec(svecs[:, ii])\n\n # Save the eigenvectors.\n out = {}\n state = pb.create_state()\n\n pp_name = pb.conf.options.get('post_process_hook')\n pp = getattr(pb.conf.funmod, pp_name if pp_name is not None else '',\n lambda out, *args, **kwargs: out)\n\n for ii in range(svecs.shape[1]):\n state.set_full(vecs[:, ii])\n aux = state.create_output_dict()\n aux2 = {}\n pp(aux2, pb, state, wmag=wmag, wdir=wdir)\n aux.update(convert_complex_output(aux2))\n out.update({key + '%03d' % ii : aux[key] for key in aux})\n\n pb.save_state(filename, out=out)\n\ndef assemble_matrices(define, mod, pars, set_wave_dir, options, wdir=None):\n \"\"\"\n Assemble the blocks of dispersion eigenvalue problem matrices.\n \"\"\"\n define_dict = define(filename_mesh=options.mesh_filename,\n pars=pars,\n approx_order=options.order,\n refinement_level=options.refine,\n solver_conf=options.solver_conf,\n plane=options.plane,\n post_process=options.post_process,\n **options.define_kwargs)\n\n conf = ProblemConf.from_dict(define_dict, mod)\n\n pb = Problem.from_conf(conf)\n pb.dispersion_options = options\n pb.set_output_dir(options.output_dir)\n dim = pb.domain.shape.dim\n\n # Set the normalized wave vector direction to the material(s).\n if wdir is None:\n wdir = nm.asarray(options.wave_dir[:dim], dtype=nm.float64)\n wdir = wdir / nm.linalg.norm(wdir)\n set_wave_dir(pb, wdir)\n\n bbox = pb.domain.mesh.get_bounding_box()\n size = (bbox[1] - bbox[0]).max()\n scaling0 = apply_unit_multipliers([1.0], ['length'],\n options.unit_multipliers)[0]\n scaling = scaling0\n if options.mesh_size is not None:\n scaling *= options.mesh_size / size\n output('scaling factor of periodic cell mesh coordinates:', scaling)\n output('new mesh size with applied unit multipliers:', scaling * size)\n pb.domain.mesh.coors[:] *= scaling\n pb.set_mesh_coors(pb.domain.mesh.coors, update_fields=True)\n\n bzone = 2.0 * nm.pi / (scaling * size)\n output('1. Brillouin zone size:', bzone * scaling0)\n output('1. Brillouin zone size with applied unit multipliers:', bzone)\n\n pb.time_update()\n pb.update_materials()\n\n # Assemble the matrices.\n mtxs = {}\n for key, eq in pb.equations.iteritems():\n mtxs[key] = mtx = pb.mtx_a.copy()\n mtx = eq.evaluate(mode='weak', dw_mode='matrix', asm_obj=mtx)\n mtx.eliminate_zeros()\n output_array_stats(mtx.data, 'nonzeros in %s' % key)\n\n output('symmetry checks:')\n output('%s - %s^T:' % (key, key), max_diff_csr(mtx, mtx.T))\n output('%s - %s^H:' % (key, key), max_diff_csr(mtx, mtx.H))\n\n return pb, wdir, bzone, mtxs\n\ndef setup_n_eigs(options, pb, mtxs):\n \"\"\"\n Setup the numbers of eigenvalues based on options and numbers of DOFs.\n \"\"\"\n solver_n_eigs = n_eigs = options.n_eigs\n n_dof = mtxs['K'].shape[0]\n if options.mode == 'omega':\n if options.n_eigs > n_dof:\n n_eigs = n_dof\n solver_n_eigs = None\n\n else:\n if options.n_eigs > 2 * n_dof:\n n_eigs = 2 * n_dof\n solver_n_eigs = None\n\n return solver_n_eigs, n_eigs\n\ndef build_evp_matrices(mtxs, val, mode, pb):\n \"\"\"\n Build the matrices of the dispersion eigenvalue problem.\n \"\"\"\n if mode == 'omega':\n mtx_a = mtxs['K'] + val**2 * mtxs['S'] + val * mtxs['R']\n output('A - A^H:', max_diff_csr(mtx_a, mtx_a.H))\n\n evp_mtxs = (mtx_a, mtxs['M'])\n\n else:\n evp_mtxs = (mtxs['S'], mtxs['R'], mtxs['K'] - val**2 * mtxs['M'])\n\n return evp_mtxs\n\ndef process_evp_results(eigs, svecs, val, wdir, bzone, pb, mtxs, options,\n std_wave_fun=None):\n \"\"\"\n Transform eigenvalues to either omegas or kappas, depending on `mode`.\n Transform eigenvectors, if available, depending on `mode`.\n Return also the values to log.\n \"\"\"\n if options.mode == 'omega':\n omegas = nm.sqrt(eigs)\n\n output('eigs, omegas:')\n for ii, om in enumerate(omegas):\n output('{:>3}. {: .10e}, {:.10e}'.format(ii, eigs[ii], om))\n\n if options.stepper == 'linear':\n out = tuple(eigs) + tuple(omegas)\n\n else:\n out = tuple(val * wdir) + tuple(omegas)\n\n if std_wave_fun is not None:\n out = out + std_wave_fun(val, wdir)\n\n return omegas, svecs, out\n\n else:\n kappas = eigs.copy()\n rks = kappas.copy()\n\n # Mask modes far from 1. Brillouin zone.\n max_kappa = 1.2 * bzone\n kappas[kappas.real > max_kappa] = nm.nan\n\n # Mask non-physical modes.\n kappas[kappas.real < 0] = nm.nan\n kappas[nm.abs(kappas.imag) > 1e-10] = nm.nan\n out = tuple(kappas.real)\n\n output('raw kappas, masked real part:',)\n for ii, kr in enumerate(kappas.real):\n output('{:>3}. {: 23.5e}, {:.10e}'.format(ii, rks[ii], kr))\n\n if svecs is not None:\n n_dof = mtxs['K'].shape[0]\n # Select only vectors corresponding to physical modes.\n ii = nm.isfinite(kappas.real)\n svecs = svecs[:n_dof, ii]\n\n if std_wave_fun is not None:\n out = out + tuple(ii if ii <= max_kappa else nm.nan\n for ii in std_wave_fun(val, wdir))\n\n return kappas, svecs, out\n\nhelps = {\n 'pars' :\n 'material parameters in Y1, Y2 subdomains in basic units'\n ' [default: %(default)s]',\n 'conf' :\n 'if given, an alternative problem description file with apply_units() and'\n ' define() functions [default: %(default)s]',\n 'define_kwargs' : 'additional keyword arguments passed to define()',\n 'mesh_size' :\n 'desired mesh size (max. of bounding box dimensions) in basic units'\n ' - the input periodic cell mesh is rescaled to this size'\n ' [default: %(default)s]',\n 'unit_multipliers' :\n 'basic unit multipliers (time, length, mass) [default: %(default)s]',\n 'plane' :\n 'for 2D problems, plane strain or stress hypothesis selection'\n ' [default: %(default)s]',\n 'wave_dir' : 'the wave vector direction (will be normalized)'\n ' [default: %(default)s]',\n 'mode' : 'solution mode: omega = solve a generalized EVP for omega,'\n ' kappa = solve a quadratic generalized EVP for kappa'\n ' [default: %(default)s]',\n 'stepper' : 'the range stepper. For \"brillouin\", only the number'\n ' of items from --range is used'\n ' [default: %(default)s]',\n 'range' : 'the wave vector magnitude / frequency range'\n ' (like numpy.linspace) depending on the mode option'\n ' [default: %(default)s]',\n 'order' : 'displacement field approximation order [default: %(default)s]',\n 'refine' : 'number of uniform mesh refinements [default: %(default)s]',\n 'n_eigs' : 'the number of eigenvalues to compute [default: %(default)s]',\n 'eigs_only' : 'compute only eigenvalues, not eigenvectors',\n 'post_process' : 'post-process eigenvectors',\n 'solver_conf' : 'eigenvalue problem solver configuration options'\n ' [default: %(default)s]',\n 'save_regions' : 'save defined regions into'\n ' /regions.vtk',\n 'save_materials' : 'save material parameters into'\n ' /materials.vtk',\n 'log_std_waves' : 'log also standard pressure dilatation and shear waves',\n 'no_legends' :\n 'do not show legends in the log plots',\n 'no_show' :\n 'do not show the log figure',\n 'silent' : 'do not print messages to screen',\n 'clear' :\n 'clear old solution files from output directory',\n 'output_dir' :\n 'output directory [default: %(default)s]',\n 'mesh_filename' :\n 'input periodic cell mesh file name [default: %(default)s]',\n}\n\ndef main():\n # Aluminium and epoxy.\n default_pars = '70e9,0.35,2.799e3, 3.8e9,0.27,1.142e3'\n default_solver_conf = (\"kind='eig.scipy',method='eigsh',tol=1.0e-5,\"\n \"maxiter=1000,which='LM',sigma=0.0\")\n\n parser = ArgumentParser(description=__doc__,\n formatter_class=RawDescriptionHelpFormatter)\n parser.add_argument('--pars', metavar='young1,poisson1,density1'\n ',young2,poisson2,density2',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='pars',\n default=default_pars, help=helps['pars'])\n parser.add_argument('--conf', metavar='filename',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='conf',\n default=None, help=helps['conf'])\n parser.add_argument('--define-kwargs', metavar='dict-like',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='define_kwargs',\n default=None, help=helps['define_kwargs'])\n parser.add_argument('--mesh-size', type=float, metavar='float',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='mesh_size',\n default=None, help=helps['mesh_size'])\n parser.add_argument('--unit-multipliers',\n metavar='c_time,c_length,c_mass',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='unit_multipliers',\n default='1.0,1.0,1.0', help=helps['unit_multipliers'])\n parser.add_argument('--plane', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='plane',\n choices=['strain', 'stress'],\n default='strain', help=helps['plane'])\n parser.add_argument('--wave-dir', metavar='float,float[,float]',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='wave_dir',\n default='1.0,0.0,0.0', help=helps['wave_dir'])\n parser.add_argument('--mode', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='mode',\n choices=['omega', 'kappa'],\n default='omega', help=helps['mode'])\n parser.add_argument('--stepper', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='stepper',\n choices=['linear', 'brillouin'],\n default='linear', help=helps['stepper'])\n parser.add_argument('--range', metavar='start,stop,count',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='range',\n default='0,6.4,33', help=helps['range'])\n parser.add_argument('--order', metavar='int', type=int,\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='order',\n default=1, help=helps['order'])\n parser.add_argument('--refine', metavar='int', type=int,\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='refine',\n default=0, help=helps['refine'])\n parser.add_argument('-n', '--n-eigs', metavar='int', type=int,\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='n_eigs',\n default=6, help=helps['n_eigs'])\n group = parser.add_mutually_exclusive_group()\n group.add_argument('--eigs-only',\n action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='eigs_only',\n default=False, help=helps['eigs_only'])\n group.add_argument('--post-process',\n action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='post_process',\n default=False, help=helps['post_process'])\n parser.add_argument('--solver-conf', metavar='dict-like',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='solver_conf',\n default=default_solver_conf, help=helps['solver_conf'])\n parser.add_argument('--save-regions',\n action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='save_regions',\n default=False, help=helps['save_regions'])\n parser.add_argument('--save-materials',\n action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='save_materials',\n default=False, help=helps['save_materials'])\n parser.add_argument('--log-std-waves',\n action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='log_std_waves',\n default=False, help=helps['log_std_waves'])\n parser.add_argument('--no-legends',\n action="https://huggingface.co/datasets/luna-code/sfepy/store_false", dest='show_legends',\n default=True, help=helps['no_legends'])\n parser.add_argument('--no-show',\n action="https://huggingface.co/datasets/luna-code/sfepy/store_false", dest='show',\n default=True, help=helps['no_show'])\n parser.add_argument('--silent',\n action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='silent',\n default=False, help=helps['silent'])\n parser.add_argument('-c', '--clear',\n action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='clear',\n default=False, help=helps['clear'])\n parser.add_argument('-o', '--output-dir', metavar='path',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='output_dir',\n default='output', help=helps['output_dir'])\n parser.add_argument('mesh_filename', default='',\n help=helps['mesh_filename'])\n options = parser.parse_args()\n\n output_dir = options.output_dir\n\n output.set_output(filename=os.path.join(output_dir,'output_log.txt'),\n combined=options.silent == False)\n\n if options.conf is not None:\n mod = import_file(options.conf)\n\n else:\n mod = sys.modules[__name__]\n\n apply_units = mod.apply_units\n define = mod.define\n set_wave_dir = mod.set_wave_dir\n setup_n_eigs = mod.setup_n_eigs\n build_evp_matrices = mod.build_evp_matrices\n save_materials = mod.save_materials\n get_std_wave_fun = mod.get_std_wave_fun\n get_stepper = mod.get_stepper\n process_evp_results = mod.process_evp_results\n\n options.pars = [float(ii) for ii in options.pars.split(',')]\n options.unit_multipliers = [float(ii)\n for ii in options.unit_multipliers.split(',')]\n options.wave_dir = [float(ii)\n for ii in options.wave_dir.split(',')]\n aux = options.range.split(',')\n options.range = [float(aux[0]), float(aux[1]), int(aux[2])]\n options.solver_conf = "},"completion":{"kind":"string","value":"dict_from_string(options.solver_conf)"},"api":{"kind":"string","value":"sfepy.base.conf.dict_from_string"}}},{"rowIdx":68,"cells":{"prompt":{"kind":"string","value":"#!/usr/bin/env python\n\"\"\"\nDispersion analysis of a heterogeneous finite scale periodic cell.\n\nThe periodic cell mesh has to contain two subdomains Y1 (with the cell ids 1),\nY2 (with the cell ids 2), so that different material properties can be defined\nin each of the subdomains (see ``--pars`` option). The command line parameters\ncan be given in any consistent unit set, for example the basic SI units. The\n``--unit-multipliers`` option can be used to rescale the input units to ones\nmore suitable to the simulation, for example to prevent having different\nmatrix blocks with large differences of matrix entries magnitudes. The results\nare then in the rescaled units.\n\nUsage Examples\n--------------\n\nDefault material parameters, a square periodic cell with a spherical inclusion,\nlogs also standard pressure dilatation and shear waves, no eigenvectors::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only\n\nAs above, with custom eigenvalue solver parameters, and different number of\neigenvalues, mesh size and units used in the calculation::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --solver-conf=\"kind='eig.scipy', method='eigsh', tol=1e-10, maxiter=1000, which='LM', sigma=0\" --log-std-waves -n 5 --range=0,640,101 --mode=omega --unit-multipliers=1e-6,1e-2,1e-3 --mesh-size=1e-2 --eigs-only\n\nDefault material parameters, a square periodic cell with a square inclusion,\nand a very small mesh to allow comparing the omega and kappa modes (full matrix\nsolver required!)::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf=\"kind='eig.scipy', method='eigh'\" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf=\"kind='eig.qevp', method='companion', mode='inverted', solver={kind='eig.scipy', method='eig'}\" --log-std-waves -n 500 --range=0,4000000,1001 --mesh-size=1e-2 --mode=kappa --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/kappa\n\nView/compare the resulting logs::\n\n python script/plot_logs.py output/omega/frequencies.txt --no-legends -g 1 -o mode-omega.png\n python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends -o mode-kappa.png\n python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends --swap-axes -o mode-kappa-t.png\n\nIn contrast to the heterogeneous square periodic cell, a homogeneous\nsquare periodic cell (the region Y2 is empty)::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_1m.mesh --solver-conf=\"kind='eig.scipy', method='eigh'\" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega-h\n\n python script/plot_logs.py output/omega-h/frequencies.txt --no-legends -g 1 -o mode-omega-h.png\n\nUse the Brillouin stepper::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves -n=60 --eigs-only --no-legends --stepper=brillouin\n\n python script/plot_logs.py output/frequencies.txt -g 0 --rc=\"'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4\" -o brillouin-stepper-kappas.png\n\n python script/plot_logs.py output/frequencies.txt -g 1 --no-legends --rc=\"'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4\" -o brillouin-stepper-omegas.png\n\nAdditional arguments can be passed to the problem configuration's\n:func:`define()` function using the ``--define-kwargs`` option. In this file,\nonly the mesh vertex separation parameter `mesh_eps` can be used::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only --define-kwargs=\"mesh_eps=1e-10\" --save-regions\n\"\"\"\nfrom __future__ import absolute_import\nimport os\nimport sys\nsys.path.append('.')\nimport gc\nfrom copy import copy\nfrom argparse import ArgumentParser, RawDescriptionHelpFormatter\n\nimport numpy as nm\nimport matplotlib.pyplot as plt\n\nfrom sfepy.base.base import import_file, output, Struct\nfrom sfepy.base.conf import dict_from_string, ProblemConf\nfrom sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options\nfrom sfepy.base.log import Log\nfrom sfepy.discrete.fem import MeshIO\nfrom sfepy.mechanics.matcoefs import stiffness_from_youngpoisson as stiffness\nimport sfepy.mechanics.matcoefs as mc\nfrom sfepy.mechanics.units import apply_unit_multipliers\nimport sfepy.discrete.fem.periodic as per\nfrom sfepy.discrete.fem.meshio import convert_complex_output\nfrom sfepy.homogenization.utils import define_box_regions\nfrom sfepy.discrete import Problem\nfrom sfepy.mechanics.tensors import get_von_mises_stress\nfrom sfepy.solvers import Solver\nfrom sfepy.solvers.ts import get_print_info, TimeStepper\nfrom sfepy.linalg.utils import output_array_stats, max_diff_csr\n\ndef apply_units(pars, unit_multipliers):\n new_pars = apply_unit_multipliers(pars,\n ['stress', 'one', 'density',\n 'stress', 'one' ,'density'],\n unit_multipliers)\n return new_pars\n\ndef compute_von_mises(out, pb, state, extend=False, wmag=None, wdir=None):\n \"\"\"\n Calculate the von Mises stress.\n \"\"\"\n stress = pb.evaluate('ev_cauchy_stress.i.Omega(m.D, u)', mode='el_avg')\n\n vms = get_von_mises_stress(stress.squeeze())\n vms.shape = (vms.shape[0], 1, 1, 1)\n out['von_mises_stress'] = Struct(name='output_data', mode='cell',\n data=vms)\n\n return out\n\ndef define(filename_mesh, pars, approx_order, refinement_level, solver_conf,\n plane='strain', post_process=False, mesh_eps=1e-8):\n io = MeshIO.any_from_filename(filename_mesh)\n bbox = io.read_bounding_box()\n dim = bbox.shape[1]\n\n options = {\n 'absolute_mesh_path' : True,\n 'refinement_level' : refinement_level,\n 'allow_empty_regions' : True,\n 'post_process_hook' : 'compute_von_mises' if post_process else None,\n }\n\n fields = {\n 'displacement': ('complex', dim, 'Omega', approx_order),\n }\n\n young1, poisson1, density1, young2, poisson2, density2 = pars\n materials = {\n 'm' : ({\n 'D' : {'Y1' : stiffness(dim, young=young1, poisson=poisson1,\n plane=plane),\n 'Y2' : stiffness(dim, young=young2, poisson=poisson2,\n plane=plane)},\n 'density' : {'Y1' : density1, 'Y2' : density2},\n },),\n 'wave' : 'get_wdir',\n }\n\n variables = {\n 'u' : ('unknown field', 'displacement', 0),\n 'v' : ('test field', 'displacement', 'u'),\n }\n\n regions = {\n 'Omega' : 'all',\n 'Y1': 'cells of group 1',\n 'Y2': 'cells of group 2',\n }\n regions.update(define_box_regions(dim,\n bbox[0], bbox[1], mesh_eps))\n\n ebcs = {\n }\n\n if dim == 3:\n epbcs = {\n 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},\n 'match_x_plane'),\n 'periodic_y' : (['Near', 'Far'], {'u.all' : 'u.all'},\n 'match_y_plane'),\n 'periodic_z' : (['Top', 'Bottom'], {'u.all' : 'u.all'},\n 'match_z_plane'),\n }\n else:\n epbcs = {\n 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},\n 'match_y_line'),\n 'periodic_y' : (['Bottom', 'Top'], {'u.all' : 'u.all'},\n 'match_x_line'),\n }\n\n per.set_accuracy(mesh_eps)\n functions = {\n 'match_x_plane' : (per.match_x_plane,),\n 'match_y_plane' : (per.match_y_plane,),\n 'match_z_plane' : (per.match_z_plane,),\n 'match_x_line' : (per.match_x_line,),\n 'match_y_line' : (per.match_y_line,),\n 'get_wdir' : (get_wdir,),\n }\n\n integrals = {\n 'i' : 2 * approx_order,\n }\n\n equations = {\n 'K' : 'dw_lin_elastic.i.Omega(m.D, v, u)',\n 'S' : 'dw_elastic_wave.i.Omega(m.D, wave.vec, v, u)',\n 'R' : \"\"\"1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, u, v)\n - 1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, v, u)\"\"\",\n 'M' : 'dw_volume_dot.i.Omega(m.density, v, u)',\n }\n\n solver_0 = solver_conf.copy()\n solver_0['name'] = 'eig'\n\n return locals()\n\ndef get_wdir(ts, coors, mode=None,\n equations=None, term=None, problem=None, wdir=None, **kwargs):\n if mode == 'special':\n return {'vec' : wdir}\n\ndef set_wave_dir(pb, wdir):\n materials = pb.get_materials()\n wave_mat = materials['wave']\n wave_mat.set_extra_args(wdir=wdir)\n\ndef save_materials(output_dir, pb, options):\n stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n young, poisson = mc.youngpoisson_from_stiffness(stiffness,\n plane=options.plane)\n density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n\n out = {}\n out['young'] = Struct(name='young', mode='cell',\n data=young[..., None, None])\n out['poisson'] = Struct(name='poisson', mode='cell',\n data=poisson[..., None, None])\n out['density'] = Struct(name='density', mode='cell', data=density)\n materials_filename = os.path.join(output_dir, 'materials.vtk')\n pb.save_state(materials_filename, out=out)\n\ndef get_std_wave_fun(pb, options):\n stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n young, poisson = mc.youngpoisson_from_stiffness(stiffness,\n plane=options.plane)\n density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n\n lam, mu = mc.lame_from_youngpoisson(young, poisson,\n plane=options.plane)\n alam = nm.average(lam)\n amu = nm.average(mu)\n adensity = nm.average(density)\n\n cp = nm.sqrt((alam + 2.0 * amu) / adensity)\n cs = nm.sqrt(amu / adensity)\n output('average p-wave speed:', cp)\n output('average shear wave speed:', cs)\n\n log_names = [r'$\\omega_p$', r'$\\omega_s$']\n log_plot_kwargs = [{'ls' : '--', 'color' : 'k'},\n {'ls' : '--', 'color' : 'gray'}]\n\n if options.mode == 'omega':\n fun = lambda wmag, wdir: (cp * wmag, cs * wmag)\n\n else:\n fun = lambda wmag, wdir: (wmag / cp, wmag / cs)\n\n return fun, log_names, log_plot_kwargs\n\ndef get_stepper(rng, pb, options):\n if options.stepper == 'linear':\n stepper = TimeStepper(rng[0], rng[1], dt=None, n_step=rng[2])\n return stepper\n\n bbox = pb.domain.mesh.get_bounding_box()\n\n bzone = 2.0 * nm.pi / (bbox[1] - bbox[0])\n\n num = rng[2] // 3\n\n class BrillouinStepper(Struct):\n \"\"\"\n Step over 1. Brillouin zone in xy plane.\n \"\"\"\n def __init__(self, t0, t1, dt=None, n_step=None, step=None, **kwargs):\n Struct.__init__(self, t0=t0, t1=t1, dt=dt, n_step=n_step, step=step)\n\n self.n_digit, self.format, self.suffix = get_print_info(self.n_step)\n\n def __iter__(self):\n ts = TimeStepper(0, bzone[0], dt=None, n_step=num)\n for ii, val in ts:\n yield ii, val, nm.array([1.0, 0.0])\n if ii == (num-2): break\n\n ts = TimeStepper(0, bzone[1], dt=None, n_step=num)\n for ii, k1 in ts:\n wdir = nm.array([bzone[0], k1])\n val = nm.linalg.norm(wdir)\n wdir = wdir / val\n yield num + ii, val, wdir\n if ii == (num-2): break\n\n wdir = nm.array([bzone[0], bzone[1]])\n val = nm.linalg.norm(wdir)\n wdir = wdir / val\n ts = TimeStepper(0, 1, dt=None, n_step=num)\n for ii, _ in ts:\n yield 2 * num + ii, val * (1.0 - float(ii)/(num-1)), wdir\n\n stepper = BrillouinStepper(0, 1, n_step=rng[2])\n\n return stepper\n\ndef save_eigenvectors(filename, svecs, wmag, wdir, pb):\n if svecs is None: return\n\n variables = pb.get_variables()\n # Make full eigenvectors (add DOFs fixed by boundary conditions).\n vecs = nm.empty((variables.di.ptr[-1], svecs.shape[1]),\n dtype=svecs.dtype)\n for ii in range(svecs.shape[1]):\n vecs[:, ii] = variables.make_full_vec(svecs[:, ii])\n\n # Save the eigenvectors.\n out = {}\n state = pb.create_state()\n\n pp_name = pb.conf.options.get('post_process_hook')\n pp = getattr(pb.conf.funmod, pp_name if pp_name is not None else '',\n lambda out, *args, **kwargs: out)\n\n for ii in range(svecs.shape[1]):\n state.set_full(vecs[:, ii])\n aux = state.create_output_dict()\n aux2 = {}\n pp(aux2, pb, state, wmag=wmag, wdir=wdir)\n aux.update(convert_complex_output(aux2))\n out.update({key + '%03d' % ii : aux[key] for key in aux})\n\n pb.save_state(filename, out=out)\n\ndef assemble_matrices(define, mod, pars, set_wave_dir, options, wdir=None):\n \"\"\"\n Assemble the blocks of dispersion eigenvalue problem matrices.\n \"\"\"\n define_dict = define(filename_mesh=options.mesh_filename,\n pars=pars,\n approx_order=options.order,\n refinement_level=options.refine,\n solver_conf=options.solver_conf,\n plane=options.plane,\n post_process=options.post_process,\n **options.define_kwargs)\n\n conf = ProblemConf.from_dict(define_dict, mod)\n\n pb = Problem.from_conf(conf)\n pb.dispersion_options = options\n pb.set_output_dir(options.output_dir)\n dim = pb.domain.shape.dim\n\n # Set the normalized wave vector direction to the material(s).\n if wdir is None:\n wdir = nm.asarray(options.wave_dir[:dim], dtype=nm.float64)\n wdir = wdir / nm.linalg.norm(wdir)\n set_wave_dir(pb, wdir)\n\n bbox = pb.domain.mesh.get_bounding_box()\n size = (bbox[1] - bbox[0]).max()\n scaling0 = apply_unit_multipliers([1.0], ['length'],\n options.unit_multipliers)[0]\n scaling = scaling0\n if options.mesh_size is not None:\n scaling *= options.mesh_size / size\n output('scaling factor of periodic cell mesh coordinates:', scaling)\n output('new mesh size with applied unit multipliers:', scaling * size)\n pb.domain.mesh.coors[:] *= scaling\n pb.set_mesh_coors(pb.domain.mesh.coors, update_fields=True)\n\n bzone = 2.0 * nm.pi / (scaling * size)\n output('1. Brillouin zone size:', bzone * scaling0)\n output('1. Brillouin zone size with applied unit multipliers:', bzone)\n\n pb.time_update()\n pb.update_materials()\n\n # Assemble the matrices.\n mtxs = {}\n for key, eq in pb.equations.iteritems():\n mtxs[key] = mtx = pb.mtx_a.copy()\n mtx = eq.evaluate(mode='weak', dw_mode='matrix', asm_obj=mtx)\n mtx.eliminate_zeros()\n output_array_stats(mtx.data, 'nonzeros in %s' % key)\n\n output('symmetry checks:')\n output('%s - %s^T:' % (key, key), max_diff_csr(mtx, mtx.T))\n output('%s - %s^H:' % (key, key), max_diff_csr(mtx, mtx.H))\n\n return pb, wdir, bzone, mtxs\n\ndef setup_n_eigs(options, pb, mtxs):\n \"\"\"\n Setup the numbers of eigenvalues based on options and numbers of DOFs.\n \"\"\"\n solver_n_eigs = n_eigs = options.n_eigs\n n_dof = mtxs['K'].shape[0]\n if options.mode == 'omega':\n if options.n_eigs > n_dof:\n n_eigs = n_dof\n solver_n_eigs = None\n\n else:\n if options.n_eigs > 2 * n_dof:\n n_eigs = 2 * n_dof\n solver_n_eigs = None\n\n return solver_n_eigs, n_eigs\n\ndef build_evp_matrices(mtxs, val, mode, pb):\n \"\"\"\n Build the matrices of the dispersion eigenvalue problem.\n \"\"\"\n if mode == 'omega':\n mtx_a = mtxs['K'] + val**2 * mtxs['S'] + val * mtxs['R']\n output('A - A^H:', max_diff_csr(mtx_a, mtx_a.H))\n\n evp_mtxs = (mtx_a, mtxs['M'])\n\n else:\n evp_mtxs = (mtxs['S'], mtxs['R'], mtxs['K'] - val**2 * mtxs['M'])\n\n return evp_mtxs\n\ndef process_evp_results(eigs, svecs, val, wdir, bzone, pb, mtxs, options,\n std_wave_fun=None):\n \"\"\"\n Transform eigenvalues to either omegas or kappas, depending on `mode`.\n Transform eigenvectors, if available, depending on `mode`.\n Return also the values to log.\n \"\"\"\n if options.mode == 'omega':\n omegas = nm.sqrt(eigs)\n\n output('eigs, omegas:')\n for ii, om in enumerate(omegas):\n output('{:>3}. {: .10e}, {:.10e}'.format(ii, eigs[ii], om))\n\n if options.stepper == 'linear':\n out = tuple(eigs) + tuple(omegas)\n\n else:\n out = tuple(val * wdir) + tuple(omegas)\n\n if std_wave_fun is not None:\n out = out + std_wave_fun(val, wdir)\n\n return omegas, svecs, out\n\n else:\n kappas = eigs.copy()\n rks = kappas.copy()\n\n # Mask modes far from 1. Brillouin zone.\n max_kappa = 1.2 * bzone\n kappas[kappas.real > max_kappa] = nm.nan\n\n # Mask non-physical modes.\n kappas[kappas.real < 0] = nm.nan\n kappas[nm.abs(kappas.imag) > 1e-10] = nm.nan\n out = tuple(kappas.real)\n\n output('raw kappas, masked real part:',)\n for ii, kr in enumerate(kappas.real):\n output('{:>3}. {: 23.5e}, {:.10e}'.format(ii, rks[ii], kr))\n\n if svecs is not None:\n n_dof = mtxs['K'].shape[0]\n # Select only vectors corresponding to physical modes.\n ii = nm.isfinite(kappas.real)\n svecs = svecs[:n_dof, ii]\n\n if std_wave_fun is not None:\n out = out + tuple(ii if ii <= max_kappa else nm.nan\n for ii in std_wave_fun(val, wdir))\n\n return kappas, svecs, out\n\nhelps = {\n 'pars' :\n 'material parameters in Y1, Y2 subdomains in basic units'\n ' [default: %(default)s]',\n 'conf' :\n 'if given, an alternative problem description file with apply_units() and'\n ' define() functions [default: %(default)s]',\n 'define_kwargs' : 'additional keyword arguments passed to define()',\n 'mesh_size' :\n 'desired mesh size (max. of bounding box dimensions) in basic units'\n ' - the input periodic cell mesh is rescaled to this size'\n ' [default: %(default)s]',\n 'unit_multipliers' :\n 'basic unit multipliers (time, length, mass) [default: %(default)s]',\n 'plane' :\n 'for 2D problems, plane strain or stress hypothesis selection'\n ' [default: %(default)s]',\n 'wave_dir' : 'the wave vector direction (will be normalized)'\n ' [default: %(default)s]',\n 'mode' : 'solution mode: omega = solve a generalized EVP for omega,'\n ' kappa = solve a quadratic generalized EVP for kappa'\n ' [default: %(default)s]',\n 'stepper' : 'the range stepper. For \"brillouin\", only the number'\n ' of items from --range is used'\n ' [default: %(default)s]',\n 'range' : 'the wave vector magnitude / frequency range'\n ' (like numpy.linspace) depending on the mode option'\n ' [default: %(default)s]',\n 'order' : 'displacement field approximation order [default: %(default)s]',\n 'refine' : 'number of uniform mesh refinements [default: %(default)s]',\n 'n_eigs' : 'the number of eigenvalues to compute [default: %(default)s]',\n 'eigs_only' : 'compute only eigenvalues, not eigenvectors',\n 'post_process' : 'post-process eigenvectors',\n 'solver_conf' : 'eigenvalue problem solver configuration options'\n ' [default: %(default)s]',\n 'save_regions' : 'save defined regions into'\n ' /regions.vtk',\n 'save_materials' : 'save material parameters into'\n ' /materials.vtk',\n 'log_std_waves' : 'log also standard pressure dilatation and shear waves',\n 'no_legends' :\n 'do not show legends in the log plots',\n 'no_show' :\n 'do not show the log figure',\n 'silent' : 'do not print messages to screen',\n 'clear' :\n 'clear old solution files from output directory',\n 'output_dir' :\n 'output directory [default: %(default)s]',\n 'mesh_filename' :\n 'input periodic cell mesh file name [default: %(default)s]',\n}\n\ndef main():\n # Aluminium and epoxy.\n default_pars = '70e9,0.35,2.799e3, 3.8e9,0.27,1.142e3'\n default_solver_conf = (\"kind='eig.scipy',method='eigsh',tol=1.0e-5,\"\n \"maxiter=1000,which='LM',sigma=0.0\")\n\n parser = ArgumentParser(description=__doc__,\n formatter_class=RawDescriptionHelpFormatter)\n parser.add_argument('--pars', metavar='young1,poisson1,density1'\n ',young2,poisson2,density2',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='pars',\n default=default_pars, help=helps['pars'])\n parser.add_argument('--conf', metavar='filename',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='conf',\n default=None, help=helps['conf'])\n parser.add_argument('--define-kwargs', metavar='dict-like',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='define_kwargs',\n default=None, help=helps['define_kwargs'])\n parser.add_argument('--mesh-size', type=float, metavar='float',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='mesh_size',\n default=None, help=helps['mesh_size'])\n parser.add_argument('--unit-multipliers',\n metavar='c_time,c_length,c_mass',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='unit_multipliers',\n default='1.0,1.0,1.0', help=helps['unit_multipliers'])\n parser.add_argument('--plane', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='plane',\n choices=['strain', 'stress'],\n default='strain', help=helps['plane'])\n parser.add_argument('--wave-dir', metavar='float,float[,float]',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='wave_dir',\n default='1.0,0.0,0.0', help=helps['wave_dir'])\n parser.add_argument('--mode', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='mode',\n choices=['omega', 'kappa'],\n default='omega', help=helps['mode'])\n parser.add_argument('--stepper', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='stepper',\n choices=['linear', 'brillouin'],\n default='linear', help=helps['stepper'])\n parser.add_argument('--range', metavar='start,stop,count',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='range',\n default='0,6.4,33', help=helps['range'])\n parser.add_argument('--order', metavar='int', type=int,\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='order',\n default=1, help=helps['order'])\n parser.add_argument('--refine', metavar='int', type=int,\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='refine',\n default=0, help=helps['refine'])\n parser.add_argument('-n', '--n-eigs', metavar='int', type=int,\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='n_eigs',\n default=6, help=helps['n_eigs'])\n group = parser.add_mutually_exclusive_group()\n group.add_argument('--eigs-only',\n action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='eigs_only',\n default=False, help=helps['eigs_only'])\n group.add_argument('--post-process',\n action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='post_process',\n default=False, help=helps['post_process'])\n parser.add_argument('--solver-conf', metavar='dict-like',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='solver_conf',\n default=default_solver_conf, help=helps['solver_conf'])\n parser.add_argument('--save-regions',\n action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='save_regions',\n default=False, help=helps['save_regions'])\n parser.add_argument('--save-materials',\n action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='save_materials',\n default=False, help=helps['save_materials'])\n parser.add_argument('--log-std-waves',\n action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='log_std_waves',\n default=False, help=helps['log_std_waves'])\n parser.add_argument('--no-legends',\n action="https://huggingface.co/datasets/luna-code/sfepy/store_false", dest='show_legends',\n default=True, help=helps['no_legends'])\n parser.add_argument('--no-show',\n action="https://huggingface.co/datasets/luna-code/sfepy/store_false", dest='show',\n default=True, help=helps['no_show'])\n parser.add_argument('--silent',\n action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='silent',\n default=False, help=helps['silent'])\n parser.add_argument('-c', '--clear',\n action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='clear',\n default=False, help=helps['clear'])\n parser.add_argument('-o', '--output-dir', metavar='path',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='output_dir',\n default='output', help=helps['output_dir'])\n parser.add_argument('mesh_filename', default='',\n help=helps['mesh_filename'])\n options = parser.parse_args()\n\n output_dir = options.output_dir\n\n output.set_output(filename=os.path.join(output_dir,'output_log.txt'),\n combined=options.silent == False)\n\n if options.conf is not None:\n mod = import_file(options.conf)\n\n else:\n mod = sys.modules[__name__]\n\n apply_units = mod.apply_units\n define = mod.define\n set_wave_dir = mod.set_wave_dir\n setup_n_eigs = mod.setup_n_eigs\n build_evp_matrices = mod.build_evp_matrices\n save_materials = mod.save_materials\n get_std_wave_fun = mod.get_std_wave_fun\n get_stepper = mod.get_stepper\n process_evp_results = mod.process_evp_results\n\n options.pars = [float(ii) for ii in options.pars.split(',')]\n options.unit_multipliers = [float(ii)\n for ii in options.unit_multipliers.split(',')]\n options.wave_dir = [float(ii)\n for ii in options.wave_dir.split(',')]\n aux = options.range.split(',')\n options.range = [float(aux[0]), float(aux[1]), int(aux[2])]\n options.solver_conf = dict_from_string(options.solver_conf)\n options.define_kwargs = "},"completion":{"kind":"string","value":"dict_from_string(options.define_kwargs)"},"api":{"kind":"string","value":"sfepy.base.conf.dict_from_string"}}},{"rowIdx":69,"cells":{"prompt":{"kind":"string","value":"#!/usr/bin/env python\n\"\"\"\nDispersion analysis of a heterogeneous finite scale periodic cell.\n\nThe periodic cell mesh has to contain two subdomains Y1 (with the cell ids 1),\nY2 (with the cell ids 2), so that different material properties can be defined\nin each of the subdomains (see ``--pars`` option). The command line parameters\ncan be given in any consistent unit set, for example the basic SI units. The\n``--unit-multipliers`` option can be used to rescale the input units to ones\nmore suitable to the simulation, for example to prevent having different\nmatrix blocks with large differences of matrix entries magnitudes. The results\nare then in the rescaled units.\n\nUsage Examples\n--------------\n\nDefault material parameters, a square periodic cell with a spherical inclusion,\nlogs also standard pressure dilatation and shear waves, no eigenvectors::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only\n\nAs above, with custom eigenvalue solver parameters, and different number of\neigenvalues, mesh size and units used in the calculation::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --solver-conf=\"kind='eig.scipy', method='eigsh', tol=1e-10, maxiter=1000, which='LM', sigma=0\" --log-std-waves -n 5 --range=0,640,101 --mode=omega --unit-multipliers=1e-6,1e-2,1e-3 --mesh-size=1e-2 --eigs-only\n\nDefault material parameters, a square periodic cell with a square inclusion,\nand a very small mesh to allow comparing the omega and kappa modes (full matrix\nsolver required!)::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf=\"kind='eig.scipy', method='eigh'\" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf=\"kind='eig.qevp', method='companion', mode='inverted', solver={kind='eig.scipy', method='eig'}\" --log-std-waves -n 500 --range=0,4000000,1001 --mesh-size=1e-2 --mode=kappa --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/kappa\n\nView/compare the resulting logs::\n\n python script/plot_logs.py output/omega/frequencies.txt --no-legends -g 1 -o mode-omega.png\n python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends -o mode-kappa.png\n python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends --swap-axes -o mode-kappa-t.png\n\nIn contrast to the heterogeneous square periodic cell, a homogeneous\nsquare periodic cell (the region Y2 is empty)::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_1m.mesh --solver-conf=\"kind='eig.scipy', method='eigh'\" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega-h\n\n python script/plot_logs.py output/omega-h/frequencies.txt --no-legends -g 1 -o mode-omega-h.png\n\nUse the Brillouin stepper::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves -n=60 --eigs-only --no-legends --stepper=brillouin\n\n python script/plot_logs.py output/frequencies.txt -g 0 --rc=\"'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4\" -o brillouin-stepper-kappas.png\n\n python script/plot_logs.py output/frequencies.txt -g 1 --no-legends --rc=\"'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4\" -o brillouin-stepper-omegas.png\n\nAdditional arguments can be passed to the problem configuration's\n:func:`define()` function using the ``--define-kwargs`` option. In this file,\nonly the mesh vertex separation parameter `mesh_eps` can be used::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only --define-kwargs=\"mesh_eps=1e-10\" --save-regions\n\"\"\"\nfrom __future__ import absolute_import\nimport os\nimport sys\nsys.path.append('.')\nimport gc\nfrom copy import copy\nfrom argparse import ArgumentParser, RawDescriptionHelpFormatter\n\nimport numpy as nm\nimport matplotlib.pyplot as plt\n\nfrom sfepy.base.base import import_file, output, Struct\nfrom sfepy.base.conf import dict_from_string, ProblemConf\nfrom sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options\nfrom sfepy.base.log import Log\nfrom sfepy.discrete.fem import MeshIO\nfrom sfepy.mechanics.matcoefs import stiffness_from_youngpoisson as stiffness\nimport sfepy.mechanics.matcoefs as mc\nfrom sfepy.mechanics.units import apply_unit_multipliers\nimport sfepy.discrete.fem.periodic as per\nfrom sfepy.discrete.fem.meshio import convert_complex_output\nfrom sfepy.homogenization.utils import define_box_regions\nfrom sfepy.discrete import Problem\nfrom sfepy.mechanics.tensors import get_von_mises_stress\nfrom sfepy.solvers import Solver\nfrom sfepy.solvers.ts import get_print_info, TimeStepper\nfrom sfepy.linalg.utils import output_array_stats, max_diff_csr\n\ndef apply_units(pars, unit_multipliers):\n new_pars = apply_unit_multipliers(pars,\n ['stress', 'one', 'density',\n 'stress', 'one' ,'density'],\n unit_multipliers)\n return new_pars\n\ndef compute_von_mises(out, pb, state, extend=False, wmag=None, wdir=None):\n \"\"\"\n Calculate the von Mises stress.\n \"\"\"\n stress = pb.evaluate('ev_cauchy_stress.i.Omega(m.D, u)', mode='el_avg')\n\n vms = get_von_mises_stress(stress.squeeze())\n vms.shape = (vms.shape[0], 1, 1, 1)\n out['von_mises_stress'] = Struct(name='output_data', mode='cell',\n data=vms)\n\n return out\n\ndef define(filename_mesh, pars, approx_order, refinement_level, solver_conf,\n plane='strain', post_process=False, mesh_eps=1e-8):\n io = MeshIO.any_from_filename(filename_mesh)\n bbox = io.read_bounding_box()\n dim = bbox.shape[1]\n\n options = {\n 'absolute_mesh_path' : True,\n 'refinement_level' : refinement_level,\n 'allow_empty_regions' : True,\n 'post_process_hook' : 'compute_von_mises' if post_process else None,\n }\n\n fields = {\n 'displacement': ('complex', dim, 'Omega', approx_order),\n }\n\n young1, poisson1, density1, young2, poisson2, density2 = pars\n materials = {\n 'm' : ({\n 'D' : {'Y1' : stiffness(dim, young=young1, poisson=poisson1,\n plane=plane),\n 'Y2' : stiffness(dim, young=young2, poisson=poisson2,\n plane=plane)},\n 'density' : {'Y1' : density1, 'Y2' : density2},\n },),\n 'wave' : 'get_wdir',\n }\n\n variables = {\n 'u' : ('unknown field', 'displacement', 0),\n 'v' : ('test field', 'displacement', 'u'),\n }\n\n regions = {\n 'Omega' : 'all',\n 'Y1': 'cells of group 1',\n 'Y2': 'cells of group 2',\n }\n regions.update(define_box_regions(dim,\n bbox[0], bbox[1], mesh_eps))\n\n ebcs = {\n }\n\n if dim == 3:\n epbcs = {\n 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},\n 'match_x_plane'),\n 'periodic_y' : (['Near', 'Far'], {'u.all' : 'u.all'},\n 'match_y_plane'),\n 'periodic_z' : (['Top', 'Bottom'], {'u.all' : 'u.all'},\n 'match_z_plane'),\n }\n else:\n epbcs = {\n 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},\n 'match_y_line'),\n 'periodic_y' : (['Bottom', 'Top'], {'u.all' : 'u.all'},\n 'match_x_line'),\n }\n\n per.set_accuracy(mesh_eps)\n functions = {\n 'match_x_plane' : (per.match_x_plane,),\n 'match_y_plane' : (per.match_y_plane,),\n 'match_z_plane' : (per.match_z_plane,),\n 'match_x_line' : (per.match_x_line,),\n 'match_y_line' : (per.match_y_line,),\n 'get_wdir' : (get_wdir,),\n }\n\n integrals = {\n 'i' : 2 * approx_order,\n }\n\n equations = {\n 'K' : 'dw_lin_elastic.i.Omega(m.D, v, u)',\n 'S' : 'dw_elastic_wave.i.Omega(m.D, wave.vec, v, u)',\n 'R' : \"\"\"1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, u, v)\n - 1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, v, u)\"\"\",\n 'M' : 'dw_volume_dot.i.Omega(m.density, v, u)',\n }\n\n solver_0 = solver_conf.copy()\n solver_0['name'] = 'eig'\n\n return locals()\n\ndef get_wdir(ts, coors, mode=None,\n equations=None, term=None, problem=None, wdir=None, **kwargs):\n if mode == 'special':\n return {'vec' : wdir}\n\ndef set_wave_dir(pb, wdir):\n materials = pb.get_materials()\n wave_mat = materials['wave']\n wave_mat.set_extra_args(wdir=wdir)\n\ndef save_materials(output_dir, pb, options):\n stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n young, poisson = mc.youngpoisson_from_stiffness(stiffness,\n plane=options.plane)\n density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n\n out = {}\n out['young'] = Struct(name='young', mode='cell',\n data=young[..., None, None])\n out['poisson'] = Struct(name='poisson', mode='cell',\n data=poisson[..., None, None])\n out['density'] = Struct(name='density', mode='cell', data=density)\n materials_filename = os.path.join(output_dir, 'materials.vtk')\n pb.save_state(materials_filename, out=out)\n\ndef get_std_wave_fun(pb, options):\n stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n young, poisson = mc.youngpoisson_from_stiffness(stiffness,\n plane=options.plane)\n density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n\n lam, mu = mc.lame_from_youngpoisson(young, poisson,\n plane=options.plane)\n alam = nm.average(lam)\n amu = nm.average(mu)\n adensity = nm.average(density)\n\n cp = nm.sqrt((alam + 2.0 * amu) / adensity)\n cs = nm.sqrt(amu / adensity)\n output('average p-wave speed:', cp)\n output('average shear wave speed:', cs)\n\n log_names = [r'$\\omega_p$', r'$\\omega_s$']\n log_plot_kwargs = [{'ls' : '--', 'color' : 'k'},\n {'ls' : '--', 'color' : 'gray'}]\n\n if options.mode == 'omega':\n fun = lambda wmag, wdir: (cp * wmag, cs * wmag)\n\n else:\n fun = lambda wmag, wdir: (wmag / cp, wmag / cs)\n\n return fun, log_names, log_plot_kwargs\n\ndef get_stepper(rng, pb, options):\n if options.stepper == 'linear':\n stepper = TimeStepper(rng[0], rng[1], dt=None, n_step=rng[2])\n return stepper\n\n bbox = pb.domain.mesh.get_bounding_box()\n\n bzone = 2.0 * nm.pi / (bbox[1] - bbox[0])\n\n num = rng[2] // 3\n\n class BrillouinStepper(Struct):\n \"\"\"\n Step over 1. Brillouin zone in xy plane.\n \"\"\"\n def __init__(self, t0, t1, dt=None, n_step=None, step=None, **kwargs):\n Struct.__init__(self, t0=t0, t1=t1, dt=dt, n_step=n_step, step=step)\n\n self.n_digit, self.format, self.suffix = get_print_info(self.n_step)\n\n def __iter__(self):\n ts = TimeStepper(0, bzone[0], dt=None, n_step=num)\n for ii, val in ts:\n yield ii, val, nm.array([1.0, 0.0])\n if ii == (num-2): break\n\n ts = TimeStepper(0, bzone[1], dt=None, n_step=num)\n for ii, k1 in ts:\n wdir = nm.array([bzone[0], k1])\n val = nm.linalg.norm(wdir)\n wdir = wdir / val\n yield num + ii, val, wdir\n if ii == (num-2): break\n\n wdir = nm.array([bzone[0], bzone[1]])\n val = nm.linalg.norm(wdir)\n wdir = wdir / val\n ts = TimeStepper(0, 1, dt=None, n_step=num)\n for ii, _ in ts:\n yield 2 * num + ii, val * (1.0 - float(ii)/(num-1)), wdir\n\n stepper = BrillouinStepper(0, 1, n_step=rng[2])\n\n return stepper\n\ndef save_eigenvectors(filename, svecs, wmag, wdir, pb):\n if svecs is None: return\n\n variables = pb.get_variables()\n # Make full eigenvectors (add DOFs fixed by boundary conditions).\n vecs = nm.empty((variables.di.ptr[-1], svecs.shape[1]),\n dtype=svecs.dtype)\n for ii in range(svecs.shape[1]):\n vecs[:, ii] = variables.make_full_vec(svecs[:, ii])\n\n # Save the eigenvectors.\n out = {}\n state = pb.create_state()\n\n pp_name = pb.conf.options.get('post_process_hook')\n pp = getattr(pb.conf.funmod, pp_name if pp_name is not None else '',\n lambda out, *args, **kwargs: out)\n\n for ii in range(svecs.shape[1]):\n state.set_full(vecs[:, ii])\n aux = state.create_output_dict()\n aux2 = {}\n pp(aux2, pb, state, wmag=wmag, wdir=wdir)\n aux.update(convert_complex_output(aux2))\n out.update({key + '%03d' % ii : aux[key] for key in aux})\n\n pb.save_state(filename, out=out)\n\ndef assemble_matrices(define, mod, pars, set_wave_dir, options, wdir=None):\n \"\"\"\n Assemble the blocks of dispersion eigenvalue problem matrices.\n \"\"\"\n define_dict = define(filename_mesh=options.mesh_filename,\n pars=pars,\n approx_order=options.order,\n refinement_level=options.refine,\n solver_conf=options.solver_conf,\n plane=options.plane,\n post_process=options.post_process,\n **options.define_kwargs)\n\n conf = ProblemConf.from_dict(define_dict, mod)\n\n pb = Problem.from_conf(conf)\n pb.dispersion_options = options\n pb.set_output_dir(options.output_dir)\n dim = pb.domain.shape.dim\n\n # Set the normalized wave vector direction to the material(s).\n if wdir is None:\n wdir = nm.asarray(options.wave_dir[:dim], dtype=nm.float64)\n wdir = wdir / nm.linalg.norm(wdir)\n set_wave_dir(pb, wdir)\n\n bbox = pb.domain.mesh.get_bounding_box()\n size = (bbox[1] - bbox[0]).max()\n scaling0 = apply_unit_multipliers([1.0], ['length'],\n options.unit_multipliers)[0]\n scaling = scaling0\n if options.mesh_size is not None:\n scaling *= options.mesh_size / size\n output('scaling factor of periodic cell mesh coordinates:', scaling)\n output('new mesh size with applied unit multipliers:', scaling * size)\n pb.domain.mesh.coors[:] *= scaling\n pb.set_mesh_coors(pb.domain.mesh.coors, update_fields=True)\n\n bzone = 2.0 * nm.pi / (scaling * size)\n output('1. Brillouin zone size:', bzone * scaling0)\n output('1. Brillouin zone size with applied unit multipliers:', bzone)\n\n pb.time_update()\n pb.update_materials()\n\n # Assemble the matrices.\n mtxs = {}\n for key, eq in pb.equations.iteritems():\n mtxs[key] = mtx = pb.mtx_a.copy()\n mtx = eq.evaluate(mode='weak', dw_mode='matrix', asm_obj=mtx)\n mtx.eliminate_zeros()\n output_array_stats(mtx.data, 'nonzeros in %s' % key)\n\n output('symmetry checks:')\n output('%s - %s^T:' % (key, key), max_diff_csr(mtx, mtx.T))\n output('%s - %s^H:' % (key, key), max_diff_csr(mtx, mtx.H))\n\n return pb, wdir, bzone, mtxs\n\ndef setup_n_eigs(options, pb, mtxs):\n \"\"\"\n Setup the numbers of eigenvalues based on options and numbers of DOFs.\n \"\"\"\n solver_n_eigs = n_eigs = options.n_eigs\n n_dof = mtxs['K'].shape[0]\n if options.mode == 'omega':\n if options.n_eigs > n_dof:\n n_eigs = n_dof\n solver_n_eigs = None\n\n else:\n if options.n_eigs > 2 * n_dof:\n n_eigs = 2 * n_dof\n solver_n_eigs = None\n\n return solver_n_eigs, n_eigs\n\ndef build_evp_matrices(mtxs, val, mode, pb):\n \"\"\"\n Build the matrices of the dispersion eigenvalue problem.\n \"\"\"\n if mode == 'omega':\n mtx_a = mtxs['K'] + val**2 * mtxs['S'] + val * mtxs['R']\n output('A - A^H:', max_diff_csr(mtx_a, mtx_a.H))\n\n evp_mtxs = (mtx_a, mtxs['M'])\n\n else:\n evp_mtxs = (mtxs['S'], mtxs['R'], mtxs['K'] - val**2 * mtxs['M'])\n\n return evp_mtxs\n\ndef process_evp_results(eigs, svecs, val, wdir, bzone, pb, mtxs, options,\n std_wave_fun=None):\n \"\"\"\n Transform eigenvalues to either omegas or kappas, depending on `mode`.\n Transform eigenvectors, if available, depending on `mode`.\n Return also the values to log.\n \"\"\"\n if options.mode == 'omega':\n omegas = nm.sqrt(eigs)\n\n output('eigs, omegas:')\n for ii, om in enumerate(omegas):\n output('{:>3}. {: .10e}, {:.10e}'.format(ii, eigs[ii], om))\n\n if options.stepper == 'linear':\n out = tuple(eigs) + tuple(omegas)\n\n else:\n out = tuple(val * wdir) + tuple(omegas)\n\n if std_wave_fun is not None:\n out = out + std_wave_fun(val, wdir)\n\n return omegas, svecs, out\n\n else:\n kappas = eigs.copy()\n rks = kappas.copy()\n\n # Mask modes far from 1. Brillouin zone.\n max_kappa = 1.2 * bzone\n kappas[kappas.real > max_kappa] = nm.nan\n\n # Mask non-physical modes.\n kappas[kappas.real < 0] = nm.nan\n kappas[nm.abs(kappas.imag) > 1e-10] = nm.nan\n out = tuple(kappas.real)\n\n output('raw kappas, masked real part:',)\n for ii, kr in enumerate(kappas.real):\n output('{:>3}. {: 23.5e}, {:.10e}'.format(ii, rks[ii], kr))\n\n if svecs is not None:\n n_dof = mtxs['K'].shape[0]\n # Select only vectors corresponding to physical modes.\n ii = nm.isfinite(kappas.real)\n svecs = svecs[:n_dof, ii]\n\n if std_wave_fun is not None:\n out = out + tuple(ii if ii <= max_kappa else nm.nan\n for ii in std_wave_fun(val, wdir))\n\n return kappas, svecs, out\n\nhelps = {\n 'pars' :\n 'material parameters in Y1, Y2 subdomains in basic units'\n ' [default: %(default)s]',\n 'conf' :\n 'if given, an alternative problem description file with apply_units() and'\n ' define() functions [default: %(default)s]',\n 'define_kwargs' : 'additional keyword arguments passed to define()',\n 'mesh_size' :\n 'desired mesh size (max. of bounding box dimensions) in basic units'\n ' - the input periodic cell mesh is rescaled to this size'\n ' [default: %(default)s]',\n 'unit_multipliers' :\n 'basic unit multipliers (time, length, mass) [default: %(default)s]',\n 'plane' :\n 'for 2D problems, plane strain or stress hypothesis selection'\n ' [default: %(default)s]',\n 'wave_dir' : 'the wave vector direction (will be normalized)'\n ' [default: %(default)s]',\n 'mode' : 'solution mode: omega = solve a generalized EVP for omega,'\n ' kappa = solve a quadratic generalized EVP for kappa'\n ' [default: %(default)s]',\n 'stepper' : 'the range stepper. For \"brillouin\", only the number'\n ' of items from --range is used'\n ' [default: %(default)s]',\n 'range' : 'the wave vector magnitude / frequency range'\n ' (like numpy.linspace) depending on the mode option'\n ' [default: %(default)s]',\n 'order' : 'displacement field approximation order [default: %(default)s]',\n 'refine' : 'number of uniform mesh refinements [default: %(default)s]',\n 'n_eigs' : 'the number of eigenvalues to compute [default: %(default)s]',\n 'eigs_only' : 'compute only eigenvalues, not eigenvectors',\n 'post_process' : 'post-process eigenvectors',\n 'solver_conf' : 'eigenvalue problem solver configuration options'\n ' [default: %(default)s]',\n 'save_regions' : 'save defined regions into'\n ' /regions.vtk',\n 'save_materials' : 'save material parameters into'\n ' /materials.vtk',\n 'log_std_waves' : 'log also standard pressure dilatation and shear waves',\n 'no_legends' :\n 'do not show legends in the log plots',\n 'no_show' :\n 'do not show the log figure',\n 'silent' : 'do not print messages to screen',\n 'clear' :\n 'clear old solution files from output directory',\n 'output_dir' :\n 'output directory [default: %(default)s]',\n 'mesh_filename' :\n 'input periodic cell mesh file name [default: %(default)s]',\n}\n\ndef main():\n # Aluminium and epoxy.\n default_pars = '70e9,0.35,2.799e3, 3.8e9,0.27,1.142e3'\n default_solver_conf = (\"kind='eig.scipy',method='eigsh',tol=1.0e-5,\"\n \"maxiter=1000,which='LM',sigma=0.0\")\n\n parser = ArgumentParser(description=__doc__,\n formatter_class=RawDescriptionHelpFormatter)\n parser.add_argument('--pars', metavar='young1,poisson1,density1'\n ',young2,poisson2,density2',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='pars',\n default=default_pars, help=helps['pars'])\n parser.add_argument('--conf', metavar='filename',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='conf',\n default=None, help=helps['conf'])\n parser.add_argument('--define-kwargs', metavar='dict-like',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='define_kwargs',\n default=None, help=helps['define_kwargs'])\n parser.add_argument('--mesh-size', type=float, metavar='float',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='mesh_size',\n default=None, help=helps['mesh_size'])\n parser.add_argument('--unit-multipliers',\n metavar='c_time,c_length,c_mass',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='unit_multipliers',\n default='1.0,1.0,1.0', help=helps['unit_multipliers'])\n parser.add_argument('--plane', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='plane',\n choices=['strain', 'stress'],\n default='strain', help=helps['plane'])\n parser.add_argument('--wave-dir', metavar='float,float[,float]',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='wave_dir',\n default='1.0,0.0,0.0', help=helps['wave_dir'])\n parser.add_argument('--mode', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='mode',\n choices=['omega', 'kappa'],\n default='omega', help=helps['mode'])\n parser.add_argument('--stepper', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='stepper',\n choices=['linear', 'brillouin'],\n default='linear', help=helps['stepper'])\n parser.add_argument('--range', metavar='start,stop,count',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='range',\n default='0,6.4,33', help=helps['range'])\n parser.add_argument('--order', metavar='int', type=int,\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='order',\n default=1, help=helps['order'])\n parser.add_argument('--refine', metavar='int', type=int,\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='refine',\n default=0, help=helps['refine'])\n parser.add_argument('-n', '--n-eigs', metavar='int', type=int,\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='n_eigs',\n default=6, help=helps['n_eigs'])\n group = parser.add_mutually_exclusive_group()\n group.add_argument('--eigs-only',\n action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='eigs_only',\n default=False, help=helps['eigs_only'])\n group.add_argument('--post-process',\n action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='post_process',\n default=False, help=helps['post_process'])\n parser.add_argument('--solver-conf', metavar='dict-like',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='solver_conf',\n default=default_solver_conf, help=helps['solver_conf'])\n parser.add_argument('--save-regions',\n action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='save_regions',\n default=False, help=helps['save_regions'])\n parser.add_argument('--save-materials',\n action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='save_materials',\n default=False, help=helps['save_materials'])\n parser.add_argument('--log-std-waves',\n action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='log_std_waves',\n default=False, help=helps['log_std_waves'])\n parser.add_argument('--no-legends',\n action="https://huggingface.co/datasets/luna-code/sfepy/store_false", dest='show_legends',\n default=True, help=helps['no_legends'])\n parser.add_argument('--no-show',\n action="https://huggingface.co/datasets/luna-code/sfepy/store_false", dest='show',\n default=True, help=helps['no_show'])\n parser.add_argument('--silent',\n action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='silent',\n default=False, help=helps['silent'])\n parser.add_argument('-c', '--clear',\n action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='clear',\n default=False, help=helps['clear'])\n parser.add_argument('-o', '--output-dir', metavar='path',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='output_dir',\n default='output', help=helps['output_dir'])\n parser.add_argument('mesh_filename', default='',\n help=helps['mesh_filename'])\n options = parser.parse_args()\n\n output_dir = options.output_dir\n\n output.set_output(filename=os.path.join(output_dir,'output_log.txt'),\n combined=options.silent == False)\n\n if options.conf is not None:\n mod = import_file(options.conf)\n\n else:\n mod = sys.modules[__name__]\n\n apply_units = mod.apply_units\n define = mod.define\n set_wave_dir = mod.set_wave_dir\n setup_n_eigs = mod.setup_n_eigs\n build_evp_matrices = mod.build_evp_matrices\n save_materials = mod.save_materials\n get_std_wave_fun = mod.get_std_wave_fun\n get_stepper = mod.get_stepper\n process_evp_results = mod.process_evp_results\n\n options.pars = [float(ii) for ii in options.pars.split(',')]\n options.unit_multipliers = [float(ii)\n for ii in options.unit_multipliers.split(',')]\n options.wave_dir = [float(ii)\n for ii in options.wave_dir.split(',')]\n aux = options.range.split(',')\n options.range = [float(aux[0]), float(aux[1]), int(aux[2])]\n options.solver_conf = dict_from_string(options.solver_conf)\n options.define_kwargs = dict_from_string(options.define_kwargs)\n\n if options.clear:\n remove_files_patterns(output_dir,\n ['*.h5', '*.vtk', '*.txt'],\n ignores=['output_log.txt'],\n verbose=True)\n\n filename = os.path.join(output_dir, 'options.txt')\n "},"completion":{"kind":"string","value":"ensure_path(filename)"},"api":{"kind":"string","value":"sfepy.base.ioutils.ensure_path"}}},{"rowIdx":70,"cells":{"prompt":{"kind":"string","value":"#!/usr/bin/env python\n\"\"\"\nDispersion analysis of a heterogeneous finite scale periodic cell.\n\nThe periodic cell mesh has to contain two subdomains Y1 (with the cell ids 1),\nY2 (with the cell ids 2), so that different material properties can be defined\nin each of the subdomains (see ``--pars`` option). The command line parameters\ncan be given in any consistent unit set, for example the basic SI units. The\n``--unit-multipliers`` option can be used to rescale the input units to ones\nmore suitable to the simulation, for example to prevent having different\nmatrix blocks with large differences of matrix entries magnitudes. The results\nare then in the rescaled units.\n\nUsage Examples\n--------------\n\nDefault material parameters, a square periodic cell with a spherical inclusion,\nlogs also standard pressure dilatation and shear waves, no eigenvectors::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only\n\nAs above, with custom eigenvalue solver parameters, and different number of\neigenvalues, mesh size and units used in the calculation::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --solver-conf=\"kind='eig.scipy', method='eigsh', tol=1e-10, maxiter=1000, which='LM', sigma=0\" --log-std-waves -n 5 --range=0,640,101 --mode=omega --unit-multipliers=1e-6,1e-2,1e-3 --mesh-size=1e-2 --eigs-only\n\nDefault material parameters, a square periodic cell with a square inclusion,\nand a very small mesh to allow comparing the omega and kappa modes (full matrix\nsolver required!)::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf=\"kind='eig.scipy', method='eigh'\" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf=\"kind='eig.qevp', method='companion', mode='inverted', solver={kind='eig.scipy', method='eig'}\" --log-std-waves -n 500 --range=0,4000000,1001 --mesh-size=1e-2 --mode=kappa --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/kappa\n\nView/compare the resulting logs::\n\n python script/plot_logs.py output/omega/frequencies.txt --no-legends -g 1 -o mode-omega.png\n python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends -o mode-kappa.png\n python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends --swap-axes -o mode-kappa-t.png\n\nIn contrast to the heterogeneous square periodic cell, a homogeneous\nsquare periodic cell (the region Y2 is empty)::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_1m.mesh --solver-conf=\"kind='eig.scipy', method='eigh'\" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega-h\n\n python script/plot_logs.py output/omega-h/frequencies.txt --no-legends -g 1 -o mode-omega-h.png\n\nUse the Brillouin stepper::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves -n=60 --eigs-only --no-legends --stepper=brillouin\n\n python script/plot_logs.py output/frequencies.txt -g 0 --rc=\"'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4\" -o brillouin-stepper-kappas.png\n\n python script/plot_logs.py output/frequencies.txt -g 1 --no-legends --rc=\"'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4\" -o brillouin-stepper-omegas.png\n\nAdditional arguments can be passed to the problem configuration's\n:func:`define()` function using the ``--define-kwargs`` option. In this file,\nonly the mesh vertex separation parameter `mesh_eps` can be used::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only --define-kwargs=\"mesh_eps=1e-10\" --save-regions\n\"\"\"\nfrom __future__ import absolute_import\nimport os\nimport sys\nsys.path.append('.')\nimport gc\nfrom copy import copy\nfrom argparse import ArgumentParser, RawDescriptionHelpFormatter\n\nimport numpy as nm\nimport matplotlib.pyplot as plt\n\nfrom sfepy.base.base import import_file, output, Struct\nfrom sfepy.base.conf import dict_from_string, ProblemConf\nfrom sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options\nfrom sfepy.base.log import Log\nfrom sfepy.discrete.fem import MeshIO\nfrom sfepy.mechanics.matcoefs import stiffness_from_youngpoisson as stiffness\nimport sfepy.mechanics.matcoefs as mc\nfrom sfepy.mechanics.units import apply_unit_multipliers\nimport sfepy.discrete.fem.periodic as per\nfrom sfepy.discrete.fem.meshio import convert_complex_output\nfrom sfepy.homogenization.utils import define_box_regions\nfrom sfepy.discrete import Problem\nfrom sfepy.mechanics.tensors import get_von_mises_stress\nfrom sfepy.solvers import Solver\nfrom sfepy.solvers.ts import get_print_info, TimeStepper\nfrom sfepy.linalg.utils import output_array_stats, max_diff_csr\n\ndef apply_units(pars, unit_multipliers):\n new_pars = apply_unit_multipliers(pars,\n ['stress', 'one', 'density',\n 'stress', 'one' ,'density'],\n unit_multipliers)\n return new_pars\n\ndef compute_von_mises(out, pb, state, extend=False, wmag=None, wdir=None):\n \"\"\"\n Calculate the von Mises stress.\n \"\"\"\n stress = pb.evaluate('ev_cauchy_stress.i.Omega(m.D, u)', mode='el_avg')\n\n vms = get_von_mises_stress(stress.squeeze())\n vms.shape = (vms.shape[0], 1, 1, 1)\n out['von_mises_stress'] = Struct(name='output_data', mode='cell',\n data=vms)\n\n return out\n\ndef define(filename_mesh, pars, approx_order, refinement_level, solver_conf,\n plane='strain', post_process=False, mesh_eps=1e-8):\n io = MeshIO.any_from_filename(filename_mesh)\n bbox = io.read_bounding_box()\n dim = bbox.shape[1]\n\n options = {\n 'absolute_mesh_path' : True,\n 'refinement_level' : refinement_level,\n 'allow_empty_regions' : True,\n 'post_process_hook' : 'compute_von_mises' if post_process else None,\n }\n\n fields = {\n 'displacement': ('complex', dim, 'Omega', approx_order),\n }\n\n young1, poisson1, density1, young2, poisson2, density2 = pars\n materials = {\n 'm' : ({\n 'D' : {'Y1' : stiffness(dim, young=young1, poisson=poisson1,\n plane=plane),\n 'Y2' : stiffness(dim, young=young2, poisson=poisson2,\n plane=plane)},\n 'density' : {'Y1' : density1, 'Y2' : density2},\n },),\n 'wave' : 'get_wdir',\n }\n\n variables = {\n 'u' : ('unknown field', 'displacement', 0),\n 'v' : ('test field', 'displacement', 'u'),\n }\n\n regions = {\n 'Omega' : 'all',\n 'Y1': 'cells of group 1',\n 'Y2': 'cells of group 2',\n }\n regions.update(define_box_regions(dim,\n bbox[0], bbox[1], mesh_eps))\n\n ebcs = {\n }\n\n if dim == 3:\n epbcs = {\n 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},\n 'match_x_plane'),\n 'periodic_y' : (['Near', 'Far'], {'u.all' : 'u.all'},\n 'match_y_plane'),\n 'periodic_z' : (['Top', 'Bottom'], {'u.all' : 'u.all'},\n 'match_z_plane'),\n }\n else:\n epbcs = {\n 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},\n 'match_y_line'),\n 'periodic_y' : (['Bottom', 'Top'], {'u.all' : 'u.all'},\n 'match_x_line'),\n }\n\n per.set_accuracy(mesh_eps)\n functions = {\n 'match_x_plane' : (per.match_x_plane,),\n 'match_y_plane' : (per.match_y_plane,),\n 'match_z_plane' : (per.match_z_plane,),\n 'match_x_line' : (per.match_x_line,),\n 'match_y_line' : (per.match_y_line,),\n 'get_wdir' : (get_wdir,),\n }\n\n integrals = {\n 'i' : 2 * approx_order,\n }\n\n equations = {\n 'K' : 'dw_lin_elastic.i.Omega(m.D, v, u)',\n 'S' : 'dw_elastic_wave.i.Omega(m.D, wave.vec, v, u)',\n 'R' : \"\"\"1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, u, v)\n - 1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, v, u)\"\"\",\n 'M' : 'dw_volume_dot.i.Omega(m.density, v, u)',\n }\n\n solver_0 = solver_conf.copy()\n solver_0['name'] = 'eig'\n\n return locals()\n\ndef get_wdir(ts, coors, mode=None,\n equations=None, term=None, problem=None, wdir=None, **kwargs):\n if mode == 'special':\n return {'vec' : wdir}\n\ndef set_wave_dir(pb, wdir):\n materials = pb.get_materials()\n wave_mat = materials['wave']\n wave_mat.set_extra_args(wdir=wdir)\n\ndef save_materials(output_dir, pb, options):\n stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n young, poisson = mc.youngpoisson_from_stiffness(stiffness,\n plane=options.plane)\n density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n\n out = {}\n out['young'] = Struct(name='young', mode='cell',\n data=young[..., None, None])\n out['poisson'] = Struct(name='poisson', mode='cell',\n data=poisson[..., None, None])\n out['density'] = Struct(name='density', mode='cell', data=density)\n materials_filename = os.path.join(output_dir, 'materials.vtk')\n pb.save_state(materials_filename, out=out)\n\ndef get_std_wave_fun(pb, options):\n stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n young, poisson = mc.youngpoisson_from_stiffness(stiffness,\n plane=options.plane)\n density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n\n lam, mu = mc.lame_from_youngpoisson(young, poisson,\n plane=options.plane)\n alam = nm.average(lam)\n amu = nm.average(mu)\n adensity = nm.average(density)\n\n cp = nm.sqrt((alam + 2.0 * amu) / adensity)\n cs = nm.sqrt(amu / adensity)\n output('average p-wave speed:', cp)\n output('average shear wave speed:', cs)\n\n log_names = [r'$\\omega_p$', r'$\\omega_s$']\n log_plot_kwargs = [{'ls' : '--', 'color' : 'k'},\n {'ls' : '--', 'color' : 'gray'}]\n\n if options.mode == 'omega':\n fun = lambda wmag, wdir: (cp * wmag, cs * wmag)\n\n else:\n fun = lambda wmag, wdir: (wmag / cp, wmag / cs)\n\n return fun, log_names, log_plot_kwargs\n\ndef get_stepper(rng, pb, options):\n if options.stepper == 'linear':\n stepper = TimeStepper(rng[0], rng[1], dt=None, n_step=rng[2])\n return stepper\n\n bbox = pb.domain.mesh.get_bounding_box()\n\n bzone = 2.0 * nm.pi / (bbox[1] - bbox[0])\n\n num = rng[2] // 3\n\n class BrillouinStepper(Struct):\n \"\"\"\n Step over 1. Brillouin zone in xy plane.\n \"\"\"\n def __init__(self, t0, t1, dt=None, n_step=None, step=None, **kwargs):\n Struct.__init__(self, t0=t0, t1=t1, dt=dt, n_step=n_step, step=step)\n\n self.n_digit, self.format, self.suffix = get_print_info(self.n_step)\n\n def __iter__(self):\n ts = TimeStepper(0, bzone[0], dt=None, n_step=num)\n for ii, val in ts:\n yield ii, val, nm.array([1.0, 0.0])\n if ii == (num-2): break\n\n ts = TimeStepper(0, bzone[1], dt=None, n_step=num)\n for ii, k1 in ts:\n wdir = nm.array([bzone[0], k1])\n val = nm.linalg.norm(wdir)\n wdir = wdir / val\n yield num + ii, val, wdir\n if ii == (num-2): break\n\n wdir = nm.array([bzone[0], bzone[1]])\n val = nm.linalg.norm(wdir)\n wdir = wdir / val\n ts = TimeStepper(0, 1, dt=None, n_step=num)\n for ii, _ in ts:\n yield 2 * num + ii, val * (1.0 - float(ii)/(num-1)), wdir\n\n stepper = BrillouinStepper(0, 1, n_step=rng[2])\n\n return stepper\n\ndef save_eigenvectors(filename, svecs, wmag, wdir, pb):\n if svecs is None: return\n\n variables = pb.get_variables()\n # Make full eigenvectors (add DOFs fixed by boundary conditions).\n vecs = nm.empty((variables.di.ptr[-1], svecs.shape[1]),\n dtype=svecs.dtype)\n for ii in range(svecs.shape[1]):\n vecs[:, ii] = variables.make_full_vec(svecs[:, ii])\n\n # Save the eigenvectors.\n out = {}\n state = pb.create_state()\n\n pp_name = pb.conf.options.get('post_process_hook')\n pp = getattr(pb.conf.funmod, pp_name if pp_name is not None else '',\n lambda out, *args, **kwargs: out)\n\n for ii in range(svecs.shape[1]):\n state.set_full(vecs[:, ii])\n aux = state.create_output_dict()\n aux2 = {}\n pp(aux2, pb, state, wmag=wmag, wdir=wdir)\n aux.update(convert_complex_output(aux2))\n out.update({key + '%03d' % ii : aux[key] for key in aux})\n\n pb.save_state(filename, out=out)\n\ndef assemble_matrices(define, mod, pars, set_wave_dir, options, wdir=None):\n \"\"\"\n Assemble the blocks of dispersion eigenvalue problem matrices.\n \"\"\"\n define_dict = define(filename_mesh=options.mesh_filename,\n pars=pars,\n approx_order=options.order,\n refinement_level=options.refine,\n solver_conf=options.solver_conf,\n plane=options.plane,\n post_process=options.post_process,\n **options.define_kwargs)\n\n conf = ProblemConf.from_dict(define_dict, mod)\n\n pb = Problem.from_conf(conf)\n pb.dispersion_options = options\n pb.set_output_dir(options.output_dir)\n dim = pb.domain.shape.dim\n\n # Set the normalized wave vector direction to the material(s).\n if wdir is None:\n wdir = nm.asarray(options.wave_dir[:dim], dtype=nm.float64)\n wdir = wdir / nm.linalg.norm(wdir)\n set_wave_dir(pb, wdir)\n\n bbox = pb.domain.mesh.get_bounding_box()\n size = (bbox[1] - bbox[0]).max()\n scaling0 = apply_unit_multipliers([1.0], ['length'],\n options.unit_multipliers)[0]\n scaling = scaling0\n if options.mesh_size is not None:\n scaling *= options.mesh_size / size\n output('scaling factor of periodic cell mesh coordinates:', scaling)\n output('new mesh size with applied unit multipliers:', scaling * size)\n pb.domain.mesh.coors[:] *= scaling\n pb.set_mesh_coors(pb.domain.mesh.coors, update_fields=True)\n\n bzone = 2.0 * nm.pi / (scaling * size)\n output('1. Brillouin zone size:', bzone * scaling0)\n output('1. Brillouin zone size with applied unit multipliers:', bzone)\n\n pb.time_update()\n pb.update_materials()\n\n # Assemble the matrices.\n mtxs = {}\n for key, eq in pb.equations.iteritems():\n mtxs[key] = mtx = pb.mtx_a.copy()\n mtx = eq.evaluate(mode='weak', dw_mode='matrix', asm_obj=mtx)\n mtx.eliminate_zeros()\n output_array_stats(mtx.data, 'nonzeros in %s' % key)\n\n output('symmetry checks:')\n output('%s - %s^T:' % (key, key), max_diff_csr(mtx, mtx.T))\n output('%s - %s^H:' % (key, key), max_diff_csr(mtx, mtx.H))\n\n return pb, wdir, bzone, mtxs\n\ndef setup_n_eigs(options, pb, mtxs):\n \"\"\"\n Setup the numbers of eigenvalues based on options and numbers of DOFs.\n \"\"\"\n solver_n_eigs = n_eigs = options.n_eigs\n n_dof = mtxs['K'].shape[0]\n if options.mode == 'omega':\n if options.n_eigs > n_dof:\n n_eigs = n_dof\n solver_n_eigs = None\n\n else:\n if options.n_eigs > 2 * n_dof:\n n_eigs = 2 * n_dof\n solver_n_eigs = None\n\n return solver_n_eigs, n_eigs\n\ndef build_evp_matrices(mtxs, val, mode, pb):\n \"\"\"\n Build the matrices of the dispersion eigenvalue problem.\n \"\"\"\n if mode == 'omega':\n mtx_a = mtxs['K'] + val**2 * mtxs['S'] + val * mtxs['R']\n output('A - A^H:', max_diff_csr(mtx_a, mtx_a.H))\n\n evp_mtxs = (mtx_a, mtxs['M'])\n\n else:\n evp_mtxs = (mtxs['S'], mtxs['R'], mtxs['K'] - val**2 * mtxs['M'])\n\n return evp_mtxs\n\ndef process_evp_results(eigs, svecs, val, wdir, bzone, pb, mtxs, options,\n std_wave_fun=None):\n \"\"\"\n Transform eigenvalues to either omegas or kappas, depending on `mode`.\n Transform eigenvectors, if available, depending on `mode`.\n Return also the values to log.\n \"\"\"\n if options.mode == 'omega':\n omegas = nm.sqrt(eigs)\n\n output('eigs, omegas:')\n for ii, om in enumerate(omegas):\n output('{:>3}. {: .10e}, {:.10e}'.format(ii, eigs[ii], om))\n\n if options.stepper == 'linear':\n out = tuple(eigs) + tuple(omegas)\n\n else:\n out = tuple(val * wdir) + tuple(omegas)\n\n if std_wave_fun is not None:\n out = out + std_wave_fun(val, wdir)\n\n return omegas, svecs, out\n\n else:\n kappas = eigs.copy()\n rks = kappas.copy()\n\n # Mask modes far from 1. Brillouin zone.\n max_kappa = 1.2 * bzone\n kappas[kappas.real > max_kappa] = nm.nan\n\n # Mask non-physical modes.\n kappas[kappas.real < 0] = nm.nan\n kappas[nm.abs(kappas.imag) > 1e-10] = nm.nan\n out = tuple(kappas.real)\n\n output('raw kappas, masked real part:',)\n for ii, kr in enumerate(kappas.real):\n output('{:>3}. {: 23.5e}, {:.10e}'.format(ii, rks[ii], kr))\n\n if svecs is not None:\n n_dof = mtxs['K'].shape[0]\n # Select only vectors corresponding to physical modes.\n ii = nm.isfinite(kappas.real)\n svecs = svecs[:n_dof, ii]\n\n if std_wave_fun is not None:\n out = out + tuple(ii if ii <= max_kappa else nm.nan\n for ii in std_wave_fun(val, wdir))\n\n return kappas, svecs, out\n\nhelps = {\n 'pars' :\n 'material parameters in Y1, Y2 subdomains in basic units'\n ' [default: %(default)s]',\n 'conf' :\n 'if given, an alternative problem description file with apply_units() and'\n ' define() functions [default: %(default)s]',\n 'define_kwargs' : 'additional keyword arguments passed to define()',\n 'mesh_size' :\n 'desired mesh size (max. of bounding box dimensions) in basic units'\n ' - the input periodic cell mesh is rescaled to this size'\n ' [default: %(default)s]',\n 'unit_multipliers' :\n 'basic unit multipliers (time, length, mass) [default: %(default)s]',\n 'plane' :\n 'for 2D problems, plane strain or stress hypothesis selection'\n ' [default: %(default)s]',\n 'wave_dir' : 'the wave vector direction (will be normalized)'\n ' [default: %(default)s]',\n 'mode' : 'solution mode: omega = solve a generalized EVP for omega,'\n ' kappa = solve a quadratic generalized EVP for kappa'\n ' [default: %(default)s]',\n 'stepper' : 'the range stepper. For \"brillouin\", only the number'\n ' of items from --range is used'\n ' [default: %(default)s]',\n 'range' : 'the wave vector magnitude / frequency range'\n ' (like numpy.linspace) depending on the mode option'\n ' [default: %(default)s]',\n 'order' : 'displacement field approximation order [default: %(default)s]',\n 'refine' : 'number of uniform mesh refinements [default: %(default)s]',\n 'n_eigs' : 'the number of eigenvalues to compute [default: %(default)s]',\n 'eigs_only' : 'compute only eigenvalues, not eigenvectors',\n 'post_process' : 'post-process eigenvectors',\n 'solver_conf' : 'eigenvalue problem solver configuration options'\n ' [default: %(default)s]',\n 'save_regions' : 'save defined regions into'\n ' /regions.vtk',\n 'save_materials' : 'save material parameters into'\n ' /materials.vtk',\n 'log_std_waves' : 'log also standard pressure dilatation and shear waves',\n 'no_legends' :\n 'do not show legends in the log plots',\n 'no_show' :\n 'do not show the log figure',\n 'silent' : 'do not print messages to screen',\n 'clear' :\n 'clear old solution files from output directory',\n 'output_dir' :\n 'output directory [default: %(default)s]',\n 'mesh_filename' :\n 'input periodic cell mesh file name [default: %(default)s]',\n}\n\ndef main():\n # Aluminium and epoxy.\n default_pars = '70e9,0.35,2.799e3, 3.8e9,0.27,1.142e3'\n default_solver_conf = (\"kind='eig.scipy',method='eigsh',tol=1.0e-5,\"\n \"maxiter=1000,which='LM',sigma=0.0\")\n\n parser = ArgumentParser(description=__doc__,\n formatter_class=RawDescriptionHelpFormatter)\n parser.add_argument('--pars', metavar='young1,poisson1,density1'\n ',young2,poisson2,density2',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='pars',\n default=default_pars, help=helps['pars'])\n parser.add_argument('--conf', metavar='filename',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='conf',\n default=None, help=helps['conf'])\n parser.add_argument('--define-kwargs', metavar='dict-like',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='define_kwargs',\n default=None, help=helps['define_kwargs'])\n parser.add_argument('--mesh-size', type=float, metavar='float',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='mesh_size',\n default=None, help=helps['mesh_size'])\n parser.add_argument('--unit-multipliers',\n metavar='c_time,c_length,c_mass',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='unit_multipliers',\n default='1.0,1.0,1.0', help=helps['unit_multipliers'])\n parser.add_argument('--plane', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='plane',\n choices=['strain', 'stress'],\n default='strain', help=helps['plane'])\n parser.add_argument('--wave-dir', metavar='float,float[,float]',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='wave_dir',\n default='1.0,0.0,0.0', help=helps['wave_dir'])\n parser.add_argument('--mode', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='mode',\n choices=['omega', 'kappa'],\n default='omega', help=helps['mode'])\n parser.add_argument('--stepper', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='stepper',\n choices=['linear', 'brillouin'],\n default='linear', help=helps['stepper'])\n parser.add_argument('--range', metavar='start,stop,count',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='range',\n default='0,6.4,33', help=helps['range'])\n parser.add_argument('--order', metavar='int', type=int,\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='order',\n default=1, help=helps['order'])\n parser.add_argument('--refine', metavar='int', type=int,\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='refine',\n default=0, help=helps['refine'])\n parser.add_argument('-n', '--n-eigs', metavar='int', type=int,\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='n_eigs',\n default=6, help=helps['n_eigs'])\n group = parser.add_mutually_exclusive_group()\n group.add_argument('--eigs-only',\n action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='eigs_only',\n default=False, help=helps['eigs_only'])\n group.add_argument('--post-process',\n action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='post_process',\n default=False, help=helps['post_process'])\n parser.add_argument('--solver-conf', metavar='dict-like',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='solver_conf',\n default=default_solver_conf, help=helps['solver_conf'])\n parser.add_argument('--save-regions',\n action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='save_regions',\n default=False, help=helps['save_regions'])\n parser.add_argument('--save-materials',\n action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='save_materials',\n default=False, help=helps['save_materials'])\n parser.add_argument('--log-std-waves',\n action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='log_std_waves',\n default=False, help=helps['log_std_waves'])\n parser.add_argument('--no-legends',\n action="https://huggingface.co/datasets/luna-code/sfepy/store_false", dest='show_legends',\n default=True, help=helps['no_legends'])\n parser.add_argument('--no-show',\n action="https://huggingface.co/datasets/luna-code/sfepy/store_false", dest='show',\n default=True, help=helps['no_show'])\n parser.add_argument('--silent',\n action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='silent',\n default=False, help=helps['silent'])\n parser.add_argument('-c', '--clear',\n action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='clear',\n default=False, help=helps['clear'])\n parser.add_argument('-o', '--output-dir', metavar='path',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='output_dir',\n default='output', help=helps['output_dir'])\n parser.add_argument('mesh_filename', default='',\n help=helps['mesh_filename'])\n options = parser.parse_args()\n\n output_dir = options.output_dir\n\n output.set_output(filename=os.path.join(output_dir,'output_log.txt'),\n combined=options.silent == False)\n\n if options.conf is not None:\n mod = import_file(options.conf)\n\n else:\n mod = sys.modules[__name__]\n\n apply_units = mod.apply_units\n define = mod.define\n set_wave_dir = mod.set_wave_dir\n setup_n_eigs = mod.setup_n_eigs\n build_evp_matrices = mod.build_evp_matrices\n save_materials = mod.save_materials\n get_std_wave_fun = mod.get_std_wave_fun\n get_stepper = mod.get_stepper\n process_evp_results = mod.process_evp_results\n\n options.pars = [float(ii) for ii in options.pars.split(',')]\n options.unit_multipliers = [float(ii)\n for ii in options.unit_multipliers.split(',')]\n options.wave_dir = [float(ii)\n for ii in options.wave_dir.split(',')]\n aux = options.range.split(',')\n options.range = [float(aux[0]), float(aux[1]), int(aux[2])]\n options.solver_conf = dict_from_string(options.solver_conf)\n options.define_kwargs = dict_from_string(options.define_kwargs)\n\n if options.clear:\n remove_files_patterns(output_dir,\n ['*.h5', '*.vtk', '*.txt'],\n ignores=['output_log.txt'],\n verbose=True)\n\n filename = os.path.join(output_dir, 'options.txt')\n ensure_path(filename)\n save_options(filename, [('options', vars(options))],\n quote_command_line=True)\n\n pars = apply_units(options.pars, options.unit_multipliers)\n "},"completion":{"kind":"string","value":"output('material parameters with applied unit multipliers:')"},"api":{"kind":"string","value":"sfepy.base.base.output"}}},{"rowIdx":71,"cells":{"prompt":{"kind":"string","value":"#!/usr/bin/env python\n\"\"\"\nDispersion analysis of a heterogeneous finite scale periodic cell.\n\nThe periodic cell mesh has to contain two subdomains Y1 (with the cell ids 1),\nY2 (with the cell ids 2), so that different material properties can be defined\nin each of the subdomains (see ``--pars`` option). The command line parameters\ncan be given in any consistent unit set, for example the basic SI units. The\n``--unit-multipliers`` option can be used to rescale the input units to ones\nmore suitable to the simulation, for example to prevent having different\nmatrix blocks with large differences of matrix entries magnitudes. The results\nare then in the rescaled units.\n\nUsage Examples\n--------------\n\nDefault material parameters, a square periodic cell with a spherical inclusion,\nlogs also standard pressure dilatation and shear waves, no eigenvectors::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only\n\nAs above, with custom eigenvalue solver parameters, and different number of\neigenvalues, mesh size and units used in the calculation::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --solver-conf=\"kind='eig.scipy', method='eigsh', tol=1e-10, maxiter=1000, which='LM', sigma=0\" --log-std-waves -n 5 --range=0,640,101 --mode=omega --unit-multipliers=1e-6,1e-2,1e-3 --mesh-size=1e-2 --eigs-only\n\nDefault material parameters, a square periodic cell with a square inclusion,\nand a very small mesh to allow comparing the omega and kappa modes (full matrix\nsolver required!)::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf=\"kind='eig.scipy', method='eigh'\" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf=\"kind='eig.qevp', method='companion', mode='inverted', solver={kind='eig.scipy', method='eig'}\" --log-std-waves -n 500 --range=0,4000000,1001 --mesh-size=1e-2 --mode=kappa --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/kappa\n\nView/compare the resulting logs::\n\n python script/plot_logs.py output/omega/frequencies.txt --no-legends -g 1 -o mode-omega.png\n python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends -o mode-kappa.png\n python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends --swap-axes -o mode-kappa-t.png\n\nIn contrast to the heterogeneous square periodic cell, a homogeneous\nsquare periodic cell (the region Y2 is empty)::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_1m.mesh --solver-conf=\"kind='eig.scipy', method='eigh'\" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega-h\n\n python script/plot_logs.py output/omega-h/frequencies.txt --no-legends -g 1 -o mode-omega-h.png\n\nUse the Brillouin stepper::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves -n=60 --eigs-only --no-legends --stepper=brillouin\n\n python script/plot_logs.py output/frequencies.txt -g 0 --rc=\"'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4\" -o brillouin-stepper-kappas.png\n\n python script/plot_logs.py output/frequencies.txt -g 1 --no-legends --rc=\"'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4\" -o brillouin-stepper-omegas.png\n\nAdditional arguments can be passed to the problem configuration's\n:func:`define()` function using the ``--define-kwargs`` option. In this file,\nonly the mesh vertex separation parameter `mesh_eps` can be used::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only --define-kwargs=\"mesh_eps=1e-10\" --save-regions\n\"\"\"\nfrom __future__ import absolute_import\nimport os\nimport sys\nsys.path.append('.')\nimport gc\nfrom copy import copy\nfrom argparse import ArgumentParser, RawDescriptionHelpFormatter\n\nimport numpy as nm\nimport matplotlib.pyplot as plt\n\nfrom sfepy.base.base import import_file, output, Struct\nfrom sfepy.base.conf import dict_from_string, ProblemConf\nfrom sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options\nfrom sfepy.base.log import Log\nfrom sfepy.discrete.fem import MeshIO\nfrom sfepy.mechanics.matcoefs import stiffness_from_youngpoisson as stiffness\nimport sfepy.mechanics.matcoefs as mc\nfrom sfepy.mechanics.units import apply_unit_multipliers\nimport sfepy.discrete.fem.periodic as per\nfrom sfepy.discrete.fem.meshio import convert_complex_output\nfrom sfepy.homogenization.utils import define_box_regions\nfrom sfepy.discrete import Problem\nfrom sfepy.mechanics.tensors import get_von_mises_stress\nfrom sfepy.solvers import Solver\nfrom sfepy.solvers.ts import get_print_info, TimeStepper\nfrom sfepy.linalg.utils import output_array_stats, max_diff_csr\n\ndef apply_units(pars, unit_multipliers):\n new_pars = apply_unit_multipliers(pars,\n ['stress', 'one', 'density',\n 'stress', 'one' ,'density'],\n unit_multipliers)\n return new_pars\n\ndef compute_von_mises(out, pb, state, extend=False, wmag=None, wdir=None):\n \"\"\"\n Calculate the von Mises stress.\n \"\"\"\n stress = pb.evaluate('ev_cauchy_stress.i.Omega(m.D, u)', mode='el_avg')\n\n vms = get_von_mises_stress(stress.squeeze())\n vms.shape = (vms.shape[0], 1, 1, 1)\n out['von_mises_stress'] = Struct(name='output_data', mode='cell',\n data=vms)\n\n return out\n\ndef define(filename_mesh, pars, approx_order, refinement_level, solver_conf,\n plane='strain', post_process=False, mesh_eps=1e-8):\n io = MeshIO.any_from_filename(filename_mesh)\n bbox = io.read_bounding_box()\n dim = bbox.shape[1]\n\n options = {\n 'absolute_mesh_path' : True,\n 'refinement_level' : refinement_level,\n 'allow_empty_regions' : True,\n 'post_process_hook' : 'compute_von_mises' if post_process else None,\n }\n\n fields = {\n 'displacement': ('complex', dim, 'Omega', approx_order),\n }\n\n young1, poisson1, density1, young2, poisson2, density2 = pars\n materials = {\n 'm' : ({\n 'D' : {'Y1' : stiffness(dim, young=young1, poisson=poisson1,\n plane=plane),\n 'Y2' : stiffness(dim, young=young2, poisson=poisson2,\n plane=plane)},\n 'density' : {'Y1' : density1, 'Y2' : density2},\n },),\n 'wave' : 'get_wdir',\n }\n\n variables = {\n 'u' : ('unknown field', 'displacement', 0),\n 'v' : ('test field', 'displacement', 'u'),\n }\n\n regions = {\n 'Omega' : 'all',\n 'Y1': 'cells of group 1',\n 'Y2': 'cells of group 2',\n }\n regions.update(define_box_regions(dim,\n bbox[0], bbox[1], mesh_eps))\n\n ebcs = {\n }\n\n if dim == 3:\n epbcs = {\n 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},\n 'match_x_plane'),\n 'periodic_y' : (['Near', 'Far'], {'u.all' : 'u.all'},\n 'match_y_plane'),\n 'periodic_z' : (['Top', 'Bottom'], {'u.all' : 'u.all'},\n 'match_z_plane'),\n }\n else:\n epbcs = {\n 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},\n 'match_y_line'),\n 'periodic_y' : (['Bottom', 'Top'], {'u.all' : 'u.all'},\n 'match_x_line'),\n }\n\n per.set_accuracy(mesh_eps)\n functions = {\n 'match_x_plane' : (per.match_x_plane,),\n 'match_y_plane' : (per.match_y_plane,),\n 'match_z_plane' : (per.match_z_plane,),\n 'match_x_line' : (per.match_x_line,),\n 'match_y_line' : (per.match_y_line,),\n 'get_wdir' : (get_wdir,),\n }\n\n integrals = {\n 'i' : 2 * approx_order,\n }\n\n equations = {\n 'K' : 'dw_lin_elastic.i.Omega(m.D, v, u)',\n 'S' : 'dw_elastic_wave.i.Omega(m.D, wave.vec, v, u)',\n 'R' : \"\"\"1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, u, v)\n - 1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, v, u)\"\"\",\n 'M' : 'dw_volume_dot.i.Omega(m.density, v, u)',\n }\n\n solver_0 = solver_conf.copy()\n solver_0['name'] = 'eig'\n\n return locals()\n\ndef get_wdir(ts, coors, mode=None,\n equations=None, term=None, problem=None, wdir=None, **kwargs):\n if mode == 'special':\n return {'vec' : wdir}\n\ndef set_wave_dir(pb, wdir):\n materials = pb.get_materials()\n wave_mat = materials['wave']\n wave_mat.set_extra_args(wdir=wdir)\n\ndef save_materials(output_dir, pb, options):\n stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n young, poisson = mc.youngpoisson_from_stiffness(stiffness,\n plane=options.plane)\n density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n\n out = {}\n out['young'] = Struct(name='young', mode='cell',\n data=young[..., None, None])\n out['poisson'] = Struct(name='poisson', mode='cell',\n data=poisson[..., None, None])\n out['density'] = Struct(name='density', mode='cell', data=density)\n materials_filename = os.path.join(output_dir, 'materials.vtk')\n pb.save_state(materials_filename, out=out)\n\ndef get_std_wave_fun(pb, options):\n stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n young, poisson = mc.youngpoisson_from_stiffness(stiffness,\n plane=options.plane)\n density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n\n lam, mu = mc.lame_from_youngpoisson(young, poisson,\n plane=options.plane)\n alam = nm.average(lam)\n amu = nm.average(mu)\n adensity = nm.average(density)\n\n cp = nm.sqrt((alam + 2.0 * amu) / adensity)\n cs = nm.sqrt(amu / adensity)\n output('average p-wave speed:', cp)\n output('average shear wave speed:', cs)\n\n log_names = [r'$\\omega_p$', r'$\\omega_s$']\n log_plot_kwargs = [{'ls' : '--', 'color' : 'k'},\n {'ls' : '--', 'color' : 'gray'}]\n\n if options.mode == 'omega':\n fun = lambda wmag, wdir: (cp * wmag, cs * wmag)\n\n else:\n fun = lambda wmag, wdir: (wmag / cp, wmag / cs)\n\n return fun, log_names, log_plot_kwargs\n\ndef get_stepper(rng, pb, options):\n if options.stepper == 'linear':\n stepper = TimeStepper(rng[0], rng[1], dt=None, n_step=rng[2])\n return stepper\n\n bbox = pb.domain.mesh.get_bounding_box()\n\n bzone = 2.0 * nm.pi / (bbox[1] - bbox[0])\n\n num = rng[2] // 3\n\n class BrillouinStepper(Struct):\n \"\"\"\n Step over 1. Brillouin zone in xy plane.\n \"\"\"\n def __init__(self, t0, t1, dt=None, n_step=None, step=None, **kwargs):\n Struct.__init__(self, t0=t0, t1=t1, dt=dt, n_step=n_step, step=step)\n\n self.n_digit, self.format, self.suffix = get_print_info(self.n_step)\n\n def __iter__(self):\n ts = TimeStepper(0, bzone[0], dt=None, n_step=num)\n for ii, val in ts:\n yield ii, val, nm.array([1.0, 0.0])\n if ii == (num-2): break\n\n ts = TimeStepper(0, bzone[1], dt=None, n_step=num)\n for ii, k1 in ts:\n wdir = nm.array([bzone[0], k1])\n val = nm.linalg.norm(wdir)\n wdir = wdir / val\n yield num + ii, val, wdir\n if ii == (num-2): break\n\n wdir = nm.array([bzone[0], bzone[1]])\n val = nm.linalg.norm(wdir)\n wdir = wdir / val\n ts = TimeStepper(0, 1, dt=None, n_step=num)\n for ii, _ in ts:\n yield 2 * num + ii, val * (1.0 - float(ii)/(num-1)), wdir\n\n stepper = BrillouinStepper(0, 1, n_step=rng[2])\n\n return stepper\n\ndef save_eigenvectors(filename, svecs, wmag, wdir, pb):\n if svecs is None: return\n\n variables = pb.get_variables()\n # Make full eigenvectors (add DOFs fixed by boundary conditions).\n vecs = nm.empty((variables.di.ptr[-1], svecs.shape[1]),\n dtype=svecs.dtype)\n for ii in range(svecs.shape[1]):\n vecs[:, ii] = variables.make_full_vec(svecs[:, ii])\n\n # Save the eigenvectors.\n out = {}\n state = pb.create_state()\n\n pp_name = pb.conf.options.get('post_process_hook')\n pp = getattr(pb.conf.funmod, pp_name if pp_name is not None else '',\n lambda out, *args, **kwargs: out)\n\n for ii in range(svecs.shape[1]):\n state.set_full(vecs[:, ii])\n aux = state.create_output_dict()\n aux2 = {}\n pp(aux2, pb, state, wmag=wmag, wdir=wdir)\n aux.update(convert_complex_output(aux2))\n out.update({key + '%03d' % ii : aux[key] for key in aux})\n\n pb.save_state(filename, out=out)\n\ndef assemble_matrices(define, mod, pars, set_wave_dir, options, wdir=None):\n \"\"\"\n Assemble the blocks of dispersion eigenvalue problem matrices.\n \"\"\"\n define_dict = define(filename_mesh=options.mesh_filename,\n pars=pars,\n approx_order=options.order,\n refinement_level=options.refine,\n solver_conf=options.solver_conf,\n plane=options.plane,\n post_process=options.post_process,\n **options.define_kwargs)\n\n conf = ProblemConf.from_dict(define_dict, mod)\n\n pb = Problem.from_conf(conf)\n pb.dispersion_options = options\n pb.set_output_dir(options.output_dir)\n dim = pb.domain.shape.dim\n\n # Set the normalized wave vector direction to the material(s).\n if wdir is None:\n wdir = nm.asarray(options.wave_dir[:dim], dtype=nm.float64)\n wdir = wdir / nm.linalg.norm(wdir)\n set_wave_dir(pb, wdir)\n\n bbox = pb.domain.mesh.get_bounding_box()\n size = (bbox[1] - bbox[0]).max()\n scaling0 = apply_unit_multipliers([1.0], ['length'],\n options.unit_multipliers)[0]\n scaling = scaling0\n if options.mesh_size is not None:\n scaling *= options.mesh_size / size\n output('scaling factor of periodic cell mesh coordinates:', scaling)\n output('new mesh size with applied unit multipliers:', scaling * size)\n pb.domain.mesh.coors[:] *= scaling\n pb.set_mesh_coors(pb.domain.mesh.coors, update_fields=True)\n\n bzone = 2.0 * nm.pi / (scaling * size)\n output('1. Brillouin zone size:', bzone * scaling0)\n output('1. Brillouin zone size with applied unit multipliers:', bzone)\n\n pb.time_update()\n pb.update_materials()\n\n # Assemble the matrices.\n mtxs = {}\n for key, eq in pb.equations.iteritems():\n mtxs[key] = mtx = pb.mtx_a.copy()\n mtx = eq.evaluate(mode='weak', dw_mode='matrix', asm_obj=mtx)\n mtx.eliminate_zeros()\n output_array_stats(mtx.data, 'nonzeros in %s' % key)\n\n output('symmetry checks:')\n output('%s - %s^T:' % (key, key), max_diff_csr(mtx, mtx.T))\n output('%s - %s^H:' % (key, key), max_diff_csr(mtx, mtx.H))\n\n return pb, wdir, bzone, mtxs\n\ndef setup_n_eigs(options, pb, mtxs):\n \"\"\"\n Setup the numbers of eigenvalues based on options and numbers of DOFs.\n \"\"\"\n solver_n_eigs = n_eigs = options.n_eigs\n n_dof = mtxs['K'].shape[0]\n if options.mode == 'omega':\n if options.n_eigs > n_dof:\n n_eigs = n_dof\n solver_n_eigs = None\n\n else:\n if options.n_eigs > 2 * n_dof:\n n_eigs = 2 * n_dof\n solver_n_eigs = None\n\n return solver_n_eigs, n_eigs\n\ndef build_evp_matrices(mtxs, val, mode, pb):\n \"\"\"\n Build the matrices of the dispersion eigenvalue problem.\n \"\"\"\n if mode == 'omega':\n mtx_a = mtxs['K'] + val**2 * mtxs['S'] + val * mtxs['R']\n output('A - A^H:', max_diff_csr(mtx_a, mtx_a.H))\n\n evp_mtxs = (mtx_a, mtxs['M'])\n\n else:\n evp_mtxs = (mtxs['S'], mtxs['R'], mtxs['K'] - val**2 * mtxs['M'])\n\n return evp_mtxs\n\ndef process_evp_results(eigs, svecs, val, wdir, bzone, pb, mtxs, options,\n std_wave_fun=None):\n \"\"\"\n Transform eigenvalues to either omegas or kappas, depending on `mode`.\n Transform eigenvectors, if available, depending on `mode`.\n Return also the values to log.\n \"\"\"\n if options.mode == 'omega':\n omegas = nm.sqrt(eigs)\n\n output('eigs, omegas:')\n for ii, om in enumerate(omegas):\n output('{:>3}. {: .10e}, {:.10e}'.format(ii, eigs[ii], om))\n\n if options.stepper == 'linear':\n out = tuple(eigs) + tuple(omegas)\n\n else:\n out = tuple(val * wdir) + tuple(omegas)\n\n if std_wave_fun is not None:\n out = out + std_wave_fun(val, wdir)\n\n return omegas, svecs, out\n\n else:\n kappas = eigs.copy()\n rks = kappas.copy()\n\n # Mask modes far from 1. Brillouin zone.\n max_kappa = 1.2 * bzone\n kappas[kappas.real > max_kappa] = nm.nan\n\n # Mask non-physical modes.\n kappas[kappas.real < 0] = nm.nan\n kappas[nm.abs(kappas.imag) > 1e-10] = nm.nan\n out = tuple(kappas.real)\n\n output('raw kappas, masked real part:',)\n for ii, kr in enumerate(kappas.real):\n output('{:>3}. {: 23.5e}, {:.10e}'.format(ii, rks[ii], kr))\n\n if svecs is not None:\n n_dof = mtxs['K'].shape[0]\n # Select only vectors corresponding to physical modes.\n ii = nm.isfinite(kappas.real)\n svecs = svecs[:n_dof, ii]\n\n if std_wave_fun is not None:\n out = out + tuple(ii if ii <= max_kappa else nm.nan\n for ii in std_wave_fun(val, wdir))\n\n return kappas, svecs, out\n\nhelps = {\n 'pars' :\n 'material parameters in Y1, Y2 subdomains in basic units'\n ' [default: %(default)s]',\n 'conf' :\n 'if given, an alternative problem description file with apply_units() and'\n ' define() functions [default: %(default)s]',\n 'define_kwargs' : 'additional keyword arguments passed to define()',\n 'mesh_size' :\n 'desired mesh size (max. of bounding box dimensions) in basic units'\n ' - the input periodic cell mesh is rescaled to this size'\n ' [default: %(default)s]',\n 'unit_multipliers' :\n 'basic unit multipliers (time, length, mass) [default: %(default)s]',\n 'plane' :\n 'for 2D problems, plane strain or stress hypothesis selection'\n ' [default: %(default)s]',\n 'wave_dir' : 'the wave vector direction (will be normalized)'\n ' [default: %(default)s]',\n 'mode' : 'solution mode: omega = solve a generalized EVP for omega,'\n ' kappa = solve a quadratic generalized EVP for kappa'\n ' [default: %(default)s]',\n 'stepper' : 'the range stepper. For \"brillouin\", only the number'\n ' of items from --range is used'\n ' [default: %(default)s]',\n 'range' : 'the wave vector magnitude / frequency range'\n ' (like numpy.linspace) depending on the mode option'\n ' [default: %(default)s]',\n 'order' : 'displacement field approximation order [default: %(default)s]',\n 'refine' : 'number of uniform mesh refinements [default: %(default)s]',\n 'n_eigs' : 'the number of eigenvalues to compute [default: %(default)s]',\n 'eigs_only' : 'compute only eigenvalues, not eigenvectors',\n 'post_process' : 'post-process eigenvectors',\n 'solver_conf' : 'eigenvalue problem solver configuration options'\n ' [default: %(default)s]',\n 'save_regions' : 'save defined regions into'\n ' /regions.vtk',\n 'save_materials' : 'save material parameters into'\n ' /materials.vtk',\n 'log_std_waves' : 'log also standard pressure dilatation and shear waves',\n 'no_legends' :\n 'do not show legends in the log plots',\n 'no_show' :\n 'do not show the log figure',\n 'silent' : 'do not print messages to screen',\n 'clear' :\n 'clear old solution files from output directory',\n 'output_dir' :\n 'output directory [default: %(default)s]',\n 'mesh_filename' :\n 'input periodic cell mesh file name [default: %(default)s]',\n}\n\ndef main():\n # Aluminium and epoxy.\n default_pars = '70e9,0.35,2.799e3, 3.8e9,0.27,1.142e3'\n default_solver_conf = (\"kind='eig.scipy',method='eigsh',tol=1.0e-5,\"\n \"maxiter=1000,which='LM',sigma=0.0\")\n\n parser = ArgumentParser(description=__doc__,\n formatter_class=RawDescriptionHelpFormatter)\n parser.add_argument('--pars', metavar='young1,poisson1,density1'\n ',young2,poisson2,density2',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='pars',\n default=default_pars, help=helps['pars'])\n parser.add_argument('--conf', metavar='filename',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='conf',\n default=None, help=helps['conf'])\n parser.add_argument('--define-kwargs', metavar='dict-like',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='define_kwargs',\n default=None, help=helps['define_kwargs'])\n parser.add_argument('--mesh-size', type=float, metavar='float',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='mesh_size',\n default=None, help=helps['mesh_size'])\n parser.add_argument('--unit-multipliers',\n metavar='c_time,c_length,c_mass',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='unit_multipliers',\n default='1.0,1.0,1.0', help=helps['unit_multipliers'])\n parser.add_argument('--plane', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='plane',\n choices=['strain', 'stress'],\n default='strain', help=helps['plane'])\n parser.add_argument('--wave-dir', metavar='float,float[,float]',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='wave_dir',\n default='1.0,0.0,0.0', help=helps['wave_dir'])\n parser.add_argument('--mode', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='mode',\n choices=['omega', 'kappa'],\n default='omega', help=helps['mode'])\n parser.add_argument('--stepper', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='stepper',\n choices=['linear', 'brillouin'],\n default='linear', help=helps['stepper'])\n parser.add_argument('--range', metavar='start,stop,count',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='range',\n default='0,6.4,33', help=helps['range'])\n parser.add_argument('--order', metavar='int', type=int,\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='order',\n default=1, help=helps['order'])\n parser.add_argument('--refine', metavar='int', type=int,\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='refine',\n default=0, help=helps['refine'])\n parser.add_argument('-n', '--n-eigs', metavar='int', type=int,\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='n_eigs',\n default=6, help=helps['n_eigs'])\n group = parser.add_mutually_exclusive_group()\n group.add_argument('--eigs-only',\n action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='eigs_only',\n default=False, help=helps['eigs_only'])\n group.add_argument('--post-process',\n action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='post_process',\n default=False, help=helps['post_process'])\n parser.add_argument('--solver-conf', metavar='dict-like',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='solver_conf',\n default=default_solver_conf, help=helps['solver_conf'])\n parser.add_argument('--save-regions',\n action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='save_regions',\n default=False, help=helps['save_regions'])\n parser.add_argument('--save-materials',\n action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='save_materials',\n default=False, help=helps['save_materials'])\n parser.add_argument('--log-std-waves',\n action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='log_std_waves',\n default=False, help=helps['log_std_waves'])\n parser.add_argument('--no-legends',\n action="https://huggingface.co/datasets/luna-code/sfepy/store_false", dest='show_legends',\n default=True, help=helps['no_legends'])\n parser.add_argument('--no-show',\n action="https://huggingface.co/datasets/luna-code/sfepy/store_false", dest='show',\n default=True, help=helps['no_show'])\n parser.add_argument('--silent',\n action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='silent',\n default=False, help=helps['silent'])\n parser.add_argument('-c', '--clear',\n action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='clear',\n default=False, help=helps['clear'])\n parser.add_argument('-o', '--output-dir', metavar='path',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='output_dir',\n default='output', help=helps['output_dir'])\n parser.add_argument('mesh_filename', default='',\n help=helps['mesh_filename'])\n options = parser.parse_args()\n\n output_dir = options.output_dir\n\n output.set_output(filename=os.path.join(output_dir,'output_log.txt'),\n combined=options.silent == False)\n\n if options.conf is not None:\n mod = import_file(options.conf)\n\n else:\n mod = sys.modules[__name__]\n\n apply_units = mod.apply_units\n define = mod.define\n set_wave_dir = mod.set_wave_dir\n setup_n_eigs = mod.setup_n_eigs\n build_evp_matrices = mod.build_evp_matrices\n save_materials = mod.save_materials\n get_std_wave_fun = mod.get_std_wave_fun\n get_stepper = mod.get_stepper\n process_evp_results = mod.process_evp_results\n\n options.pars = [float(ii) for ii in options.pars.split(',')]\n options.unit_multipliers = [float(ii)\n for ii in options.unit_multipliers.split(',')]\n options.wave_dir = [float(ii)\n for ii in options.wave_dir.split(',')]\n aux = options.range.split(',')\n options.range = [float(aux[0]), float(aux[1]), int(aux[2])]\n options.solver_conf = dict_from_string(options.solver_conf)\n options.define_kwargs = dict_from_string(options.define_kwargs)\n\n if options.clear:\n remove_files_patterns(output_dir,\n ['*.h5', '*.vtk', '*.txt'],\n ignores=['output_log.txt'],\n verbose=True)\n\n filename = os.path.join(output_dir, 'options.txt')\n ensure_path(filename)\n save_options(filename, [('options', vars(options))],\n quote_command_line=True)\n\n pars = apply_units(options.pars, options.unit_multipliers)\n output('material parameters with applied unit multipliers:')\n "},"completion":{"kind":"string","value":"output(pars)"},"api":{"kind":"string","value":"sfepy.base.base.output"}}},{"rowIdx":72,"cells":{"prompt":{"kind":"string","value":"#!/usr/bin/env python\n\"\"\"\nDispersion analysis of a heterogeneous finite scale periodic cell.\n\nThe periodic cell mesh has to contain two subdomains Y1 (with the cell ids 1),\nY2 (with the cell ids 2), so that different material properties can be defined\nin each of the subdomains (see ``--pars`` option). The command line parameters\ncan be given in any consistent unit set, for example the basic SI units. The\n``--unit-multipliers`` option can be used to rescale the input units to ones\nmore suitable to the simulation, for example to prevent having different\nmatrix blocks with large differences of matrix entries magnitudes. The results\nare then in the rescaled units.\n\nUsage Examples\n--------------\n\nDefault material parameters, a square periodic cell with a spherical inclusion,\nlogs also standard pressure dilatation and shear waves, no eigenvectors::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only\n\nAs above, with custom eigenvalue solver parameters, and different number of\neigenvalues, mesh size and units used in the calculation::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --solver-conf=\"kind='eig.scipy', method='eigsh', tol=1e-10, maxiter=1000, which='LM', sigma=0\" --log-std-waves -n 5 --range=0,640,101 --mode=omega --unit-multipliers=1e-6,1e-2,1e-3 --mesh-size=1e-2 --eigs-only\n\nDefault material parameters, a square periodic cell with a square inclusion,\nand a very small mesh to allow comparing the omega and kappa modes (full matrix\nsolver required!)::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf=\"kind='eig.scipy', method='eigh'\" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf=\"kind='eig.qevp', method='companion', mode='inverted', solver={kind='eig.scipy', method='eig'}\" --log-std-waves -n 500 --range=0,4000000,1001 --mesh-size=1e-2 --mode=kappa --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/kappa\n\nView/compare the resulting logs::\n\n python script/plot_logs.py output/omega/frequencies.txt --no-legends -g 1 -o mode-omega.png\n python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends -o mode-kappa.png\n python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends --swap-axes -o mode-kappa-t.png\n\nIn contrast to the heterogeneous square periodic cell, a homogeneous\nsquare periodic cell (the region Y2 is empty)::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_1m.mesh --solver-conf=\"kind='eig.scipy', method='eigh'\" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega-h\n\n python script/plot_logs.py output/omega-h/frequencies.txt --no-legends -g 1 -o mode-omega-h.png\n\nUse the Brillouin stepper::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves -n=60 --eigs-only --no-legends --stepper=brillouin\n\n python script/plot_logs.py output/frequencies.txt -g 0 --rc=\"'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4\" -o brillouin-stepper-kappas.png\n\n python script/plot_logs.py output/frequencies.txt -g 1 --no-legends --rc=\"'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4\" -o brillouin-stepper-omegas.png\n\nAdditional arguments can be passed to the problem configuration's\n:func:`define()` function using the ``--define-kwargs`` option. In this file,\nonly the mesh vertex separation parameter `mesh_eps` can be used::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only --define-kwargs=\"mesh_eps=1e-10\" --save-regions\n\"\"\"\nfrom __future__ import absolute_import\nimport os\nimport sys\nsys.path.append('.')\nimport gc\nfrom copy import copy\nfrom argparse import ArgumentParser, RawDescriptionHelpFormatter\n\nimport numpy as nm\nimport matplotlib.pyplot as plt\n\nfrom sfepy.base.base import import_file, output, Struct\nfrom sfepy.base.conf import dict_from_string, ProblemConf\nfrom sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options\nfrom sfepy.base.log import Log\nfrom sfepy.discrete.fem import MeshIO\nfrom sfepy.mechanics.matcoefs import stiffness_from_youngpoisson as stiffness\nimport sfepy.mechanics.matcoefs as mc\nfrom sfepy.mechanics.units import apply_unit_multipliers\nimport sfepy.discrete.fem.periodic as per\nfrom sfepy.discrete.fem.meshio import convert_complex_output\nfrom sfepy.homogenization.utils import define_box_regions\nfrom sfepy.discrete import Problem\nfrom sfepy.mechanics.tensors import get_von_mises_stress\nfrom sfepy.solvers import Solver\nfrom sfepy.solvers.ts import get_print_info, TimeStepper\nfrom sfepy.linalg.utils import output_array_stats, max_diff_csr\n\ndef apply_units(pars, unit_multipliers):\n new_pars = apply_unit_multipliers(pars,\n ['stress', 'one', 'density',\n 'stress', 'one' ,'density'],\n unit_multipliers)\n return new_pars\n\ndef compute_von_mises(out, pb, state, extend=False, wmag=None, wdir=None):\n \"\"\"\n Calculate the von Mises stress.\n \"\"\"\n stress = pb.evaluate('ev_cauchy_stress.i.Omega(m.D, u)', mode='el_avg')\n\n vms = get_von_mises_stress(stress.squeeze())\n vms.shape = (vms.shape[0], 1, 1, 1)\n out['von_mises_stress'] = Struct(name='output_data', mode='cell',\n data=vms)\n\n return out\n\ndef define(filename_mesh, pars, approx_order, refinement_level, solver_conf,\n plane='strain', post_process=False, mesh_eps=1e-8):\n io = MeshIO.any_from_filename(filename_mesh)\n bbox = io.read_bounding_box()\n dim = bbox.shape[1]\n\n options = {\n 'absolute_mesh_path' : True,\n 'refinement_level' : refinement_level,\n 'allow_empty_regions' : True,\n 'post_process_hook' : 'compute_von_mises' if post_process else None,\n }\n\n fields = {\n 'displacement': ('complex', dim, 'Omega', approx_order),\n }\n\n young1, poisson1, density1, young2, poisson2, density2 = pars\n materials = {\n 'm' : ({\n 'D' : {'Y1' : stiffness(dim, young=young1, poisson=poisson1,\n plane=plane),\n 'Y2' : stiffness(dim, young=young2, poisson=poisson2,\n plane=plane)},\n 'density' : {'Y1' : density1, 'Y2' : density2},\n },),\n 'wave' : 'get_wdir',\n }\n\n variables = {\n 'u' : ('unknown field', 'displacement', 0),\n 'v' : ('test field', 'displacement', 'u'),\n }\n\n regions = {\n 'Omega' : 'all',\n 'Y1': 'cells of group 1',\n 'Y2': 'cells of group 2',\n }\n regions.update(define_box_regions(dim,\n bbox[0], bbox[1], mesh_eps))\n\n ebcs = {\n }\n\n if dim == 3:\n epbcs = {\n 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},\n 'match_x_plane'),\n 'periodic_y' : (['Near', 'Far'], {'u.all' : 'u.all'},\n 'match_y_plane'),\n 'periodic_z' : (['Top', 'Bottom'], {'u.all' : 'u.all'},\n 'match_z_plane'),\n }\n else:\n epbcs = {\n 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},\n 'match_y_line'),\n 'periodic_y' : (['Bottom', 'Top'], {'u.all' : 'u.all'},\n 'match_x_line'),\n }\n\n per.set_accuracy(mesh_eps)\n functions = {\n 'match_x_plane' : (per.match_x_plane,),\n 'match_y_plane' : (per.match_y_plane,),\n 'match_z_plane' : (per.match_z_plane,),\n 'match_x_line' : (per.match_x_line,),\n 'match_y_line' : (per.match_y_line,),\n 'get_wdir' : (get_wdir,),\n }\n\n integrals = {\n 'i' : 2 * approx_order,\n }\n\n equations = {\n 'K' : 'dw_lin_elastic.i.Omega(m.D, v, u)',\n 'S' : 'dw_elastic_wave.i.Omega(m.D, wave.vec, v, u)',\n 'R' : \"\"\"1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, u, v)\n - 1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, v, u)\"\"\",\n 'M' : 'dw_volume_dot.i.Omega(m.density, v, u)',\n }\n\n solver_0 = solver_conf.copy()\n solver_0['name'] = 'eig'\n\n return locals()\n\ndef get_wdir(ts, coors, mode=None,\n equations=None, term=None, problem=None, wdir=None, **kwargs):\n if mode == 'special':\n return {'vec' : wdir}\n\ndef set_wave_dir(pb, wdir):\n materials = pb.get_materials()\n wave_mat = materials['wave']\n wave_mat.set_extra_args(wdir=wdir)\n\ndef save_materials(output_dir, pb, options):\n stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n young, poisson = mc.youngpoisson_from_stiffness(stiffness,\n plane=options.plane)\n density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n\n out = {}\n out['young'] = Struct(name='young', mode='cell',\n data=young[..., None, None])\n out['poisson'] = Struct(name='poisson', mode='cell',\n data=poisson[..., None, None])\n out['density'] = Struct(name='density', mode='cell', data=density)\n materials_filename = os.path.join(output_dir, 'materials.vtk')\n pb.save_state(materials_filename, out=out)\n\ndef get_std_wave_fun(pb, options):\n stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n young, poisson = mc.youngpoisson_from_stiffness(stiffness,\n plane=options.plane)\n density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n\n lam, mu = mc.lame_from_youngpoisson(young, poisson,\n plane=options.plane)\n alam = nm.average(lam)\n amu = nm.average(mu)\n adensity = nm.average(density)\n\n cp = nm.sqrt((alam + 2.0 * amu) / adensity)\n cs = nm.sqrt(amu / adensity)\n output('average p-wave speed:', cp)\n output('average shear wave speed:', cs)\n\n log_names = [r'$\\omega_p$', r'$\\omega_s$']\n log_plot_kwargs = [{'ls' : '--', 'color' : 'k'},\n {'ls' : '--', 'color' : 'gray'}]\n\n if options.mode == 'omega':\n fun = lambda wmag, wdir: (cp * wmag, cs * wmag)\n\n else:\n fun = lambda wmag, wdir: (wmag / cp, wmag / cs)\n\n return fun, log_names, log_plot_kwargs\n\ndef get_stepper(rng, pb, options):\n if options.stepper == 'linear':\n stepper = TimeStepper(rng[0], rng[1], dt=None, n_step=rng[2])\n return stepper\n\n bbox = pb.domain.mesh.get_bounding_box()\n\n bzone = 2.0 * nm.pi / (bbox[1] - bbox[0])\n\n num = rng[2] // 3\n\n class BrillouinStepper(Struct):\n \"\"\"\n Step over 1. Brillouin zone in xy plane.\n \"\"\"\n def __init__(self, t0, t1, dt=None, n_step=None, step=None, **kwargs):\n Struct.__init__(self, t0=t0, t1=t1, dt=dt, n_step=n_step, step=step)\n\n self.n_digit, self.format, self.suffix = get_print_info(self.n_step)\n\n def __iter__(self):\n ts = TimeStepper(0, bzone[0], dt=None, n_step=num)\n for ii, val in ts:\n yield ii, val, nm.array([1.0, 0.0])\n if ii == (num-2): break\n\n ts = TimeStepper(0, bzone[1], dt=None, n_step=num)\n for ii, k1 in ts:\n wdir = nm.array([bzone[0], k1])\n val = nm.linalg.norm(wdir)\n wdir = wdir / val\n yield num + ii, val, wdir\n if ii == (num-2): break\n\n wdir = nm.array([bzone[0], bzone[1]])\n val = nm.linalg.norm(wdir)\n wdir = wdir / val\n ts = TimeStepper(0, 1, dt=None, n_step=num)\n for ii, _ in ts:\n yield 2 * num + ii, val * (1.0 - float(ii)/(num-1)), wdir\n\n stepper = BrillouinStepper(0, 1, n_step=rng[2])\n\n return stepper\n\ndef save_eigenvectors(filename, svecs, wmag, wdir, pb):\n if svecs is None: return\n\n variables = pb.get_variables()\n # Make full eigenvectors (add DOFs fixed by boundary conditions).\n vecs = nm.empty((variables.di.ptr[-1], svecs.shape[1]),\n dtype=svecs.dtype)\n for ii in range(svecs.shape[1]):\n vecs[:, ii] = variables.make_full_vec(svecs[:, ii])\n\n # Save the eigenvectors.\n out = {}\n state = pb.create_state()\n\n pp_name = pb.conf.options.get('post_process_hook')\n pp = getattr(pb.conf.funmod, pp_name if pp_name is not None else '',\n lambda out, *args, **kwargs: out)\n\n for ii in range(svecs.shape[1]):\n state.set_full(vecs[:, ii])\n aux = state.create_output_dict()\n aux2 = {}\n pp(aux2, pb, state, wmag=wmag, wdir=wdir)\n aux.update(convert_complex_output(aux2))\n out.update({key + '%03d' % ii : aux[key] for key in aux})\n\n pb.save_state(filename, out=out)\n\ndef assemble_matrices(define, mod, pars, set_wave_dir, options, wdir=None):\n \"\"\"\n Assemble the blocks of dispersion eigenvalue problem matrices.\n \"\"\"\n define_dict = define(filename_mesh=options.mesh_filename,\n pars=pars,\n approx_order=options.order,\n refinement_level=options.refine,\n solver_conf=options.solver_conf,\n plane=options.plane,\n post_process=options.post_process,\n **options.define_kwargs)\n\n conf = ProblemConf.from_dict(define_dict, mod)\n\n pb = Problem.from_conf(conf)\n pb.dispersion_options = options\n pb.set_output_dir(options.output_dir)\n dim = pb.domain.shape.dim\n\n # Set the normalized wave vector direction to the material(s).\n if wdir is None:\n wdir = nm.asarray(options.wave_dir[:dim], dtype=nm.float64)\n wdir = wdir / nm.linalg.norm(wdir)\n set_wave_dir(pb, wdir)\n\n bbox = pb.domain.mesh.get_bounding_box()\n size = (bbox[1] - bbox[0]).max()\n scaling0 = apply_unit_multipliers([1.0], ['length'],\n options.unit_multipliers)[0]\n scaling = scaling0\n if options.mesh_size is not None:\n scaling *= options.mesh_size / size\n output('scaling factor of periodic cell mesh coordinates:', scaling)\n output('new mesh size with applied unit multipliers:', scaling * size)\n pb.domain.mesh.coors[:] *= scaling\n pb.set_mesh_coors(pb.domain.mesh.coors, update_fields=True)\n\n bzone = 2.0 * nm.pi / (scaling * size)\n output('1. Brillouin zone size:', bzone * scaling0)\n output('1. Brillouin zone size with applied unit multipliers:', bzone)\n\n pb.time_update()\n pb.update_materials()\n\n # Assemble the matrices.\n mtxs = {}\n for key, eq in pb.equations.iteritems():\n mtxs[key] = mtx = pb.mtx_a.copy()\n mtx = eq.evaluate(mode='weak', dw_mode='matrix', asm_obj=mtx)\n mtx.eliminate_zeros()\n output_array_stats(mtx.data, 'nonzeros in %s' % key)\n\n output('symmetry checks:')\n output('%s - %s^T:' % (key, key), max_diff_csr(mtx, mtx.T))\n output('%s - %s^H:' % (key, key), max_diff_csr(mtx, mtx.H))\n\n return pb, wdir, bzone, mtxs\n\ndef setup_n_eigs(options, pb, mtxs):\n \"\"\"\n Setup the numbers of eigenvalues based on options and numbers of DOFs.\n \"\"\"\n solver_n_eigs = n_eigs = options.n_eigs\n n_dof = mtxs['K'].shape[0]\n if options.mode == 'omega':\n if options.n_eigs > n_dof:\n n_eigs = n_dof\n solver_n_eigs = None\n\n else:\n if options.n_eigs > 2 * n_dof:\n n_eigs = 2 * n_dof\n solver_n_eigs = None\n\n return solver_n_eigs, n_eigs\n\ndef build_evp_matrices(mtxs, val, mode, pb):\n \"\"\"\n Build the matrices of the dispersion eigenvalue problem.\n \"\"\"\n if mode == 'omega':\n mtx_a = mtxs['K'] + val**2 * mtxs['S'] + val * mtxs['R']\n output('A - A^H:', max_diff_csr(mtx_a, mtx_a.H))\n\n evp_mtxs = (mtx_a, mtxs['M'])\n\n else:\n evp_mtxs = (mtxs['S'], mtxs['R'], mtxs['K'] - val**2 * mtxs['M'])\n\n return evp_mtxs\n\ndef process_evp_results(eigs, svecs, val, wdir, bzone, pb, mtxs, options,\n std_wave_fun=None):\n \"\"\"\n Transform eigenvalues to either omegas or kappas, depending on `mode`.\n Transform eigenvectors, if available, depending on `mode`.\n Return also the values to log.\n \"\"\"\n if options.mode == 'omega':\n omegas = nm.sqrt(eigs)\n\n output('eigs, omegas:')\n for ii, om in enumerate(omegas):\n output('{:>3}. {: .10e}, {:.10e}'.format(ii, eigs[ii], om))\n\n if options.stepper == 'linear':\n out = tuple(eigs) + tuple(omegas)\n\n else:\n out = tuple(val * wdir) + tuple(omegas)\n\n if std_wave_fun is not None:\n out = out + std_wave_fun(val, wdir)\n\n return omegas, svecs, out\n\n else:\n kappas = eigs.copy()\n rks = kappas.copy()\n\n # Mask modes far from 1. Brillouin zone.\n max_kappa = 1.2 * bzone\n kappas[kappas.real > max_kappa] = nm.nan\n\n # Mask non-physical modes.\n kappas[kappas.real < 0] = nm.nan\n kappas[nm.abs(kappas.imag) > 1e-10] = nm.nan\n out = tuple(kappas.real)\n\n output('raw kappas, masked real part:',)\n for ii, kr in enumerate(kappas.real):\n output('{:>3}. {: 23.5e}, {:.10e}'.format(ii, rks[ii], kr))\n\n if svecs is not None:\n n_dof = mtxs['K'].shape[0]\n # Select only vectors corresponding to physical modes.\n ii = nm.isfinite(kappas.real)\n svecs = svecs[:n_dof, ii]\n\n if std_wave_fun is not None:\n out = out + tuple(ii if ii <= max_kappa else nm.nan\n for ii in std_wave_fun(val, wdir))\n\n return kappas, svecs, out\n\nhelps = {\n 'pars' :\n 'material parameters in Y1, Y2 subdomains in basic units'\n ' [default: %(default)s]',\n 'conf' :\n 'if given, an alternative problem description file with apply_units() and'\n ' define() functions [default: %(default)s]',\n 'define_kwargs' : 'additional keyword arguments passed to define()',\n 'mesh_size' :\n 'desired mesh size (max. of bounding box dimensions) in basic units'\n ' - the input periodic cell mesh is rescaled to this size'\n ' [default: %(default)s]',\n 'unit_multipliers' :\n 'basic unit multipliers (time, length, mass) [default: %(default)s]',\n 'plane' :\n 'for 2D problems, plane strain or stress hypothesis selection'\n ' [default: %(default)s]',\n 'wave_dir' : 'the wave vector direction (will be normalized)'\n ' [default: %(default)s]',\n 'mode' : 'solution mode: omega = solve a generalized EVP for omega,'\n ' kappa = solve a quadratic generalized EVP for kappa'\n ' [default: %(default)s]',\n 'stepper' : 'the range stepper. For \"brillouin\", only the number'\n ' of items from --range is used'\n ' [default: %(default)s]',\n 'range' : 'the wave vector magnitude / frequency range'\n ' (like numpy.linspace) depending on the mode option'\n ' [default: %(default)s]',\n 'order' : 'displacement field approximation order [default: %(default)s]',\n 'refine' : 'number of uniform mesh refinements [default: %(default)s]',\n 'n_eigs' : 'the number of eigenvalues to compute [default: %(default)s]',\n 'eigs_only' : 'compute only eigenvalues, not eigenvectors',\n 'post_process' : 'post-process eigenvectors',\n 'solver_conf' : 'eigenvalue problem solver configuration options'\n ' [default: %(default)s]',\n 'save_regions' : 'save defined regions into'\n ' /regions.vtk',\n 'save_materials' : 'save material parameters into'\n ' /materials.vtk',\n 'log_std_waves' : 'log also standard pressure dilatation and shear waves',\n 'no_legends' :\n 'do not show legends in the log plots',\n 'no_show' :\n 'do not show the log figure',\n 'silent' : 'do not print messages to screen',\n 'clear' :\n 'clear old solution files from output directory',\n 'output_dir' :\n 'output directory [default: %(default)s]',\n 'mesh_filename' :\n 'input periodic cell mesh file name [default: %(default)s]',\n}\n\ndef main():\n # Aluminium and epoxy.\n default_pars = '70e9,0.35,2.799e3, 3.8e9,0.27,1.142e3'\n default_solver_conf = (\"kind='eig.scipy',method='eigsh',tol=1.0e-5,\"\n \"maxiter=1000,which='LM',sigma=0.0\")\n\n parser = ArgumentParser(description=__doc__,\n formatter_class=RawDescriptionHelpFormatter)\n parser.add_argument('--pars', metavar='young1,poisson1,density1'\n ',young2,poisson2,density2',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='pars',\n default=default_pars, help=helps['pars'])\n parser.add_argument('--conf', metavar='filename',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='conf',\n default=None, help=helps['conf'])\n parser.add_argument('--define-kwargs', metavar='dict-like',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='define_kwargs',\n default=None, help=helps['define_kwargs'])\n parser.add_argument('--mesh-size', type=float, metavar='float',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='mesh_size',\n default=None, help=helps['mesh_size'])\n parser.add_argument('--unit-multipliers',\n metavar='c_time,c_length,c_mass',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='unit_multipliers',\n default='1.0,1.0,1.0', help=helps['unit_multipliers'])\n parser.add_argument('--plane', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='plane',\n choices=['strain', 'stress'],\n default='strain', help=helps['plane'])\n parser.add_argument('--wave-dir', metavar='float,float[,float]',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='wave_dir',\n default='1.0,0.0,0.0', help=helps['wave_dir'])\n parser.add_argument('--mode', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='mode',\n choices=['omega', 'kappa'],\n default='omega', help=helps['mode'])\n parser.add_argument('--stepper', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='stepper',\n choices=['linear', 'brillouin'],\n default='linear', help=helps['stepper'])\n parser.add_argument('--range', metavar='start,stop,count',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='range',\n default='0,6.4,33', help=helps['range'])\n parser.add_argument('--order', metavar='int', type=int,\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='order',\n default=1, help=helps['order'])\n parser.add_argument('--refine', metavar='int', type=int,\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='refine',\n default=0, help=helps['refine'])\n parser.add_argument('-n', '--n-eigs', metavar='int', type=int,\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='n_eigs',\n default=6, help=helps['n_eigs'])\n group = parser.add_mutually_exclusive_group()\n group.add_argument('--eigs-only',\n action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='eigs_only',\n default=False, help=helps['eigs_only'])\n group.add_argument('--post-process',\n action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='post_process',\n default=False, help=helps['post_process'])\n parser.add_argument('--solver-conf', metavar='dict-like',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='solver_conf',\n default=default_solver_conf, help=helps['solver_conf'])\n parser.add_argument('--save-regions',\n action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='save_regions',\n default=False, help=helps['save_regions'])\n parser.add_argument('--save-materials',\n action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='save_materials',\n default=False, help=helps['save_materials'])\n parser.add_argument('--log-std-waves',\n action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='log_std_waves',\n default=False, help=helps['log_std_waves'])\n parser.add_argument('--no-legends',\n action="https://huggingface.co/datasets/luna-code/sfepy/store_false", dest='show_legends',\n default=True, help=helps['no_legends'])\n parser.add_argument('--no-show',\n action="https://huggingface.co/datasets/luna-code/sfepy/store_false", dest='show',\n default=True, help=helps['no_show'])\n parser.add_argument('--silent',\n action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='silent',\n default=False, help=helps['silent'])\n parser.add_argument('-c', '--clear',\n action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='clear',\n default=False, help=helps['clear'])\n parser.add_argument('-o', '--output-dir', metavar='path',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='output_dir',\n default='output', help=helps['output_dir'])\n parser.add_argument('mesh_filename', default='',\n help=helps['mesh_filename'])\n options = parser.parse_args()\n\n output_dir = options.output_dir\n\n output.set_output(filename=os.path.join(output_dir,'output_log.txt'),\n combined=options.silent == False)\n\n if options.conf is not None:\n mod = import_file(options.conf)\n\n else:\n mod = sys.modules[__name__]\n\n apply_units = mod.apply_units\n define = mod.define\n set_wave_dir = mod.set_wave_dir\n setup_n_eigs = mod.setup_n_eigs\n build_evp_matrices = mod.build_evp_matrices\n save_materials = mod.save_materials\n get_std_wave_fun = mod.get_std_wave_fun\n get_stepper = mod.get_stepper\n process_evp_results = mod.process_evp_results\n\n options.pars = [float(ii) for ii in options.pars.split(',')]\n options.unit_multipliers = [float(ii)\n for ii in options.unit_multipliers.split(',')]\n options.wave_dir = [float(ii)\n for ii in options.wave_dir.split(',')]\n aux = options.range.split(',')\n options.range = [float(aux[0]), float(aux[1]), int(aux[2])]\n options.solver_conf = dict_from_string(options.solver_conf)\n options.define_kwargs = dict_from_string(options.define_kwargs)\n\n if options.clear:\n remove_files_patterns(output_dir,\n ['*.h5', '*.vtk', '*.txt'],\n ignores=['output_log.txt'],\n verbose=True)\n\n filename = os.path.join(output_dir, 'options.txt')\n ensure_path(filename)\n save_options(filename, [('options', vars(options))],\n quote_command_line=True)\n\n pars = apply_units(options.pars, options.unit_multipliers)\n output('material parameters with applied unit multipliers:')\n output(pars)\n\n if options.mode == 'omega':\n rng = copy(options.range)\n rng[:2] = apply_unit_multipliers(options.range[:2],\n ['wave_number', 'wave_number'],\n options.unit_multipliers)\n output('wave number range with applied unit multipliers:', rng)\n\n else:\n if options.stepper == 'brillouin':\n raise ValueError('Cannot use \"brillouin\" stepper in kappa mode!')\n\n rng = copy(options.range)\n rng[:2] = apply_unit_multipliers(options.range[:2],\n ['frequency', 'frequency'],\n options.unit_multipliers)\n output('frequency range with applied unit multipliers:', rng)\n\n pb, wdir, bzone, mtxs = assemble_matrices(define, mod, pars, set_wave_dir,\n options)\n dim = pb.domain.shape.dim\n\n if dim != 2:\n options.plane = 'strain'\n\n if options.save_regions:\n pb.save_regions_as_groups(os.path.join(output_dir, 'regions'))\n\n if options.save_materials:\n save_materials(output_dir, pb, options)\n\n conf = pb.solver_confs['eig']\n eig_solver = "},"completion":{"kind":"string","value":"Solver.any_from_conf(conf)"},"api":{"kind":"string","value":"sfepy.solvers.Solver.any_from_conf"}}},{"rowIdx":73,"cells":{"prompt":{"kind":"string","value":"#!/usr/bin/env python\n\"\"\"\nDispersion analysis of a heterogeneous finite scale periodic cell.\n\nThe periodic cell mesh has to contain two subdomains Y1 (with the cell ids 1),\nY2 (with the cell ids 2), so that different material properties can be defined\nin each of the subdomains (see ``--pars`` option). The command line parameters\ncan be given in any consistent unit set, for example the basic SI units. The\n``--unit-multipliers`` option can be used to rescale the input units to ones\nmore suitable to the simulation, for example to prevent having different\nmatrix blocks with large differences of matrix entries magnitudes. The results\nare then in the rescaled units.\n\nUsage Examples\n--------------\n\nDefault material parameters, a square periodic cell with a spherical inclusion,\nlogs also standard pressure dilatation and shear waves, no eigenvectors::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only\n\nAs above, with custom eigenvalue solver parameters, and different number of\neigenvalues, mesh size and units used in the calculation::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --solver-conf=\"kind='eig.scipy', method='eigsh', tol=1e-10, maxiter=1000, which='LM', sigma=0\" --log-std-waves -n 5 --range=0,640,101 --mode=omega --unit-multipliers=1e-6,1e-2,1e-3 --mesh-size=1e-2 --eigs-only\n\nDefault material parameters, a square periodic cell with a square inclusion,\nand a very small mesh to allow comparing the omega and kappa modes (full matrix\nsolver required!)::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf=\"kind='eig.scipy', method='eigh'\" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf=\"kind='eig.qevp', method='companion', mode='inverted', solver={kind='eig.scipy', method='eig'}\" --log-std-waves -n 500 --range=0,4000000,1001 --mesh-size=1e-2 --mode=kappa --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/kappa\n\nView/compare the resulting logs::\n\n python script/plot_logs.py output/omega/frequencies.txt --no-legends -g 1 -o mode-omega.png\n python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends -o mode-kappa.png\n python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends --swap-axes -o mode-kappa-t.png\n\nIn contrast to the heterogeneous square periodic cell, a homogeneous\nsquare periodic cell (the region Y2 is empty)::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_1m.mesh --solver-conf=\"kind='eig.scipy', method='eigh'\" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega-h\n\n python script/plot_logs.py output/omega-h/frequencies.txt --no-legends -g 1 -o mode-omega-h.png\n\nUse the Brillouin stepper::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves -n=60 --eigs-only --no-legends --stepper=brillouin\n\n python script/plot_logs.py output/frequencies.txt -g 0 --rc=\"'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4\" -o brillouin-stepper-kappas.png\n\n python script/plot_logs.py output/frequencies.txt -g 1 --no-legends --rc=\"'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4\" -o brillouin-stepper-omegas.png\n\nAdditional arguments can be passed to the problem configuration's\n:func:`define()` function using the ``--define-kwargs`` option. In this file,\nonly the mesh vertex separation parameter `mesh_eps` can be used::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only --define-kwargs=\"mesh_eps=1e-10\" --save-regions\n\"\"\"\nfrom __future__ import absolute_import\nimport os\nimport sys\nsys.path.append('.')\nimport gc\nfrom copy import copy\nfrom argparse import ArgumentParser, RawDescriptionHelpFormatter\n\nimport numpy as nm\nimport matplotlib.pyplot as plt\n\nfrom sfepy.base.base import import_file, output, Struct\nfrom sfepy.base.conf import dict_from_string, ProblemConf\nfrom sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options\nfrom sfepy.base.log import Log\nfrom sfepy.discrete.fem import MeshIO\nfrom sfepy.mechanics.matcoefs import stiffness_from_youngpoisson as stiffness\nimport sfepy.mechanics.matcoefs as mc\nfrom sfepy.mechanics.units import apply_unit_multipliers\nimport sfepy.discrete.fem.periodic as per\nfrom sfepy.discrete.fem.meshio import convert_complex_output\nfrom sfepy.homogenization.utils import define_box_regions\nfrom sfepy.discrete import Problem\nfrom sfepy.mechanics.tensors import get_von_mises_stress\nfrom sfepy.solvers import Solver\nfrom sfepy.solvers.ts import get_print_info, TimeStepper\nfrom sfepy.linalg.utils import output_array_stats, max_diff_csr\n\ndef apply_units(pars, unit_multipliers):\n new_pars = apply_unit_multipliers(pars,\n ['stress', 'one', 'density',\n 'stress', 'one' ,'density'],\n unit_multipliers)\n return new_pars\n\ndef compute_von_mises(out, pb, state, extend=False, wmag=None, wdir=None):\n \"\"\"\n Calculate the von Mises stress.\n \"\"\"\n stress = pb.evaluate('ev_cauchy_stress.i.Omega(m.D, u)', mode='el_avg')\n\n vms = get_von_mises_stress(stress.squeeze())\n vms.shape = (vms.shape[0], 1, 1, 1)\n out['von_mises_stress'] = Struct(name='output_data', mode='cell',\n data=vms)\n\n return out\n\ndef define(filename_mesh, pars, approx_order, refinement_level, solver_conf,\n plane='strain', post_process=False, mesh_eps=1e-8):\n io = MeshIO.any_from_filename(filename_mesh)\n bbox = io.read_bounding_box()\n dim = bbox.shape[1]\n\n options = {\n 'absolute_mesh_path' : True,\n 'refinement_level' : refinement_level,\n 'allow_empty_regions' : True,\n 'post_process_hook' : 'compute_von_mises' if post_process else None,\n }\n\n fields = {\n 'displacement': ('complex', dim, 'Omega', approx_order),\n }\n\n young1, poisson1, density1, young2, poisson2, density2 = pars\n materials = {\n 'm' : ({\n 'D' : {'Y1' : stiffness(dim, young=young1, poisson=poisson1,\n plane=plane),\n 'Y2' : stiffness(dim, young=young2, poisson=poisson2,\n plane=plane)},\n 'density' : {'Y1' : density1, 'Y2' : density2},\n },),\n 'wave' : 'get_wdir',\n }\n\n variables = {\n 'u' : ('unknown field', 'displacement', 0),\n 'v' : ('test field', 'displacement', 'u'),\n }\n\n regions = {\n 'Omega' : 'all',\n 'Y1': 'cells of group 1',\n 'Y2': 'cells of group 2',\n }\n regions.update(define_box_regions(dim,\n bbox[0], bbox[1], mesh_eps))\n\n ebcs = {\n }\n\n if dim == 3:\n epbcs = {\n 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},\n 'match_x_plane'),\n 'periodic_y' : (['Near', 'Far'], {'u.all' : 'u.all'},\n 'match_y_plane'),\n 'periodic_z' : (['Top', 'Bottom'], {'u.all' : 'u.all'},\n 'match_z_plane'),\n }\n else:\n epbcs = {\n 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},\n 'match_y_line'),\n 'periodic_y' : (['Bottom', 'Top'], {'u.all' : 'u.all'},\n 'match_x_line'),\n }\n\n per.set_accuracy(mesh_eps)\n functions = {\n 'match_x_plane' : (per.match_x_plane,),\n 'match_y_plane' : (per.match_y_plane,),\n 'match_z_plane' : (per.match_z_plane,),\n 'match_x_line' : (per.match_x_line,),\n 'match_y_line' : (per.match_y_line,),\n 'get_wdir' : (get_wdir,),\n }\n\n integrals = {\n 'i' : 2 * approx_order,\n }\n\n equations = {\n 'K' : 'dw_lin_elastic.i.Omega(m.D, v, u)',\n 'S' : 'dw_elastic_wave.i.Omega(m.D, wave.vec, v, u)',\n 'R' : \"\"\"1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, u, v)\n - 1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, v, u)\"\"\",\n 'M' : 'dw_volume_dot.i.Omega(m.density, v, u)',\n }\n\n solver_0 = solver_conf.copy()\n solver_0['name'] = 'eig'\n\n return locals()\n\ndef get_wdir(ts, coors, mode=None,\n equations=None, term=None, problem=None, wdir=None, **kwargs):\n if mode == 'special':\n return {'vec' : wdir}\n\ndef set_wave_dir(pb, wdir):\n materials = pb.get_materials()\n wave_mat = materials['wave']\n wave_mat.set_extra_args(wdir=wdir)\n\ndef save_materials(output_dir, pb, options):\n stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n young, poisson = mc.youngpoisson_from_stiffness(stiffness,\n plane=options.plane)\n density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n\n out = {}\n out['young'] = Struct(name='young', mode='cell',\n data=young[..., None, None])\n out['poisson'] = Struct(name='poisson', mode='cell',\n data=poisson[..., None, None])\n out['density'] = Struct(name='density', mode='cell', data=density)\n materials_filename = os.path.join(output_dir, 'materials.vtk')\n pb.save_state(materials_filename, out=out)\n\ndef get_std_wave_fun(pb, options):\n stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n young, poisson = mc.youngpoisson_from_stiffness(stiffness,\n plane=options.plane)\n density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n\n lam, mu = mc.lame_from_youngpoisson(young, poisson,\n plane=options.plane)\n alam = nm.average(lam)\n amu = nm.average(mu)\n adensity = nm.average(density)\n\n cp = nm.sqrt((alam + 2.0 * amu) / adensity)\n cs = nm.sqrt(amu / adensity)\n output('average p-wave speed:', cp)\n output('average shear wave speed:', cs)\n\n log_names = [r'$\\omega_p$', r'$\\omega_s$']\n log_plot_kwargs = [{'ls' : '--', 'color' : 'k'},\n {'ls' : '--', 'color' : 'gray'}]\n\n if options.mode == 'omega':\n fun = lambda wmag, wdir: (cp * wmag, cs * wmag)\n\n else:\n fun = lambda wmag, wdir: (wmag / cp, wmag / cs)\n\n return fun, log_names, log_plot_kwargs\n\ndef get_stepper(rng, pb, options):\n if options.stepper == 'linear':\n stepper = "},"completion":{"kind":"string","value":"TimeStepper(rng[0], rng[1], dt=None, n_step=rng[2])"},"api":{"kind":"string","value":"sfepy.solvers.ts.TimeStepper"}}},{"rowIdx":74,"cells":{"prompt":{"kind":"string","value":"#!/usr/bin/env python\n\"\"\"\nDispersion analysis of a heterogeneous finite scale periodic cell.\n\nThe periodic cell mesh has to contain two subdomains Y1 (with the cell ids 1),\nY2 (with the cell ids 2), so that different material properties can be defined\nin each of the subdomains (see ``--pars`` option). The command line parameters\ncan be given in any consistent unit set, for example the basic SI units. The\n``--unit-multipliers`` option can be used to rescale the input units to ones\nmore suitable to the simulation, for example to prevent having different\nmatrix blocks with large differences of matrix entries magnitudes. The results\nare then in the rescaled units.\n\nUsage Examples\n--------------\n\nDefault material parameters, a square periodic cell with a spherical inclusion,\nlogs also standard pressure dilatation and shear waves, no eigenvectors::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only\n\nAs above, with custom eigenvalue solver parameters, and different number of\neigenvalues, mesh size and units used in the calculation::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --solver-conf=\"kind='eig.scipy', method='eigsh', tol=1e-10, maxiter=1000, which='LM', sigma=0\" --log-std-waves -n 5 --range=0,640,101 --mode=omega --unit-multipliers=1e-6,1e-2,1e-3 --mesh-size=1e-2 --eigs-only\n\nDefault material parameters, a square periodic cell with a square inclusion,\nand a very small mesh to allow comparing the omega and kappa modes (full matrix\nsolver required!)::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf=\"kind='eig.scipy', method='eigh'\" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf=\"kind='eig.qevp', method='companion', mode='inverted', solver={kind='eig.scipy', method='eig'}\" --log-std-waves -n 500 --range=0,4000000,1001 --mesh-size=1e-2 --mode=kappa --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/kappa\n\nView/compare the resulting logs::\n\n python script/plot_logs.py output/omega/frequencies.txt --no-legends -g 1 -o mode-omega.png\n python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends -o mode-kappa.png\n python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends --swap-axes -o mode-kappa-t.png\n\nIn contrast to the heterogeneous square periodic cell, a homogeneous\nsquare periodic cell (the region Y2 is empty)::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_1m.mesh --solver-conf=\"kind='eig.scipy', method='eigh'\" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega-h\n\n python script/plot_logs.py output/omega-h/frequencies.txt --no-legends -g 1 -o mode-omega-h.png\n\nUse the Brillouin stepper::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves -n=60 --eigs-only --no-legends --stepper=brillouin\n\n python script/plot_logs.py output/frequencies.txt -g 0 --rc=\"'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4\" -o brillouin-stepper-kappas.png\n\n python script/plot_logs.py output/frequencies.txt -g 1 --no-legends --rc=\"'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4\" -o brillouin-stepper-omegas.png\n\nAdditional arguments can be passed to the problem configuration's\n:func:`define()` function using the ``--define-kwargs`` option. In this file,\nonly the mesh vertex separation parameter `mesh_eps` can be used::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only --define-kwargs=\"mesh_eps=1e-10\" --save-regions\n\"\"\"\nfrom __future__ import absolute_import\nimport os\nimport sys\nsys.path.append('.')\nimport gc\nfrom copy import copy\nfrom argparse import ArgumentParser, RawDescriptionHelpFormatter\n\nimport numpy as nm\nimport matplotlib.pyplot as plt\n\nfrom sfepy.base.base import import_file, output, Struct\nfrom sfepy.base.conf import dict_from_string, ProblemConf\nfrom sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options\nfrom sfepy.base.log import Log\nfrom sfepy.discrete.fem import MeshIO\nfrom sfepy.mechanics.matcoefs import stiffness_from_youngpoisson as stiffness\nimport sfepy.mechanics.matcoefs as mc\nfrom sfepy.mechanics.units import apply_unit_multipliers\nimport sfepy.discrete.fem.periodic as per\nfrom sfepy.discrete.fem.meshio import convert_complex_output\nfrom sfepy.homogenization.utils import define_box_regions\nfrom sfepy.discrete import Problem\nfrom sfepy.mechanics.tensors import get_von_mises_stress\nfrom sfepy.solvers import Solver\nfrom sfepy.solvers.ts import get_print_info, TimeStepper\nfrom sfepy.linalg.utils import output_array_stats, max_diff_csr\n\ndef apply_units(pars, unit_multipliers):\n new_pars = apply_unit_multipliers(pars,\n ['stress', 'one', 'density',\n 'stress', 'one' ,'density'],\n unit_multipliers)\n return new_pars\n\ndef compute_von_mises(out, pb, state, extend=False, wmag=None, wdir=None):\n \"\"\"\n Calculate the von Mises stress.\n \"\"\"\n stress = pb.evaluate('ev_cauchy_stress.i.Omega(m.D, u)', mode='el_avg')\n\n vms = get_von_mises_stress(stress.squeeze())\n vms.shape = (vms.shape[0], 1, 1, 1)\n out['von_mises_stress'] = Struct(name='output_data', mode='cell',\n data=vms)\n\n return out\n\ndef define(filename_mesh, pars, approx_order, refinement_level, solver_conf,\n plane='strain', post_process=False, mesh_eps=1e-8):\n io = MeshIO.any_from_filename(filename_mesh)\n bbox = io.read_bounding_box()\n dim = bbox.shape[1]\n\n options = {\n 'absolute_mesh_path' : True,\n 'refinement_level' : refinement_level,\n 'allow_empty_regions' : True,\n 'post_process_hook' : 'compute_von_mises' if post_process else None,\n }\n\n fields = {\n 'displacement': ('complex', dim, 'Omega', approx_order),\n }\n\n young1, poisson1, density1, young2, poisson2, density2 = pars\n materials = {\n 'm' : ({\n 'D' : {'Y1' : stiffness(dim, young=young1, poisson=poisson1,\n plane=plane),\n 'Y2' : stiffness(dim, young=young2, poisson=poisson2,\n plane=plane)},\n 'density' : {'Y1' : density1, 'Y2' : density2},\n },),\n 'wave' : 'get_wdir',\n }\n\n variables = {\n 'u' : ('unknown field', 'displacement', 0),\n 'v' : ('test field', 'displacement', 'u'),\n }\n\n regions = {\n 'Omega' : 'all',\n 'Y1': 'cells of group 1',\n 'Y2': 'cells of group 2',\n }\n regions.update(define_box_regions(dim,\n bbox[0], bbox[1], mesh_eps))\n\n ebcs = {\n }\n\n if dim == 3:\n epbcs = {\n 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},\n 'match_x_plane'),\n 'periodic_y' : (['Near', 'Far'], {'u.all' : 'u.all'},\n 'match_y_plane'),\n 'periodic_z' : (['Top', 'Bottom'], {'u.all' : 'u.all'},\n 'match_z_plane'),\n }\n else:\n epbcs = {\n 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},\n 'match_y_line'),\n 'periodic_y' : (['Bottom', 'Top'], {'u.all' : 'u.all'},\n 'match_x_line'),\n }\n\n per.set_accuracy(mesh_eps)\n functions = {\n 'match_x_plane' : (per.match_x_plane,),\n 'match_y_plane' : (per.match_y_plane,),\n 'match_z_plane' : (per.match_z_plane,),\n 'match_x_line' : (per.match_x_line,),\n 'match_y_line' : (per.match_y_line,),\n 'get_wdir' : (get_wdir,),\n }\n\n integrals = {\n 'i' : 2 * approx_order,\n }\n\n equations = {\n 'K' : 'dw_lin_elastic.i.Omega(m.D, v, u)',\n 'S' : 'dw_elastic_wave.i.Omega(m.D, wave.vec, v, u)',\n 'R' : \"\"\"1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, u, v)\n - 1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, v, u)\"\"\",\n 'M' : 'dw_volume_dot.i.Omega(m.density, v, u)',\n }\n\n solver_0 = solver_conf.copy()\n solver_0['name'] = 'eig'\n\n return locals()\n\ndef get_wdir(ts, coors, mode=None,\n equations=None, term=None, problem=None, wdir=None, **kwargs):\n if mode == 'special':\n return {'vec' : wdir}\n\ndef set_wave_dir(pb, wdir):\n materials = pb.get_materials()\n wave_mat = materials['wave']\n wave_mat.set_extra_args(wdir=wdir)\n\ndef save_materials(output_dir, pb, options):\n stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n young, poisson = mc.youngpoisson_from_stiffness(stiffness,\n plane=options.plane)\n density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n\n out = {}\n out['young'] = Struct(name='young', mode='cell',\n data=young[..., None, None])\n out['poisson'] = Struct(name='poisson', mode='cell',\n data=poisson[..., None, None])\n out['density'] = Struct(name='density', mode='cell', data=density)\n materials_filename = os.path.join(output_dir, 'materials.vtk')\n pb.save_state(materials_filename, out=out)\n\ndef get_std_wave_fun(pb, options):\n stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n young, poisson = mc.youngpoisson_from_stiffness(stiffness,\n plane=options.plane)\n density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n\n lam, mu = mc.lame_from_youngpoisson(young, poisson,\n plane=options.plane)\n alam = nm.average(lam)\n amu = nm.average(mu)\n adensity = nm.average(density)\n\n cp = nm.sqrt((alam + 2.0 * amu) / adensity)\n cs = nm.sqrt(amu / adensity)\n output('average p-wave speed:', cp)\n output('average shear wave speed:', cs)\n\n log_names = [r'$\\omega_p$', r'$\\omega_s$']\n log_plot_kwargs = [{'ls' : '--', 'color' : 'k'},\n {'ls' : '--', 'color' : 'gray'}]\n\n if options.mode == 'omega':\n fun = lambda wmag, wdir: (cp * wmag, cs * wmag)\n\n else:\n fun = lambda wmag, wdir: (wmag / cp, wmag / cs)\n\n return fun, log_names, log_plot_kwargs\n\ndef get_stepper(rng, pb, options):\n if options.stepper == 'linear':\n stepper = TimeStepper(rng[0], rng[1], dt=None, n_step=rng[2])\n return stepper\n\n bbox = pb.domain.mesh.get_bounding_box()\n\n bzone = 2.0 * nm.pi / (bbox[1] - bbox[0])\n\n num = rng[2] // 3\n\n class BrillouinStepper(Struct):\n \"\"\"\n Step over 1. Brillouin zone in xy plane.\n \"\"\"\n def __init__(self, t0, t1, dt=None, n_step=None, step=None, **kwargs):\n Struct.__init__(self, t0=t0, t1=t1, dt=dt, n_step=n_step, step=step)\n\n self.n_digit, self.format, self.suffix = get_print_info(self.n_step)\n\n def __iter__(self):\n ts = TimeStepper(0, bzone[0], dt=None, n_step=num)\n for ii, val in ts:\n yield ii, val, nm.array([1.0, 0.0])\n if ii == (num-2): break\n\n ts = TimeStepper(0, bzone[1], dt=None, n_step=num)\n for ii, k1 in ts:\n wdir = nm.array([bzone[0], k1])\n val = nm.linalg.norm(wdir)\n wdir = wdir / val\n yield num + ii, val, wdir\n if ii == (num-2): break\n\n wdir = nm.array([bzone[0], bzone[1]])\n val = nm.linalg.norm(wdir)\n wdir = wdir / val\n ts = TimeStepper(0, 1, dt=None, n_step=num)\n for ii, _ in ts:\n yield 2 * num + ii, val * (1.0 - float(ii)/(num-1)), wdir\n\n stepper = BrillouinStepper(0, 1, n_step=rng[2])\n\n return stepper\n\ndef save_eigenvectors(filename, svecs, wmag, wdir, pb):\n if svecs is None: return\n\n variables = pb.get_variables()\n # Make full eigenvectors (add DOFs fixed by boundary conditions).\n vecs = nm.empty((variables.di.ptr[-1], svecs.shape[1]),\n dtype=svecs.dtype)\n for ii in range(svecs.shape[1]):\n vecs[:, ii] = variables.make_full_vec(svecs[:, ii])\n\n # Save the eigenvectors.\n out = {}\n state = pb.create_state()\n\n pp_name = pb.conf.options.get('post_process_hook')\n pp = getattr(pb.conf.funmod, pp_name if pp_name is not None else '',\n lambda out, *args, **kwargs: out)\n\n for ii in range(svecs.shape[1]):\n state.set_full(vecs[:, ii])\n aux = state.create_output_dict()\n aux2 = {}\n pp(aux2, pb, state, wmag=wmag, wdir=wdir)\n aux.update(convert_complex_output(aux2))\n out.update({key + '%03d' % ii : aux[key] for key in aux})\n\n pb.save_state(filename, out=out)\n\ndef assemble_matrices(define, mod, pars, set_wave_dir, options, wdir=None):\n \"\"\"\n Assemble the blocks of dispersion eigenvalue problem matrices.\n \"\"\"\n define_dict = define(filename_mesh=options.mesh_filename,\n pars=pars,\n approx_order=options.order,\n refinement_level=options.refine,\n solver_conf=options.solver_conf,\n plane=options.plane,\n post_process=options.post_process,\n **options.define_kwargs)\n\n conf = ProblemConf.from_dict(define_dict, mod)\n\n pb = Problem.from_conf(conf)\n pb.dispersion_options = options\n pb.set_output_dir(options.output_dir)\n dim = pb.domain.shape.dim\n\n # Set the normalized wave vector direction to the material(s).\n if wdir is None:\n wdir = nm.asarray(options.wave_dir[:dim], dtype=nm.float64)\n wdir = wdir / nm.linalg.norm(wdir)\n set_wave_dir(pb, wdir)\n\n bbox = pb.domain.mesh.get_bounding_box()\n size = (bbox[1] - bbox[0]).max()\n scaling0 = apply_unit_multipliers([1.0], ['length'],\n options.unit_multipliers)[0]\n scaling = scaling0\n if options.mesh_size is not None:\n scaling *= options.mesh_size / size\n output('scaling factor of periodic cell mesh coordinates:', scaling)\n output('new mesh size with applied unit multipliers:', scaling * size)\n pb.domain.mesh.coors[:] *= scaling\n pb.set_mesh_coors(pb.domain.mesh.coors, update_fields=True)\n\n bzone = 2.0 * nm.pi / (scaling * size)\n output('1. Brillouin zone size:', bzone * scaling0)\n output('1. Brillouin zone size with applied unit multipliers:', bzone)\n\n pb.time_update()\n pb.update_materials()\n\n # Assemble the matrices.\n mtxs = {}\n for key, eq in pb.equations.iteritems():\n mtxs[key] = mtx = pb.mtx_a.copy()\n mtx = eq.evaluate(mode='weak', dw_mode='matrix', asm_obj=mtx)\n mtx.eliminate_zeros()\n "},"completion":{"kind":"string","value":"output_array_stats(mtx.data, 'nonzeros in %s' % key)"},"api":{"kind":"string","value":"sfepy.linalg.utils.output_array_stats"}}},{"rowIdx":75,"cells":{"prompt":{"kind":"string","value":"#!/usr/bin/env python\n\"\"\"\nDispersion analysis of a heterogeneous finite scale periodic cell.\n\nThe periodic cell mesh has to contain two subdomains Y1 (with the cell ids 1),\nY2 (with the cell ids 2), so that different material properties can be defined\nin each of the subdomains (see ``--pars`` option). The command line parameters\ncan be given in any consistent unit set, for example the basic SI units. The\n``--unit-multipliers`` option can be used to rescale the input units to ones\nmore suitable to the simulation, for example to prevent having different\nmatrix blocks with large differences of matrix entries magnitudes. The results\nare then in the rescaled units.\n\nUsage Examples\n--------------\n\nDefault material parameters, a square periodic cell with a spherical inclusion,\nlogs also standard pressure dilatation and shear waves, no eigenvectors::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only\n\nAs above, with custom eigenvalue solver parameters, and different number of\neigenvalues, mesh size and units used in the calculation::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --solver-conf=\"kind='eig.scipy', method='eigsh', tol=1e-10, maxiter=1000, which='LM', sigma=0\" --log-std-waves -n 5 --range=0,640,101 --mode=omega --unit-multipliers=1e-6,1e-2,1e-3 --mesh-size=1e-2 --eigs-only\n\nDefault material parameters, a square periodic cell with a square inclusion,\nand a very small mesh to allow comparing the omega and kappa modes (full matrix\nsolver required!)::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf=\"kind='eig.scipy', method='eigh'\" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf=\"kind='eig.qevp', method='companion', mode='inverted', solver={kind='eig.scipy', method='eig'}\" --log-std-waves -n 500 --range=0,4000000,1001 --mesh-size=1e-2 --mode=kappa --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/kappa\n\nView/compare the resulting logs::\n\n python script/plot_logs.py output/omega/frequencies.txt --no-legends -g 1 -o mode-omega.png\n python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends -o mode-kappa.png\n python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends --swap-axes -o mode-kappa-t.png\n\nIn contrast to the heterogeneous square periodic cell, a homogeneous\nsquare periodic cell (the region Y2 is empty)::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_1m.mesh --solver-conf=\"kind='eig.scipy', method='eigh'\" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega-h\n\n python script/plot_logs.py output/omega-h/frequencies.txt --no-legends -g 1 -o mode-omega-h.png\n\nUse the Brillouin stepper::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves -n=60 --eigs-only --no-legends --stepper=brillouin\n\n python script/plot_logs.py output/frequencies.txt -g 0 --rc=\"'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4\" -o brillouin-stepper-kappas.png\n\n python script/plot_logs.py output/frequencies.txt -g 1 --no-legends --rc=\"'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4\" -o brillouin-stepper-omegas.png\n\nAdditional arguments can be passed to the problem configuration's\n:func:`define()` function using the ``--define-kwargs`` option. In this file,\nonly the mesh vertex separation parameter `mesh_eps` can be used::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only --define-kwargs=\"mesh_eps=1e-10\" --save-regions\n\"\"\"\nfrom __future__ import absolute_import\nimport os\nimport sys\nsys.path.append('.')\nimport gc\nfrom copy import copy\nfrom argparse import ArgumentParser, RawDescriptionHelpFormatter\n\nimport numpy as nm\nimport matplotlib.pyplot as plt\n\nfrom sfepy.base.base import import_file, output, Struct\nfrom sfepy.base.conf import dict_from_string, ProblemConf\nfrom sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options\nfrom sfepy.base.log import Log\nfrom sfepy.discrete.fem import MeshIO\nfrom sfepy.mechanics.matcoefs import stiffness_from_youngpoisson as stiffness\nimport sfepy.mechanics.matcoefs as mc\nfrom sfepy.mechanics.units import apply_unit_multipliers\nimport sfepy.discrete.fem.periodic as per\nfrom sfepy.discrete.fem.meshio import convert_complex_output\nfrom sfepy.homogenization.utils import define_box_regions\nfrom sfepy.discrete import Problem\nfrom sfepy.mechanics.tensors import get_von_mises_stress\nfrom sfepy.solvers import Solver\nfrom sfepy.solvers.ts import get_print_info, TimeStepper\nfrom sfepy.linalg.utils import output_array_stats, max_diff_csr\n\ndef apply_units(pars, unit_multipliers):\n new_pars = apply_unit_multipliers(pars,\n ['stress', 'one', 'density',\n 'stress', 'one' ,'density'],\n unit_multipliers)\n return new_pars\n\ndef compute_von_mises(out, pb, state, extend=False, wmag=None, wdir=None):\n \"\"\"\n Calculate the von Mises stress.\n \"\"\"\n stress = pb.evaluate('ev_cauchy_stress.i.Omega(m.D, u)', mode='el_avg')\n\n vms = get_von_mises_stress(stress.squeeze())\n vms.shape = (vms.shape[0], 1, 1, 1)\n out['von_mises_stress'] = Struct(name='output_data', mode='cell',\n data=vms)\n\n return out\n\ndef define(filename_mesh, pars, approx_order, refinement_level, solver_conf,\n plane='strain', post_process=False, mesh_eps=1e-8):\n io = MeshIO.any_from_filename(filename_mesh)\n bbox = io.read_bounding_box()\n dim = bbox.shape[1]\n\n options = {\n 'absolute_mesh_path' : True,\n 'refinement_level' : refinement_level,\n 'allow_empty_regions' : True,\n 'post_process_hook' : 'compute_von_mises' if post_process else None,\n }\n\n fields = {\n 'displacement': ('complex', dim, 'Omega', approx_order),\n }\n\n young1, poisson1, density1, young2, poisson2, density2 = pars\n materials = {\n 'm' : ({\n 'D' : {'Y1' : stiffness(dim, young=young1, poisson=poisson1,\n plane=plane),\n 'Y2' : stiffness(dim, young=young2, poisson=poisson2,\n plane=plane)},\n 'density' : {'Y1' : density1, 'Y2' : density2},\n },),\n 'wave' : 'get_wdir',\n }\n\n variables = {\n 'u' : ('unknown field', 'displacement', 0),\n 'v' : ('test field', 'displacement', 'u'),\n }\n\n regions = {\n 'Omega' : 'all',\n 'Y1': 'cells of group 1',\n 'Y2': 'cells of group 2',\n }\n regions.update(define_box_regions(dim,\n bbox[0], bbox[1], mesh_eps))\n\n ebcs = {\n }\n\n if dim == 3:\n epbcs = {\n 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},\n 'match_x_plane'),\n 'periodic_y' : (['Near', 'Far'], {'u.all' : 'u.all'},\n 'match_y_plane'),\n 'periodic_z' : (['Top', 'Bottom'], {'u.all' : 'u.all'},\n 'match_z_plane'),\n }\n else:\n epbcs = {\n 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},\n 'match_y_line'),\n 'periodic_y' : (['Bottom', 'Top'], {'u.all' : 'u.all'},\n 'match_x_line'),\n }\n\n per.set_accuracy(mesh_eps)\n functions = {\n 'match_x_plane' : (per.match_x_plane,),\n 'match_y_plane' : (per.match_y_plane,),\n 'match_z_plane' : (per.match_z_plane,),\n 'match_x_line' : (per.match_x_line,),\n 'match_y_line' : (per.match_y_line,),\n 'get_wdir' : (get_wdir,),\n }\n\n integrals = {\n 'i' : 2 * approx_order,\n }\n\n equations = {\n 'K' : 'dw_lin_elastic.i.Omega(m.D, v, u)',\n 'S' : 'dw_elastic_wave.i.Omega(m.D, wave.vec, v, u)',\n 'R' : \"\"\"1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, u, v)\n - 1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, v, u)\"\"\",\n 'M' : 'dw_volume_dot.i.Omega(m.density, v, u)',\n }\n\n solver_0 = solver_conf.copy()\n solver_0['name'] = 'eig'\n\n return locals()\n\ndef get_wdir(ts, coors, mode=None,\n equations=None, term=None, problem=None, wdir=None, **kwargs):\n if mode == 'special':\n return {'vec' : wdir}\n\ndef set_wave_dir(pb, wdir):\n materials = pb.get_materials()\n wave_mat = materials['wave']\n wave_mat.set_extra_args(wdir=wdir)\n\ndef save_materials(output_dir, pb, options):\n stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n young, poisson = mc.youngpoisson_from_stiffness(stiffness,\n plane=options.plane)\n density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n\n out = {}\n out['young'] = Struct(name='young', mode='cell',\n data=young[..., None, None])\n out['poisson'] = Struct(name='poisson', mode='cell',\n data=poisson[..., None, None])\n out['density'] = Struct(name='density', mode='cell', data=density)\n materials_filename = os.path.join(output_dir, 'materials.vtk')\n pb.save_state(materials_filename, out=out)\n\ndef get_std_wave_fun(pb, options):\n stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n young, poisson = mc.youngpoisson_from_stiffness(stiffness,\n plane=options.plane)\n density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n\n lam, mu = mc.lame_from_youngpoisson(young, poisson,\n plane=options.plane)\n alam = nm.average(lam)\n amu = nm.average(mu)\n adensity = nm.average(density)\n\n cp = nm.sqrt((alam + 2.0 * amu) / adensity)\n cs = nm.sqrt(amu / adensity)\n output('average p-wave speed:', cp)\n output('average shear wave speed:', cs)\n\n log_names = [r'$\\omega_p$', r'$\\omega_s$']\n log_plot_kwargs = [{'ls' : '--', 'color' : 'k'},\n {'ls' : '--', 'color' : 'gray'}]\n\n if options.mode == 'omega':\n fun = lambda wmag, wdir: (cp * wmag, cs * wmag)\n\n else:\n fun = lambda wmag, wdir: (wmag / cp, wmag / cs)\n\n return fun, log_names, log_plot_kwargs\n\ndef get_stepper(rng, pb, options):\n if options.stepper == 'linear':\n stepper = TimeStepper(rng[0], rng[1], dt=None, n_step=rng[2])\n return stepper\n\n bbox = pb.domain.mesh.get_bounding_box()\n\n bzone = 2.0 * nm.pi / (bbox[1] - bbox[0])\n\n num = rng[2] // 3\n\n class BrillouinStepper(Struct):\n \"\"\"\n Step over 1. Brillouin zone in xy plane.\n \"\"\"\n def __init__(self, t0, t1, dt=None, n_step=None, step=None, **kwargs):\n Struct.__init__(self, t0=t0, t1=t1, dt=dt, n_step=n_step, step=step)\n\n self.n_digit, self.format, self.suffix = get_print_info(self.n_step)\n\n def __iter__(self):\n ts = TimeStepper(0, bzone[0], dt=None, n_step=num)\n for ii, val in ts:\n yield ii, val, nm.array([1.0, 0.0])\n if ii == (num-2): break\n\n ts = TimeStepper(0, bzone[1], dt=None, n_step=num)\n for ii, k1 in ts:\n wdir = nm.array([bzone[0], k1])\n val = nm.linalg.norm(wdir)\n wdir = wdir / val\n yield num + ii, val, wdir\n if ii == (num-2): break\n\n wdir = nm.array([bzone[0], bzone[1]])\n val = nm.linalg.norm(wdir)\n wdir = wdir / val\n ts = TimeStepper(0, 1, dt=None, n_step=num)\n for ii, _ in ts:\n yield 2 * num + ii, val * (1.0 - float(ii)/(num-1)), wdir\n\n stepper = BrillouinStepper(0, 1, n_step=rng[2])\n\n return stepper\n\ndef save_eigenvectors(filename, svecs, wmag, wdir, pb):\n if svecs is None: return\n\n variables = pb.get_variables()\n # Make full eigenvectors (add DOFs fixed by boundary conditions).\n vecs = nm.empty((variables.di.ptr[-1], svecs.shape[1]),\n dtype=svecs.dtype)\n for ii in range(svecs.shape[1]):\n vecs[:, ii] = variables.make_full_vec(svecs[:, ii])\n\n # Save the eigenvectors.\n out = {}\n state = pb.create_state()\n\n pp_name = pb.conf.options.get('post_process_hook')\n pp = getattr(pb.conf.funmod, pp_name if pp_name is not None else '',\n lambda out, *args, **kwargs: out)\n\n for ii in range(svecs.shape[1]):\n state.set_full(vecs[:, ii])\n aux = state.create_output_dict()\n aux2 = {}\n pp(aux2, pb, state, wmag=wmag, wdir=wdir)\n aux.update(convert_complex_output(aux2))\n out.update({key + '%03d' % ii : aux[key] for key in aux})\n\n pb.save_state(filename, out=out)\n\ndef assemble_matrices(define, mod, pars, set_wave_dir, options, wdir=None):\n \"\"\"\n Assemble the blocks of dispersion eigenvalue problem matrices.\n \"\"\"\n define_dict = define(filename_mesh=options.mesh_filename,\n pars=pars,\n approx_order=options.order,\n refinement_level=options.refine,\n solver_conf=options.solver_conf,\n plane=options.plane,\n post_process=options.post_process,\n **options.define_kwargs)\n\n conf = ProblemConf.from_dict(define_dict, mod)\n\n pb = Problem.from_conf(conf)\n pb.dispersion_options = options\n pb.set_output_dir(options.output_dir)\n dim = pb.domain.shape.dim\n\n # Set the normalized wave vector direction to the material(s).\n if wdir is None:\n wdir = nm.asarray(options.wave_dir[:dim], dtype=nm.float64)\n wdir = wdir / nm.linalg.norm(wdir)\n set_wave_dir(pb, wdir)\n\n bbox = pb.domain.mesh.get_bounding_box()\n size = (bbox[1] - bbox[0]).max()\n scaling0 = apply_unit_multipliers([1.0], ['length'],\n options.unit_multipliers)[0]\n scaling = scaling0\n if options.mesh_size is not None:\n scaling *= options.mesh_size / size\n output('scaling factor of periodic cell mesh coordinates:', scaling)\n output('new mesh size with applied unit multipliers:', scaling * size)\n pb.domain.mesh.coors[:] *= scaling\n pb.set_mesh_coors(pb.domain.mesh.coors, update_fields=True)\n\n bzone = 2.0 * nm.pi / (scaling * size)\n output('1. Brillouin zone size:', bzone * scaling0)\n output('1. Brillouin zone size with applied unit multipliers:', bzone)\n\n pb.time_update()\n pb.update_materials()\n\n # Assemble the matrices.\n mtxs = {}\n for key, eq in pb.equations.iteritems():\n mtxs[key] = mtx = pb.mtx_a.copy()\n mtx = eq.evaluate(mode='weak', dw_mode='matrix', asm_obj=mtx)\n mtx.eliminate_zeros()\n output_array_stats(mtx.data, 'nonzeros in %s' % key)\n\n "},"completion":{"kind":"string","value":"output('symmetry checks:')"},"api":{"kind":"string","value":"sfepy.base.base.output"}}},{"rowIdx":76,"cells":{"prompt":{"kind":"string","value":"#!/usr/bin/env python\n\"\"\"\nDispersion analysis of a heterogeneous finite scale periodic cell.\n\nThe periodic cell mesh has to contain two subdomains Y1 (with the cell ids 1),\nY2 (with the cell ids 2), so that different material properties can be defined\nin each of the subdomains (see ``--pars`` option). The command line parameters\ncan be given in any consistent unit set, for example the basic SI units. The\n``--unit-multipliers`` option can be used to rescale the input units to ones\nmore suitable to the simulation, for example to prevent having different\nmatrix blocks with large differences of matrix entries magnitudes. The results\nare then in the rescaled units.\n\nUsage Examples\n--------------\n\nDefault material parameters, a square periodic cell with a spherical inclusion,\nlogs also standard pressure dilatation and shear waves, no eigenvectors::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only\n\nAs above, with custom eigenvalue solver parameters, and different number of\neigenvalues, mesh size and units used in the calculation::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --solver-conf=\"kind='eig.scipy', method='eigsh', tol=1e-10, maxiter=1000, which='LM', sigma=0\" --log-std-waves -n 5 --range=0,640,101 --mode=omega --unit-multipliers=1e-6,1e-2,1e-3 --mesh-size=1e-2 --eigs-only\n\nDefault material parameters, a square periodic cell with a square inclusion,\nand a very small mesh to allow comparing the omega and kappa modes (full matrix\nsolver required!)::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf=\"kind='eig.scipy', method='eigh'\" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf=\"kind='eig.qevp', method='companion', mode='inverted', solver={kind='eig.scipy', method='eig'}\" --log-std-waves -n 500 --range=0,4000000,1001 --mesh-size=1e-2 --mode=kappa --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/kappa\n\nView/compare the resulting logs::\n\n python script/plot_logs.py output/omega/frequencies.txt --no-legends -g 1 -o mode-omega.png\n python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends -o mode-kappa.png\n python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends --swap-axes -o mode-kappa-t.png\n\nIn contrast to the heterogeneous square periodic cell, a homogeneous\nsquare periodic cell (the region Y2 is empty)::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_1m.mesh --solver-conf=\"kind='eig.scipy', method='eigh'\" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega-h\n\n python script/plot_logs.py output/omega-h/frequencies.txt --no-legends -g 1 -o mode-omega-h.png\n\nUse the Brillouin stepper::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves -n=60 --eigs-only --no-legends --stepper=brillouin\n\n python script/plot_logs.py output/frequencies.txt -g 0 --rc=\"'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4\" -o brillouin-stepper-kappas.png\n\n python script/plot_logs.py output/frequencies.txt -g 1 --no-legends --rc=\"'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4\" -o brillouin-stepper-omegas.png\n\nAdditional arguments can be passed to the problem configuration's\n:func:`define()` function using the ``--define-kwargs`` option. In this file,\nonly the mesh vertex separation parameter `mesh_eps` can be used::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only --define-kwargs=\"mesh_eps=1e-10\" --save-regions\n\"\"\"\nfrom __future__ import absolute_import\nimport os\nimport sys\nsys.path.append('.')\nimport gc\nfrom copy import copy\nfrom argparse import ArgumentParser, RawDescriptionHelpFormatter\n\nimport numpy as nm\nimport matplotlib.pyplot as plt\n\nfrom sfepy.base.base import import_file, output, Struct\nfrom sfepy.base.conf import dict_from_string, ProblemConf\nfrom sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options\nfrom sfepy.base.log import Log\nfrom sfepy.discrete.fem import MeshIO\nfrom sfepy.mechanics.matcoefs import stiffness_from_youngpoisson as stiffness\nimport sfepy.mechanics.matcoefs as mc\nfrom sfepy.mechanics.units import apply_unit_multipliers\nimport sfepy.discrete.fem.periodic as per\nfrom sfepy.discrete.fem.meshio import convert_complex_output\nfrom sfepy.homogenization.utils import define_box_regions\nfrom sfepy.discrete import Problem\nfrom sfepy.mechanics.tensors import get_von_mises_stress\nfrom sfepy.solvers import Solver\nfrom sfepy.solvers.ts import get_print_info, TimeStepper\nfrom sfepy.linalg.utils import output_array_stats, max_diff_csr\n\ndef apply_units(pars, unit_multipliers):\n new_pars = apply_unit_multipliers(pars,\n ['stress', 'one', 'density',\n 'stress', 'one' ,'density'],\n unit_multipliers)\n return new_pars\n\ndef compute_von_mises(out, pb, state, extend=False, wmag=None, wdir=None):\n \"\"\"\n Calculate the von Mises stress.\n \"\"\"\n stress = pb.evaluate('ev_cauchy_stress.i.Omega(m.D, u)', mode='el_avg')\n\n vms = get_von_mises_stress(stress.squeeze())\n vms.shape = (vms.shape[0], 1, 1, 1)\n out['von_mises_stress'] = Struct(name='output_data', mode='cell',\n data=vms)\n\n return out\n\ndef define(filename_mesh, pars, approx_order, refinement_level, solver_conf,\n plane='strain', post_process=False, mesh_eps=1e-8):\n io = MeshIO.any_from_filename(filename_mesh)\n bbox = io.read_bounding_box()\n dim = bbox.shape[1]\n\n options = {\n 'absolute_mesh_path' : True,\n 'refinement_level' : refinement_level,\n 'allow_empty_regions' : True,\n 'post_process_hook' : 'compute_von_mises' if post_process else None,\n }\n\n fields = {\n 'displacement': ('complex', dim, 'Omega', approx_order),\n }\n\n young1, poisson1, density1, young2, poisson2, density2 = pars\n materials = {\n 'm' : ({\n 'D' : {'Y1' : stiffness(dim, young=young1, poisson=poisson1,\n plane=plane),\n 'Y2' : stiffness(dim, young=young2, poisson=poisson2,\n plane=plane)},\n 'density' : {'Y1' : density1, 'Y2' : density2},\n },),\n 'wave' : 'get_wdir',\n }\n\n variables = {\n 'u' : ('unknown field', 'displacement', 0),\n 'v' : ('test field', 'displacement', 'u'),\n }\n\n regions = {\n 'Omega' : 'all',\n 'Y1': 'cells of group 1',\n 'Y2': 'cells of group 2',\n }\n regions.update(define_box_regions(dim,\n bbox[0], bbox[1], mesh_eps))\n\n ebcs = {\n }\n\n if dim == 3:\n epbcs = {\n 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},\n 'match_x_plane'),\n 'periodic_y' : (['Near', 'Far'], {'u.all' : 'u.all'},\n 'match_y_plane'),\n 'periodic_z' : (['Top', 'Bottom'], {'u.all' : 'u.all'},\n 'match_z_plane'),\n }\n else:\n epbcs = {\n 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},\n 'match_y_line'),\n 'periodic_y' : (['Bottom', 'Top'], {'u.all' : 'u.all'},\n 'match_x_line'),\n }\n\n per.set_accuracy(mesh_eps)\n functions = {\n 'match_x_plane' : (per.match_x_plane,),\n 'match_y_plane' : (per.match_y_plane,),\n 'match_z_plane' : (per.match_z_plane,),\n 'match_x_line' : (per.match_x_line,),\n 'match_y_line' : (per.match_y_line,),\n 'get_wdir' : (get_wdir,),\n }\n\n integrals = {\n 'i' : 2 * approx_order,\n }\n\n equations = {\n 'K' : 'dw_lin_elastic.i.Omega(m.D, v, u)',\n 'S' : 'dw_elastic_wave.i.Omega(m.D, wave.vec, v, u)',\n 'R' : \"\"\"1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, u, v)\n - 1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, v, u)\"\"\",\n 'M' : 'dw_volume_dot.i.Omega(m.density, v, u)',\n }\n\n solver_0 = solver_conf.copy()\n solver_0['name'] = 'eig'\n\n return locals()\n\ndef get_wdir(ts, coors, mode=None,\n equations=None, term=None, problem=None, wdir=None, **kwargs):\n if mode == 'special':\n return {'vec' : wdir}\n\ndef set_wave_dir(pb, wdir):\n materials = pb.get_materials()\n wave_mat = materials['wave']\n wave_mat.set_extra_args(wdir=wdir)\n\ndef save_materials(output_dir, pb, options):\n stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n young, poisson = mc.youngpoisson_from_stiffness(stiffness,\n plane=options.plane)\n density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n\n out = {}\n out['young'] = Struct(name='young', mode='cell',\n data=young[..., None, None])\n out['poisson'] = Struct(name='poisson', mode='cell',\n data=poisson[..., None, None])\n out['density'] = Struct(name='density', mode='cell', data=density)\n materials_filename = os.path.join(output_dir, 'materials.vtk')\n pb.save_state(materials_filename, out=out)\n\ndef get_std_wave_fun(pb, options):\n stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n young, poisson = mc.youngpoisson_from_stiffness(stiffness,\n plane=options.plane)\n density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n\n lam, mu = mc.lame_from_youngpoisson(young, poisson,\n plane=options.plane)\n alam = nm.average(lam)\n amu = nm.average(mu)\n adensity = nm.average(density)\n\n cp = nm.sqrt((alam + 2.0 * amu) / adensity)\n cs = nm.sqrt(amu / adensity)\n output('average p-wave speed:', cp)\n output('average shear wave speed:', cs)\n\n log_names = [r'$\\omega_p$', r'$\\omega_s$']\n log_plot_kwargs = [{'ls' : '--', 'color' : 'k'},\n {'ls' : '--', 'color' : 'gray'}]\n\n if options.mode == 'omega':\n fun = lambda wmag, wdir: (cp * wmag, cs * wmag)\n\n else:\n fun = lambda wmag, wdir: (wmag / cp, wmag / cs)\n\n return fun, log_names, log_plot_kwargs\n\ndef get_stepper(rng, pb, options):\n if options.stepper == 'linear':\n stepper = TimeStepper(rng[0], rng[1], dt=None, n_step=rng[2])\n return stepper\n\n bbox = pb.domain.mesh.get_bounding_box()\n\n bzone = 2.0 * nm.pi / (bbox[1] - bbox[0])\n\n num = rng[2] // 3\n\n class BrillouinStepper(Struct):\n \"\"\"\n Step over 1. Brillouin zone in xy plane.\n \"\"\"\n def __init__(self, t0, t1, dt=None, n_step=None, step=None, **kwargs):\n Struct.__init__(self, t0=t0, t1=t1, dt=dt, n_step=n_step, step=step)\n\n self.n_digit, self.format, self.suffix = get_print_info(self.n_step)\n\n def __iter__(self):\n ts = TimeStepper(0, bzone[0], dt=None, n_step=num)\n for ii, val in ts:\n yield ii, val, nm.array([1.0, 0.0])\n if ii == (num-2): break\n\n ts = TimeStepper(0, bzone[1], dt=None, n_step=num)\n for ii, k1 in ts:\n wdir = nm.array([bzone[0], k1])\n val = nm.linalg.norm(wdir)\n wdir = wdir / val\n yield num + ii, val, wdir\n if ii == (num-2): break\n\n wdir = nm.array([bzone[0], bzone[1]])\n val = nm.linalg.norm(wdir)\n wdir = wdir / val\n ts = TimeStepper(0, 1, dt=None, n_step=num)\n for ii, _ in ts:\n yield 2 * num + ii, val * (1.0 - float(ii)/(num-1)), wdir\n\n stepper = BrillouinStepper(0, 1, n_step=rng[2])\n\n return stepper\n\ndef save_eigenvectors(filename, svecs, wmag, wdir, pb):\n if svecs is None: return\n\n variables = pb.get_variables()\n # Make full eigenvectors (add DOFs fixed by boundary conditions).\n vecs = nm.empty((variables.di.ptr[-1], svecs.shape[1]),\n dtype=svecs.dtype)\n for ii in range(svecs.shape[1]):\n vecs[:, ii] = variables.make_full_vec(svecs[:, ii])\n\n # Save the eigenvectors.\n out = {}\n state = pb.create_state()\n\n pp_name = pb.conf.options.get('post_process_hook')\n pp = getattr(pb.conf.funmod, pp_name if pp_name is not None else '',\n lambda out, *args, **kwargs: out)\n\n for ii in range(svecs.shape[1]):\n state.set_full(vecs[:, ii])\n aux = state.create_output_dict()\n aux2 = {}\n pp(aux2, pb, state, wmag=wmag, wdir=wdir)\n aux.update(convert_complex_output(aux2))\n out.update({key + '%03d' % ii : aux[key] for key in aux})\n\n pb.save_state(filename, out=out)\n\ndef assemble_matrices(define, mod, pars, set_wave_dir, options, wdir=None):\n \"\"\"\n Assemble the blocks of dispersion eigenvalue problem matrices.\n \"\"\"\n define_dict = define(filename_mesh=options.mesh_filename,\n pars=pars,\n approx_order=options.order,\n refinement_level=options.refine,\n solver_conf=options.solver_conf,\n plane=options.plane,\n post_process=options.post_process,\n **options.define_kwargs)\n\n conf = ProblemConf.from_dict(define_dict, mod)\n\n pb = Problem.from_conf(conf)\n pb.dispersion_options = options\n pb.set_output_dir(options.output_dir)\n dim = pb.domain.shape.dim\n\n # Set the normalized wave vector direction to the material(s).\n if wdir is None:\n wdir = nm.asarray(options.wave_dir[:dim], dtype=nm.float64)\n wdir = wdir / nm.linalg.norm(wdir)\n set_wave_dir(pb, wdir)\n\n bbox = pb.domain.mesh.get_bounding_box()\n size = (bbox[1] - bbox[0]).max()\n scaling0 = apply_unit_multipliers([1.0], ['length'],\n options.unit_multipliers)[0]\n scaling = scaling0\n if options.mesh_size is not None:\n scaling *= options.mesh_size / size\n output('scaling factor of periodic cell mesh coordinates:', scaling)\n output('new mesh size with applied unit multipliers:', scaling * size)\n pb.domain.mesh.coors[:] *= scaling\n pb.set_mesh_coors(pb.domain.mesh.coors, update_fields=True)\n\n bzone = 2.0 * nm.pi / (scaling * size)\n output('1. Brillouin zone size:', bzone * scaling0)\n output('1. Brillouin zone size with applied unit multipliers:', bzone)\n\n pb.time_update()\n pb.update_materials()\n\n # Assemble the matrices.\n mtxs = {}\n for key, eq in pb.equations.iteritems():\n mtxs[key] = mtx = pb.mtx_a.copy()\n mtx = eq.evaluate(mode='weak', dw_mode='matrix', asm_obj=mtx)\n mtx.eliminate_zeros()\n output_array_stats(mtx.data, 'nonzeros in %s' % key)\n\n output('symmetry checks:')\n output('%s - %s^T:' % (key, key), max_diff_csr(mtx, mtx.T))\n output('%s - %s^H:' % (key, key), max_diff_csr(mtx, mtx.H))\n\n return pb, wdir, bzone, mtxs\n\ndef setup_n_eigs(options, pb, mtxs):\n \"\"\"\n Setup the numbers of eigenvalues based on options and numbers of DOFs.\n \"\"\"\n solver_n_eigs = n_eigs = options.n_eigs\n n_dof = mtxs['K'].shape[0]\n if options.mode == 'omega':\n if options.n_eigs > n_dof:\n n_eigs = n_dof\n solver_n_eigs = None\n\n else:\n if options.n_eigs > 2 * n_dof:\n n_eigs = 2 * n_dof\n solver_n_eigs = None\n\n return solver_n_eigs, n_eigs\n\ndef build_evp_matrices(mtxs, val, mode, pb):\n \"\"\"\n Build the matrices of the dispersion eigenvalue problem.\n \"\"\"\n if mode == 'omega':\n mtx_a = mtxs['K'] + val**2 * mtxs['S'] + val * mtxs['R']\n output('A - A^H:', max_diff_csr(mtx_a, mtx_a.H))\n\n evp_mtxs = (mtx_a, mtxs['M'])\n\n else:\n evp_mtxs = (mtxs['S'], mtxs['R'], mtxs['K'] - val**2 * mtxs['M'])\n\n return evp_mtxs\n\ndef process_evp_results(eigs, svecs, val, wdir, bzone, pb, mtxs, options,\n std_wave_fun=None):\n \"\"\"\n Transform eigenvalues to either omegas or kappas, depending on `mode`.\n Transform eigenvectors, if available, depending on `mode`.\n Return also the values to log.\n \"\"\"\n if options.mode == 'omega':\n omegas = nm.sqrt(eigs)\n\n "},"completion":{"kind":"string","value":"output('eigs, omegas:')"},"api":{"kind":"string","value":"sfepy.base.base.output"}}},{"rowIdx":77,"cells":{"prompt":{"kind":"string","value":"#!/usr/bin/env python\n\"\"\"\nDispersion analysis of a heterogeneous finite scale periodic cell.\n\nThe periodic cell mesh has to contain two subdomains Y1 (with the cell ids 1),\nY2 (with the cell ids 2), so that different material properties can be defined\nin each of the subdomains (see ``--pars`` option). The command line parameters\ncan be given in any consistent unit set, for example the basic SI units. The\n``--unit-multipliers`` option can be used to rescale the input units to ones\nmore suitable to the simulation, for example to prevent having different\nmatrix blocks with large differences of matrix entries magnitudes. The results\nare then in the rescaled units.\n\nUsage Examples\n--------------\n\nDefault material parameters, a square periodic cell with a spherical inclusion,\nlogs also standard pressure dilatation and shear waves, no eigenvectors::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only\n\nAs above, with custom eigenvalue solver parameters, and different number of\neigenvalues, mesh size and units used in the calculation::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --solver-conf=\"kind='eig.scipy', method='eigsh', tol=1e-10, maxiter=1000, which='LM', sigma=0\" --log-std-waves -n 5 --range=0,640,101 --mode=omega --unit-multipliers=1e-6,1e-2,1e-3 --mesh-size=1e-2 --eigs-only\n\nDefault material parameters, a square periodic cell with a square inclusion,\nand a very small mesh to allow comparing the omega and kappa modes (full matrix\nsolver required!)::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf=\"kind='eig.scipy', method='eigh'\" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf=\"kind='eig.qevp', method='companion', mode='inverted', solver={kind='eig.scipy', method='eig'}\" --log-std-waves -n 500 --range=0,4000000,1001 --mesh-size=1e-2 --mode=kappa --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/kappa\n\nView/compare the resulting logs::\n\n python script/plot_logs.py output/omega/frequencies.txt --no-legends -g 1 -o mode-omega.png\n python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends -o mode-kappa.png\n python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends --swap-axes -o mode-kappa-t.png\n\nIn contrast to the heterogeneous square periodic cell, a homogeneous\nsquare periodic cell (the region Y2 is empty)::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_1m.mesh --solver-conf=\"kind='eig.scipy', method='eigh'\" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega-h\n\n python script/plot_logs.py output/omega-h/frequencies.txt --no-legends -g 1 -o mode-omega-h.png\n\nUse the Brillouin stepper::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves -n=60 --eigs-only --no-legends --stepper=brillouin\n\n python script/plot_logs.py output/frequencies.txt -g 0 --rc=\"'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4\" -o brillouin-stepper-kappas.png\n\n python script/plot_logs.py output/frequencies.txt -g 1 --no-legends --rc=\"'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4\" -o brillouin-stepper-omegas.png\n\nAdditional arguments can be passed to the problem configuration's\n:func:`define()` function using the ``--define-kwargs`` option. In this file,\nonly the mesh vertex separation parameter `mesh_eps` can be used::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only --define-kwargs=\"mesh_eps=1e-10\" --save-regions\n\"\"\"\nfrom __future__ import absolute_import\nimport os\nimport sys\nsys.path.append('.')\nimport gc\nfrom copy import copy\nfrom argparse import ArgumentParser, RawDescriptionHelpFormatter\n\nimport numpy as nm\nimport matplotlib.pyplot as plt\n\nfrom sfepy.base.base import import_file, output, Struct\nfrom sfepy.base.conf import dict_from_string, ProblemConf\nfrom sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options\nfrom sfepy.base.log import Log\nfrom sfepy.discrete.fem import MeshIO\nfrom sfepy.mechanics.matcoefs import stiffness_from_youngpoisson as stiffness\nimport sfepy.mechanics.matcoefs as mc\nfrom sfepy.mechanics.units import apply_unit_multipliers\nimport sfepy.discrete.fem.periodic as per\nfrom sfepy.discrete.fem.meshio import convert_complex_output\nfrom sfepy.homogenization.utils import define_box_regions\nfrom sfepy.discrete import Problem\nfrom sfepy.mechanics.tensors import get_von_mises_stress\nfrom sfepy.solvers import Solver\nfrom sfepy.solvers.ts import get_print_info, TimeStepper\nfrom sfepy.linalg.utils import output_array_stats, max_diff_csr\n\ndef apply_units(pars, unit_multipliers):\n new_pars = apply_unit_multipliers(pars,\n ['stress', 'one', 'density',\n 'stress', 'one' ,'density'],\n unit_multipliers)\n return new_pars\n\ndef compute_von_mises(out, pb, state, extend=False, wmag=None, wdir=None):\n \"\"\"\n Calculate the von Mises stress.\n \"\"\"\n stress = pb.evaluate('ev_cauchy_stress.i.Omega(m.D, u)', mode='el_avg')\n\n vms = get_von_mises_stress(stress.squeeze())\n vms.shape = (vms.shape[0], 1, 1, 1)\n out['von_mises_stress'] = Struct(name='output_data', mode='cell',\n data=vms)\n\n return out\n\ndef define(filename_mesh, pars, approx_order, refinement_level, solver_conf,\n plane='strain', post_process=False, mesh_eps=1e-8):\n io = MeshIO.any_from_filename(filename_mesh)\n bbox = io.read_bounding_box()\n dim = bbox.shape[1]\n\n options = {\n 'absolute_mesh_path' : True,\n 'refinement_level' : refinement_level,\n 'allow_empty_regions' : True,\n 'post_process_hook' : 'compute_von_mises' if post_process else None,\n }\n\n fields = {\n 'displacement': ('complex', dim, 'Omega', approx_order),\n }\n\n young1, poisson1, density1, young2, poisson2, density2 = pars\n materials = {\n 'm' : ({\n 'D' : {'Y1' : stiffness(dim, young=young1, poisson=poisson1,\n plane=plane),\n 'Y2' : stiffness(dim, young=young2, poisson=poisson2,\n plane=plane)},\n 'density' : {'Y1' : density1, 'Y2' : density2},\n },),\n 'wave' : 'get_wdir',\n }\n\n variables = {\n 'u' : ('unknown field', 'displacement', 0),\n 'v' : ('test field', 'displacement', 'u'),\n }\n\n regions = {\n 'Omega' : 'all',\n 'Y1': 'cells of group 1',\n 'Y2': 'cells of group 2',\n }\n regions.update(define_box_regions(dim,\n bbox[0], bbox[1], mesh_eps))\n\n ebcs = {\n }\n\n if dim == 3:\n epbcs = {\n 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},\n 'match_x_plane'),\n 'periodic_y' : (['Near', 'Far'], {'u.all' : 'u.all'},\n 'match_y_plane'),\n 'periodic_z' : (['Top', 'Bottom'], {'u.all' : 'u.all'},\n 'match_z_plane'),\n }\n else:\n epbcs = {\n 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},\n 'match_y_line'),\n 'periodic_y' : (['Bottom', 'Top'], {'u.all' : 'u.all'},\n 'match_x_line'),\n }\n\n per.set_accuracy(mesh_eps)\n functions = {\n 'match_x_plane' : (per.match_x_plane,),\n 'match_y_plane' : (per.match_y_plane,),\n 'match_z_plane' : (per.match_z_plane,),\n 'match_x_line' : (per.match_x_line,),\n 'match_y_line' : (per.match_y_line,),\n 'get_wdir' : (get_wdir,),\n }\n\n integrals = {\n 'i' : 2 * approx_order,\n }\n\n equations = {\n 'K' : 'dw_lin_elastic.i.Omega(m.D, v, u)',\n 'S' : 'dw_elastic_wave.i.Omega(m.D, wave.vec, v, u)',\n 'R' : \"\"\"1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, u, v)\n - 1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, v, u)\"\"\",\n 'M' : 'dw_volume_dot.i.Omega(m.density, v, u)',\n }\n\n solver_0 = solver_conf.copy()\n solver_0['name'] = 'eig'\n\n return locals()\n\ndef get_wdir(ts, coors, mode=None,\n equations=None, term=None, problem=None, wdir=None, **kwargs):\n if mode == 'special':\n return {'vec' : wdir}\n\ndef set_wave_dir(pb, wdir):\n materials = pb.get_materials()\n wave_mat = materials['wave']\n wave_mat.set_extra_args(wdir=wdir)\n\ndef save_materials(output_dir, pb, options):\n stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n young, poisson = mc.youngpoisson_from_stiffness(stiffness,\n plane=options.plane)\n density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n\n out = {}\n out['young'] = Struct(name='young', mode='cell',\n data=young[..., None, None])\n out['poisson'] = Struct(name='poisson', mode='cell',\n data=poisson[..., None, None])\n out['density'] = Struct(name='density', mode='cell', data=density)\n materials_filename = os.path.join(output_dir, 'materials.vtk')\n pb.save_state(materials_filename, out=out)\n\ndef get_std_wave_fun(pb, options):\n stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n young, poisson = mc.youngpoisson_from_stiffness(stiffness,\n plane=options.plane)\n density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n\n lam, mu = mc.lame_from_youngpoisson(young, poisson,\n plane=options.plane)\n alam = nm.average(lam)\n amu = nm.average(mu)\n adensity = nm.average(density)\n\n cp = nm.sqrt((alam + 2.0 * amu) / adensity)\n cs = nm.sqrt(amu / adensity)\n output('average p-wave speed:', cp)\n output('average shear wave speed:', cs)\n\n log_names = [r'$\\omega_p$', r'$\\omega_s$']\n log_plot_kwargs = [{'ls' : '--', 'color' : 'k'},\n {'ls' : '--', 'color' : 'gray'}]\n\n if options.mode == 'omega':\n fun = lambda wmag, wdir: (cp * wmag, cs * wmag)\n\n else:\n fun = lambda wmag, wdir: (wmag / cp, wmag / cs)\n\n return fun, log_names, log_plot_kwargs\n\ndef get_stepper(rng, pb, options):\n if options.stepper == 'linear':\n stepper = TimeStepper(rng[0], rng[1], dt=None, n_step=rng[2])\n return stepper\n\n bbox = pb.domain.mesh.get_bounding_box()\n\n bzone = 2.0 * nm.pi / (bbox[1] - bbox[0])\n\n num = rng[2] // 3\n\n class BrillouinStepper(Struct):\n \"\"\"\n Step over 1. Brillouin zone in xy plane.\n \"\"\"\n def __init__(self, t0, t1, dt=None, n_step=None, step=None, **kwargs):\n Struct.__init__(self, t0=t0, t1=t1, dt=dt, n_step=n_step, step=step)\n\n self.n_digit, self.format, self.suffix = get_print_info(self.n_step)\n\n def __iter__(self):\n ts = TimeStepper(0, bzone[0], dt=None, n_step=num)\n for ii, val in ts:\n yield ii, val, nm.array([1.0, 0.0])\n if ii == (num-2): break\n\n ts = TimeStepper(0, bzone[1], dt=None, n_step=num)\n for ii, k1 in ts:\n wdir = nm.array([bzone[0], k1])\n val = nm.linalg.norm(wdir)\n wdir = wdir / val\n yield num + ii, val, wdir\n if ii == (num-2): break\n\n wdir = nm.array([bzone[0], bzone[1]])\n val = nm.linalg.norm(wdir)\n wdir = wdir / val\n ts = TimeStepper(0, 1, dt=None, n_step=num)\n for ii, _ in ts:\n yield 2 * num + ii, val * (1.0 - float(ii)/(num-1)), wdir\n\n stepper = BrillouinStepper(0, 1, n_step=rng[2])\n\n return stepper\n\ndef save_eigenvectors(filename, svecs, wmag, wdir, pb):\n if svecs is None: return\n\n variables = pb.get_variables()\n # Make full eigenvectors (add DOFs fixed by boundary conditions).\n vecs = nm.empty((variables.di.ptr[-1], svecs.shape[1]),\n dtype=svecs.dtype)\n for ii in range(svecs.shape[1]):\n vecs[:, ii] = variables.make_full_vec(svecs[:, ii])\n\n # Save the eigenvectors.\n out = {}\n state = pb.create_state()\n\n pp_name = pb.conf.options.get('post_process_hook')\n pp = getattr(pb.conf.funmod, pp_name if pp_name is not None else '',\n lambda out, *args, **kwargs: out)\n\n for ii in range(svecs.shape[1]):\n state.set_full(vecs[:, ii])\n aux = state.create_output_dict()\n aux2 = {}\n pp(aux2, pb, state, wmag=wmag, wdir=wdir)\n aux.update(convert_complex_output(aux2))\n out.update({key + '%03d' % ii : aux[key] for key in aux})\n\n pb.save_state(filename, out=out)\n\ndef assemble_matrices(define, mod, pars, set_wave_dir, options, wdir=None):\n \"\"\"\n Assemble the blocks of dispersion eigenvalue problem matrices.\n \"\"\"\n define_dict = define(filename_mesh=options.mesh_filename,\n pars=pars,\n approx_order=options.order,\n refinement_level=options.refine,\n solver_conf=options.solver_conf,\n plane=options.plane,\n post_process=options.post_process,\n **options.define_kwargs)\n\n conf = ProblemConf.from_dict(define_dict, mod)\n\n pb = Problem.from_conf(conf)\n pb.dispersion_options = options\n pb.set_output_dir(options.output_dir)\n dim = pb.domain.shape.dim\n\n # Set the normalized wave vector direction to the material(s).\n if wdir is None:\n wdir = nm.asarray(options.wave_dir[:dim], dtype=nm.float64)\n wdir = wdir / nm.linalg.norm(wdir)\n set_wave_dir(pb, wdir)\n\n bbox = pb.domain.mesh.get_bounding_box()\n size = (bbox[1] - bbox[0]).max()\n scaling0 = apply_unit_multipliers([1.0], ['length'],\n options.unit_multipliers)[0]\n scaling = scaling0\n if options.mesh_size is not None:\n scaling *= options.mesh_size / size\n output('scaling factor of periodic cell mesh coordinates:', scaling)\n output('new mesh size with applied unit multipliers:', scaling * size)\n pb.domain.mesh.coors[:] *= scaling\n pb.set_mesh_coors(pb.domain.mesh.coors, update_fields=True)\n\n bzone = 2.0 * nm.pi / (scaling * size)\n output('1. Brillouin zone size:', bzone * scaling0)\n output('1. Brillouin zone size with applied unit multipliers:', bzone)\n\n pb.time_update()\n pb.update_materials()\n\n # Assemble the matrices.\n mtxs = {}\n for key, eq in pb.equations.iteritems():\n mtxs[key] = mtx = pb.mtx_a.copy()\n mtx = eq.evaluate(mode='weak', dw_mode='matrix', asm_obj=mtx)\n mtx.eliminate_zeros()\n output_array_stats(mtx.data, 'nonzeros in %s' % key)\n\n output('symmetry checks:')\n output('%s - %s^T:' % (key, key), max_diff_csr(mtx, mtx.T))\n output('%s - %s^H:' % (key, key), max_diff_csr(mtx, mtx.H))\n\n return pb, wdir, bzone, mtxs\n\ndef setup_n_eigs(options, pb, mtxs):\n \"\"\"\n Setup the numbers of eigenvalues based on options and numbers of DOFs.\n \"\"\"\n solver_n_eigs = n_eigs = options.n_eigs\n n_dof = mtxs['K'].shape[0]\n if options.mode == 'omega':\n if options.n_eigs > n_dof:\n n_eigs = n_dof\n solver_n_eigs = None\n\n else:\n if options.n_eigs > 2 * n_dof:\n n_eigs = 2 * n_dof\n solver_n_eigs = None\n\n return solver_n_eigs, n_eigs\n\ndef build_evp_matrices(mtxs, val, mode, pb):\n \"\"\"\n Build the matrices of the dispersion eigenvalue problem.\n \"\"\"\n if mode == 'omega':\n mtx_a = mtxs['K'] + val**2 * mtxs['S'] + val * mtxs['R']\n output('A - A^H:', max_diff_csr(mtx_a, mtx_a.H))\n\n evp_mtxs = (mtx_a, mtxs['M'])\n\n else:\n evp_mtxs = (mtxs['S'], mtxs['R'], mtxs['K'] - val**2 * mtxs['M'])\n\n return evp_mtxs\n\ndef process_evp_results(eigs, svecs, val, wdir, bzone, pb, mtxs, options,\n std_wave_fun=None):\n \"\"\"\n Transform eigenvalues to either omegas or kappas, depending on `mode`.\n Transform eigenvectors, if available, depending on `mode`.\n Return also the values to log.\n \"\"\"\n if options.mode == 'omega':\n omegas = nm.sqrt(eigs)\n\n output('eigs, omegas:')\n for ii, om in enumerate(omegas):\n output('{:>3}. {: .10e}, {:.10e}'.format(ii, eigs[ii], om))\n\n if options.stepper == 'linear':\n out = tuple(eigs) + tuple(omegas)\n\n else:\n out = tuple(val * wdir) + tuple(omegas)\n\n if std_wave_fun is not None:\n out = out + std_wave_fun(val, wdir)\n\n return omegas, svecs, out\n\n else:\n kappas = eigs.copy()\n rks = kappas.copy()\n\n # Mask modes far from 1. Brillouin zone.\n max_kappa = 1.2 * bzone\n kappas[kappas.real > max_kappa] = nm.nan\n\n # Mask non-physical modes.\n kappas[kappas.real < 0] = nm.nan\n kappas[nm.abs(kappas.imag) > 1e-10] = nm.nan\n out = tuple(kappas.real)\n\n output('raw kappas, masked real part:',)\n for ii, kr in enumerate(kappas.real):\n output('{:>3}. {: 23.5e}, {:.10e}'.format(ii, rks[ii], kr))\n\n if svecs is not None:\n n_dof = mtxs['K'].shape[0]\n # Select only vectors corresponding to physical modes.\n ii = nm.isfinite(kappas.real)\n svecs = svecs[:n_dof, ii]\n\n if std_wave_fun is not None:\n out = out + tuple(ii if ii <= max_kappa else nm.nan\n for ii in std_wave_fun(val, wdir))\n\n return kappas, svecs, out\n\nhelps = {\n 'pars' :\n 'material parameters in Y1, Y2 subdomains in basic units'\n ' [default: %(default)s]',\n 'conf' :\n 'if given, an alternative problem description file with apply_units() and'\n ' define() functions [default: %(default)s]',\n 'define_kwargs' : 'additional keyword arguments passed to define()',\n 'mesh_size' :\n 'desired mesh size (max. of bounding box dimensions) in basic units'\n ' - the input periodic cell mesh is rescaled to this size'\n ' [default: %(default)s]',\n 'unit_multipliers' :\n 'basic unit multipliers (time, length, mass) [default: %(default)s]',\n 'plane' :\n 'for 2D problems, plane strain or stress hypothesis selection'\n ' [default: %(default)s]',\n 'wave_dir' : 'the wave vector direction (will be normalized)'\n ' [default: %(default)s]',\n 'mode' : 'solution mode: omega = solve a generalized EVP for omega,'\n ' kappa = solve a quadratic generalized EVP for kappa'\n ' [default: %(default)s]',\n 'stepper' : 'the range stepper. For \"brillouin\", only the number'\n ' of items from --range is used'\n ' [default: %(default)s]',\n 'range' : 'the wave vector magnitude / frequency range'\n ' (like numpy.linspace) depending on the mode option'\n ' [default: %(default)s]',\n 'order' : 'displacement field approximation order [default: %(default)s]',\n 'refine' : 'number of uniform mesh refinements [default: %(default)s]',\n 'n_eigs' : 'the number of eigenvalues to compute [default: %(default)s]',\n 'eigs_only' : 'compute only eigenvalues, not eigenvectors',\n 'post_process' : 'post-process eigenvectors',\n 'solver_conf' : 'eigenvalue problem solver configuration options'\n ' [default: %(default)s]',\n 'save_regions' : 'save defined regions into'\n ' /regions.vtk',\n 'save_materials' : 'save material parameters into'\n ' /materials.vtk',\n 'log_std_waves' : 'log also standard pressure dilatation and shear waves',\n 'no_legends' :\n 'do not show legends in the log plots',\n 'no_show' :\n 'do not show the log figure',\n 'silent' : 'do not print messages to screen',\n 'clear' :\n 'clear old solution files from output directory',\n 'output_dir' :\n 'output directory [default: %(default)s]',\n 'mesh_filename' :\n 'input periodic cell mesh file name [default: %(default)s]',\n}\n\ndef main():\n # Aluminium and epoxy.\n default_pars = '70e9,0.35,2.799e3, 3.8e9,0.27,1.142e3'\n default_solver_conf = (\"kind='eig.scipy',method='eigsh',tol=1.0e-5,\"\n \"maxiter=1000,which='LM',sigma=0.0\")\n\n parser = ArgumentParser(description=__doc__,\n formatter_class=RawDescriptionHelpFormatter)\n parser.add_argument('--pars', metavar='young1,poisson1,density1'\n ',young2,poisson2,density2',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='pars',\n default=default_pars, help=helps['pars'])\n parser.add_argument('--conf', metavar='filename',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='conf',\n default=None, help=helps['conf'])\n parser.add_argument('--define-kwargs', metavar='dict-like',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='define_kwargs',\n default=None, help=helps['define_kwargs'])\n parser.add_argument('--mesh-size', type=float, metavar='float',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='mesh_size',\n default=None, help=helps['mesh_size'])\n parser.add_argument('--unit-multipliers',\n metavar='c_time,c_length,c_mass',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='unit_multipliers',\n default='1.0,1.0,1.0', help=helps['unit_multipliers'])\n parser.add_argument('--plane', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='plane',\n choices=['strain', 'stress'],\n default='strain', help=helps['plane'])\n parser.add_argument('--wave-dir', metavar='float,float[,float]',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='wave_dir',\n default='1.0,0.0,0.0', help=helps['wave_dir'])\n parser.add_argument('--mode', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='mode',\n choices=['omega', 'kappa'],\n default='omega', help=helps['mode'])\n parser.add_argument('--stepper', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='stepper',\n choices=['linear', 'brillouin'],\n default='linear', help=helps['stepper'])\n parser.add_argument('--range', metavar='start,stop,count',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='range',\n default='0,6.4,33', help=helps['range'])\n parser.add_argument('--order', metavar='int', type=int,\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='order',\n default=1, help=helps['order'])\n parser.add_argument('--refine', metavar='int', type=int,\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='refine',\n default=0, help=helps['refine'])\n parser.add_argument('-n', '--n-eigs', metavar='int', type=int,\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='n_eigs',\n default=6, help=helps['n_eigs'])\n group = parser.add_mutually_exclusive_group()\n group.add_argument('--eigs-only',\n action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='eigs_only',\n default=False, help=helps['eigs_only'])\n group.add_argument('--post-process',\n action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='post_process',\n default=False, help=helps['post_process'])\n parser.add_argument('--solver-conf', metavar='dict-like',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='solver_conf',\n default=default_solver_conf, help=helps['solver_conf'])\n parser.add_argument('--save-regions',\n action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='save_regions',\n default=False, help=helps['save_regions'])\n parser.add_argument('--save-materials',\n action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='save_materials',\n default=False, help=helps['save_materials'])\n parser.add_argument('--log-std-waves',\n action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='log_std_waves',\n default=False, help=helps['log_std_waves'])\n parser.add_argument('--no-legends',\n action="https://huggingface.co/datasets/luna-code/sfepy/store_false", dest='show_legends',\n default=True, help=helps['no_legends'])\n parser.add_argument('--no-show',\n action="https://huggingface.co/datasets/luna-code/sfepy/store_false", dest='show',\n default=True, help=helps['no_show'])\n parser.add_argument('--silent',\n action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='silent',\n default=False, help=helps['silent'])\n parser.add_argument('-c', '--clear',\n action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='clear',\n default=False, help=helps['clear'])\n parser.add_argument('-o', '--output-dir', metavar='path',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='output_dir',\n default='output', help=helps['output_dir'])\n parser.add_argument('mesh_filename', default='',\n help=helps['mesh_filename'])\n options = parser.parse_args()\n\n output_dir = options.output_dir\n\n output.set_output(filename=os.path.join(output_dir,'output_log.txt'),\n combined=options.silent == False)\n\n if options.conf is not None:\n mod = "},"completion":{"kind":"string","value":"import_file(options.conf)"},"api":{"kind":"string","value":"sfepy.base.base.import_file"}}},{"rowIdx":78,"cells":{"prompt":{"kind":"string","value":"#!/usr/bin/env python\n\"\"\"\nDispersion analysis of a heterogeneous finite scale periodic cell.\n\nThe periodic cell mesh has to contain two subdomains Y1 (with the cell ids 1),\nY2 (with the cell ids 2), so that different material properties can be defined\nin each of the subdomains (see ``--pars`` option). The command line parameters\ncan be given in any consistent unit set, for example the basic SI units. The\n``--unit-multipliers`` option can be used to rescale the input units to ones\nmore suitable to the simulation, for example to prevent having different\nmatrix blocks with large differences of matrix entries magnitudes. The results\nare then in the rescaled units.\n\nUsage Examples\n--------------\n\nDefault material parameters, a square periodic cell with a spherical inclusion,\nlogs also standard pressure dilatation and shear waves, no eigenvectors::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only\n\nAs above, with custom eigenvalue solver parameters, and different number of\neigenvalues, mesh size and units used in the calculation::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --solver-conf=\"kind='eig.scipy', method='eigsh', tol=1e-10, maxiter=1000, which='LM', sigma=0\" --log-std-waves -n 5 --range=0,640,101 --mode=omega --unit-multipliers=1e-6,1e-2,1e-3 --mesh-size=1e-2 --eigs-only\n\nDefault material parameters, a square periodic cell with a square inclusion,\nand a very small mesh to allow comparing the omega and kappa modes (full matrix\nsolver required!)::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf=\"kind='eig.scipy', method='eigh'\" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf=\"kind='eig.qevp', method='companion', mode='inverted', solver={kind='eig.scipy', method='eig'}\" --log-std-waves -n 500 --range=0,4000000,1001 --mesh-size=1e-2 --mode=kappa --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/kappa\n\nView/compare the resulting logs::\n\n python script/plot_logs.py output/omega/frequencies.txt --no-legends -g 1 -o mode-omega.png\n python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends -o mode-kappa.png\n python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends --swap-axes -o mode-kappa-t.png\n\nIn contrast to the heterogeneous square periodic cell, a homogeneous\nsquare periodic cell (the region Y2 is empty)::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_1m.mesh --solver-conf=\"kind='eig.scipy', method='eigh'\" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega-h\n\n python script/plot_logs.py output/omega-h/frequencies.txt --no-legends -g 1 -o mode-omega-h.png\n\nUse the Brillouin stepper::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves -n=60 --eigs-only --no-legends --stepper=brillouin\n\n python script/plot_logs.py output/frequencies.txt -g 0 --rc=\"'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4\" -o brillouin-stepper-kappas.png\n\n python script/plot_logs.py output/frequencies.txt -g 1 --no-legends --rc=\"'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4\" -o brillouin-stepper-omegas.png\n\nAdditional arguments can be passed to the problem configuration's\n:func:`define()` function using the ``--define-kwargs`` option. In this file,\nonly the mesh vertex separation parameter `mesh_eps` can be used::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only --define-kwargs=\"mesh_eps=1e-10\" --save-regions\n\"\"\"\nfrom __future__ import absolute_import\nimport os\nimport sys\nsys.path.append('.')\nimport gc\nfrom copy import copy\nfrom argparse import ArgumentParser, RawDescriptionHelpFormatter\n\nimport numpy as nm\nimport matplotlib.pyplot as plt\n\nfrom sfepy.base.base import import_file, output, Struct\nfrom sfepy.base.conf import dict_from_string, ProblemConf\nfrom sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options\nfrom sfepy.base.log import Log\nfrom sfepy.discrete.fem import MeshIO\nfrom sfepy.mechanics.matcoefs import stiffness_from_youngpoisson as stiffness\nimport sfepy.mechanics.matcoefs as mc\nfrom sfepy.mechanics.units import apply_unit_multipliers\nimport sfepy.discrete.fem.periodic as per\nfrom sfepy.discrete.fem.meshio import convert_complex_output\nfrom sfepy.homogenization.utils import define_box_regions\nfrom sfepy.discrete import Problem\nfrom sfepy.mechanics.tensors import get_von_mises_stress\nfrom sfepy.solvers import Solver\nfrom sfepy.solvers.ts import get_print_info, TimeStepper\nfrom sfepy.linalg.utils import output_array_stats, max_diff_csr\n\ndef apply_units(pars, unit_multipliers):\n new_pars = apply_unit_multipliers(pars,\n ['stress', 'one', 'density',\n 'stress', 'one' ,'density'],\n unit_multipliers)\n return new_pars\n\ndef compute_von_mises(out, pb, state, extend=False, wmag=None, wdir=None):\n \"\"\"\n Calculate the von Mises stress.\n \"\"\"\n stress = pb.evaluate('ev_cauchy_stress.i.Omega(m.D, u)', mode='el_avg')\n\n vms = get_von_mises_stress(stress.squeeze())\n vms.shape = (vms.shape[0], 1, 1, 1)\n out['von_mises_stress'] = Struct(name='output_data', mode='cell',\n data=vms)\n\n return out\n\ndef define(filename_mesh, pars, approx_order, refinement_level, solver_conf,\n plane='strain', post_process=False, mesh_eps=1e-8):\n io = MeshIO.any_from_filename(filename_mesh)\n bbox = io.read_bounding_box()\n dim = bbox.shape[1]\n\n options = {\n 'absolute_mesh_path' : True,\n 'refinement_level' : refinement_level,\n 'allow_empty_regions' : True,\n 'post_process_hook' : 'compute_von_mises' if post_process else None,\n }\n\n fields = {\n 'displacement': ('complex', dim, 'Omega', approx_order),\n }\n\n young1, poisson1, density1, young2, poisson2, density2 = pars\n materials = {\n 'm' : ({\n 'D' : {'Y1' : stiffness(dim, young=young1, poisson=poisson1,\n plane=plane),\n 'Y2' : stiffness(dim, young=young2, poisson=poisson2,\n plane=plane)},\n 'density' : {'Y1' : density1, 'Y2' : density2},\n },),\n 'wave' : 'get_wdir',\n }\n\n variables = {\n 'u' : ('unknown field', 'displacement', 0),\n 'v' : ('test field', 'displacement', 'u'),\n }\n\n regions = {\n 'Omega' : 'all',\n 'Y1': 'cells of group 1',\n 'Y2': 'cells of group 2',\n }\n regions.update(define_box_regions(dim,\n bbox[0], bbox[1], mesh_eps))\n\n ebcs = {\n }\n\n if dim == 3:\n epbcs = {\n 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},\n 'match_x_plane'),\n 'periodic_y' : (['Near', 'Far'], {'u.all' : 'u.all'},\n 'match_y_plane'),\n 'periodic_z' : (['Top', 'Bottom'], {'u.all' : 'u.all'},\n 'match_z_plane'),\n }\n else:\n epbcs = {\n 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},\n 'match_y_line'),\n 'periodic_y' : (['Bottom', 'Top'], {'u.all' : 'u.all'},\n 'match_x_line'),\n }\n\n per.set_accuracy(mesh_eps)\n functions = {\n 'match_x_plane' : (per.match_x_plane,),\n 'match_y_plane' : (per.match_y_plane,),\n 'match_z_plane' : (per.match_z_plane,),\n 'match_x_line' : (per.match_x_line,),\n 'match_y_line' : (per.match_y_line,),\n 'get_wdir' : (get_wdir,),\n }\n\n integrals = {\n 'i' : 2 * approx_order,\n }\n\n equations = {\n 'K' : 'dw_lin_elastic.i.Omega(m.D, v, u)',\n 'S' : 'dw_elastic_wave.i.Omega(m.D, wave.vec, v, u)',\n 'R' : \"\"\"1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, u, v)\n - 1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, v, u)\"\"\",\n 'M' : 'dw_volume_dot.i.Omega(m.density, v, u)',\n }\n\n solver_0 = solver_conf.copy()\n solver_0['name'] = 'eig'\n\n return locals()\n\ndef get_wdir(ts, coors, mode=None,\n equations=None, term=None, problem=None, wdir=None, **kwargs):\n if mode == 'special':\n return {'vec' : wdir}\n\ndef set_wave_dir(pb, wdir):\n materials = pb.get_materials()\n wave_mat = materials['wave']\n wave_mat.set_extra_args(wdir=wdir)\n\ndef save_materials(output_dir, pb, options):\n stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n young, poisson = mc.youngpoisson_from_stiffness(stiffness,\n plane=options.plane)\n density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n\n out = {}\n out['young'] = Struct(name='young', mode='cell',\n data=young[..., None, None])\n out['poisson'] = Struct(name='poisson', mode='cell',\n data=poisson[..., None, None])\n out['density'] = Struct(name='density', mode='cell', data=density)\n materials_filename = os.path.join(output_dir, 'materials.vtk')\n pb.save_state(materials_filename, out=out)\n\ndef get_std_wave_fun(pb, options):\n stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n young, poisson = mc.youngpoisson_from_stiffness(stiffness,\n plane=options.plane)\n density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n\n lam, mu = mc.lame_from_youngpoisson(young, poisson,\n plane=options.plane)\n alam = nm.average(lam)\n amu = nm.average(mu)\n adensity = nm.average(density)\n\n cp = nm.sqrt((alam + 2.0 * amu) / adensity)\n cs = nm.sqrt(amu / adensity)\n output('average p-wave speed:', cp)\n output('average shear wave speed:', cs)\n\n log_names = [r'$\\omega_p$', r'$\\omega_s$']\n log_plot_kwargs = [{'ls' : '--', 'color' : 'k'},\n {'ls' : '--', 'color' : 'gray'}]\n\n if options.mode == 'omega':\n fun = lambda wmag, wdir: (cp * wmag, cs * wmag)\n\n else:\n fun = lambda wmag, wdir: (wmag / cp, wmag / cs)\n\n return fun, log_names, log_plot_kwargs\n\ndef get_stepper(rng, pb, options):\n if options.stepper == 'linear':\n stepper = TimeStepper(rng[0], rng[1], dt=None, n_step=rng[2])\n return stepper\n\n bbox = pb.domain.mesh.get_bounding_box()\n\n bzone = 2.0 * nm.pi / (bbox[1] - bbox[0])\n\n num = rng[2] // 3\n\n class BrillouinStepper(Struct):\n \"\"\"\n Step over 1. Brillouin zone in xy plane.\n \"\"\"\n def __init__(self, t0, t1, dt=None, n_step=None, step=None, **kwargs):\n Struct.__init__(self, t0=t0, t1=t1, dt=dt, n_step=n_step, step=step)\n\n self.n_digit, self.format, self.suffix = get_print_info(self.n_step)\n\n def __iter__(self):\n ts = TimeStepper(0, bzone[0], dt=None, n_step=num)\n for ii, val in ts:\n yield ii, val, nm.array([1.0, 0.0])\n if ii == (num-2): break\n\n ts = TimeStepper(0, bzone[1], dt=None, n_step=num)\n for ii, k1 in ts:\n wdir = nm.array([bzone[0], k1])\n val = nm.linalg.norm(wdir)\n wdir = wdir / val\n yield num + ii, val, wdir\n if ii == (num-2): break\n\n wdir = nm.array([bzone[0], bzone[1]])\n val = nm.linalg.norm(wdir)\n wdir = wdir / val\n ts = TimeStepper(0, 1, dt=None, n_step=num)\n for ii, _ in ts:\n yield 2 * num + ii, val * (1.0 - float(ii)/(num-1)), wdir\n\n stepper = BrillouinStepper(0, 1, n_step=rng[2])\n\n return stepper\n\ndef save_eigenvectors(filename, svecs, wmag, wdir, pb):\n if svecs is None: return\n\n variables = pb.get_variables()\n # Make full eigenvectors (add DOFs fixed by boundary conditions).\n vecs = nm.empty((variables.di.ptr[-1], svecs.shape[1]),\n dtype=svecs.dtype)\n for ii in range(svecs.shape[1]):\n vecs[:, ii] = variables.make_full_vec(svecs[:, ii])\n\n # Save the eigenvectors.\n out = {}\n state = pb.create_state()\n\n pp_name = pb.conf.options.get('post_process_hook')\n pp = getattr(pb.conf.funmod, pp_name if pp_name is not None else '',\n lambda out, *args, **kwargs: out)\n\n for ii in range(svecs.shape[1]):\n state.set_full(vecs[:, ii])\n aux = state.create_output_dict()\n aux2 = {}\n pp(aux2, pb, state, wmag=wmag, wdir=wdir)\n aux.update(convert_complex_output(aux2))\n out.update({key + '%03d' % ii : aux[key] for key in aux})\n\n pb.save_state(filename, out=out)\n\ndef assemble_matrices(define, mod, pars, set_wave_dir, options, wdir=None):\n \"\"\"\n Assemble the blocks of dispersion eigenvalue problem matrices.\n \"\"\"\n define_dict = define(filename_mesh=options.mesh_filename,\n pars=pars,\n approx_order=options.order,\n refinement_level=options.refine,\n solver_conf=options.solver_conf,\n plane=options.plane,\n post_process=options.post_process,\n **options.define_kwargs)\n\n conf = ProblemConf.from_dict(define_dict, mod)\n\n pb = Problem.from_conf(conf)\n pb.dispersion_options = options\n pb.set_output_dir(options.output_dir)\n dim = pb.domain.shape.dim\n\n # Set the normalized wave vector direction to the material(s).\n if wdir is None:\n wdir = nm.asarray(options.wave_dir[:dim], dtype=nm.float64)\n wdir = wdir / nm.linalg.norm(wdir)\n set_wave_dir(pb, wdir)\n\n bbox = pb.domain.mesh.get_bounding_box()\n size = (bbox[1] - bbox[0]).max()\n scaling0 = apply_unit_multipliers([1.0], ['length'],\n options.unit_multipliers)[0]\n scaling = scaling0\n if options.mesh_size is not None:\n scaling *= options.mesh_size / size\n output('scaling factor of periodic cell mesh coordinates:', scaling)\n output('new mesh size with applied unit multipliers:', scaling * size)\n pb.domain.mesh.coors[:] *= scaling\n pb.set_mesh_coors(pb.domain.mesh.coors, update_fields=True)\n\n bzone = 2.0 * nm.pi / (scaling * size)\n output('1. Brillouin zone size:', bzone * scaling0)\n output('1. Brillouin zone size with applied unit multipliers:', bzone)\n\n pb.time_update()\n pb.update_materials()\n\n # Assemble the matrices.\n mtxs = {}\n for key, eq in pb.equations.iteritems():\n mtxs[key] = mtx = pb.mtx_a.copy()\n mtx = eq.evaluate(mode='weak', dw_mode='matrix', asm_obj=mtx)\n mtx.eliminate_zeros()\n output_array_stats(mtx.data, 'nonzeros in %s' % key)\n\n output('symmetry checks:')\n output('%s - %s^T:' % (key, key), max_diff_csr(mtx, mtx.T))\n output('%s - %s^H:' % (key, key), max_diff_csr(mtx, mtx.H))\n\n return pb, wdir, bzone, mtxs\n\ndef setup_n_eigs(options, pb, mtxs):\n \"\"\"\n Setup the numbers of eigenvalues based on options and numbers of DOFs.\n \"\"\"\n solver_n_eigs = n_eigs = options.n_eigs\n n_dof = mtxs['K'].shape[0]\n if options.mode == 'omega':\n if options.n_eigs > n_dof:\n n_eigs = n_dof\n solver_n_eigs = None\n\n else:\n if options.n_eigs > 2 * n_dof:\n n_eigs = 2 * n_dof\n solver_n_eigs = None\n\n return solver_n_eigs, n_eigs\n\ndef build_evp_matrices(mtxs, val, mode, pb):\n \"\"\"\n Build the matrices of the dispersion eigenvalue problem.\n \"\"\"\n if mode == 'omega':\n mtx_a = mtxs['K'] + val**2 * mtxs['S'] + val * mtxs['R']\n output('A - A^H:', max_diff_csr(mtx_a, mtx_a.H))\n\n evp_mtxs = (mtx_a, mtxs['M'])\n\n else:\n evp_mtxs = (mtxs['S'], mtxs['R'], mtxs['K'] - val**2 * mtxs['M'])\n\n return evp_mtxs\n\ndef process_evp_results(eigs, svecs, val, wdir, bzone, pb, mtxs, options,\n std_wave_fun=None):\n \"\"\"\n Transform eigenvalues to either omegas or kappas, depending on `mode`.\n Transform eigenvectors, if available, depending on `mode`.\n Return also the values to log.\n \"\"\"\n if options.mode == 'omega':\n omegas = nm.sqrt(eigs)\n\n output('eigs, omegas:')\n for ii, om in enumerate(omegas):\n output('{:>3}. {: .10e}, {:.10e}'.format(ii, eigs[ii], om))\n\n if options.stepper == 'linear':\n out = tuple(eigs) + tuple(omegas)\n\n else:\n out = tuple(val * wdir) + tuple(omegas)\n\n if std_wave_fun is not None:\n out = out + std_wave_fun(val, wdir)\n\n return omegas, svecs, out\n\n else:\n kappas = eigs.copy()\n rks = kappas.copy()\n\n # Mask modes far from 1. Brillouin zone.\n max_kappa = 1.2 * bzone\n kappas[kappas.real > max_kappa] = nm.nan\n\n # Mask non-physical modes.\n kappas[kappas.real < 0] = nm.nan\n kappas[nm.abs(kappas.imag) > 1e-10] = nm.nan\n out = tuple(kappas.real)\n\n output('raw kappas, masked real part:',)\n for ii, kr in enumerate(kappas.real):\n output('{:>3}. {: 23.5e}, {:.10e}'.format(ii, rks[ii], kr))\n\n if svecs is not None:\n n_dof = mtxs['K'].shape[0]\n # Select only vectors corresponding to physical modes.\n ii = nm.isfinite(kappas.real)\n svecs = svecs[:n_dof, ii]\n\n if std_wave_fun is not None:\n out = out + tuple(ii if ii <= max_kappa else nm.nan\n for ii in std_wave_fun(val, wdir))\n\n return kappas, svecs, out\n\nhelps = {\n 'pars' :\n 'material parameters in Y1, Y2 subdomains in basic units'\n ' [default: %(default)s]',\n 'conf' :\n 'if given, an alternative problem description file with apply_units() and'\n ' define() functions [default: %(default)s]',\n 'define_kwargs' : 'additional keyword arguments passed to define()',\n 'mesh_size' :\n 'desired mesh size (max. of bounding box dimensions) in basic units'\n ' - the input periodic cell mesh is rescaled to this size'\n ' [default: %(default)s]',\n 'unit_multipliers' :\n 'basic unit multipliers (time, length, mass) [default: %(default)s]',\n 'plane' :\n 'for 2D problems, plane strain or stress hypothesis selection'\n ' [default: %(default)s]',\n 'wave_dir' : 'the wave vector direction (will be normalized)'\n ' [default: %(default)s]',\n 'mode' : 'solution mode: omega = solve a generalized EVP for omega,'\n ' kappa = solve a quadratic generalized EVP for kappa'\n ' [default: %(default)s]',\n 'stepper' : 'the range stepper. For \"brillouin\", only the number'\n ' of items from --range is used'\n ' [default: %(default)s]',\n 'range' : 'the wave vector magnitude / frequency range'\n ' (like numpy.linspace) depending on the mode option'\n ' [default: %(default)s]',\n 'order' : 'displacement field approximation order [default: %(default)s]',\n 'refine' : 'number of uniform mesh refinements [default: %(default)s]',\n 'n_eigs' : 'the number of eigenvalues to compute [default: %(default)s]',\n 'eigs_only' : 'compute only eigenvalues, not eigenvectors',\n 'post_process' : 'post-process eigenvectors',\n 'solver_conf' : 'eigenvalue problem solver configuration options'\n ' [default: %(default)s]',\n 'save_regions' : 'save defined regions into'\n ' /regions.vtk',\n 'save_materials' : 'save material parameters into'\n ' /materials.vtk',\n 'log_std_waves' : 'log also standard pressure dilatation and shear waves',\n 'no_legends' :\n 'do not show legends in the log plots',\n 'no_show' :\n 'do not show the log figure',\n 'silent' : 'do not print messages to screen',\n 'clear' :\n 'clear old solution files from output directory',\n 'output_dir' :\n 'output directory [default: %(default)s]',\n 'mesh_filename' :\n 'input periodic cell mesh file name [default: %(default)s]',\n}\n\ndef main():\n # Aluminium and epoxy.\n default_pars = '70e9,0.35,2.799e3, 3.8e9,0.27,1.142e3'\n default_solver_conf = (\"kind='eig.scipy',method='eigsh',tol=1.0e-5,\"\n \"maxiter=1000,which='LM',sigma=0.0\")\n\n parser = ArgumentParser(description=__doc__,\n formatter_class=RawDescriptionHelpFormatter)\n parser.add_argument('--pars', metavar='young1,poisson1,density1'\n ',young2,poisson2,density2',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='pars',\n default=default_pars, help=helps['pars'])\n parser.add_argument('--conf', metavar='filename',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='conf',\n default=None, help=helps['conf'])\n parser.add_argument('--define-kwargs', metavar='dict-like',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='define_kwargs',\n default=None, help=helps['define_kwargs'])\n parser.add_argument('--mesh-size', type=float, metavar='float',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='mesh_size',\n default=None, help=helps['mesh_size'])\n parser.add_argument('--unit-multipliers',\n metavar='c_time,c_length,c_mass',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='unit_multipliers',\n default='1.0,1.0,1.0', help=helps['unit_multipliers'])\n parser.add_argument('--plane', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='plane',\n choices=['strain', 'stress'],\n default='strain', help=helps['plane'])\n parser.add_argument('--wave-dir', metavar='float,float[,float]',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='wave_dir',\n default='1.0,0.0,0.0', help=helps['wave_dir'])\n parser.add_argument('--mode', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='mode',\n choices=['omega', 'kappa'],\n default='omega', help=helps['mode'])\n parser.add_argument('--stepper', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='stepper',\n choices=['linear', 'brillouin'],\n default='linear', help=helps['stepper'])\n parser.add_argument('--range', metavar='start,stop,count',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='range',\n default='0,6.4,33', help=helps['range'])\n parser.add_argument('--order', metavar='int', type=int,\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='order',\n default=1, help=helps['order'])\n parser.add_argument('--refine', metavar='int', type=int,\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='refine',\n default=0, help=helps['refine'])\n parser.add_argument('-n', '--n-eigs', metavar='int', type=int,\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='n_eigs',\n default=6, help=helps['n_eigs'])\n group = parser.add_mutually_exclusive_group()\n group.add_argument('--eigs-only',\n action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='eigs_only',\n default=False, help=helps['eigs_only'])\n group.add_argument('--post-process',\n action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='post_process',\n default=False, help=helps['post_process'])\n parser.add_argument('--solver-conf', metavar='dict-like',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='solver_conf',\n default=default_solver_conf, help=helps['solver_conf'])\n parser.add_argument('--save-regions',\n action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='save_regions',\n default=False, help=helps['save_regions'])\n parser.add_argument('--save-materials',\n action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='save_materials',\n default=False, help=helps['save_materials'])\n parser.add_argument('--log-std-waves',\n action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='log_std_waves',\n default=False, help=helps['log_std_waves'])\n parser.add_argument('--no-legends',\n action="https://huggingface.co/datasets/luna-code/sfepy/store_false", dest='show_legends',\n default=True, help=helps['no_legends'])\n parser.add_argument('--no-show',\n action="https://huggingface.co/datasets/luna-code/sfepy/store_false", dest='show',\n default=True, help=helps['no_show'])\n parser.add_argument('--silent',\n action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='silent',\n default=False, help=helps['silent'])\n parser.add_argument('-c', '--clear',\n action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='clear',\n default=False, help=helps['clear'])\n parser.add_argument('-o', '--output-dir', metavar='path',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='output_dir',\n default='output', help=helps['output_dir'])\n parser.add_argument('mesh_filename', default='',\n help=helps['mesh_filename'])\n options = parser.parse_args()\n\n output_dir = options.output_dir\n\n output.set_output(filename=os.path.join(output_dir,'output_log.txt'),\n combined=options.silent == False)\n\n if options.conf is not None:\n mod = import_file(options.conf)\n\n else:\n mod = sys.modules[__name__]\n\n apply_units = mod.apply_units\n define = mod.define\n set_wave_dir = mod.set_wave_dir\n setup_n_eigs = mod.setup_n_eigs\n build_evp_matrices = mod.build_evp_matrices\n save_materials = mod.save_materials\n get_std_wave_fun = mod.get_std_wave_fun\n get_stepper = mod.get_stepper\n process_evp_results = mod.process_evp_results\n\n options.pars = [float(ii) for ii in options.pars.split(',')]\n options.unit_multipliers = [float(ii)\n for ii in options.unit_multipliers.split(',')]\n options.wave_dir = [float(ii)\n for ii in options.wave_dir.split(',')]\n aux = options.range.split(',')\n options.range = [float(aux[0]), float(aux[1]), int(aux[2])]\n options.solver_conf = dict_from_string(options.solver_conf)\n options.define_kwargs = dict_from_string(options.define_kwargs)\n\n if options.clear:\n remove_files_patterns(output_dir,\n ['*.h5', '*.vtk', '*.txt'],\n ignores=['output_log.txt'],\n verbose=True)\n\n filename = os.path.join(output_dir, 'options.txt')\n ensure_path(filename)\n save_options(filename, [('options', vars(options))],\n quote_command_line=True)\n\n pars = apply_units(options.pars, options.unit_multipliers)\n output('material parameters with applied unit multipliers:')\n output(pars)\n\n if options.mode == 'omega':\n rng = copy(options.range)\n rng[:2] = apply_unit_multipliers(options.range[:2],\n ['wave_number', 'wave_number'],\n options.unit_multipliers)\n "},"completion":{"kind":"string","value":"output('wave number range with applied unit multipliers:', rng)"},"api":{"kind":"string","value":"sfepy.base.base.output"}}},{"rowIdx":79,"cells":{"prompt":{"kind":"string","value":"#!/usr/bin/env python\n\"\"\"\nDispersion analysis of a heterogeneous finite scale periodic cell.\n\nThe periodic cell mesh has to contain two subdomains Y1 (with the cell ids 1),\nY2 (with the cell ids 2), so that different material properties can be defined\nin each of the subdomains (see ``--pars`` option). The command line parameters\ncan be given in any consistent unit set, for example the basic SI units. The\n``--unit-multipliers`` option can be used to rescale the input units to ones\nmore suitable to the simulation, for example to prevent having different\nmatrix blocks with large differences of matrix entries magnitudes. The results\nare then in the rescaled units.\n\nUsage Examples\n--------------\n\nDefault material parameters, a square periodic cell with a spherical inclusion,\nlogs also standard pressure dilatation and shear waves, no eigenvectors::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only\n\nAs above, with custom eigenvalue solver parameters, and different number of\neigenvalues, mesh size and units used in the calculation::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --solver-conf=\"kind='eig.scipy', method='eigsh', tol=1e-10, maxiter=1000, which='LM', sigma=0\" --log-std-waves -n 5 --range=0,640,101 --mode=omega --unit-multipliers=1e-6,1e-2,1e-3 --mesh-size=1e-2 --eigs-only\n\nDefault material parameters, a square periodic cell with a square inclusion,\nand a very small mesh to allow comparing the omega and kappa modes (full matrix\nsolver required!)::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf=\"kind='eig.scipy', method='eigh'\" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf=\"kind='eig.qevp', method='companion', mode='inverted', solver={kind='eig.scipy', method='eig'}\" --log-std-waves -n 500 --range=0,4000000,1001 --mesh-size=1e-2 --mode=kappa --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/kappa\n\nView/compare the resulting logs::\n\n python script/plot_logs.py output/omega/frequencies.txt --no-legends -g 1 -o mode-omega.png\n python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends -o mode-kappa.png\n python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends --swap-axes -o mode-kappa-t.png\n\nIn contrast to the heterogeneous square periodic cell, a homogeneous\nsquare periodic cell (the region Y2 is empty)::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_1m.mesh --solver-conf=\"kind='eig.scipy', method='eigh'\" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega-h\n\n python script/plot_logs.py output/omega-h/frequencies.txt --no-legends -g 1 -o mode-omega-h.png\n\nUse the Brillouin stepper::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves -n=60 --eigs-only --no-legends --stepper=brillouin\n\n python script/plot_logs.py output/frequencies.txt -g 0 --rc=\"'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4\" -o brillouin-stepper-kappas.png\n\n python script/plot_logs.py output/frequencies.txt -g 1 --no-legends --rc=\"'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4\" -o brillouin-stepper-omegas.png\n\nAdditional arguments can be passed to the problem configuration's\n:func:`define()` function using the ``--define-kwargs`` option. In this file,\nonly the mesh vertex separation parameter `mesh_eps` can be used::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only --define-kwargs=\"mesh_eps=1e-10\" --save-regions\n\"\"\"\nfrom __future__ import absolute_import\nimport os\nimport sys\nsys.path.append('.')\nimport gc\nfrom copy import copy\nfrom argparse import ArgumentParser, RawDescriptionHelpFormatter\n\nimport numpy as nm\nimport matplotlib.pyplot as plt\n\nfrom sfepy.base.base import import_file, output, Struct\nfrom sfepy.base.conf import dict_from_string, ProblemConf\nfrom sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options\nfrom sfepy.base.log import Log\nfrom sfepy.discrete.fem import MeshIO\nfrom sfepy.mechanics.matcoefs import stiffness_from_youngpoisson as stiffness\nimport sfepy.mechanics.matcoefs as mc\nfrom sfepy.mechanics.units import apply_unit_multipliers\nimport sfepy.discrete.fem.periodic as per\nfrom sfepy.discrete.fem.meshio import convert_complex_output\nfrom sfepy.homogenization.utils import define_box_regions\nfrom sfepy.discrete import Problem\nfrom sfepy.mechanics.tensors import get_von_mises_stress\nfrom sfepy.solvers import Solver\nfrom sfepy.solvers.ts import get_print_info, TimeStepper\nfrom sfepy.linalg.utils import output_array_stats, max_diff_csr\n\ndef apply_units(pars, unit_multipliers):\n new_pars = apply_unit_multipliers(pars,\n ['stress', 'one', 'density',\n 'stress', 'one' ,'density'],\n unit_multipliers)\n return new_pars\n\ndef compute_von_mises(out, pb, state, extend=False, wmag=None, wdir=None):\n \"\"\"\n Calculate the von Mises stress.\n \"\"\"\n stress = pb.evaluate('ev_cauchy_stress.i.Omega(m.D, u)', mode='el_avg')\n\n vms = get_von_mises_stress(stress.squeeze())\n vms.shape = (vms.shape[0], 1, 1, 1)\n out['von_mises_stress'] = Struct(name='output_data', mode='cell',\n data=vms)\n\n return out\n\ndef define(filename_mesh, pars, approx_order, refinement_level, solver_conf,\n plane='strain', post_process=False, mesh_eps=1e-8):\n io = MeshIO.any_from_filename(filename_mesh)\n bbox = io.read_bounding_box()\n dim = bbox.shape[1]\n\n options = {\n 'absolute_mesh_path' : True,\n 'refinement_level' : refinement_level,\n 'allow_empty_regions' : True,\n 'post_process_hook' : 'compute_von_mises' if post_process else None,\n }\n\n fields = {\n 'displacement': ('complex', dim, 'Omega', approx_order),\n }\n\n young1, poisson1, density1, young2, poisson2, density2 = pars\n materials = {\n 'm' : ({\n 'D' : {'Y1' : stiffness(dim, young=young1, poisson=poisson1,\n plane=plane),\n 'Y2' : stiffness(dim, young=young2, poisson=poisson2,\n plane=plane)},\n 'density' : {'Y1' : density1, 'Y2' : density2},\n },),\n 'wave' : 'get_wdir',\n }\n\n variables = {\n 'u' : ('unknown field', 'displacement', 0),\n 'v' : ('test field', 'displacement', 'u'),\n }\n\n regions = {\n 'Omega' : 'all',\n 'Y1': 'cells of group 1',\n 'Y2': 'cells of group 2',\n }\n regions.update(define_box_regions(dim,\n bbox[0], bbox[1], mesh_eps))\n\n ebcs = {\n }\n\n if dim == 3:\n epbcs = {\n 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},\n 'match_x_plane'),\n 'periodic_y' : (['Near', 'Far'], {'u.all' : 'u.all'},\n 'match_y_plane'),\n 'periodic_z' : (['Top', 'Bottom'], {'u.all' : 'u.all'},\n 'match_z_plane'),\n }\n else:\n epbcs = {\n 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},\n 'match_y_line'),\n 'periodic_y' : (['Bottom', 'Top'], {'u.all' : 'u.all'},\n 'match_x_line'),\n }\n\n per.set_accuracy(mesh_eps)\n functions = {\n 'match_x_plane' : (per.match_x_plane,),\n 'match_y_plane' : (per.match_y_plane,),\n 'match_z_plane' : (per.match_z_plane,),\n 'match_x_line' : (per.match_x_line,),\n 'match_y_line' : (per.match_y_line,),\n 'get_wdir' : (get_wdir,),\n }\n\n integrals = {\n 'i' : 2 * approx_order,\n }\n\n equations = {\n 'K' : 'dw_lin_elastic.i.Omega(m.D, v, u)',\n 'S' : 'dw_elastic_wave.i.Omega(m.D, wave.vec, v, u)',\n 'R' : \"\"\"1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, u, v)\n - 1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, v, u)\"\"\",\n 'M' : 'dw_volume_dot.i.Omega(m.density, v, u)',\n }\n\n solver_0 = solver_conf.copy()\n solver_0['name'] = 'eig'\n\n return locals()\n\ndef get_wdir(ts, coors, mode=None,\n equations=None, term=None, problem=None, wdir=None, **kwargs):\n if mode == 'special':\n return {'vec' : wdir}\n\ndef set_wave_dir(pb, wdir):\n materials = pb.get_materials()\n wave_mat = materials['wave']\n wave_mat.set_extra_args(wdir=wdir)\n\ndef save_materials(output_dir, pb, options):\n stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n young, poisson = mc.youngpoisson_from_stiffness(stiffness,\n plane=options.plane)\n density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n\n out = {}\n out['young'] = Struct(name='young', mode='cell',\n data=young[..., None, None])\n out['poisson'] = Struct(name='poisson', mode='cell',\n data=poisson[..., None, None])\n out['density'] = Struct(name='density', mode='cell', data=density)\n materials_filename = os.path.join(output_dir, 'materials.vtk')\n pb.save_state(materials_filename, out=out)\n\ndef get_std_wave_fun(pb, options):\n stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n young, poisson = mc.youngpoisson_from_stiffness(stiffness,\n plane=options.plane)\n density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n\n lam, mu = mc.lame_from_youngpoisson(young, poisson,\n plane=options.plane)\n alam = nm.average(lam)\n amu = nm.average(mu)\n adensity = nm.average(density)\n\n cp = nm.sqrt((alam + 2.0 * amu) / adensity)\n cs = nm.sqrt(amu / adensity)\n output('average p-wave speed:', cp)\n output('average shear wave speed:', cs)\n\n log_names = [r'$\\omega_p$', r'$\\omega_s$']\n log_plot_kwargs = [{'ls' : '--', 'color' : 'k'},\n {'ls' : '--', 'color' : 'gray'}]\n\n if options.mode == 'omega':\n fun = lambda wmag, wdir: (cp * wmag, cs * wmag)\n\n else:\n fun = lambda wmag, wdir: (wmag / cp, wmag / cs)\n\n return fun, log_names, log_plot_kwargs\n\ndef get_stepper(rng, pb, options):\n if options.stepper == 'linear':\n stepper = TimeStepper(rng[0], rng[1], dt=None, n_step=rng[2])\n return stepper\n\n bbox = pb.domain.mesh.get_bounding_box()\n\n bzone = 2.0 * nm.pi / (bbox[1] - bbox[0])\n\n num = rng[2] // 3\n\n class BrillouinStepper(Struct):\n \"\"\"\n Step over 1. Brillouin zone in xy plane.\n \"\"\"\n def __init__(self, t0, t1, dt=None, n_step=None, step=None, **kwargs):\n Struct.__init__(self, t0=t0, t1=t1, dt=dt, n_step=n_step, step=step)\n\n self.n_digit, self.format, self.suffix = get_print_info(self.n_step)\n\n def __iter__(self):\n ts = TimeStepper(0, bzone[0], dt=None, n_step=num)\n for ii, val in ts:\n yield ii, val, nm.array([1.0, 0.0])\n if ii == (num-2): break\n\n ts = TimeStepper(0, bzone[1], dt=None, n_step=num)\n for ii, k1 in ts:\n wdir = nm.array([bzone[0], k1])\n val = nm.linalg.norm(wdir)\n wdir = wdir / val\n yield num + ii, val, wdir\n if ii == (num-2): break\n\n wdir = nm.array([bzone[0], bzone[1]])\n val = nm.linalg.norm(wdir)\n wdir = wdir / val\n ts = TimeStepper(0, 1, dt=None, n_step=num)\n for ii, _ in ts:\n yield 2 * num + ii, val * (1.0 - float(ii)/(num-1)), wdir\n\n stepper = BrillouinStepper(0, 1, n_step=rng[2])\n\n return stepper\n\ndef save_eigenvectors(filename, svecs, wmag, wdir, pb):\n if svecs is None: return\n\n variables = pb.get_variables()\n # Make full eigenvectors (add DOFs fixed by boundary conditions).\n vecs = nm.empty((variables.di.ptr[-1], svecs.shape[1]),\n dtype=svecs.dtype)\n for ii in range(svecs.shape[1]):\n vecs[:, ii] = variables.make_full_vec(svecs[:, ii])\n\n # Save the eigenvectors.\n out = {}\n state = pb.create_state()\n\n pp_name = pb.conf.options.get('post_process_hook')\n pp = getattr(pb.conf.funmod, pp_name if pp_name is not None else '',\n lambda out, *args, **kwargs: out)\n\n for ii in range(svecs.shape[1]):\n state.set_full(vecs[:, ii])\n aux = state.create_output_dict()\n aux2 = {}\n pp(aux2, pb, state, wmag=wmag, wdir=wdir)\n aux.update(convert_complex_output(aux2))\n out.update({key + '%03d' % ii : aux[key] for key in aux})\n\n pb.save_state(filename, out=out)\n\ndef assemble_matrices(define, mod, pars, set_wave_dir, options, wdir=None):\n \"\"\"\n Assemble the blocks of dispersion eigenvalue problem matrices.\n \"\"\"\n define_dict = define(filename_mesh=options.mesh_filename,\n pars=pars,\n approx_order=options.order,\n refinement_level=options.refine,\n solver_conf=options.solver_conf,\n plane=options.plane,\n post_process=options.post_process,\n **options.define_kwargs)\n\n conf = ProblemConf.from_dict(define_dict, mod)\n\n pb = Problem.from_conf(conf)\n pb.dispersion_options = options\n pb.set_output_dir(options.output_dir)\n dim = pb.domain.shape.dim\n\n # Set the normalized wave vector direction to the material(s).\n if wdir is None:\n wdir = nm.asarray(options.wave_dir[:dim], dtype=nm.float64)\n wdir = wdir / nm.linalg.norm(wdir)\n set_wave_dir(pb, wdir)\n\n bbox = pb.domain.mesh.get_bounding_box()\n size = (bbox[1] - bbox[0]).max()\n scaling0 = apply_unit_multipliers([1.0], ['length'],\n options.unit_multipliers)[0]\n scaling = scaling0\n if options.mesh_size is not None:\n scaling *= options.mesh_size / size\n output('scaling factor of periodic cell mesh coordinates:', scaling)\n output('new mesh size with applied unit multipliers:', scaling * size)\n pb.domain.mesh.coors[:] *= scaling\n pb.set_mesh_coors(pb.domain.mesh.coors, update_fields=True)\n\n bzone = 2.0 * nm.pi / (scaling * size)\n output('1. Brillouin zone size:', bzone * scaling0)\n output('1. Brillouin zone size with applied unit multipliers:', bzone)\n\n pb.time_update()\n pb.update_materials()\n\n # Assemble the matrices.\n mtxs = {}\n for key, eq in pb.equations.iteritems():\n mtxs[key] = mtx = pb.mtx_a.copy()\n mtx = eq.evaluate(mode='weak', dw_mode='matrix', asm_obj=mtx)\n mtx.eliminate_zeros()\n output_array_stats(mtx.data, 'nonzeros in %s' % key)\n\n output('symmetry checks:')\n output('%s - %s^T:' % (key, key), max_diff_csr(mtx, mtx.T))\n output('%s - %s^H:' % (key, key), max_diff_csr(mtx, mtx.H))\n\n return pb, wdir, bzone, mtxs\n\ndef setup_n_eigs(options, pb, mtxs):\n \"\"\"\n Setup the numbers of eigenvalues based on options and numbers of DOFs.\n \"\"\"\n solver_n_eigs = n_eigs = options.n_eigs\n n_dof = mtxs['K'].shape[0]\n if options.mode == 'omega':\n if options.n_eigs > n_dof:\n n_eigs = n_dof\n solver_n_eigs = None\n\n else:\n if options.n_eigs > 2 * n_dof:\n n_eigs = 2 * n_dof\n solver_n_eigs = None\n\n return solver_n_eigs, n_eigs\n\ndef build_evp_matrices(mtxs, val, mode, pb):\n \"\"\"\n Build the matrices of the dispersion eigenvalue problem.\n \"\"\"\n if mode == 'omega':\n mtx_a = mtxs['K'] + val**2 * mtxs['S'] + val * mtxs['R']\n output('A - A^H:', max_diff_csr(mtx_a, mtx_a.H))\n\n evp_mtxs = (mtx_a, mtxs['M'])\n\n else:\n evp_mtxs = (mtxs['S'], mtxs['R'], mtxs['K'] - val**2 * mtxs['M'])\n\n return evp_mtxs\n\ndef process_evp_results(eigs, svecs, val, wdir, bzone, pb, mtxs, options,\n std_wave_fun=None):\n \"\"\"\n Transform eigenvalues to either omegas or kappas, depending on `mode`.\n Transform eigenvectors, if available, depending on `mode`.\n Return also the values to log.\n \"\"\"\n if options.mode == 'omega':\n omegas = nm.sqrt(eigs)\n\n output('eigs, omegas:')\n for ii, om in enumerate(omegas):\n output('{:>3}. {: .10e}, {:.10e}'.format(ii, eigs[ii], om))\n\n if options.stepper == 'linear':\n out = tuple(eigs) + tuple(omegas)\n\n else:\n out = tuple(val * wdir) + tuple(omegas)\n\n if std_wave_fun is not None:\n out = out + std_wave_fun(val, wdir)\n\n return omegas, svecs, out\n\n else:\n kappas = eigs.copy()\n rks = kappas.copy()\n\n # Mask modes far from 1. Brillouin zone.\n max_kappa = 1.2 * bzone\n kappas[kappas.real > max_kappa] = nm.nan\n\n # Mask non-physical modes.\n kappas[kappas.real < 0] = nm.nan\n kappas[nm.abs(kappas.imag) > 1e-10] = nm.nan\n out = tuple(kappas.real)\n\n output('raw kappas, masked real part:',)\n for ii, kr in enumerate(kappas.real):\n output('{:>3}. {: 23.5e}, {:.10e}'.format(ii, rks[ii], kr))\n\n if svecs is not None:\n n_dof = mtxs['K'].shape[0]\n # Select only vectors corresponding to physical modes.\n ii = nm.isfinite(kappas.real)\n svecs = svecs[:n_dof, ii]\n\n if std_wave_fun is not None:\n out = out + tuple(ii if ii <= max_kappa else nm.nan\n for ii in std_wave_fun(val, wdir))\n\n return kappas, svecs, out\n\nhelps = {\n 'pars' :\n 'material parameters in Y1, Y2 subdomains in basic units'\n ' [default: %(default)s]',\n 'conf' :\n 'if given, an alternative problem description file with apply_units() and'\n ' define() functions [default: %(default)s]',\n 'define_kwargs' : 'additional keyword arguments passed to define()',\n 'mesh_size' :\n 'desired mesh size (max. of bounding box dimensions) in basic units'\n ' - the input periodic cell mesh is rescaled to this size'\n ' [default: %(default)s]',\n 'unit_multipliers' :\n 'basic unit multipliers (time, length, mass) [default: %(default)s]',\n 'plane' :\n 'for 2D problems, plane strain or stress hypothesis selection'\n ' [default: %(default)s]',\n 'wave_dir' : 'the wave vector direction (will be normalized)'\n ' [default: %(default)s]',\n 'mode' : 'solution mode: omega = solve a generalized EVP for omega,'\n ' kappa = solve a quadratic generalized EVP for kappa'\n ' [default: %(default)s]',\n 'stepper' : 'the range stepper. For \"brillouin\", only the number'\n ' of items from --range is used'\n ' [default: %(default)s]',\n 'range' : 'the wave vector magnitude / frequency range'\n ' (like numpy.linspace) depending on the mode option'\n ' [default: %(default)s]',\n 'order' : 'displacement field approximation order [default: %(default)s]',\n 'refine' : 'number of uniform mesh refinements [default: %(default)s]',\n 'n_eigs' : 'the number of eigenvalues to compute [default: %(default)s]',\n 'eigs_only' : 'compute only eigenvalues, not eigenvectors',\n 'post_process' : 'post-process eigenvectors',\n 'solver_conf' : 'eigenvalue problem solver configuration options'\n ' [default: %(default)s]',\n 'save_regions' : 'save defined regions into'\n ' /regions.vtk',\n 'save_materials' : 'save material parameters into'\n ' /materials.vtk',\n 'log_std_waves' : 'log also standard pressure dilatation and shear waves',\n 'no_legends' :\n 'do not show legends in the log plots',\n 'no_show' :\n 'do not show the log figure',\n 'silent' : 'do not print messages to screen',\n 'clear' :\n 'clear old solution files from output directory',\n 'output_dir' :\n 'output directory [default: %(default)s]',\n 'mesh_filename' :\n 'input periodic cell mesh file name [default: %(default)s]',\n}\n\ndef main():\n # Aluminium and epoxy.\n default_pars = '70e9,0.35,2.799e3, 3.8e9,0.27,1.142e3'\n default_solver_conf = (\"kind='eig.scipy',method='eigsh',tol=1.0e-5,\"\n \"maxiter=1000,which='LM',sigma=0.0\")\n\n parser = ArgumentParser(description=__doc__,\n formatter_class=RawDescriptionHelpFormatter)\n parser.add_argument('--pars', metavar='young1,poisson1,density1'\n ',young2,poisson2,density2',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='pars',\n default=default_pars, help=helps['pars'])\n parser.add_argument('--conf', metavar='filename',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='conf',\n default=None, help=helps['conf'])\n parser.add_argument('--define-kwargs', metavar='dict-like',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='define_kwargs',\n default=None, help=helps['define_kwargs'])\n parser.add_argument('--mesh-size', type=float, metavar='float',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='mesh_size',\n default=None, help=helps['mesh_size'])\n parser.add_argument('--unit-multipliers',\n metavar='c_time,c_length,c_mass',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='unit_multipliers',\n default='1.0,1.0,1.0', help=helps['unit_multipliers'])\n parser.add_argument('--plane', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='plane',\n choices=['strain', 'stress'],\n default='strain', help=helps['plane'])\n parser.add_argument('--wave-dir', metavar='float,float[,float]',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='wave_dir',\n default='1.0,0.0,0.0', help=helps['wave_dir'])\n parser.add_argument('--mode', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='mode',\n choices=['omega', 'kappa'],\n default='omega', help=helps['mode'])\n parser.add_argument('--stepper', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='stepper',\n choices=['linear', 'brillouin'],\n default='linear', help=helps['stepper'])\n parser.add_argument('--range', metavar='start,stop,count',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='range',\n default='0,6.4,33', help=helps['range'])\n parser.add_argument('--order', metavar='int', type=int,\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='order',\n default=1, help=helps['order'])\n parser.add_argument('--refine', metavar='int', type=int,\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='refine',\n default=0, help=helps['refine'])\n parser.add_argument('-n', '--n-eigs', metavar='int', type=int,\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='n_eigs',\n default=6, help=helps['n_eigs'])\n group = parser.add_mutually_exclusive_group()\n group.add_argument('--eigs-only',\n action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='eigs_only',\n default=False, help=helps['eigs_only'])\n group.add_argument('--post-process',\n action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='post_process',\n default=False, help=helps['post_process'])\n parser.add_argument('--solver-conf', metavar='dict-like',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='solver_conf',\n default=default_solver_conf, help=helps['solver_conf'])\n parser.add_argument('--save-regions',\n action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='save_regions',\n default=False, help=helps['save_regions'])\n parser.add_argument('--save-materials',\n action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='save_materials',\n default=False, help=helps['save_materials'])\n parser.add_argument('--log-std-waves',\n action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='log_std_waves',\n default=False, help=helps['log_std_waves'])\n parser.add_argument('--no-legends',\n action="https://huggingface.co/datasets/luna-code/sfepy/store_false", dest='show_legends',\n default=True, help=helps['no_legends'])\n parser.add_argument('--no-show',\n action="https://huggingface.co/datasets/luna-code/sfepy/store_false", dest='show',\n default=True, help=helps['no_show'])\n parser.add_argument('--silent',\n action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='silent',\n default=False, help=helps['silent'])\n parser.add_argument('-c', '--clear',\n action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='clear',\n default=False, help=helps['clear'])\n parser.add_argument('-o', '--output-dir', metavar='path',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='output_dir',\n default='output', help=helps['output_dir'])\n parser.add_argument('mesh_filename', default='',\n help=helps['mesh_filename'])\n options = parser.parse_args()\n\n output_dir = options.output_dir\n\n output.set_output(filename=os.path.join(output_dir,'output_log.txt'),\n combined=options.silent == False)\n\n if options.conf is not None:\n mod = import_file(options.conf)\n\n else:\n mod = sys.modules[__name__]\n\n apply_units = mod.apply_units\n define = mod.define\n set_wave_dir = mod.set_wave_dir\n setup_n_eigs = mod.setup_n_eigs\n build_evp_matrices = mod.build_evp_matrices\n save_materials = mod.save_materials\n get_std_wave_fun = mod.get_std_wave_fun\n get_stepper = mod.get_stepper\n process_evp_results = mod.process_evp_results\n\n options.pars = [float(ii) for ii in options.pars.split(',')]\n options.unit_multipliers = [float(ii)\n for ii in options.unit_multipliers.split(',')]\n options.wave_dir = [float(ii)\n for ii in options.wave_dir.split(',')]\n aux = options.range.split(',')\n options.range = [float(aux[0]), float(aux[1]), int(aux[2])]\n options.solver_conf = dict_from_string(options.solver_conf)\n options.define_kwargs = dict_from_string(options.define_kwargs)\n\n if options.clear:\n remove_files_patterns(output_dir,\n ['*.h5', '*.vtk', '*.txt'],\n ignores=['output_log.txt'],\n verbose=True)\n\n filename = os.path.join(output_dir, 'options.txt')\n ensure_path(filename)\n save_options(filename, [('options', vars(options))],\n quote_command_line=True)\n\n pars = apply_units(options.pars, options.unit_multipliers)\n output('material parameters with applied unit multipliers:')\n output(pars)\n\n if options.mode == 'omega':\n rng = copy(options.range)\n rng[:2] = apply_unit_multipliers(options.range[:2],\n ['wave_number', 'wave_number'],\n options.unit_multipliers)\n output('wave number range with applied unit multipliers:', rng)\n\n else:\n if options.stepper == 'brillouin':\n raise ValueError('Cannot use \"brillouin\" stepper in kappa mode!')\n\n rng = copy(options.range)\n rng[:2] = apply_unit_multipliers(options.range[:2],\n ['frequency', 'frequency'],\n options.unit_multipliers)\n "},"completion":{"kind":"string","value":"output('frequency range with applied unit multipliers:', rng)"},"api":{"kind":"string","value":"sfepy.base.base.output"}}},{"rowIdx":80,"cells":{"prompt":{"kind":"string","value":"#!/usr/bin/env python\n\"\"\"\nDispersion analysis of a heterogeneous finite scale periodic cell.\n\nThe periodic cell mesh has to contain two subdomains Y1 (with the cell ids 1),\nY2 (with the cell ids 2), so that different material properties can be defined\nin each of the subdomains (see ``--pars`` option). The command line parameters\ncan be given in any consistent unit set, for example the basic SI units. The\n``--unit-multipliers`` option can be used to rescale the input units to ones\nmore suitable to the simulation, for example to prevent having different\nmatrix blocks with large differences of matrix entries magnitudes. The results\nare then in the rescaled units.\n\nUsage Examples\n--------------\n\nDefault material parameters, a square periodic cell with a spherical inclusion,\nlogs also standard pressure dilatation and shear waves, no eigenvectors::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only\n\nAs above, with custom eigenvalue solver parameters, and different number of\neigenvalues, mesh size and units used in the calculation::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --solver-conf=\"kind='eig.scipy', method='eigsh', tol=1e-10, maxiter=1000, which='LM', sigma=0\" --log-std-waves -n 5 --range=0,640,101 --mode=omega --unit-multipliers=1e-6,1e-2,1e-3 --mesh-size=1e-2 --eigs-only\n\nDefault material parameters, a square periodic cell with a square inclusion,\nand a very small mesh to allow comparing the omega and kappa modes (full matrix\nsolver required!)::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf=\"kind='eig.scipy', method='eigh'\" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf=\"kind='eig.qevp', method='companion', mode='inverted', solver={kind='eig.scipy', method='eig'}\" --log-std-waves -n 500 --range=0,4000000,1001 --mesh-size=1e-2 --mode=kappa --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/kappa\n\nView/compare the resulting logs::\n\n python script/plot_logs.py output/omega/frequencies.txt --no-legends -g 1 -o mode-omega.png\n python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends -o mode-kappa.png\n python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends --swap-axes -o mode-kappa-t.png\n\nIn contrast to the heterogeneous square periodic cell, a homogeneous\nsquare periodic cell (the region Y2 is empty)::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_1m.mesh --solver-conf=\"kind='eig.scipy', method='eigh'\" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega-h\n\n python script/plot_logs.py output/omega-h/frequencies.txt --no-legends -g 1 -o mode-omega-h.png\n\nUse the Brillouin stepper::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves -n=60 --eigs-only --no-legends --stepper=brillouin\n\n python script/plot_logs.py output/frequencies.txt -g 0 --rc=\"'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4\" -o brillouin-stepper-kappas.png\n\n python script/plot_logs.py output/frequencies.txt -g 1 --no-legends --rc=\"'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4\" -o brillouin-stepper-omegas.png\n\nAdditional arguments can be passed to the problem configuration's\n:func:`define()` function using the ``--define-kwargs`` option. In this file,\nonly the mesh vertex separation parameter `mesh_eps` can be used::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only --define-kwargs=\"mesh_eps=1e-10\" --save-regions\n\"\"\"\nfrom __future__ import absolute_import\nimport os\nimport sys\nsys.path.append('.')\nimport gc\nfrom copy import copy\nfrom argparse import ArgumentParser, RawDescriptionHelpFormatter\n\nimport numpy as nm\nimport matplotlib.pyplot as plt\n\nfrom sfepy.base.base import import_file, output, Struct\nfrom sfepy.base.conf import dict_from_string, ProblemConf\nfrom sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options\nfrom sfepy.base.log import Log\nfrom sfepy.discrete.fem import MeshIO\nfrom sfepy.mechanics.matcoefs import stiffness_from_youngpoisson as stiffness\nimport sfepy.mechanics.matcoefs as mc\nfrom sfepy.mechanics.units import apply_unit_multipliers\nimport sfepy.discrete.fem.periodic as per\nfrom sfepy.discrete.fem.meshio import convert_complex_output\nfrom sfepy.homogenization.utils import define_box_regions\nfrom sfepy.discrete import Problem\nfrom sfepy.mechanics.tensors import get_von_mises_stress\nfrom sfepy.solvers import Solver\nfrom sfepy.solvers.ts import get_print_info, TimeStepper\nfrom sfepy.linalg.utils import output_array_stats, max_diff_csr\n\ndef apply_units(pars, unit_multipliers):\n new_pars = apply_unit_multipliers(pars,\n ['stress', 'one', 'density',\n 'stress', 'one' ,'density'],\n unit_multipliers)\n return new_pars\n\ndef compute_von_mises(out, pb, state, extend=False, wmag=None, wdir=None):\n \"\"\"\n Calculate the von Mises stress.\n \"\"\"\n stress = pb.evaluate('ev_cauchy_stress.i.Omega(m.D, u)', mode='el_avg')\n\n vms = get_von_mises_stress(stress.squeeze())\n vms.shape = (vms.shape[0], 1, 1, 1)\n out['von_mises_stress'] = Struct(name='output_data', mode='cell',\n data=vms)\n\n return out\n\ndef define(filename_mesh, pars, approx_order, refinement_level, solver_conf,\n plane='strain', post_process=False, mesh_eps=1e-8):\n io = MeshIO.any_from_filename(filename_mesh)\n bbox = io.read_bounding_box()\n dim = bbox.shape[1]\n\n options = {\n 'absolute_mesh_path' : True,\n 'refinement_level' : refinement_level,\n 'allow_empty_regions' : True,\n 'post_process_hook' : 'compute_von_mises' if post_process else None,\n }\n\n fields = {\n 'displacement': ('complex', dim, 'Omega', approx_order),\n }\n\n young1, poisson1, density1, young2, poisson2, density2 = pars\n materials = {\n 'm' : ({\n 'D' : {'Y1' : stiffness(dim, young=young1, poisson=poisson1,\n plane=plane),\n 'Y2' : stiffness(dim, young=young2, poisson=poisson2,\n plane=plane)},\n 'density' : {'Y1' : density1, 'Y2' : density2},\n },),\n 'wave' : 'get_wdir',\n }\n\n variables = {\n 'u' : ('unknown field', 'displacement', 0),\n 'v' : ('test field', 'displacement', 'u'),\n }\n\n regions = {\n 'Omega' : 'all',\n 'Y1': 'cells of group 1',\n 'Y2': 'cells of group 2',\n }\n regions.update(define_box_regions(dim,\n bbox[0], bbox[1], mesh_eps))\n\n ebcs = {\n }\n\n if dim == 3:\n epbcs = {\n 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},\n 'match_x_plane'),\n 'periodic_y' : (['Near', 'Far'], {'u.all' : 'u.all'},\n 'match_y_plane'),\n 'periodic_z' : (['Top', 'Bottom'], {'u.all' : 'u.all'},\n 'match_z_plane'),\n }\n else:\n epbcs = {\n 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},\n 'match_y_line'),\n 'periodic_y' : (['Bottom', 'Top'], {'u.all' : 'u.all'},\n 'match_x_line'),\n }\n\n per.set_accuracy(mesh_eps)\n functions = {\n 'match_x_plane' : (per.match_x_plane,),\n 'match_y_plane' : (per.match_y_plane,),\n 'match_z_plane' : (per.match_z_plane,),\n 'match_x_line' : (per.match_x_line,),\n 'match_y_line' : (per.match_y_line,),\n 'get_wdir' : (get_wdir,),\n }\n\n integrals = {\n 'i' : 2 * approx_order,\n }\n\n equations = {\n 'K' : 'dw_lin_elastic.i.Omega(m.D, v, u)',\n 'S' : 'dw_elastic_wave.i.Omega(m.D, wave.vec, v, u)',\n 'R' : \"\"\"1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, u, v)\n - 1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, v, u)\"\"\",\n 'M' : 'dw_volume_dot.i.Omega(m.density, v, u)',\n }\n\n solver_0 = solver_conf.copy()\n solver_0['name'] = 'eig'\n\n return locals()\n\ndef get_wdir(ts, coors, mode=None,\n equations=None, term=None, problem=None, wdir=None, **kwargs):\n if mode == 'special':\n return {'vec' : wdir}\n\ndef set_wave_dir(pb, wdir):\n materials = pb.get_materials()\n wave_mat = materials['wave']\n wave_mat.set_extra_args(wdir=wdir)\n\ndef save_materials(output_dir, pb, options):\n stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n young, poisson = mc.youngpoisson_from_stiffness(stiffness,\n plane=options.plane)\n density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n\n out = {}\n out['young'] = Struct(name='young', mode='cell',\n data=young[..., None, None])\n out['poisson'] = Struct(name='poisson', mode='cell',\n data=poisson[..., None, None])\n out['density'] = Struct(name='density', mode='cell', data=density)\n materials_filename = os.path.join(output_dir, 'materials.vtk')\n pb.save_state(materials_filename, out=out)\n\ndef get_std_wave_fun(pb, options):\n stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n young, poisson = mc.youngpoisson_from_stiffness(stiffness,\n plane=options.plane)\n density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n\n lam, mu = mc.lame_from_youngpoisson(young, poisson,\n plane=options.plane)\n alam = nm.average(lam)\n amu = nm.average(mu)\n adensity = nm.average(density)\n\n cp = nm.sqrt((alam + 2.0 * amu) / adensity)\n cs = nm.sqrt(amu / adensity)\n output('average p-wave speed:', cp)\n output('average shear wave speed:', cs)\n\n log_names = [r'$\\omega_p$', r'$\\omega_s$']\n log_plot_kwargs = [{'ls' : '--', 'color' : 'k'},\n {'ls' : '--', 'color' : 'gray'}]\n\n if options.mode == 'omega':\n fun = lambda wmag, wdir: (cp * wmag, cs * wmag)\n\n else:\n fun = lambda wmag, wdir: (wmag / cp, wmag / cs)\n\n return fun, log_names, log_plot_kwargs\n\ndef get_stepper(rng, pb, options):\n if options.stepper == 'linear':\n stepper = TimeStepper(rng[0], rng[1], dt=None, n_step=rng[2])\n return stepper\n\n bbox = pb.domain.mesh.get_bounding_box()\n\n bzone = 2.0 * nm.pi / (bbox[1] - bbox[0])\n\n num = rng[2] // 3\n\n class BrillouinStepper(Struct):\n \"\"\"\n Step over 1. Brillouin zone in xy plane.\n \"\"\"\n def __init__(self, t0, t1, dt=None, n_step=None, step=None, **kwargs):\n "},"completion":{"kind":"string","value":"Struct.__init__(self, t0=t0, t1=t1, dt=dt, n_step=n_step, step=step)"},"api":{"kind":"string","value":"sfepy.base.base.Struct.__init__"}}},{"rowIdx":81,"cells":{"prompt":{"kind":"string","value":"#!/usr/bin/env python\n\"\"\"\nDispersion analysis of a heterogeneous finite scale periodic cell.\n\nThe periodic cell mesh has to contain two subdomains Y1 (with the cell ids 1),\nY2 (with the cell ids 2), so that different material properties can be defined\nin each of the subdomains (see ``--pars`` option). The command line parameters\ncan be given in any consistent unit set, for example the basic SI units. The\n``--unit-multipliers`` option can be used to rescale the input units to ones\nmore suitable to the simulation, for example to prevent having different\nmatrix blocks with large differences of matrix entries magnitudes. The results\nare then in the rescaled units.\n\nUsage Examples\n--------------\n\nDefault material parameters, a square periodic cell with a spherical inclusion,\nlogs also standard pressure dilatation and shear waves, no eigenvectors::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only\n\nAs above, with custom eigenvalue solver parameters, and different number of\neigenvalues, mesh size and units used in the calculation::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --solver-conf=\"kind='eig.scipy', method='eigsh', tol=1e-10, maxiter=1000, which='LM', sigma=0\" --log-std-waves -n 5 --range=0,640,101 --mode=omega --unit-multipliers=1e-6,1e-2,1e-3 --mesh-size=1e-2 --eigs-only\n\nDefault material parameters, a square periodic cell with a square inclusion,\nand a very small mesh to allow comparing the omega and kappa modes (full matrix\nsolver required!)::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf=\"kind='eig.scipy', method='eigh'\" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf=\"kind='eig.qevp', method='companion', mode='inverted', solver={kind='eig.scipy', method='eig'}\" --log-std-waves -n 500 --range=0,4000000,1001 --mesh-size=1e-2 --mode=kappa --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/kappa\n\nView/compare the resulting logs::\n\n python script/plot_logs.py output/omega/frequencies.txt --no-legends -g 1 -o mode-omega.png\n python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends -o mode-kappa.png\n python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends --swap-axes -o mode-kappa-t.png\n\nIn contrast to the heterogeneous square periodic cell, a homogeneous\nsquare periodic cell (the region Y2 is empty)::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_1m.mesh --solver-conf=\"kind='eig.scipy', method='eigh'\" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega-h\n\n python script/plot_logs.py output/omega-h/frequencies.txt --no-legends -g 1 -o mode-omega-h.png\n\nUse the Brillouin stepper::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves -n=60 --eigs-only --no-legends --stepper=brillouin\n\n python script/plot_logs.py output/frequencies.txt -g 0 --rc=\"'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4\" -o brillouin-stepper-kappas.png\n\n python script/plot_logs.py output/frequencies.txt -g 1 --no-legends --rc=\"'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4\" -o brillouin-stepper-omegas.png\n\nAdditional arguments can be passed to the problem configuration's\n:func:`define()` function using the ``--define-kwargs`` option. In this file,\nonly the mesh vertex separation parameter `mesh_eps` can be used::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only --define-kwargs=\"mesh_eps=1e-10\" --save-regions\n\"\"\"\nfrom __future__ import absolute_import\nimport os\nimport sys\nsys.path.append('.')\nimport gc\nfrom copy import copy\nfrom argparse import ArgumentParser, RawDescriptionHelpFormatter\n\nimport numpy as nm\nimport matplotlib.pyplot as plt\n\nfrom sfepy.base.base import import_file, output, Struct\nfrom sfepy.base.conf import dict_from_string, ProblemConf\nfrom sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options\nfrom sfepy.base.log import Log\nfrom sfepy.discrete.fem import MeshIO\nfrom sfepy.mechanics.matcoefs import stiffness_from_youngpoisson as stiffness\nimport sfepy.mechanics.matcoefs as mc\nfrom sfepy.mechanics.units import apply_unit_multipliers\nimport sfepy.discrete.fem.periodic as per\nfrom sfepy.discrete.fem.meshio import convert_complex_output\nfrom sfepy.homogenization.utils import define_box_regions\nfrom sfepy.discrete import Problem\nfrom sfepy.mechanics.tensors import get_von_mises_stress\nfrom sfepy.solvers import Solver\nfrom sfepy.solvers.ts import get_print_info, TimeStepper\nfrom sfepy.linalg.utils import output_array_stats, max_diff_csr\n\ndef apply_units(pars, unit_multipliers):\n new_pars = apply_unit_multipliers(pars,\n ['stress', 'one', 'density',\n 'stress', 'one' ,'density'],\n unit_multipliers)\n return new_pars\n\ndef compute_von_mises(out, pb, state, extend=False, wmag=None, wdir=None):\n \"\"\"\n Calculate the von Mises stress.\n \"\"\"\n stress = pb.evaluate('ev_cauchy_stress.i.Omega(m.D, u)', mode='el_avg')\n\n vms = get_von_mises_stress(stress.squeeze())\n vms.shape = (vms.shape[0], 1, 1, 1)\n out['von_mises_stress'] = Struct(name='output_data', mode='cell',\n data=vms)\n\n return out\n\ndef define(filename_mesh, pars, approx_order, refinement_level, solver_conf,\n plane='strain', post_process=False, mesh_eps=1e-8):\n io = MeshIO.any_from_filename(filename_mesh)\n bbox = io.read_bounding_box()\n dim = bbox.shape[1]\n\n options = {\n 'absolute_mesh_path' : True,\n 'refinement_level' : refinement_level,\n 'allow_empty_regions' : True,\n 'post_process_hook' : 'compute_von_mises' if post_process else None,\n }\n\n fields = {\n 'displacement': ('complex', dim, 'Omega', approx_order),\n }\n\n young1, poisson1, density1, young2, poisson2, density2 = pars\n materials = {\n 'm' : ({\n 'D' : {'Y1' : stiffness(dim, young=young1, poisson=poisson1,\n plane=plane),\n 'Y2' : stiffness(dim, young=young2, poisson=poisson2,\n plane=plane)},\n 'density' : {'Y1' : density1, 'Y2' : density2},\n },),\n 'wave' : 'get_wdir',\n }\n\n variables = {\n 'u' : ('unknown field', 'displacement', 0),\n 'v' : ('test field', 'displacement', 'u'),\n }\n\n regions = {\n 'Omega' : 'all',\n 'Y1': 'cells of group 1',\n 'Y2': 'cells of group 2',\n }\n regions.update(define_box_regions(dim,\n bbox[0], bbox[1], mesh_eps))\n\n ebcs = {\n }\n\n if dim == 3:\n epbcs = {\n 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},\n 'match_x_plane'),\n 'periodic_y' : (['Near', 'Far'], {'u.all' : 'u.all'},\n 'match_y_plane'),\n 'periodic_z' : (['Top', 'Bottom'], {'u.all' : 'u.all'},\n 'match_z_plane'),\n }\n else:\n epbcs = {\n 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},\n 'match_y_line'),\n 'periodic_y' : (['Bottom', 'Top'], {'u.all' : 'u.all'},\n 'match_x_line'),\n }\n\n per.set_accuracy(mesh_eps)\n functions = {\n 'match_x_plane' : (per.match_x_plane,),\n 'match_y_plane' : (per.match_y_plane,),\n 'match_z_plane' : (per.match_z_plane,),\n 'match_x_line' : (per.match_x_line,),\n 'match_y_line' : (per.match_y_line,),\n 'get_wdir' : (get_wdir,),\n }\n\n integrals = {\n 'i' : 2 * approx_order,\n }\n\n equations = {\n 'K' : 'dw_lin_elastic.i.Omega(m.D, v, u)',\n 'S' : 'dw_elastic_wave.i.Omega(m.D, wave.vec, v, u)',\n 'R' : \"\"\"1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, u, v)\n - 1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, v, u)\"\"\",\n 'M' : 'dw_volume_dot.i.Omega(m.density, v, u)',\n }\n\n solver_0 = solver_conf.copy()\n solver_0['name'] = 'eig'\n\n return locals()\n\ndef get_wdir(ts, coors, mode=None,\n equations=None, term=None, problem=None, wdir=None, **kwargs):\n if mode == 'special':\n return {'vec' : wdir}\n\ndef set_wave_dir(pb, wdir):\n materials = pb.get_materials()\n wave_mat = materials['wave']\n wave_mat.set_extra_args(wdir=wdir)\n\ndef save_materials(output_dir, pb, options):\n stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n young, poisson = mc.youngpoisson_from_stiffness(stiffness,\n plane=options.plane)\n density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n\n out = {}\n out['young'] = Struct(name='young', mode='cell',\n data=young[..., None, None])\n out['poisson'] = Struct(name='poisson', mode='cell',\n data=poisson[..., None, None])\n out['density'] = Struct(name='density', mode='cell', data=density)\n materials_filename = os.path.join(output_dir, 'materials.vtk')\n pb.save_state(materials_filename, out=out)\n\ndef get_std_wave_fun(pb, options):\n stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n young, poisson = mc.youngpoisson_from_stiffness(stiffness,\n plane=options.plane)\n density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n\n lam, mu = mc.lame_from_youngpoisson(young, poisson,\n plane=options.plane)\n alam = nm.average(lam)\n amu = nm.average(mu)\n adensity = nm.average(density)\n\n cp = nm.sqrt((alam + 2.0 * amu) / adensity)\n cs = nm.sqrt(amu / adensity)\n output('average p-wave speed:', cp)\n output('average shear wave speed:', cs)\n\n log_names = [r'$\\omega_p$', r'$\\omega_s$']\n log_plot_kwargs = [{'ls' : '--', 'color' : 'k'},\n {'ls' : '--', 'color' : 'gray'}]\n\n if options.mode == 'omega':\n fun = lambda wmag, wdir: (cp * wmag, cs * wmag)\n\n else:\n fun = lambda wmag, wdir: (wmag / cp, wmag / cs)\n\n return fun, log_names, log_plot_kwargs\n\ndef get_stepper(rng, pb, options):\n if options.stepper == 'linear':\n stepper = TimeStepper(rng[0], rng[1], dt=None, n_step=rng[2])\n return stepper\n\n bbox = pb.domain.mesh.get_bounding_box()\n\n bzone = 2.0 * nm.pi / (bbox[1] - bbox[0])\n\n num = rng[2] // 3\n\n class BrillouinStepper(Struct):\n \"\"\"\n Step over 1. Brillouin zone in xy plane.\n \"\"\"\n def __init__(self, t0, t1, dt=None, n_step=None, step=None, **kwargs):\n Struct.__init__(self, t0=t0, t1=t1, dt=dt, n_step=n_step, step=step)\n\n self.n_digit, self.format, self.suffix = "},"completion":{"kind":"string","value":"get_print_info(self.n_step)"},"api":{"kind":"string","value":"sfepy.solvers.ts.get_print_info"}}},{"rowIdx":82,"cells":{"prompt":{"kind":"string","value":"#!/usr/bin/env python\n\"\"\"\nDispersion analysis of a heterogeneous finite scale periodic cell.\n\nThe periodic cell mesh has to contain two subdomains Y1 (with the cell ids 1),\nY2 (with the cell ids 2), so that different material properties can be defined\nin each of the subdomains (see ``--pars`` option). The command line parameters\ncan be given in any consistent unit set, for example the basic SI units. The\n``--unit-multipliers`` option can be used to rescale the input units to ones\nmore suitable to the simulation, for example to prevent having different\nmatrix blocks with large differences of matrix entries magnitudes. The results\nare then in the rescaled units.\n\nUsage Examples\n--------------\n\nDefault material parameters, a square periodic cell with a spherical inclusion,\nlogs also standard pressure dilatation and shear waves, no eigenvectors::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only\n\nAs above, with custom eigenvalue solver parameters, and different number of\neigenvalues, mesh size and units used in the calculation::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --solver-conf=\"kind='eig.scipy', method='eigsh', tol=1e-10, maxiter=1000, which='LM', sigma=0\" --log-std-waves -n 5 --range=0,640,101 --mode=omega --unit-multipliers=1e-6,1e-2,1e-3 --mesh-size=1e-2 --eigs-only\n\nDefault material parameters, a square periodic cell with a square inclusion,\nand a very small mesh to allow comparing the omega and kappa modes (full matrix\nsolver required!)::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf=\"kind='eig.scipy', method='eigh'\" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf=\"kind='eig.qevp', method='companion', mode='inverted', solver={kind='eig.scipy', method='eig'}\" --log-std-waves -n 500 --range=0,4000000,1001 --mesh-size=1e-2 --mode=kappa --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/kappa\n\nView/compare the resulting logs::\n\n python script/plot_logs.py output/omega/frequencies.txt --no-legends -g 1 -o mode-omega.png\n python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends -o mode-kappa.png\n python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends --swap-axes -o mode-kappa-t.png\n\nIn contrast to the heterogeneous square periodic cell, a homogeneous\nsquare periodic cell (the region Y2 is empty)::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_1m.mesh --solver-conf=\"kind='eig.scipy', method='eigh'\" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega-h\n\n python script/plot_logs.py output/omega-h/frequencies.txt --no-legends -g 1 -o mode-omega-h.png\n\nUse the Brillouin stepper::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves -n=60 --eigs-only --no-legends --stepper=brillouin\n\n python script/plot_logs.py output/frequencies.txt -g 0 --rc=\"'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4\" -o brillouin-stepper-kappas.png\n\n python script/plot_logs.py output/frequencies.txt -g 1 --no-legends --rc=\"'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4\" -o brillouin-stepper-omegas.png\n\nAdditional arguments can be passed to the problem configuration's\n:func:`define()` function using the ``--define-kwargs`` option. In this file,\nonly the mesh vertex separation parameter `mesh_eps` can be used::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only --define-kwargs=\"mesh_eps=1e-10\" --save-regions\n\"\"\"\nfrom __future__ import absolute_import\nimport os\nimport sys\nsys.path.append('.')\nimport gc\nfrom copy import copy\nfrom argparse import ArgumentParser, RawDescriptionHelpFormatter\n\nimport numpy as nm\nimport matplotlib.pyplot as plt\n\nfrom sfepy.base.base import import_file, output, Struct\nfrom sfepy.base.conf import dict_from_string, ProblemConf\nfrom sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options\nfrom sfepy.base.log import Log\nfrom sfepy.discrete.fem import MeshIO\nfrom sfepy.mechanics.matcoefs import stiffness_from_youngpoisson as stiffness\nimport sfepy.mechanics.matcoefs as mc\nfrom sfepy.mechanics.units import apply_unit_multipliers\nimport sfepy.discrete.fem.periodic as per\nfrom sfepy.discrete.fem.meshio import convert_complex_output\nfrom sfepy.homogenization.utils import define_box_regions\nfrom sfepy.discrete import Problem\nfrom sfepy.mechanics.tensors import get_von_mises_stress\nfrom sfepy.solvers import Solver\nfrom sfepy.solvers.ts import get_print_info, TimeStepper\nfrom sfepy.linalg.utils import output_array_stats, max_diff_csr\n\ndef apply_units(pars, unit_multipliers):\n new_pars = apply_unit_multipliers(pars,\n ['stress', 'one', 'density',\n 'stress', 'one' ,'density'],\n unit_multipliers)\n return new_pars\n\ndef compute_von_mises(out, pb, state, extend=False, wmag=None, wdir=None):\n \"\"\"\n Calculate the von Mises stress.\n \"\"\"\n stress = pb.evaluate('ev_cauchy_stress.i.Omega(m.D, u)', mode='el_avg')\n\n vms = get_von_mises_stress(stress.squeeze())\n vms.shape = (vms.shape[0], 1, 1, 1)\n out['von_mises_stress'] = Struct(name='output_data', mode='cell',\n data=vms)\n\n return out\n\ndef define(filename_mesh, pars, approx_order, refinement_level, solver_conf,\n plane='strain', post_process=False, mesh_eps=1e-8):\n io = MeshIO.any_from_filename(filename_mesh)\n bbox = io.read_bounding_box()\n dim = bbox.shape[1]\n\n options = {\n 'absolute_mesh_path' : True,\n 'refinement_level' : refinement_level,\n 'allow_empty_regions' : True,\n 'post_process_hook' : 'compute_von_mises' if post_process else None,\n }\n\n fields = {\n 'displacement': ('complex', dim, 'Omega', approx_order),\n }\n\n young1, poisson1, density1, young2, poisson2, density2 = pars\n materials = {\n 'm' : ({\n 'D' : {'Y1' : stiffness(dim, young=young1, poisson=poisson1,\n plane=plane),\n 'Y2' : stiffness(dim, young=young2, poisson=poisson2,\n plane=plane)},\n 'density' : {'Y1' : density1, 'Y2' : density2},\n },),\n 'wave' : 'get_wdir',\n }\n\n variables = {\n 'u' : ('unknown field', 'displacement', 0),\n 'v' : ('test field', 'displacement', 'u'),\n }\n\n regions = {\n 'Omega' : 'all',\n 'Y1': 'cells of group 1',\n 'Y2': 'cells of group 2',\n }\n regions.update(define_box_regions(dim,\n bbox[0], bbox[1], mesh_eps))\n\n ebcs = {\n }\n\n if dim == 3:\n epbcs = {\n 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},\n 'match_x_plane'),\n 'periodic_y' : (['Near', 'Far'], {'u.all' : 'u.all'},\n 'match_y_plane'),\n 'periodic_z' : (['Top', 'Bottom'], {'u.all' : 'u.all'},\n 'match_z_plane'),\n }\n else:\n epbcs = {\n 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},\n 'match_y_line'),\n 'periodic_y' : (['Bottom', 'Top'], {'u.all' : 'u.all'},\n 'match_x_line'),\n }\n\n per.set_accuracy(mesh_eps)\n functions = {\n 'match_x_plane' : (per.match_x_plane,),\n 'match_y_plane' : (per.match_y_plane,),\n 'match_z_plane' : (per.match_z_plane,),\n 'match_x_line' : (per.match_x_line,),\n 'match_y_line' : (per.match_y_line,),\n 'get_wdir' : (get_wdir,),\n }\n\n integrals = {\n 'i' : 2 * approx_order,\n }\n\n equations = {\n 'K' : 'dw_lin_elastic.i.Omega(m.D, v, u)',\n 'S' : 'dw_elastic_wave.i.Omega(m.D, wave.vec, v, u)',\n 'R' : \"\"\"1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, u, v)\n - 1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, v, u)\"\"\",\n 'M' : 'dw_volume_dot.i.Omega(m.density, v, u)',\n }\n\n solver_0 = solver_conf.copy()\n solver_0['name'] = 'eig'\n\n return locals()\n\ndef get_wdir(ts, coors, mode=None,\n equations=None, term=None, problem=None, wdir=None, **kwargs):\n if mode == 'special':\n return {'vec' : wdir}\n\ndef set_wave_dir(pb, wdir):\n materials = pb.get_materials()\n wave_mat = materials['wave']\n wave_mat.set_extra_args(wdir=wdir)\n\ndef save_materials(output_dir, pb, options):\n stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n young, poisson = mc.youngpoisson_from_stiffness(stiffness,\n plane=options.plane)\n density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n\n out = {}\n out['young'] = Struct(name='young', mode='cell',\n data=young[..., None, None])\n out['poisson'] = Struct(name='poisson', mode='cell',\n data=poisson[..., None, None])\n out['density'] = Struct(name='density', mode='cell', data=density)\n materials_filename = os.path.join(output_dir, 'materials.vtk')\n pb.save_state(materials_filename, out=out)\n\ndef get_std_wave_fun(pb, options):\n stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n young, poisson = mc.youngpoisson_from_stiffness(stiffness,\n plane=options.plane)\n density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n\n lam, mu = mc.lame_from_youngpoisson(young, poisson,\n plane=options.plane)\n alam = nm.average(lam)\n amu = nm.average(mu)\n adensity = nm.average(density)\n\n cp = nm.sqrt((alam + 2.0 * amu) / adensity)\n cs = nm.sqrt(amu / adensity)\n output('average p-wave speed:', cp)\n output('average shear wave speed:', cs)\n\n log_names = [r'$\\omega_p$', r'$\\omega_s$']\n log_plot_kwargs = [{'ls' : '--', 'color' : 'k'},\n {'ls' : '--', 'color' : 'gray'}]\n\n if options.mode == 'omega':\n fun = lambda wmag, wdir: (cp * wmag, cs * wmag)\n\n else:\n fun = lambda wmag, wdir: (wmag / cp, wmag / cs)\n\n return fun, log_names, log_plot_kwargs\n\ndef get_stepper(rng, pb, options):\n if options.stepper == 'linear':\n stepper = TimeStepper(rng[0], rng[1], dt=None, n_step=rng[2])\n return stepper\n\n bbox = pb.domain.mesh.get_bounding_box()\n\n bzone = 2.0 * nm.pi / (bbox[1] - bbox[0])\n\n num = rng[2] // 3\n\n class BrillouinStepper(Struct):\n \"\"\"\n Step over 1. Brillouin zone in xy plane.\n \"\"\"\n def __init__(self, t0, t1, dt=None, n_step=None, step=None, **kwargs):\n Struct.__init__(self, t0=t0, t1=t1, dt=dt, n_step=n_step, step=step)\n\n self.n_digit, self.format, self.suffix = get_print_info(self.n_step)\n\n def __iter__(self):\n ts = "},"completion":{"kind":"string","value":"TimeStepper(0, bzone[0], dt=None, n_step=num)"},"api":{"kind":"string","value":"sfepy.solvers.ts.TimeStepper"}}},{"rowIdx":83,"cells":{"prompt":{"kind":"string","value":"#!/usr/bin/env python\n\"\"\"\nDispersion analysis of a heterogeneous finite scale periodic cell.\n\nThe periodic cell mesh has to contain two subdomains Y1 (with the cell ids 1),\nY2 (with the cell ids 2), so that different material properties can be defined\nin each of the subdomains (see ``--pars`` option). The command line parameters\ncan be given in any consistent unit set, for example the basic SI units. The\n``--unit-multipliers`` option can be used to rescale the input units to ones\nmore suitable to the simulation, for example to prevent having different\nmatrix blocks with large differences of matrix entries magnitudes. The results\nare then in the rescaled units.\n\nUsage Examples\n--------------\n\nDefault material parameters, a square periodic cell with a spherical inclusion,\nlogs also standard pressure dilatation and shear waves, no eigenvectors::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only\n\nAs above, with custom eigenvalue solver parameters, and different number of\neigenvalues, mesh size and units used in the calculation::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --solver-conf=\"kind='eig.scipy', method='eigsh', tol=1e-10, maxiter=1000, which='LM', sigma=0\" --log-std-waves -n 5 --range=0,640,101 --mode=omega --unit-multipliers=1e-6,1e-2,1e-3 --mesh-size=1e-2 --eigs-only\n\nDefault material parameters, a square periodic cell with a square inclusion,\nand a very small mesh to allow comparing the omega and kappa modes (full matrix\nsolver required!)::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf=\"kind='eig.scipy', method='eigh'\" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf=\"kind='eig.qevp', method='companion', mode='inverted', solver={kind='eig.scipy', method='eig'}\" --log-std-waves -n 500 --range=0,4000000,1001 --mesh-size=1e-2 --mode=kappa --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/kappa\n\nView/compare the resulting logs::\n\n python script/plot_logs.py output/omega/frequencies.txt --no-legends -g 1 -o mode-omega.png\n python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends -o mode-kappa.png\n python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends --swap-axes -o mode-kappa-t.png\n\nIn contrast to the heterogeneous square periodic cell, a homogeneous\nsquare periodic cell (the region Y2 is empty)::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_1m.mesh --solver-conf=\"kind='eig.scipy', method='eigh'\" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega-h\n\n python script/plot_logs.py output/omega-h/frequencies.txt --no-legends -g 1 -o mode-omega-h.png\n\nUse the Brillouin stepper::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves -n=60 --eigs-only --no-legends --stepper=brillouin\n\n python script/plot_logs.py output/frequencies.txt -g 0 --rc=\"'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4\" -o brillouin-stepper-kappas.png\n\n python script/plot_logs.py output/frequencies.txt -g 1 --no-legends --rc=\"'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4\" -o brillouin-stepper-omegas.png\n\nAdditional arguments can be passed to the problem configuration's\n:func:`define()` function using the ``--define-kwargs`` option. In this file,\nonly the mesh vertex separation parameter `mesh_eps` can be used::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only --define-kwargs=\"mesh_eps=1e-10\" --save-regions\n\"\"\"\nfrom __future__ import absolute_import\nimport os\nimport sys\nsys.path.append('.')\nimport gc\nfrom copy import copy\nfrom argparse import ArgumentParser, RawDescriptionHelpFormatter\n\nimport numpy as nm\nimport matplotlib.pyplot as plt\n\nfrom sfepy.base.base import import_file, output, Struct\nfrom sfepy.base.conf import dict_from_string, ProblemConf\nfrom sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options\nfrom sfepy.base.log import Log\nfrom sfepy.discrete.fem import MeshIO\nfrom sfepy.mechanics.matcoefs import stiffness_from_youngpoisson as stiffness\nimport sfepy.mechanics.matcoefs as mc\nfrom sfepy.mechanics.units import apply_unit_multipliers\nimport sfepy.discrete.fem.periodic as per\nfrom sfepy.discrete.fem.meshio import convert_complex_output\nfrom sfepy.homogenization.utils import define_box_regions\nfrom sfepy.discrete import Problem\nfrom sfepy.mechanics.tensors import get_von_mises_stress\nfrom sfepy.solvers import Solver\nfrom sfepy.solvers.ts import get_print_info, TimeStepper\nfrom sfepy.linalg.utils import output_array_stats, max_diff_csr\n\ndef apply_units(pars, unit_multipliers):\n new_pars = apply_unit_multipliers(pars,\n ['stress', 'one', 'density',\n 'stress', 'one' ,'density'],\n unit_multipliers)\n return new_pars\n\ndef compute_von_mises(out, pb, state, extend=False, wmag=None, wdir=None):\n \"\"\"\n Calculate the von Mises stress.\n \"\"\"\n stress = pb.evaluate('ev_cauchy_stress.i.Omega(m.D, u)', mode='el_avg')\n\n vms = get_von_mises_stress(stress.squeeze())\n vms.shape = (vms.shape[0], 1, 1, 1)\n out['von_mises_stress'] = Struct(name='output_data', mode='cell',\n data=vms)\n\n return out\n\ndef define(filename_mesh, pars, approx_order, refinement_level, solver_conf,\n plane='strain', post_process=False, mesh_eps=1e-8):\n io = MeshIO.any_from_filename(filename_mesh)\n bbox = io.read_bounding_box()\n dim = bbox.shape[1]\n\n options = {\n 'absolute_mesh_path' : True,\n 'refinement_level' : refinement_level,\n 'allow_empty_regions' : True,\n 'post_process_hook' : 'compute_von_mises' if post_process else None,\n }\n\n fields = {\n 'displacement': ('complex', dim, 'Omega', approx_order),\n }\n\n young1, poisson1, density1, young2, poisson2, density2 = pars\n materials = {\n 'm' : ({\n 'D' : {'Y1' : stiffness(dim, young=young1, poisson=poisson1,\n plane=plane),\n 'Y2' : stiffness(dim, young=young2, poisson=poisson2,\n plane=plane)},\n 'density' : {'Y1' : density1, 'Y2' : density2},\n },),\n 'wave' : 'get_wdir',\n }\n\n variables = {\n 'u' : ('unknown field', 'displacement', 0),\n 'v' : ('test field', 'displacement', 'u'),\n }\n\n regions = {\n 'Omega' : 'all',\n 'Y1': 'cells of group 1',\n 'Y2': 'cells of group 2',\n }\n regions.update(define_box_regions(dim,\n bbox[0], bbox[1], mesh_eps))\n\n ebcs = {\n }\n\n if dim == 3:\n epbcs = {\n 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},\n 'match_x_plane'),\n 'periodic_y' : (['Near', 'Far'], {'u.all' : 'u.all'},\n 'match_y_plane'),\n 'periodic_z' : (['Top', 'Bottom'], {'u.all' : 'u.all'},\n 'match_z_plane'),\n }\n else:\n epbcs = {\n 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},\n 'match_y_line'),\n 'periodic_y' : (['Bottom', 'Top'], {'u.all' : 'u.all'},\n 'match_x_line'),\n }\n\n per.set_accuracy(mesh_eps)\n functions = {\n 'match_x_plane' : (per.match_x_plane,),\n 'match_y_plane' : (per.match_y_plane,),\n 'match_z_plane' : (per.match_z_plane,),\n 'match_x_line' : (per.match_x_line,),\n 'match_y_line' : (per.match_y_line,),\n 'get_wdir' : (get_wdir,),\n }\n\n integrals = {\n 'i' : 2 * approx_order,\n }\n\n equations = {\n 'K' : 'dw_lin_elastic.i.Omega(m.D, v, u)',\n 'S' : 'dw_elastic_wave.i.Omega(m.D, wave.vec, v, u)',\n 'R' : \"\"\"1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, u, v)\n - 1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, v, u)\"\"\",\n 'M' : 'dw_volume_dot.i.Omega(m.density, v, u)',\n }\n\n solver_0 = solver_conf.copy()\n solver_0['name'] = 'eig'\n\n return locals()\n\ndef get_wdir(ts, coors, mode=None,\n equations=None, term=None, problem=None, wdir=None, **kwargs):\n if mode == 'special':\n return {'vec' : wdir}\n\ndef set_wave_dir(pb, wdir):\n materials = pb.get_materials()\n wave_mat = materials['wave']\n wave_mat.set_extra_args(wdir=wdir)\n\ndef save_materials(output_dir, pb, options):\n stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n young, poisson = mc.youngpoisson_from_stiffness(stiffness,\n plane=options.plane)\n density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n\n out = {}\n out['young'] = Struct(name='young', mode='cell',\n data=young[..., None, None])\n out['poisson'] = Struct(name='poisson', mode='cell',\n data=poisson[..., None, None])\n out['density'] = Struct(name='density', mode='cell', data=density)\n materials_filename = os.path.join(output_dir, 'materials.vtk')\n pb.save_state(materials_filename, out=out)\n\ndef get_std_wave_fun(pb, options):\n stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n young, poisson = mc.youngpoisson_from_stiffness(stiffness,\n plane=options.plane)\n density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n\n lam, mu = mc.lame_from_youngpoisson(young, poisson,\n plane=options.plane)\n alam = nm.average(lam)\n amu = nm.average(mu)\n adensity = nm.average(density)\n\n cp = nm.sqrt((alam + 2.0 * amu) / adensity)\n cs = nm.sqrt(amu / adensity)\n output('average p-wave speed:', cp)\n output('average shear wave speed:', cs)\n\n log_names = [r'$\\omega_p$', r'$\\omega_s$']\n log_plot_kwargs = [{'ls' : '--', 'color' : 'k'},\n {'ls' : '--', 'color' : 'gray'}]\n\n if options.mode == 'omega':\n fun = lambda wmag, wdir: (cp * wmag, cs * wmag)\n\n else:\n fun = lambda wmag, wdir: (wmag / cp, wmag / cs)\n\n return fun, log_names, log_plot_kwargs\n\ndef get_stepper(rng, pb, options):\n if options.stepper == 'linear':\n stepper = TimeStepper(rng[0], rng[1], dt=None, n_step=rng[2])\n return stepper\n\n bbox = pb.domain.mesh.get_bounding_box()\n\n bzone = 2.0 * nm.pi / (bbox[1] - bbox[0])\n\n num = rng[2] // 3\n\n class BrillouinStepper(Struct):\n \"\"\"\n Step over 1. Brillouin zone in xy plane.\n \"\"\"\n def __init__(self, t0, t1, dt=None, n_step=None, step=None, **kwargs):\n Struct.__init__(self, t0=t0, t1=t1, dt=dt, n_step=n_step, step=step)\n\n self.n_digit, self.format, self.suffix = get_print_info(self.n_step)\n\n def __iter__(self):\n ts = TimeStepper(0, bzone[0], dt=None, n_step=num)\n for ii, val in ts:\n yield ii, val, nm.array([1.0, 0.0])\n if ii == (num-2): break\n\n ts = "},"completion":{"kind":"string","value":"TimeStepper(0, bzone[1], dt=None, n_step=num)"},"api":{"kind":"string","value":"sfepy.solvers.ts.TimeStepper"}}},{"rowIdx":84,"cells":{"prompt":{"kind":"string","value":"#!/usr/bin/env python\n\"\"\"\nDispersion analysis of a heterogeneous finite scale periodic cell.\n\nThe periodic cell mesh has to contain two subdomains Y1 (with the cell ids 1),\nY2 (with the cell ids 2), so that different material properties can be defined\nin each of the subdomains (see ``--pars`` option). The command line parameters\ncan be given in any consistent unit set, for example the basic SI units. The\n``--unit-multipliers`` option can be used to rescale the input units to ones\nmore suitable to the simulation, for example to prevent having different\nmatrix blocks with large differences of matrix entries magnitudes. The results\nare then in the rescaled units.\n\nUsage Examples\n--------------\n\nDefault material parameters, a square periodic cell with a spherical inclusion,\nlogs also standard pressure dilatation and shear waves, no eigenvectors::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only\n\nAs above, with custom eigenvalue solver parameters, and different number of\neigenvalues, mesh size and units used in the calculation::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --solver-conf=\"kind='eig.scipy', method='eigsh', tol=1e-10, maxiter=1000, which='LM', sigma=0\" --log-std-waves -n 5 --range=0,640,101 --mode=omega --unit-multipliers=1e-6,1e-2,1e-3 --mesh-size=1e-2 --eigs-only\n\nDefault material parameters, a square periodic cell with a square inclusion,\nand a very small mesh to allow comparing the omega and kappa modes (full matrix\nsolver required!)::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf=\"kind='eig.scipy', method='eigh'\" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf=\"kind='eig.qevp', method='companion', mode='inverted', solver={kind='eig.scipy', method='eig'}\" --log-std-waves -n 500 --range=0,4000000,1001 --mesh-size=1e-2 --mode=kappa --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/kappa\n\nView/compare the resulting logs::\n\n python script/plot_logs.py output/omega/frequencies.txt --no-legends -g 1 -o mode-omega.png\n python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends -o mode-kappa.png\n python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends --swap-axes -o mode-kappa-t.png\n\nIn contrast to the heterogeneous square periodic cell, a homogeneous\nsquare periodic cell (the region Y2 is empty)::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_1m.mesh --solver-conf=\"kind='eig.scipy', method='eigh'\" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega-h\n\n python script/plot_logs.py output/omega-h/frequencies.txt --no-legends -g 1 -o mode-omega-h.png\n\nUse the Brillouin stepper::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves -n=60 --eigs-only --no-legends --stepper=brillouin\n\n python script/plot_logs.py output/frequencies.txt -g 0 --rc=\"'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4\" -o brillouin-stepper-kappas.png\n\n python script/plot_logs.py output/frequencies.txt -g 1 --no-legends --rc=\"'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4\" -o brillouin-stepper-omegas.png\n\nAdditional arguments can be passed to the problem configuration's\n:func:`define()` function using the ``--define-kwargs`` option. In this file,\nonly the mesh vertex separation parameter `mesh_eps` can be used::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only --define-kwargs=\"mesh_eps=1e-10\" --save-regions\n\"\"\"\nfrom __future__ import absolute_import\nimport os\nimport sys\nsys.path.append('.')\nimport gc\nfrom copy import copy\nfrom argparse import ArgumentParser, RawDescriptionHelpFormatter\n\nimport numpy as nm\nimport matplotlib.pyplot as plt\n\nfrom sfepy.base.base import import_file, output, Struct\nfrom sfepy.base.conf import dict_from_string, ProblemConf\nfrom sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options\nfrom sfepy.base.log import Log\nfrom sfepy.discrete.fem import MeshIO\nfrom sfepy.mechanics.matcoefs import stiffness_from_youngpoisson as stiffness\nimport sfepy.mechanics.matcoefs as mc\nfrom sfepy.mechanics.units import apply_unit_multipliers\nimport sfepy.discrete.fem.periodic as per\nfrom sfepy.discrete.fem.meshio import convert_complex_output\nfrom sfepy.homogenization.utils import define_box_regions\nfrom sfepy.discrete import Problem\nfrom sfepy.mechanics.tensors import get_von_mises_stress\nfrom sfepy.solvers import Solver\nfrom sfepy.solvers.ts import get_print_info, TimeStepper\nfrom sfepy.linalg.utils import output_array_stats, max_diff_csr\n\ndef apply_units(pars, unit_multipliers):\n new_pars = apply_unit_multipliers(pars,\n ['stress', 'one', 'density',\n 'stress', 'one' ,'density'],\n unit_multipliers)\n return new_pars\n\ndef compute_von_mises(out, pb, state, extend=False, wmag=None, wdir=None):\n \"\"\"\n Calculate the von Mises stress.\n \"\"\"\n stress = pb.evaluate('ev_cauchy_stress.i.Omega(m.D, u)', mode='el_avg')\n\n vms = get_von_mises_stress(stress.squeeze())\n vms.shape = (vms.shape[0], 1, 1, 1)\n out['von_mises_stress'] = Struct(name='output_data', mode='cell',\n data=vms)\n\n return out\n\ndef define(filename_mesh, pars, approx_order, refinement_level, solver_conf,\n plane='strain', post_process=False, mesh_eps=1e-8):\n io = MeshIO.any_from_filename(filename_mesh)\n bbox = io.read_bounding_box()\n dim = bbox.shape[1]\n\n options = {\n 'absolute_mesh_path' : True,\n 'refinement_level' : refinement_level,\n 'allow_empty_regions' : True,\n 'post_process_hook' : 'compute_von_mises' if post_process else None,\n }\n\n fields = {\n 'displacement': ('complex', dim, 'Omega', approx_order),\n }\n\n young1, poisson1, density1, young2, poisson2, density2 = pars\n materials = {\n 'm' : ({\n 'D' : {'Y1' : stiffness(dim, young=young1, poisson=poisson1,\n plane=plane),\n 'Y2' : stiffness(dim, young=young2, poisson=poisson2,\n plane=plane)},\n 'density' : {'Y1' : density1, 'Y2' : density2},\n },),\n 'wave' : 'get_wdir',\n }\n\n variables = {\n 'u' : ('unknown field', 'displacement', 0),\n 'v' : ('test field', 'displacement', 'u'),\n }\n\n regions = {\n 'Omega' : 'all',\n 'Y1': 'cells of group 1',\n 'Y2': 'cells of group 2',\n }\n regions.update(define_box_regions(dim,\n bbox[0], bbox[1], mesh_eps))\n\n ebcs = {\n }\n\n if dim == 3:\n epbcs = {\n 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},\n 'match_x_plane'),\n 'periodic_y' : (['Near', 'Far'], {'u.all' : 'u.all'},\n 'match_y_plane'),\n 'periodic_z' : (['Top', 'Bottom'], {'u.all' : 'u.all'},\n 'match_z_plane'),\n }\n else:\n epbcs = {\n 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},\n 'match_y_line'),\n 'periodic_y' : (['Bottom', 'Top'], {'u.all' : 'u.all'},\n 'match_x_line'),\n }\n\n per.set_accuracy(mesh_eps)\n functions = {\n 'match_x_plane' : (per.match_x_plane,),\n 'match_y_plane' : (per.match_y_plane,),\n 'match_z_plane' : (per.match_z_plane,),\n 'match_x_line' : (per.match_x_line,),\n 'match_y_line' : (per.match_y_line,),\n 'get_wdir' : (get_wdir,),\n }\n\n integrals = {\n 'i' : 2 * approx_order,\n }\n\n equations = {\n 'K' : 'dw_lin_elastic.i.Omega(m.D, v, u)',\n 'S' : 'dw_elastic_wave.i.Omega(m.D, wave.vec, v, u)',\n 'R' : \"\"\"1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, u, v)\n - 1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, v, u)\"\"\",\n 'M' : 'dw_volume_dot.i.Omega(m.density, v, u)',\n }\n\n solver_0 = solver_conf.copy()\n solver_0['name'] = 'eig'\n\n return locals()\n\ndef get_wdir(ts, coors, mode=None,\n equations=None, term=None, problem=None, wdir=None, **kwargs):\n if mode == 'special':\n return {'vec' : wdir}\n\ndef set_wave_dir(pb, wdir):\n materials = pb.get_materials()\n wave_mat = materials['wave']\n wave_mat.set_extra_args(wdir=wdir)\n\ndef save_materials(output_dir, pb, options):\n stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n young, poisson = mc.youngpoisson_from_stiffness(stiffness,\n plane=options.plane)\n density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n\n out = {}\n out['young'] = Struct(name='young', mode='cell',\n data=young[..., None, None])\n out['poisson'] = Struct(name='poisson', mode='cell',\n data=poisson[..., None, None])\n out['density'] = Struct(name='density', mode='cell', data=density)\n materials_filename = os.path.join(output_dir, 'materials.vtk')\n pb.save_state(materials_filename, out=out)\n\ndef get_std_wave_fun(pb, options):\n stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n young, poisson = mc.youngpoisson_from_stiffness(stiffness,\n plane=options.plane)\n density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n\n lam, mu = mc.lame_from_youngpoisson(young, poisson,\n plane=options.plane)\n alam = nm.average(lam)\n amu = nm.average(mu)\n adensity = nm.average(density)\n\n cp = nm.sqrt((alam + 2.0 * amu) / adensity)\n cs = nm.sqrt(amu / adensity)\n output('average p-wave speed:', cp)\n output('average shear wave speed:', cs)\n\n log_names = [r'$\\omega_p$', r'$\\omega_s$']\n log_plot_kwargs = [{'ls' : '--', 'color' : 'k'},\n {'ls' : '--', 'color' : 'gray'}]\n\n if options.mode == 'omega':\n fun = lambda wmag, wdir: (cp * wmag, cs * wmag)\n\n else:\n fun = lambda wmag, wdir: (wmag / cp, wmag / cs)\n\n return fun, log_names, log_plot_kwargs\n\ndef get_stepper(rng, pb, options):\n if options.stepper == 'linear':\n stepper = TimeStepper(rng[0], rng[1], dt=None, n_step=rng[2])\n return stepper\n\n bbox = pb.domain.mesh.get_bounding_box()\n\n bzone = 2.0 * nm.pi / (bbox[1] - bbox[0])\n\n num = rng[2] // 3\n\n class BrillouinStepper(Struct):\n \"\"\"\n Step over 1. Brillouin zone in xy plane.\n \"\"\"\n def __init__(self, t0, t1, dt=None, n_step=None, step=None, **kwargs):\n Struct.__init__(self, t0=t0, t1=t1, dt=dt, n_step=n_step, step=step)\n\n self.n_digit, self.format, self.suffix = get_print_info(self.n_step)\n\n def __iter__(self):\n ts = TimeStepper(0, bzone[0], dt=None, n_step=num)\n for ii, val in ts:\n yield ii, val, nm.array([1.0, 0.0])\n if ii == (num-2): break\n\n ts = TimeStepper(0, bzone[1], dt=None, n_step=num)\n for ii, k1 in ts:\n wdir = nm.array([bzone[0], k1])\n val = nm.linalg.norm(wdir)\n wdir = wdir / val\n yield num + ii, val, wdir\n if ii == (num-2): break\n\n wdir = nm.array([bzone[0], bzone[1]])\n val = nm.linalg.norm(wdir)\n wdir = wdir / val\n ts = "},"completion":{"kind":"string","value":"TimeStepper(0, 1, dt=None, n_step=num)"},"api":{"kind":"string","value":"sfepy.solvers.ts.TimeStepper"}}},{"rowIdx":85,"cells":{"prompt":{"kind":"string","value":"#!/usr/bin/env python\n\"\"\"\nDispersion analysis of a heterogeneous finite scale periodic cell.\n\nThe periodic cell mesh has to contain two subdomains Y1 (with the cell ids 1),\nY2 (with the cell ids 2), so that different material properties can be defined\nin each of the subdomains (see ``--pars`` option). The command line parameters\ncan be given in any consistent unit set, for example the basic SI units. The\n``--unit-multipliers`` option can be used to rescale the input units to ones\nmore suitable to the simulation, for example to prevent having different\nmatrix blocks with large differences of matrix entries magnitudes. The results\nare then in the rescaled units.\n\nUsage Examples\n--------------\n\nDefault material parameters, a square periodic cell with a spherical inclusion,\nlogs also standard pressure dilatation and shear waves, no eigenvectors::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only\n\nAs above, with custom eigenvalue solver parameters, and different number of\neigenvalues, mesh size and units used in the calculation::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --solver-conf=\"kind='eig.scipy', method='eigsh', tol=1e-10, maxiter=1000, which='LM', sigma=0\" --log-std-waves -n 5 --range=0,640,101 --mode=omega --unit-multipliers=1e-6,1e-2,1e-3 --mesh-size=1e-2 --eigs-only\n\nDefault material parameters, a square periodic cell with a square inclusion,\nand a very small mesh to allow comparing the omega and kappa modes (full matrix\nsolver required!)::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf=\"kind='eig.scipy', method='eigh'\" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf=\"kind='eig.qevp', method='companion', mode='inverted', solver={kind='eig.scipy', method='eig'}\" --log-std-waves -n 500 --range=0,4000000,1001 --mesh-size=1e-2 --mode=kappa --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/kappa\n\nView/compare the resulting logs::\n\n python script/plot_logs.py output/omega/frequencies.txt --no-legends -g 1 -o mode-omega.png\n python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends -o mode-kappa.png\n python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends --swap-axes -o mode-kappa-t.png\n\nIn contrast to the heterogeneous square periodic cell, a homogeneous\nsquare periodic cell (the region Y2 is empty)::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_1m.mesh --solver-conf=\"kind='eig.scipy', method='eigh'\" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega-h\n\n python script/plot_logs.py output/omega-h/frequencies.txt --no-legends -g 1 -o mode-omega-h.png\n\nUse the Brillouin stepper::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves -n=60 --eigs-only --no-legends --stepper=brillouin\n\n python script/plot_logs.py output/frequencies.txt -g 0 --rc=\"'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4\" -o brillouin-stepper-kappas.png\n\n python script/plot_logs.py output/frequencies.txt -g 1 --no-legends --rc=\"'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4\" -o brillouin-stepper-omegas.png\n\nAdditional arguments can be passed to the problem configuration's\n:func:`define()` function using the ``--define-kwargs`` option. In this file,\nonly the mesh vertex separation parameter `mesh_eps` can be used::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only --define-kwargs=\"mesh_eps=1e-10\" --save-regions\n\"\"\"\nfrom __future__ import absolute_import\nimport os\nimport sys\nsys.path.append('.')\nimport gc\nfrom copy import copy\nfrom argparse import ArgumentParser, RawDescriptionHelpFormatter\n\nimport numpy as nm\nimport matplotlib.pyplot as plt\n\nfrom sfepy.base.base import import_file, output, Struct\nfrom sfepy.base.conf import dict_from_string, ProblemConf\nfrom sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options\nfrom sfepy.base.log import Log\nfrom sfepy.discrete.fem import MeshIO\nfrom sfepy.mechanics.matcoefs import stiffness_from_youngpoisson as stiffness\nimport sfepy.mechanics.matcoefs as mc\nfrom sfepy.mechanics.units import apply_unit_multipliers\nimport sfepy.discrete.fem.periodic as per\nfrom sfepy.discrete.fem.meshio import convert_complex_output\nfrom sfepy.homogenization.utils import define_box_regions\nfrom sfepy.discrete import Problem\nfrom sfepy.mechanics.tensors import get_von_mises_stress\nfrom sfepy.solvers import Solver\nfrom sfepy.solvers.ts import get_print_info, TimeStepper\nfrom sfepy.linalg.utils import output_array_stats, max_diff_csr\n\ndef apply_units(pars, unit_multipliers):\n new_pars = apply_unit_multipliers(pars,\n ['stress', 'one', 'density',\n 'stress', 'one' ,'density'],\n unit_multipliers)\n return new_pars\n\ndef compute_von_mises(out, pb, state, extend=False, wmag=None, wdir=None):\n \"\"\"\n Calculate the von Mises stress.\n \"\"\"\n stress = pb.evaluate('ev_cauchy_stress.i.Omega(m.D, u)', mode='el_avg')\n\n vms = get_von_mises_stress(stress.squeeze())\n vms.shape = (vms.shape[0], 1, 1, 1)\n out['von_mises_stress'] = Struct(name='output_data', mode='cell',\n data=vms)\n\n return out\n\ndef define(filename_mesh, pars, approx_order, refinement_level, solver_conf,\n plane='strain', post_process=False, mesh_eps=1e-8):\n io = MeshIO.any_from_filename(filename_mesh)\n bbox = io.read_bounding_box()\n dim = bbox.shape[1]\n\n options = {\n 'absolute_mesh_path' : True,\n 'refinement_level' : refinement_level,\n 'allow_empty_regions' : True,\n 'post_process_hook' : 'compute_von_mises' if post_process else None,\n }\n\n fields = {\n 'displacement': ('complex', dim, 'Omega', approx_order),\n }\n\n young1, poisson1, density1, young2, poisson2, density2 = pars\n materials = {\n 'm' : ({\n 'D' : {'Y1' : stiffness(dim, young=young1, poisson=poisson1,\n plane=plane),\n 'Y2' : stiffness(dim, young=young2, poisson=poisson2,\n plane=plane)},\n 'density' : {'Y1' : density1, 'Y2' : density2},\n },),\n 'wave' : 'get_wdir',\n }\n\n variables = {\n 'u' : ('unknown field', 'displacement', 0),\n 'v' : ('test field', 'displacement', 'u'),\n }\n\n regions = {\n 'Omega' : 'all',\n 'Y1': 'cells of group 1',\n 'Y2': 'cells of group 2',\n }\n regions.update(define_box_regions(dim,\n bbox[0], bbox[1], mesh_eps))\n\n ebcs = {\n }\n\n if dim == 3:\n epbcs = {\n 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},\n 'match_x_plane'),\n 'periodic_y' : (['Near', 'Far'], {'u.all' : 'u.all'},\n 'match_y_plane'),\n 'periodic_z' : (['Top', 'Bottom'], {'u.all' : 'u.all'},\n 'match_z_plane'),\n }\n else:\n epbcs = {\n 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},\n 'match_y_line'),\n 'periodic_y' : (['Bottom', 'Top'], {'u.all' : 'u.all'},\n 'match_x_line'),\n }\n\n per.set_accuracy(mesh_eps)\n functions = {\n 'match_x_plane' : (per.match_x_plane,),\n 'match_y_plane' : (per.match_y_plane,),\n 'match_z_plane' : (per.match_z_plane,),\n 'match_x_line' : (per.match_x_line,),\n 'match_y_line' : (per.match_y_line,),\n 'get_wdir' : (get_wdir,),\n }\n\n integrals = {\n 'i' : 2 * approx_order,\n }\n\n equations = {\n 'K' : 'dw_lin_elastic.i.Omega(m.D, v, u)',\n 'S' : 'dw_elastic_wave.i.Omega(m.D, wave.vec, v, u)',\n 'R' : \"\"\"1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, u, v)\n - 1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, v, u)\"\"\",\n 'M' : 'dw_volume_dot.i.Omega(m.density, v, u)',\n }\n\n solver_0 = solver_conf.copy()\n solver_0['name'] = 'eig'\n\n return locals()\n\ndef get_wdir(ts, coors, mode=None,\n equations=None, term=None, problem=None, wdir=None, **kwargs):\n if mode == 'special':\n return {'vec' : wdir}\n\ndef set_wave_dir(pb, wdir):\n materials = pb.get_materials()\n wave_mat = materials['wave']\n wave_mat.set_extra_args(wdir=wdir)\n\ndef save_materials(output_dir, pb, options):\n stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n young, poisson = mc.youngpoisson_from_stiffness(stiffness,\n plane=options.plane)\n density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n\n out = {}\n out['young'] = Struct(name='young', mode='cell',\n data=young[..., None, None])\n out['poisson'] = Struct(name='poisson', mode='cell',\n data=poisson[..., None, None])\n out['density'] = Struct(name='density', mode='cell', data=density)\n materials_filename = os.path.join(output_dir, 'materials.vtk')\n pb.save_state(materials_filename, out=out)\n\ndef get_std_wave_fun(pb, options):\n stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n young, poisson = mc.youngpoisson_from_stiffness(stiffness,\n plane=options.plane)\n density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n\n lam, mu = mc.lame_from_youngpoisson(young, poisson,\n plane=options.plane)\n alam = nm.average(lam)\n amu = nm.average(mu)\n adensity = nm.average(density)\n\n cp = nm.sqrt((alam + 2.0 * amu) / adensity)\n cs = nm.sqrt(amu / adensity)\n output('average p-wave speed:', cp)\n output('average shear wave speed:', cs)\n\n log_names = [r'$\\omega_p$', r'$\\omega_s$']\n log_plot_kwargs = [{'ls' : '--', 'color' : 'k'},\n {'ls' : '--', 'color' : 'gray'}]\n\n if options.mode == 'omega':\n fun = lambda wmag, wdir: (cp * wmag, cs * wmag)\n\n else:\n fun = lambda wmag, wdir: (wmag / cp, wmag / cs)\n\n return fun, log_names, log_plot_kwargs\n\ndef get_stepper(rng, pb, options):\n if options.stepper == 'linear':\n stepper = TimeStepper(rng[0], rng[1], dt=None, n_step=rng[2])\n return stepper\n\n bbox = pb.domain.mesh.get_bounding_box()\n\n bzone = 2.0 * nm.pi / (bbox[1] - bbox[0])\n\n num = rng[2] // 3\n\n class BrillouinStepper(Struct):\n \"\"\"\n Step over 1. Brillouin zone in xy plane.\n \"\"\"\n def __init__(self, t0, t1, dt=None, n_step=None, step=None, **kwargs):\n Struct.__init__(self, t0=t0, t1=t1, dt=dt, n_step=n_step, step=step)\n\n self.n_digit, self.format, self.suffix = get_print_info(self.n_step)\n\n def __iter__(self):\n ts = TimeStepper(0, bzone[0], dt=None, n_step=num)\n for ii, val in ts:\n yield ii, val, nm.array([1.0, 0.0])\n if ii == (num-2): break\n\n ts = TimeStepper(0, bzone[1], dt=None, n_step=num)\n for ii, k1 in ts:\n wdir = nm.array([bzone[0], k1])\n val = nm.linalg.norm(wdir)\n wdir = wdir / val\n yield num + ii, val, wdir\n if ii == (num-2): break\n\n wdir = nm.array([bzone[0], bzone[1]])\n val = nm.linalg.norm(wdir)\n wdir = wdir / val\n ts = TimeStepper(0, 1, dt=None, n_step=num)\n for ii, _ in ts:\n yield 2 * num + ii, val * (1.0 - float(ii)/(num-1)), wdir\n\n stepper = BrillouinStepper(0, 1, n_step=rng[2])\n\n return stepper\n\ndef save_eigenvectors(filename, svecs, wmag, wdir, pb):\n if svecs is None: return\n\n variables = pb.get_variables()\n # Make full eigenvectors (add DOFs fixed by boundary conditions).\n vecs = nm.empty((variables.di.ptr[-1], svecs.shape[1]),\n dtype=svecs.dtype)\n for ii in range(svecs.shape[1]):\n vecs[:, ii] = variables.make_full_vec(svecs[:, ii])\n\n # Save the eigenvectors.\n out = {}\n state = pb.create_state()\n\n pp_name = pb.conf.options.get('post_process_hook')\n pp = getattr(pb.conf.funmod, pp_name if pp_name is not None else '',\n lambda out, *args, **kwargs: out)\n\n for ii in range(svecs.shape[1]):\n state.set_full(vecs[:, ii])\n aux = state.create_output_dict()\n aux2 = {}\n pp(aux2, pb, state, wmag=wmag, wdir=wdir)\n aux.update("},"completion":{"kind":"string","value":"convert_complex_output(aux2)"},"api":{"kind":"string","value":"sfepy.discrete.fem.meshio.convert_complex_output"}}},{"rowIdx":86,"cells":{"prompt":{"kind":"string","value":"#!/usr/bin/env python\n\"\"\"\nDispersion analysis of a heterogeneous finite scale periodic cell.\n\nThe periodic cell mesh has to contain two subdomains Y1 (with the cell ids 1),\nY2 (with the cell ids 2), so that different material properties can be defined\nin each of the subdomains (see ``--pars`` option). The command line parameters\ncan be given in any consistent unit set, for example the basic SI units. The\n``--unit-multipliers`` option can be used to rescale the input units to ones\nmore suitable to the simulation, for example to prevent having different\nmatrix blocks with large differences of matrix entries magnitudes. The results\nare then in the rescaled units.\n\nUsage Examples\n--------------\n\nDefault material parameters, a square periodic cell with a spherical inclusion,\nlogs also standard pressure dilatation and shear waves, no eigenvectors::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only\n\nAs above, with custom eigenvalue solver parameters, and different number of\neigenvalues, mesh size and units used in the calculation::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --solver-conf=\"kind='eig.scipy', method='eigsh', tol=1e-10, maxiter=1000, which='LM', sigma=0\" --log-std-waves -n 5 --range=0,640,101 --mode=omega --unit-multipliers=1e-6,1e-2,1e-3 --mesh-size=1e-2 --eigs-only\n\nDefault material parameters, a square periodic cell with a square inclusion,\nand a very small mesh to allow comparing the omega and kappa modes (full matrix\nsolver required!)::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf=\"kind='eig.scipy', method='eigh'\" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf=\"kind='eig.qevp', method='companion', mode='inverted', solver={kind='eig.scipy', method='eig'}\" --log-std-waves -n 500 --range=0,4000000,1001 --mesh-size=1e-2 --mode=kappa --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/kappa\n\nView/compare the resulting logs::\n\n python script/plot_logs.py output/omega/frequencies.txt --no-legends -g 1 -o mode-omega.png\n python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends -o mode-kappa.png\n python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends --swap-axes -o mode-kappa-t.png\n\nIn contrast to the heterogeneous square periodic cell, a homogeneous\nsquare periodic cell (the region Y2 is empty)::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_1m.mesh --solver-conf=\"kind='eig.scipy', method='eigh'\" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega-h\n\n python script/plot_logs.py output/omega-h/frequencies.txt --no-legends -g 1 -o mode-omega-h.png\n\nUse the Brillouin stepper::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves -n=60 --eigs-only --no-legends --stepper=brillouin\n\n python script/plot_logs.py output/frequencies.txt -g 0 --rc=\"'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4\" -o brillouin-stepper-kappas.png\n\n python script/plot_logs.py output/frequencies.txt -g 1 --no-legends --rc=\"'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4\" -o brillouin-stepper-omegas.png\n\nAdditional arguments can be passed to the problem configuration's\n:func:`define()` function using the ``--define-kwargs`` option. In this file,\nonly the mesh vertex separation parameter `mesh_eps` can be used::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only --define-kwargs=\"mesh_eps=1e-10\" --save-regions\n\"\"\"\nfrom __future__ import absolute_import\nimport os\nimport sys\nsys.path.append('.')\nimport gc\nfrom copy import copy\nfrom argparse import ArgumentParser, RawDescriptionHelpFormatter\n\nimport numpy as nm\nimport matplotlib.pyplot as plt\n\nfrom sfepy.base.base import import_file, output, Struct\nfrom sfepy.base.conf import dict_from_string, ProblemConf\nfrom sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options\nfrom sfepy.base.log import Log\nfrom sfepy.discrete.fem import MeshIO\nfrom sfepy.mechanics.matcoefs import stiffness_from_youngpoisson as stiffness\nimport sfepy.mechanics.matcoefs as mc\nfrom sfepy.mechanics.units import apply_unit_multipliers\nimport sfepy.discrete.fem.periodic as per\nfrom sfepy.discrete.fem.meshio import convert_complex_output\nfrom sfepy.homogenization.utils import define_box_regions\nfrom sfepy.discrete import Problem\nfrom sfepy.mechanics.tensors import get_von_mises_stress\nfrom sfepy.solvers import Solver\nfrom sfepy.solvers.ts import get_print_info, TimeStepper\nfrom sfepy.linalg.utils import output_array_stats, max_diff_csr\n\ndef apply_units(pars, unit_multipliers):\n new_pars = apply_unit_multipliers(pars,\n ['stress', 'one', 'density',\n 'stress', 'one' ,'density'],\n unit_multipliers)\n return new_pars\n\ndef compute_von_mises(out, pb, state, extend=False, wmag=None, wdir=None):\n \"\"\"\n Calculate the von Mises stress.\n \"\"\"\n stress = pb.evaluate('ev_cauchy_stress.i.Omega(m.D, u)', mode='el_avg')\n\n vms = get_von_mises_stress(stress.squeeze())\n vms.shape = (vms.shape[0], 1, 1, 1)\n out['von_mises_stress'] = Struct(name='output_data', mode='cell',\n data=vms)\n\n return out\n\ndef define(filename_mesh, pars, approx_order, refinement_level, solver_conf,\n plane='strain', post_process=False, mesh_eps=1e-8):\n io = MeshIO.any_from_filename(filename_mesh)\n bbox = io.read_bounding_box()\n dim = bbox.shape[1]\n\n options = {\n 'absolute_mesh_path' : True,\n 'refinement_level' : refinement_level,\n 'allow_empty_regions' : True,\n 'post_process_hook' : 'compute_von_mises' if post_process else None,\n }\n\n fields = {\n 'displacement': ('complex', dim, 'Omega', approx_order),\n }\n\n young1, poisson1, density1, young2, poisson2, density2 = pars\n materials = {\n 'm' : ({\n 'D' : {'Y1' : stiffness(dim, young=young1, poisson=poisson1,\n plane=plane),\n 'Y2' : stiffness(dim, young=young2, poisson=poisson2,\n plane=plane)},\n 'density' : {'Y1' : density1, 'Y2' : density2},\n },),\n 'wave' : 'get_wdir',\n }\n\n variables = {\n 'u' : ('unknown field', 'displacement', 0),\n 'v' : ('test field', 'displacement', 'u'),\n }\n\n regions = {\n 'Omega' : 'all',\n 'Y1': 'cells of group 1',\n 'Y2': 'cells of group 2',\n }\n regions.update(define_box_regions(dim,\n bbox[0], bbox[1], mesh_eps))\n\n ebcs = {\n }\n\n if dim == 3:\n epbcs = {\n 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},\n 'match_x_plane'),\n 'periodic_y' : (['Near', 'Far'], {'u.all' : 'u.all'},\n 'match_y_plane'),\n 'periodic_z' : (['Top', 'Bottom'], {'u.all' : 'u.all'},\n 'match_z_plane'),\n }\n else:\n epbcs = {\n 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},\n 'match_y_line'),\n 'periodic_y' : (['Bottom', 'Top'], {'u.all' : 'u.all'},\n 'match_x_line'),\n }\n\n per.set_accuracy(mesh_eps)\n functions = {\n 'match_x_plane' : (per.match_x_plane,),\n 'match_y_plane' : (per.match_y_plane,),\n 'match_z_plane' : (per.match_z_plane,),\n 'match_x_line' : (per.match_x_line,),\n 'match_y_line' : (per.match_y_line,),\n 'get_wdir' : (get_wdir,),\n }\n\n integrals = {\n 'i' : 2 * approx_order,\n }\n\n equations = {\n 'K' : 'dw_lin_elastic.i.Omega(m.D, v, u)',\n 'S' : 'dw_elastic_wave.i.Omega(m.D, wave.vec, v, u)',\n 'R' : \"\"\"1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, u, v)\n - 1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, v, u)\"\"\",\n 'M' : 'dw_volume_dot.i.Omega(m.density, v, u)',\n }\n\n solver_0 = solver_conf.copy()\n solver_0['name'] = 'eig'\n\n return locals()\n\ndef get_wdir(ts, coors, mode=None,\n equations=None, term=None, problem=None, wdir=None, **kwargs):\n if mode == 'special':\n return {'vec' : wdir}\n\ndef set_wave_dir(pb, wdir):\n materials = pb.get_materials()\n wave_mat = materials['wave']\n wave_mat.set_extra_args(wdir=wdir)\n\ndef save_materials(output_dir, pb, options):\n stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n young, poisson = mc.youngpoisson_from_stiffness(stiffness,\n plane=options.plane)\n density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n\n out = {}\n out['young'] = Struct(name='young', mode='cell',\n data=young[..., None, None])\n out['poisson'] = Struct(name='poisson', mode='cell',\n data=poisson[..., None, None])\n out['density'] = Struct(name='density', mode='cell', data=density)\n materials_filename = os.path.join(output_dir, 'materials.vtk')\n pb.save_state(materials_filename, out=out)\n\ndef get_std_wave_fun(pb, options):\n stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n young, poisson = mc.youngpoisson_from_stiffness(stiffness,\n plane=options.plane)\n density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n\n lam, mu = mc.lame_from_youngpoisson(young, poisson,\n plane=options.plane)\n alam = nm.average(lam)\n amu = nm.average(mu)\n adensity = nm.average(density)\n\n cp = nm.sqrt((alam + 2.0 * amu) / adensity)\n cs = nm.sqrt(amu / adensity)\n output('average p-wave speed:', cp)\n output('average shear wave speed:', cs)\n\n log_names = [r'$\\omega_p$', r'$\\omega_s$']\n log_plot_kwargs = [{'ls' : '--', 'color' : 'k'},\n {'ls' : '--', 'color' : 'gray'}]\n\n if options.mode == 'omega':\n fun = lambda wmag, wdir: (cp * wmag, cs * wmag)\n\n else:\n fun = lambda wmag, wdir: (wmag / cp, wmag / cs)\n\n return fun, log_names, log_plot_kwargs\n\ndef get_stepper(rng, pb, options):\n if options.stepper == 'linear':\n stepper = TimeStepper(rng[0], rng[1], dt=None, n_step=rng[2])\n return stepper\n\n bbox = pb.domain.mesh.get_bounding_box()\n\n bzone = 2.0 * nm.pi / (bbox[1] - bbox[0])\n\n num = rng[2] // 3\n\n class BrillouinStepper(Struct):\n \"\"\"\n Step over 1. Brillouin zone in xy plane.\n \"\"\"\n def __init__(self, t0, t1, dt=None, n_step=None, step=None, **kwargs):\n Struct.__init__(self, t0=t0, t1=t1, dt=dt, n_step=n_step, step=step)\n\n self.n_digit, self.format, self.suffix = get_print_info(self.n_step)\n\n def __iter__(self):\n ts = TimeStepper(0, bzone[0], dt=None, n_step=num)\n for ii, val in ts:\n yield ii, val, nm.array([1.0, 0.0])\n if ii == (num-2): break\n\n ts = TimeStepper(0, bzone[1], dt=None, n_step=num)\n for ii, k1 in ts:\n wdir = nm.array([bzone[0], k1])\n val = nm.linalg.norm(wdir)\n wdir = wdir / val\n yield num + ii, val, wdir\n if ii == (num-2): break\n\n wdir = nm.array([bzone[0], bzone[1]])\n val = nm.linalg.norm(wdir)\n wdir = wdir / val\n ts = TimeStepper(0, 1, dt=None, n_step=num)\n for ii, _ in ts:\n yield 2 * num + ii, val * (1.0 - float(ii)/(num-1)), wdir\n\n stepper = BrillouinStepper(0, 1, n_step=rng[2])\n\n return stepper\n\ndef save_eigenvectors(filename, svecs, wmag, wdir, pb):\n if svecs is None: return\n\n variables = pb.get_variables()\n # Make full eigenvectors (add DOFs fixed by boundary conditions).\n vecs = nm.empty((variables.di.ptr[-1], svecs.shape[1]),\n dtype=svecs.dtype)\n for ii in range(svecs.shape[1]):\n vecs[:, ii] = variables.make_full_vec(svecs[:, ii])\n\n # Save the eigenvectors.\n out = {}\n state = pb.create_state()\n\n pp_name = pb.conf.options.get('post_process_hook')\n pp = getattr(pb.conf.funmod, pp_name if pp_name is not None else '',\n lambda out, *args, **kwargs: out)\n\n for ii in range(svecs.shape[1]):\n state.set_full(vecs[:, ii])\n aux = state.create_output_dict()\n aux2 = {}\n pp(aux2, pb, state, wmag=wmag, wdir=wdir)\n aux.update(convert_complex_output(aux2))\n out.update({key + '%03d' % ii : aux[key] for key in aux})\n\n pb.save_state(filename, out=out)\n\ndef assemble_matrices(define, mod, pars, set_wave_dir, options, wdir=None):\n \"\"\"\n Assemble the blocks of dispersion eigenvalue problem matrices.\n \"\"\"\n define_dict = define(filename_mesh=options.mesh_filename,\n pars=pars,\n approx_order=options.order,\n refinement_level=options.refine,\n solver_conf=options.solver_conf,\n plane=options.plane,\n post_process=options.post_process,\n **options.define_kwargs)\n\n conf = ProblemConf.from_dict(define_dict, mod)\n\n pb = Problem.from_conf(conf)\n pb.dispersion_options = options\n pb.set_output_dir(options.output_dir)\n dim = pb.domain.shape.dim\n\n # Set the normalized wave vector direction to the material(s).\n if wdir is None:\n wdir = nm.asarray(options.wave_dir[:dim], dtype=nm.float64)\n wdir = wdir / nm.linalg.norm(wdir)\n set_wave_dir(pb, wdir)\n\n bbox = pb.domain.mesh.get_bounding_box()\n size = (bbox[1] - bbox[0]).max()\n scaling0 = apply_unit_multipliers([1.0], ['length'],\n options.unit_multipliers)[0]\n scaling = scaling0\n if options.mesh_size is not None:\n scaling *= options.mesh_size / size\n output('scaling factor of periodic cell mesh coordinates:', scaling)\n output('new mesh size with applied unit multipliers:', scaling * size)\n pb.domain.mesh.coors[:] *= scaling\n pb.set_mesh_coors(pb.domain.mesh.coors, update_fields=True)\n\n bzone = 2.0 * nm.pi / (scaling * size)\n output('1. Brillouin zone size:', bzone * scaling0)\n output('1. Brillouin zone size with applied unit multipliers:', bzone)\n\n pb.time_update()\n pb.update_materials()\n\n # Assemble the matrices.\n mtxs = {}\n for key, eq in pb.equations.iteritems():\n mtxs[key] = mtx = pb.mtx_a.copy()\n mtx = eq.evaluate(mode='weak', dw_mode='matrix', asm_obj=mtx)\n mtx.eliminate_zeros()\n output_array_stats(mtx.data, 'nonzeros in %s' % key)\n\n output('symmetry checks:')\n output('%s - %s^T:' % (key, key), "},"completion":{"kind":"string","value":"max_diff_csr(mtx, mtx.T)"},"api":{"kind":"string","value":"sfepy.linalg.utils.max_diff_csr"}}},{"rowIdx":87,"cells":{"prompt":{"kind":"string","value":"#!/usr/bin/env python\n\"\"\"\nDispersion analysis of a heterogeneous finite scale periodic cell.\n\nThe periodic cell mesh has to contain two subdomains Y1 (with the cell ids 1),\nY2 (with the cell ids 2), so that different material properties can be defined\nin each of the subdomains (see ``--pars`` option). The command line parameters\ncan be given in any consistent unit set, for example the basic SI units. The\n``--unit-multipliers`` option can be used to rescale the input units to ones\nmore suitable to the simulation, for example to prevent having different\nmatrix blocks with large differences of matrix entries magnitudes. The results\nare then in the rescaled units.\n\nUsage Examples\n--------------\n\nDefault material parameters, a square periodic cell with a spherical inclusion,\nlogs also standard pressure dilatation and shear waves, no eigenvectors::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only\n\nAs above, with custom eigenvalue solver parameters, and different number of\neigenvalues, mesh size and units used in the calculation::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --solver-conf=\"kind='eig.scipy', method='eigsh', tol=1e-10, maxiter=1000, which='LM', sigma=0\" --log-std-waves -n 5 --range=0,640,101 --mode=omega --unit-multipliers=1e-6,1e-2,1e-3 --mesh-size=1e-2 --eigs-only\n\nDefault material parameters, a square periodic cell with a square inclusion,\nand a very small mesh to allow comparing the omega and kappa modes (full matrix\nsolver required!)::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf=\"kind='eig.scipy', method='eigh'\" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf=\"kind='eig.qevp', method='companion', mode='inverted', solver={kind='eig.scipy', method='eig'}\" --log-std-waves -n 500 --range=0,4000000,1001 --mesh-size=1e-2 --mode=kappa --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/kappa\n\nView/compare the resulting logs::\n\n python script/plot_logs.py output/omega/frequencies.txt --no-legends -g 1 -o mode-omega.png\n python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends -o mode-kappa.png\n python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends --swap-axes -o mode-kappa-t.png\n\nIn contrast to the heterogeneous square periodic cell, a homogeneous\nsquare periodic cell (the region Y2 is empty)::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_1m.mesh --solver-conf=\"kind='eig.scipy', method='eigh'\" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega-h\n\n python script/plot_logs.py output/omega-h/frequencies.txt --no-legends -g 1 -o mode-omega-h.png\n\nUse the Brillouin stepper::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves -n=60 --eigs-only --no-legends --stepper=brillouin\n\n python script/plot_logs.py output/frequencies.txt -g 0 --rc=\"'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4\" -o brillouin-stepper-kappas.png\n\n python script/plot_logs.py output/frequencies.txt -g 1 --no-legends --rc=\"'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4\" -o brillouin-stepper-omegas.png\n\nAdditional arguments can be passed to the problem configuration's\n:func:`define()` function using the ``--define-kwargs`` option. In this file,\nonly the mesh vertex separation parameter `mesh_eps` can be used::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only --define-kwargs=\"mesh_eps=1e-10\" --save-regions\n\"\"\"\nfrom __future__ import absolute_import\nimport os\nimport sys\nsys.path.append('.')\nimport gc\nfrom copy import copy\nfrom argparse import ArgumentParser, RawDescriptionHelpFormatter\n\nimport numpy as nm\nimport matplotlib.pyplot as plt\n\nfrom sfepy.base.base import import_file, output, Struct\nfrom sfepy.base.conf import dict_from_string, ProblemConf\nfrom sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options\nfrom sfepy.base.log import Log\nfrom sfepy.discrete.fem import MeshIO\nfrom sfepy.mechanics.matcoefs import stiffness_from_youngpoisson as stiffness\nimport sfepy.mechanics.matcoefs as mc\nfrom sfepy.mechanics.units import apply_unit_multipliers\nimport sfepy.discrete.fem.periodic as per\nfrom sfepy.discrete.fem.meshio import convert_complex_output\nfrom sfepy.homogenization.utils import define_box_regions\nfrom sfepy.discrete import Problem\nfrom sfepy.mechanics.tensors import get_von_mises_stress\nfrom sfepy.solvers import Solver\nfrom sfepy.solvers.ts import get_print_info, TimeStepper\nfrom sfepy.linalg.utils import output_array_stats, max_diff_csr\n\ndef apply_units(pars, unit_multipliers):\n new_pars = apply_unit_multipliers(pars,\n ['stress', 'one', 'density',\n 'stress', 'one' ,'density'],\n unit_multipliers)\n return new_pars\n\ndef compute_von_mises(out, pb, state, extend=False, wmag=None, wdir=None):\n \"\"\"\n Calculate the von Mises stress.\n \"\"\"\n stress = pb.evaluate('ev_cauchy_stress.i.Omega(m.D, u)', mode='el_avg')\n\n vms = get_von_mises_stress(stress.squeeze())\n vms.shape = (vms.shape[0], 1, 1, 1)\n out['von_mises_stress'] = Struct(name='output_data', mode='cell',\n data=vms)\n\n return out\n\ndef define(filename_mesh, pars, approx_order, refinement_level, solver_conf,\n plane='strain', post_process=False, mesh_eps=1e-8):\n io = MeshIO.any_from_filename(filename_mesh)\n bbox = io.read_bounding_box()\n dim = bbox.shape[1]\n\n options = {\n 'absolute_mesh_path' : True,\n 'refinement_level' : refinement_level,\n 'allow_empty_regions' : True,\n 'post_process_hook' : 'compute_von_mises' if post_process else None,\n }\n\n fields = {\n 'displacement': ('complex', dim, 'Omega', approx_order),\n }\n\n young1, poisson1, density1, young2, poisson2, density2 = pars\n materials = {\n 'm' : ({\n 'D' : {'Y1' : stiffness(dim, young=young1, poisson=poisson1,\n plane=plane),\n 'Y2' : stiffness(dim, young=young2, poisson=poisson2,\n plane=plane)},\n 'density' : {'Y1' : density1, 'Y2' : density2},\n },),\n 'wave' : 'get_wdir',\n }\n\n variables = {\n 'u' : ('unknown field', 'displacement', 0),\n 'v' : ('test field', 'displacement', 'u'),\n }\n\n regions = {\n 'Omega' : 'all',\n 'Y1': 'cells of group 1',\n 'Y2': 'cells of group 2',\n }\n regions.update(define_box_regions(dim,\n bbox[0], bbox[1], mesh_eps))\n\n ebcs = {\n }\n\n if dim == 3:\n epbcs = {\n 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},\n 'match_x_plane'),\n 'periodic_y' : (['Near', 'Far'], {'u.all' : 'u.all'},\n 'match_y_plane'),\n 'periodic_z' : (['Top', 'Bottom'], {'u.all' : 'u.all'},\n 'match_z_plane'),\n }\n else:\n epbcs = {\n 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},\n 'match_y_line'),\n 'periodic_y' : (['Bottom', 'Top'], {'u.all' : 'u.all'},\n 'match_x_line'),\n }\n\n per.set_accuracy(mesh_eps)\n functions = {\n 'match_x_plane' : (per.match_x_plane,),\n 'match_y_plane' : (per.match_y_plane,),\n 'match_z_plane' : (per.match_z_plane,),\n 'match_x_line' : (per.match_x_line,),\n 'match_y_line' : (per.match_y_line,),\n 'get_wdir' : (get_wdir,),\n }\n\n integrals = {\n 'i' : 2 * approx_order,\n }\n\n equations = {\n 'K' : 'dw_lin_elastic.i.Omega(m.D, v, u)',\n 'S' : 'dw_elastic_wave.i.Omega(m.D, wave.vec, v, u)',\n 'R' : \"\"\"1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, u, v)\n - 1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, v, u)\"\"\",\n 'M' : 'dw_volume_dot.i.Omega(m.density, v, u)',\n }\n\n solver_0 = solver_conf.copy()\n solver_0['name'] = 'eig'\n\n return locals()\n\ndef get_wdir(ts, coors, mode=None,\n equations=None, term=None, problem=None, wdir=None, **kwargs):\n if mode == 'special':\n return {'vec' : wdir}\n\ndef set_wave_dir(pb, wdir):\n materials = pb.get_materials()\n wave_mat = materials['wave']\n wave_mat.set_extra_args(wdir=wdir)\n\ndef save_materials(output_dir, pb, options):\n stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n young, poisson = mc.youngpoisson_from_stiffness(stiffness,\n plane=options.plane)\n density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n\n out = {}\n out['young'] = Struct(name='young', mode='cell',\n data=young[..., None, None])\n out['poisson'] = Struct(name='poisson', mode='cell',\n data=poisson[..., None, None])\n out['density'] = Struct(name='density', mode='cell', data=density)\n materials_filename = os.path.join(output_dir, 'materials.vtk')\n pb.save_state(materials_filename, out=out)\n\ndef get_std_wave_fun(pb, options):\n stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n young, poisson = mc.youngpoisson_from_stiffness(stiffness,\n plane=options.plane)\n density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n\n lam, mu = mc.lame_from_youngpoisson(young, poisson,\n plane=options.plane)\n alam = nm.average(lam)\n amu = nm.average(mu)\n adensity = nm.average(density)\n\n cp = nm.sqrt((alam + 2.0 * amu) / adensity)\n cs = nm.sqrt(amu / adensity)\n output('average p-wave speed:', cp)\n output('average shear wave speed:', cs)\n\n log_names = [r'$\\omega_p$', r'$\\omega_s$']\n log_plot_kwargs = [{'ls' : '--', 'color' : 'k'},\n {'ls' : '--', 'color' : 'gray'}]\n\n if options.mode == 'omega':\n fun = lambda wmag, wdir: (cp * wmag, cs * wmag)\n\n else:\n fun = lambda wmag, wdir: (wmag / cp, wmag / cs)\n\n return fun, log_names, log_plot_kwargs\n\ndef get_stepper(rng, pb, options):\n if options.stepper == 'linear':\n stepper = TimeStepper(rng[0], rng[1], dt=None, n_step=rng[2])\n return stepper\n\n bbox = pb.domain.mesh.get_bounding_box()\n\n bzone = 2.0 * nm.pi / (bbox[1] - bbox[0])\n\n num = rng[2] // 3\n\n class BrillouinStepper(Struct):\n \"\"\"\n Step over 1. Brillouin zone in xy plane.\n \"\"\"\n def __init__(self, t0, t1, dt=None, n_step=None, step=None, **kwargs):\n Struct.__init__(self, t0=t0, t1=t1, dt=dt, n_step=n_step, step=step)\n\n self.n_digit, self.format, self.suffix = get_print_info(self.n_step)\n\n def __iter__(self):\n ts = TimeStepper(0, bzone[0], dt=None, n_step=num)\n for ii, val in ts:\n yield ii, val, nm.array([1.0, 0.0])\n if ii == (num-2): break\n\n ts = TimeStepper(0, bzone[1], dt=None, n_step=num)\n for ii, k1 in ts:\n wdir = nm.array([bzone[0], k1])\n val = nm.linalg.norm(wdir)\n wdir = wdir / val\n yield num + ii, val, wdir\n if ii == (num-2): break\n\n wdir = nm.array([bzone[0], bzone[1]])\n val = nm.linalg.norm(wdir)\n wdir = wdir / val\n ts = TimeStepper(0, 1, dt=None, n_step=num)\n for ii, _ in ts:\n yield 2 * num + ii, val * (1.0 - float(ii)/(num-1)), wdir\n\n stepper = BrillouinStepper(0, 1, n_step=rng[2])\n\n return stepper\n\ndef save_eigenvectors(filename, svecs, wmag, wdir, pb):\n if svecs is None: return\n\n variables = pb.get_variables()\n # Make full eigenvectors (add DOFs fixed by boundary conditions).\n vecs = nm.empty((variables.di.ptr[-1], svecs.shape[1]),\n dtype=svecs.dtype)\n for ii in range(svecs.shape[1]):\n vecs[:, ii] = variables.make_full_vec(svecs[:, ii])\n\n # Save the eigenvectors.\n out = {}\n state = pb.create_state()\n\n pp_name = pb.conf.options.get('post_process_hook')\n pp = getattr(pb.conf.funmod, pp_name if pp_name is not None else '',\n lambda out, *args, **kwargs: out)\n\n for ii in range(svecs.shape[1]):\n state.set_full(vecs[:, ii])\n aux = state.create_output_dict()\n aux2 = {}\n pp(aux2, pb, state, wmag=wmag, wdir=wdir)\n aux.update(convert_complex_output(aux2))\n out.update({key + '%03d' % ii : aux[key] for key in aux})\n\n pb.save_state(filename, out=out)\n\ndef assemble_matrices(define, mod, pars, set_wave_dir, options, wdir=None):\n \"\"\"\n Assemble the blocks of dispersion eigenvalue problem matrices.\n \"\"\"\n define_dict = define(filename_mesh=options.mesh_filename,\n pars=pars,\n approx_order=options.order,\n refinement_level=options.refine,\n solver_conf=options.solver_conf,\n plane=options.plane,\n post_process=options.post_process,\n **options.define_kwargs)\n\n conf = ProblemConf.from_dict(define_dict, mod)\n\n pb = Problem.from_conf(conf)\n pb.dispersion_options = options\n pb.set_output_dir(options.output_dir)\n dim = pb.domain.shape.dim\n\n # Set the normalized wave vector direction to the material(s).\n if wdir is None:\n wdir = nm.asarray(options.wave_dir[:dim], dtype=nm.float64)\n wdir = wdir / nm.linalg.norm(wdir)\n set_wave_dir(pb, wdir)\n\n bbox = pb.domain.mesh.get_bounding_box()\n size = (bbox[1] - bbox[0]).max()\n scaling0 = apply_unit_multipliers([1.0], ['length'],\n options.unit_multipliers)[0]\n scaling = scaling0\n if options.mesh_size is not None:\n scaling *= options.mesh_size / size\n output('scaling factor of periodic cell mesh coordinates:', scaling)\n output('new mesh size with applied unit multipliers:', scaling * size)\n pb.domain.mesh.coors[:] *= scaling\n pb.set_mesh_coors(pb.domain.mesh.coors, update_fields=True)\n\n bzone = 2.0 * nm.pi / (scaling * size)\n output('1. Brillouin zone size:', bzone * scaling0)\n output('1. Brillouin zone size with applied unit multipliers:', bzone)\n\n pb.time_update()\n pb.update_materials()\n\n # Assemble the matrices.\n mtxs = {}\n for key, eq in pb.equations.iteritems():\n mtxs[key] = mtx = pb.mtx_a.copy()\n mtx = eq.evaluate(mode='weak', dw_mode='matrix', asm_obj=mtx)\n mtx.eliminate_zeros()\n output_array_stats(mtx.data, 'nonzeros in %s' % key)\n\n output('symmetry checks:')\n output('%s - %s^T:' % (key, key), max_diff_csr(mtx, mtx.T))\n output('%s - %s^H:' % (key, key), "},"completion":{"kind":"string","value":"max_diff_csr(mtx, mtx.H)"},"api":{"kind":"string","value":"sfepy.linalg.utils.max_diff_csr"}}},{"rowIdx":88,"cells":{"prompt":{"kind":"string","value":"#!/usr/bin/env python\n\"\"\"\nDispersion analysis of a heterogeneous finite scale periodic cell.\n\nThe periodic cell mesh has to contain two subdomains Y1 (with the cell ids 1),\nY2 (with the cell ids 2), so that different material properties can be defined\nin each of the subdomains (see ``--pars`` option). The command line parameters\ncan be given in any consistent unit set, for example the basic SI units. The\n``--unit-multipliers`` option can be used to rescale the input units to ones\nmore suitable to the simulation, for example to prevent having different\nmatrix blocks with large differences of matrix entries magnitudes. The results\nare then in the rescaled units.\n\nUsage Examples\n--------------\n\nDefault material parameters, a square periodic cell with a spherical inclusion,\nlogs also standard pressure dilatation and shear waves, no eigenvectors::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only\n\nAs above, with custom eigenvalue solver parameters, and different number of\neigenvalues, mesh size and units used in the calculation::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --solver-conf=\"kind='eig.scipy', method='eigsh', tol=1e-10, maxiter=1000, which='LM', sigma=0\" --log-std-waves -n 5 --range=0,640,101 --mode=omega --unit-multipliers=1e-6,1e-2,1e-3 --mesh-size=1e-2 --eigs-only\n\nDefault material parameters, a square periodic cell with a square inclusion,\nand a very small mesh to allow comparing the omega and kappa modes (full matrix\nsolver required!)::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf=\"kind='eig.scipy', method='eigh'\" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf=\"kind='eig.qevp', method='companion', mode='inverted', solver={kind='eig.scipy', method='eig'}\" --log-std-waves -n 500 --range=0,4000000,1001 --mesh-size=1e-2 --mode=kappa --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/kappa\n\nView/compare the resulting logs::\n\n python script/plot_logs.py output/omega/frequencies.txt --no-legends -g 1 -o mode-omega.png\n python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends -o mode-kappa.png\n python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends --swap-axes -o mode-kappa-t.png\n\nIn contrast to the heterogeneous square periodic cell, a homogeneous\nsquare periodic cell (the region Y2 is empty)::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_1m.mesh --solver-conf=\"kind='eig.scipy', method='eigh'\" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega-h\n\n python script/plot_logs.py output/omega-h/frequencies.txt --no-legends -g 1 -o mode-omega-h.png\n\nUse the Brillouin stepper::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves -n=60 --eigs-only --no-legends --stepper=brillouin\n\n python script/plot_logs.py output/frequencies.txt -g 0 --rc=\"'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4\" -o brillouin-stepper-kappas.png\n\n python script/plot_logs.py output/frequencies.txt -g 1 --no-legends --rc=\"'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4\" -o brillouin-stepper-omegas.png\n\nAdditional arguments can be passed to the problem configuration's\n:func:`define()` function using the ``--define-kwargs`` option. In this file,\nonly the mesh vertex separation parameter `mesh_eps` can be used::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only --define-kwargs=\"mesh_eps=1e-10\" --save-regions\n\"\"\"\nfrom __future__ import absolute_import\nimport os\nimport sys\nsys.path.append('.')\nimport gc\nfrom copy import copy\nfrom argparse import ArgumentParser, RawDescriptionHelpFormatter\n\nimport numpy as nm\nimport matplotlib.pyplot as plt\n\nfrom sfepy.base.base import import_file, output, Struct\nfrom sfepy.base.conf import dict_from_string, ProblemConf\nfrom sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options\nfrom sfepy.base.log import Log\nfrom sfepy.discrete.fem import MeshIO\nfrom sfepy.mechanics.matcoefs import stiffness_from_youngpoisson as stiffness\nimport sfepy.mechanics.matcoefs as mc\nfrom sfepy.mechanics.units import apply_unit_multipliers\nimport sfepy.discrete.fem.periodic as per\nfrom sfepy.discrete.fem.meshio import convert_complex_output\nfrom sfepy.homogenization.utils import define_box_regions\nfrom sfepy.discrete import Problem\nfrom sfepy.mechanics.tensors import get_von_mises_stress\nfrom sfepy.solvers import Solver\nfrom sfepy.solvers.ts import get_print_info, TimeStepper\nfrom sfepy.linalg.utils import output_array_stats, max_diff_csr\n\ndef apply_units(pars, unit_multipliers):\n new_pars = apply_unit_multipliers(pars,\n ['stress', 'one', 'density',\n 'stress', 'one' ,'density'],\n unit_multipliers)\n return new_pars\n\ndef compute_von_mises(out, pb, state, extend=False, wmag=None, wdir=None):\n \"\"\"\n Calculate the von Mises stress.\n \"\"\"\n stress = pb.evaluate('ev_cauchy_stress.i.Omega(m.D, u)', mode='el_avg')\n\n vms = get_von_mises_stress(stress.squeeze())\n vms.shape = (vms.shape[0], 1, 1, 1)\n out['von_mises_stress'] = Struct(name='output_data', mode='cell',\n data=vms)\n\n return out\n\ndef define(filename_mesh, pars, approx_order, refinement_level, solver_conf,\n plane='strain', post_process=False, mesh_eps=1e-8):\n io = MeshIO.any_from_filename(filename_mesh)\n bbox = io.read_bounding_box()\n dim = bbox.shape[1]\n\n options = {\n 'absolute_mesh_path' : True,\n 'refinement_level' : refinement_level,\n 'allow_empty_regions' : True,\n 'post_process_hook' : 'compute_von_mises' if post_process else None,\n }\n\n fields = {\n 'displacement': ('complex', dim, 'Omega', approx_order),\n }\n\n young1, poisson1, density1, young2, poisson2, density2 = pars\n materials = {\n 'm' : ({\n 'D' : {'Y1' : stiffness(dim, young=young1, poisson=poisson1,\n plane=plane),\n 'Y2' : stiffness(dim, young=young2, poisson=poisson2,\n plane=plane)},\n 'density' : {'Y1' : density1, 'Y2' : density2},\n },),\n 'wave' : 'get_wdir',\n }\n\n variables = {\n 'u' : ('unknown field', 'displacement', 0),\n 'v' : ('test field', 'displacement', 'u'),\n }\n\n regions = {\n 'Omega' : 'all',\n 'Y1': 'cells of group 1',\n 'Y2': 'cells of group 2',\n }\n regions.update(define_box_regions(dim,\n bbox[0], bbox[1], mesh_eps))\n\n ebcs = {\n }\n\n if dim == 3:\n epbcs = {\n 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},\n 'match_x_plane'),\n 'periodic_y' : (['Near', 'Far'], {'u.all' : 'u.all'},\n 'match_y_plane'),\n 'periodic_z' : (['Top', 'Bottom'], {'u.all' : 'u.all'},\n 'match_z_plane'),\n }\n else:\n epbcs = {\n 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},\n 'match_y_line'),\n 'periodic_y' : (['Bottom', 'Top'], {'u.all' : 'u.all'},\n 'match_x_line'),\n }\n\n per.set_accuracy(mesh_eps)\n functions = {\n 'match_x_plane' : (per.match_x_plane,),\n 'match_y_plane' : (per.match_y_plane,),\n 'match_z_plane' : (per.match_z_plane,),\n 'match_x_line' : (per.match_x_line,),\n 'match_y_line' : (per.match_y_line,),\n 'get_wdir' : (get_wdir,),\n }\n\n integrals = {\n 'i' : 2 * approx_order,\n }\n\n equations = {\n 'K' : 'dw_lin_elastic.i.Omega(m.D, v, u)',\n 'S' : 'dw_elastic_wave.i.Omega(m.D, wave.vec, v, u)',\n 'R' : \"\"\"1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, u, v)\n - 1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, v, u)\"\"\",\n 'M' : 'dw_volume_dot.i.Omega(m.density, v, u)',\n }\n\n solver_0 = solver_conf.copy()\n solver_0['name'] = 'eig'\n\n return locals()\n\ndef get_wdir(ts, coors, mode=None,\n equations=None, term=None, problem=None, wdir=None, **kwargs):\n if mode == 'special':\n return {'vec' : wdir}\n\ndef set_wave_dir(pb, wdir):\n materials = pb.get_materials()\n wave_mat = materials['wave']\n wave_mat.set_extra_args(wdir=wdir)\n\ndef save_materials(output_dir, pb, options):\n stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n young, poisson = mc.youngpoisson_from_stiffness(stiffness,\n plane=options.plane)\n density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n\n out = {}\n out['young'] = Struct(name='young', mode='cell',\n data=young[..., None, None])\n out['poisson'] = Struct(name='poisson', mode='cell',\n data=poisson[..., None, None])\n out['density'] = Struct(name='density', mode='cell', data=density)\n materials_filename = os.path.join(output_dir, 'materials.vtk')\n pb.save_state(materials_filename, out=out)\n\ndef get_std_wave_fun(pb, options):\n stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n young, poisson = mc.youngpoisson_from_stiffness(stiffness,\n plane=options.plane)\n density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n\n lam, mu = mc.lame_from_youngpoisson(young, poisson,\n plane=options.plane)\n alam = nm.average(lam)\n amu = nm.average(mu)\n adensity = nm.average(density)\n\n cp = nm.sqrt((alam + 2.0 * amu) / adensity)\n cs = nm.sqrt(amu / adensity)\n output('average p-wave speed:', cp)\n output('average shear wave speed:', cs)\n\n log_names = [r'$\\omega_p$', r'$\\omega_s$']\n log_plot_kwargs = [{'ls' : '--', 'color' : 'k'},\n {'ls' : '--', 'color' : 'gray'}]\n\n if options.mode == 'omega':\n fun = lambda wmag, wdir: (cp * wmag, cs * wmag)\n\n else:\n fun = lambda wmag, wdir: (wmag / cp, wmag / cs)\n\n return fun, log_names, log_plot_kwargs\n\ndef get_stepper(rng, pb, options):\n if options.stepper == 'linear':\n stepper = TimeStepper(rng[0], rng[1], dt=None, n_step=rng[2])\n return stepper\n\n bbox = pb.domain.mesh.get_bounding_box()\n\n bzone = 2.0 * nm.pi / (bbox[1] - bbox[0])\n\n num = rng[2] // 3\n\n class BrillouinStepper(Struct):\n \"\"\"\n Step over 1. Brillouin zone in xy plane.\n \"\"\"\n def __init__(self, t0, t1, dt=None, n_step=None, step=None, **kwargs):\n Struct.__init__(self, t0=t0, t1=t1, dt=dt, n_step=n_step, step=step)\n\n self.n_digit, self.format, self.suffix = get_print_info(self.n_step)\n\n def __iter__(self):\n ts = TimeStepper(0, bzone[0], dt=None, n_step=num)\n for ii, val in ts:\n yield ii, val, nm.array([1.0, 0.0])\n if ii == (num-2): break\n\n ts = TimeStepper(0, bzone[1], dt=None, n_step=num)\n for ii, k1 in ts:\n wdir = nm.array([bzone[0], k1])\n val = nm.linalg.norm(wdir)\n wdir = wdir / val\n yield num + ii, val, wdir\n if ii == (num-2): break\n\n wdir = nm.array([bzone[0], bzone[1]])\n val = nm.linalg.norm(wdir)\n wdir = wdir / val\n ts = TimeStepper(0, 1, dt=None, n_step=num)\n for ii, _ in ts:\n yield 2 * num + ii, val * (1.0 - float(ii)/(num-1)), wdir\n\n stepper = BrillouinStepper(0, 1, n_step=rng[2])\n\n return stepper\n\ndef save_eigenvectors(filename, svecs, wmag, wdir, pb):\n if svecs is None: return\n\n variables = pb.get_variables()\n # Make full eigenvectors (add DOFs fixed by boundary conditions).\n vecs = nm.empty((variables.di.ptr[-1], svecs.shape[1]),\n dtype=svecs.dtype)\n for ii in range(svecs.shape[1]):\n vecs[:, ii] = variables.make_full_vec(svecs[:, ii])\n\n # Save the eigenvectors.\n out = {}\n state = pb.create_state()\n\n pp_name = pb.conf.options.get('post_process_hook')\n pp = getattr(pb.conf.funmod, pp_name if pp_name is not None else '',\n lambda out, *args, **kwargs: out)\n\n for ii in range(svecs.shape[1]):\n state.set_full(vecs[:, ii])\n aux = state.create_output_dict()\n aux2 = {}\n pp(aux2, pb, state, wmag=wmag, wdir=wdir)\n aux.update(convert_complex_output(aux2))\n out.update({key + '%03d' % ii : aux[key] for key in aux})\n\n pb.save_state(filename, out=out)\n\ndef assemble_matrices(define, mod, pars, set_wave_dir, options, wdir=None):\n \"\"\"\n Assemble the blocks of dispersion eigenvalue problem matrices.\n \"\"\"\n define_dict = define(filename_mesh=options.mesh_filename,\n pars=pars,\n approx_order=options.order,\n refinement_level=options.refine,\n solver_conf=options.solver_conf,\n plane=options.plane,\n post_process=options.post_process,\n **options.define_kwargs)\n\n conf = ProblemConf.from_dict(define_dict, mod)\n\n pb = Problem.from_conf(conf)\n pb.dispersion_options = options\n pb.set_output_dir(options.output_dir)\n dim = pb.domain.shape.dim\n\n # Set the normalized wave vector direction to the material(s).\n if wdir is None:\n wdir = nm.asarray(options.wave_dir[:dim], dtype=nm.float64)\n wdir = wdir / nm.linalg.norm(wdir)\n set_wave_dir(pb, wdir)\n\n bbox = pb.domain.mesh.get_bounding_box()\n size = (bbox[1] - bbox[0]).max()\n scaling0 = apply_unit_multipliers([1.0], ['length'],\n options.unit_multipliers)[0]\n scaling = scaling0\n if options.mesh_size is not None:\n scaling *= options.mesh_size / size\n output('scaling factor of periodic cell mesh coordinates:', scaling)\n output('new mesh size with applied unit multipliers:', scaling * size)\n pb.domain.mesh.coors[:] *= scaling\n pb.set_mesh_coors(pb.domain.mesh.coors, update_fields=True)\n\n bzone = 2.0 * nm.pi / (scaling * size)\n output('1. Brillouin zone size:', bzone * scaling0)\n output('1. Brillouin zone size with applied unit multipliers:', bzone)\n\n pb.time_update()\n pb.update_materials()\n\n # Assemble the matrices.\n mtxs = {}\n for key, eq in pb.equations.iteritems():\n mtxs[key] = mtx = pb.mtx_a.copy()\n mtx = eq.evaluate(mode='weak', dw_mode='matrix', asm_obj=mtx)\n mtx.eliminate_zeros()\n output_array_stats(mtx.data, 'nonzeros in %s' % key)\n\n output('symmetry checks:')\n output('%s - %s^T:' % (key, key), max_diff_csr(mtx, mtx.T))\n output('%s - %s^H:' % (key, key), max_diff_csr(mtx, mtx.H))\n\n return pb, wdir, bzone, mtxs\n\ndef setup_n_eigs(options, pb, mtxs):\n \"\"\"\n Setup the numbers of eigenvalues based on options and numbers of DOFs.\n \"\"\"\n solver_n_eigs = n_eigs = options.n_eigs\n n_dof = mtxs['K'].shape[0]\n if options.mode == 'omega':\n if options.n_eigs > n_dof:\n n_eigs = n_dof\n solver_n_eigs = None\n\n else:\n if options.n_eigs > 2 * n_dof:\n n_eigs = 2 * n_dof\n solver_n_eigs = None\n\n return solver_n_eigs, n_eigs\n\ndef build_evp_matrices(mtxs, val, mode, pb):\n \"\"\"\n Build the matrices of the dispersion eigenvalue problem.\n \"\"\"\n if mode == 'omega':\n mtx_a = mtxs['K'] + val**2 * mtxs['S'] + val * mtxs['R']\n output('A - A^H:', "},"completion":{"kind":"string","value":"max_diff_csr(mtx_a, mtx_a.H)"},"api":{"kind":"string","value":"sfepy.linalg.utils.max_diff_csr"}}},{"rowIdx":89,"cells":{"prompt":{"kind":"string","value":"#!/usr/bin/env python\n\"\"\"\nDispersion analysis of a heterogeneous finite scale periodic cell.\n\nThe periodic cell mesh has to contain two subdomains Y1 (with the cell ids 1),\nY2 (with the cell ids 2), so that different material properties can be defined\nin each of the subdomains (see ``--pars`` option). The command line parameters\ncan be given in any consistent unit set, for example the basic SI units. The\n``--unit-multipliers`` option can be used to rescale the input units to ones\nmore suitable to the simulation, for example to prevent having different\nmatrix blocks with large differences of matrix entries magnitudes. The results\nare then in the rescaled units.\n\nUsage Examples\n--------------\n\nDefault material parameters, a square periodic cell with a spherical inclusion,\nlogs also standard pressure dilatation and shear waves, no eigenvectors::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only\n\nAs above, with custom eigenvalue solver parameters, and different number of\neigenvalues, mesh size and units used in the calculation::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --solver-conf=\"kind='eig.scipy', method='eigsh', tol=1e-10, maxiter=1000, which='LM', sigma=0\" --log-std-waves -n 5 --range=0,640,101 --mode=omega --unit-multipliers=1e-6,1e-2,1e-3 --mesh-size=1e-2 --eigs-only\n\nDefault material parameters, a square periodic cell with a square inclusion,\nand a very small mesh to allow comparing the omega and kappa modes (full matrix\nsolver required!)::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf=\"kind='eig.scipy', method='eigh'\" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf=\"kind='eig.qevp', method='companion', mode='inverted', solver={kind='eig.scipy', method='eig'}\" --log-std-waves -n 500 --range=0,4000000,1001 --mesh-size=1e-2 --mode=kappa --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/kappa\n\nView/compare the resulting logs::\n\n python script/plot_logs.py output/omega/frequencies.txt --no-legends -g 1 -o mode-omega.png\n python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends -o mode-kappa.png\n python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends --swap-axes -o mode-kappa-t.png\n\nIn contrast to the heterogeneous square periodic cell, a homogeneous\nsquare periodic cell (the region Y2 is empty)::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_1m.mesh --solver-conf=\"kind='eig.scipy', method='eigh'\" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega-h\n\n python script/plot_logs.py output/omega-h/frequencies.txt --no-legends -g 1 -o mode-omega-h.png\n\nUse the Brillouin stepper::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves -n=60 --eigs-only --no-legends --stepper=brillouin\n\n python script/plot_logs.py output/frequencies.txt -g 0 --rc=\"'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4\" -o brillouin-stepper-kappas.png\n\n python script/plot_logs.py output/frequencies.txt -g 1 --no-legends --rc=\"'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4\" -o brillouin-stepper-omegas.png\n\nAdditional arguments can be passed to the problem configuration's\n:func:`define()` function using the ``--define-kwargs`` option. In this file,\nonly the mesh vertex separation parameter `mesh_eps` can be used::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only --define-kwargs=\"mesh_eps=1e-10\" --save-regions\n\"\"\"\nfrom __future__ import absolute_import\nimport os\nimport sys\nsys.path.append('.')\nimport gc\nfrom copy import copy\nfrom argparse import ArgumentParser, RawDescriptionHelpFormatter\n\nimport numpy as nm\nimport matplotlib.pyplot as plt\n\nfrom sfepy.base.base import import_file, output, Struct\nfrom sfepy.base.conf import dict_from_string, ProblemConf\nfrom sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options\nfrom sfepy.base.log import Log\nfrom sfepy.discrete.fem import MeshIO\nfrom sfepy.mechanics.matcoefs import stiffness_from_youngpoisson as stiffness\nimport sfepy.mechanics.matcoefs as mc\nfrom sfepy.mechanics.units import apply_unit_multipliers\nimport sfepy.discrete.fem.periodic as per\nfrom sfepy.discrete.fem.meshio import convert_complex_output\nfrom sfepy.homogenization.utils import define_box_regions\nfrom sfepy.discrete import Problem\nfrom sfepy.mechanics.tensors import get_von_mises_stress\nfrom sfepy.solvers import Solver\nfrom sfepy.solvers.ts import get_print_info, TimeStepper\nfrom sfepy.linalg.utils import output_array_stats, max_diff_csr\n\ndef apply_units(pars, unit_multipliers):\n new_pars = apply_unit_multipliers(pars,\n ['stress', 'one', 'density',\n 'stress', 'one' ,'density'],\n unit_multipliers)\n return new_pars\n\ndef compute_von_mises(out, pb, state, extend=False, wmag=None, wdir=None):\n \"\"\"\n Calculate the von Mises stress.\n \"\"\"\n stress = pb.evaluate('ev_cauchy_stress.i.Omega(m.D, u)', mode='el_avg')\n\n vms = get_von_mises_stress(stress.squeeze())\n vms.shape = (vms.shape[0], 1, 1, 1)\n out['von_mises_stress'] = Struct(name='output_data', mode='cell',\n data=vms)\n\n return out\n\ndef define(filename_mesh, pars, approx_order, refinement_level, solver_conf,\n plane='strain', post_process=False, mesh_eps=1e-8):\n io = MeshIO.any_from_filename(filename_mesh)\n bbox = io.read_bounding_box()\n dim = bbox.shape[1]\n\n options = {\n 'absolute_mesh_path' : True,\n 'refinement_level' : refinement_level,\n 'allow_empty_regions' : True,\n 'post_process_hook' : 'compute_von_mises' if post_process else None,\n }\n\n fields = {\n 'displacement': ('complex', dim, 'Omega', approx_order),\n }\n\n young1, poisson1, density1, young2, poisson2, density2 = pars\n materials = {\n 'm' : ({\n 'D' : {'Y1' : stiffness(dim, young=young1, poisson=poisson1,\n plane=plane),\n 'Y2' : stiffness(dim, young=young2, poisson=poisson2,\n plane=plane)},\n 'density' : {'Y1' : density1, 'Y2' : density2},\n },),\n 'wave' : 'get_wdir',\n }\n\n variables = {\n 'u' : ('unknown field', 'displacement', 0),\n 'v' : ('test field', 'displacement', 'u'),\n }\n\n regions = {\n 'Omega' : 'all',\n 'Y1': 'cells of group 1',\n 'Y2': 'cells of group 2',\n }\n regions.update(define_box_regions(dim,\n bbox[0], bbox[1], mesh_eps))\n\n ebcs = {\n }\n\n if dim == 3:\n epbcs = {\n 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},\n 'match_x_plane'),\n 'periodic_y' : (['Near', 'Far'], {'u.all' : 'u.all'},\n 'match_y_plane'),\n 'periodic_z' : (['Top', 'Bottom'], {'u.all' : 'u.all'},\n 'match_z_plane'),\n }\n else:\n epbcs = {\n 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},\n 'match_y_line'),\n 'periodic_y' : (['Bottom', 'Top'], {'u.all' : 'u.all'},\n 'match_x_line'),\n }\n\n per.set_accuracy(mesh_eps)\n functions = {\n 'match_x_plane' : (per.match_x_plane,),\n 'match_y_plane' : (per.match_y_plane,),\n 'match_z_plane' : (per.match_z_plane,),\n 'match_x_line' : (per.match_x_line,),\n 'match_y_line' : (per.match_y_line,),\n 'get_wdir' : (get_wdir,),\n }\n\n integrals = {\n 'i' : 2 * approx_order,\n }\n\n equations = {\n 'K' : 'dw_lin_elastic.i.Omega(m.D, v, u)',\n 'S' : 'dw_elastic_wave.i.Omega(m.D, wave.vec, v, u)',\n 'R' : \"\"\"1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, u, v)\n - 1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, v, u)\"\"\",\n 'M' : 'dw_volume_dot.i.Omega(m.density, v, u)',\n }\n\n solver_0 = solver_conf.copy()\n solver_0['name'] = 'eig'\n\n return locals()\n\ndef get_wdir(ts, coors, mode=None,\n equations=None, term=None, problem=None, wdir=None, **kwargs):\n if mode == 'special':\n return {'vec' : wdir}\n\ndef set_wave_dir(pb, wdir):\n materials = pb.get_materials()\n wave_mat = materials['wave']\n wave_mat.set_extra_args(wdir=wdir)\n\ndef save_materials(output_dir, pb, options):\n stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n young, poisson = mc.youngpoisson_from_stiffness(stiffness,\n plane=options.plane)\n density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n\n out = {}\n out['young'] = Struct(name='young', mode='cell',\n data=young[..., None, None])\n out['poisson'] = Struct(name='poisson', mode='cell',\n data=poisson[..., None, None])\n out['density'] = Struct(name='density', mode='cell', data=density)\n materials_filename = os.path.join(output_dir, 'materials.vtk')\n pb.save_state(materials_filename, out=out)\n\ndef get_std_wave_fun(pb, options):\n stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n young, poisson = mc.youngpoisson_from_stiffness(stiffness,\n plane=options.plane)\n density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n\n lam, mu = mc.lame_from_youngpoisson(young, poisson,\n plane=options.plane)\n alam = nm.average(lam)\n amu = nm.average(mu)\n adensity = nm.average(density)\n\n cp = nm.sqrt((alam + 2.0 * amu) / adensity)\n cs = nm.sqrt(amu / adensity)\n output('average p-wave speed:', cp)\n output('average shear wave speed:', cs)\n\n log_names = [r'$\\omega_p$', r'$\\omega_s$']\n log_plot_kwargs = [{'ls' : '--', 'color' : 'k'},\n {'ls' : '--', 'color' : 'gray'}]\n\n if options.mode == 'omega':\n fun = lambda wmag, wdir: (cp * wmag, cs * wmag)\n\n else:\n fun = lambda wmag, wdir: (wmag / cp, wmag / cs)\n\n return fun, log_names, log_plot_kwargs\n\ndef get_stepper(rng, pb, options):\n if options.stepper == 'linear':\n stepper = TimeStepper(rng[0], rng[1], dt=None, n_step=rng[2])\n return stepper\n\n bbox = pb.domain.mesh.get_bounding_box()\n\n bzone = 2.0 * nm.pi / (bbox[1] - bbox[0])\n\n num = rng[2] // 3\n\n class BrillouinStepper(Struct):\n \"\"\"\n Step over 1. Brillouin zone in xy plane.\n \"\"\"\n def __init__(self, t0, t1, dt=None, n_step=None, step=None, **kwargs):\n Struct.__init__(self, t0=t0, t1=t1, dt=dt, n_step=n_step, step=step)\n\n self.n_digit, self.format, self.suffix = get_print_info(self.n_step)\n\n def __iter__(self):\n ts = TimeStepper(0, bzone[0], dt=None, n_step=num)\n for ii, val in ts:\n yield ii, val, nm.array([1.0, 0.0])\n if ii == (num-2): break\n\n ts = TimeStepper(0, bzone[1], dt=None, n_step=num)\n for ii, k1 in ts:\n wdir = nm.array([bzone[0], k1])\n val = nm.linalg.norm(wdir)\n wdir = wdir / val\n yield num + ii, val, wdir\n if ii == (num-2): break\n\n wdir = nm.array([bzone[0], bzone[1]])\n val = nm.linalg.norm(wdir)\n wdir = wdir / val\n ts = TimeStepper(0, 1, dt=None, n_step=num)\n for ii, _ in ts:\n yield 2 * num + ii, val * (1.0 - float(ii)/(num-1)), wdir\n\n stepper = BrillouinStepper(0, 1, n_step=rng[2])\n\n return stepper\n\ndef save_eigenvectors(filename, svecs, wmag, wdir, pb):\n if svecs is None: return\n\n variables = pb.get_variables()\n # Make full eigenvectors (add DOFs fixed by boundary conditions).\n vecs = nm.empty((variables.di.ptr[-1], svecs.shape[1]),\n dtype=svecs.dtype)\n for ii in range(svecs.shape[1]):\n vecs[:, ii] = variables.make_full_vec(svecs[:, ii])\n\n # Save the eigenvectors.\n out = {}\n state = pb.create_state()\n\n pp_name = pb.conf.options.get('post_process_hook')\n pp = getattr(pb.conf.funmod, pp_name if pp_name is not None else '',\n lambda out, *args, **kwargs: out)\n\n for ii in range(svecs.shape[1]):\n state.set_full(vecs[:, ii])\n aux = state.create_output_dict()\n aux2 = {}\n pp(aux2, pb, state, wmag=wmag, wdir=wdir)\n aux.update(convert_complex_output(aux2))\n out.update({key + '%03d' % ii : aux[key] for key in aux})\n\n pb.save_state(filename, out=out)\n\ndef assemble_matrices(define, mod, pars, set_wave_dir, options, wdir=None):\n \"\"\"\n Assemble the blocks of dispersion eigenvalue problem matrices.\n \"\"\"\n define_dict = define(filename_mesh=options.mesh_filename,\n pars=pars,\n approx_order=options.order,\n refinement_level=options.refine,\n solver_conf=options.solver_conf,\n plane=options.plane,\n post_process=options.post_process,\n **options.define_kwargs)\n\n conf = ProblemConf.from_dict(define_dict, mod)\n\n pb = Problem.from_conf(conf)\n pb.dispersion_options = options\n pb.set_output_dir(options.output_dir)\n dim = pb.domain.shape.dim\n\n # Set the normalized wave vector direction to the material(s).\n if wdir is None:\n wdir = nm.asarray(options.wave_dir[:dim], dtype=nm.float64)\n wdir = wdir / nm.linalg.norm(wdir)\n set_wave_dir(pb, wdir)\n\n bbox = pb.domain.mesh.get_bounding_box()\n size = (bbox[1] - bbox[0]).max()\n scaling0 = apply_unit_multipliers([1.0], ['length'],\n options.unit_multipliers)[0]\n scaling = scaling0\n if options.mesh_size is not None:\n scaling *= options.mesh_size / size\n output('scaling factor of periodic cell mesh coordinates:', scaling)\n output('new mesh size with applied unit multipliers:', scaling * size)\n pb.domain.mesh.coors[:] *= scaling\n pb.set_mesh_coors(pb.domain.mesh.coors, update_fields=True)\n\n bzone = 2.0 * nm.pi / (scaling * size)\n output('1. Brillouin zone size:', bzone * scaling0)\n output('1. Brillouin zone size with applied unit multipliers:', bzone)\n\n pb.time_update()\n pb.update_materials()\n\n # Assemble the matrices.\n mtxs = {}\n for key, eq in pb.equations.iteritems():\n mtxs[key] = mtx = pb.mtx_a.copy()\n mtx = eq.evaluate(mode='weak', dw_mode='matrix', asm_obj=mtx)\n mtx.eliminate_zeros()\n output_array_stats(mtx.data, 'nonzeros in %s' % key)\n\n output('symmetry checks:')\n output('%s - %s^T:' % (key, key), max_diff_csr(mtx, mtx.T))\n output('%s - %s^H:' % (key, key), max_diff_csr(mtx, mtx.H))\n\n return pb, wdir, bzone, mtxs\n\ndef setup_n_eigs(options, pb, mtxs):\n \"\"\"\n Setup the numbers of eigenvalues based on options and numbers of DOFs.\n \"\"\"\n solver_n_eigs = n_eigs = options.n_eigs\n n_dof = mtxs['K'].shape[0]\n if options.mode == 'omega':\n if options.n_eigs > n_dof:\n n_eigs = n_dof\n solver_n_eigs = None\n\n else:\n if options.n_eigs > 2 * n_dof:\n n_eigs = 2 * n_dof\n solver_n_eigs = None\n\n return solver_n_eigs, n_eigs\n\ndef build_evp_matrices(mtxs, val, mode, pb):\n \"\"\"\n Build the matrices of the dispersion eigenvalue problem.\n \"\"\"\n if mode == 'omega':\n mtx_a = mtxs['K'] + val**2 * mtxs['S'] + val * mtxs['R']\n output('A - A^H:', max_diff_csr(mtx_a, mtx_a.H))\n\n evp_mtxs = (mtx_a, mtxs['M'])\n\n else:\n evp_mtxs = (mtxs['S'], mtxs['R'], mtxs['K'] - val**2 * mtxs['M'])\n\n return evp_mtxs\n\ndef process_evp_results(eigs, svecs, val, wdir, bzone, pb, mtxs, options,\n std_wave_fun=None):\n \"\"\"\n Transform eigenvalues to either omegas or kappas, depending on `mode`.\n Transform eigenvectors, if available, depending on `mode`.\n Return also the values to log.\n \"\"\"\n if options.mode == 'omega':\n omegas = nm.sqrt(eigs)\n\n output('eigs, omegas:')\n for ii, om in enumerate(omegas):\n output('{:>3}. {: .10e}, {:.10e}'.format(ii, eigs[ii], om))\n\n if options.stepper == 'linear':\n out = tuple(eigs) + tuple(omegas)\n\n else:\n out = tuple(val * wdir) + tuple(omegas)\n\n if std_wave_fun is not None:\n out = out + std_wave_fun(val, wdir)\n\n return omegas, svecs, out\n\n else:\n kappas = eigs.copy()\n rks = kappas.copy()\n\n # Mask modes far from 1. Brillouin zone.\n max_kappa = 1.2 * bzone\n kappas[kappas.real > max_kappa] = nm.nan\n\n # Mask non-physical modes.\n kappas[kappas.real < 0] = nm.nan\n kappas[nm.abs(kappas.imag) > 1e-10] = nm.nan\n out = tuple(kappas.real)\n\n output('raw kappas, masked real part:',)\n for ii, kr in enumerate(kappas.real):\n output('{:>3}. {: 23.5e}, {:.10e}'.format(ii, rks[ii], kr))\n\n if svecs is not None:\n n_dof = mtxs['K'].shape[0]\n # Select only vectors corresponding to physical modes.\n ii = nm.isfinite(kappas.real)\n svecs = svecs[:n_dof, ii]\n\n if std_wave_fun is not None:\n out = out + tuple(ii if ii <= max_kappa else nm.nan\n for ii in std_wave_fun(val, wdir))\n\n return kappas, svecs, out\n\nhelps = {\n 'pars' :\n 'material parameters in Y1, Y2 subdomains in basic units'\n ' [default: %(default)s]',\n 'conf' :\n 'if given, an alternative problem description file with apply_units() and'\n ' define() functions [default: %(default)s]',\n 'define_kwargs' : 'additional keyword arguments passed to define()',\n 'mesh_size' :\n 'desired mesh size (max. of bounding box dimensions) in basic units'\n ' - the input periodic cell mesh is rescaled to this size'\n ' [default: %(default)s]',\n 'unit_multipliers' :\n 'basic unit multipliers (time, length, mass) [default: %(default)s]',\n 'plane' :\n 'for 2D problems, plane strain or stress hypothesis selection'\n ' [default: %(default)s]',\n 'wave_dir' : 'the wave vector direction (will be normalized)'\n ' [default: %(default)s]',\n 'mode' : 'solution mode: omega = solve a generalized EVP for omega,'\n ' kappa = solve a quadratic generalized EVP for kappa'\n ' [default: %(default)s]',\n 'stepper' : 'the range stepper. For \"brillouin\", only the number'\n ' of items from --range is used'\n ' [default: %(default)s]',\n 'range' : 'the wave vector magnitude / frequency range'\n ' (like numpy.linspace) depending on the mode option'\n ' [default: %(default)s]',\n 'order' : 'displacement field approximation order [default: %(default)s]',\n 'refine' : 'number of uniform mesh refinements [default: %(default)s]',\n 'n_eigs' : 'the number of eigenvalues to compute [default: %(default)s]',\n 'eigs_only' : 'compute only eigenvalues, not eigenvectors',\n 'post_process' : 'post-process eigenvectors',\n 'solver_conf' : 'eigenvalue problem solver configuration options'\n ' [default: %(default)s]',\n 'save_regions' : 'save defined regions into'\n ' /regions.vtk',\n 'save_materials' : 'save material parameters into'\n ' /materials.vtk',\n 'log_std_waves' : 'log also standard pressure dilatation and shear waves',\n 'no_legends' :\n 'do not show legends in the log plots',\n 'no_show' :\n 'do not show the log figure',\n 'silent' : 'do not print messages to screen',\n 'clear' :\n 'clear old solution files from output directory',\n 'output_dir' :\n 'output directory [default: %(default)s]',\n 'mesh_filename' :\n 'input periodic cell mesh file name [default: %(default)s]',\n}\n\ndef main():\n # Aluminium and epoxy.\n default_pars = '70e9,0.35,2.799e3, 3.8e9,0.27,1.142e3'\n default_solver_conf = (\"kind='eig.scipy',method='eigsh',tol=1.0e-5,\"\n \"maxiter=1000,which='LM',sigma=0.0\")\n\n parser = ArgumentParser(description=__doc__,\n formatter_class=RawDescriptionHelpFormatter)\n parser.add_argument('--pars', metavar='young1,poisson1,density1'\n ',young2,poisson2,density2',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='pars',\n default=default_pars, help=helps['pars'])\n parser.add_argument('--conf', metavar='filename',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='conf',\n default=None, help=helps['conf'])\n parser.add_argument('--define-kwargs', metavar='dict-like',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='define_kwargs',\n default=None, help=helps['define_kwargs'])\n parser.add_argument('--mesh-size', type=float, metavar='float',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='mesh_size',\n default=None, help=helps['mesh_size'])\n parser.add_argument('--unit-multipliers',\n metavar='c_time,c_length,c_mass',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='unit_multipliers',\n default='1.0,1.0,1.0', help=helps['unit_multipliers'])\n parser.add_argument('--plane', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='plane',\n choices=['strain', 'stress'],\n default='strain', help=helps['plane'])\n parser.add_argument('--wave-dir', metavar='float,float[,float]',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='wave_dir',\n default='1.0,0.0,0.0', help=helps['wave_dir'])\n parser.add_argument('--mode', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='mode',\n choices=['omega', 'kappa'],\n default='omega', help=helps['mode'])\n parser.add_argument('--stepper', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='stepper',\n choices=['linear', 'brillouin'],\n default='linear', help=helps['stepper'])\n parser.add_argument('--range', metavar='start,stop,count',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='range',\n default='0,6.4,33', help=helps['range'])\n parser.add_argument('--order', metavar='int', type=int,\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='order',\n default=1, help=helps['order'])\n parser.add_argument('--refine', metavar='int', type=int,\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='refine',\n default=0, help=helps['refine'])\n parser.add_argument('-n', '--n-eigs', metavar='int', type=int,\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='n_eigs',\n default=6, help=helps['n_eigs'])\n group = parser.add_mutually_exclusive_group()\n group.add_argument('--eigs-only',\n action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='eigs_only',\n default=False, help=helps['eigs_only'])\n group.add_argument('--post-process',\n action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='post_process',\n default=False, help=helps['post_process'])\n parser.add_argument('--solver-conf', metavar='dict-like',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='solver_conf',\n default=default_solver_conf, help=helps['solver_conf'])\n parser.add_argument('--save-regions',\n action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='save_regions',\n default=False, help=helps['save_regions'])\n parser.add_argument('--save-materials',\n action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='save_materials',\n default=False, help=helps['save_materials'])\n parser.add_argument('--log-std-waves',\n action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='log_std_waves',\n default=False, help=helps['log_std_waves'])\n parser.add_argument('--no-legends',\n action="https://huggingface.co/datasets/luna-code/sfepy/store_false", dest='show_legends',\n default=True, help=helps['no_legends'])\n parser.add_argument('--no-show',\n action="https://huggingface.co/datasets/luna-code/sfepy/store_false", dest='show',\n default=True, help=helps['no_show'])\n parser.add_argument('--silent',\n action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='silent',\n default=False, help=helps['silent'])\n parser.add_argument('-c', '--clear',\n action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='clear',\n default=False, help=helps['clear'])\n parser.add_argument('-o', '--output-dir', metavar='path',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='output_dir',\n default='output', help=helps['output_dir'])\n parser.add_argument('mesh_filename', default='',\n help=helps['mesh_filename'])\n options = parser.parse_args()\n\n output_dir = options.output_dir\n\n output.set_output(filename=os.path.join(output_dir,'output_log.txt'),\n combined=options.silent == False)\n\n if options.conf is not None:\n mod = import_file(options.conf)\n\n else:\n mod = sys.modules[__name__]\n\n apply_units = mod.apply_units\n define = mod.define\n set_wave_dir = mod.set_wave_dir\n setup_n_eigs = mod.setup_n_eigs\n build_evp_matrices = mod.build_evp_matrices\n save_materials = mod.save_materials\n get_std_wave_fun = mod.get_std_wave_fun\n get_stepper = mod.get_stepper\n process_evp_results = mod.process_evp_results\n\n options.pars = [float(ii) for ii in options.pars.split(',')]\n options.unit_multipliers = [float(ii)\n for ii in options.unit_multipliers.split(',')]\n options.wave_dir = [float(ii)\n for ii in options.wave_dir.split(',')]\n aux = options.range.split(',')\n options.range = [float(aux[0]), float(aux[1]), int(aux[2])]\n options.solver_conf = dict_from_string(options.solver_conf)\n options.define_kwargs = dict_from_string(options.define_kwargs)\n\n if options.clear:\n remove_files_patterns(output_dir,\n ['*.h5', '*.vtk', '*.txt'],\n ignores=['output_log.txt'],\n verbose=True)\n\n filename = os.path.join(output_dir, 'options.txt')\n ensure_path(filename)\n save_options(filename, [('options', vars(options))],\n quote_command_line=True)\n\n pars = apply_units(options.pars, options.unit_multipliers)\n output('material parameters with applied unit multipliers:')\n output(pars)\n\n if options.mode == 'omega':\n rng = copy(options.range)\n rng[:2] = apply_unit_multipliers(options.range[:2],\n ['wave_number', 'wave_number'],\n options.unit_multipliers)\n output('wave number range with applied unit multipliers:', rng)\n\n else:\n if options.stepper == 'brillouin':\n raise ValueError('Cannot use \"brillouin\" stepper in kappa mode!')\n\n rng = copy(options.range)\n rng[:2] = apply_unit_multipliers(options.range[:2],\n ['frequency', 'frequency'],\n options.unit_multipliers)\n output('frequency range with applied unit multipliers:', rng)\n\n pb, wdir, bzone, mtxs = assemble_matrices(define, mod, pars, set_wave_dir,\n options)\n dim = pb.domain.shape.dim\n\n if dim != 2:\n options.plane = 'strain'\n\n if options.save_regions:\n pb.save_regions_as_groups(os.path.join(output_dir, 'regions'))\n\n if options.save_materials:\n save_materials(output_dir, pb, options)\n\n conf = pb.solver_confs['eig']\n eig_solver = Solver.any_from_conf(conf)\n\n n_eigs, options.n_eigs = setup_n_eigs(options, pb, mtxs)\n\n get_color = lambda ii: plt.cm.viridis((float(ii) / (options.n_eigs - 1)))\n plot_kwargs = [{'color' : get_color(ii), 'ls' : '', 'marker' : 'o'}\n for ii in range(options.n_eigs)]\n get_color_dim = lambda ii: plt.cm.viridis((float(ii) / (dim-1)))\n plot_kwargs_dim = [{'color' : get_color_dim(ii), 'ls' : '', 'marker' : 'o'}\n for ii in range(dim)]\n\n log_names = []\n log_plot_kwargs = []\n if options.log_std_waves:\n std_wave_fun, log_names, log_plot_kwargs = get_std_wave_fun(\n pb, options)\n\n else:\n std_wave_fun = None\n\n stepper = get_stepper(rng, pb, options)\n\n if options.mode == 'omega':\n eigenshapes_filename = os.path.join(output_dir,\n 'frequency-eigenshapes-%s.vtk'\n % stepper.suffix)\n\n if options.stepper == 'linear':\n log = Log([[r'$\\lambda_{%d}$' % ii for ii in range(options.n_eigs)],\n [r'$\\omega_{%d}$'\n % ii for ii in range(options.n_eigs)] + log_names],\n plot_kwargs=[plot_kwargs, plot_kwargs + log_plot_kwargs],\n formats=[['{:.5e}'] * options.n_eigs,\n ['{:.5e}'] * (options.n_eigs + len(log_names))],\n yscales=['linear', 'linear'],\n xlabels=[r'$\\kappa$', r'$\\kappa$'],\n ylabels=[r'eigenvalues $\\lambda_i$',\n r'frequencies $\\omega_i$'],\n show_legends=options.show_legends,\n is_plot=options.show,\n log_filename=os.path.join(output_dir, 'frequencies.txt'),\n aggregate=1000, sleep=0.1)\n\n else:\n log = Log([[r'$\\kappa_{%d}$'% ii for ii in range(dim)],\n [r'$\\omega_{%d}$'\n % ii for ii in range(options.n_eigs)] + log_names],\n plot_kwargs=[plot_kwargs_dim,\n plot_kwargs + log_plot_kwargs],\n formats=[['{:.5e}'] * dim,\n ['{:.5e}'] * (options.n_eigs + len(log_names))],\n yscales=['linear', 'linear'],\n xlabels=[r'', r''],\n ylabels=[r'wave vector $\\kappa$',\n r'frequencies $\\omega_i$'],\n show_legends=options.show_legends,\n is_plot=options.show,\n log_filename=os.path.join(output_dir, 'frequencies.txt'),\n aggregate=1000, sleep=0.1)\n\n for aux in stepper:\n if options.stepper == 'linear':\n iv, wmag = aux\n\n else:\n iv, wmag, wdir = aux\n\n "},"completion":{"kind":"string","value":"output('step %d: wave vector %s' % (iv, wmag * wdir))"},"api":{"kind":"string","value":"sfepy.base.base.output"}}},{"rowIdx":90,"cells":{"prompt":{"kind":"string","value":"#!/usr/bin/env python\n\"\"\"\nDispersion analysis of a heterogeneous finite scale periodic cell.\n\nThe periodic cell mesh has to contain two subdomains Y1 (with the cell ids 1),\nY2 (with the cell ids 2), so that different material properties can be defined\nin each of the subdomains (see ``--pars`` option). The command line parameters\ncan be given in any consistent unit set, for example the basic SI units. The\n``--unit-multipliers`` option can be used to rescale the input units to ones\nmore suitable to the simulation, for example to prevent having different\nmatrix blocks with large differences of matrix entries magnitudes. The results\nare then in the rescaled units.\n\nUsage Examples\n--------------\n\nDefault material parameters, a square periodic cell with a spherical inclusion,\nlogs also standard pressure dilatation and shear waves, no eigenvectors::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only\n\nAs above, with custom eigenvalue solver parameters, and different number of\neigenvalues, mesh size and units used in the calculation::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --solver-conf=\"kind='eig.scipy', method='eigsh', tol=1e-10, maxiter=1000, which='LM', sigma=0\" --log-std-waves -n 5 --range=0,640,101 --mode=omega --unit-multipliers=1e-6,1e-2,1e-3 --mesh-size=1e-2 --eigs-only\n\nDefault material parameters, a square periodic cell with a square inclusion,\nand a very small mesh to allow comparing the omega and kappa modes (full matrix\nsolver required!)::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf=\"kind='eig.scipy', method='eigh'\" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf=\"kind='eig.qevp', method='companion', mode='inverted', solver={kind='eig.scipy', method='eig'}\" --log-std-waves -n 500 --range=0,4000000,1001 --mesh-size=1e-2 --mode=kappa --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/kappa\n\nView/compare the resulting logs::\n\n python script/plot_logs.py output/omega/frequencies.txt --no-legends -g 1 -o mode-omega.png\n python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends -o mode-kappa.png\n python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends --swap-axes -o mode-kappa-t.png\n\nIn contrast to the heterogeneous square periodic cell, a homogeneous\nsquare periodic cell (the region Y2 is empty)::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_1m.mesh --solver-conf=\"kind='eig.scipy', method='eigh'\" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega-h\n\n python script/plot_logs.py output/omega-h/frequencies.txt --no-legends -g 1 -o mode-omega-h.png\n\nUse the Brillouin stepper::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves -n=60 --eigs-only --no-legends --stepper=brillouin\n\n python script/plot_logs.py output/frequencies.txt -g 0 --rc=\"'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4\" -o brillouin-stepper-kappas.png\n\n python script/plot_logs.py output/frequencies.txt -g 1 --no-legends --rc=\"'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4\" -o brillouin-stepper-omegas.png\n\nAdditional arguments can be passed to the problem configuration's\n:func:`define()` function using the ``--define-kwargs`` option. In this file,\nonly the mesh vertex separation parameter `mesh_eps` can be used::\n\n python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only --define-kwargs=\"mesh_eps=1e-10\" --save-regions\n\"\"\"\nfrom __future__ import absolute_import\nimport os\nimport sys\nsys.path.append('.')\nimport gc\nfrom copy import copy\nfrom argparse import ArgumentParser, RawDescriptionHelpFormatter\n\nimport numpy as nm\nimport matplotlib.pyplot as plt\n\nfrom sfepy.base.base import import_file, output, Struct\nfrom sfepy.base.conf import dict_from_string, ProblemConf\nfrom sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options\nfrom sfepy.base.log import Log\nfrom sfepy.discrete.fem import MeshIO\nfrom sfepy.mechanics.matcoefs import stiffness_from_youngpoisson as stiffness\nimport sfepy.mechanics.matcoefs as mc\nfrom sfepy.mechanics.units import apply_unit_multipliers\nimport sfepy.discrete.fem.periodic as per\nfrom sfepy.discrete.fem.meshio import convert_complex_output\nfrom sfepy.homogenization.utils import define_box_regions\nfrom sfepy.discrete import Problem\nfrom sfepy.mechanics.tensors import get_von_mises_stress\nfrom sfepy.solvers import Solver\nfrom sfepy.solvers.ts import get_print_info, TimeStepper\nfrom sfepy.linalg.utils import output_array_stats, max_diff_csr\n\ndef apply_units(pars, unit_multipliers):\n new_pars = apply_unit_multipliers(pars,\n ['stress', 'one', 'density',\n 'stress', 'one' ,'density'],\n unit_multipliers)\n return new_pars\n\ndef compute_von_mises(out, pb, state, extend=False, wmag=None, wdir=None):\n \"\"\"\n Calculate the von Mises stress.\n \"\"\"\n stress = pb.evaluate('ev_cauchy_stress.i.Omega(m.D, u)', mode='el_avg')\n\n vms = get_von_mises_stress(stress.squeeze())\n vms.shape = (vms.shape[0], 1, 1, 1)\n out['von_mises_stress'] = Struct(name='output_data', mode='cell',\n data=vms)\n\n return out\n\ndef define(filename_mesh, pars, approx_order, refinement_level, solver_conf,\n plane='strain', post_process=False, mesh_eps=1e-8):\n io = MeshIO.any_from_filename(filename_mesh)\n bbox = io.read_bounding_box()\n dim = bbox.shape[1]\n\n options = {\n 'absolute_mesh_path' : True,\n 'refinement_level' : refinement_level,\n 'allow_empty_regions' : True,\n 'post_process_hook' : 'compute_von_mises' if post_process else None,\n }\n\n fields = {\n 'displacement': ('complex', dim, 'Omega', approx_order),\n }\n\n young1, poisson1, density1, young2, poisson2, density2 = pars\n materials = {\n 'm' : ({\n 'D' : {'Y1' : stiffness(dim, young=young1, poisson=poisson1,\n plane=plane),\n 'Y2' : stiffness(dim, young=young2, poisson=poisson2,\n plane=plane)},\n 'density' : {'Y1' : density1, 'Y2' : density2},\n },),\n 'wave' : 'get_wdir',\n }\n\n variables = {\n 'u' : ('unknown field', 'displacement', 0),\n 'v' : ('test field', 'displacement', 'u'),\n }\n\n regions = {\n 'Omega' : 'all',\n 'Y1': 'cells of group 1',\n 'Y2': 'cells of group 2',\n }\n regions.update(define_box_regions(dim,\n bbox[0], bbox[1], mesh_eps))\n\n ebcs = {\n }\n\n if dim == 3:\n epbcs = {\n 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},\n 'match_x_plane'),\n 'periodic_y' : (['Near', 'Far'], {'u.all' : 'u.all'},\n 'match_y_plane'),\n 'periodic_z' : (['Top', 'Bottom'], {'u.all' : 'u.all'},\n 'match_z_plane'),\n }\n else:\n epbcs = {\n 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},\n 'match_y_line'),\n 'periodic_y' : (['Bottom', 'Top'], {'u.all' : 'u.all'},\n 'match_x_line'),\n }\n\n per.set_accuracy(mesh_eps)\n functions = {\n 'match_x_plane' : (per.match_x_plane,),\n 'match_y_plane' : (per.match_y_plane,),\n 'match_z_plane' : (per.match_z_plane,),\n 'match_x_line' : (per.match_x_line,),\n 'match_y_line' : (per.match_y_line,),\n 'get_wdir' : (get_wdir,),\n }\n\n integrals = {\n 'i' : 2 * approx_order,\n }\n\n equations = {\n 'K' : 'dw_lin_elastic.i.Omega(m.D, v, u)',\n 'S' : 'dw_elastic_wave.i.Omega(m.D, wave.vec, v, u)',\n 'R' : \"\"\"1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, u, v)\n - 1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, v, u)\"\"\",\n 'M' : 'dw_volume_dot.i.Omega(m.density, v, u)',\n }\n\n solver_0 = solver_conf.copy()\n solver_0['name'] = 'eig'\n\n return locals()\n\ndef get_wdir(ts, coors, mode=None,\n equations=None, term=None, problem=None, wdir=None, **kwargs):\n if mode == 'special':\n return {'vec' : wdir}\n\ndef set_wave_dir(pb, wdir):\n materials = pb.get_materials()\n wave_mat = materials['wave']\n wave_mat.set_extra_args(wdir=wdir)\n\ndef save_materials(output_dir, pb, options):\n stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n young, poisson = mc.youngpoisson_from_stiffness(stiffness,\n plane=options.plane)\n density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n\n out = {}\n out['young'] = Struct(name='young', mode='cell',\n data=young[..., None, None])\n out['poisson'] = Struct(name='poisson', mode='cell',\n data=poisson[..., None, None])\n out['density'] = Struct(name='density', mode='cell', data=density)\n materials_filename = os.path.join(output_dir, 'materials.vtk')\n pb.save_state(materials_filename, out=out)\n\ndef get_std_wave_fun(pb, options):\n stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n young, poisson = mc.youngpoisson_from_stiffness(stiffness,\n plane=options.plane)\n density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',\n mode='el_avg', copy_materials=False, verbose=False)\n\n lam, mu = mc.lame_from_youngpoisson(young, poisson,\n plane=options.plane)\n alam = nm.average(lam)\n amu = nm.average(mu)\n adensity = nm.average(density)\n\n cp = nm.sqrt((alam + 2.0 * amu) / adensity)\n cs = nm.sqrt(amu / adensity)\n output('average p-wave speed:', cp)\n output('average shear wave speed:', cs)\n\n log_names = [r'$\\omega_p$', r'$\\omega_s$']\n log_plot_kwargs = [{'ls' : '--', 'color' : 'k'},\n {'ls' : '--', 'color' : 'gray'}]\n\n if options.mode == 'omega':\n fun = lambda wmag, wdir: (cp * wmag, cs * wmag)\n\n else:\n fun = lambda wmag, wdir: (wmag / cp, wmag / cs)\n\n return fun, log_names, log_plot_kwargs\n\ndef get_stepper(rng, pb, options):\n if options.stepper == 'linear':\n stepper = TimeStepper(rng[0], rng[1], dt=None, n_step=rng[2])\n return stepper\n\n bbox = pb.domain.mesh.get_bounding_box()\n\n bzone = 2.0 * nm.pi / (bbox[1] - bbox[0])\n\n num = rng[2] // 3\n\n class BrillouinStepper(Struct):\n \"\"\"\n Step over 1. Brillouin zone in xy plane.\n \"\"\"\n def __init__(self, t0, t1, dt=None, n_step=None, step=None, **kwargs):\n Struct.__init__(self, t0=t0, t1=t1, dt=dt, n_step=n_step, step=step)\n\n self.n_digit, self.format, self.suffix = get_print_info(self.n_step)\n\n def __iter__(self):\n ts = TimeStepper(0, bzone[0], dt=None, n_step=num)\n for ii, val in ts:\n yield ii, val, nm.array([1.0, 0.0])\n if ii == (num-2): break\n\n ts = TimeStepper(0, bzone[1], dt=None, n_step=num)\n for ii, k1 in ts:\n wdir = nm.array([bzone[0], k1])\n val = nm.linalg.norm(wdir)\n wdir = wdir / val\n yield num + ii, val, wdir\n if ii == (num-2): break\n\n wdir = nm.array([bzone[0], bzone[1]])\n val = nm.linalg.norm(wdir)\n wdir = wdir / val\n ts = TimeStepper(0, 1, dt=None, n_step=num)\n for ii, _ in ts:\n yield 2 * num + ii, val * (1.0 - float(ii)/(num-1)), wdir\n\n stepper = BrillouinStepper(0, 1, n_step=rng[2])\n\n return stepper\n\ndef save_eigenvectors(filename, svecs, wmag, wdir, pb):\n if svecs is None: return\n\n variables = pb.get_variables()\n # Make full eigenvectors (add DOFs fixed by boundary conditions).\n vecs = nm.empty((variables.di.ptr[-1], svecs.shape[1]),\n dtype=svecs.dtype)\n for ii in range(svecs.shape[1]):\n vecs[:, ii] = variables.make_full_vec(svecs[:, ii])\n\n # Save the eigenvectors.\n out = {}\n state = pb.create_state()\n\n pp_name = pb.conf.options.get('post_process_hook')\n pp = getattr(pb.conf.funmod, pp_name if pp_name is not None else '',\n lambda out, *args, **kwargs: out)\n\n for ii in range(svecs.shape[1]):\n state.set_full(vecs[:, ii])\n aux = state.create_output_dict()\n aux2 = {}\n pp(aux2, pb, state, wmag=wmag, wdir=wdir)\n aux.update(convert_complex_output(aux2))\n out.update({key + '%03d' % ii : aux[key] for key in aux})\n\n pb.save_state(filename, out=out)\n\ndef assemble_matrices(define, mod, pars, set_wave_dir, options, wdir=None):\n \"\"\"\n Assemble the blocks of dispersion eigenvalue problem matrices.\n \"\"\"\n define_dict = define(filename_mesh=options.mesh_filename,\n pars=pars,\n approx_order=options.order,\n refinement_level=options.refine,\n solver_conf=options.solver_conf,\n plane=options.plane,\n post_process=options.post_process,\n **options.define_kwargs)\n\n conf = ProblemConf.from_dict(define_dict, mod)\n\n pb = Problem.from_conf(conf)\n pb.dispersion_options = options\n pb.set_output_dir(options.output_dir)\n dim = pb.domain.shape.dim\n\n # Set the normalized wave vector direction to the material(s).\n if wdir is None:\n wdir = nm.asarray(options.wave_dir[:dim], dtype=nm.float64)\n wdir = wdir / nm.linalg.norm(wdir)\n set_wave_dir(pb, wdir)\n\n bbox = pb.domain.mesh.get_bounding_box()\n size = (bbox[1] - bbox[0]).max()\n scaling0 = apply_unit_multipliers([1.0], ['length'],\n options.unit_multipliers)[0]\n scaling = scaling0\n if options.mesh_size is not None:\n scaling *= options.mesh_size / size\n output('scaling factor of periodic cell mesh coordinates:', scaling)\n output('new mesh size with applied unit multipliers:', scaling * size)\n pb.domain.mesh.coors[:] *= scaling\n pb.set_mesh_coors(pb.domain.mesh.coors, update_fields=True)\n\n bzone = 2.0 * nm.pi / (scaling * size)\n output('1. Brillouin zone size:', bzone * scaling0)\n output('1. Brillouin zone size with applied unit multipliers:', bzone)\n\n pb.time_update()\n pb.update_materials()\n\n # Assemble the matrices.\n mtxs = {}\n for key, eq in pb.equations.iteritems():\n mtxs[key] = mtx = pb.mtx_a.copy()\n mtx = eq.evaluate(mode='weak', dw_mode='matrix', asm_obj=mtx)\n mtx.eliminate_zeros()\n output_array_stats(mtx.data, 'nonzeros in %s' % key)\n\n output('symmetry checks:')\n output('%s - %s^T:' % (key, key), max_diff_csr(mtx, mtx.T))\n output('%s - %s^H:' % (key, key), max_diff_csr(mtx, mtx.H))\n\n return pb, wdir, bzone, mtxs\n\ndef setup_n_eigs(options, pb, mtxs):\n \"\"\"\n Setup the numbers of eigenvalues based on options and numbers of DOFs.\n \"\"\"\n solver_n_eigs = n_eigs = options.n_eigs\n n_dof = mtxs['K'].shape[0]\n if options.mode == 'omega':\n if options.n_eigs > n_dof:\n n_eigs = n_dof\n solver_n_eigs = None\n\n else:\n if options.n_eigs > 2 * n_dof:\n n_eigs = 2 * n_dof\n solver_n_eigs = None\n\n return solver_n_eigs, n_eigs\n\ndef build_evp_matrices(mtxs, val, mode, pb):\n \"\"\"\n Build the matrices of the dispersion eigenvalue problem.\n \"\"\"\n if mode == 'omega':\n mtx_a = mtxs['K'] + val**2 * mtxs['S'] + val * mtxs['R']\n output('A - A^H:', max_diff_csr(mtx_a, mtx_a.H))\n\n evp_mtxs = (mtx_a, mtxs['M'])\n\n else:\n evp_mtxs = (mtxs['S'], mtxs['R'], mtxs['K'] - val**2 * mtxs['M'])\n\n return evp_mtxs\n\ndef process_evp_results(eigs, svecs, val, wdir, bzone, pb, mtxs, options,\n std_wave_fun=None):\n \"\"\"\n Transform eigenvalues to either omegas or kappas, depending on `mode`.\n Transform eigenvectors, if available, depending on `mode`.\n Return also the values to log.\n \"\"\"\n if options.mode == 'omega':\n omegas = nm.sqrt(eigs)\n\n output('eigs, omegas:')\n for ii, om in enumerate(omegas):\n output('{:>3}. {: .10e}, {:.10e}'.format(ii, eigs[ii], om))\n\n if options.stepper == 'linear':\n out = tuple(eigs) + tuple(omegas)\n\n else:\n out = tuple(val * wdir) + tuple(omegas)\n\n if std_wave_fun is not None:\n out = out + std_wave_fun(val, wdir)\n\n return omegas, svecs, out\n\n else:\n kappas = eigs.copy()\n rks = kappas.copy()\n\n # Mask modes far from 1. Brillouin zone.\n max_kappa = 1.2 * bzone\n kappas[kappas.real > max_kappa] = nm.nan\n\n # Mask non-physical modes.\n kappas[kappas.real < 0] = nm.nan\n kappas[nm.abs(kappas.imag) > 1e-10] = nm.nan\n out = tuple(kappas.real)\n\n output('raw kappas, masked real part:',)\n for ii, kr in enumerate(kappas.real):\n output('{:>3}. {: 23.5e}, {:.10e}'.format(ii, rks[ii], kr))\n\n if svecs is not None:\n n_dof = mtxs['K'].shape[0]\n # Select only vectors corresponding to physical modes.\n ii = nm.isfinite(kappas.real)\n svecs = svecs[:n_dof, ii]\n\n if std_wave_fun is not None:\n out = out + tuple(ii if ii <= max_kappa else nm.nan\n for ii in std_wave_fun(val, wdir))\n\n return kappas, svecs, out\n\nhelps = {\n 'pars' :\n 'material parameters in Y1, Y2 subdomains in basic units'\n ' [default: %(default)s]',\n 'conf' :\n 'if given, an alternative problem description file with apply_units() and'\n ' define() functions [default: %(default)s]',\n 'define_kwargs' : 'additional keyword arguments passed to define()',\n 'mesh_size' :\n 'desired mesh size (max. of bounding box dimensions) in basic units'\n ' - the input periodic cell mesh is rescaled to this size'\n ' [default: %(default)s]',\n 'unit_multipliers' :\n 'basic unit multipliers (time, length, mass) [default: %(default)s]',\n 'plane' :\n 'for 2D problems, plane strain or stress hypothesis selection'\n ' [default: %(default)s]',\n 'wave_dir' : 'the wave vector direction (will be normalized)'\n ' [default: %(default)s]',\n 'mode' : 'solution mode: omega = solve a generalized EVP for omega,'\n ' kappa = solve a quadratic generalized EVP for kappa'\n ' [default: %(default)s]',\n 'stepper' : 'the range stepper. For \"brillouin\", only the number'\n ' of items from --range is used'\n ' [default: %(default)s]',\n 'range' : 'the wave vector magnitude / frequency range'\n ' (like numpy.linspace) depending on the mode option'\n ' [default: %(default)s]',\n 'order' : 'displacement field approximation order [default: %(default)s]',\n 'refine' : 'number of uniform mesh refinements [default: %(default)s]',\n 'n_eigs' : 'the number of eigenvalues to compute [default: %(default)s]',\n 'eigs_only' : 'compute only eigenvalues, not eigenvectors',\n 'post_process' : 'post-process eigenvectors',\n 'solver_conf' : 'eigenvalue problem solver configuration options'\n ' [default: %(default)s]',\n 'save_regions' : 'save defined regions into'\n ' /regions.vtk',\n 'save_materials' : 'save material parameters into'\n ' /materials.vtk',\n 'log_std_waves' : 'log also standard pressure dilatation and shear waves',\n 'no_legends' :\n 'do not show legends in the log plots',\n 'no_show' :\n 'do not show the log figure',\n 'silent' : 'do not print messages to screen',\n 'clear' :\n 'clear old solution files from output directory',\n 'output_dir' :\n 'output directory [default: %(default)s]',\n 'mesh_filename' :\n 'input periodic cell mesh file name [default: %(default)s]',\n}\n\ndef main():\n # Aluminium and epoxy.\n default_pars = '70e9,0.35,2.799e3, 3.8e9,0.27,1.142e3'\n default_solver_conf = (\"kind='eig.scipy',method='eigsh',tol=1.0e-5,\"\n \"maxiter=1000,which='LM',sigma=0.0\")\n\n parser = ArgumentParser(description=__doc__,\n formatter_class=RawDescriptionHelpFormatter)\n parser.add_argument('--pars', metavar='young1,poisson1,density1'\n ',young2,poisson2,density2',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='pars',\n default=default_pars, help=helps['pars'])\n parser.add_argument('--conf', metavar='filename',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='conf',\n default=None, help=helps['conf'])\n parser.add_argument('--define-kwargs', metavar='dict-like',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='define_kwargs',\n default=None, help=helps['define_kwargs'])\n parser.add_argument('--mesh-size', type=float, metavar='float',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='mesh_size',\n default=None, help=helps['mesh_size'])\n parser.add_argument('--unit-multipliers',\n metavar='c_time,c_length,c_mass',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='unit_multipliers',\n default='1.0,1.0,1.0', help=helps['unit_multipliers'])\n parser.add_argument('--plane', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='plane',\n choices=['strain', 'stress'],\n default='strain', help=helps['plane'])\n parser.add_argument('--wave-dir', metavar='float,float[,float]',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='wave_dir',\n default='1.0,0.0,0.0', help=helps['wave_dir'])\n parser.add_argument('--mode', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='mode',\n choices=['omega', 'kappa'],\n default='omega', help=helps['mode'])\n parser.add_argument('--stepper', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='stepper',\n choices=['linear', 'brillouin'],\n default='linear', help=helps['stepper'])\n parser.add_argument('--range', metavar='start,stop,count',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='range',\n default='0,6.4,33', help=helps['range'])\n parser.add_argument('--order', metavar='int', type=int,\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='order',\n default=1, help=helps['order'])\n parser.add_argument('--refine', metavar='int', type=int,\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='refine',\n default=0, help=helps['refine'])\n parser.add_argument('-n', '--n-eigs', metavar='int', type=int,\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='n_eigs',\n default=6, help=helps['n_eigs'])\n group = parser.add_mutually_exclusive_group()\n group.add_argument('--eigs-only',\n action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='eigs_only',\n default=False, help=helps['eigs_only'])\n group.add_argument('--post-process',\n action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='post_process',\n default=False, help=helps['post_process'])\n parser.add_argument('--solver-conf', metavar='dict-like',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='solver_conf',\n default=default_solver_conf, help=helps['solver_conf'])\n parser.add_argument('--save-regions',\n action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='save_regions',\n default=False, help=helps['save_regions'])\n parser.add_argument('--save-materials',\n action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='save_materials',\n default=False, help=helps['save_materials'])\n parser.add_argument('--log-std-waves',\n action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='log_std_waves',\n default=False, help=helps['log_std_waves'])\n parser.add_argument('--no-legends',\n action="https://huggingface.co/datasets/luna-code/sfepy/store_false", dest='show_legends',\n default=True, help=helps['no_legends'])\n parser.add_argument('--no-show',\n action="https://huggingface.co/datasets/luna-code/sfepy/store_false", dest='show',\n default=True, help=helps['no_show'])\n parser.add_argument('--silent',\n action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='silent',\n default=False, help=helps['silent'])\n parser.add_argument('-c', '--clear',\n action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='clear',\n default=False, help=helps['clear'])\n parser.add_argument('-o', '--output-dir', metavar='path',\n action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='output_dir',\n default='output', help=helps['output_dir'])\n parser.add_argument('mesh_filename', default='',\n help=helps['mesh_filename'])\n options = parser.parse_args()\n\n output_dir = options.output_dir\n\n output.set_output(filename=os.path.join(output_dir,'output_log.txt'),\n combined=options.silent == False)\n\n if options.conf is not None:\n mod = import_file(options.conf)\n\n else:\n mod = sys.modules[__name__]\n\n apply_units = mod.apply_units\n define = mod.define\n set_wave_dir = mod.set_wave_dir\n setup_n_eigs = mod.setup_n_eigs\n build_evp_matrices = mod.build_evp_matrices\n save_materials = mod.save_materials\n get_std_wave_fun = mod.get_std_wave_fun\n get_stepper = mod.get_stepper\n process_evp_results = mod.process_evp_results\n\n options.pars = [float(ii) for ii in options.pars.split(',')]\n options.unit_multipliers = [float(ii)\n for ii in options.unit_multipliers.split(',')]\n options.wave_dir = [float(ii)\n for ii in options.wave_dir.split(',')]\n aux = options.range.split(',')\n options.range = [float(aux[0]), float(aux[1]), int(aux[2])]\n options.solver_conf = dict_from_string(options.solver_conf)\n options.define_kwargs = dict_from_string(options.define_kwargs)\n\n if options.clear:\n remove_files_patterns(output_dir,\n ['*.h5', '*.vtk', '*.txt'],\n ignores=['output_log.txt'],\n verbose=True)\n\n filename = os.path.join(output_dir, 'options.txt')\n ensure_path(filename)\n save_options(filename, [('options', vars(options))],\n quote_command_line=True)\n\n pars = apply_units(options.pars, options.unit_multipliers)\n output('material parameters with applied unit multipliers:')\n output(pars)\n\n if options.mode == 'omega':\n rng = copy(options.range)\n rng[:2] = apply_unit_multipliers(options.range[:2],\n ['wave_number', 'wave_number'],\n options.unit_multipliers)\n output('wave number range with applied unit multipliers:', rng)\n\n else:\n if options.stepper == 'brillouin':\n raise ValueError('Cannot use \"brillouin\" stepper in kappa mode!')\n\n rng = copy(options.range)\n rng[:2] = apply_unit_multipliers(options.range[:2],\n ['frequency', 'frequency'],\n options.unit_multipliers)\n output('frequency range with applied unit multipliers:', rng)\n\n pb, wdir, bzone, mtxs = assemble_matrices(define, mod, pars, set_wave_dir,\n options)\n dim = pb.domain.shape.dim\n\n if dim != 2:\n options.plane = 'strain'\n\n if options.save_regions:\n pb.save_regions_as_groups(os.path.join(output_dir, 'regions'))\n\n if options.save_materials:\n save_materials(output_dir, pb, options)\n\n conf = pb.solver_confs['eig']\n eig_solver = Solver.any_from_conf(conf)\n\n n_eigs, options.n_eigs = setup_n_eigs(options, pb, mtxs)\n\n get_color = lambda ii: plt.cm.viridis((float(ii) / (options.n_eigs - 1)))\n plot_kwargs = [{'color' : get_color(ii), 'ls' : '', 'marker' : 'o'}\n for ii in range(options.n_eigs)]\n get_color_dim = lambda ii: plt.cm.viridis((float(ii) / (dim-1)))\n plot_kwargs_dim = [{'color' : get_color_dim(ii), 'ls' : '', 'marker' : 'o'}\n for ii in range(dim)]\n\n log_names = []\n log_plot_kwargs = []\n if options.log_std_waves:\n std_wave_fun, log_names, log_plot_kwargs = get_std_wave_fun(\n pb, options)\n\n else:\n std_wave_fun = None\n\n stepper = get_stepper(rng, pb, options)\n\n if options.mode == 'omega':\n eigenshapes_filename = os.path.join(output_dir,\n 'frequency-eigenshapes-%s.vtk'\n % stepper.suffix)\n\n if options.stepper == 'linear':\n log = Log([[r'$\\lambda_{%d}$' % ii for ii in range(options.n_eigs)],\n [r'$\\omega_{%d}$'\n % ii for ii in range(options.n_eigs)] + log_names],\n plot_kwargs=[plot_kwargs, plot_kwargs + log_plot_kwargs],\n formats=[['{:.5e}'] * options.n_eigs,\n ['{:.5e}'] * (options.n_eigs + len(log_names))],\n yscales=['linear', 'linear'],\n xlabels=[r'$\\kappa$', r'$\\kappa$'],\n ylabels=[r'eigenvalues $\\lambda_i$',\n r'frequencies $\\omega_i$'],\n show_legends=options.show_legends,\n is_plot=options.show,\n log_filename=os.path.join(output_dir, 'frequencies.txt'),\n aggregate=1000, sleep=0.1)\n\n else:\n log = Log([[r'$\\kappa_{%d}$'% ii for ii in range(dim)],\n [r'$\\omega_{%d}$'\n % ii for ii in range(options.n_eigs)] + log_names],\n plot_kwargs=[plot_kwargs_dim,\n plot_kwargs + log_plot_kwargs],\n formats=[['{:.5e}'] * dim,\n ['{:.5e}'] * (options.n_eigs + len(log_names))],\n yscales=['linear', 'linear'],\n xlabels=[r'', r''],\n ylabels=[r'wave vector $\\kappa$',\n r'frequencies $\\omega_i$'],\n show_legends=options.show_legends,\n is_plot=options.show,\n log_filename=os.path.join(output_dir, 'frequencies.txt'),\n aggregate=1000, sleep=0.1)\n\n for aux in stepper:\n if options.stepper == 'linear':\n iv, wmag = aux\n\n else:\n iv, wmag, wdir = aux\n\n output('step %d: wave vector %s' % (iv, wmag * wdir))\n\n if options.stepper == 'brillouin':\n pb, _, bzone, mtxs = assemble_matrices(\n define, mod, pars, set_wave_dir, options, wdir=wdir)\n\n evp_mtxs = build_evp_matrices(mtxs, wmag, options.mode, pb)\n\n if options.eigs_only:\n eigs = eig_solver(*evp_mtxs, n_eigs=n_eigs,\n eigenvectors=False)\n svecs = None\n\n else:\n eigs, svecs = eig_solver(*evp_mtxs, n_eigs=n_eigs,\n eigenvectors=True)\n\n omegas, svecs, out = process_evp_results(\n eigs, svecs, wmag, wdir, bzone, pb, mtxs, options,\n std_wave_fun=std_wave_fun\n )\n if options.stepper == 'linear':\n log(*out, x=[wmag, wmag])\n\n else:\n log(*out, x=[iv, iv])\n\n save_eigenvectors(eigenshapes_filename % iv, svecs, wmag, wdir, pb)\n\n gc.collect()\n\n log(save_figure=os.path.join(output_dir, 'frequencies.png'))\n log(finished=True)\n\n else:\n eigenshapes_filename = os.path.join(output_dir,\n 'wave-number-eigenshapes-%s.vtk'\n % stepper.suffix)\n\n log = Log([[r'$\\kappa_{%d}$' % ii for ii in range(options.n_eigs)]\n + log_names],\n plot_kwargs=[plot_kwargs + log_plot_kwargs],\n formats=[['{:.5e}'] * (options.n_eigs + len(log_names))],\n yscales=['linear'],\n xlabels=[r'$\\omega$'],\n ylabels=[r'wave numbers $\\kappa_i$'],\n show_legends=options.show_legends,\n is_plot=options.show,\n log_filename=os.path.join(output_dir, 'wave-numbers.txt'),\n aggregate=1000, sleep=0.1)\n for io, omega in stepper:\n "},"completion":{"kind":"string","value":"output('step %d: frequency %s' % (io, omega))"},"api":{"kind":"string","value":"sfepy.base.base.output"}}},{"rowIdx":91,"cells":{"prompt":{"kind":"string","value":"from __future__ import absolute_import\nfrom copy import copy\n\nimport numpy as nm\n\nfrom sfepy.base.testing import TestCommon\nfrom sfepy.base.base import ordered_iteritems\nfrom sfepy import data_dir\n\nfilename_meshes = [data_dir + '/meshes/elements/%s_2.mesh' % geom\n for geom in ['1_2', '2_3', '2_4', '3_4', '3_8', '3_2_4']]\n\ndef make_term_args(arg_shapes, arg_kinds, arg_types, ats_mode, domain,\n material_value=None, poly_space_base=None):\n from sfepy.base.base import basestr\n from sfepy.discrete import FieldVariable, Material, Variables, Materials\n from sfepy.discrete.fem import Field\n from sfepy.solvers.ts import TimeStepper\n from sfepy.mechanics.tensors import dim2sym\n\n omega = domain.regions['Omega']\n dim = domain.shape.dim\n sym = "},"completion":{"kind":"string","value":"dim2sym(dim)"},"api":{"kind":"string","value":"sfepy.mechanics.tensors.dim2sym"}}},{"rowIdx":92,"cells":{"prompt":{"kind":"string","value":"from __future__ import absolute_import\nfrom copy import copy\n\nimport numpy as nm\n\nfrom sfepy.base.testing import TestCommon\nfrom sfepy.base.base import ordered_iteritems\nfrom sfepy import data_dir\n\nfilename_meshes = [data_dir + '/meshes/elements/%s_2.mesh' % geom\n for geom in ['1_2', '2_3', '2_4', '3_4', '3_8', '3_2_4']]\n\ndef make_term_args(arg_shapes, arg_kinds, arg_types, ats_mode, domain,\n material_value=None, poly_space_base=None):\n from sfepy.base.base import basestr\n from sfepy.discrete import FieldVariable, Material, Variables, Materials\n from sfepy.discrete.fem import Field\n from sfepy.solvers.ts import TimeStepper\n from sfepy.mechanics.tensors import dim2sym\n\n omega = domain.regions['Omega']\n dim = domain.shape.dim\n sym = dim2sym(dim)\n\n def _parse_scalar_shape(sh):\n if isinstance(sh, basestr):\n if sh == 'D':\n return dim\n\n elif sh == 'D2':\n return dim**2\n\n elif sh == 'S':\n return sym\n\n elif sh == 'N': # General number ;)\n return 1\n\n else:\n return int(sh)\n\n else:\n return sh\n\n def _parse_tuple_shape(sh):\n if isinstance(sh, basestr):\n return [_parse_scalar_shape(ii.strip()) for ii in sh.split(',')]\n\n else:\n return (int(sh),)\n\n args = {}\n str_args = []\n materials = []\n variables = []\n for ii, arg_kind in enumerate(arg_kinds):\n if arg_kind != 'ts':\n if ats_mode is not None:\n extended_ats = arg_types[ii] + ('/%s' % ats_mode)\n\n else:\n extended_ats = arg_types[ii]\n\n try:\n sh = arg_shapes[arg_types[ii]]\n\n except KeyError:\n sh = arg_shapes[extended_ats]\n\n if arg_kind.endswith('variable'):\n shape = _parse_scalar_shape(sh[0] if isinstance(sh, tuple) else sh)\n field = Field.from_args('f%d' % ii, nm.float64, shape, omega,\n approx_order=1,\n poly_space_base=poly_space_base)\n\n if arg_kind == 'virtual_variable':\n if sh[1] is not None:\n istate = arg_types.index(sh[1])\n\n else:\n # Only virtual variable in arguments.\n istate = -1\n # -> Make fake variable.\n var = FieldVariable('u-1', 'unknown', field)\n var.set_constant(0.0)\n variables.append(var)\n\n var = FieldVariable('v', 'test', field,\n primary_var_name='u%d' % istate)\n\n elif arg_kind == 'state_variable':\n var = FieldVariable('u%d' % ii, 'unknown', field)\n var.set_constant(0.0)\n\n elif arg_kind == 'parameter_variable':\n var = FieldVariable('p%d' % ii, 'parameter', field,\n primary_var_name='(set-to-None)')\n var.set_constant(0.0)\n\n variables.append(var)\n str_args.append(var.name)\n args[var.name] = var\n\n elif arg_kind.endswith('material'):\n if sh is None: # Switched-off opt_material.\n continue\n\n prefix = ''\n if isinstance(sh, basestr):\n aux = sh.split(':')\n if len(aux) == 2:\n prefix, sh = aux\n\n if material_value is None:\n material_value = 1.0\n\n shape = _parse_tuple_shape(sh)\n if (len(shape) > 1) or (shape[0] > 1):\n if ((len(shape) == 2) and (shape[0] == shape[1])\n and (material_value != 0.0)):\n # Identity matrix.\n val = nm.eye(shape[0], dtype=nm.float64)\n\n else:\n # Array.\n val = nm.empty(shape, dtype=nm.float64)\n val.fill(material_value)\n\n values = {'%sc%d' % (prefix, ii)\n : val}\n\n elif (len(shape) == 1) and (shape[0] == 1):\n # Single scalar as a special value.\n values = {'.c%d' % ii : material_value}\n\n else:\n raise ValueError('wrong material shape! (%s)' % shape)\n\n mat = Material('m%d' % ii, values=values)\n\n materials.append(mat)\n str_args.append(mat.name + '.' + 'c%d' % ii)\n args[mat.name] = mat\n\n elif arg_kind == 'ts':\n ts = TimeStepper(0.0, 1.0, 1.0, 5)\n str_args.append('ts')\n args['ts'] = ts\n\n else:\n str_args.append('user%d' % ii)\n args[str_args[-1]] = None\n\n materials = "},"completion":{"kind":"string","value":"Materials(materials)"},"api":{"kind":"string","value":"sfepy.discrete.Materials"}}},{"rowIdx":93,"cells":{"prompt":{"kind":"string","value":"from __future__ import absolute_import\nfrom copy import copy\n\nimport numpy as nm\n\nfrom sfepy.base.testing import TestCommon\nfrom sfepy.base.base import ordered_iteritems\nfrom sfepy import data_dir\n\nfilename_meshes = [data_dir + '/meshes/elements/%s_2.mesh' % geom\n for geom in ['1_2', '2_3', '2_4', '3_4', '3_8', '3_2_4']]\n\ndef make_term_args(arg_shapes, arg_kinds, arg_types, ats_mode, domain,\n material_value=None, poly_space_base=None):\n from sfepy.base.base import basestr\n from sfepy.discrete import FieldVariable, Material, Variables, Materials\n from sfepy.discrete.fem import Field\n from sfepy.solvers.ts import TimeStepper\n from sfepy.mechanics.tensors import dim2sym\n\n omega = domain.regions['Omega']\n dim = domain.shape.dim\n sym = dim2sym(dim)\n\n def _parse_scalar_shape(sh):\n if isinstance(sh, basestr):\n if sh == 'D':\n return dim\n\n elif sh == 'D2':\n return dim**2\n\n elif sh == 'S':\n return sym\n\n elif sh == 'N': # General number ;)\n return 1\n\n else:\n return int(sh)\n\n else:\n return sh\n\n def _parse_tuple_shape(sh):\n if isinstance(sh, basestr):\n return [_parse_scalar_shape(ii.strip()) for ii in sh.split(',')]\n\n else:\n return (int(sh),)\n\n args = {}\n str_args = []\n materials = []\n variables = []\n for ii, arg_kind in enumerate(arg_kinds):\n if arg_kind != 'ts':\n if ats_mode is not None:\n extended_ats = arg_types[ii] + ('/%s' % ats_mode)\n\n else:\n extended_ats = arg_types[ii]\n\n try:\n sh = arg_shapes[arg_types[ii]]\n\n except KeyError:\n sh = arg_shapes[extended_ats]\n\n if arg_kind.endswith('variable'):\n shape = _parse_scalar_shape(sh[0] if isinstance(sh, tuple) else sh)\n field = Field.from_args('f%d' % ii, nm.float64, shape, omega,\n approx_order=1,\n poly_space_base=poly_space_base)\n\n if arg_kind == 'virtual_variable':\n if sh[1] is not None:\n istate = arg_types.index(sh[1])\n\n else:\n # Only virtual variable in arguments.\n istate = -1\n # -> Make fake variable.\n var = FieldVariable('u-1', 'unknown', field)\n var.set_constant(0.0)\n variables.append(var)\n\n var = FieldVariable('v', 'test', field,\n primary_var_name='u%d' % istate)\n\n elif arg_kind == 'state_variable':\n var = FieldVariable('u%d' % ii, 'unknown', field)\n var.set_constant(0.0)\n\n elif arg_kind == 'parameter_variable':\n var = FieldVariable('p%d' % ii, 'parameter', field,\n primary_var_name='(set-to-None)')\n var.set_constant(0.0)\n\n variables.append(var)\n str_args.append(var.name)\n args[var.name] = var\n\n elif arg_kind.endswith('material'):\n if sh is None: # Switched-off opt_material.\n continue\n\n prefix = ''\n if isinstance(sh, basestr):\n aux = sh.split(':')\n if len(aux) == 2:\n prefix, sh = aux\n\n if material_value is None:\n material_value = 1.0\n\n shape = _parse_tuple_shape(sh)\n if (len(shape) > 1) or (shape[0] > 1):\n if ((len(shape) == 2) and (shape[0] == shape[1])\n and (material_value != 0.0)):\n # Identity matrix.\n val = nm.eye(shape[0], dtype=nm.float64)\n\n else:\n # Array.\n val = nm.empty(shape, dtype=nm.float64)\n val.fill(material_value)\n\n values = {'%sc%d' % (prefix, ii)\n : val}\n\n elif (len(shape) == 1) and (shape[0] == 1):\n # Single scalar as a special value.\n values = {'.c%d' % ii : material_value}\n\n else:\n raise ValueError('wrong material shape! (%s)' % shape)\n\n mat = Material('m%d' % ii, values=values)\n\n materials.append(mat)\n str_args.append(mat.name + '.' + 'c%d' % ii)\n args[mat.name] = mat\n\n elif arg_kind == 'ts':\n ts = TimeStepper(0.0, 1.0, 1.0, 5)\n str_args.append('ts')\n args['ts'] = ts\n\n else:\n str_args.append('user%d' % ii)\n args[str_args[-1]] = None\n\n materials = Materials(materials)\n variables = "},"completion":{"kind":"string","value":"Variables(variables)"},"api":{"kind":"string","value":"sfepy.discrete.Variables"}}},{"rowIdx":94,"cells":{"prompt":{"kind":"string","value":"from __future__ import absolute_import\nfrom copy import copy\n\nimport numpy as nm\n\nfrom sfepy.base.testing import TestCommon\nfrom sfepy.base.base import ordered_iteritems\nfrom sfepy import data_dir\n\nfilename_meshes = [data_dir + '/meshes/elements/%s_2.mesh' % geom\n for geom in ['1_2', '2_3', '2_4', '3_4', '3_8', '3_2_4']]\n\ndef make_term_args(arg_shapes, arg_kinds, arg_types, ats_mode, domain,\n material_value=None, poly_space_base=None):\n from sfepy.base.base import basestr\n from sfepy.discrete import FieldVariable, Material, Variables, Materials\n from sfepy.discrete.fem import Field\n from sfepy.solvers.ts import TimeStepper\n from sfepy.mechanics.tensors import dim2sym\n\n omega = domain.regions['Omega']\n dim = domain.shape.dim\n sym = dim2sym(dim)\n\n def _parse_scalar_shape(sh):\n if isinstance(sh, basestr):\n if sh == 'D':\n return dim\n\n elif sh == 'D2':\n return dim**2\n\n elif sh == 'S':\n return sym\n\n elif sh == 'N': # General number ;)\n return 1\n\n else:\n return int(sh)\n\n else:\n return sh\n\n def _parse_tuple_shape(sh):\n if isinstance(sh, basestr):\n return [_parse_scalar_shape(ii.strip()) for ii in sh.split(',')]\n\n else:\n return (int(sh),)\n\n args = {}\n str_args = []\n materials = []\n variables = []\n for ii, arg_kind in enumerate(arg_kinds):\n if arg_kind != 'ts':\n if ats_mode is not None:\n extended_ats = arg_types[ii] + ('/%s' % ats_mode)\n\n else:\n extended_ats = arg_types[ii]\n\n try:\n sh = arg_shapes[arg_types[ii]]\n\n except KeyError:\n sh = arg_shapes[extended_ats]\n\n if arg_kind.endswith('variable'):\n shape = _parse_scalar_shape(sh[0] if isinstance(sh, tuple) else sh)\n field = Field.from_args('f%d' % ii, nm.float64, shape, omega,\n approx_order=1,\n poly_space_base=poly_space_base)\n\n if arg_kind == 'virtual_variable':\n if sh[1] is not None:\n istate = arg_types.index(sh[1])\n\n else:\n # Only virtual variable in arguments.\n istate = -1\n # -> Make fake variable.\n var = FieldVariable('u-1', 'unknown', field)\n var.set_constant(0.0)\n variables.append(var)\n\n var = FieldVariable('v', 'test', field,\n primary_var_name='u%d' % istate)\n\n elif arg_kind == 'state_variable':\n var = FieldVariable('u%d' % ii, 'unknown', field)\n var.set_constant(0.0)\n\n elif arg_kind == 'parameter_variable':\n var = FieldVariable('p%d' % ii, 'parameter', field,\n primary_var_name='(set-to-None)')\n var.set_constant(0.0)\n\n variables.append(var)\n str_args.append(var.name)\n args[var.name] = var\n\n elif arg_kind.endswith('material'):\n if sh is None: # Switched-off opt_material.\n continue\n\n prefix = ''\n if isinstance(sh, basestr):\n aux = sh.split(':')\n if len(aux) == 2:\n prefix, sh = aux\n\n if material_value is None:\n material_value = 1.0\n\n shape = _parse_tuple_shape(sh)\n if (len(shape) > 1) or (shape[0] > 1):\n if ((len(shape) == 2) and (shape[0] == shape[1])\n and (material_value != 0.0)):\n # Identity matrix.\n val = nm.eye(shape[0], dtype=nm.float64)\n\n else:\n # Array.\n val = nm.empty(shape, dtype=nm.float64)\n val.fill(material_value)\n\n values = {'%sc%d' % (prefix, ii)\n : val}\n\n elif (len(shape) == 1) and (shape[0] == 1):\n # Single scalar as a special value.\n values = {'.c%d' % ii : material_value}\n\n else:\n raise ValueError('wrong material shape! (%s)' % shape)\n\n mat = Material('m%d' % ii, values=values)\n\n materials.append(mat)\n str_args.append(mat.name + '.' + 'c%d' % ii)\n args[mat.name] = mat\n\n elif arg_kind == 'ts':\n ts = TimeStepper(0.0, 1.0, 1.0, 5)\n str_args.append('ts')\n args['ts'] = ts\n\n else:\n str_args.append('user%d' % ii)\n args[str_args[-1]] = None\n\n materials = Materials(materials)\n variables = Variables(variables)\n\n return args, str_args, materials, variables\n\nclass Test(TestCommon):\n\n @staticmethod\n def from_conf(conf, options):\n from sfepy.discrete import Integral\n from sfepy.discrete.fem import Mesh, FEDomain\n\n domains = []\n for filename in filename_meshes:\n mesh = Mesh.from_file(filename)\n domain = FEDomain('domain_%s' % mesh.name.replace(data_dir, ''),\n mesh)\n domain.create_region('Omega', 'all')\n domain.create_region('Gamma', 'vertices of surface', 'facet')\n\n domains.append(domain)\n\n integral = "},"completion":{"kind":"string","value":"Integral('i', order=3)"},"api":{"kind":"string","value":"sfepy.discrete.Integral"}}},{"rowIdx":95,"cells":{"prompt":{"kind":"string","value":"from __future__ import absolute_import\nfrom copy import copy\n\nimport numpy as nm\n\nfrom sfepy.base.testing import TestCommon\nfrom sfepy.base.base import ordered_iteritems\nfrom sfepy import data_dir\n\nfilename_meshes = [data_dir + '/meshes/elements/%s_2.mesh' % geom\n for geom in ['1_2', '2_3', '2_4', '3_4', '3_8', '3_2_4']]\n\ndef make_term_args(arg_shapes, arg_kinds, arg_types, ats_mode, domain,\n material_value=None, poly_space_base=None):\n from sfepy.base.base import basestr\n from sfepy.discrete import FieldVariable, Material, Variables, Materials\n from sfepy.discrete.fem import Field\n from sfepy.solvers.ts import TimeStepper\n from sfepy.mechanics.tensors import dim2sym\n\n omega = domain.regions['Omega']\n dim = domain.shape.dim\n sym = dim2sym(dim)\n\n def _parse_scalar_shape(sh):\n if isinstance(sh, basestr):\n if sh == 'D':\n return dim\n\n elif sh == 'D2':\n return dim**2\n\n elif sh == 'S':\n return sym\n\n elif sh == 'N': # General number ;)\n return 1\n\n else:\n return int(sh)\n\n else:\n return sh\n\n def _parse_tuple_shape(sh):\n if isinstance(sh, basestr):\n return [_parse_scalar_shape(ii.strip()) for ii in sh.split(',')]\n\n else:\n return (int(sh),)\n\n args = {}\n str_args = []\n materials = []\n variables = []\n for ii, arg_kind in enumerate(arg_kinds):\n if arg_kind != 'ts':\n if ats_mode is not None:\n extended_ats = arg_types[ii] + ('/%s' % ats_mode)\n\n else:\n extended_ats = arg_types[ii]\n\n try:\n sh = arg_shapes[arg_types[ii]]\n\n except KeyError:\n sh = arg_shapes[extended_ats]\n\n if arg_kind.endswith('variable'):\n shape = _parse_scalar_shape(sh[0] if isinstance(sh, tuple) else sh)\n field = Field.from_args('f%d' % ii, nm.float64, shape, omega,\n approx_order=1,\n poly_space_base=poly_space_base)\n\n if arg_kind == 'virtual_variable':\n if sh[1] is not None:\n istate = arg_types.index(sh[1])\n\n else:\n # Only virtual variable in arguments.\n istate = -1\n # -> Make fake variable.\n var = FieldVariable('u-1', 'unknown', field)\n var.set_constant(0.0)\n variables.append(var)\n\n var = FieldVariable('v', 'test', field,\n primary_var_name='u%d' % istate)\n\n elif arg_kind == 'state_variable':\n var = FieldVariable('u%d' % ii, 'unknown', field)\n var.set_constant(0.0)\n\n elif arg_kind == 'parameter_variable':\n var = FieldVariable('p%d' % ii, 'parameter', field,\n primary_var_name='(set-to-None)')\n var.set_constant(0.0)\n\n variables.append(var)\n str_args.append(var.name)\n args[var.name] = var\n\n elif arg_kind.endswith('material'):\n if sh is None: # Switched-off opt_material.\n continue\n\n prefix = ''\n if isinstance(sh, basestr):\n aux = sh.split(':')\n if len(aux) == 2:\n prefix, sh = aux\n\n if material_value is None:\n material_value = 1.0\n\n shape = _parse_tuple_shape(sh)\n if (len(shape) > 1) or (shape[0] > 1):\n if ((len(shape) == 2) and (shape[0] == shape[1])\n and (material_value != 0.0)):\n # Identity matrix.\n val = nm.eye(shape[0], dtype=nm.float64)\n\n else:\n # Array.\n val = nm.empty(shape, dtype=nm.float64)\n val.fill(material_value)\n\n values = {'%sc%d' % (prefix, ii)\n : val}\n\n elif (len(shape) == 1) and (shape[0] == 1):\n # Single scalar as a special value.\n values = {'.c%d' % ii : material_value}\n\n else:\n raise ValueError('wrong material shape! (%s)' % shape)\n\n mat = Material('m%d' % ii, values=values)\n\n materials.append(mat)\n str_args.append(mat.name + '.' + 'c%d' % ii)\n args[mat.name] = mat\n\n elif arg_kind == 'ts':\n ts = TimeStepper(0.0, 1.0, 1.0, 5)\n str_args.append('ts')\n args['ts'] = ts\n\n else:\n str_args.append('user%d' % ii)\n args[str_args[-1]] = None\n\n materials = Materials(materials)\n variables = Variables(variables)\n\n return args, str_args, materials, variables\n\nclass Test(TestCommon):\n\n @staticmethod\n def from_conf(conf, options):\n from sfepy.discrete import Integral\n from sfepy.discrete.fem import Mesh, FEDomain\n\n domains = []\n for filename in filename_meshes:\n mesh = "},"completion":{"kind":"string","value":"Mesh.from_file(filename)"},"api":{"kind":"string","value":"sfepy.discrete.fem.Mesh.from_file"}}},{"rowIdx":96,"cells":{"prompt":{"kind":"string","value":"from __future__ import absolute_import\nfrom copy import copy\n\nimport numpy as nm\n\nfrom sfepy.base.testing import TestCommon\nfrom sfepy.base.base import ordered_iteritems\nfrom sfepy import data_dir\n\nfilename_meshes = [data_dir + '/meshes/elements/%s_2.mesh' % geom\n for geom in ['1_2', '2_3', '2_4', '3_4', '3_8', '3_2_4']]\n\ndef make_term_args(arg_shapes, arg_kinds, arg_types, ats_mode, domain,\n material_value=None, poly_space_base=None):\n from sfepy.base.base import basestr\n from sfepy.discrete import FieldVariable, Material, Variables, Materials\n from sfepy.discrete.fem import Field\n from sfepy.solvers.ts import TimeStepper\n from sfepy.mechanics.tensors import dim2sym\n\n omega = domain.regions['Omega']\n dim = domain.shape.dim\n sym = dim2sym(dim)\n\n def _parse_scalar_shape(sh):\n if isinstance(sh, basestr):\n if sh == 'D':\n return dim\n\n elif sh == 'D2':\n return dim**2\n\n elif sh == 'S':\n return sym\n\n elif sh == 'N': # General number ;)\n return 1\n\n else:\n return int(sh)\n\n else:\n return sh\n\n def _parse_tuple_shape(sh):\n if isinstance(sh, basestr):\n return [_parse_scalar_shape(ii.strip()) for ii in sh.split(',')]\n\n else:\n return (int(sh),)\n\n args = {}\n str_args = []\n materials = []\n variables = []\n for ii, arg_kind in enumerate(arg_kinds):\n if arg_kind != 'ts':\n if ats_mode is not None:\n extended_ats = arg_types[ii] + ('/%s' % ats_mode)\n\n else:\n extended_ats = arg_types[ii]\n\n try:\n sh = arg_shapes[arg_types[ii]]\n\n except KeyError:\n sh = arg_shapes[extended_ats]\n\n if arg_kind.endswith('variable'):\n shape = _parse_scalar_shape(sh[0] if isinstance(sh, tuple) else sh)\n field = Field.from_args('f%d' % ii, nm.float64, shape, omega,\n approx_order=1,\n poly_space_base=poly_space_base)\n\n if arg_kind == 'virtual_variable':\n if sh[1] is not None:\n istate = arg_types.index(sh[1])\n\n else:\n # Only virtual variable in arguments.\n istate = -1\n # -> Make fake variable.\n var = FieldVariable('u-1', 'unknown', field)\n var.set_constant(0.0)\n variables.append(var)\n\n var = FieldVariable('v', 'test', field,\n primary_var_name='u%d' % istate)\n\n elif arg_kind == 'state_variable':\n var = FieldVariable('u%d' % ii, 'unknown', field)\n var.set_constant(0.0)\n\n elif arg_kind == 'parameter_variable':\n var = FieldVariable('p%d' % ii, 'parameter', field,\n primary_var_name='(set-to-None)')\n var.set_constant(0.0)\n\n variables.append(var)\n str_args.append(var.name)\n args[var.name] = var\n\n elif arg_kind.endswith('material'):\n if sh is None: # Switched-off opt_material.\n continue\n\n prefix = ''\n if isinstance(sh, basestr):\n aux = sh.split(':')\n if len(aux) == 2:\n prefix, sh = aux\n\n if material_value is None:\n material_value = 1.0\n\n shape = _parse_tuple_shape(sh)\n if (len(shape) > 1) or (shape[0] > 1):\n if ((len(shape) == 2) and (shape[0] == shape[1])\n and (material_value != 0.0)):\n # Identity matrix.\n val = nm.eye(shape[0], dtype=nm.float64)\n\n else:\n # Array.\n val = nm.empty(shape, dtype=nm.float64)\n val.fill(material_value)\n\n values = {'%sc%d' % (prefix, ii)\n : val}\n\n elif (len(shape) == 1) and (shape[0] == 1):\n # Single scalar as a special value.\n values = {'.c%d' % ii : material_value}\n\n else:\n raise ValueError('wrong material shape! (%s)' % shape)\n\n mat = Material('m%d' % ii, values=values)\n\n materials.append(mat)\n str_args.append(mat.name + '.' + 'c%d' % ii)\n args[mat.name] = mat\n\n elif arg_kind == 'ts':\n ts = TimeStepper(0.0, 1.0, 1.0, 5)\n str_args.append('ts')\n args['ts'] = ts\n\n else:\n str_args.append('user%d' % ii)\n args[str_args[-1]] = None\n\n materials = Materials(materials)\n variables = Variables(variables)\n\n return args, str_args, materials, variables\n\nclass Test(TestCommon):\n\n @staticmethod\n def from_conf(conf, options):\n from sfepy.discrete import Integral\n from sfepy.discrete.fem import Mesh, FEDomain\n\n domains = []\n for filename in filename_meshes:\n mesh = Mesh.from_file(filename)\n domain = FEDomain('domain_%s' % mesh.name.replace(data_dir, ''),\n mesh)\n domain.create_region('Omega', 'all')\n domain.create_region('Gamma', 'vertices of surface', 'facet')\n\n domains.append(domain)\n\n integral = Integral('i', order=3)\n qp_coors, qp_weights = integral.get_qp('3_8')\n custom_integral = Integral('i', coors=qp_coors, weights=qp_weights,\n order='custom')\n\n test = Test(domains=domains, integral=integral,\n custom_integral=custom_integral,\n conf=conf, options=options)\n return test\n\n def test_term_call_modes(self):\n from sfepy.terms import term_table\n ok = True\n\n failed = []\n for domain in self.domains:\n self.report('domain: %s' % domain.name)\n\n domain_geometry = list(domain.geom_els.values())[0].name\n if domain.shape.dim != domain.shape.tdim:\n domain_geometry = '%d_%s' % (domain.shape.dim, domain_geometry)\n\n for _, term_cls in "},"completion":{"kind":"string","value":"ordered_iteritems(term_table)"},"api":{"kind":"string","value":"sfepy.base.base.ordered_iteritems"}}},{"rowIdx":97,"cells":{"prompt":{"kind":"string","value":"from __future__ import absolute_import\nfrom copy import copy\n\nimport numpy as nm\n\nfrom sfepy.base.testing import TestCommon\nfrom sfepy.base.base import ordered_iteritems\nfrom sfepy import data_dir\n\nfilename_meshes = [data_dir + '/meshes/elements/%s_2.mesh' % geom\n for geom in ['1_2', '2_3', '2_4', '3_4', '3_8', '3_2_4']]\n\ndef make_term_args(arg_shapes, arg_kinds, arg_types, ats_mode, domain,\n material_value=None, poly_space_base=None):\n from sfepy.base.base import basestr\n from sfepy.discrete import FieldVariable, Material, Variables, Materials\n from sfepy.discrete.fem import Field\n from sfepy.solvers.ts import TimeStepper\n from sfepy.mechanics.tensors import dim2sym\n\n omega = domain.regions['Omega']\n dim = domain.shape.dim\n sym = dim2sym(dim)\n\n def _parse_scalar_shape(sh):\n if isinstance(sh, basestr):\n if sh == 'D':\n return dim\n\n elif sh == 'D2':\n return dim**2\n\n elif sh == 'S':\n return sym\n\n elif sh == 'N': # General number ;)\n return 1\n\n else:\n return int(sh)\n\n else:\n return sh\n\n def _parse_tuple_shape(sh):\n if isinstance(sh, basestr):\n return [_parse_scalar_shape(ii.strip()) for ii in sh.split(',')]\n\n else:\n return (int(sh),)\n\n args = {}\n str_args = []\n materials = []\n variables = []\n for ii, arg_kind in enumerate(arg_kinds):\n if arg_kind != 'ts':\n if ats_mode is not None:\n extended_ats = arg_types[ii] + ('/%s' % ats_mode)\n\n else:\n extended_ats = arg_types[ii]\n\n try:\n sh = arg_shapes[arg_types[ii]]\n\n except KeyError:\n sh = arg_shapes[extended_ats]\n\n if arg_kind.endswith('variable'):\n shape = _parse_scalar_shape(sh[0] if isinstance(sh, tuple) else sh)\n field = Field.from_args('f%d' % ii, nm.float64, shape, omega,\n approx_order=1,\n poly_space_base=poly_space_base)\n\n if arg_kind == 'virtual_variable':\n if sh[1] is not None:\n istate = arg_types.index(sh[1])\n\n else:\n # Only virtual variable in arguments.\n istate = -1\n # -> Make fake variable.\n var = FieldVariable('u-1', 'unknown', field)\n var.set_constant(0.0)\n variables.append(var)\n\n var = FieldVariable('v', 'test', field,\n primary_var_name='u%d' % istate)\n\n elif arg_kind == 'state_variable':\n var = FieldVariable('u%d' % ii, 'unknown', field)\n var.set_constant(0.0)\n\n elif arg_kind == 'parameter_variable':\n var = FieldVariable('p%d' % ii, 'parameter', field,\n primary_var_name='(set-to-None)')\n var.set_constant(0.0)\n\n variables.append(var)\n str_args.append(var.name)\n args[var.name] = var\n\n elif arg_kind.endswith('material'):\n if sh is None: # Switched-off opt_material.\n continue\n\n prefix = ''\n if isinstance(sh, basestr):\n aux = sh.split(':')\n if len(aux) == 2:\n prefix, sh = aux\n\n if material_value is None:\n material_value = 1.0\n\n shape = _parse_tuple_shape(sh)\n if (len(shape) > 1) or (shape[0] > 1):\n if ((len(shape) == 2) and (shape[0] == shape[1])\n and (material_value != 0.0)):\n # Identity matrix.\n val = nm.eye(shape[0], dtype=nm.float64)\n\n else:\n # Array.\n val = nm.empty(shape, dtype=nm.float64)\n val.fill(material_value)\n\n values = {'%sc%d' % (prefix, ii)\n : val}\n\n elif (len(shape) == 1) and (shape[0] == 1):\n # Single scalar as a special value.\n values = {'.c%d' % ii : material_value}\n\n else:\n raise ValueError('wrong material shape! (%s)' % shape)\n\n mat = "},"completion":{"kind":"string","value":"Material('m%d' % ii, values=values)"},"api":{"kind":"string","value":"sfepy.discrete.Material"}}},{"rowIdx":98,"cells":{"prompt":{"kind":"string","value":"from __future__ import absolute_import\nfrom copy import copy\n\nimport numpy as nm\n\nfrom sfepy.base.testing import TestCommon\nfrom sfepy.base.base import ordered_iteritems\nfrom sfepy import data_dir\n\nfilename_meshes = [data_dir + '/meshes/elements/%s_2.mesh' % geom\n for geom in ['1_2', '2_3', '2_4', '3_4', '3_8', '3_2_4']]\n\ndef make_term_args(arg_shapes, arg_kinds, arg_types, ats_mode, domain,\n material_value=None, poly_space_base=None):\n from sfepy.base.base import basestr\n from sfepy.discrete import FieldVariable, Material, Variables, Materials\n from sfepy.discrete.fem import Field\n from sfepy.solvers.ts import TimeStepper\n from sfepy.mechanics.tensors import dim2sym\n\n omega = domain.regions['Omega']\n dim = domain.shape.dim\n sym = dim2sym(dim)\n\n def _parse_scalar_shape(sh):\n if isinstance(sh, basestr):\n if sh == 'D':\n return dim\n\n elif sh == 'D2':\n return dim**2\n\n elif sh == 'S':\n return sym\n\n elif sh == 'N': # General number ;)\n return 1\n\n else:\n return int(sh)\n\n else:\n return sh\n\n def _parse_tuple_shape(sh):\n if isinstance(sh, basestr):\n return [_parse_scalar_shape(ii.strip()) for ii in sh.split(',')]\n\n else:\n return (int(sh),)\n\n args = {}\n str_args = []\n materials = []\n variables = []\n for ii, arg_kind in enumerate(arg_kinds):\n if arg_kind != 'ts':\n if ats_mode is not None:\n extended_ats = arg_types[ii] + ('/%s' % ats_mode)\n\n else:\n extended_ats = arg_types[ii]\n\n try:\n sh = arg_shapes[arg_types[ii]]\n\n except KeyError:\n sh = arg_shapes[extended_ats]\n\n if arg_kind.endswith('variable'):\n shape = _parse_scalar_shape(sh[0] if isinstance(sh, tuple) else sh)\n field = Field.from_args('f%d' % ii, nm.float64, shape, omega,\n approx_order=1,\n poly_space_base=poly_space_base)\n\n if arg_kind == 'virtual_variable':\n if sh[1] is not None:\n istate = arg_types.index(sh[1])\n\n else:\n # Only virtual variable in arguments.\n istate = -1\n # -> Make fake variable.\n var = FieldVariable('u-1', 'unknown', field)\n var.set_constant(0.0)\n variables.append(var)\n\n var = FieldVariable('v', 'test', field,\n primary_var_name='u%d' % istate)\n\n elif arg_kind == 'state_variable':\n var = FieldVariable('u%d' % ii, 'unknown', field)\n var.set_constant(0.0)\n\n elif arg_kind == 'parameter_variable':\n var = FieldVariable('p%d' % ii, 'parameter', field,\n primary_var_name='(set-to-None)')\n var.set_constant(0.0)\n\n variables.append(var)\n str_args.append(var.name)\n args[var.name] = var\n\n elif arg_kind.endswith('material'):\n if sh is None: # Switched-off opt_material.\n continue\n\n prefix = ''\n if isinstance(sh, basestr):\n aux = sh.split(':')\n if len(aux) == 2:\n prefix, sh = aux\n\n if material_value is None:\n material_value = 1.0\n\n shape = _parse_tuple_shape(sh)\n if (len(shape) > 1) or (shape[0] > 1):\n if ((len(shape) == 2) and (shape[0] == shape[1])\n and (material_value != 0.0)):\n # Identity matrix.\n val = nm.eye(shape[0], dtype=nm.float64)\n\n else:\n # Array.\n val = nm.empty(shape, dtype=nm.float64)\n val.fill(material_value)\n\n values = {'%sc%d' % (prefix, ii)\n : val}\n\n elif (len(shape) == 1) and (shape[0] == 1):\n # Single scalar as a special value.\n values = {'.c%d' % ii : material_value}\n\n else:\n raise ValueError('wrong material shape! (%s)' % shape)\n\n mat = Material('m%d' % ii, values=values)\n\n materials.append(mat)\n str_args.append(mat.name + '.' + 'c%d' % ii)\n args[mat.name] = mat\n\n elif arg_kind == 'ts':\n ts = TimeStepper(0.0, 1.0, 1.0, 5)\n str_args.append('ts')\n args['ts'] = ts\n\n else:\n str_args.append('user%d' % ii)\n args[str_args[-1]] = None\n\n materials = Materials(materials)\n variables = Variables(variables)\n\n return args, str_args, materials, variables\n\nclass Test(TestCommon):\n\n @staticmethod\n def from_conf(conf, options):\n from sfepy.discrete import Integral\n from sfepy.discrete.fem import Mesh, FEDomain\n\n domains = []\n for filename in filename_meshes:\n mesh = Mesh.from_file(filename)\n domain = FEDomain('domain_%s' % mesh.name.replace(data_dir, ''),\n mesh)\n domain.create_region('Omega', 'all')\n domain.create_region('Gamma', 'vertices of surface', 'facet')\n\n domains.append(domain)\n\n integral = Integral('i', order=3)\n qp_coors, qp_weights = integral.get_qp('3_8')\n custom_integral = Integral('i', coors=qp_coors, weights=qp_weights,\n order='custom')\n\n test = Test(domains=domains, integral=integral,\n custom_integral=custom_integral,\n conf=conf, options=options)\n return test\n\n def test_term_call_modes(self):\n from sfepy.terms import term_table\n ok = True\n\n failed = []\n for domain in self.domains:\n self.report('domain: %s' % domain.name)\n\n domain_geometry = list(domain.geom_els.values())[0].name\n if domain.shape.dim != domain.shape.tdim:\n domain_geometry = '%d_%s' % (domain.shape.dim, domain_geometry)\n\n for _, term_cls in ordered_iteritems(term_table):\n if (domain_geometry not in term_cls.geometries) \\\n or (\"dg\" in term_cls.name) \\\n or (term_cls.name == \"dw_ns_dot_grad_s\"):\n continue\n\n vint = ('volume', 'point', 'custom')\n rname = 'Omega' if term_cls.integration in vint else 'Gamma'\n\n self.report('<-- %s ...' % term_cls.name)\n\n if rname == 'Gamma' and domain.mesh.dim == 1:\n self.report('--> 1D Gamma region: not tested!')\n\n elif term_cls.arg_shapes:\n try:\n _ok = self._test_single_term(term_cls, domain, rname)\n\n except:\n _ok = False\n\n if not _ok:\n failed.append((domain.name, term_cls.name))\n\n ok = ok and _ok\n self.report('--> ok: %s' % _ok)\n\n else:\n self.report('--> not tested!')\n\n self.report('failed:', failed)\n\n return ok\n\n def _test_single_term(self, term_cls, domain, rname):\n from sfepy.terms import Term\n from sfepy.terms.terms import get_arg_kinds\n\n ok = True\n\n term_call = term_cls.name + '(%s)'\n\n arg_shapes_list = term_cls.arg_shapes\n if not isinstance(arg_shapes_list, list):\n arg_shapes_list = [arg_shapes_list]\n\n if term_cls.integration != 'custom':\n integral = self.integral\n\n else:\n integral = self.custom_integral\n\n poly_space_base = getattr(term_cls, 'poly_space_base', 'lagrange')\n\n prev_shapes = {}\n for _arg_shapes in arg_shapes_list:\n # Unset shapes are taken from the previous iteration.\n arg_shapes = copy(prev_shapes)\n arg_shapes.update(_arg_shapes)\n prev_shapes = arg_shapes\n\n self.report('arg_shapes:', arg_shapes)\n arg_types = term_cls.arg_types\n if not isinstance(arg_types[0], tuple):\n arg_types = (arg_types,)\n\n for iat, ats in enumerate(arg_types):\n self.report('arg_types:', ats)\n\n arg_kinds = "},"completion":{"kind":"string","value":"get_arg_kinds(ats)"},"api":{"kind":"string","value":"sfepy.terms.terms.get_arg_kinds"}}},{"rowIdx":99,"cells":{"prompt":{"kind":"string","value":"from __future__ import absolute_import\nfrom copy import copy\n\nimport numpy as nm\n\nfrom sfepy.base.testing import TestCommon\nfrom sfepy.base.base import ordered_iteritems\nfrom sfepy import data_dir\n\nfilename_meshes = [data_dir + '/meshes/elements/%s_2.mesh' % geom\n for geom in ['1_2', '2_3', '2_4', '3_4', '3_8', '3_2_4']]\n\ndef make_term_args(arg_shapes, arg_kinds, arg_types, ats_mode, domain,\n material_value=None, poly_space_base=None):\n from sfepy.base.base import basestr\n from sfepy.discrete import FieldVariable, Material, Variables, Materials\n from sfepy.discrete.fem import Field\n from sfepy.solvers.ts import TimeStepper\n from sfepy.mechanics.tensors import dim2sym\n\n omega = domain.regions['Omega']\n dim = domain.shape.dim\n sym = dim2sym(dim)\n\n def _parse_scalar_shape(sh):\n if isinstance(sh, basestr):\n if sh == 'D':\n return dim\n\n elif sh == 'D2':\n return dim**2\n\n elif sh == 'S':\n return sym\n\n elif sh == 'N': # General number ;)\n return 1\n\n else:\n return int(sh)\n\n else:\n return sh\n\n def _parse_tuple_shape(sh):\n if isinstance(sh, basestr):\n return [_parse_scalar_shape(ii.strip()) for ii in sh.split(',')]\n\n else:\n return (int(sh),)\n\n args = {}\n str_args = []\n materials = []\n variables = []\n for ii, arg_kind in enumerate(arg_kinds):\n if arg_kind != 'ts':\n if ats_mode is not None:\n extended_ats = arg_types[ii] + ('/%s' % ats_mode)\n\n else:\n extended_ats = arg_types[ii]\n\n try:\n sh = arg_shapes[arg_types[ii]]\n\n except KeyError:\n sh = arg_shapes[extended_ats]\n\n if arg_kind.endswith('variable'):\n shape = _parse_scalar_shape(sh[0] if isinstance(sh, tuple) else sh)\n field = Field.from_args('f%d' % ii, nm.float64, shape, omega,\n approx_order=1,\n poly_space_base=poly_space_base)\n\n if arg_kind == 'virtual_variable':\n if sh[1] is not None:\n istate = arg_types.index(sh[1])\n\n else:\n # Only virtual variable in arguments.\n istate = -1\n # -> Make fake variable.\n var = FieldVariable('u-1', 'unknown', field)\n var.set_constant(0.0)\n variables.append(var)\n\n var = FieldVariable('v', 'test', field,\n primary_var_name='u%d' % istate)\n\n elif arg_kind == 'state_variable':\n var = FieldVariable('u%d' % ii, 'unknown', field)\n var.set_constant(0.0)\n\n elif arg_kind == 'parameter_variable':\n var = FieldVariable('p%d' % ii, 'parameter', field,\n primary_var_name='(set-to-None)')\n var.set_constant(0.0)\n\n variables.append(var)\n str_args.append(var.name)\n args[var.name] = var\n\n elif arg_kind.endswith('material'):\n if sh is None: # Switched-off opt_material.\n continue\n\n prefix = ''\n if isinstance(sh, basestr):\n aux = sh.split(':')\n if len(aux) == 2:\n prefix, sh = aux\n\n if material_value is None:\n material_value = 1.0\n\n shape = _parse_tuple_shape(sh)\n if (len(shape) > 1) or (shape[0] > 1):\n if ((len(shape) == 2) and (shape[0] == shape[1])\n and (material_value != 0.0)):\n # Identity matrix.\n val = nm.eye(shape[0], dtype=nm.float64)\n\n else:\n # Array.\n val = nm.empty(shape, dtype=nm.float64)\n val.fill(material_value)\n\n values = {'%sc%d' % (prefix, ii)\n : val}\n\n elif (len(shape) == 1) and (shape[0] == 1):\n # Single scalar as a special value.\n values = {'.c%d' % ii : material_value}\n\n else:\n raise ValueError('wrong material shape! (%s)' % shape)\n\n mat = Material('m%d' % ii, values=values)\n\n materials.append(mat)\n str_args.append(mat.name + '.' + 'c%d' % ii)\n args[mat.name] = mat\n\n elif arg_kind == 'ts':\n ts = TimeStepper(0.0, 1.0, 1.0, 5)\n str_args.append('ts')\n args['ts'] = ts\n\n else:\n str_args.append('user%d' % ii)\n args[str_args[-1]] = None\n\n materials = Materials(materials)\n variables = Variables(variables)\n\n return args, str_args, materials, variables\n\nclass Test(TestCommon):\n\n @staticmethod\n def from_conf(conf, options):\n from sfepy.discrete import Integral\n from sfepy.discrete.fem import Mesh, FEDomain\n\n domains = []\n for filename in filename_meshes:\n mesh = Mesh.from_file(filename)\n domain = FEDomain('domain_%s' % mesh.name.replace(data_dir, ''),\n mesh)\n domain.create_region('Omega', 'all')\n domain.create_region('Gamma', 'vertices of surface', 'facet')\n\n domains.append(domain)\n\n integral = Integral('i', order=3)\n qp_coors, qp_weights = integral.get_qp('3_8')\n custom_integral = Integral('i', coors=qp_coors, weights=qp_weights,\n order='custom')\n\n test = Test(domains=domains, integral=integral,\n custom_integral=custom_integral,\n conf=conf, options=options)\n return test\n\n def test_term_call_modes(self):\n from sfepy.terms import term_table\n ok = True\n\n failed = []\n for domain in self.domains:\n self.report('domain: %s' % domain.name)\n\n domain_geometry = list(domain.geom_els.values())[0].name\n if domain.shape.dim != domain.shape.tdim:\n domain_geometry = '%d_%s' % (domain.shape.dim, domain_geometry)\n\n for _, term_cls in ordered_iteritems(term_table):\n if (domain_geometry not in term_cls.geometries) \\\n or (\"dg\" in term_cls.name) \\\n or (term_cls.name == \"dw_ns_dot_grad_s\"):\n continue\n\n vint = ('volume', 'point', 'custom')\n rname = 'Omega' if term_cls.integration in vint else 'Gamma'\n\n self.report('<-- %s ...' % term_cls.name)\n\n if rname == 'Gamma' and domain.mesh.dim == 1:\n self.report('--> 1D Gamma region: not tested!')\n\n elif term_cls.arg_shapes:\n try:\n _ok = self._test_single_term(term_cls, domain, rname)\n\n except:\n _ok = False\n\n if not _ok:\n failed.append((domain.name, term_cls.name))\n\n ok = ok and _ok\n self.report('--> ok: %s' % _ok)\n\n else:\n self.report('--> not tested!')\n\n self.report('failed:', failed)\n\n return ok\n\n def _test_single_term(self, term_cls, domain, rname):\n from sfepy.terms import Term\n from sfepy.terms.terms import get_arg_kinds\n\n ok = True\n\n term_call = term_cls.name + '(%s)'\n\n arg_shapes_list = term_cls.arg_shapes\n if not isinstance(arg_shapes_list, list):\n arg_shapes_list = [arg_shapes_list]\n\n if term_cls.integration != 'custom':\n integral = self.integral\n\n else:\n integral = self.custom_integral\n\n poly_space_base = getattr(term_cls, 'poly_space_base', 'lagrange')\n\n prev_shapes = {}\n for _arg_shapes in arg_shapes_list:\n # Unset shapes are taken from the previous iteration.\n arg_shapes = copy(prev_shapes)\n arg_shapes.update(_arg_shapes)\n prev_shapes = arg_shapes\n\n self.report('arg_shapes:', arg_shapes)\n arg_types = term_cls.arg_types\n if not isinstance(arg_types[0], tuple):\n arg_types = (arg_types,)\n\n for iat, ats in enumerate(arg_types):\n self.report('arg_types:', ats)\n\n arg_kinds = get_arg_kinds(ats)\n modes = getattr(term_cls, 'modes', None)\n mode = modes[iat] if modes is not None else None\n\n if 'dw_s_dot_grad_i_s' in term_cls.name:\n material_value = 0.0\n\n else:\n material_value = 1.0\n aux = make_term_args(arg_shapes, arg_kinds, ats, mode, domain,\n material_value=material_value,\n poly_space_base=poly_space_base)\n args, str_args, materials, variables = aux\n\n self.report('args:', str_args)\n\n name = term_call % (', '.join(str_args))\n term = "},"completion":{"kind":"string","value":"Term.new(name, integral, domain.regions[rname], **args)"},"api":{"kind":"string","value":"sfepy.terms.Term.new"}}}],"truncated":false,"partial":false},"paginationData":{"pageIndex":0,"numItemsPerPage":100,"numTotalItems":1364,"offset":0,"length":100}},"jwt":"eyJhbGciOiJFZERTQSJ9.eyJyZWFkIjp0cnVlLCJwZXJtaXNzaW9ucyI6eyJyZXBvLmNvbnRlbnQucmVhZCI6dHJ1ZX0sImlhdCI6MTc1NDY1Mzc4MCwic3ViIjoiL2RhdGFzZXRzL2x1bmEtY29kZS9zZmVweSIsImV4cCI6MTc1NDY1NzM4MCwiaXNzIjoiaHR0cHM6Ly9odWdnaW5nZmFjZS5jbyJ9.FCZixMMV3SYTuXVHmHx5Qv33X4swkiw8727R_ujTSimdUYmBIMRPXtuevT9ubtWdmaNxx_FJs-D8YzVJGDsYAQ","displayUrls":true},"discussionsStats":{"closed":0,"open":1,"total":1},"fullWidth":true,"hasGatedAccess":true,"hasFullAccess":true,"isEmbedded":false,"savedQueries":{"community":[],"user":[]}}">

Datasets:

---

luna-code

/

sfepy

like 0

Follow

Learning UnkNown librAry 5

Dataset card Data Studio Files Files and versions Community

1

Subset (1)

default · 1.52k rows

default (1.52k rows)

Split (2)

train · 1.36k rows

train (1.36k rows)test (159 rows)

SQL

Console

prompt stringlengths 174 59.5k	completion stringlengths 7 228	api stringlengths 12 64
import numpy as nm from sfepy.linalg import dot_sequences from sfepy.terms.terms import Term, terms class DivGradTerm(Term): r""" Diffusion term. :Definition: .. math:: \int_{\Omega} \nu\ \nabla \ul{v} : \nabla \ul{u} \mbox{ , } \int_{\Omega} \nu\ \nabla \ul{u} : \nabla \ul{w} \\ \int_{\Omega} \nabla \ul{v} : \nabla \ul{u} \mbox{ , } \int_{\Omega} \nabla \ul{u} : \nabla \ul{w} :Arguments 1: - material : :math:`\nu` (viscosity, optional) - virtual : :math:`\ul{v}` - state : :math:`\ul{u}` :Arguments 2: - material : :math:`\nu` (viscosity, optional) - parameter_1 : :math:`\ul{u}` - parameter_2 : :math:`\ul{w}` """ name = 'dw_div_grad' arg_types = (('opt_material', 'virtual', 'state'), ('opt_material', 'parameter_1', 'parameter_2')) arg_shapes = {'opt_material' : '1, 1', 'virtual' : ('D', 'state'), 'state' : 'D', 'parameter_1' : 'D', 'parameter_2' : 'D'} modes = ('weak', 'eval') function = staticmethod(terms.term_ns_asm_div_grad) def d_div_grad(self, out, grad1, grad2, mat, vg, fmode): sh = grad1.shape g1 = grad1.reshape((sh[0], sh[1], sh[2] * sh[3])) g2 = grad2.reshape((sh[0], sh[1], sh[2] * sh[3])) aux = mat *	dot_sequences(g1[..., None], g2, 'ATB')	sfepy.linalg.dot_sequences
#!/usr/bin/env python3 # -*- coding: utf-8 -*- """ Created on Mon Dec 28 09:33:53 2020 @author: dhulls """ from __future__ import print_function from __future__ import absolute_import from argparse import ArgumentParser import numpy as nm import sys sys.path.append('.') from sfepy.base.base import IndexedStruct, Struct from sfepy.discrete import (FieldVariable, Material, Integral, Function, Equation, Equations, Problem) from sfepy.discrete.fem import Mesh, FEDomain, Field from sfepy.terms import Term from sfepy.discrete.conditions import Conditions, EssentialBC, InitialCondition from sfepy.solvers.ls import ScipyDirect from sfepy.solvers.nls import Newton from sfepy.postprocess.viewer import Viewer from sfepy.postprocess.probes_vtk import ProbeFromFile, Probe import numpy as np helps = { 'show' : 'show the results figure', } from sfepy import data_dir parser = ArgumentParser() parser.add_argument('--version', action="https://huggingface.co/datasets/luna-code/sfepy/version", version='%(prog)s') parser.add_argument('-s', '--show', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='show', default=False, help=helps['show']) options = parser.parse_args() mesh =	Mesh.from_file(data_dir + '/meshes/3d/fluid_mesh.inp')	sfepy.discrete.fem.Mesh.from_file
#!/usr/bin/env python3 # -*- coding: utf-8 -*- """ Created on Mon Dec 28 09:33:53 2020 @author: dhulls """ from __future__ import print_function from __future__ import absolute_import from argparse import ArgumentParser import numpy as nm import sys sys.path.append('.') from sfepy.base.base import IndexedStruct, Struct from sfepy.discrete import (FieldVariable, Material, Integral, Function, Equation, Equations, Problem) from sfepy.discrete.fem import Mesh, FEDomain, Field from sfepy.terms import Term from sfepy.discrete.conditions import Conditions, EssentialBC, InitialCondition from sfepy.solvers.ls import ScipyDirect from sfepy.solvers.nls import Newton from sfepy.postprocess.viewer import Viewer from sfepy.postprocess.probes_vtk import ProbeFromFile, Probe import numpy as np helps = { 'show' : 'show the results figure', } from sfepy import data_dir parser = ArgumentParser() parser.add_argument('--version', action="https://huggingface.co/datasets/luna-code/sfepy/version", version='%(prog)s') parser.add_argument('-s', '--show', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='show', default=False, help=helps['show']) options = parser.parse_args() mesh = Mesh.from_file(data_dir + '/meshes/3d/fluid_mesh.inp') domain =	FEDomain('domain', mesh)	sfepy.discrete.fem.FEDomain
#!/usr/bin/env python3 # -*- coding: utf-8 -*- """ Created on Mon Dec 28 09:33:53 2020 @author: dhulls """ from __future__ import print_function from __future__ import absolute_import from argparse import ArgumentParser import numpy as nm import sys sys.path.append('.') from sfepy.base.base import IndexedStruct, Struct from sfepy.discrete import (FieldVariable, Material, Integral, Function, Equation, Equations, Problem) from sfepy.discrete.fem import Mesh, FEDomain, Field from sfepy.terms import Term from sfepy.discrete.conditions import Conditions, EssentialBC, InitialCondition from sfepy.solvers.ls import ScipyDirect from sfepy.solvers.nls import Newton from sfepy.postprocess.viewer import Viewer from sfepy.postprocess.probes_vtk import ProbeFromFile, Probe import numpy as np helps = { 'show' : 'show the results figure', } from sfepy import data_dir parser = ArgumentParser() parser.add_argument('--version', action="https://huggingface.co/datasets/luna-code/sfepy/version", version='%(prog)s') parser.add_argument('-s', '--show', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='show', default=False, help=helps['show']) options = parser.parse_args() mesh = Mesh.from_file(data_dir + '/meshes/3d/fluid_mesh.inp') domain = FEDomain('domain', mesh) omega = domain.create_region('Omega', 'all') field_1 =	Field.from_args(name='3_velocity', dtype=nm.float64, shape=3, region=omega, approx_order=1)	sfepy.discrete.fem.Field.from_args
#!/usr/bin/env python3 # -*- coding: utf-8 -*- """ Created on Mon Dec 28 09:33:53 2020 @author: dhulls """ from __future__ import print_function from __future__ import absolute_import from argparse import ArgumentParser import numpy as nm import sys sys.path.append('.') from sfepy.base.base import IndexedStruct, Struct from sfepy.discrete import (FieldVariable, Material, Integral, Function, Equation, Equations, Problem) from sfepy.discrete.fem import Mesh, FEDomain, Field from sfepy.terms import Term from sfepy.discrete.conditions import Conditions, EssentialBC, InitialCondition from sfepy.solvers.ls import ScipyDirect from sfepy.solvers.nls import Newton from sfepy.postprocess.viewer import Viewer from sfepy.postprocess.probes_vtk import ProbeFromFile, Probe import numpy as np helps = { 'show' : 'show the results figure', } from sfepy import data_dir parser = ArgumentParser() parser.add_argument('--version', action="https://huggingface.co/datasets/luna-code/sfepy/version", version='%(prog)s') parser.add_argument('-s', '--show', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='show', default=False, help=helps['show']) options = parser.parse_args() mesh = Mesh.from_file(data_dir + '/meshes/3d/fluid_mesh.inp') domain = FEDomain('domain', mesh) omega = domain.create_region('Omega', 'all') field_1 = Field.from_args(name='3_velocity', dtype=nm.float64, shape=3, region=omega, approx_order=1) field_2 =	Field.from_args(name='pressure', dtype=nm.float64, shape=1, region=omega, approx_order=1)	sfepy.discrete.fem.Field.from_args
#!/usr/bin/env python3 # -*- coding: utf-8 -*- """ Created on Mon Dec 28 09:33:53 2020 @author: dhulls """ from __future__ import print_function from __future__ import absolute_import from argparse import ArgumentParser import numpy as nm import sys sys.path.append('.') from sfepy.base.base import IndexedStruct, Struct from sfepy.discrete import (FieldVariable, Material, Integral, Function, Equation, Equations, Problem) from sfepy.discrete.fem import Mesh, FEDomain, Field from sfepy.terms import Term from sfepy.discrete.conditions import Conditions, EssentialBC, InitialCondition from sfepy.solvers.ls import ScipyDirect from sfepy.solvers.nls import Newton from sfepy.postprocess.viewer import Viewer from sfepy.postprocess.probes_vtk import ProbeFromFile, Probe import numpy as np helps = { 'show' : 'show the results figure', } from sfepy import data_dir parser = ArgumentParser() parser.add_argument('--version', action="https://huggingface.co/datasets/luna-code/sfepy/version", version='%(prog)s') parser.add_argument('-s', '--show', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='show', default=False, help=helps['show']) options = parser.parse_args() mesh = Mesh.from_file(data_dir + '/meshes/3d/fluid_mesh.inp') domain = FEDomain('domain', mesh) omega = domain.create_region('Omega', 'all') field_1 = Field.from_args(name='3_velocity', dtype=nm.float64, shape=3, region=omega, approx_order=1) field_2 = Field.from_args(name='pressure', dtype=nm.float64, shape=1, region=omega, approx_order=1) region_0 = domain.create_region(name='Walls1', select='vertices in (y < -0.049)', kind='facet') region_1 = domain.create_region(name='Walls2', select='vertices in (y > 0.049)', kind='facet') region_2 = domain.create_region(name='Inlet', select='vertices in (x < -0.499)', kind='facet') region_3 = domain.create_region(name='Outlet', select='vertices in (x > -0.499)', kind='facet') ebc_1 = EssentialBC(name='Walls1', region=region_0, dofs={'u.[0,1,2]' : 0.0}) ebc_2 = EssentialBC(name='Walls2', region=region_1, dofs={'u.[0,1,2]' : 0.0}) ebc_3 = EssentialBC(name='Inlet', region=region_2, dofs={'u.0' : 1.0, 'u.[1,2]' : 0.0}) ebc_4 =	EssentialBC(name='Outlet', region=region_3, dofs={'p':0.0, 'u.[1,2]' : 0.0})	sfepy.discrete.conditions.EssentialBC
#!/usr/bin/env python3 # -*- coding: utf-8 -*- """ Created on Mon Dec 28 09:33:53 2020 @author: dhulls """ from __future__ import print_function from __future__ import absolute_import from argparse import ArgumentParser import numpy as nm import sys sys.path.append('.') from sfepy.base.base import IndexedStruct, Struct from sfepy.discrete import (FieldVariable, Material, Integral, Function, Equation, Equations, Problem) from sfepy.discrete.fem import Mesh, FEDomain, Field from sfepy.terms import Term from sfepy.discrete.conditions import Conditions, EssentialBC, InitialCondition from sfepy.solvers.ls import ScipyDirect from sfepy.solvers.nls import Newton from sfepy.postprocess.viewer import Viewer from sfepy.postprocess.probes_vtk import ProbeFromFile, Probe import numpy as np helps = { 'show' : 'show the results figure', } from sfepy import data_dir parser = ArgumentParser() parser.add_argument('--version', action="https://huggingface.co/datasets/luna-code/sfepy/version", version='%(prog)s') parser.add_argument('-s', '--show', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='show', default=False, help=helps['show']) options = parser.parse_args() mesh = Mesh.from_file(data_dir + '/meshes/3d/fluid_mesh.inp') domain = FEDomain('domain', mesh) omega = domain.create_region('Omega', 'all') field_1 = Field.from_args(name='3_velocity', dtype=nm.float64, shape=3, region=omega, approx_order=1) field_2 = Field.from_args(name='pressure', dtype=nm.float64, shape=1, region=omega, approx_order=1) region_0 = domain.create_region(name='Walls1', select='vertices in (y < -0.049)', kind='facet') region_1 = domain.create_region(name='Walls2', select='vertices in (y > 0.049)', kind='facet') region_2 = domain.create_region(name='Inlet', select='vertices in (x < -0.499)', kind='facet') region_3 = domain.create_region(name='Outlet', select='vertices in (x > -0.499)', kind='facet') ebc_1 = EssentialBC(name='Walls1', region=region_0, dofs={'u.[0,1,2]' : 0.0}) ebc_2 = EssentialBC(name='Walls2', region=region_1, dofs={'u.[0,1,2]' : 0.0}) ebc_3 = EssentialBC(name='Inlet', region=region_2, dofs={'u.0' : 1.0, 'u.[1,2]' : 0.0}) ebc_4 = EssentialBC(name='Outlet', region=region_3, dofs={'p':0.0, 'u.[1,2]' : 0.0}) viscosity =	Material(name='viscosity', value=1.25e-3)	sfepy.discrete.Material
#!/usr/bin/env python3 # -*- coding: utf-8 -*- """ Created on Mon Dec 28 09:33:53 2020 @author: dhulls """ from __future__ import print_function from __future__ import absolute_import from argparse import ArgumentParser import numpy as nm import sys sys.path.append('.') from sfepy.base.base import IndexedStruct, Struct from sfepy.discrete import (FieldVariable, Material, Integral, Function, Equation, Equations, Problem) from sfepy.discrete.fem import Mesh, FEDomain, Field from sfepy.terms import Term from sfepy.discrete.conditions import Conditions, EssentialBC, InitialCondition from sfepy.solvers.ls import ScipyDirect from sfepy.solvers.nls import Newton from sfepy.postprocess.viewer import Viewer from sfepy.postprocess.probes_vtk import ProbeFromFile, Probe import numpy as np helps = { 'show' : 'show the results figure', } from sfepy import data_dir parser = ArgumentParser() parser.add_argument('--version', action="https://huggingface.co/datasets/luna-code/sfepy/version", version='%(prog)s') parser.add_argument('-s', '--show', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='show', default=False, help=helps['show']) options = parser.parse_args() mesh = Mesh.from_file(data_dir + '/meshes/3d/fluid_mesh.inp') domain = FEDomain('domain', mesh) omega = domain.create_region('Omega', 'all') field_1 = Field.from_args(name='3_velocity', dtype=nm.float64, shape=3, region=omega, approx_order=1) field_2 = Field.from_args(name='pressure', dtype=nm.float64, shape=1, region=omega, approx_order=1) region_0 = domain.create_region(name='Walls1', select='vertices in (y < -0.049)', kind='facet') region_1 = domain.create_region(name='Walls2', select='vertices in (y > 0.049)', kind='facet') region_2 = domain.create_region(name='Inlet', select='vertices in (x < -0.499)', kind='facet') region_3 = domain.create_region(name='Outlet', select='vertices in (x > -0.499)', kind='facet') ebc_1 = EssentialBC(name='Walls1', region=region_0, dofs={'u.[0,1,2]' : 0.0}) ebc_2 = EssentialBC(name='Walls2', region=region_1, dofs={'u.[0,1,2]' : 0.0}) ebc_3 = EssentialBC(name='Inlet', region=region_2, dofs={'u.0' : 1.0, 'u.[1,2]' : 0.0}) ebc_4 = EssentialBC(name='Outlet', region=region_3, dofs={'p':0.0, 'u.[1,2]' : 0.0}) viscosity = Material(name='viscosity', value=1.25e-3) variable_1 =	FieldVariable('u', 'unknown', field_1)	sfepy.discrete.FieldVariable
#!/usr/bin/env python3 # -*- coding: utf-8 -*- """ Created on Mon Dec 28 09:33:53 2020 @author: dhulls """ from __future__ import print_function from __future__ import absolute_import from argparse import ArgumentParser import numpy as nm import sys sys.path.append('.') from sfepy.base.base import IndexedStruct, Struct from sfepy.discrete import (FieldVariable, Material, Integral, Function, Equation, Equations, Problem) from sfepy.discrete.fem import Mesh, FEDomain, Field from sfepy.terms import Term from sfepy.discrete.conditions import Conditions, EssentialBC, InitialCondition from sfepy.solvers.ls import ScipyDirect from sfepy.solvers.nls import Newton from sfepy.postprocess.viewer import Viewer from sfepy.postprocess.probes_vtk import ProbeFromFile, Probe import numpy as np helps = { 'show' : 'show the results figure', } from sfepy import data_dir parser = ArgumentParser() parser.add_argument('--version', action="https://huggingface.co/datasets/luna-code/sfepy/version", version='%(prog)s') parser.add_argument('-s', '--show', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='show', default=False, help=helps['show']) options = parser.parse_args() mesh = Mesh.from_file(data_dir + '/meshes/3d/fluid_mesh.inp') domain = FEDomain('domain', mesh) omega = domain.create_region('Omega', 'all') field_1 = Field.from_args(name='3_velocity', dtype=nm.float64, shape=3, region=omega, approx_order=1) field_2 = Field.from_args(name='pressure', dtype=nm.float64, shape=1, region=omega, approx_order=1) region_0 = domain.create_region(name='Walls1', select='vertices in (y < -0.049)', kind='facet') region_1 = domain.create_region(name='Walls2', select='vertices in (y > 0.049)', kind='facet') region_2 = domain.create_region(name='Inlet', select='vertices in (x < -0.499)', kind='facet') region_3 = domain.create_region(name='Outlet', select='vertices in (x > -0.499)', kind='facet') ebc_1 = EssentialBC(name='Walls1', region=region_0, dofs={'u.[0,1,2]' : 0.0}) ebc_2 = EssentialBC(name='Walls2', region=region_1, dofs={'u.[0,1,2]' : 0.0}) ebc_3 = EssentialBC(name='Inlet', region=region_2, dofs={'u.0' : 1.0, 'u.[1,2]' : 0.0}) ebc_4 = EssentialBC(name='Outlet', region=region_3, dofs={'p':0.0, 'u.[1,2]' : 0.0}) viscosity = Material(name='viscosity', value=1.25e-3) variable_1 = FieldVariable('u', 'unknown', field_1) variable_2 =	FieldVariable(name='v', kind='test', field=field_1, primary_var_name='u')	sfepy.discrete.FieldVariable
#!/usr/bin/env python3 # -*- coding: utf-8 -*- """ Created on Mon Dec 28 09:33:53 2020 @author: dhulls """ from __future__ import print_function from __future__ import absolute_import from argparse import ArgumentParser import numpy as nm import sys sys.path.append('.') from sfepy.base.base import IndexedStruct, Struct from sfepy.discrete import (FieldVariable, Material, Integral, Function, Equation, Equations, Problem) from sfepy.discrete.fem import Mesh, FEDomain, Field from sfepy.terms import Term from sfepy.discrete.conditions import Conditions, EssentialBC, InitialCondition from sfepy.solvers.ls import ScipyDirect from sfepy.solvers.nls import Newton from sfepy.postprocess.viewer import Viewer from sfepy.postprocess.probes_vtk import ProbeFromFile, Probe import numpy as np helps = { 'show' : 'show the results figure', } from sfepy import data_dir parser = ArgumentParser() parser.add_argument('--version', action="https://huggingface.co/datasets/luna-code/sfepy/version", version='%(prog)s') parser.add_argument('-s', '--show', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='show', default=False, help=helps['show']) options = parser.parse_args() mesh = Mesh.from_file(data_dir + '/meshes/3d/fluid_mesh.inp') domain = FEDomain('domain', mesh) omega = domain.create_region('Omega', 'all') field_1 = Field.from_args(name='3_velocity', dtype=nm.float64, shape=3, region=omega, approx_order=1) field_2 = Field.from_args(name='pressure', dtype=nm.float64, shape=1, region=omega, approx_order=1) region_0 = domain.create_region(name='Walls1', select='vertices in (y < -0.049)', kind='facet') region_1 = domain.create_region(name='Walls2', select='vertices in (y > 0.049)', kind='facet') region_2 = domain.create_region(name='Inlet', select='vertices in (x < -0.499)', kind='facet') region_3 = domain.create_region(name='Outlet', select='vertices in (x > -0.499)', kind='facet') ebc_1 = EssentialBC(name='Walls1', region=region_0, dofs={'u.[0,1,2]' : 0.0}) ebc_2 = EssentialBC(name='Walls2', region=region_1, dofs={'u.[0,1,2]' : 0.0}) ebc_3 = EssentialBC(name='Inlet', region=region_2, dofs={'u.0' : 1.0, 'u.[1,2]' : 0.0}) ebc_4 = EssentialBC(name='Outlet', region=region_3, dofs={'p':0.0, 'u.[1,2]' : 0.0}) viscosity = Material(name='viscosity', value=1.25e-3) variable_1 = FieldVariable('u', 'unknown', field_1) variable_2 = FieldVariable(name='v', kind='test', field=field_1, primary_var_name='u') variable_3 =	FieldVariable(name='p', kind='unknown', field=field_2)	sfepy.discrete.FieldVariable
#!/usr/bin/env python3 # -*- coding: utf-8 -*- """ Created on Mon Dec 28 09:33:53 2020 @author: dhulls """ from __future__ import print_function from __future__ import absolute_import from argparse import ArgumentParser import numpy as nm import sys sys.path.append('.') from sfepy.base.base import IndexedStruct, Struct from sfepy.discrete import (FieldVariable, Material, Integral, Function, Equation, Equations, Problem) from sfepy.discrete.fem import Mesh, FEDomain, Field from sfepy.terms import Term from sfepy.discrete.conditions import Conditions, EssentialBC, InitialCondition from sfepy.solvers.ls import ScipyDirect from sfepy.solvers.nls import Newton from sfepy.postprocess.viewer import Viewer from sfepy.postprocess.probes_vtk import ProbeFromFile, Probe import numpy as np helps = { 'show' : 'show the results figure', } from sfepy import data_dir parser = ArgumentParser() parser.add_argument('--version', action="https://huggingface.co/datasets/luna-code/sfepy/version", version='%(prog)s') parser.add_argument('-s', '--show', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='show', default=False, help=helps['show']) options = parser.parse_args() mesh = Mesh.from_file(data_dir + '/meshes/3d/fluid_mesh.inp') domain = FEDomain('domain', mesh) omega = domain.create_region('Omega', 'all') field_1 = Field.from_args(name='3_velocity', dtype=nm.float64, shape=3, region=omega, approx_order=1) field_2 = Field.from_args(name='pressure', dtype=nm.float64, shape=1, region=omega, approx_order=1) region_0 = domain.create_region(name='Walls1', select='vertices in (y < -0.049)', kind='facet') region_1 = domain.create_region(name='Walls2', select='vertices in (y > 0.049)', kind='facet') region_2 = domain.create_region(name='Inlet', select='vertices in (x < -0.499)', kind='facet') region_3 = domain.create_region(name='Outlet', select='vertices in (x > -0.499)', kind='facet') ebc_1 = EssentialBC(name='Walls1', region=region_0, dofs={'u.[0,1,2]' : 0.0}) ebc_2 = EssentialBC(name='Walls2', region=region_1, dofs={'u.[0,1,2]' : 0.0}) ebc_3 = EssentialBC(name='Inlet', region=region_2, dofs={'u.0' : 1.0, 'u.[1,2]' : 0.0}) ebc_4 = EssentialBC(name='Outlet', region=region_3, dofs={'p':0.0, 'u.[1,2]' : 0.0}) viscosity = Material(name='viscosity', value=1.25e-3) variable_1 = FieldVariable('u', 'unknown', field_1) variable_2 = FieldVariable(name='v', kind='test', field=field_1, primary_var_name='u') variable_3 = FieldVariable(name='p', kind='unknown', field=field_2) variable_4 =	FieldVariable(name='q', kind='test', field=field_2, primary_var_name='p')	sfepy.discrete.FieldVariable
#!/usr/bin/env python3 # -*- coding: utf-8 -*- """ Created on Mon Dec 28 09:33:53 2020 @author: dhulls """ from __future__ import print_function from __future__ import absolute_import from argparse import ArgumentParser import numpy as nm import sys sys.path.append('.') from sfepy.base.base import IndexedStruct, Struct from sfepy.discrete import (FieldVariable, Material, Integral, Function, Equation, Equations, Problem) from sfepy.discrete.fem import Mesh, FEDomain, Field from sfepy.terms import Term from sfepy.discrete.conditions import Conditions, EssentialBC, InitialCondition from sfepy.solvers.ls import ScipyDirect from sfepy.solvers.nls import Newton from sfepy.postprocess.viewer import Viewer from sfepy.postprocess.probes_vtk import ProbeFromFile, Probe import numpy as np helps = { 'show' : 'show the results figure', } from sfepy import data_dir parser = ArgumentParser() parser.add_argument('--version', action="https://huggingface.co/datasets/luna-code/sfepy/version", version='%(prog)s') parser.add_argument('-s', '--show', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='show', default=False, help=helps['show']) options = parser.parse_args() mesh = Mesh.from_file(data_dir + '/meshes/3d/fluid_mesh.inp') domain = FEDomain('domain', mesh) omega = domain.create_region('Omega', 'all') field_1 = Field.from_args(name='3_velocity', dtype=nm.float64, shape=3, region=omega, approx_order=1) field_2 = Field.from_args(name='pressure', dtype=nm.float64, shape=1, region=omega, approx_order=1) region_0 = domain.create_region(name='Walls1', select='vertices in (y < -0.049)', kind='facet') region_1 = domain.create_region(name='Walls2', select='vertices in (y > 0.049)', kind='facet') region_2 = domain.create_region(name='Inlet', select='vertices in (x < -0.499)', kind='facet') region_3 = domain.create_region(name='Outlet', select='vertices in (x > -0.499)', kind='facet') ebc_1 = EssentialBC(name='Walls1', region=region_0, dofs={'u.[0,1,2]' : 0.0}) ebc_2 = EssentialBC(name='Walls2', region=region_1, dofs={'u.[0,1,2]' : 0.0}) ebc_3 = EssentialBC(name='Inlet', region=region_2, dofs={'u.0' : 1.0, 'u.[1,2]' : 0.0}) ebc_4 = EssentialBC(name='Outlet', region=region_3, dofs={'p':0.0, 'u.[1,2]' : 0.0}) viscosity = Material(name='viscosity', value=1.25e-3) variable_1 = FieldVariable('u', 'unknown', field_1) variable_2 = FieldVariable(name='v', kind='test', field=field_1, primary_var_name='u') variable_3 = FieldVariable(name='p', kind='unknown', field=field_2) variable_4 = FieldVariable(name='q', kind='test', field=field_2, primary_var_name='p') integral_1 =	Integral('i1', order=2)	sfepy.discrete.Integral
#!/usr/bin/env python3 # -*- coding: utf-8 -*- """ Created on Mon Dec 28 09:33:53 2020 @author: dhulls """ from __future__ import print_function from __future__ import absolute_import from argparse import ArgumentParser import numpy as nm import sys sys.path.append('.') from sfepy.base.base import IndexedStruct, Struct from sfepy.discrete import (FieldVariable, Material, Integral, Function, Equation, Equations, Problem) from sfepy.discrete.fem import Mesh, FEDomain, Field from sfepy.terms import Term from sfepy.discrete.conditions import Conditions, EssentialBC, InitialCondition from sfepy.solvers.ls import ScipyDirect from sfepy.solvers.nls import Newton from sfepy.postprocess.viewer import Viewer from sfepy.postprocess.probes_vtk import ProbeFromFile, Probe import numpy as np helps = { 'show' : 'show the results figure', } from sfepy import data_dir parser = ArgumentParser() parser.add_argument('--version', action="https://huggingface.co/datasets/luna-code/sfepy/version", version='%(prog)s') parser.add_argument('-s', '--show', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='show', default=False, help=helps['show']) options = parser.parse_args() mesh = Mesh.from_file(data_dir + '/meshes/3d/fluid_mesh.inp') domain = FEDomain('domain', mesh) omega = domain.create_region('Omega', 'all') field_1 = Field.from_args(name='3_velocity', dtype=nm.float64, shape=3, region=omega, approx_order=1) field_2 = Field.from_args(name='pressure', dtype=nm.float64, shape=1, region=omega, approx_order=1) region_0 = domain.create_region(name='Walls1', select='vertices in (y < -0.049)', kind='facet') region_1 = domain.create_region(name='Walls2', select='vertices in (y > 0.049)', kind='facet') region_2 = domain.create_region(name='Inlet', select='vertices in (x < -0.499)', kind='facet') region_3 = domain.create_region(name='Outlet', select='vertices in (x > -0.499)', kind='facet') ebc_1 = EssentialBC(name='Walls1', region=region_0, dofs={'u.[0,1,2]' : 0.0}) ebc_2 = EssentialBC(name='Walls2', region=region_1, dofs={'u.[0,1,2]' : 0.0}) ebc_3 = EssentialBC(name='Inlet', region=region_2, dofs={'u.0' : 1.0, 'u.[1,2]' : 0.0}) ebc_4 = EssentialBC(name='Outlet', region=region_3, dofs={'p':0.0, 'u.[1,2]' : 0.0}) viscosity = Material(name='viscosity', value=1.25e-3) variable_1 = FieldVariable('u', 'unknown', field_1) variable_2 = FieldVariable(name='v', kind='test', field=field_1, primary_var_name='u') variable_3 = FieldVariable(name='p', kind='unknown', field=field_2) variable_4 = FieldVariable(name='q', kind='test', field=field_2, primary_var_name='p') integral_1 = Integral('i1', order=2) integral_2 =	Integral('i2', order=3)	sfepy.discrete.Integral
#!/usr/bin/env python3 # -*- coding: utf-8 -*- """ Created on Mon Dec 28 09:33:53 2020 @author: dhulls """ from __future__ import print_function from __future__ import absolute_import from argparse import ArgumentParser import numpy as nm import sys sys.path.append('.') from sfepy.base.base import IndexedStruct, Struct from sfepy.discrete import (FieldVariable, Material, Integral, Function, Equation, Equations, Problem) from sfepy.discrete.fem import Mesh, FEDomain, Field from sfepy.terms import Term from sfepy.discrete.conditions import Conditions, EssentialBC, InitialCondition from sfepy.solvers.ls import ScipyDirect from sfepy.solvers.nls import Newton from sfepy.postprocess.viewer import Viewer from sfepy.postprocess.probes_vtk import ProbeFromFile, Probe import numpy as np helps = { 'show' : 'show the results figure', } from sfepy import data_dir parser = ArgumentParser() parser.add_argument('--version', action="https://huggingface.co/datasets/luna-code/sfepy/version", version='%(prog)s') parser.add_argument('-s', '--show', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='show', default=False, help=helps['show']) options = parser.parse_args() mesh = Mesh.from_file(data_dir + '/meshes/3d/fluid_mesh.inp') domain = FEDomain('domain', mesh) omega = domain.create_region('Omega', 'all') field_1 = Field.from_args(name='3_velocity', dtype=nm.float64, shape=3, region=omega, approx_order=1) field_2 = Field.from_args(name='pressure', dtype=nm.float64, shape=1, region=omega, approx_order=1) region_0 = domain.create_region(name='Walls1', select='vertices in (y < -0.049)', kind='facet') region_1 = domain.create_region(name='Walls2', select='vertices in (y > 0.049)', kind='facet') region_2 = domain.create_region(name='Inlet', select='vertices in (x < -0.499)', kind='facet') region_3 = domain.create_region(name='Outlet', select='vertices in (x > -0.499)', kind='facet') ebc_1 = EssentialBC(name='Walls1', region=region_0, dofs={'u.[0,1,2]' : 0.0}) ebc_2 = EssentialBC(name='Walls2', region=region_1, dofs={'u.[0,1,2]' : 0.0}) ebc_3 = EssentialBC(name='Inlet', region=region_2, dofs={'u.0' : 1.0, 'u.[1,2]' : 0.0}) ebc_4 = EssentialBC(name='Outlet', region=region_3, dofs={'p':0.0, 'u.[1,2]' : 0.0}) viscosity = Material(name='viscosity', value=1.25e-3) variable_1 = FieldVariable('u', 'unknown', field_1) variable_2 = FieldVariable(name='v', kind='test', field=field_1, primary_var_name='u') variable_3 = FieldVariable(name='p', kind='unknown', field=field_2) variable_4 = FieldVariable(name='q', kind='test', field=field_2, primary_var_name='p') integral_1 = Integral('i1', order=2) integral_2 = Integral('i2', order=3) t1 = Term.new(name='dw_div_grad(viscosity.value, v, u)', integral=integral_2, region=omega, viscosity=viscosity, v=variable_2, u=variable_1) t2 = Term.new(name='dw_convect(v, u)', integral=integral_2, region=omega, v=variable_2, u=variable_1) t3 = Term.new(name='dw_stokes(v, p)', integral=integral_1, region=omega, v=variable_2, p=variable_3) t4 = Term.new(name='dw_stokes(u, q)', integral=integral_1, region=omega, u=variable_1, q=variable_4) eq1 =	Equation('balance', t1+t2-t3)	sfepy.discrete.Equation
#!/usr/bin/env python3 # -*- coding: utf-8 -*- """ Created on Mon Dec 28 09:33:53 2020 @author: dhulls """ from __future__ import print_function from __future__ import absolute_import from argparse import ArgumentParser import numpy as nm import sys sys.path.append('.') from sfepy.base.base import IndexedStruct, Struct from sfepy.discrete import (FieldVariable, Material, Integral, Function, Equation, Equations, Problem) from sfepy.discrete.fem import Mesh, FEDomain, Field from sfepy.terms import Term from sfepy.discrete.conditions import Conditions, EssentialBC, InitialCondition from sfepy.solvers.ls import ScipyDirect from sfepy.solvers.nls import Newton from sfepy.postprocess.viewer import Viewer from sfepy.postprocess.probes_vtk import ProbeFromFile, Probe import numpy as np helps = { 'show' : 'show the results figure', } from sfepy import data_dir parser = ArgumentParser() parser.add_argument('--version', action="https://huggingface.co/datasets/luna-code/sfepy/version", version='%(prog)s') parser.add_argument('-s', '--show', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='show', default=False, help=helps['show']) options = parser.parse_args() mesh = Mesh.from_file(data_dir + '/meshes/3d/fluid_mesh.inp') domain = FEDomain('domain', mesh) omega = domain.create_region('Omega', 'all') field_1 = Field.from_args(name='3_velocity', dtype=nm.float64, shape=3, region=omega, approx_order=1) field_2 = Field.from_args(name='pressure', dtype=nm.float64, shape=1, region=omega, approx_order=1) region_0 = domain.create_region(name='Walls1', select='vertices in (y < -0.049)', kind='facet') region_1 = domain.create_region(name='Walls2', select='vertices in (y > 0.049)', kind='facet') region_2 = domain.create_region(name='Inlet', select='vertices in (x < -0.499)', kind='facet') region_3 = domain.create_region(name='Outlet', select='vertices in (x > -0.499)', kind='facet') ebc_1 = EssentialBC(name='Walls1', region=region_0, dofs={'u.[0,1,2]' : 0.0}) ebc_2 = EssentialBC(name='Walls2', region=region_1, dofs={'u.[0,1,2]' : 0.0}) ebc_3 = EssentialBC(name='Inlet', region=region_2, dofs={'u.0' : 1.0, 'u.[1,2]' : 0.0}) ebc_4 = EssentialBC(name='Outlet', region=region_3, dofs={'p':0.0, 'u.[1,2]' : 0.0}) viscosity = Material(name='viscosity', value=1.25e-3) variable_1 = FieldVariable('u', 'unknown', field_1) variable_2 = FieldVariable(name='v', kind='test', field=field_1, primary_var_name='u') variable_3 = FieldVariable(name='p', kind='unknown', field=field_2) variable_4 = FieldVariable(name='q', kind='test', field=field_2, primary_var_name='p') integral_1 = Integral('i1', order=2) integral_2 = Integral('i2', order=3) t1 = Term.new(name='dw_div_grad(viscosity.value, v, u)', integral=integral_2, region=omega, viscosity=viscosity, v=variable_2, u=variable_1) t2 = Term.new(name='dw_convect(v, u)', integral=integral_2, region=omega, v=variable_2, u=variable_1) t3 = Term.new(name='dw_stokes(v, p)', integral=integral_1, region=omega, v=variable_2, p=variable_3) t4 = Term.new(name='dw_stokes(u, q)', integral=integral_1, region=omega, u=variable_1, q=variable_4) eq1 = Equation('balance', t1+t2-t3) eq2 =	Equation('incompressibility', t4)	sfepy.discrete.Equation
#!/usr/bin/env python3 # -*- coding: utf-8 -*- """ Created on Mon Dec 28 09:33:53 2020 @author: dhulls """ from __future__ import print_function from __future__ import absolute_import from argparse import ArgumentParser import numpy as nm import sys sys.path.append('.') from sfepy.base.base import IndexedStruct, Struct from sfepy.discrete import (FieldVariable, Material, Integral, Function, Equation, Equations, Problem) from sfepy.discrete.fem import Mesh, FEDomain, Field from sfepy.terms import Term from sfepy.discrete.conditions import Conditions, EssentialBC, InitialCondition from sfepy.solvers.ls import ScipyDirect from sfepy.solvers.nls import Newton from sfepy.postprocess.viewer import Viewer from sfepy.postprocess.probes_vtk import ProbeFromFile, Probe import numpy as np helps = { 'show' : 'show the results figure', } from sfepy import data_dir parser = ArgumentParser() parser.add_argument('--version', action="https://huggingface.co/datasets/luna-code/sfepy/version", version='%(prog)s') parser.add_argument('-s', '--show', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='show', default=False, help=helps['show']) options = parser.parse_args() mesh = Mesh.from_file(data_dir + '/meshes/3d/fluid_mesh.inp') domain = FEDomain('domain', mesh) omega = domain.create_region('Omega', 'all') field_1 = Field.from_args(name='3_velocity', dtype=nm.float64, shape=3, region=omega, approx_order=1) field_2 = Field.from_args(name='pressure', dtype=nm.float64, shape=1, region=omega, approx_order=1) region_0 = domain.create_region(name='Walls1', select='vertices in (y < -0.049)', kind='facet') region_1 = domain.create_region(name='Walls2', select='vertices in (y > 0.049)', kind='facet') region_2 = domain.create_region(name='Inlet', select='vertices in (x < -0.499)', kind='facet') region_3 = domain.create_region(name='Outlet', select='vertices in (x > -0.499)', kind='facet') ebc_1 = EssentialBC(name='Walls1', region=region_0, dofs={'u.[0,1,2]' : 0.0}) ebc_2 = EssentialBC(name='Walls2', region=region_1, dofs={'u.[0,1,2]' : 0.0}) ebc_3 = EssentialBC(name='Inlet', region=region_2, dofs={'u.0' : 1.0, 'u.[1,2]' : 0.0}) ebc_4 = EssentialBC(name='Outlet', region=region_3, dofs={'p':0.0, 'u.[1,2]' : 0.0}) viscosity = Material(name='viscosity', value=1.25e-3) variable_1 = FieldVariable('u', 'unknown', field_1) variable_2 = FieldVariable(name='v', kind='test', field=field_1, primary_var_name='u') variable_3 = FieldVariable(name='p', kind='unknown', field=field_2) variable_4 = FieldVariable(name='q', kind='test', field=field_2, primary_var_name='p') integral_1 = Integral('i1', order=2) integral_2 = Integral('i2', order=3) t1 = Term.new(name='dw_div_grad(viscosity.value, v, u)', integral=integral_2, region=omega, viscosity=viscosity, v=variable_2, u=variable_1) t2 = Term.new(name='dw_convect(v, u)', integral=integral_2, region=omega, v=variable_2, u=variable_1) t3 = Term.new(name='dw_stokes(v, p)', integral=integral_1, region=omega, v=variable_2, p=variable_3) t4 = Term.new(name='dw_stokes(u, q)', integral=integral_1, region=omega, u=variable_1, q=variable_4) eq1 = Equation('balance', t1+t2-t3) eq2 = Equation('incompressibility', t4) eqs =	Equations([eq1,eq2])	sfepy.discrete.Equations
#!/usr/bin/env python3 # -*- coding: utf-8 -*- """ Created on Mon Dec 28 09:33:53 2020 @author: dhulls """ from __future__ import print_function from __future__ import absolute_import from argparse import ArgumentParser import numpy as nm import sys sys.path.append('.') from sfepy.base.base import IndexedStruct, Struct from sfepy.discrete import (FieldVariable, Material, Integral, Function, Equation, Equations, Problem) from sfepy.discrete.fem import Mesh, FEDomain, Field from sfepy.terms import Term from sfepy.discrete.conditions import Conditions, EssentialBC, InitialCondition from sfepy.solvers.ls import ScipyDirect from sfepy.solvers.nls import Newton from sfepy.postprocess.viewer import Viewer from sfepy.postprocess.probes_vtk import ProbeFromFile, Probe import numpy as np helps = { 'show' : 'show the results figure', } from sfepy import data_dir parser = ArgumentParser() parser.add_argument('--version', action="https://huggingface.co/datasets/luna-code/sfepy/version", version='%(prog)s') parser.add_argument('-s', '--show', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='show', default=False, help=helps['show']) options = parser.parse_args() mesh = Mesh.from_file(data_dir + '/meshes/3d/fluid_mesh.inp') domain = FEDomain('domain', mesh) omega = domain.create_region('Omega', 'all') field_1 = Field.from_args(name='3_velocity', dtype=nm.float64, shape=3, region=omega, approx_order=1) field_2 = Field.from_args(name='pressure', dtype=nm.float64, shape=1, region=omega, approx_order=1) region_0 = domain.create_region(name='Walls1', select='vertices in (y < -0.049)', kind='facet') region_1 = domain.create_region(name='Walls2', select='vertices in (y > 0.049)', kind='facet') region_2 = domain.create_region(name='Inlet', select='vertices in (x < -0.499)', kind='facet') region_3 = domain.create_region(name='Outlet', select='vertices in (x > -0.499)', kind='facet') ebc_1 = EssentialBC(name='Walls1', region=region_0, dofs={'u.[0,1,2]' : 0.0}) ebc_2 = EssentialBC(name='Walls2', region=region_1, dofs={'u.[0,1,2]' : 0.0}) ebc_3 = EssentialBC(name='Inlet', region=region_2, dofs={'u.0' : 1.0, 'u.[1,2]' : 0.0}) ebc_4 = EssentialBC(name='Outlet', region=region_3, dofs={'p':0.0, 'u.[1,2]' : 0.0}) viscosity = Material(name='viscosity', value=1.25e-3) variable_1 = FieldVariable('u', 'unknown', field_1) variable_2 = FieldVariable(name='v', kind='test', field=field_1, primary_var_name='u') variable_3 = FieldVariable(name='p', kind='unknown', field=field_2) variable_4 = FieldVariable(name='q', kind='test', field=field_2, primary_var_name='p') integral_1 = Integral('i1', order=2) integral_2 = Integral('i2', order=3) t1 = Term.new(name='dw_div_grad(viscosity.value, v, u)', integral=integral_2, region=omega, viscosity=viscosity, v=variable_2, u=variable_1) t2 = Term.new(name='dw_convect(v, u)', integral=integral_2, region=omega, v=variable_2, u=variable_1) t3 = Term.new(name='dw_stokes(v, p)', integral=integral_1, region=omega, v=variable_2, p=variable_3) t4 = Term.new(name='dw_stokes(u, q)', integral=integral_1, region=omega, u=variable_1, q=variable_4) eq1 = Equation('balance', t1+t2-t3) eq2 = Equation('incompressibility', t4) eqs = Equations([eq1,eq2]) ls =	ScipyDirect({})	sfepy.solvers.ls.ScipyDirect
#!/usr/bin/env python3 # -*- coding: utf-8 -*- """ Created on Mon Dec 28 09:33:53 2020 @author: dhulls """ from __future__ import print_function from __future__ import absolute_import from argparse import ArgumentParser import numpy as nm import sys sys.path.append('.') from sfepy.base.base import IndexedStruct, Struct from sfepy.discrete import (FieldVariable, Material, Integral, Function, Equation, Equations, Problem) from sfepy.discrete.fem import Mesh, FEDomain, Field from sfepy.terms import Term from sfepy.discrete.conditions import Conditions, EssentialBC, InitialCondition from sfepy.solvers.ls import ScipyDirect from sfepy.solvers.nls import Newton from sfepy.postprocess.viewer import Viewer from sfepy.postprocess.probes_vtk import ProbeFromFile, Probe import numpy as np helps = { 'show' : 'show the results figure', } from sfepy import data_dir parser = ArgumentParser() parser.add_argument('--version', action="https://huggingface.co/datasets/luna-code/sfepy/version", version='%(prog)s') parser.add_argument('-s', '--show', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='show', default=False, help=helps['show']) options = parser.parse_args() mesh = Mesh.from_file(data_dir + '/meshes/3d/fluid_mesh.inp') domain = FEDomain('domain', mesh) omega = domain.create_region('Omega', 'all') field_1 = Field.from_args(name='3_velocity', dtype=nm.float64, shape=3, region=omega, approx_order=1) field_2 = Field.from_args(name='pressure', dtype=nm.float64, shape=1, region=omega, approx_order=1) region_0 = domain.create_region(name='Walls1', select='vertices in (y < -0.049)', kind='facet') region_1 = domain.create_region(name='Walls2', select='vertices in (y > 0.049)', kind='facet') region_2 = domain.create_region(name='Inlet', select='vertices in (x < -0.499)', kind='facet') region_3 = domain.create_region(name='Outlet', select='vertices in (x > -0.499)', kind='facet') ebc_1 = EssentialBC(name='Walls1', region=region_0, dofs={'u.[0,1,2]' : 0.0}) ebc_2 = EssentialBC(name='Walls2', region=region_1, dofs={'u.[0,1,2]' : 0.0}) ebc_3 = EssentialBC(name='Inlet', region=region_2, dofs={'u.0' : 1.0, 'u.[1,2]' : 0.0}) ebc_4 = EssentialBC(name='Outlet', region=region_3, dofs={'p':0.0, 'u.[1,2]' : 0.0}) viscosity = Material(name='viscosity', value=1.25e-3) variable_1 = FieldVariable('u', 'unknown', field_1) variable_2 = FieldVariable(name='v', kind='test', field=field_1, primary_var_name='u') variable_3 = FieldVariable(name='p', kind='unknown', field=field_2) variable_4 = FieldVariable(name='q', kind='test', field=field_2, primary_var_name='p') integral_1 = Integral('i1', order=2) integral_2 = Integral('i2', order=3) t1 = Term.new(name='dw_div_grad(viscosity.value, v, u)', integral=integral_2, region=omega, viscosity=viscosity, v=variable_2, u=variable_1) t2 = Term.new(name='dw_convect(v, u)', integral=integral_2, region=omega, v=variable_2, u=variable_1) t3 = Term.new(name='dw_stokes(v, p)', integral=integral_1, region=omega, v=variable_2, p=variable_3) t4 = Term.new(name='dw_stokes(u, q)', integral=integral_1, region=omega, u=variable_1, q=variable_4) eq1 = Equation('balance', t1+t2-t3) eq2 = Equation('incompressibility', t4) eqs = Equations([eq1,eq2]) ls = ScipyDirect({}) nls_status =	IndexedStruct()	sfepy.base.base.IndexedStruct
#!/usr/bin/env python3 # -*- coding: utf-8 -*- """ Created on Mon Dec 28 09:33:53 2020 @author: dhulls """ from __future__ import print_function from __future__ import absolute_import from argparse import ArgumentParser import numpy as nm import sys sys.path.append('.') from sfepy.base.base import IndexedStruct, Struct from sfepy.discrete import (FieldVariable, Material, Integral, Function, Equation, Equations, Problem) from sfepy.discrete.fem import Mesh, FEDomain, Field from sfepy.terms import Term from sfepy.discrete.conditions import Conditions, EssentialBC, InitialCondition from sfepy.solvers.ls import ScipyDirect from sfepy.solvers.nls import Newton from sfepy.postprocess.viewer import Viewer from sfepy.postprocess.probes_vtk import ProbeFromFile, Probe import numpy as np helps = { 'show' : 'show the results figure', } from sfepy import data_dir parser = ArgumentParser() parser.add_argument('--version', action="https://huggingface.co/datasets/luna-code/sfepy/version", version='%(prog)s') parser.add_argument('-s', '--show', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='show', default=False, help=helps['show']) options = parser.parse_args() mesh = Mesh.from_file(data_dir + '/meshes/3d/fluid_mesh.inp') domain = FEDomain('domain', mesh) omega = domain.create_region('Omega', 'all') field_1 = Field.from_args(name='3_velocity', dtype=nm.float64, shape=3, region=omega, approx_order=1) field_2 = Field.from_args(name='pressure', dtype=nm.float64, shape=1, region=omega, approx_order=1) region_0 = domain.create_region(name='Walls1', select='vertices in (y < -0.049)', kind='facet') region_1 = domain.create_region(name='Walls2', select='vertices in (y > 0.049)', kind='facet') region_2 = domain.create_region(name='Inlet', select='vertices in (x < -0.499)', kind='facet') region_3 = domain.create_region(name='Outlet', select='vertices in (x > -0.499)', kind='facet') ebc_1 = EssentialBC(name='Walls1', region=region_0, dofs={'u.[0,1,2]' : 0.0}) ebc_2 = EssentialBC(name='Walls2', region=region_1, dofs={'u.[0,1,2]' : 0.0}) ebc_3 = EssentialBC(name='Inlet', region=region_2, dofs={'u.0' : 1.0, 'u.[1,2]' : 0.0}) ebc_4 = EssentialBC(name='Outlet', region=region_3, dofs={'p':0.0, 'u.[1,2]' : 0.0}) viscosity = Material(name='viscosity', value=1.25e-3) variable_1 = FieldVariable('u', 'unknown', field_1) variable_2 = FieldVariable(name='v', kind='test', field=field_1, primary_var_name='u') variable_3 = FieldVariable(name='p', kind='unknown', field=field_2) variable_4 = FieldVariable(name='q', kind='test', field=field_2, primary_var_name='p') integral_1 = Integral('i1', order=2) integral_2 = Integral('i2', order=3) t1 = Term.new(name='dw_div_grad(viscosity.value, v, u)', integral=integral_2, region=omega, viscosity=viscosity, v=variable_2, u=variable_1) t2 = Term.new(name='dw_convect(v, u)', integral=integral_2, region=omega, v=variable_2, u=variable_1) t3 = Term.new(name='dw_stokes(v, p)', integral=integral_1, region=omega, v=variable_2, p=variable_3) t4 = Term.new(name='dw_stokes(u, q)', integral=integral_1, region=omega, u=variable_1, q=variable_4) eq1 = Equation('balance', t1+t2-t3) eq2 = Equation('incompressibility', t4) eqs = Equations([eq1,eq2]) ls = ScipyDirect({}) nls_status = IndexedStruct() nls =	Newton({'i_max' : 20, 'eps_a' : 1e-8, 'eps_r' : 1.0, 'macheps' : 1e-16, 'lin_red' : 1e-2, 'ls_red' : 0.1, 'ls_red_warp' : 0.001, 'ls_on' : 0.99999, 'ls_min' : 1e-5, 'check' : 0, 'delta' : 1e-6}, lin_solver=ls, status=nls_status)	sfepy.solvers.nls.Newton
#!/usr/bin/env python3 # -*- coding: utf-8 -*- """ Created on Mon Dec 28 09:33:53 2020 @author: dhulls """ from __future__ import print_function from __future__ import absolute_import from argparse import ArgumentParser import numpy as nm import sys sys.path.append('.') from sfepy.base.base import IndexedStruct, Struct from sfepy.discrete import (FieldVariable, Material, Integral, Function, Equation, Equations, Problem) from sfepy.discrete.fem import Mesh, FEDomain, Field from sfepy.terms import Term from sfepy.discrete.conditions import Conditions, EssentialBC, InitialCondition from sfepy.solvers.ls import ScipyDirect from sfepy.solvers.nls import Newton from sfepy.postprocess.viewer import Viewer from sfepy.postprocess.probes_vtk import ProbeFromFile, Probe import numpy as np helps = { 'show' : 'show the results figure', } from sfepy import data_dir parser = ArgumentParser() parser.add_argument('--version', action="https://huggingface.co/datasets/luna-code/sfepy/version", version='%(prog)s') parser.add_argument('-s', '--show', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='show', default=False, help=helps['show']) options = parser.parse_args() mesh = Mesh.from_file(data_dir + '/meshes/3d/fluid_mesh.inp') domain = FEDomain('domain', mesh) omega = domain.create_region('Omega', 'all') field_1 = Field.from_args(name='3_velocity', dtype=nm.float64, shape=3, region=omega, approx_order=1) field_2 = Field.from_args(name='pressure', dtype=nm.float64, shape=1, region=omega, approx_order=1) region_0 = domain.create_region(name='Walls1', select='vertices in (y < -0.049)', kind='facet') region_1 = domain.create_region(name='Walls2', select='vertices in (y > 0.049)', kind='facet') region_2 = domain.create_region(name='Inlet', select='vertices in (x < -0.499)', kind='facet') region_3 = domain.create_region(name='Outlet', select='vertices in (x > -0.499)', kind='facet') ebc_1 = EssentialBC(name='Walls1', region=region_0, dofs={'u.[0,1,2]' : 0.0}) ebc_2 = EssentialBC(name='Walls2', region=region_1, dofs={'u.[0,1,2]' : 0.0}) ebc_3 = EssentialBC(name='Inlet', region=region_2, dofs={'u.0' : 1.0, 'u.[1,2]' : 0.0}) ebc_4 = EssentialBC(name='Outlet', region=region_3, dofs={'p':0.0, 'u.[1,2]' : 0.0}) viscosity = Material(name='viscosity', value=1.25e-3) variable_1 = FieldVariable('u', 'unknown', field_1) variable_2 = FieldVariable(name='v', kind='test', field=field_1, primary_var_name='u') variable_3 = FieldVariable(name='p', kind='unknown', field=field_2) variable_4 = FieldVariable(name='q', kind='test', field=field_2, primary_var_name='p') integral_1 = Integral('i1', order=2) integral_2 = Integral('i2', order=3) t1 = Term.new(name='dw_div_grad(viscosity.value, v, u)', integral=integral_2, region=omega, viscosity=viscosity, v=variable_2, u=variable_1) t2 = Term.new(name='dw_convect(v, u)', integral=integral_2, region=omega, v=variable_2, u=variable_1) t3 = Term.new(name='dw_stokes(v, p)', integral=integral_1, region=omega, v=variable_2, p=variable_3) t4 = Term.new(name='dw_stokes(u, q)', integral=integral_1, region=omega, u=variable_1, q=variable_4) eq1 = Equation('balance', t1+t2-t3) eq2 = Equation('incompressibility', t4) eqs = Equations([eq1,eq2]) ls = ScipyDirect({}) nls_status = IndexedStruct() nls = Newton({'i_max' : 20, 'eps_a' : 1e-8, 'eps_r' : 1.0, 'macheps' : 1e-16, 'lin_red' : 1e-2, 'ls_red' : 0.1, 'ls_red_warp' : 0.001, 'ls_on' : 0.99999, 'ls_min' : 1e-5, 'check' : 0, 'delta' : 1e-6}, lin_solver=ls, status=nls_status) pb =	Problem('Navier-Stokes', equations=eqs)	sfepy.discrete.Problem
#!/usr/bin/env python3 # -*- coding: utf-8 -*- """ Created on Mon Dec 28 09:33:53 2020 @author: dhulls """ from __future__ import print_function from __future__ import absolute_import from argparse import ArgumentParser import numpy as nm import sys sys.path.append('.') from sfepy.base.base import IndexedStruct, Struct from sfepy.discrete import (FieldVariable, Material, Integral, Function, Equation, Equations, Problem) from sfepy.discrete.fem import Mesh, FEDomain, Field from sfepy.terms import Term from sfepy.discrete.conditions import Conditions, EssentialBC, InitialCondition from sfepy.solvers.ls import ScipyDirect from sfepy.solvers.nls import Newton from sfepy.postprocess.viewer import Viewer from sfepy.postprocess.probes_vtk import ProbeFromFile, Probe import numpy as np helps = { 'show' : 'show the results figure', } from sfepy import data_dir parser = ArgumentParser() parser.add_argument('--version', action="https://huggingface.co/datasets/luna-code/sfepy/version", version='%(prog)s') parser.add_argument('-s', '--show', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='show', default=False, help=helps['show']) options = parser.parse_args() mesh = Mesh.from_file(data_dir + '/meshes/3d/fluid_mesh.inp') domain = FEDomain('domain', mesh) omega = domain.create_region('Omega', 'all') field_1 = Field.from_args(name='3_velocity', dtype=nm.float64, shape=3, region=omega, approx_order=1) field_2 = Field.from_args(name='pressure', dtype=nm.float64, shape=1, region=omega, approx_order=1) region_0 = domain.create_region(name='Walls1', select='vertices in (y < -0.049)', kind='facet') region_1 = domain.create_region(name='Walls2', select='vertices in (y > 0.049)', kind='facet') region_2 = domain.create_region(name='Inlet', select='vertices in (x < -0.499)', kind='facet') region_3 = domain.create_region(name='Outlet', select='vertices in (x > -0.499)', kind='facet') ebc_1 = EssentialBC(name='Walls1', region=region_0, dofs={'u.[0,1,2]' : 0.0}) ebc_2 = EssentialBC(name='Walls2', region=region_1, dofs={'u.[0,1,2]' : 0.0}) ebc_3 = EssentialBC(name='Inlet', region=region_2, dofs={'u.0' : 1.0, 'u.[1,2]' : 0.0}) ebc_4 = EssentialBC(name='Outlet', region=region_3, dofs={'p':0.0, 'u.[1,2]' : 0.0}) viscosity = Material(name='viscosity', value=1.25e-3) variable_1 = FieldVariable('u', 'unknown', field_1) variable_2 = FieldVariable(name='v', kind='test', field=field_1, primary_var_name='u') variable_3 = FieldVariable(name='p', kind='unknown', field=field_2) variable_4 = FieldVariable(name='q', kind='test', field=field_2, primary_var_name='p') integral_1 = Integral('i1', order=2) integral_2 = Integral('i2', order=3) t1 = Term.new(name='dw_div_grad(viscosity.value, v, u)', integral=integral_2, region=omega, viscosity=viscosity, v=variable_2, u=variable_1) t2 = Term.new(name='dw_convect(v, u)', integral=integral_2, region=omega, v=variable_2, u=variable_1) t3 = Term.new(name='dw_stokes(v, p)', integral=integral_1, region=omega, v=variable_2, p=variable_3) t4 = Term.new(name='dw_stokes(u, q)', integral=integral_1, region=omega, u=variable_1, q=variable_4) eq1 = Equation('balance', t1+t2-t3) eq2 = Equation('incompressibility', t4) eqs = Equations([eq1,eq2]) ls = ScipyDirect({}) nls_status = IndexedStruct() nls = Newton({'i_max' : 20, 'eps_a' : 1e-8, 'eps_r' : 1.0, 'macheps' : 1e-16, 'lin_red' : 1e-2, 'ls_red' : 0.1, 'ls_red_warp' : 0.001, 'ls_on' : 0.99999, 'ls_min' : 1e-5, 'check' : 0, 'delta' : 1e-6}, lin_solver=ls, status=nls_status) pb = Problem('Navier-Stokes', equations=eqs) pb.set_bcs(ebcs=Conditions([ebc_1, ebc_2, ebc_3])) pb.set_solver(nls) status =	IndexedStruct()	sfepy.base.base.IndexedStruct
#!/usr/bin/env python3 # -*- coding: utf-8 -*- """ Created on Mon Dec 28 09:33:53 2020 @author: dhulls """ from __future__ import print_function from __future__ import absolute_import from argparse import ArgumentParser import numpy as nm import sys sys.path.append('.') from sfepy.base.base import IndexedStruct, Struct from sfepy.discrete import (FieldVariable, Material, Integral, Function, Equation, Equations, Problem) from sfepy.discrete.fem import Mesh, FEDomain, Field from sfepy.terms import Term from sfepy.discrete.conditions import Conditions, EssentialBC, InitialCondition from sfepy.solvers.ls import ScipyDirect from sfepy.solvers.nls import Newton from sfepy.postprocess.viewer import Viewer from sfepy.postprocess.probes_vtk import ProbeFromFile, Probe import numpy as np helps = { 'show' : 'show the results figure', } from sfepy import data_dir parser = ArgumentParser() parser.add_argument('--version', action="https://huggingface.co/datasets/luna-code/sfepy/version", version='%(prog)s') parser.add_argument('-s', '--show', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='show', default=False, help=helps['show']) options = parser.parse_args() mesh = Mesh.from_file(data_dir + '/meshes/3d/fluid_mesh.inp') domain = FEDomain('domain', mesh) omega = domain.create_region('Omega', 'all') field_1 = Field.from_args(name='3_velocity', dtype=nm.float64, shape=3, region=omega, approx_order=1) field_2 = Field.from_args(name='pressure', dtype=nm.float64, shape=1, region=omega, approx_order=1) region_0 = domain.create_region(name='Walls1', select='vertices in (y < -0.049)', kind='facet') region_1 = domain.create_region(name='Walls2', select='vertices in (y > 0.049)', kind='facet') region_2 = domain.create_region(name='Inlet', select='vertices in (x < -0.499)', kind='facet') region_3 = domain.create_region(name='Outlet', select='vertices in (x > -0.499)', kind='facet') ebc_1 = EssentialBC(name='Walls1', region=region_0, dofs={'u.[0,1,2]' : 0.0}) ebc_2 = EssentialBC(name='Walls2', region=region_1, dofs={'u.[0,1,2]' : 0.0}) ebc_3 = EssentialBC(name='Inlet', region=region_2, dofs={'u.0' : 1.0, 'u.[1,2]' : 0.0}) ebc_4 = EssentialBC(name='Outlet', region=region_3, dofs={'p':0.0, 'u.[1,2]' : 0.0}) viscosity = Material(name='viscosity', value=1.25e-3) variable_1 = FieldVariable('u', 'unknown', field_1) variable_2 = FieldVariable(name='v', kind='test', field=field_1, primary_var_name='u') variable_3 = FieldVariable(name='p', kind='unknown', field=field_2) variable_4 = FieldVariable(name='q', kind='test', field=field_2, primary_var_name='p') integral_1 = Integral('i1', order=2) integral_2 = Integral('i2', order=3) t1 = Term.new(name='dw_div_grad(viscosity.value, v, u)', integral=integral_2, region=omega, viscosity=viscosity, v=variable_2, u=variable_1) t2 = Term.new(name='dw_convect(v, u)', integral=integral_2, region=omega, v=variable_2, u=variable_1) t3 = Term.new(name='dw_stokes(v, p)', integral=integral_1, region=omega, v=variable_2, p=variable_3) t4 = Term.new(name='dw_stokes(u, q)', integral=integral_1, region=omega, u=variable_1, q=variable_4) eq1 = Equation('balance', t1+t2-t3) eq2 = Equation('incompressibility', t4) eqs = Equations([eq1,eq2]) ls = ScipyDirect({}) nls_status = IndexedStruct() nls = Newton({'i_max' : 20, 'eps_a' : 1e-8, 'eps_r' : 1.0, 'macheps' : 1e-16, 'lin_red' : 1e-2, 'ls_red' : 0.1, 'ls_red_warp' : 0.001, 'ls_on' : 0.99999, 'ls_min' : 1e-5, 'check' : 0, 'delta' : 1e-6}, lin_solver=ls, status=nls_status) pb = Problem('Navier-Stokes', equations=eqs) pb.set_bcs(ebcs=Conditions([ebc_1, ebc_2, ebc_3])) pb.set_solver(nls) status = IndexedStruct() state = pb.solve(status=status, save_results=True) out = state.create_output_dict() pb.save_state('Navier_Stokes.vtk', out=out) view =	Viewer('Navier_Stokes.vtk')	sfepy.postprocess.viewer.Viewer
#!/usr/bin/env python3 # -*- coding: utf-8 -*- """ Created on Mon Dec 28 09:33:53 2020 @author: dhulls """ from __future__ import print_function from __future__ import absolute_import from argparse import ArgumentParser import numpy as nm import sys sys.path.append('.') from sfepy.base.base import IndexedStruct, Struct from sfepy.discrete import (FieldVariable, Material, Integral, Function, Equation, Equations, Problem) from sfepy.discrete.fem import Mesh, FEDomain, Field from sfepy.terms import Term from sfepy.discrete.conditions import Conditions, EssentialBC, InitialCondition from sfepy.solvers.ls import ScipyDirect from sfepy.solvers.nls import Newton from sfepy.postprocess.viewer import Viewer from sfepy.postprocess.probes_vtk import ProbeFromFile, Probe import numpy as np helps = { 'show' : 'show the results figure', } from sfepy import data_dir parser = ArgumentParser() parser.add_argument('--version', action="https://huggingface.co/datasets/luna-code/sfepy/version", version='%(prog)s') parser.add_argument('-s', '--show', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='show', default=False, help=helps['show']) options = parser.parse_args() mesh = Mesh.from_file(data_dir + '/meshes/3d/fluid_mesh.inp') domain = FEDomain('domain', mesh) omega = domain.create_region('Omega', 'all') field_1 = Field.from_args(name='3_velocity', dtype=nm.float64, shape=3, region=omega, approx_order=1) field_2 = Field.from_args(name='pressure', dtype=nm.float64, shape=1, region=omega, approx_order=1) region_0 = domain.create_region(name='Walls1', select='vertices in (y < -0.049)', kind='facet') region_1 = domain.create_region(name='Walls2', select='vertices in (y > 0.049)', kind='facet') region_2 = domain.create_region(name='Inlet', select='vertices in (x < -0.499)', kind='facet') region_3 = domain.create_region(name='Outlet', select='vertices in (x > -0.499)', kind='facet') ebc_1 = EssentialBC(name='Walls1', region=region_0, dofs={'u.[0,1,2]' : 0.0}) ebc_2 = EssentialBC(name='Walls2', region=region_1, dofs={'u.[0,1,2]' : 0.0}) ebc_3 = EssentialBC(name='Inlet', region=region_2, dofs={'u.0' : 1.0, 'u.[1,2]' : 0.0}) ebc_4 = EssentialBC(name='Outlet', region=region_3, dofs={'p':0.0, 'u.[1,2]' : 0.0}) viscosity = Material(name='viscosity', value=1.25e-3) variable_1 = FieldVariable('u', 'unknown', field_1) variable_2 = FieldVariable(name='v', kind='test', field=field_1, primary_var_name='u') variable_3 = FieldVariable(name='p', kind='unknown', field=field_2) variable_4 = FieldVariable(name='q', kind='test', field=field_2, primary_var_name='p') integral_1 = Integral('i1', order=2) integral_2 = Integral('i2', order=3) t1 = Term.new(name='dw_div_grad(viscosity.value, v, u)', integral=integral_2, region=omega, viscosity=viscosity, v=variable_2, u=variable_1) t2 = Term.new(name='dw_convect(v, u)', integral=integral_2, region=omega, v=variable_2, u=variable_1) t3 = Term.new(name='dw_stokes(v, p)', integral=integral_1, region=omega, v=variable_2, p=variable_3) t4 = Term.new(name='dw_stokes(u, q)', integral=integral_1, region=omega, u=variable_1, q=variable_4) eq1 = Equation('balance', t1+t2-t3) eq2 = Equation('incompressibility', t4) eqs = Equations([eq1,eq2]) ls = ScipyDirect({}) nls_status = IndexedStruct() nls = Newton({'i_max' : 20, 'eps_a' : 1e-8, 'eps_r' : 1.0, 'macheps' : 1e-16, 'lin_red' : 1e-2, 'ls_red' : 0.1, 'ls_red_warp' : 0.001, 'ls_on' : 0.99999, 'ls_min' : 1e-5, 'check' : 0, 'delta' : 1e-6}, lin_solver=ls, status=nls_status) pb = Problem('Navier-Stokes', equations=eqs) pb.set_bcs(ebcs=	Conditions([ebc_1, ebc_2, ebc_3])	sfepy.discrete.conditions.Conditions
r""" Piezo-elasticity problem - linear elastic material with piezoelectric effects. Find :math:`\ul{u}`, :math:`\phi` such that: .. math:: - \omega^2 \int_{Y} \rho\ \ul{v} \cdot \ul{u} + \int_{Y} D_{ijkl}\ e_{ij}(\ul{v}) e_{kl}(\ul{u}) - \int_{Y_2} g_{kij}\ e_{ij}(\ul{v}) \nabla_k \phi = 0 \;, \quad \forall \ul{v} \;, \int_{Y_2} g_{kij}\ e_{ij}(\ul{u}) \nabla_k \psi + \int_{Y} K_{ij} \nabla_i \psi \nabla_j \phi = 0 \;, \quad \forall \psi \;, where .. math:: D_{ijkl} = \mu (\delta_{ik} \delta_{jl}+\delta_{il} \delta_{jk}) + \lambda \ \delta_{ij} \delta_{kl} \;. """ import os import numpy as nm from sfepy import data_dir from sfepy.discrete.fem import MeshIO filename_mesh = data_dir + '/meshes/2d/special/circle_in_square.mesh' ## filename_mesh = data_dir + '/meshes/2d/special/circle_in_square_small.mesh' ## filename_mesh = data_dir + '/meshes/3d/special/cube_sphere.mesh' ## filename_mesh = data_dir + '/meshes/2d/special/cube_cylinder.mesh' omega = 1 omega_squared = omega**2 conf_dir = os.path.dirname(__file__) io =	MeshIO.any_from_filename(filename_mesh, prefix_dir=conf_dir)	sfepy.discrete.fem.MeshIO.any_from_filename
#!/usr/bin/env python """ Convert a mesh file from one SfePy-supported format to another. Examples:: $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s2.5 $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 -c 0 $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.mesh --remesh='q2/0 a1e-8 O9/7 V' $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new2.mesh --remesh='rq2/0 a1e-8 O9/7 V' """ from __future__ import absolute_import import sys import os.path as op from six.moves import range sys.path.append('.') from argparse import ArgumentParser, RawDescriptionHelpFormatter from sfepy.base.base import nm, output from sfepy.base.ioutils import remove_files from sfepy.discrete.fem import Mesh, FEDomain from sfepy.discrete.fem.meshio import (output_mesh_formats, MeshIO, supported_cell_types) from sfepy.discrete.fem.mesh import fix_double_nodes from sfepy.mesh.mesh_tools import elems_q2t helps = { 'scale' : 'scale factor (float or comma-separated list for each axis)' ' [default: %(default)s]', 'center' : 'center of the output mesh (0 for origin or' ' comma-separated list for each axis) applied after scaling' ' [default: %(default)s]', 'refine' : 'uniform refinement level [default: %(default)s]', 'format' : 'output mesh format (overrides filename_out extension)', 'list' : 'list supported readable/writable output mesh formats', 'merge' : 'remove duplicate vertices', 'tri-tetra' : 'convert elements: quad->tri, hexa->tetra', '2d' : 'force a 2D mesh by removing the z coordinates - assumes a 3D mesh' ' in the xy plane', 'save-per-mat': 'extract cells by material id and save them into' ' separate mesh files with a name based on filename_out and the id' ' numbers (preserves original mesh vertices)', 'remesh' : """when given, remesh the given mesh using tetgen. The options can be the following, separated by spaces, in this order: 1. "r" causes remeshing of the mesh volume - if not present the mesh surface is extracted and used for the volume mesh generation. 2. "q[<float>/<float>]" (required) - the two numbers after "q" are a maximum radius-edge ratio bound and a minimum dihedral angle bound. 3. "a<float>" (optional) - the number imposes a maximum volume constraint on all tetrahedra. 4. O[<0-9>/<0-7>] - the two numbers correspond to a mesh optimization level and a choice of optimizing operations. 5. "V" (optional) - if present, mesh statistics are printed. Consult the tetgen documentation for details.""", } def _parse_val_or_vec(option, name, parser): if option is not None: try: try: option = float(option) except ValueError: option = [float(ii) for ii in option.split(',')] option = nm.array(option, dtype=nm.float64, ndmin=1) except: output('bad %s! (%s)' % (name, option)) parser.print_help() sys.exit(1) return option def main(): parser = ArgumentParser(description=__doc__, formatter_class=RawDescriptionHelpFormatter) parser.add_argument('-s', '--scale', metavar='scale', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='scale', default=None, help=helps['scale']) parser.add_argument('-c', '--center', metavar='center', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='center', default=None, help=helps['center']) parser.add_argument('-r', '--refine', metavar='level', action="https://huggingface.co/datasets/luna-code/sfepy/store", type=int, dest='refine', default=0, help=helps['refine']) parser.add_argument('-f', '--format', metavar='format', action="https://huggingface.co/datasets/luna-code/sfepy/store", type=str, dest='format', default=None, help=helps['format']) parser.add_argument('-l', '--list', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='list', help=helps['list']) parser.add_argument('-m', '--merge', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='merge', help=helps['merge']) parser.add_argument('-t', '--tri-tetra', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='tri_tetra', help=helps['tri-tetra']) parser.add_argument('-2', '--2d', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='force_2d', help=helps['2d']) parser.add_argument('--save-per-mat', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='save_per_mat', help=helps['save-per-mat']) parser.add_argument('--remesh', metavar='options', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='remesh', default=None, help=helps['remesh']) parser.add_argument('filename_in') parser.add_argument('filename_out') options = parser.parse_args() if options.list: output('Supported readable mesh formats:') output('--------------------------------') output_mesh_formats('r') output('') output('Supported writable mesh formats:') output('--------------------------------') output_mesh_formats('w') sys.exit(0) scale = _parse_val_or_vec(options.scale, 'scale', parser) center = _parse_val_or_vec(options.center, 'center', parser) filename_in = options.filename_in filename_out = options.filename_out if options.remesh: import tempfile import shlex import subprocess dirname = tempfile.mkdtemp() is_surface = options.remesh.startswith('q') if is_surface: mesh = Mesh.from_file(filename_in) domain = FEDomain(mesh.name, mesh) region = domain.create_region('surf', 'vertices of surface', 'facet') surf_mesh = Mesh.from_region(region, mesh, localize=True, is_surface=True) filename = op.join(dirname, 'surf.mesh') surf_mesh.write(filename, io='auto') else: import shutil shutil.copy(filename_in, dirname) filename = op.join(dirname, op.basename(filename_in)) qopts = ''.join(options.remesh.split()) # Remove spaces. command = 'tetgen -BFENkACp%s %s' % (qopts, filename) args = shlex.split(command) subprocess.call(args) root, ext = op.splitext(filename) mesh = Mesh.from_file(root + '.1.vtk') remove_files(dirname) else: mesh = Mesh.from_file(filename_in) if options.force_2d: data = list(mesh._get_io_data()) data[0] = data[0][:, :2] mesh = Mesh.from_data(mesh.name, *data) if scale is not None: if len(scale) == 1: tr = nm.eye(mesh.dim, dtype=nm.float64) * scale elif len(scale) == mesh.dim: tr = nm.diag(scale) else: raise ValueError('bad scale! (%s)' % scale) mesh.transform_coors(tr) if center is not None: cc = 0.5 * mesh.get_bounding_box().sum(0) shift = center - cc tr = nm.c_[nm.eye(mesh.dim, dtype=nm.float64), shift[:, None]] mesh.transform_coors(tr) if options.refine > 0: domain = FEDomain(mesh.name, mesh) output('initial mesh: %d nodes %d elements' % (domain.shape.n_nod, domain.shape.n_el)) for ii in range(options.refine): output('refine %d...' % ii) domain = domain.refine() output('... %d nodes %d elements' % (domain.shape.n_nod, domain.shape.n_el)) mesh = domain.mesh if options.tri_tetra > 0: conns = None for k, new_desc in [('3_8', '3_4'), ('2_4', '2_3')]: if k in mesh.descs: conns = mesh.get_conn(k) break if conns is not None: nelo = conns.shape[0] output('initial mesh: %d elements' % nelo) new_conns = elems_q2t(conns) nn = new_conns.shape[0] // nelo new_cgroups = nm.repeat(mesh.cmesh.cell_groups, nn) output('new mesh: %d elements' % new_conns.shape[0]) mesh = Mesh.from_data(mesh.name, mesh.coors, mesh.cmesh.vertex_groups, [new_conns], [new_cgroups], [new_desc]) if options.merge: desc = mesh.descs[0] coor, ngroups, conns = fix_double_nodes(mesh.coors, mesh.cmesh.vertex_groups, mesh.get_conn(desc), 1e-9) mesh = Mesh.from_data(mesh.name + '_merged', coor, ngroups, [conns], [mesh.cmesh.cell_groups], [desc]) if options.save_per_mat: desc = mesh.descs[0] conns, cgroups = mesh.get_conn(desc), mesh.cmesh.cell_groups coors, ngroups = mesh.coors, mesh.cmesh.vertex_groups mat_ids = nm.unique(cgroups) for mat_id in mat_ids: idxs = nm.where(cgroups == mat_id)[0] imesh = Mesh.from_data(mesh.name + '_matid_%d' % mat_id, coors, ngroups, [conns[idxs]], [cgroups[idxs]], [desc]) fbase, fext = op.splitext(filename_out) ifilename_out = '%s_matid_%d%s' % (fbase, mat_id, fext) io = MeshIO.for_format(ifilename_out, format=options.format, writable=True) output('writing %s...' % ifilename_out) imesh.write(ifilename_out, io=io) output('...done') io = MeshIO.for_format(filename_out, format=options.format, writable=True) cell_types = ', '.join(supported_cell_types[io.format])	output('writing [%s] %s...' % (cell_types, filename_out))	sfepy.base.base.output
#!/usr/bin/env python """ Convert a mesh file from one SfePy-supported format to another. Examples:: $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s2.5 $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 -c 0 $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.mesh --remesh='q2/0 a1e-8 O9/7 V' $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new2.mesh --remesh='rq2/0 a1e-8 O9/7 V' """ from __future__ import absolute_import import sys import os.path as op from six.moves import range sys.path.append('.') from argparse import ArgumentParser, RawDescriptionHelpFormatter from sfepy.base.base import nm, output from sfepy.base.ioutils import remove_files from sfepy.discrete.fem import Mesh, FEDomain from sfepy.discrete.fem.meshio import (output_mesh_formats, MeshIO, supported_cell_types) from sfepy.discrete.fem.mesh import fix_double_nodes from sfepy.mesh.mesh_tools import elems_q2t helps = { 'scale' : 'scale factor (float or comma-separated list for each axis)' ' [default: %(default)s]', 'center' : 'center of the output mesh (0 for origin or' ' comma-separated list for each axis) applied after scaling' ' [default: %(default)s]', 'refine' : 'uniform refinement level [default: %(default)s]', 'format' : 'output mesh format (overrides filename_out extension)', 'list' : 'list supported readable/writable output mesh formats', 'merge' : 'remove duplicate vertices', 'tri-tetra' : 'convert elements: quad->tri, hexa->tetra', '2d' : 'force a 2D mesh by removing the z coordinates - assumes a 3D mesh' ' in the xy plane', 'save-per-mat': 'extract cells by material id and save them into' ' separate mesh files with a name based on filename_out and the id' ' numbers (preserves original mesh vertices)', 'remesh' : """when given, remesh the given mesh using tetgen. The options can be the following, separated by spaces, in this order: 1. "r" causes remeshing of the mesh volume - if not present the mesh surface is extracted and used for the volume mesh generation. 2. "q[<float>/<float>]" (required) - the two numbers after "q" are a maximum radius-edge ratio bound and a minimum dihedral angle bound. 3. "a<float>" (optional) - the number imposes a maximum volume constraint on all tetrahedra. 4. O[<0-9>/<0-7>] - the two numbers correspond to a mesh optimization level and a choice of optimizing operations. 5. "V" (optional) - if present, mesh statistics are printed. Consult the tetgen documentation for details.""", } def _parse_val_or_vec(option, name, parser): if option is not None: try: try: option = float(option) except ValueError: option = [float(ii) for ii in option.split(',')] option = nm.array(option, dtype=nm.float64, ndmin=1) except: output('bad %s! (%s)' % (name, option)) parser.print_help() sys.exit(1) return option def main(): parser = ArgumentParser(description=__doc__, formatter_class=RawDescriptionHelpFormatter) parser.add_argument('-s', '--scale', metavar='scale', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='scale', default=None, help=helps['scale']) parser.add_argument('-c', '--center', metavar='center', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='center', default=None, help=helps['center']) parser.add_argument('-r', '--refine', metavar='level', action="https://huggingface.co/datasets/luna-code/sfepy/store", type=int, dest='refine', default=0, help=helps['refine']) parser.add_argument('-f', '--format', metavar='format', action="https://huggingface.co/datasets/luna-code/sfepy/store", type=str, dest='format', default=None, help=helps['format']) parser.add_argument('-l', '--list', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='list', help=helps['list']) parser.add_argument('-m', '--merge', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='merge', help=helps['merge']) parser.add_argument('-t', '--tri-tetra', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='tri_tetra', help=helps['tri-tetra']) parser.add_argument('-2', '--2d', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='force_2d', help=helps['2d']) parser.add_argument('--save-per-mat', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='save_per_mat', help=helps['save-per-mat']) parser.add_argument('--remesh', metavar='options', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='remesh', default=None, help=helps['remesh']) parser.add_argument('filename_in') parser.add_argument('filename_out') options = parser.parse_args() if options.list: output('Supported readable mesh formats:') output('--------------------------------') output_mesh_formats('r') output('') output('Supported writable mesh formats:') output('--------------------------------') output_mesh_formats('w') sys.exit(0) scale = _parse_val_or_vec(options.scale, 'scale', parser) center = _parse_val_or_vec(options.center, 'center', parser) filename_in = options.filename_in filename_out = options.filename_out if options.remesh: import tempfile import shlex import subprocess dirname = tempfile.mkdtemp() is_surface = options.remesh.startswith('q') if is_surface: mesh = Mesh.from_file(filename_in) domain = FEDomain(mesh.name, mesh) region = domain.create_region('surf', 'vertices of surface', 'facet') surf_mesh = Mesh.from_region(region, mesh, localize=True, is_surface=True) filename = op.join(dirname, 'surf.mesh') surf_mesh.write(filename, io='auto') else: import shutil shutil.copy(filename_in, dirname) filename = op.join(dirname, op.basename(filename_in)) qopts = ''.join(options.remesh.split()) # Remove spaces. command = 'tetgen -BFENkACp%s %s' % (qopts, filename) args = shlex.split(command) subprocess.call(args) root, ext = op.splitext(filename) mesh = Mesh.from_file(root + '.1.vtk') remove_files(dirname) else: mesh = Mesh.from_file(filename_in) if options.force_2d: data = list(mesh._get_io_data()) data[0] = data[0][:, :2] mesh = Mesh.from_data(mesh.name, *data) if scale is not None: if len(scale) == 1: tr = nm.eye(mesh.dim, dtype=nm.float64) * scale elif len(scale) == mesh.dim: tr = nm.diag(scale) else: raise ValueError('bad scale! (%s)' % scale) mesh.transform_coors(tr) if center is not None: cc = 0.5 * mesh.get_bounding_box().sum(0) shift = center - cc tr = nm.c_[nm.eye(mesh.dim, dtype=nm.float64), shift[:, None]] mesh.transform_coors(tr) if options.refine > 0: domain = FEDomain(mesh.name, mesh) output('initial mesh: %d nodes %d elements' % (domain.shape.n_nod, domain.shape.n_el)) for ii in range(options.refine): output('refine %d...' % ii) domain = domain.refine() output('... %d nodes %d elements' % (domain.shape.n_nod, domain.shape.n_el)) mesh = domain.mesh if options.tri_tetra > 0: conns = None for k, new_desc in [('3_8', '3_4'), ('2_4', '2_3')]: if k in mesh.descs: conns = mesh.get_conn(k) break if conns is not None: nelo = conns.shape[0] output('initial mesh: %d elements' % nelo) new_conns = elems_q2t(conns) nn = new_conns.shape[0] // nelo new_cgroups = nm.repeat(mesh.cmesh.cell_groups, nn) output('new mesh: %d elements' % new_conns.shape[0]) mesh = Mesh.from_data(mesh.name, mesh.coors, mesh.cmesh.vertex_groups, [new_conns], [new_cgroups], [new_desc]) if options.merge: desc = mesh.descs[0] coor, ngroups, conns = fix_double_nodes(mesh.coors, mesh.cmesh.vertex_groups, mesh.get_conn(desc), 1e-9) mesh = Mesh.from_data(mesh.name + '_merged', coor, ngroups, [conns], [mesh.cmesh.cell_groups], [desc]) if options.save_per_mat: desc = mesh.descs[0] conns, cgroups = mesh.get_conn(desc), mesh.cmesh.cell_groups coors, ngroups = mesh.coors, mesh.cmesh.vertex_groups mat_ids = nm.unique(cgroups) for mat_id in mat_ids: idxs = nm.where(cgroups == mat_id)[0] imesh = Mesh.from_data(mesh.name + '_matid_%d' % mat_id, coors, ngroups, [conns[idxs]], [cgroups[idxs]], [desc]) fbase, fext = op.splitext(filename_out) ifilename_out = '%s_matid_%d%s' % (fbase, mat_id, fext) io = MeshIO.for_format(ifilename_out, format=options.format, writable=True) output('writing %s...' % ifilename_out) imesh.write(ifilename_out, io=io) output('...done') io = MeshIO.for_format(filename_out, format=options.format, writable=True) cell_types = ', '.join(supported_cell_types[io.format]) output('writing [%s] %s...' % (cell_types, filename_out)) mesh.write(filename_out, io=io)	output('...done')	sfepy.base.base.output
#!/usr/bin/env python """ Convert a mesh file from one SfePy-supported format to another. Examples:: $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s2.5 $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 -c 0 $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.mesh --remesh='q2/0 a1e-8 O9/7 V' $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new2.mesh --remesh='rq2/0 a1e-8 O9/7 V' """ from __future__ import absolute_import import sys import os.path as op from six.moves import range sys.path.append('.') from argparse import ArgumentParser, RawDescriptionHelpFormatter from sfepy.base.base import nm, output from sfepy.base.ioutils import remove_files from sfepy.discrete.fem import Mesh, FEDomain from sfepy.discrete.fem.meshio import (output_mesh_formats, MeshIO, supported_cell_types) from sfepy.discrete.fem.mesh import fix_double_nodes from sfepy.mesh.mesh_tools import elems_q2t helps = { 'scale' : 'scale factor (float or comma-separated list for each axis)' ' [default: %(default)s]', 'center' : 'center of the output mesh (0 for origin or' ' comma-separated list for each axis) applied after scaling' ' [default: %(default)s]', 'refine' : 'uniform refinement level [default: %(default)s]', 'format' : 'output mesh format (overrides filename_out extension)', 'list' : 'list supported readable/writable output mesh formats', 'merge' : 'remove duplicate vertices', 'tri-tetra' : 'convert elements: quad->tri, hexa->tetra', '2d' : 'force a 2D mesh by removing the z coordinates - assumes a 3D mesh' ' in the xy plane', 'save-per-mat': 'extract cells by material id and save them into' ' separate mesh files with a name based on filename_out and the id' ' numbers (preserves original mesh vertices)', 'remesh' : """when given, remesh the given mesh using tetgen. The options can be the following, separated by spaces, in this order: 1. "r" causes remeshing of the mesh volume - if not present the mesh surface is extracted and used for the volume mesh generation. 2. "q[<float>/<float>]" (required) - the two numbers after "q" are a maximum radius-edge ratio bound and a minimum dihedral angle bound. 3. "a<float>" (optional) - the number imposes a maximum volume constraint on all tetrahedra. 4. O[<0-9>/<0-7>] - the two numbers correspond to a mesh optimization level and a choice of optimizing operations. 5. "V" (optional) - if present, mesh statistics are printed. Consult the tetgen documentation for details.""", } def _parse_val_or_vec(option, name, parser): if option is not None: try: try: option = float(option) except ValueError: option = [float(ii) for ii in option.split(',')] option = nm.array(option, dtype=nm.float64, ndmin=1) except: output('bad %s! (%s)' % (name, option)) parser.print_help() sys.exit(1) return option def main(): parser = ArgumentParser(description=__doc__, formatter_class=RawDescriptionHelpFormatter) parser.add_argument('-s', '--scale', metavar='scale', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='scale', default=None, help=helps['scale']) parser.add_argument('-c', '--center', metavar='center', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='center', default=None, help=helps['center']) parser.add_argument('-r', '--refine', metavar='level', action="https://huggingface.co/datasets/luna-code/sfepy/store", type=int, dest='refine', default=0, help=helps['refine']) parser.add_argument('-f', '--format', metavar='format', action="https://huggingface.co/datasets/luna-code/sfepy/store", type=str, dest='format', default=None, help=helps['format']) parser.add_argument('-l', '--list', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='list', help=helps['list']) parser.add_argument('-m', '--merge', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='merge', help=helps['merge']) parser.add_argument('-t', '--tri-tetra', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='tri_tetra', help=helps['tri-tetra']) parser.add_argument('-2', '--2d', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='force_2d', help=helps['2d']) parser.add_argument('--save-per-mat', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='save_per_mat', help=helps['save-per-mat']) parser.add_argument('--remesh', metavar='options', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='remesh', default=None, help=helps['remesh']) parser.add_argument('filename_in') parser.add_argument('filename_out') options = parser.parse_args() if options.list:	output('Supported readable mesh formats:')	sfepy.base.base.output
#!/usr/bin/env python """ Convert a mesh file from one SfePy-supported format to another. Examples:: $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s2.5 $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 -c 0 $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.mesh --remesh='q2/0 a1e-8 O9/7 V' $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new2.mesh --remesh='rq2/0 a1e-8 O9/7 V' """ from __future__ import absolute_import import sys import os.path as op from six.moves import range sys.path.append('.') from argparse import ArgumentParser, RawDescriptionHelpFormatter from sfepy.base.base import nm, output from sfepy.base.ioutils import remove_files from sfepy.discrete.fem import Mesh, FEDomain from sfepy.discrete.fem.meshio import (output_mesh_formats, MeshIO, supported_cell_types) from sfepy.discrete.fem.mesh import fix_double_nodes from sfepy.mesh.mesh_tools import elems_q2t helps = { 'scale' : 'scale factor (float or comma-separated list for each axis)' ' [default: %(default)s]', 'center' : 'center of the output mesh (0 for origin or' ' comma-separated list for each axis) applied after scaling' ' [default: %(default)s]', 'refine' : 'uniform refinement level [default: %(default)s]', 'format' : 'output mesh format (overrides filename_out extension)', 'list' : 'list supported readable/writable output mesh formats', 'merge' : 'remove duplicate vertices', 'tri-tetra' : 'convert elements: quad->tri, hexa->tetra', '2d' : 'force a 2D mesh by removing the z coordinates - assumes a 3D mesh' ' in the xy plane', 'save-per-mat': 'extract cells by material id and save them into' ' separate mesh files with a name based on filename_out and the id' ' numbers (preserves original mesh vertices)', 'remesh' : """when given, remesh the given mesh using tetgen. The options can be the following, separated by spaces, in this order: 1. "r" causes remeshing of the mesh volume - if not present the mesh surface is extracted and used for the volume mesh generation. 2. "q[<float>/<float>]" (required) - the two numbers after "q" are a maximum radius-edge ratio bound and a minimum dihedral angle bound. 3. "a<float>" (optional) - the number imposes a maximum volume constraint on all tetrahedra. 4. O[<0-9>/<0-7>] - the two numbers correspond to a mesh optimization level and a choice of optimizing operations. 5. "V" (optional) - if present, mesh statistics are printed. Consult the tetgen documentation for details.""", } def _parse_val_or_vec(option, name, parser): if option is not None: try: try: option = float(option) except ValueError: option = [float(ii) for ii in option.split(',')] option = nm.array(option, dtype=nm.float64, ndmin=1) except: output('bad %s! (%s)' % (name, option)) parser.print_help() sys.exit(1) return option def main(): parser = ArgumentParser(description=__doc__, formatter_class=RawDescriptionHelpFormatter) parser.add_argument('-s', '--scale', metavar='scale', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='scale', default=None, help=helps['scale']) parser.add_argument('-c', '--center', metavar='center', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='center', default=None, help=helps['center']) parser.add_argument('-r', '--refine', metavar='level', action="https://huggingface.co/datasets/luna-code/sfepy/store", type=int, dest='refine', default=0, help=helps['refine']) parser.add_argument('-f', '--format', metavar='format', action="https://huggingface.co/datasets/luna-code/sfepy/store", type=str, dest='format', default=None, help=helps['format']) parser.add_argument('-l', '--list', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='list', help=helps['list']) parser.add_argument('-m', '--merge', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='merge', help=helps['merge']) parser.add_argument('-t', '--tri-tetra', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='tri_tetra', help=helps['tri-tetra']) parser.add_argument('-2', '--2d', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='force_2d', help=helps['2d']) parser.add_argument('--save-per-mat', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='save_per_mat', help=helps['save-per-mat']) parser.add_argument('--remesh', metavar='options', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='remesh', default=None, help=helps['remesh']) parser.add_argument('filename_in') parser.add_argument('filename_out') options = parser.parse_args() if options.list: output('Supported readable mesh formats:')	output('--------------------------------')	sfepy.base.base.output
#!/usr/bin/env python """ Convert a mesh file from one SfePy-supported format to another. Examples:: $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s2.5 $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 -c 0 $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.mesh --remesh='q2/0 a1e-8 O9/7 V' $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new2.mesh --remesh='rq2/0 a1e-8 O9/7 V' """ from __future__ import absolute_import import sys import os.path as op from six.moves import range sys.path.append('.') from argparse import ArgumentParser, RawDescriptionHelpFormatter from sfepy.base.base import nm, output from sfepy.base.ioutils import remove_files from sfepy.discrete.fem import Mesh, FEDomain from sfepy.discrete.fem.meshio import (output_mesh_formats, MeshIO, supported_cell_types) from sfepy.discrete.fem.mesh import fix_double_nodes from sfepy.mesh.mesh_tools import elems_q2t helps = { 'scale' : 'scale factor (float or comma-separated list for each axis)' ' [default: %(default)s]', 'center' : 'center of the output mesh (0 for origin or' ' comma-separated list for each axis) applied after scaling' ' [default: %(default)s]', 'refine' : 'uniform refinement level [default: %(default)s]', 'format' : 'output mesh format (overrides filename_out extension)', 'list' : 'list supported readable/writable output mesh formats', 'merge' : 'remove duplicate vertices', 'tri-tetra' : 'convert elements: quad->tri, hexa->tetra', '2d' : 'force a 2D mesh by removing the z coordinates - assumes a 3D mesh' ' in the xy plane', 'save-per-mat': 'extract cells by material id and save them into' ' separate mesh files with a name based on filename_out and the id' ' numbers (preserves original mesh vertices)', 'remesh' : """when given, remesh the given mesh using tetgen. The options can be the following, separated by spaces, in this order: 1. "r" causes remeshing of the mesh volume - if not present the mesh surface is extracted and used for the volume mesh generation. 2. "q[<float>/<float>]" (required) - the two numbers after "q" are a maximum radius-edge ratio bound and a minimum dihedral angle bound. 3. "a<float>" (optional) - the number imposes a maximum volume constraint on all tetrahedra. 4. O[<0-9>/<0-7>] - the two numbers correspond to a mesh optimization level and a choice of optimizing operations. 5. "V" (optional) - if present, mesh statistics are printed. Consult the tetgen documentation for details.""", } def _parse_val_or_vec(option, name, parser): if option is not None: try: try: option = float(option) except ValueError: option = [float(ii) for ii in option.split(',')] option = nm.array(option, dtype=nm.float64, ndmin=1) except: output('bad %s! (%s)' % (name, option)) parser.print_help() sys.exit(1) return option def main(): parser = ArgumentParser(description=__doc__, formatter_class=RawDescriptionHelpFormatter) parser.add_argument('-s', '--scale', metavar='scale', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='scale', default=None, help=helps['scale']) parser.add_argument('-c', '--center', metavar='center', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='center', default=None, help=helps['center']) parser.add_argument('-r', '--refine', metavar='level', action="https://huggingface.co/datasets/luna-code/sfepy/store", type=int, dest='refine', default=0, help=helps['refine']) parser.add_argument('-f', '--format', metavar='format', action="https://huggingface.co/datasets/luna-code/sfepy/store", type=str, dest='format', default=None, help=helps['format']) parser.add_argument('-l', '--list', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='list', help=helps['list']) parser.add_argument('-m', '--merge', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='merge', help=helps['merge']) parser.add_argument('-t', '--tri-tetra', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='tri_tetra', help=helps['tri-tetra']) parser.add_argument('-2', '--2d', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='force_2d', help=helps['2d']) parser.add_argument('--save-per-mat', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='save_per_mat', help=helps['save-per-mat']) parser.add_argument('--remesh', metavar='options', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='remesh', default=None, help=helps['remesh']) parser.add_argument('filename_in') parser.add_argument('filename_out') options = parser.parse_args() if options.list: output('Supported readable mesh formats:') output('--------------------------------')	output_mesh_formats('r')	sfepy.discrete.fem.meshio.output_mesh_formats
#!/usr/bin/env python """ Convert a mesh file from one SfePy-supported format to another. Examples:: $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s2.5 $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 -c 0 $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.mesh --remesh='q2/0 a1e-8 O9/7 V' $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new2.mesh --remesh='rq2/0 a1e-8 O9/7 V' """ from __future__ import absolute_import import sys import os.path as op from six.moves import range sys.path.append('.') from argparse import ArgumentParser, RawDescriptionHelpFormatter from sfepy.base.base import nm, output from sfepy.base.ioutils import remove_files from sfepy.discrete.fem import Mesh, FEDomain from sfepy.discrete.fem.meshio import (output_mesh_formats, MeshIO, supported_cell_types) from sfepy.discrete.fem.mesh import fix_double_nodes from sfepy.mesh.mesh_tools import elems_q2t helps = { 'scale' : 'scale factor (float or comma-separated list for each axis)' ' [default: %(default)s]', 'center' : 'center of the output mesh (0 for origin or' ' comma-separated list for each axis) applied after scaling' ' [default: %(default)s]', 'refine' : 'uniform refinement level [default: %(default)s]', 'format' : 'output mesh format (overrides filename_out extension)', 'list' : 'list supported readable/writable output mesh formats', 'merge' : 'remove duplicate vertices', 'tri-tetra' : 'convert elements: quad->tri, hexa->tetra', '2d' : 'force a 2D mesh by removing the z coordinates - assumes a 3D mesh' ' in the xy plane', 'save-per-mat': 'extract cells by material id and save them into' ' separate mesh files with a name based on filename_out and the id' ' numbers (preserves original mesh vertices)', 'remesh' : """when given, remesh the given mesh using tetgen. The options can be the following, separated by spaces, in this order: 1. "r" causes remeshing of the mesh volume - if not present the mesh surface is extracted and used for the volume mesh generation. 2. "q[<float>/<float>]" (required) - the two numbers after "q" are a maximum radius-edge ratio bound and a minimum dihedral angle bound. 3. "a<float>" (optional) - the number imposes a maximum volume constraint on all tetrahedra. 4. O[<0-9>/<0-7>] - the two numbers correspond to a mesh optimization level and a choice of optimizing operations. 5. "V" (optional) - if present, mesh statistics are printed. Consult the tetgen documentation for details.""", } def _parse_val_or_vec(option, name, parser): if option is not None: try: try: option = float(option) except ValueError: option = [float(ii) for ii in option.split(',')] option = nm.array(option, dtype=nm.float64, ndmin=1) except: output('bad %s! (%s)' % (name, option)) parser.print_help() sys.exit(1) return option def main(): parser = ArgumentParser(description=__doc__, formatter_class=RawDescriptionHelpFormatter) parser.add_argument('-s', '--scale', metavar='scale', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='scale', default=None, help=helps['scale']) parser.add_argument('-c', '--center', metavar='center', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='center', default=None, help=helps['center']) parser.add_argument('-r', '--refine', metavar='level', action="https://huggingface.co/datasets/luna-code/sfepy/store", type=int, dest='refine', default=0, help=helps['refine']) parser.add_argument('-f', '--format', metavar='format', action="https://huggingface.co/datasets/luna-code/sfepy/store", type=str, dest='format', default=None, help=helps['format']) parser.add_argument('-l', '--list', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='list', help=helps['list']) parser.add_argument('-m', '--merge', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='merge', help=helps['merge']) parser.add_argument('-t', '--tri-tetra', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='tri_tetra', help=helps['tri-tetra']) parser.add_argument('-2', '--2d', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='force_2d', help=helps['2d']) parser.add_argument('--save-per-mat', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='save_per_mat', help=helps['save-per-mat']) parser.add_argument('--remesh', metavar='options', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='remesh', default=None, help=helps['remesh']) parser.add_argument('filename_in') parser.add_argument('filename_out') options = parser.parse_args() if options.list: output('Supported readable mesh formats:') output('--------------------------------') output_mesh_formats('r')	output('')	sfepy.base.base.output
#!/usr/bin/env python """ Convert a mesh file from one SfePy-supported format to another. Examples:: $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s2.5 $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 -c 0 $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.mesh --remesh='q2/0 a1e-8 O9/7 V' $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new2.mesh --remesh='rq2/0 a1e-8 O9/7 V' """ from __future__ import absolute_import import sys import os.path as op from six.moves import range sys.path.append('.') from argparse import ArgumentParser, RawDescriptionHelpFormatter from sfepy.base.base import nm, output from sfepy.base.ioutils import remove_files from sfepy.discrete.fem import Mesh, FEDomain from sfepy.discrete.fem.meshio import (output_mesh_formats, MeshIO, supported_cell_types) from sfepy.discrete.fem.mesh import fix_double_nodes from sfepy.mesh.mesh_tools import elems_q2t helps = { 'scale' : 'scale factor (float or comma-separated list for each axis)' ' [default: %(default)s]', 'center' : 'center of the output mesh (0 for origin or' ' comma-separated list for each axis) applied after scaling' ' [default: %(default)s]', 'refine' : 'uniform refinement level [default: %(default)s]', 'format' : 'output mesh format (overrides filename_out extension)', 'list' : 'list supported readable/writable output mesh formats', 'merge' : 'remove duplicate vertices', 'tri-tetra' : 'convert elements: quad->tri, hexa->tetra', '2d' : 'force a 2D mesh by removing the z coordinates - assumes a 3D mesh' ' in the xy plane', 'save-per-mat': 'extract cells by material id and save them into' ' separate mesh files with a name based on filename_out and the id' ' numbers (preserves original mesh vertices)', 'remesh' : """when given, remesh the given mesh using tetgen. The options can be the following, separated by spaces, in this order: 1. "r" causes remeshing of the mesh volume - if not present the mesh surface is extracted and used for the volume mesh generation. 2. "q[<float>/<float>]" (required) - the two numbers after "q" are a maximum radius-edge ratio bound and a minimum dihedral angle bound. 3. "a<float>" (optional) - the number imposes a maximum volume constraint on all tetrahedra. 4. O[<0-9>/<0-7>] - the two numbers correspond to a mesh optimization level and a choice of optimizing operations. 5. "V" (optional) - if present, mesh statistics are printed. Consult the tetgen documentation for details.""", } def _parse_val_or_vec(option, name, parser): if option is not None: try: try: option = float(option) except ValueError: option = [float(ii) for ii in option.split(',')] option = nm.array(option, dtype=nm.float64, ndmin=1) except: output('bad %s! (%s)' % (name, option)) parser.print_help() sys.exit(1) return option def main(): parser = ArgumentParser(description=__doc__, formatter_class=RawDescriptionHelpFormatter) parser.add_argument('-s', '--scale', metavar='scale', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='scale', default=None, help=helps['scale']) parser.add_argument('-c', '--center', metavar='center', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='center', default=None, help=helps['center']) parser.add_argument('-r', '--refine', metavar='level', action="https://huggingface.co/datasets/luna-code/sfepy/store", type=int, dest='refine', default=0, help=helps['refine']) parser.add_argument('-f', '--format', metavar='format', action="https://huggingface.co/datasets/luna-code/sfepy/store", type=str, dest='format', default=None, help=helps['format']) parser.add_argument('-l', '--list', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='list', help=helps['list']) parser.add_argument('-m', '--merge', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='merge', help=helps['merge']) parser.add_argument('-t', '--tri-tetra', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='tri_tetra', help=helps['tri-tetra']) parser.add_argument('-2', '--2d', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='force_2d', help=helps['2d']) parser.add_argument('--save-per-mat', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='save_per_mat', help=helps['save-per-mat']) parser.add_argument('--remesh', metavar='options', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='remesh', default=None, help=helps['remesh']) parser.add_argument('filename_in') parser.add_argument('filename_out') options = parser.parse_args() if options.list: output('Supported readable mesh formats:') output('--------------------------------') output_mesh_formats('r') output('')	output('Supported writable mesh formats:')	sfepy.base.base.output
#!/usr/bin/env python """ Convert a mesh file from one SfePy-supported format to another. Examples:: $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s2.5 $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 -c 0 $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.mesh --remesh='q2/0 a1e-8 O9/7 V' $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new2.mesh --remesh='rq2/0 a1e-8 O9/7 V' """ from __future__ import absolute_import import sys import os.path as op from six.moves import range sys.path.append('.') from argparse import ArgumentParser, RawDescriptionHelpFormatter from sfepy.base.base import nm, output from sfepy.base.ioutils import remove_files from sfepy.discrete.fem import Mesh, FEDomain from sfepy.discrete.fem.meshio import (output_mesh_formats, MeshIO, supported_cell_types) from sfepy.discrete.fem.mesh import fix_double_nodes from sfepy.mesh.mesh_tools import elems_q2t helps = { 'scale' : 'scale factor (float or comma-separated list for each axis)' ' [default: %(default)s]', 'center' : 'center of the output mesh (0 for origin or' ' comma-separated list for each axis) applied after scaling' ' [default: %(default)s]', 'refine' : 'uniform refinement level [default: %(default)s]', 'format' : 'output mesh format (overrides filename_out extension)', 'list' : 'list supported readable/writable output mesh formats', 'merge' : 'remove duplicate vertices', 'tri-tetra' : 'convert elements: quad->tri, hexa->tetra', '2d' : 'force a 2D mesh by removing the z coordinates - assumes a 3D mesh' ' in the xy plane', 'save-per-mat': 'extract cells by material id and save them into' ' separate mesh files with a name based on filename_out and the id' ' numbers (preserves original mesh vertices)', 'remesh' : """when given, remesh the given mesh using tetgen. The options can be the following, separated by spaces, in this order: 1. "r" causes remeshing of the mesh volume - if not present the mesh surface is extracted and used for the volume mesh generation. 2. "q[<float>/<float>]" (required) - the two numbers after "q" are a maximum radius-edge ratio bound and a minimum dihedral angle bound. 3. "a<float>" (optional) - the number imposes a maximum volume constraint on all tetrahedra. 4. O[<0-9>/<0-7>] - the two numbers correspond to a mesh optimization level and a choice of optimizing operations. 5. "V" (optional) - if present, mesh statistics are printed. Consult the tetgen documentation for details.""", } def _parse_val_or_vec(option, name, parser): if option is not None: try: try: option = float(option) except ValueError: option = [float(ii) for ii in option.split(',')] option = nm.array(option, dtype=nm.float64, ndmin=1) except: output('bad %s! (%s)' % (name, option)) parser.print_help() sys.exit(1) return option def main(): parser = ArgumentParser(description=__doc__, formatter_class=RawDescriptionHelpFormatter) parser.add_argument('-s', '--scale', metavar='scale', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='scale', default=None, help=helps['scale']) parser.add_argument('-c', '--center', metavar='center', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='center', default=None, help=helps['center']) parser.add_argument('-r', '--refine', metavar='level', action="https://huggingface.co/datasets/luna-code/sfepy/store", type=int, dest='refine', default=0, help=helps['refine']) parser.add_argument('-f', '--format', metavar='format', action="https://huggingface.co/datasets/luna-code/sfepy/store", type=str, dest='format', default=None, help=helps['format']) parser.add_argument('-l', '--list', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='list', help=helps['list']) parser.add_argument('-m', '--merge', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='merge', help=helps['merge']) parser.add_argument('-t', '--tri-tetra', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='tri_tetra', help=helps['tri-tetra']) parser.add_argument('-2', '--2d', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='force_2d', help=helps['2d']) parser.add_argument('--save-per-mat', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='save_per_mat', help=helps['save-per-mat']) parser.add_argument('--remesh', metavar='options', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='remesh', default=None, help=helps['remesh']) parser.add_argument('filename_in') parser.add_argument('filename_out') options = parser.parse_args() if options.list: output('Supported readable mesh formats:') output('--------------------------------') output_mesh_formats('r') output('') output('Supported writable mesh formats:')	output('--------------------------------')	sfepy.base.base.output
#!/usr/bin/env python """ Convert a mesh file from one SfePy-supported format to another. Examples:: $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s2.5 $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 -c 0 $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.mesh --remesh='q2/0 a1e-8 O9/7 V' $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new2.mesh --remesh='rq2/0 a1e-8 O9/7 V' """ from __future__ import absolute_import import sys import os.path as op from six.moves import range sys.path.append('.') from argparse import ArgumentParser, RawDescriptionHelpFormatter from sfepy.base.base import nm, output from sfepy.base.ioutils import remove_files from sfepy.discrete.fem import Mesh, FEDomain from sfepy.discrete.fem.meshio import (output_mesh_formats, MeshIO, supported_cell_types) from sfepy.discrete.fem.mesh import fix_double_nodes from sfepy.mesh.mesh_tools import elems_q2t helps = { 'scale' : 'scale factor (float or comma-separated list for each axis)' ' [default: %(default)s]', 'center' : 'center of the output mesh (0 for origin or' ' comma-separated list for each axis) applied after scaling' ' [default: %(default)s]', 'refine' : 'uniform refinement level [default: %(default)s]', 'format' : 'output mesh format (overrides filename_out extension)', 'list' : 'list supported readable/writable output mesh formats', 'merge' : 'remove duplicate vertices', 'tri-tetra' : 'convert elements: quad->tri, hexa->tetra', '2d' : 'force a 2D mesh by removing the z coordinates - assumes a 3D mesh' ' in the xy plane', 'save-per-mat': 'extract cells by material id and save them into' ' separate mesh files with a name based on filename_out and the id' ' numbers (preserves original mesh vertices)', 'remesh' : """when given, remesh the given mesh using tetgen. The options can be the following, separated by spaces, in this order: 1. "r" causes remeshing of the mesh volume - if not present the mesh surface is extracted and used for the volume mesh generation. 2. "q[<float>/<float>]" (required) - the two numbers after "q" are a maximum radius-edge ratio bound and a minimum dihedral angle bound. 3. "a<float>" (optional) - the number imposes a maximum volume constraint on all tetrahedra. 4. O[<0-9>/<0-7>] - the two numbers correspond to a mesh optimization level and a choice of optimizing operations. 5. "V" (optional) - if present, mesh statistics are printed. Consult the tetgen documentation for details.""", } def _parse_val_or_vec(option, name, parser): if option is not None: try: try: option = float(option) except ValueError: option = [float(ii) for ii in option.split(',')] option = nm.array(option, dtype=nm.float64, ndmin=1) except: output('bad %s! (%s)' % (name, option)) parser.print_help() sys.exit(1) return option def main(): parser = ArgumentParser(description=__doc__, formatter_class=RawDescriptionHelpFormatter) parser.add_argument('-s', '--scale', metavar='scale', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='scale', default=None, help=helps['scale']) parser.add_argument('-c', '--center', metavar='center', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='center', default=None, help=helps['center']) parser.add_argument('-r', '--refine', metavar='level', action="https://huggingface.co/datasets/luna-code/sfepy/store", type=int, dest='refine', default=0, help=helps['refine']) parser.add_argument('-f', '--format', metavar='format', action="https://huggingface.co/datasets/luna-code/sfepy/store", type=str, dest='format', default=None, help=helps['format']) parser.add_argument('-l', '--list', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='list', help=helps['list']) parser.add_argument('-m', '--merge', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='merge', help=helps['merge']) parser.add_argument('-t', '--tri-tetra', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='tri_tetra', help=helps['tri-tetra']) parser.add_argument('-2', '--2d', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='force_2d', help=helps['2d']) parser.add_argument('--save-per-mat', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='save_per_mat', help=helps['save-per-mat']) parser.add_argument('--remesh', metavar='options', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='remesh', default=None, help=helps['remesh']) parser.add_argument('filename_in') parser.add_argument('filename_out') options = parser.parse_args() if options.list: output('Supported readable mesh formats:') output('--------------------------------') output_mesh_formats('r') output('') output('Supported writable mesh formats:') output('--------------------------------')	output_mesh_formats('w')	sfepy.discrete.fem.meshio.output_mesh_formats
#!/usr/bin/env python """ Convert a mesh file from one SfePy-supported format to another. Examples:: $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s2.5 $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 -c 0 $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.mesh --remesh='q2/0 a1e-8 O9/7 V' $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new2.mesh --remesh='rq2/0 a1e-8 O9/7 V' """ from __future__ import absolute_import import sys import os.path as op from six.moves import range sys.path.append('.') from argparse import ArgumentParser, RawDescriptionHelpFormatter from sfepy.base.base import nm, output from sfepy.base.ioutils import remove_files from sfepy.discrete.fem import Mesh, FEDomain from sfepy.discrete.fem.meshio import (output_mesh_formats, MeshIO, supported_cell_types) from sfepy.discrete.fem.mesh import fix_double_nodes from sfepy.mesh.mesh_tools import elems_q2t helps = { 'scale' : 'scale factor (float or comma-separated list for each axis)' ' [default: %(default)s]', 'center' : 'center of the output mesh (0 for origin or' ' comma-separated list for each axis) applied after scaling' ' [default: %(default)s]', 'refine' : 'uniform refinement level [default: %(default)s]', 'format' : 'output mesh format (overrides filename_out extension)', 'list' : 'list supported readable/writable output mesh formats', 'merge' : 'remove duplicate vertices', 'tri-tetra' : 'convert elements: quad->tri, hexa->tetra', '2d' : 'force a 2D mesh by removing the z coordinates - assumes a 3D mesh' ' in the xy plane', 'save-per-mat': 'extract cells by material id and save them into' ' separate mesh files with a name based on filename_out and the id' ' numbers (preserves original mesh vertices)', 'remesh' : """when given, remesh the given mesh using tetgen. The options can be the following, separated by spaces, in this order: 1. "r" causes remeshing of the mesh volume - if not present the mesh surface is extracted and used for the volume mesh generation. 2. "q[<float>/<float>]" (required) - the two numbers after "q" are a maximum radius-edge ratio bound and a minimum dihedral angle bound. 3. "a<float>" (optional) - the number imposes a maximum volume constraint on all tetrahedra. 4. O[<0-9>/<0-7>] - the two numbers correspond to a mesh optimization level and a choice of optimizing operations. 5. "V" (optional) - if present, mesh statistics are printed. Consult the tetgen documentation for details.""", } def _parse_val_or_vec(option, name, parser): if option is not None: try: try: option = float(option) except ValueError: option = [float(ii) for ii in option.split(',')] option = nm.array(option, dtype=nm.float64, ndmin=1) except: output('bad %s! (%s)' % (name, option)) parser.print_help() sys.exit(1) return option def main(): parser = ArgumentParser(description=__doc__, formatter_class=RawDescriptionHelpFormatter) parser.add_argument('-s', '--scale', metavar='scale', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='scale', default=None, help=helps['scale']) parser.add_argument('-c', '--center', metavar='center', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='center', default=None, help=helps['center']) parser.add_argument('-r', '--refine', metavar='level', action="https://huggingface.co/datasets/luna-code/sfepy/store", type=int, dest='refine', default=0, help=helps['refine']) parser.add_argument('-f', '--format', metavar='format', action="https://huggingface.co/datasets/luna-code/sfepy/store", type=str, dest='format', default=None, help=helps['format']) parser.add_argument('-l', '--list', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='list', help=helps['list']) parser.add_argument('-m', '--merge', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='merge', help=helps['merge']) parser.add_argument('-t', '--tri-tetra', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='tri_tetra', help=helps['tri-tetra']) parser.add_argument('-2', '--2d', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='force_2d', help=helps['2d']) parser.add_argument('--save-per-mat', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='save_per_mat', help=helps['save-per-mat']) parser.add_argument('--remesh', metavar='options', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='remesh', default=None, help=helps['remesh']) parser.add_argument('filename_in') parser.add_argument('filename_out') options = parser.parse_args() if options.list: output('Supported readable mesh formats:') output('--------------------------------') output_mesh_formats('r') output('') output('Supported writable mesh formats:') output('--------------------------------') output_mesh_formats('w') sys.exit(0) scale = _parse_val_or_vec(options.scale, 'scale', parser) center = _parse_val_or_vec(options.center, 'center', parser) filename_in = options.filename_in filename_out = options.filename_out if options.remesh: import tempfile import shlex import subprocess dirname = tempfile.mkdtemp() is_surface = options.remesh.startswith('q') if is_surface: mesh = Mesh.from_file(filename_in) domain = FEDomain(mesh.name, mesh) region = domain.create_region('surf', 'vertices of surface', 'facet') surf_mesh = Mesh.from_region(region, mesh, localize=True, is_surface=True) filename = op.join(dirname, 'surf.mesh') surf_mesh.write(filename, io='auto') else: import shutil shutil.copy(filename_in, dirname) filename = op.join(dirname, op.basename(filename_in)) qopts = ''.join(options.remesh.split()) # Remove spaces. command = 'tetgen -BFENkACp%s %s' % (qopts, filename) args = shlex.split(command) subprocess.call(args) root, ext = op.splitext(filename) mesh =	Mesh.from_file(root + '.1.vtk')	sfepy.discrete.fem.Mesh.from_file
#!/usr/bin/env python """ Convert a mesh file from one SfePy-supported format to another. Examples:: $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s2.5 $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 -c 0 $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.mesh --remesh='q2/0 a1e-8 O9/7 V' $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new2.mesh --remesh='rq2/0 a1e-8 O9/7 V' """ from __future__ import absolute_import import sys import os.path as op from six.moves import range sys.path.append('.') from argparse import ArgumentParser, RawDescriptionHelpFormatter from sfepy.base.base import nm, output from sfepy.base.ioutils import remove_files from sfepy.discrete.fem import Mesh, FEDomain from sfepy.discrete.fem.meshio import (output_mesh_formats, MeshIO, supported_cell_types) from sfepy.discrete.fem.mesh import fix_double_nodes from sfepy.mesh.mesh_tools import elems_q2t helps = { 'scale' : 'scale factor (float or comma-separated list for each axis)' ' [default: %(default)s]', 'center' : 'center of the output mesh (0 for origin or' ' comma-separated list for each axis) applied after scaling' ' [default: %(default)s]', 'refine' : 'uniform refinement level [default: %(default)s]', 'format' : 'output mesh format (overrides filename_out extension)', 'list' : 'list supported readable/writable output mesh formats', 'merge' : 'remove duplicate vertices', 'tri-tetra' : 'convert elements: quad->tri, hexa->tetra', '2d' : 'force a 2D mesh by removing the z coordinates - assumes a 3D mesh' ' in the xy plane', 'save-per-mat': 'extract cells by material id and save them into' ' separate mesh files with a name based on filename_out and the id' ' numbers (preserves original mesh vertices)', 'remesh' : """when given, remesh the given mesh using tetgen. The options can be the following, separated by spaces, in this order: 1. "r" causes remeshing of the mesh volume - if not present the mesh surface is extracted and used for the volume mesh generation. 2. "q[<float>/<float>]" (required) - the two numbers after "q" are a maximum radius-edge ratio bound and a minimum dihedral angle bound. 3. "a<float>" (optional) - the number imposes a maximum volume constraint on all tetrahedra. 4. O[<0-9>/<0-7>] - the two numbers correspond to a mesh optimization level and a choice of optimizing operations. 5. "V" (optional) - if present, mesh statistics are printed. Consult the tetgen documentation for details.""", } def _parse_val_or_vec(option, name, parser): if option is not None: try: try: option = float(option) except ValueError: option = [float(ii) for ii in option.split(',')] option = nm.array(option, dtype=nm.float64, ndmin=1) except: output('bad %s! (%s)' % (name, option)) parser.print_help() sys.exit(1) return option def main(): parser = ArgumentParser(description=__doc__, formatter_class=RawDescriptionHelpFormatter) parser.add_argument('-s', '--scale', metavar='scale', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='scale', default=None, help=helps['scale']) parser.add_argument('-c', '--center', metavar='center', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='center', default=None, help=helps['center']) parser.add_argument('-r', '--refine', metavar='level', action="https://huggingface.co/datasets/luna-code/sfepy/store", type=int, dest='refine', default=0, help=helps['refine']) parser.add_argument('-f', '--format', metavar='format', action="https://huggingface.co/datasets/luna-code/sfepy/store", type=str, dest='format', default=None, help=helps['format']) parser.add_argument('-l', '--list', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='list', help=helps['list']) parser.add_argument('-m', '--merge', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='merge', help=helps['merge']) parser.add_argument('-t', '--tri-tetra', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='tri_tetra', help=helps['tri-tetra']) parser.add_argument('-2', '--2d', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='force_2d', help=helps['2d']) parser.add_argument('--save-per-mat', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='save_per_mat', help=helps['save-per-mat']) parser.add_argument('--remesh', metavar='options', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='remesh', default=None, help=helps['remesh']) parser.add_argument('filename_in') parser.add_argument('filename_out') options = parser.parse_args() if options.list: output('Supported readable mesh formats:') output('--------------------------------') output_mesh_formats('r') output('') output('Supported writable mesh formats:') output('--------------------------------') output_mesh_formats('w') sys.exit(0) scale = _parse_val_or_vec(options.scale, 'scale', parser) center = _parse_val_or_vec(options.center, 'center', parser) filename_in = options.filename_in filename_out = options.filename_out if options.remesh: import tempfile import shlex import subprocess dirname = tempfile.mkdtemp() is_surface = options.remesh.startswith('q') if is_surface: mesh = Mesh.from_file(filename_in) domain = FEDomain(mesh.name, mesh) region = domain.create_region('surf', 'vertices of surface', 'facet') surf_mesh = Mesh.from_region(region, mesh, localize=True, is_surface=True) filename = op.join(dirname, 'surf.mesh') surf_mesh.write(filename, io='auto') else: import shutil shutil.copy(filename_in, dirname) filename = op.join(dirname, op.basename(filename_in)) qopts = ''.join(options.remesh.split()) # Remove spaces. command = 'tetgen -BFENkACp%s %s' % (qopts, filename) args = shlex.split(command) subprocess.call(args) root, ext = op.splitext(filename) mesh = Mesh.from_file(root + '.1.vtk')	remove_files(dirname)	sfepy.base.ioutils.remove_files
#!/usr/bin/env python """ Convert a mesh file from one SfePy-supported format to another. Examples:: $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s2.5 $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 -c 0 $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.mesh --remesh='q2/0 a1e-8 O9/7 V' $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new2.mesh --remesh='rq2/0 a1e-8 O9/7 V' """ from __future__ import absolute_import import sys import os.path as op from six.moves import range sys.path.append('.') from argparse import ArgumentParser, RawDescriptionHelpFormatter from sfepy.base.base import nm, output from sfepy.base.ioutils import remove_files from sfepy.discrete.fem import Mesh, FEDomain from sfepy.discrete.fem.meshio import (output_mesh_formats, MeshIO, supported_cell_types) from sfepy.discrete.fem.mesh import fix_double_nodes from sfepy.mesh.mesh_tools import elems_q2t helps = { 'scale' : 'scale factor (float or comma-separated list for each axis)' ' [default: %(default)s]', 'center' : 'center of the output mesh (0 for origin or' ' comma-separated list for each axis) applied after scaling' ' [default: %(default)s]', 'refine' : 'uniform refinement level [default: %(default)s]', 'format' : 'output mesh format (overrides filename_out extension)', 'list' : 'list supported readable/writable output mesh formats', 'merge' : 'remove duplicate vertices', 'tri-tetra' : 'convert elements: quad->tri, hexa->tetra', '2d' : 'force a 2D mesh by removing the z coordinates - assumes a 3D mesh' ' in the xy plane', 'save-per-mat': 'extract cells by material id and save them into' ' separate mesh files with a name based on filename_out and the id' ' numbers (preserves original mesh vertices)', 'remesh' : """when given, remesh the given mesh using tetgen. The options can be the following, separated by spaces, in this order: 1. "r" causes remeshing of the mesh volume - if not present the mesh surface is extracted and used for the volume mesh generation. 2. "q[<float>/<float>]" (required) - the two numbers after "q" are a maximum radius-edge ratio bound and a minimum dihedral angle bound. 3. "a<float>" (optional) - the number imposes a maximum volume constraint on all tetrahedra. 4. O[<0-9>/<0-7>] - the two numbers correspond to a mesh optimization level and a choice of optimizing operations. 5. "V" (optional) - if present, mesh statistics are printed. Consult the tetgen documentation for details.""", } def _parse_val_or_vec(option, name, parser): if option is not None: try: try: option = float(option) except ValueError: option = [float(ii) for ii in option.split(',')] option = nm.array(option, dtype=nm.float64, ndmin=1) except: output('bad %s! (%s)' % (name, option)) parser.print_help() sys.exit(1) return option def main(): parser = ArgumentParser(description=__doc__, formatter_class=RawDescriptionHelpFormatter) parser.add_argument('-s', '--scale', metavar='scale', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='scale', default=None, help=helps['scale']) parser.add_argument('-c', '--center', metavar='center', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='center', default=None, help=helps['center']) parser.add_argument('-r', '--refine', metavar='level', action="https://huggingface.co/datasets/luna-code/sfepy/store", type=int, dest='refine', default=0, help=helps['refine']) parser.add_argument('-f', '--format', metavar='format', action="https://huggingface.co/datasets/luna-code/sfepy/store", type=str, dest='format', default=None, help=helps['format']) parser.add_argument('-l', '--list', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='list', help=helps['list']) parser.add_argument('-m', '--merge', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='merge', help=helps['merge']) parser.add_argument('-t', '--tri-tetra', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='tri_tetra', help=helps['tri-tetra']) parser.add_argument('-2', '--2d', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='force_2d', help=helps['2d']) parser.add_argument('--save-per-mat', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='save_per_mat', help=helps['save-per-mat']) parser.add_argument('--remesh', metavar='options', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='remesh', default=None, help=helps['remesh']) parser.add_argument('filename_in') parser.add_argument('filename_out') options = parser.parse_args() if options.list: output('Supported readable mesh formats:') output('--------------------------------') output_mesh_formats('r') output('') output('Supported writable mesh formats:') output('--------------------------------') output_mesh_formats('w') sys.exit(0) scale = _parse_val_or_vec(options.scale, 'scale', parser) center = _parse_val_or_vec(options.center, 'center', parser) filename_in = options.filename_in filename_out = options.filename_out if options.remesh: import tempfile import shlex import subprocess dirname = tempfile.mkdtemp() is_surface = options.remesh.startswith('q') if is_surface: mesh = Mesh.from_file(filename_in) domain = FEDomain(mesh.name, mesh) region = domain.create_region('surf', 'vertices of surface', 'facet') surf_mesh = Mesh.from_region(region, mesh, localize=True, is_surface=True) filename = op.join(dirname, 'surf.mesh') surf_mesh.write(filename, io='auto') else: import shutil shutil.copy(filename_in, dirname) filename = op.join(dirname, op.basename(filename_in)) qopts = ''.join(options.remesh.split()) # Remove spaces. command = 'tetgen -BFENkACp%s %s' % (qopts, filename) args = shlex.split(command) subprocess.call(args) root, ext = op.splitext(filename) mesh = Mesh.from_file(root + '.1.vtk') remove_files(dirname) else: mesh =	Mesh.from_file(filename_in)	sfepy.discrete.fem.Mesh.from_file
#!/usr/bin/env python """ Convert a mesh file from one SfePy-supported format to another. Examples:: $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s2.5 $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 -c 0 $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.mesh --remesh='q2/0 a1e-8 O9/7 V' $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new2.mesh --remesh='rq2/0 a1e-8 O9/7 V' """ from __future__ import absolute_import import sys import os.path as op from six.moves import range sys.path.append('.') from argparse import ArgumentParser, RawDescriptionHelpFormatter from sfepy.base.base import nm, output from sfepy.base.ioutils import remove_files from sfepy.discrete.fem import Mesh, FEDomain from sfepy.discrete.fem.meshio import (output_mesh_formats, MeshIO, supported_cell_types) from sfepy.discrete.fem.mesh import fix_double_nodes from sfepy.mesh.mesh_tools import elems_q2t helps = { 'scale' : 'scale factor (float or comma-separated list for each axis)' ' [default: %(default)s]', 'center' : 'center of the output mesh (0 for origin or' ' comma-separated list for each axis) applied after scaling' ' [default: %(default)s]', 'refine' : 'uniform refinement level [default: %(default)s]', 'format' : 'output mesh format (overrides filename_out extension)', 'list' : 'list supported readable/writable output mesh formats', 'merge' : 'remove duplicate vertices', 'tri-tetra' : 'convert elements: quad->tri, hexa->tetra', '2d' : 'force a 2D mesh by removing the z coordinates - assumes a 3D mesh' ' in the xy plane', 'save-per-mat': 'extract cells by material id and save them into' ' separate mesh files with a name based on filename_out and the id' ' numbers (preserves original mesh vertices)', 'remesh' : """when given, remesh the given mesh using tetgen. The options can be the following, separated by spaces, in this order: 1. "r" causes remeshing of the mesh volume - if not present the mesh surface is extracted and used for the volume mesh generation. 2. "q[<float>/<float>]" (required) - the two numbers after "q" are a maximum radius-edge ratio bound and a minimum dihedral angle bound. 3. "a<float>" (optional) - the number imposes a maximum volume constraint on all tetrahedra. 4. O[<0-9>/<0-7>] - the two numbers correspond to a mesh optimization level and a choice of optimizing operations. 5. "V" (optional) - if present, mesh statistics are printed. Consult the tetgen documentation for details.""", } def _parse_val_or_vec(option, name, parser): if option is not None: try: try: option = float(option) except ValueError: option = [float(ii) for ii in option.split(',')] option = nm.array(option, dtype=nm.float64, ndmin=1) except: output('bad %s! (%s)' % (name, option)) parser.print_help() sys.exit(1) return option def main(): parser = ArgumentParser(description=__doc__, formatter_class=RawDescriptionHelpFormatter) parser.add_argument('-s', '--scale', metavar='scale', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='scale', default=None, help=helps['scale']) parser.add_argument('-c', '--center', metavar='center', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='center', default=None, help=helps['center']) parser.add_argument('-r', '--refine', metavar='level', action="https://huggingface.co/datasets/luna-code/sfepy/store", type=int, dest='refine', default=0, help=helps['refine']) parser.add_argument('-f', '--format', metavar='format', action="https://huggingface.co/datasets/luna-code/sfepy/store", type=str, dest='format', default=None, help=helps['format']) parser.add_argument('-l', '--list', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='list', help=helps['list']) parser.add_argument('-m', '--merge', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='merge', help=helps['merge']) parser.add_argument('-t', '--tri-tetra', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='tri_tetra', help=helps['tri-tetra']) parser.add_argument('-2', '--2d', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='force_2d', help=helps['2d']) parser.add_argument('--save-per-mat', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='save_per_mat', help=helps['save-per-mat']) parser.add_argument('--remesh', metavar='options', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='remesh', default=None, help=helps['remesh']) parser.add_argument('filename_in') parser.add_argument('filename_out') options = parser.parse_args() if options.list: output('Supported readable mesh formats:') output('--------------------------------') output_mesh_formats('r') output('') output('Supported writable mesh formats:') output('--------------------------------') output_mesh_formats('w') sys.exit(0) scale = _parse_val_or_vec(options.scale, 'scale', parser) center = _parse_val_or_vec(options.center, 'center', parser) filename_in = options.filename_in filename_out = options.filename_out if options.remesh: import tempfile import shlex import subprocess dirname = tempfile.mkdtemp() is_surface = options.remesh.startswith('q') if is_surface: mesh = Mesh.from_file(filename_in) domain = FEDomain(mesh.name, mesh) region = domain.create_region('surf', 'vertices of surface', 'facet') surf_mesh = Mesh.from_region(region, mesh, localize=True, is_surface=True) filename = op.join(dirname, 'surf.mesh') surf_mesh.write(filename, io='auto') else: import shutil shutil.copy(filename_in, dirname) filename = op.join(dirname, op.basename(filename_in)) qopts = ''.join(options.remesh.split()) # Remove spaces. command = 'tetgen -BFENkACp%s %s' % (qopts, filename) args = shlex.split(command) subprocess.call(args) root, ext = op.splitext(filename) mesh = Mesh.from_file(root + '.1.vtk') remove_files(dirname) else: mesh = Mesh.from_file(filename_in) if options.force_2d: data = list(mesh._get_io_data()) data[0] = data[0][:, :2] mesh =	Mesh.from_data(mesh.name, *data)	sfepy.discrete.fem.Mesh.from_data
#!/usr/bin/env python """ Convert a mesh file from one SfePy-supported format to another. Examples:: $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s2.5 $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 -c 0 $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.mesh --remesh='q2/0 a1e-8 O9/7 V' $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new2.mesh --remesh='rq2/0 a1e-8 O9/7 V' """ from __future__ import absolute_import import sys import os.path as op from six.moves import range sys.path.append('.') from argparse import ArgumentParser, RawDescriptionHelpFormatter from sfepy.base.base import nm, output from sfepy.base.ioutils import remove_files from sfepy.discrete.fem import Mesh, FEDomain from sfepy.discrete.fem.meshio import (output_mesh_formats, MeshIO, supported_cell_types) from sfepy.discrete.fem.mesh import fix_double_nodes from sfepy.mesh.mesh_tools import elems_q2t helps = { 'scale' : 'scale factor (float or comma-separated list for each axis)' ' [default: %(default)s]', 'center' : 'center of the output mesh (0 for origin or' ' comma-separated list for each axis) applied after scaling' ' [default: %(default)s]', 'refine' : 'uniform refinement level [default: %(default)s]', 'format' : 'output mesh format (overrides filename_out extension)', 'list' : 'list supported readable/writable output mesh formats', 'merge' : 'remove duplicate vertices', 'tri-tetra' : 'convert elements: quad->tri, hexa->tetra', '2d' : 'force a 2D mesh by removing the z coordinates - assumes a 3D mesh' ' in the xy plane', 'save-per-mat': 'extract cells by material id and save them into' ' separate mesh files with a name based on filename_out and the id' ' numbers (preserves original mesh vertices)', 'remesh' : """when given, remesh the given mesh using tetgen. The options can be the following, separated by spaces, in this order: 1. "r" causes remeshing of the mesh volume - if not present the mesh surface is extracted and used for the volume mesh generation. 2. "q[<float>/<float>]" (required) - the two numbers after "q" are a maximum radius-edge ratio bound and a minimum dihedral angle bound. 3. "a<float>" (optional) - the number imposes a maximum volume constraint on all tetrahedra. 4. O[<0-9>/<0-7>] - the two numbers correspond to a mesh optimization level and a choice of optimizing operations. 5. "V" (optional) - if present, mesh statistics are printed. Consult the tetgen documentation for details.""", } def _parse_val_or_vec(option, name, parser): if option is not None: try: try: option = float(option) except ValueError: option = [float(ii) for ii in option.split(',')] option = nm.array(option, dtype=nm.float64, ndmin=1) except: output('bad %s! (%s)' % (name, option)) parser.print_help() sys.exit(1) return option def main(): parser = ArgumentParser(description=__doc__, formatter_class=RawDescriptionHelpFormatter) parser.add_argument('-s', '--scale', metavar='scale', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='scale', default=None, help=helps['scale']) parser.add_argument('-c', '--center', metavar='center', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='center', default=None, help=helps['center']) parser.add_argument('-r', '--refine', metavar='level', action="https://huggingface.co/datasets/luna-code/sfepy/store", type=int, dest='refine', default=0, help=helps['refine']) parser.add_argument('-f', '--format', metavar='format', action="https://huggingface.co/datasets/luna-code/sfepy/store", type=str, dest='format', default=None, help=helps['format']) parser.add_argument('-l', '--list', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='list', help=helps['list']) parser.add_argument('-m', '--merge', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='merge', help=helps['merge']) parser.add_argument('-t', '--tri-tetra', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='tri_tetra', help=helps['tri-tetra']) parser.add_argument('-2', '--2d', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='force_2d', help=helps['2d']) parser.add_argument('--save-per-mat', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='save_per_mat', help=helps['save-per-mat']) parser.add_argument('--remesh', metavar='options', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='remesh', default=None, help=helps['remesh']) parser.add_argument('filename_in') parser.add_argument('filename_out') options = parser.parse_args() if options.list: output('Supported readable mesh formats:') output('--------------------------------') output_mesh_formats('r') output('') output('Supported writable mesh formats:') output('--------------------------------') output_mesh_formats('w') sys.exit(0) scale = _parse_val_or_vec(options.scale, 'scale', parser) center = _parse_val_or_vec(options.center, 'center', parser) filename_in = options.filename_in filename_out = options.filename_out if options.remesh: import tempfile import shlex import subprocess dirname = tempfile.mkdtemp() is_surface = options.remesh.startswith('q') if is_surface: mesh = Mesh.from_file(filename_in) domain = FEDomain(mesh.name, mesh) region = domain.create_region('surf', 'vertices of surface', 'facet') surf_mesh = Mesh.from_region(region, mesh, localize=True, is_surface=True) filename = op.join(dirname, 'surf.mesh') surf_mesh.write(filename, io='auto') else: import shutil shutil.copy(filename_in, dirname) filename = op.join(dirname, op.basename(filename_in)) qopts = ''.join(options.remesh.split()) # Remove spaces. command = 'tetgen -BFENkACp%s %s' % (qopts, filename) args = shlex.split(command) subprocess.call(args) root, ext = op.splitext(filename) mesh = Mesh.from_file(root + '.1.vtk') remove_files(dirname) else: mesh = Mesh.from_file(filename_in) if options.force_2d: data = list(mesh._get_io_data()) data[0] = data[0][:, :2] mesh = Mesh.from_data(mesh.name, *data) if scale is not None: if len(scale) == 1: tr = nm.eye(mesh.dim, dtype=nm.float64) * scale elif len(scale) == mesh.dim: tr = nm.diag(scale) else: raise ValueError('bad scale! (%s)' % scale) mesh.transform_coors(tr) if center is not None: cc = 0.5 * mesh.get_bounding_box().sum(0) shift = center - cc tr = nm.c_[nm.eye(mesh.dim, dtype=nm.float64), shift[:, None]] mesh.transform_coors(tr) if options.refine > 0: domain =	FEDomain(mesh.name, mesh)	sfepy.discrete.fem.FEDomain
#!/usr/bin/env python """ Convert a mesh file from one SfePy-supported format to another. Examples:: $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s2.5 $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 -c 0 $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.mesh --remesh='q2/0 a1e-8 O9/7 V' $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new2.mesh --remesh='rq2/0 a1e-8 O9/7 V' """ from __future__ import absolute_import import sys import os.path as op from six.moves import range sys.path.append('.') from argparse import ArgumentParser, RawDescriptionHelpFormatter from sfepy.base.base import nm, output from sfepy.base.ioutils import remove_files from sfepy.discrete.fem import Mesh, FEDomain from sfepy.discrete.fem.meshio import (output_mesh_formats, MeshIO, supported_cell_types) from sfepy.discrete.fem.mesh import fix_double_nodes from sfepy.mesh.mesh_tools import elems_q2t helps = { 'scale' : 'scale factor (float or comma-separated list for each axis)' ' [default: %(default)s]', 'center' : 'center of the output mesh (0 for origin or' ' comma-separated list for each axis) applied after scaling' ' [default: %(default)s]', 'refine' : 'uniform refinement level [default: %(default)s]', 'format' : 'output mesh format (overrides filename_out extension)', 'list' : 'list supported readable/writable output mesh formats', 'merge' : 'remove duplicate vertices', 'tri-tetra' : 'convert elements: quad->tri, hexa->tetra', '2d' : 'force a 2D mesh by removing the z coordinates - assumes a 3D mesh' ' in the xy plane', 'save-per-mat': 'extract cells by material id and save them into' ' separate mesh files with a name based on filename_out and the id' ' numbers (preserves original mesh vertices)', 'remesh' : """when given, remesh the given mesh using tetgen. The options can be the following, separated by spaces, in this order: 1. "r" causes remeshing of the mesh volume - if not present the mesh surface is extracted and used for the volume mesh generation. 2. "q[<float>/<float>]" (required) - the two numbers after "q" are a maximum radius-edge ratio bound and a minimum dihedral angle bound. 3. "a<float>" (optional) - the number imposes a maximum volume constraint on all tetrahedra. 4. O[<0-9>/<0-7>] - the two numbers correspond to a mesh optimization level and a choice of optimizing operations. 5. "V" (optional) - if present, mesh statistics are printed. Consult the tetgen documentation for details.""", } def _parse_val_or_vec(option, name, parser): if option is not None: try: try: option = float(option) except ValueError: option = [float(ii) for ii in option.split(',')] option = nm.array(option, dtype=nm.float64, ndmin=1) except: output('bad %s! (%s)' % (name, option)) parser.print_help() sys.exit(1) return option def main(): parser = ArgumentParser(description=__doc__, formatter_class=RawDescriptionHelpFormatter) parser.add_argument('-s', '--scale', metavar='scale', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='scale', default=None, help=helps['scale']) parser.add_argument('-c', '--center', metavar='center', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='center', default=None, help=helps['center']) parser.add_argument('-r', '--refine', metavar='level', action="https://huggingface.co/datasets/luna-code/sfepy/store", type=int, dest='refine', default=0, help=helps['refine']) parser.add_argument('-f', '--format', metavar='format', action="https://huggingface.co/datasets/luna-code/sfepy/store", type=str, dest='format', default=None, help=helps['format']) parser.add_argument('-l', '--list', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='list', help=helps['list']) parser.add_argument('-m', '--merge', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='merge', help=helps['merge']) parser.add_argument('-t', '--tri-tetra', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='tri_tetra', help=helps['tri-tetra']) parser.add_argument('-2', '--2d', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='force_2d', help=helps['2d']) parser.add_argument('--save-per-mat', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='save_per_mat', help=helps['save-per-mat']) parser.add_argument('--remesh', metavar='options', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='remesh', default=None, help=helps['remesh']) parser.add_argument('filename_in') parser.add_argument('filename_out') options = parser.parse_args() if options.list: output('Supported readable mesh formats:') output('--------------------------------') output_mesh_formats('r') output('') output('Supported writable mesh formats:') output('--------------------------------') output_mesh_formats('w') sys.exit(0) scale = _parse_val_or_vec(options.scale, 'scale', parser) center = _parse_val_or_vec(options.center, 'center', parser) filename_in = options.filename_in filename_out = options.filename_out if options.remesh: import tempfile import shlex import subprocess dirname = tempfile.mkdtemp() is_surface = options.remesh.startswith('q') if is_surface: mesh = Mesh.from_file(filename_in) domain = FEDomain(mesh.name, mesh) region = domain.create_region('surf', 'vertices of surface', 'facet') surf_mesh = Mesh.from_region(region, mesh, localize=True, is_surface=True) filename = op.join(dirname, 'surf.mesh') surf_mesh.write(filename, io='auto') else: import shutil shutil.copy(filename_in, dirname) filename = op.join(dirname, op.basename(filename_in)) qopts = ''.join(options.remesh.split()) # Remove spaces. command = 'tetgen -BFENkACp%s %s' % (qopts, filename) args = shlex.split(command) subprocess.call(args) root, ext = op.splitext(filename) mesh = Mesh.from_file(root + '.1.vtk') remove_files(dirname) else: mesh = Mesh.from_file(filename_in) if options.force_2d: data = list(mesh._get_io_data()) data[0] = data[0][:, :2] mesh = Mesh.from_data(mesh.name, *data) if scale is not None: if len(scale) == 1: tr = nm.eye(mesh.dim, dtype=nm.float64) * scale elif len(scale) == mesh.dim: tr = nm.diag(scale) else: raise ValueError('bad scale! (%s)' % scale) mesh.transform_coors(tr) if center is not None: cc = 0.5 * mesh.get_bounding_box().sum(0) shift = center - cc tr = nm.c_[nm.eye(mesh.dim, dtype=nm.float64), shift[:, None]] mesh.transform_coors(tr) if options.refine > 0: domain = FEDomain(mesh.name, mesh) output('initial mesh: %d nodes %d elements' % (domain.shape.n_nod, domain.shape.n_el)) for ii in range(options.refine): output('refine %d...' % ii) domain = domain.refine() output('... %d nodes %d elements' % (domain.shape.n_nod, domain.shape.n_el)) mesh = domain.mesh if options.tri_tetra > 0: conns = None for k, new_desc in [('3_8', '3_4'), ('2_4', '2_3')]: if k in mesh.descs: conns = mesh.get_conn(k) break if conns is not None: nelo = conns.shape[0] output('initial mesh: %d elements' % nelo) new_conns = elems_q2t(conns) nn = new_conns.shape[0] // nelo new_cgroups = nm.repeat(mesh.cmesh.cell_groups, nn) output('new mesh: %d elements' % new_conns.shape[0]) mesh = Mesh.from_data(mesh.name, mesh.coors, mesh.cmesh.vertex_groups, [new_conns], [new_cgroups], [new_desc]) if options.merge: desc = mesh.descs[0] coor, ngroups, conns = fix_double_nodes(mesh.coors, mesh.cmesh.vertex_groups, mesh.get_conn(desc), 1e-9) mesh = Mesh.from_data(mesh.name + '_merged', coor, ngroups, [conns], [mesh.cmesh.cell_groups], [desc]) if options.save_per_mat: desc = mesh.descs[0] conns, cgroups = mesh.get_conn(desc), mesh.cmesh.cell_groups coors, ngroups = mesh.coors, mesh.cmesh.vertex_groups mat_ids =	nm.unique(cgroups)	sfepy.base.base.nm.unique
#!/usr/bin/env python """ Convert a mesh file from one SfePy-supported format to another. Examples:: $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s2.5 $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 -c 0 $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.mesh --remesh='q2/0 a1e-8 O9/7 V' $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new2.mesh --remesh='rq2/0 a1e-8 O9/7 V' """ from __future__ import absolute_import import sys import os.path as op from six.moves import range sys.path.append('.') from argparse import ArgumentParser, RawDescriptionHelpFormatter from sfepy.base.base import nm, output from sfepy.base.ioutils import remove_files from sfepy.discrete.fem import Mesh, FEDomain from sfepy.discrete.fem.meshio import (output_mesh_formats, MeshIO, supported_cell_types) from sfepy.discrete.fem.mesh import fix_double_nodes from sfepy.mesh.mesh_tools import elems_q2t helps = { 'scale' : 'scale factor (float or comma-separated list for each axis)' ' [default: %(default)s]', 'center' : 'center of the output mesh (0 for origin or' ' comma-separated list for each axis) applied after scaling' ' [default: %(default)s]', 'refine' : 'uniform refinement level [default: %(default)s]', 'format' : 'output mesh format (overrides filename_out extension)', 'list' : 'list supported readable/writable output mesh formats', 'merge' : 'remove duplicate vertices', 'tri-tetra' : 'convert elements: quad->tri, hexa->tetra', '2d' : 'force a 2D mesh by removing the z coordinates - assumes a 3D mesh' ' in the xy plane', 'save-per-mat': 'extract cells by material id and save them into' ' separate mesh files with a name based on filename_out and the id' ' numbers (preserves original mesh vertices)', 'remesh' : """when given, remesh the given mesh using tetgen. The options can be the following, separated by spaces, in this order: 1. "r" causes remeshing of the mesh volume - if not present the mesh surface is extracted and used for the volume mesh generation. 2. "q[<float>/<float>]" (required) - the two numbers after "q" are a maximum radius-edge ratio bound and a minimum dihedral angle bound. 3. "a<float>" (optional) - the number imposes a maximum volume constraint on all tetrahedra. 4. O[<0-9>/<0-7>] - the two numbers correspond to a mesh optimization level and a choice of optimizing operations. 5. "V" (optional) - if present, mesh statistics are printed. Consult the tetgen documentation for details.""", } def _parse_val_or_vec(option, name, parser): if option is not None: try: try: option = float(option) except ValueError: option = [float(ii) for ii in option.split(',')] option =	nm.array(option, dtype=nm.float64, ndmin=1)	sfepy.base.base.nm.array
#!/usr/bin/env python """ Convert a mesh file from one SfePy-supported format to another. Examples:: $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s2.5 $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 -c 0 $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.mesh --remesh='q2/0 a1e-8 O9/7 V' $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new2.mesh --remesh='rq2/0 a1e-8 O9/7 V' """ from __future__ import absolute_import import sys import os.path as op from six.moves import range sys.path.append('.') from argparse import ArgumentParser, RawDescriptionHelpFormatter from sfepy.base.base import nm, output from sfepy.base.ioutils import remove_files from sfepy.discrete.fem import Mesh, FEDomain from sfepy.discrete.fem.meshio import (output_mesh_formats, MeshIO, supported_cell_types) from sfepy.discrete.fem.mesh import fix_double_nodes from sfepy.mesh.mesh_tools import elems_q2t helps = { 'scale' : 'scale factor (float or comma-separated list for each axis)' ' [default: %(default)s]', 'center' : 'center of the output mesh (0 for origin or' ' comma-separated list for each axis) applied after scaling' ' [default: %(default)s]', 'refine' : 'uniform refinement level [default: %(default)s]', 'format' : 'output mesh format (overrides filename_out extension)', 'list' : 'list supported readable/writable output mesh formats', 'merge' : 'remove duplicate vertices', 'tri-tetra' : 'convert elements: quad->tri, hexa->tetra', '2d' : 'force a 2D mesh by removing the z coordinates - assumes a 3D mesh' ' in the xy plane', 'save-per-mat': 'extract cells by material id and save them into' ' separate mesh files with a name based on filename_out and the id' ' numbers (preserves original mesh vertices)', 'remesh' : """when given, remesh the given mesh using tetgen. The options can be the following, separated by spaces, in this order: 1. "r" causes remeshing of the mesh volume - if not present the mesh surface is extracted and used for the volume mesh generation. 2. "q[<float>/<float>]" (required) - the two numbers after "q" are a maximum radius-edge ratio bound and a minimum dihedral angle bound. 3. "a<float>" (optional) - the number imposes a maximum volume constraint on all tetrahedra. 4. O[<0-9>/<0-7>] - the two numbers correspond to a mesh optimization level and a choice of optimizing operations. 5. "V" (optional) - if present, mesh statistics are printed. Consult the tetgen documentation for details.""", } def _parse_val_or_vec(option, name, parser): if option is not None: try: try: option = float(option) except ValueError: option = [float(ii) for ii in option.split(',')] option = nm.array(option, dtype=nm.float64, ndmin=1) except: output('bad %s! (%s)' % (name, option)) parser.print_help() sys.exit(1) return option def main(): parser = ArgumentParser(description=__doc__, formatter_class=RawDescriptionHelpFormatter) parser.add_argument('-s', '--scale', metavar='scale', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='scale', default=None, help=helps['scale']) parser.add_argument('-c', '--center', metavar='center', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='center', default=None, help=helps['center']) parser.add_argument('-r', '--refine', metavar='level', action="https://huggingface.co/datasets/luna-code/sfepy/store", type=int, dest='refine', default=0, help=helps['refine']) parser.add_argument('-f', '--format', metavar='format', action="https://huggingface.co/datasets/luna-code/sfepy/store", type=str, dest='format', default=None, help=helps['format']) parser.add_argument('-l', '--list', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='list', help=helps['list']) parser.add_argument('-m', '--merge', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='merge', help=helps['merge']) parser.add_argument('-t', '--tri-tetra', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='tri_tetra', help=helps['tri-tetra']) parser.add_argument('-2', '--2d', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='force_2d', help=helps['2d']) parser.add_argument('--save-per-mat', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='save_per_mat', help=helps['save-per-mat']) parser.add_argument('--remesh', metavar='options', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='remesh', default=None, help=helps['remesh']) parser.add_argument('filename_in') parser.add_argument('filename_out') options = parser.parse_args() if options.list: output('Supported readable mesh formats:') output('--------------------------------') output_mesh_formats('r') output('') output('Supported writable mesh formats:') output('--------------------------------') output_mesh_formats('w') sys.exit(0) scale = _parse_val_or_vec(options.scale, 'scale', parser) center = _parse_val_or_vec(options.center, 'center', parser) filename_in = options.filename_in filename_out = options.filename_out if options.remesh: import tempfile import shlex import subprocess dirname = tempfile.mkdtemp() is_surface = options.remesh.startswith('q') if is_surface: mesh =	Mesh.from_file(filename_in)	sfepy.discrete.fem.Mesh.from_file
#!/usr/bin/env python """ Convert a mesh file from one SfePy-supported format to another. Examples:: $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s2.5 $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 -c 0 $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.mesh --remesh='q2/0 a1e-8 O9/7 V' $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new2.mesh --remesh='rq2/0 a1e-8 O9/7 V' """ from __future__ import absolute_import import sys import os.path as op from six.moves import range sys.path.append('.') from argparse import ArgumentParser, RawDescriptionHelpFormatter from sfepy.base.base import nm, output from sfepy.base.ioutils import remove_files from sfepy.discrete.fem import Mesh, FEDomain from sfepy.discrete.fem.meshio import (output_mesh_formats, MeshIO, supported_cell_types) from sfepy.discrete.fem.mesh import fix_double_nodes from sfepy.mesh.mesh_tools import elems_q2t helps = { 'scale' : 'scale factor (float or comma-separated list for each axis)' ' [default: %(default)s]', 'center' : 'center of the output mesh (0 for origin or' ' comma-separated list for each axis) applied after scaling' ' [default: %(default)s]', 'refine' : 'uniform refinement level [default: %(default)s]', 'format' : 'output mesh format (overrides filename_out extension)', 'list' : 'list supported readable/writable output mesh formats', 'merge' : 'remove duplicate vertices', 'tri-tetra' : 'convert elements: quad->tri, hexa->tetra', '2d' : 'force a 2D mesh by removing the z coordinates - assumes a 3D mesh' ' in the xy plane', 'save-per-mat': 'extract cells by material id and save them into' ' separate mesh files with a name based on filename_out and the id' ' numbers (preserves original mesh vertices)', 'remesh' : """when given, remesh the given mesh using tetgen. The options can be the following, separated by spaces, in this order: 1. "r" causes remeshing of the mesh volume - if not present the mesh surface is extracted and used for the volume mesh generation. 2. "q[<float>/<float>]" (required) - the two numbers after "q" are a maximum radius-edge ratio bound and a minimum dihedral angle bound. 3. "a<float>" (optional) - the number imposes a maximum volume constraint on all tetrahedra. 4. O[<0-9>/<0-7>] - the two numbers correspond to a mesh optimization level and a choice of optimizing operations. 5. "V" (optional) - if present, mesh statistics are printed. Consult the tetgen documentation for details.""", } def _parse_val_or_vec(option, name, parser): if option is not None: try: try: option = float(option) except ValueError: option = [float(ii) for ii in option.split(',')] option = nm.array(option, dtype=nm.float64, ndmin=1) except: output('bad %s! (%s)' % (name, option)) parser.print_help() sys.exit(1) return option def main(): parser = ArgumentParser(description=__doc__, formatter_class=RawDescriptionHelpFormatter) parser.add_argument('-s', '--scale', metavar='scale', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='scale', default=None, help=helps['scale']) parser.add_argument('-c', '--center', metavar='center', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='center', default=None, help=helps['center']) parser.add_argument('-r', '--refine', metavar='level', action="https://huggingface.co/datasets/luna-code/sfepy/store", type=int, dest='refine', default=0, help=helps['refine']) parser.add_argument('-f', '--format', metavar='format', action="https://huggingface.co/datasets/luna-code/sfepy/store", type=str, dest='format', default=None, help=helps['format']) parser.add_argument('-l', '--list', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='list', help=helps['list']) parser.add_argument('-m', '--merge', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='merge', help=helps['merge']) parser.add_argument('-t', '--tri-tetra', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='tri_tetra', help=helps['tri-tetra']) parser.add_argument('-2', '--2d', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='force_2d', help=helps['2d']) parser.add_argument('--save-per-mat', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='save_per_mat', help=helps['save-per-mat']) parser.add_argument('--remesh', metavar='options', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='remesh', default=None, help=helps['remesh']) parser.add_argument('filename_in') parser.add_argument('filename_out') options = parser.parse_args() if options.list: output('Supported readable mesh formats:') output('--------------------------------') output_mesh_formats('r') output('') output('Supported writable mesh formats:') output('--------------------------------') output_mesh_formats('w') sys.exit(0) scale = _parse_val_or_vec(options.scale, 'scale', parser) center = _parse_val_or_vec(options.center, 'center', parser) filename_in = options.filename_in filename_out = options.filename_out if options.remesh: import tempfile import shlex import subprocess dirname = tempfile.mkdtemp() is_surface = options.remesh.startswith('q') if is_surface: mesh = Mesh.from_file(filename_in) domain =	FEDomain(mesh.name, mesh)	sfepy.discrete.fem.FEDomain
#!/usr/bin/env python """ Convert a mesh file from one SfePy-supported format to another. Examples:: $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s2.5 $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 -c 0 $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.mesh --remesh='q2/0 a1e-8 O9/7 V' $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new2.mesh --remesh='rq2/0 a1e-8 O9/7 V' """ from __future__ import absolute_import import sys import os.path as op from six.moves import range sys.path.append('.') from argparse import ArgumentParser, RawDescriptionHelpFormatter from sfepy.base.base import nm, output from sfepy.base.ioutils import remove_files from sfepy.discrete.fem import Mesh, FEDomain from sfepy.discrete.fem.meshio import (output_mesh_formats, MeshIO, supported_cell_types) from sfepy.discrete.fem.mesh import fix_double_nodes from sfepy.mesh.mesh_tools import elems_q2t helps = { 'scale' : 'scale factor (float or comma-separated list for each axis)' ' [default: %(default)s]', 'center' : 'center of the output mesh (0 for origin or' ' comma-separated list for each axis) applied after scaling' ' [default: %(default)s]', 'refine' : 'uniform refinement level [default: %(default)s]', 'format' : 'output mesh format (overrides filename_out extension)', 'list' : 'list supported readable/writable output mesh formats', 'merge' : 'remove duplicate vertices', 'tri-tetra' : 'convert elements: quad->tri, hexa->tetra', '2d' : 'force a 2D mesh by removing the z coordinates - assumes a 3D mesh' ' in the xy plane', 'save-per-mat': 'extract cells by material id and save them into' ' separate mesh files with a name based on filename_out and the id' ' numbers (preserves original mesh vertices)', 'remesh' : """when given, remesh the given mesh using tetgen. The options can be the following, separated by spaces, in this order: 1. "r" causes remeshing of the mesh volume - if not present the mesh surface is extracted and used for the volume mesh generation. 2. "q[<float>/<float>]" (required) - the two numbers after "q" are a maximum radius-edge ratio bound and a minimum dihedral angle bound. 3. "a<float>" (optional) - the number imposes a maximum volume constraint on all tetrahedra. 4. O[<0-9>/<0-7>] - the two numbers correspond to a mesh optimization level and a choice of optimizing operations. 5. "V" (optional) - if present, mesh statistics are printed. Consult the tetgen documentation for details.""", } def _parse_val_or_vec(option, name, parser): if option is not None: try: try: option = float(option) except ValueError: option = [float(ii) for ii in option.split(',')] option = nm.array(option, dtype=nm.float64, ndmin=1) except: output('bad %s! (%s)' % (name, option)) parser.print_help() sys.exit(1) return option def main(): parser = ArgumentParser(description=__doc__, formatter_class=RawDescriptionHelpFormatter) parser.add_argument('-s', '--scale', metavar='scale', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='scale', default=None, help=helps['scale']) parser.add_argument('-c', '--center', metavar='center', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='center', default=None, help=helps['center']) parser.add_argument('-r', '--refine', metavar='level', action="https://huggingface.co/datasets/luna-code/sfepy/store", type=int, dest='refine', default=0, help=helps['refine']) parser.add_argument('-f', '--format', metavar='format', action="https://huggingface.co/datasets/luna-code/sfepy/store", type=str, dest='format', default=None, help=helps['format']) parser.add_argument('-l', '--list', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='list', help=helps['list']) parser.add_argument('-m', '--merge', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='merge', help=helps['merge']) parser.add_argument('-t', '--tri-tetra', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='tri_tetra', help=helps['tri-tetra']) parser.add_argument('-2', '--2d', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='force_2d', help=helps['2d']) parser.add_argument('--save-per-mat', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='save_per_mat', help=helps['save-per-mat']) parser.add_argument('--remesh', metavar='options', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='remesh', default=None, help=helps['remesh']) parser.add_argument('filename_in') parser.add_argument('filename_out') options = parser.parse_args() if options.list: output('Supported readable mesh formats:') output('--------------------------------') output_mesh_formats('r') output('') output('Supported writable mesh formats:') output('--------------------------------') output_mesh_formats('w') sys.exit(0) scale = _parse_val_or_vec(options.scale, 'scale', parser) center = _parse_val_or_vec(options.center, 'center', parser) filename_in = options.filename_in filename_out = options.filename_out if options.remesh: import tempfile import shlex import subprocess dirname = tempfile.mkdtemp() is_surface = options.remesh.startswith('q') if is_surface: mesh = Mesh.from_file(filename_in) domain = FEDomain(mesh.name, mesh) region = domain.create_region('surf', 'vertices of surface', 'facet') surf_mesh = Mesh.from_region(region, mesh, localize=True, is_surface=True) filename = op.join(dirname, 'surf.mesh') surf_mesh.write(filename, io='auto') else: import shutil shutil.copy(filename_in, dirname) filename = op.join(dirname, op.basename(filename_in)) qopts = ''.join(options.remesh.split()) # Remove spaces. command = 'tetgen -BFENkACp%s %s' % (qopts, filename) args = shlex.split(command) subprocess.call(args) root, ext = op.splitext(filename) mesh = Mesh.from_file(root + '.1.vtk') remove_files(dirname) else: mesh = Mesh.from_file(filename_in) if options.force_2d: data = list(mesh._get_io_data()) data[0] = data[0][:, :2] mesh = Mesh.from_data(mesh.name, *data) if scale is not None: if len(scale) == 1: tr = nm.eye(mesh.dim, dtype=nm.float64) * scale elif len(scale) == mesh.dim: tr = nm.diag(scale) else: raise ValueError('bad scale! (%s)' % scale) mesh.transform_coors(tr) if center is not None: cc = 0.5 * mesh.get_bounding_box().sum(0) shift = center - cc tr = nm.c_[nm.eye(mesh.dim, dtype=nm.float64), shift[:, None]] mesh.transform_coors(tr) if options.refine > 0: domain = FEDomain(mesh.name, mesh) output('initial mesh: %d nodes %d elements' % (domain.shape.n_nod, domain.shape.n_el)) for ii in range(options.refine):	output('refine %d...' % ii)	sfepy.base.base.output
#!/usr/bin/env python """ Convert a mesh file from one SfePy-supported format to another. Examples:: $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s2.5 $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 -c 0 $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.mesh --remesh='q2/0 a1e-8 O9/7 V' $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new2.mesh --remesh='rq2/0 a1e-8 O9/7 V' """ from __future__ import absolute_import import sys import os.path as op from six.moves import range sys.path.append('.') from argparse import ArgumentParser, RawDescriptionHelpFormatter from sfepy.base.base import nm, output from sfepy.base.ioutils import remove_files from sfepy.discrete.fem import Mesh, FEDomain from sfepy.discrete.fem.meshio import (output_mesh_formats, MeshIO, supported_cell_types) from sfepy.discrete.fem.mesh import fix_double_nodes from sfepy.mesh.mesh_tools import elems_q2t helps = { 'scale' : 'scale factor (float or comma-separated list for each axis)' ' [default: %(default)s]', 'center' : 'center of the output mesh (0 for origin or' ' comma-separated list for each axis) applied after scaling' ' [default: %(default)s]', 'refine' : 'uniform refinement level [default: %(default)s]', 'format' : 'output mesh format (overrides filename_out extension)', 'list' : 'list supported readable/writable output mesh formats', 'merge' : 'remove duplicate vertices', 'tri-tetra' : 'convert elements: quad->tri, hexa->tetra', '2d' : 'force a 2D mesh by removing the z coordinates - assumes a 3D mesh' ' in the xy plane', 'save-per-mat': 'extract cells by material id and save them into' ' separate mesh files with a name based on filename_out and the id' ' numbers (preserves original mesh vertices)', 'remesh' : """when given, remesh the given mesh using tetgen. The options can be the following, separated by spaces, in this order: 1. "r" causes remeshing of the mesh volume - if not present the mesh surface is extracted and used for the volume mesh generation. 2. "q[<float>/<float>]" (required) - the two numbers after "q" are a maximum radius-edge ratio bound and a minimum dihedral angle bound. 3. "a<float>" (optional) - the number imposes a maximum volume constraint on all tetrahedra. 4. O[<0-9>/<0-7>] - the two numbers correspond to a mesh optimization level and a choice of optimizing operations. 5. "V" (optional) - if present, mesh statistics are printed. Consult the tetgen documentation for details.""", } def _parse_val_or_vec(option, name, parser): if option is not None: try: try: option = float(option) except ValueError: option = [float(ii) for ii in option.split(',')] option = nm.array(option, dtype=nm.float64, ndmin=1) except: output('bad %s! (%s)' % (name, option)) parser.print_help() sys.exit(1) return option def main(): parser = ArgumentParser(description=__doc__, formatter_class=RawDescriptionHelpFormatter) parser.add_argument('-s', '--scale', metavar='scale', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='scale', default=None, help=helps['scale']) parser.add_argument('-c', '--center', metavar='center', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='center', default=None, help=helps['center']) parser.add_argument('-r', '--refine', metavar='level', action="https://huggingface.co/datasets/luna-code/sfepy/store", type=int, dest='refine', default=0, help=helps['refine']) parser.add_argument('-f', '--format', metavar='format', action="https://huggingface.co/datasets/luna-code/sfepy/store", type=str, dest='format', default=None, help=helps['format']) parser.add_argument('-l', '--list', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='list', help=helps['list']) parser.add_argument('-m', '--merge', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='merge', help=helps['merge']) parser.add_argument('-t', '--tri-tetra', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='tri_tetra', help=helps['tri-tetra']) parser.add_argument('-2', '--2d', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='force_2d', help=helps['2d']) parser.add_argument('--save-per-mat', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='save_per_mat', help=helps['save-per-mat']) parser.add_argument('--remesh', metavar='options', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='remesh', default=None, help=helps['remesh']) parser.add_argument('filename_in') parser.add_argument('filename_out') options = parser.parse_args() if options.list: output('Supported readable mesh formats:') output('--------------------------------') output_mesh_formats('r') output('') output('Supported writable mesh formats:') output('--------------------------------') output_mesh_formats('w') sys.exit(0) scale = _parse_val_or_vec(options.scale, 'scale', parser) center = _parse_val_or_vec(options.center, 'center', parser) filename_in = options.filename_in filename_out = options.filename_out if options.remesh: import tempfile import shlex import subprocess dirname = tempfile.mkdtemp() is_surface = options.remesh.startswith('q') if is_surface: mesh = Mesh.from_file(filename_in) domain = FEDomain(mesh.name, mesh) region = domain.create_region('surf', 'vertices of surface', 'facet') surf_mesh = Mesh.from_region(region, mesh, localize=True, is_surface=True) filename = op.join(dirname, 'surf.mesh') surf_mesh.write(filename, io='auto') else: import shutil shutil.copy(filename_in, dirname) filename = op.join(dirname, op.basename(filename_in)) qopts = ''.join(options.remesh.split()) # Remove spaces. command = 'tetgen -BFENkACp%s %s' % (qopts, filename) args = shlex.split(command) subprocess.call(args) root, ext = op.splitext(filename) mesh = Mesh.from_file(root + '.1.vtk') remove_files(dirname) else: mesh = Mesh.from_file(filename_in) if options.force_2d: data = list(mesh._get_io_data()) data[0] = data[0][:, :2] mesh = Mesh.from_data(mesh.name, *data) if scale is not None: if len(scale) == 1: tr = nm.eye(mesh.dim, dtype=nm.float64) * scale elif len(scale) == mesh.dim: tr = nm.diag(scale) else: raise ValueError('bad scale! (%s)' % scale) mesh.transform_coors(tr) if center is not None: cc = 0.5 * mesh.get_bounding_box().sum(0) shift = center - cc tr = nm.c_[nm.eye(mesh.dim, dtype=nm.float64), shift[:, None]] mesh.transform_coors(tr) if options.refine > 0: domain = FEDomain(mesh.name, mesh) output('initial mesh: %d nodes %d elements' % (domain.shape.n_nod, domain.shape.n_el)) for ii in range(options.refine): output('refine %d...' % ii) domain = domain.refine() output('... %d nodes %d elements' % (domain.shape.n_nod, domain.shape.n_el)) mesh = domain.mesh if options.tri_tetra > 0: conns = None for k, new_desc in [('3_8', '3_4'), ('2_4', '2_3')]: if k in mesh.descs: conns = mesh.get_conn(k) break if conns is not None: nelo = conns.shape[0]	output('initial mesh: %d elements' % nelo)	sfepy.base.base.output
#!/usr/bin/env python """ Convert a mesh file from one SfePy-supported format to another. Examples:: $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s2.5 $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 -c 0 $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.mesh --remesh='q2/0 a1e-8 O9/7 V' $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new2.mesh --remesh='rq2/0 a1e-8 O9/7 V' """ from __future__ import absolute_import import sys import os.path as op from six.moves import range sys.path.append('.') from argparse import ArgumentParser, RawDescriptionHelpFormatter from sfepy.base.base import nm, output from sfepy.base.ioutils import remove_files from sfepy.discrete.fem import Mesh, FEDomain from sfepy.discrete.fem.meshio import (output_mesh_formats, MeshIO, supported_cell_types) from sfepy.discrete.fem.mesh import fix_double_nodes from sfepy.mesh.mesh_tools import elems_q2t helps = { 'scale' : 'scale factor (float or comma-separated list for each axis)' ' [default: %(default)s]', 'center' : 'center of the output mesh (0 for origin or' ' comma-separated list for each axis) applied after scaling' ' [default: %(default)s]', 'refine' : 'uniform refinement level [default: %(default)s]', 'format' : 'output mesh format (overrides filename_out extension)', 'list' : 'list supported readable/writable output mesh formats', 'merge' : 'remove duplicate vertices', 'tri-tetra' : 'convert elements: quad->tri, hexa->tetra', '2d' : 'force a 2D mesh by removing the z coordinates - assumes a 3D mesh' ' in the xy plane', 'save-per-mat': 'extract cells by material id and save them into' ' separate mesh files with a name based on filename_out and the id' ' numbers (preserves original mesh vertices)', 'remesh' : """when given, remesh the given mesh using tetgen. The options can be the following, separated by spaces, in this order: 1. "r" causes remeshing of the mesh volume - if not present the mesh surface is extracted and used for the volume mesh generation. 2. "q[<float>/<float>]" (required) - the two numbers after "q" are a maximum radius-edge ratio bound and a minimum dihedral angle bound. 3. "a<float>" (optional) - the number imposes a maximum volume constraint on all tetrahedra. 4. O[<0-9>/<0-7>] - the two numbers correspond to a mesh optimization level and a choice of optimizing operations. 5. "V" (optional) - if present, mesh statistics are printed. Consult the tetgen documentation for details.""", } def _parse_val_or_vec(option, name, parser): if option is not None: try: try: option = float(option) except ValueError: option = [float(ii) for ii in option.split(',')] option = nm.array(option, dtype=nm.float64, ndmin=1) except: output('bad %s! (%s)' % (name, option)) parser.print_help() sys.exit(1) return option def main(): parser = ArgumentParser(description=__doc__, formatter_class=RawDescriptionHelpFormatter) parser.add_argument('-s', '--scale', metavar='scale', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='scale', default=None, help=helps['scale']) parser.add_argument('-c', '--center', metavar='center', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='center', default=None, help=helps['center']) parser.add_argument('-r', '--refine', metavar='level', action="https://huggingface.co/datasets/luna-code/sfepy/store", type=int, dest='refine', default=0, help=helps['refine']) parser.add_argument('-f', '--format', metavar='format', action="https://huggingface.co/datasets/luna-code/sfepy/store", type=str, dest='format', default=None, help=helps['format']) parser.add_argument('-l', '--list', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='list', help=helps['list']) parser.add_argument('-m', '--merge', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='merge', help=helps['merge']) parser.add_argument('-t', '--tri-tetra', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='tri_tetra', help=helps['tri-tetra']) parser.add_argument('-2', '--2d', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='force_2d', help=helps['2d']) parser.add_argument('--save-per-mat', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='save_per_mat', help=helps['save-per-mat']) parser.add_argument('--remesh', metavar='options', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='remesh', default=None, help=helps['remesh']) parser.add_argument('filename_in') parser.add_argument('filename_out') options = parser.parse_args() if options.list: output('Supported readable mesh formats:') output('--------------------------------') output_mesh_formats('r') output('') output('Supported writable mesh formats:') output('--------------------------------') output_mesh_formats('w') sys.exit(0) scale = _parse_val_or_vec(options.scale, 'scale', parser) center = _parse_val_or_vec(options.center, 'center', parser) filename_in = options.filename_in filename_out = options.filename_out if options.remesh: import tempfile import shlex import subprocess dirname = tempfile.mkdtemp() is_surface = options.remesh.startswith('q') if is_surface: mesh = Mesh.from_file(filename_in) domain = FEDomain(mesh.name, mesh) region = domain.create_region('surf', 'vertices of surface', 'facet') surf_mesh = Mesh.from_region(region, mesh, localize=True, is_surface=True) filename = op.join(dirname, 'surf.mesh') surf_mesh.write(filename, io='auto') else: import shutil shutil.copy(filename_in, dirname) filename = op.join(dirname, op.basename(filename_in)) qopts = ''.join(options.remesh.split()) # Remove spaces. command = 'tetgen -BFENkACp%s %s' % (qopts, filename) args = shlex.split(command) subprocess.call(args) root, ext = op.splitext(filename) mesh = Mesh.from_file(root + '.1.vtk') remove_files(dirname) else: mesh = Mesh.from_file(filename_in) if options.force_2d: data = list(mesh._get_io_data()) data[0] = data[0][:, :2] mesh = Mesh.from_data(mesh.name, *data) if scale is not None: if len(scale) == 1: tr = nm.eye(mesh.dim, dtype=nm.float64) * scale elif len(scale) == mesh.dim: tr = nm.diag(scale) else: raise ValueError('bad scale! (%s)' % scale) mesh.transform_coors(tr) if center is not None: cc = 0.5 * mesh.get_bounding_box().sum(0) shift = center - cc tr = nm.c_[nm.eye(mesh.dim, dtype=nm.float64), shift[:, None]] mesh.transform_coors(tr) if options.refine > 0: domain = FEDomain(mesh.name, mesh) output('initial mesh: %d nodes %d elements' % (domain.shape.n_nod, domain.shape.n_el)) for ii in range(options.refine): output('refine %d...' % ii) domain = domain.refine() output('... %d nodes %d elements' % (domain.shape.n_nod, domain.shape.n_el)) mesh = domain.mesh if options.tri_tetra > 0: conns = None for k, new_desc in [('3_8', '3_4'), ('2_4', '2_3')]: if k in mesh.descs: conns = mesh.get_conn(k) break if conns is not None: nelo = conns.shape[0] output('initial mesh: %d elements' % nelo) new_conns =	elems_q2t(conns)	sfepy.mesh.mesh_tools.elems_q2t
#!/usr/bin/env python """ Convert a mesh file from one SfePy-supported format to another. Examples:: $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s2.5 $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 -c 0 $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.mesh --remesh='q2/0 a1e-8 O9/7 V' $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new2.mesh --remesh='rq2/0 a1e-8 O9/7 V' """ from __future__ import absolute_import import sys import os.path as op from six.moves import range sys.path.append('.') from argparse import ArgumentParser, RawDescriptionHelpFormatter from sfepy.base.base import nm, output from sfepy.base.ioutils import remove_files from sfepy.discrete.fem import Mesh, FEDomain from sfepy.discrete.fem.meshio import (output_mesh_formats, MeshIO, supported_cell_types) from sfepy.discrete.fem.mesh import fix_double_nodes from sfepy.mesh.mesh_tools import elems_q2t helps = { 'scale' : 'scale factor (float or comma-separated list for each axis)' ' [default: %(default)s]', 'center' : 'center of the output mesh (0 for origin or' ' comma-separated list for each axis) applied after scaling' ' [default: %(default)s]', 'refine' : 'uniform refinement level [default: %(default)s]', 'format' : 'output mesh format (overrides filename_out extension)', 'list' : 'list supported readable/writable output mesh formats', 'merge' : 'remove duplicate vertices', 'tri-tetra' : 'convert elements: quad->tri, hexa->tetra', '2d' : 'force a 2D mesh by removing the z coordinates - assumes a 3D mesh' ' in the xy plane', 'save-per-mat': 'extract cells by material id and save them into' ' separate mesh files with a name based on filename_out and the id' ' numbers (preserves original mesh vertices)', 'remesh' : """when given, remesh the given mesh using tetgen. The options can be the following, separated by spaces, in this order: 1. "r" causes remeshing of the mesh volume - if not present the mesh surface is extracted and used for the volume mesh generation. 2. "q[<float>/<float>]" (required) - the two numbers after "q" are a maximum radius-edge ratio bound and a minimum dihedral angle bound. 3. "a<float>" (optional) - the number imposes a maximum volume constraint on all tetrahedra. 4. O[<0-9>/<0-7>] - the two numbers correspond to a mesh optimization level and a choice of optimizing operations. 5. "V" (optional) - if present, mesh statistics are printed. Consult the tetgen documentation for details.""", } def _parse_val_or_vec(option, name, parser): if option is not None: try: try: option = float(option) except ValueError: option = [float(ii) for ii in option.split(',')] option = nm.array(option, dtype=nm.float64, ndmin=1) except: output('bad %s! (%s)' % (name, option)) parser.print_help() sys.exit(1) return option def main(): parser = ArgumentParser(description=__doc__, formatter_class=RawDescriptionHelpFormatter) parser.add_argument('-s', '--scale', metavar='scale', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='scale', default=None, help=helps['scale']) parser.add_argument('-c', '--center', metavar='center', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='center', default=None, help=helps['center']) parser.add_argument('-r', '--refine', metavar='level', action="https://huggingface.co/datasets/luna-code/sfepy/store", type=int, dest='refine', default=0, help=helps['refine']) parser.add_argument('-f', '--format', metavar='format', action="https://huggingface.co/datasets/luna-code/sfepy/store", type=str, dest='format', default=None, help=helps['format']) parser.add_argument('-l', '--list', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='list', help=helps['list']) parser.add_argument('-m', '--merge', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='merge', help=helps['merge']) parser.add_argument('-t', '--tri-tetra', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='tri_tetra', help=helps['tri-tetra']) parser.add_argument('-2', '--2d', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='force_2d', help=helps['2d']) parser.add_argument('--save-per-mat', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='save_per_mat', help=helps['save-per-mat']) parser.add_argument('--remesh', metavar='options', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='remesh', default=None, help=helps['remesh']) parser.add_argument('filename_in') parser.add_argument('filename_out') options = parser.parse_args() if options.list: output('Supported readable mesh formats:') output('--------------------------------') output_mesh_formats('r') output('') output('Supported writable mesh formats:') output('--------------------------------') output_mesh_formats('w') sys.exit(0) scale = _parse_val_or_vec(options.scale, 'scale', parser) center = _parse_val_or_vec(options.center, 'center', parser) filename_in = options.filename_in filename_out = options.filename_out if options.remesh: import tempfile import shlex import subprocess dirname = tempfile.mkdtemp() is_surface = options.remesh.startswith('q') if is_surface: mesh = Mesh.from_file(filename_in) domain = FEDomain(mesh.name, mesh) region = domain.create_region('surf', 'vertices of surface', 'facet') surf_mesh = Mesh.from_region(region, mesh, localize=True, is_surface=True) filename = op.join(dirname, 'surf.mesh') surf_mesh.write(filename, io='auto') else: import shutil shutil.copy(filename_in, dirname) filename = op.join(dirname, op.basename(filename_in)) qopts = ''.join(options.remesh.split()) # Remove spaces. command = 'tetgen -BFENkACp%s %s' % (qopts, filename) args = shlex.split(command) subprocess.call(args) root, ext = op.splitext(filename) mesh = Mesh.from_file(root + '.1.vtk') remove_files(dirname) else: mesh = Mesh.from_file(filename_in) if options.force_2d: data = list(mesh._get_io_data()) data[0] = data[0][:, :2] mesh = Mesh.from_data(mesh.name, *data) if scale is not None: if len(scale) == 1: tr = nm.eye(mesh.dim, dtype=nm.float64) * scale elif len(scale) == mesh.dim: tr = nm.diag(scale) else: raise ValueError('bad scale! (%s)' % scale) mesh.transform_coors(tr) if center is not None: cc = 0.5 * mesh.get_bounding_box().sum(0) shift = center - cc tr = nm.c_[nm.eye(mesh.dim, dtype=nm.float64), shift[:, None]] mesh.transform_coors(tr) if options.refine > 0: domain = FEDomain(mesh.name, mesh) output('initial mesh: %d nodes %d elements' % (domain.shape.n_nod, domain.shape.n_el)) for ii in range(options.refine): output('refine %d...' % ii) domain = domain.refine() output('... %d nodes %d elements' % (domain.shape.n_nod, domain.shape.n_el)) mesh = domain.mesh if options.tri_tetra > 0: conns = None for k, new_desc in [('3_8', '3_4'), ('2_4', '2_3')]: if k in mesh.descs: conns = mesh.get_conn(k) break if conns is not None: nelo = conns.shape[0] output('initial mesh: %d elements' % nelo) new_conns = elems_q2t(conns) nn = new_conns.shape[0] // nelo new_cgroups =	nm.repeat(mesh.cmesh.cell_groups, nn)	sfepy.base.base.nm.repeat
#!/usr/bin/env python """ Convert a mesh file from one SfePy-supported format to another. Examples:: $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s2.5 $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 -c 0 $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.mesh --remesh='q2/0 a1e-8 O9/7 V' $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new2.mesh --remesh='rq2/0 a1e-8 O9/7 V' """ from __future__ import absolute_import import sys import os.path as op from six.moves import range sys.path.append('.') from argparse import ArgumentParser, RawDescriptionHelpFormatter from sfepy.base.base import nm, output from sfepy.base.ioutils import remove_files from sfepy.discrete.fem import Mesh, FEDomain from sfepy.discrete.fem.meshio import (output_mesh_formats, MeshIO, supported_cell_types) from sfepy.discrete.fem.mesh import fix_double_nodes from sfepy.mesh.mesh_tools import elems_q2t helps = { 'scale' : 'scale factor (float or comma-separated list for each axis)' ' [default: %(default)s]', 'center' : 'center of the output mesh (0 for origin or' ' comma-separated list for each axis) applied after scaling' ' [default: %(default)s]', 'refine' : 'uniform refinement level [default: %(default)s]', 'format' : 'output mesh format (overrides filename_out extension)', 'list' : 'list supported readable/writable output mesh formats', 'merge' : 'remove duplicate vertices', 'tri-tetra' : 'convert elements: quad->tri, hexa->tetra', '2d' : 'force a 2D mesh by removing the z coordinates - assumes a 3D mesh' ' in the xy plane', 'save-per-mat': 'extract cells by material id and save them into' ' separate mesh files with a name based on filename_out and the id' ' numbers (preserves original mesh vertices)', 'remesh' : """when given, remesh the given mesh using tetgen. The options can be the following, separated by spaces, in this order: 1. "r" causes remeshing of the mesh volume - if not present the mesh surface is extracted and used for the volume mesh generation. 2. "q[<float>/<float>]" (required) - the two numbers after "q" are a maximum radius-edge ratio bound and a minimum dihedral angle bound. 3. "a<float>" (optional) - the number imposes a maximum volume constraint on all tetrahedra. 4. O[<0-9>/<0-7>] - the two numbers correspond to a mesh optimization level and a choice of optimizing operations. 5. "V" (optional) - if present, mesh statistics are printed. Consult the tetgen documentation for details.""", } def _parse_val_or_vec(option, name, parser): if option is not None: try: try: option = float(option) except ValueError: option = [float(ii) for ii in option.split(',')] option = nm.array(option, dtype=nm.float64, ndmin=1) except: output('bad %s! (%s)' % (name, option)) parser.print_help() sys.exit(1) return option def main(): parser = ArgumentParser(description=__doc__, formatter_class=RawDescriptionHelpFormatter) parser.add_argument('-s', '--scale', metavar='scale', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='scale', default=None, help=helps['scale']) parser.add_argument('-c', '--center', metavar='center', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='center', default=None, help=helps['center']) parser.add_argument('-r', '--refine', metavar='level', action="https://huggingface.co/datasets/luna-code/sfepy/store", type=int, dest='refine', default=0, help=helps['refine']) parser.add_argument('-f', '--format', metavar='format', action="https://huggingface.co/datasets/luna-code/sfepy/store", type=str, dest='format', default=None, help=helps['format']) parser.add_argument('-l', '--list', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='list', help=helps['list']) parser.add_argument('-m', '--merge', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='merge', help=helps['merge']) parser.add_argument('-t', '--tri-tetra', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='tri_tetra', help=helps['tri-tetra']) parser.add_argument('-2', '--2d', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='force_2d', help=helps['2d']) parser.add_argument('--save-per-mat', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='save_per_mat', help=helps['save-per-mat']) parser.add_argument('--remesh', metavar='options', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='remesh', default=None, help=helps['remesh']) parser.add_argument('filename_in') parser.add_argument('filename_out') options = parser.parse_args() if options.list: output('Supported readable mesh formats:') output('--------------------------------') output_mesh_formats('r') output('') output('Supported writable mesh formats:') output('--------------------------------') output_mesh_formats('w') sys.exit(0) scale = _parse_val_or_vec(options.scale, 'scale', parser) center = _parse_val_or_vec(options.center, 'center', parser) filename_in = options.filename_in filename_out = options.filename_out if options.remesh: import tempfile import shlex import subprocess dirname = tempfile.mkdtemp() is_surface = options.remesh.startswith('q') if is_surface: mesh = Mesh.from_file(filename_in) domain = FEDomain(mesh.name, mesh) region = domain.create_region('surf', 'vertices of surface', 'facet') surf_mesh = Mesh.from_region(region, mesh, localize=True, is_surface=True) filename = op.join(dirname, 'surf.mesh') surf_mesh.write(filename, io='auto') else: import shutil shutil.copy(filename_in, dirname) filename = op.join(dirname, op.basename(filename_in)) qopts = ''.join(options.remesh.split()) # Remove spaces. command = 'tetgen -BFENkACp%s %s' % (qopts, filename) args = shlex.split(command) subprocess.call(args) root, ext = op.splitext(filename) mesh = Mesh.from_file(root + '.1.vtk') remove_files(dirname) else: mesh = Mesh.from_file(filename_in) if options.force_2d: data = list(mesh._get_io_data()) data[0] = data[0][:, :2] mesh = Mesh.from_data(mesh.name, *data) if scale is not None: if len(scale) == 1: tr = nm.eye(mesh.dim, dtype=nm.float64) * scale elif len(scale) == mesh.dim: tr = nm.diag(scale) else: raise ValueError('bad scale! (%s)' % scale) mesh.transform_coors(tr) if center is not None: cc = 0.5 * mesh.get_bounding_box().sum(0) shift = center - cc tr = nm.c_[nm.eye(mesh.dim, dtype=nm.float64), shift[:, None]] mesh.transform_coors(tr) if options.refine > 0: domain = FEDomain(mesh.name, mesh) output('initial mesh: %d nodes %d elements' % (domain.shape.n_nod, domain.shape.n_el)) for ii in range(options.refine): output('refine %d...' % ii) domain = domain.refine() output('... %d nodes %d elements' % (domain.shape.n_nod, domain.shape.n_el)) mesh = domain.mesh if options.tri_tetra > 0: conns = None for k, new_desc in [('3_8', '3_4'), ('2_4', '2_3')]: if k in mesh.descs: conns = mesh.get_conn(k) break if conns is not None: nelo = conns.shape[0] output('initial mesh: %d elements' % nelo) new_conns = elems_q2t(conns) nn = new_conns.shape[0] // nelo new_cgroups = nm.repeat(mesh.cmesh.cell_groups, nn)	output('new mesh: %d elements' % new_conns.shape[0])	sfepy.base.base.output
#!/usr/bin/env python """ Convert a mesh file from one SfePy-supported format to another. Examples:: $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s2.5 $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 -c 0 $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.mesh --remesh='q2/0 a1e-8 O9/7 V' $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new2.mesh --remesh='rq2/0 a1e-8 O9/7 V' """ from __future__ import absolute_import import sys import os.path as op from six.moves import range sys.path.append('.') from argparse import ArgumentParser, RawDescriptionHelpFormatter from sfepy.base.base import nm, output from sfepy.base.ioutils import remove_files from sfepy.discrete.fem import Mesh, FEDomain from sfepy.discrete.fem.meshio import (output_mesh_formats, MeshIO, supported_cell_types) from sfepy.discrete.fem.mesh import fix_double_nodes from sfepy.mesh.mesh_tools import elems_q2t helps = { 'scale' : 'scale factor (float or comma-separated list for each axis)' ' [default: %(default)s]', 'center' : 'center of the output mesh (0 for origin or' ' comma-separated list for each axis) applied after scaling' ' [default: %(default)s]', 'refine' : 'uniform refinement level [default: %(default)s]', 'format' : 'output mesh format (overrides filename_out extension)', 'list' : 'list supported readable/writable output mesh formats', 'merge' : 'remove duplicate vertices', 'tri-tetra' : 'convert elements: quad->tri, hexa->tetra', '2d' : 'force a 2D mesh by removing the z coordinates - assumes a 3D mesh' ' in the xy plane', 'save-per-mat': 'extract cells by material id and save them into' ' separate mesh files with a name based on filename_out and the id' ' numbers (preserves original mesh vertices)', 'remesh' : """when given, remesh the given mesh using tetgen. The options can be the following, separated by spaces, in this order: 1. "r" causes remeshing of the mesh volume - if not present the mesh surface is extracted and used for the volume mesh generation. 2. "q[<float>/<float>]" (required) - the two numbers after "q" are a maximum radius-edge ratio bound and a minimum dihedral angle bound. 3. "a<float>" (optional) - the number imposes a maximum volume constraint on all tetrahedra. 4. O[<0-9>/<0-7>] - the two numbers correspond to a mesh optimization level and a choice of optimizing operations. 5. "V" (optional) - if present, mesh statistics are printed. Consult the tetgen documentation for details.""", } def _parse_val_or_vec(option, name, parser): if option is not None: try: try: option = float(option) except ValueError: option = [float(ii) for ii in option.split(',')] option = nm.array(option, dtype=nm.float64, ndmin=1) except: output('bad %s! (%s)' % (name, option)) parser.print_help() sys.exit(1) return option def main(): parser = ArgumentParser(description=__doc__, formatter_class=RawDescriptionHelpFormatter) parser.add_argument('-s', '--scale', metavar='scale', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='scale', default=None, help=helps['scale']) parser.add_argument('-c', '--center', metavar='center', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='center', default=None, help=helps['center']) parser.add_argument('-r', '--refine', metavar='level', action="https://huggingface.co/datasets/luna-code/sfepy/store", type=int, dest='refine', default=0, help=helps['refine']) parser.add_argument('-f', '--format', metavar='format', action="https://huggingface.co/datasets/luna-code/sfepy/store", type=str, dest='format', default=None, help=helps['format']) parser.add_argument('-l', '--list', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='list', help=helps['list']) parser.add_argument('-m', '--merge', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='merge', help=helps['merge']) parser.add_argument('-t', '--tri-tetra', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='tri_tetra', help=helps['tri-tetra']) parser.add_argument('-2', '--2d', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='force_2d', help=helps['2d']) parser.add_argument('--save-per-mat', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='save_per_mat', help=helps['save-per-mat']) parser.add_argument('--remesh', metavar='options', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='remesh', default=None, help=helps['remesh']) parser.add_argument('filename_in') parser.add_argument('filename_out') options = parser.parse_args() if options.list: output('Supported readable mesh formats:') output('--------------------------------') output_mesh_formats('r') output('') output('Supported writable mesh formats:') output('--------------------------------') output_mesh_formats('w') sys.exit(0) scale = _parse_val_or_vec(options.scale, 'scale', parser) center = _parse_val_or_vec(options.center, 'center', parser) filename_in = options.filename_in filename_out = options.filename_out if options.remesh: import tempfile import shlex import subprocess dirname = tempfile.mkdtemp() is_surface = options.remesh.startswith('q') if is_surface: mesh = Mesh.from_file(filename_in) domain = FEDomain(mesh.name, mesh) region = domain.create_region('surf', 'vertices of surface', 'facet') surf_mesh = Mesh.from_region(region, mesh, localize=True, is_surface=True) filename = op.join(dirname, 'surf.mesh') surf_mesh.write(filename, io='auto') else: import shutil shutil.copy(filename_in, dirname) filename = op.join(dirname, op.basename(filename_in)) qopts = ''.join(options.remesh.split()) # Remove spaces. command = 'tetgen -BFENkACp%s %s' % (qopts, filename) args = shlex.split(command) subprocess.call(args) root, ext = op.splitext(filename) mesh = Mesh.from_file(root + '.1.vtk') remove_files(dirname) else: mesh = Mesh.from_file(filename_in) if options.force_2d: data = list(mesh._get_io_data()) data[0] = data[0][:, :2] mesh = Mesh.from_data(mesh.name, *data) if scale is not None: if len(scale) == 1: tr = nm.eye(mesh.dim, dtype=nm.float64) * scale elif len(scale) == mesh.dim: tr = nm.diag(scale) else: raise ValueError('bad scale! (%s)' % scale) mesh.transform_coors(tr) if center is not None: cc = 0.5 * mesh.get_bounding_box().sum(0) shift = center - cc tr = nm.c_[nm.eye(mesh.dim, dtype=nm.float64), shift[:, None]] mesh.transform_coors(tr) if options.refine > 0: domain = FEDomain(mesh.name, mesh) output('initial mesh: %d nodes %d elements' % (domain.shape.n_nod, domain.shape.n_el)) for ii in range(options.refine): output('refine %d...' % ii) domain = domain.refine() output('... %d nodes %d elements' % (domain.shape.n_nod, domain.shape.n_el)) mesh = domain.mesh if options.tri_tetra > 0: conns = None for k, new_desc in [('3_8', '3_4'), ('2_4', '2_3')]: if k in mesh.descs: conns = mesh.get_conn(k) break if conns is not None: nelo = conns.shape[0] output('initial mesh: %d elements' % nelo) new_conns = elems_q2t(conns) nn = new_conns.shape[0] // nelo new_cgroups = nm.repeat(mesh.cmesh.cell_groups, nn) output('new mesh: %d elements' % new_conns.shape[0]) mesh = Mesh.from_data(mesh.name, mesh.coors, mesh.cmesh.vertex_groups, [new_conns], [new_cgroups], [new_desc]) if options.merge: desc = mesh.descs[0] coor, ngroups, conns = fix_double_nodes(mesh.coors, mesh.cmesh.vertex_groups, mesh.get_conn(desc), 1e-9) mesh = Mesh.from_data(mesh.name + '_merged', coor, ngroups, [conns], [mesh.cmesh.cell_groups], [desc]) if options.save_per_mat: desc = mesh.descs[0] conns, cgroups = mesh.get_conn(desc), mesh.cmesh.cell_groups coors, ngroups = mesh.coors, mesh.cmesh.vertex_groups mat_ids = nm.unique(cgroups) for mat_id in mat_ids: idxs = nm.where(cgroups == mat_id)[0] imesh = Mesh.from_data(mesh.name + '_matid_%d' % mat_id, coors, ngroups, [conns[idxs]], [cgroups[idxs]], [desc]) fbase, fext = op.splitext(filename_out) ifilename_out = '%s_matid_%d%s' % (fbase, mat_id, fext) io = MeshIO.for_format(ifilename_out, format=options.format, writable=True)	output('writing %s...' % ifilename_out)	sfepy.base.base.output
#!/usr/bin/env python """ Convert a mesh file from one SfePy-supported format to another. Examples:: $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s2.5 $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 -c 0 $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.mesh --remesh='q2/0 a1e-8 O9/7 V' $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new2.mesh --remesh='rq2/0 a1e-8 O9/7 V' """ from __future__ import absolute_import import sys import os.path as op from six.moves import range sys.path.append('.') from argparse import ArgumentParser, RawDescriptionHelpFormatter from sfepy.base.base import nm, output from sfepy.base.ioutils import remove_files from sfepy.discrete.fem import Mesh, FEDomain from sfepy.discrete.fem.meshio import (output_mesh_formats, MeshIO, supported_cell_types) from sfepy.discrete.fem.mesh import fix_double_nodes from sfepy.mesh.mesh_tools import elems_q2t helps = { 'scale' : 'scale factor (float or comma-separated list for each axis)' ' [default: %(default)s]', 'center' : 'center of the output mesh (0 for origin or' ' comma-separated list for each axis) applied after scaling' ' [default: %(default)s]', 'refine' : 'uniform refinement level [default: %(default)s]', 'format' : 'output mesh format (overrides filename_out extension)', 'list' : 'list supported readable/writable output mesh formats', 'merge' : 'remove duplicate vertices', 'tri-tetra' : 'convert elements: quad->tri, hexa->tetra', '2d' : 'force a 2D mesh by removing the z coordinates - assumes a 3D mesh' ' in the xy plane', 'save-per-mat': 'extract cells by material id and save them into' ' separate mesh files with a name based on filename_out and the id' ' numbers (preserves original mesh vertices)', 'remesh' : """when given, remesh the given mesh using tetgen. The options can be the following, separated by spaces, in this order: 1. "r" causes remeshing of the mesh volume - if not present the mesh surface is extracted and used for the volume mesh generation. 2. "q[<float>/<float>]" (required) - the two numbers after "q" are a maximum radius-edge ratio bound and a minimum dihedral angle bound. 3. "a<float>" (optional) - the number imposes a maximum volume constraint on all tetrahedra. 4. O[<0-9>/<0-7>] - the two numbers correspond to a mesh optimization level and a choice of optimizing operations. 5. "V" (optional) - if present, mesh statistics are printed. Consult the tetgen documentation for details.""", } def _parse_val_or_vec(option, name, parser): if option is not None: try: try: option = float(option) except ValueError: option = [float(ii) for ii in option.split(',')] option = nm.array(option, dtype=nm.float64, ndmin=1) except: output('bad %s! (%s)' % (name, option)) parser.print_help() sys.exit(1) return option def main(): parser = ArgumentParser(description=__doc__, formatter_class=RawDescriptionHelpFormatter) parser.add_argument('-s', '--scale', metavar='scale', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='scale', default=None, help=helps['scale']) parser.add_argument('-c', '--center', metavar='center', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='center', default=None, help=helps['center']) parser.add_argument('-r', '--refine', metavar='level', action="https://huggingface.co/datasets/luna-code/sfepy/store", type=int, dest='refine', default=0, help=helps['refine']) parser.add_argument('-f', '--format', metavar='format', action="https://huggingface.co/datasets/luna-code/sfepy/store", type=str, dest='format', default=None, help=helps['format']) parser.add_argument('-l', '--list', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='list', help=helps['list']) parser.add_argument('-m', '--merge', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='merge', help=helps['merge']) parser.add_argument('-t', '--tri-tetra', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='tri_tetra', help=helps['tri-tetra']) parser.add_argument('-2', '--2d', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='force_2d', help=helps['2d']) parser.add_argument('--save-per-mat', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='save_per_mat', help=helps['save-per-mat']) parser.add_argument('--remesh', metavar='options', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='remesh', default=None, help=helps['remesh']) parser.add_argument('filename_in') parser.add_argument('filename_out') options = parser.parse_args() if options.list: output('Supported readable mesh formats:') output('--------------------------------') output_mesh_formats('r') output('') output('Supported writable mesh formats:') output('--------------------------------') output_mesh_formats('w') sys.exit(0) scale = _parse_val_or_vec(options.scale, 'scale', parser) center = _parse_val_or_vec(options.center, 'center', parser) filename_in = options.filename_in filename_out = options.filename_out if options.remesh: import tempfile import shlex import subprocess dirname = tempfile.mkdtemp() is_surface = options.remesh.startswith('q') if is_surface: mesh = Mesh.from_file(filename_in) domain = FEDomain(mesh.name, mesh) region = domain.create_region('surf', 'vertices of surface', 'facet') surf_mesh = Mesh.from_region(region, mesh, localize=True, is_surface=True) filename = op.join(dirname, 'surf.mesh') surf_mesh.write(filename, io='auto') else: import shutil shutil.copy(filename_in, dirname) filename = op.join(dirname, op.basename(filename_in)) qopts = ''.join(options.remesh.split()) # Remove spaces. command = 'tetgen -BFENkACp%s %s' % (qopts, filename) args = shlex.split(command) subprocess.call(args) root, ext = op.splitext(filename) mesh = Mesh.from_file(root + '.1.vtk') remove_files(dirname) else: mesh = Mesh.from_file(filename_in) if options.force_2d: data = list(mesh._get_io_data()) data[0] = data[0][:, :2] mesh = Mesh.from_data(mesh.name, *data) if scale is not None: if len(scale) == 1: tr = nm.eye(mesh.dim, dtype=nm.float64) * scale elif len(scale) == mesh.dim: tr = nm.diag(scale) else: raise ValueError('bad scale! (%s)' % scale) mesh.transform_coors(tr) if center is not None: cc = 0.5 * mesh.get_bounding_box().sum(0) shift = center - cc tr = nm.c_[nm.eye(mesh.dim, dtype=nm.float64), shift[:, None]] mesh.transform_coors(tr) if options.refine > 0: domain = FEDomain(mesh.name, mesh) output('initial mesh: %d nodes %d elements' % (domain.shape.n_nod, domain.shape.n_el)) for ii in range(options.refine): output('refine %d...' % ii) domain = domain.refine() output('... %d nodes %d elements' % (domain.shape.n_nod, domain.shape.n_el)) mesh = domain.mesh if options.tri_tetra > 0: conns = None for k, new_desc in [('3_8', '3_4'), ('2_4', '2_3')]: if k in mesh.descs: conns = mesh.get_conn(k) break if conns is not None: nelo = conns.shape[0] output('initial mesh: %d elements' % nelo) new_conns = elems_q2t(conns) nn = new_conns.shape[0] // nelo new_cgroups = nm.repeat(mesh.cmesh.cell_groups, nn) output('new mesh: %d elements' % new_conns.shape[0]) mesh = Mesh.from_data(mesh.name, mesh.coors, mesh.cmesh.vertex_groups, [new_conns], [new_cgroups], [new_desc]) if options.merge: desc = mesh.descs[0] coor, ngroups, conns = fix_double_nodes(mesh.coors, mesh.cmesh.vertex_groups, mesh.get_conn(desc), 1e-9) mesh = Mesh.from_data(mesh.name + '_merged', coor, ngroups, [conns], [mesh.cmesh.cell_groups], [desc]) if options.save_per_mat: desc = mesh.descs[0] conns, cgroups = mesh.get_conn(desc), mesh.cmesh.cell_groups coors, ngroups = mesh.coors, mesh.cmesh.vertex_groups mat_ids = nm.unique(cgroups) for mat_id in mat_ids: idxs = nm.where(cgroups == mat_id)[0] imesh = Mesh.from_data(mesh.name + '_matid_%d' % mat_id, coors, ngroups, [conns[idxs]], [cgroups[idxs]], [desc]) fbase, fext = op.splitext(filename_out) ifilename_out = '%s_matid_%d%s' % (fbase, mat_id, fext) io = MeshIO.for_format(ifilename_out, format=options.format, writable=True) output('writing %s...' % ifilename_out) imesh.write(ifilename_out, io=io)	output('...done')	sfepy.base.base.output
#!/usr/bin/env python """ Convert a mesh file from one SfePy-supported format to another. Examples:: $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s2.5 $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 -c 0 $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.mesh --remesh='q2/0 a1e-8 O9/7 V' $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new2.mesh --remesh='rq2/0 a1e-8 O9/7 V' """ from __future__ import absolute_import import sys import os.path as op from six.moves import range sys.path.append('.') from argparse import ArgumentParser, RawDescriptionHelpFormatter from sfepy.base.base import nm, output from sfepy.base.ioutils import remove_files from sfepy.discrete.fem import Mesh, FEDomain from sfepy.discrete.fem.meshio import (output_mesh_formats, MeshIO, supported_cell_types) from sfepy.discrete.fem.mesh import fix_double_nodes from sfepy.mesh.mesh_tools import elems_q2t helps = { 'scale' : 'scale factor (float or comma-separated list for each axis)' ' [default: %(default)s]', 'center' : 'center of the output mesh (0 for origin or' ' comma-separated list for each axis) applied after scaling' ' [default: %(default)s]', 'refine' : 'uniform refinement level [default: %(default)s]', 'format' : 'output mesh format (overrides filename_out extension)', 'list' : 'list supported readable/writable output mesh formats', 'merge' : 'remove duplicate vertices', 'tri-tetra' : 'convert elements: quad->tri, hexa->tetra', '2d' : 'force a 2D mesh by removing the z coordinates - assumes a 3D mesh' ' in the xy plane', 'save-per-mat': 'extract cells by material id and save them into' ' separate mesh files with a name based on filename_out and the id' ' numbers (preserves original mesh vertices)', 'remesh' : """when given, remesh the given mesh using tetgen. The options can be the following, separated by spaces, in this order: 1. "r" causes remeshing of the mesh volume - if not present the mesh surface is extracted and used for the volume mesh generation. 2. "q[<float>/<float>]" (required) - the two numbers after "q" are a maximum radius-edge ratio bound and a minimum dihedral angle bound. 3. "a<float>" (optional) - the number imposes a maximum volume constraint on all tetrahedra. 4. O[<0-9>/<0-7>] - the two numbers correspond to a mesh optimization level and a choice of optimizing operations. 5. "V" (optional) - if present, mesh statistics are printed. Consult the tetgen documentation for details.""", } def _parse_val_or_vec(option, name, parser): if option is not None: try: try: option = float(option) except ValueError: option = [float(ii) for ii in option.split(',')] option = nm.array(option, dtype=nm.float64, ndmin=1) except:	output('bad %s! (%s)' % (name, option))	sfepy.base.base.output
#!/usr/bin/env python """ Convert a mesh file from one SfePy-supported format to another. Examples:: $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s2.5 $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 -c 0 $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.mesh --remesh='q2/0 a1e-8 O9/7 V' $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new2.mesh --remesh='rq2/0 a1e-8 O9/7 V' """ from __future__ import absolute_import import sys import os.path as op from six.moves import range sys.path.append('.') from argparse import ArgumentParser, RawDescriptionHelpFormatter from sfepy.base.base import nm, output from sfepy.base.ioutils import remove_files from sfepy.discrete.fem import Mesh, FEDomain from sfepy.discrete.fem.meshio import (output_mesh_formats, MeshIO, supported_cell_types) from sfepy.discrete.fem.mesh import fix_double_nodes from sfepy.mesh.mesh_tools import elems_q2t helps = { 'scale' : 'scale factor (float or comma-separated list for each axis)' ' [default: %(default)s]', 'center' : 'center of the output mesh (0 for origin or' ' comma-separated list for each axis) applied after scaling' ' [default: %(default)s]', 'refine' : 'uniform refinement level [default: %(default)s]', 'format' : 'output mesh format (overrides filename_out extension)', 'list' : 'list supported readable/writable output mesh formats', 'merge' : 'remove duplicate vertices', 'tri-tetra' : 'convert elements: quad->tri, hexa->tetra', '2d' : 'force a 2D mesh by removing the z coordinates - assumes a 3D mesh' ' in the xy plane', 'save-per-mat': 'extract cells by material id and save them into' ' separate mesh files with a name based on filename_out and the id' ' numbers (preserves original mesh vertices)', 'remesh' : """when given, remesh the given mesh using tetgen. The options can be the following, separated by spaces, in this order: 1. "r" causes remeshing of the mesh volume - if not present the mesh surface is extracted and used for the volume mesh generation. 2. "q[<float>/<float>]" (required) - the two numbers after "q" are a maximum radius-edge ratio bound and a minimum dihedral angle bound. 3. "a<float>" (optional) - the number imposes a maximum volume constraint on all tetrahedra. 4. O[<0-9>/<0-7>] - the two numbers correspond to a mesh optimization level and a choice of optimizing operations. 5. "V" (optional) - if present, mesh statistics are printed. Consult the tetgen documentation for details.""", } def _parse_val_or_vec(option, name, parser): if option is not None: try: try: option = float(option) except ValueError: option = [float(ii) for ii in option.split(',')] option = nm.array(option, dtype=nm.float64, ndmin=1) except: output('bad %s! (%s)' % (name, option)) parser.print_help() sys.exit(1) return option def main(): parser = ArgumentParser(description=__doc__, formatter_class=RawDescriptionHelpFormatter) parser.add_argument('-s', '--scale', metavar='scale', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='scale', default=None, help=helps['scale']) parser.add_argument('-c', '--center', metavar='center', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='center', default=None, help=helps['center']) parser.add_argument('-r', '--refine', metavar='level', action="https://huggingface.co/datasets/luna-code/sfepy/store", type=int, dest='refine', default=0, help=helps['refine']) parser.add_argument('-f', '--format', metavar='format', action="https://huggingface.co/datasets/luna-code/sfepy/store", type=str, dest='format', default=None, help=helps['format']) parser.add_argument('-l', '--list', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='list', help=helps['list']) parser.add_argument('-m', '--merge', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='merge', help=helps['merge']) parser.add_argument('-t', '--tri-tetra', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='tri_tetra', help=helps['tri-tetra']) parser.add_argument('-2', '--2d', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='force_2d', help=helps['2d']) parser.add_argument('--save-per-mat', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='save_per_mat', help=helps['save-per-mat']) parser.add_argument('--remesh', metavar='options', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='remesh', default=None, help=helps['remesh']) parser.add_argument('filename_in') parser.add_argument('filename_out') options = parser.parse_args() if options.list: output('Supported readable mesh formats:') output('--------------------------------') output_mesh_formats('r') output('') output('Supported writable mesh formats:') output('--------------------------------') output_mesh_formats('w') sys.exit(0) scale = _parse_val_or_vec(options.scale, 'scale', parser) center = _parse_val_or_vec(options.center, 'center', parser) filename_in = options.filename_in filename_out = options.filename_out if options.remesh: import tempfile import shlex import subprocess dirname = tempfile.mkdtemp() is_surface = options.remesh.startswith('q') if is_surface: mesh = Mesh.from_file(filename_in) domain = FEDomain(mesh.name, mesh) region = domain.create_region('surf', 'vertices of surface', 'facet') surf_mesh = Mesh.from_region(region, mesh, localize=True, is_surface=True) filename = op.join(dirname, 'surf.mesh') surf_mesh.write(filename, io='auto') else: import shutil shutil.copy(filename_in, dirname) filename = op.join(dirname, op.basename(filename_in)) qopts = ''.join(options.remesh.split()) # Remove spaces. command = 'tetgen -BFENkACp%s %s' % (qopts, filename) args = shlex.split(command) subprocess.call(args) root, ext = op.splitext(filename) mesh = Mesh.from_file(root + '.1.vtk') remove_files(dirname) else: mesh = Mesh.from_file(filename_in) if options.force_2d: data = list(mesh._get_io_data()) data[0] = data[0][:, :2] mesh = Mesh.from_data(mesh.name, *data) if scale is not None: if len(scale) == 1: tr =	nm.eye(mesh.dim, dtype=nm.float64)	sfepy.base.base.nm.eye
#!/usr/bin/env python """ Convert a mesh file from one SfePy-supported format to another. Examples:: $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s2.5 $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 -c 0 $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.mesh --remesh='q2/0 a1e-8 O9/7 V' $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new2.mesh --remesh='rq2/0 a1e-8 O9/7 V' """ from __future__ import absolute_import import sys import os.path as op from six.moves import range sys.path.append('.') from argparse import ArgumentParser, RawDescriptionHelpFormatter from sfepy.base.base import nm, output from sfepy.base.ioutils import remove_files from sfepy.discrete.fem import Mesh, FEDomain from sfepy.discrete.fem.meshio import (output_mesh_formats, MeshIO, supported_cell_types) from sfepy.discrete.fem.mesh import fix_double_nodes from sfepy.mesh.mesh_tools import elems_q2t helps = { 'scale' : 'scale factor (float or comma-separated list for each axis)' ' [default: %(default)s]', 'center' : 'center of the output mesh (0 for origin or' ' comma-separated list for each axis) applied after scaling' ' [default: %(default)s]', 'refine' : 'uniform refinement level [default: %(default)s]', 'format' : 'output mesh format (overrides filename_out extension)', 'list' : 'list supported readable/writable output mesh formats', 'merge' : 'remove duplicate vertices', 'tri-tetra' : 'convert elements: quad->tri, hexa->tetra', '2d' : 'force a 2D mesh by removing the z coordinates - assumes a 3D mesh' ' in the xy plane', 'save-per-mat': 'extract cells by material id and save them into' ' separate mesh files with a name based on filename_out and the id' ' numbers (preserves original mesh vertices)', 'remesh' : """when given, remesh the given mesh using tetgen. The options can be the following, separated by spaces, in this order: 1. "r" causes remeshing of the mesh volume - if not present the mesh surface is extracted and used for the volume mesh generation. 2. "q[<float>/<float>]" (required) - the two numbers after "q" are a maximum radius-edge ratio bound and a minimum dihedral angle bound. 3. "a<float>" (optional) - the number imposes a maximum volume constraint on all tetrahedra. 4. O[<0-9>/<0-7>] - the two numbers correspond to a mesh optimization level and a choice of optimizing operations. 5. "V" (optional) - if present, mesh statistics are printed. Consult the tetgen documentation for details.""", } def _parse_val_or_vec(option, name, parser): if option is not None: try: try: option = float(option) except ValueError: option = [float(ii) for ii in option.split(',')] option = nm.array(option, dtype=nm.float64, ndmin=1) except: output('bad %s! (%s)' % (name, option)) parser.print_help() sys.exit(1) return option def main(): parser = ArgumentParser(description=__doc__, formatter_class=RawDescriptionHelpFormatter) parser.add_argument('-s', '--scale', metavar='scale', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='scale', default=None, help=helps['scale']) parser.add_argument('-c', '--center', metavar='center', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='center', default=None, help=helps['center']) parser.add_argument('-r', '--refine', metavar='level', action="https://huggingface.co/datasets/luna-code/sfepy/store", type=int, dest='refine', default=0, help=helps['refine']) parser.add_argument('-f', '--format', metavar='format', action="https://huggingface.co/datasets/luna-code/sfepy/store", type=str, dest='format', default=None, help=helps['format']) parser.add_argument('-l', '--list', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='list', help=helps['list']) parser.add_argument('-m', '--merge', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='merge', help=helps['merge']) parser.add_argument('-t', '--tri-tetra', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='tri_tetra', help=helps['tri-tetra']) parser.add_argument('-2', '--2d', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='force_2d', help=helps['2d']) parser.add_argument('--save-per-mat', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='save_per_mat', help=helps['save-per-mat']) parser.add_argument('--remesh', metavar='options', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='remesh', default=None, help=helps['remesh']) parser.add_argument('filename_in') parser.add_argument('filename_out') options = parser.parse_args() if options.list: output('Supported readable mesh formats:') output('--------------------------------') output_mesh_formats('r') output('') output('Supported writable mesh formats:') output('--------------------------------') output_mesh_formats('w') sys.exit(0) scale = _parse_val_or_vec(options.scale, 'scale', parser) center = _parse_val_or_vec(options.center, 'center', parser) filename_in = options.filename_in filename_out = options.filename_out if options.remesh: import tempfile import shlex import subprocess dirname = tempfile.mkdtemp() is_surface = options.remesh.startswith('q') if is_surface: mesh = Mesh.from_file(filename_in) domain = FEDomain(mesh.name, mesh) region = domain.create_region('surf', 'vertices of surface', 'facet') surf_mesh = Mesh.from_region(region, mesh, localize=True, is_surface=True) filename = op.join(dirname, 'surf.mesh') surf_mesh.write(filename, io='auto') else: import shutil shutil.copy(filename_in, dirname) filename = op.join(dirname, op.basename(filename_in)) qopts = ''.join(options.remesh.split()) # Remove spaces. command = 'tetgen -BFENkACp%s %s' % (qopts, filename) args = shlex.split(command) subprocess.call(args) root, ext = op.splitext(filename) mesh = Mesh.from_file(root + '.1.vtk') remove_files(dirname) else: mesh = Mesh.from_file(filename_in) if options.force_2d: data = list(mesh._get_io_data()) data[0] = data[0][:, :2] mesh = Mesh.from_data(mesh.name, *data) if scale is not None: if len(scale) == 1: tr = nm.eye(mesh.dim, dtype=nm.float64) * scale elif len(scale) == mesh.dim: tr =	nm.diag(scale)	sfepy.base.base.nm.diag
#!/usr/bin/env python """ Convert a mesh file from one SfePy-supported format to another. Examples:: $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s2.5 $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 -c 0 $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.mesh --remesh='q2/0 a1e-8 O9/7 V' $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new2.mesh --remesh='rq2/0 a1e-8 O9/7 V' """ from __future__ import absolute_import import sys import os.path as op from six.moves import range sys.path.append('.') from argparse import ArgumentParser, RawDescriptionHelpFormatter from sfepy.base.base import nm, output from sfepy.base.ioutils import remove_files from sfepy.discrete.fem import Mesh, FEDomain from sfepy.discrete.fem.meshio import (output_mesh_formats, MeshIO, supported_cell_types) from sfepy.discrete.fem.mesh import fix_double_nodes from sfepy.mesh.mesh_tools import elems_q2t helps = { 'scale' : 'scale factor (float or comma-separated list for each axis)' ' [default: %(default)s]', 'center' : 'center of the output mesh (0 for origin or' ' comma-separated list for each axis) applied after scaling' ' [default: %(default)s]', 'refine' : 'uniform refinement level [default: %(default)s]', 'format' : 'output mesh format (overrides filename_out extension)', 'list' : 'list supported readable/writable output mesh formats', 'merge' : 'remove duplicate vertices', 'tri-tetra' : 'convert elements: quad->tri, hexa->tetra', '2d' : 'force a 2D mesh by removing the z coordinates - assumes a 3D mesh' ' in the xy plane', 'save-per-mat': 'extract cells by material id and save them into' ' separate mesh files with a name based on filename_out and the id' ' numbers (preserves original mesh vertices)', 'remesh' : """when given, remesh the given mesh using tetgen. The options can be the following, separated by spaces, in this order: 1. "r" causes remeshing of the mesh volume - if not present the mesh surface is extracted and used for the volume mesh generation. 2. "q[<float>/<float>]" (required) - the two numbers after "q" are a maximum radius-edge ratio bound and a minimum dihedral angle bound. 3. "a<float>" (optional) - the number imposes a maximum volume constraint on all tetrahedra. 4. O[<0-9>/<0-7>] - the two numbers correspond to a mesh optimization level and a choice of optimizing operations. 5. "V" (optional) - if present, mesh statistics are printed. Consult the tetgen documentation for details.""", } def _parse_val_or_vec(option, name, parser): if option is not None: try: try: option = float(option) except ValueError: option = [float(ii) for ii in option.split(',')] option = nm.array(option, dtype=nm.float64, ndmin=1) except: output('bad %s! (%s)' % (name, option)) parser.print_help() sys.exit(1) return option def main(): parser = ArgumentParser(description=__doc__, formatter_class=RawDescriptionHelpFormatter) parser.add_argument('-s', '--scale', metavar='scale', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='scale', default=None, help=helps['scale']) parser.add_argument('-c', '--center', metavar='center', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='center', default=None, help=helps['center']) parser.add_argument('-r', '--refine', metavar='level', action="https://huggingface.co/datasets/luna-code/sfepy/store", type=int, dest='refine', default=0, help=helps['refine']) parser.add_argument('-f', '--format', metavar='format', action="https://huggingface.co/datasets/luna-code/sfepy/store", type=str, dest='format', default=None, help=helps['format']) parser.add_argument('-l', '--list', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='list', help=helps['list']) parser.add_argument('-m', '--merge', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='merge', help=helps['merge']) parser.add_argument('-t', '--tri-tetra', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='tri_tetra', help=helps['tri-tetra']) parser.add_argument('-2', '--2d', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='force_2d', help=helps['2d']) parser.add_argument('--save-per-mat', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='save_per_mat', help=helps['save-per-mat']) parser.add_argument('--remesh', metavar='options', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='remesh', default=None, help=helps['remesh']) parser.add_argument('filename_in') parser.add_argument('filename_out') options = parser.parse_args() if options.list: output('Supported readable mesh formats:') output('--------------------------------') output_mesh_formats('r') output('') output('Supported writable mesh formats:') output('--------------------------------') output_mesh_formats('w') sys.exit(0) scale = _parse_val_or_vec(options.scale, 'scale', parser) center = _parse_val_or_vec(options.center, 'center', parser) filename_in = options.filename_in filename_out = options.filename_out if options.remesh: import tempfile import shlex import subprocess dirname = tempfile.mkdtemp() is_surface = options.remesh.startswith('q') if is_surface: mesh = Mesh.from_file(filename_in) domain = FEDomain(mesh.name, mesh) region = domain.create_region('surf', 'vertices of surface', 'facet') surf_mesh = Mesh.from_region(region, mesh, localize=True, is_surface=True) filename = op.join(dirname, 'surf.mesh') surf_mesh.write(filename, io='auto') else: import shutil shutil.copy(filename_in, dirname) filename = op.join(dirname, op.basename(filename_in)) qopts = ''.join(options.remesh.split()) # Remove spaces. command = 'tetgen -BFENkACp%s %s' % (qopts, filename) args = shlex.split(command) subprocess.call(args) root, ext = op.splitext(filename) mesh = Mesh.from_file(root + '.1.vtk') remove_files(dirname) else: mesh = Mesh.from_file(filename_in) if options.force_2d: data = list(mesh._get_io_data()) data[0] = data[0][:, :2] mesh = Mesh.from_data(mesh.name, *data) if scale is not None: if len(scale) == 1: tr = nm.eye(mesh.dim, dtype=nm.float64) * scale elif len(scale) == mesh.dim: tr = nm.diag(scale) else: raise ValueError('bad scale! (%s)' % scale) mesh.transform_coors(tr) if center is not None: cc = 0.5 * mesh.get_bounding_box().sum(0) shift = center - cc tr = nm.c_[	nm.eye(mesh.dim, dtype=nm.float64)	sfepy.base.base.nm.eye
#!/usr/bin/env python """ Convert a mesh file from one SfePy-supported format to another. Examples:: $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s2.5 $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 -c 0 $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.mesh --remesh='q2/0 a1e-8 O9/7 V' $ ./script/convert_mesh.py meshes/3d/cylinder.mesh new2.mesh --remesh='rq2/0 a1e-8 O9/7 V' """ from __future__ import absolute_import import sys import os.path as op from six.moves import range sys.path.append('.') from argparse import ArgumentParser, RawDescriptionHelpFormatter from sfepy.base.base import nm, output from sfepy.base.ioutils import remove_files from sfepy.discrete.fem import Mesh, FEDomain from sfepy.discrete.fem.meshio import (output_mesh_formats, MeshIO, supported_cell_types) from sfepy.discrete.fem.mesh import fix_double_nodes from sfepy.mesh.mesh_tools import elems_q2t helps = { 'scale' : 'scale factor (float or comma-separated list for each axis)' ' [default: %(default)s]', 'center' : 'center of the output mesh (0 for origin or' ' comma-separated list for each axis) applied after scaling' ' [default: %(default)s]', 'refine' : 'uniform refinement level [default: %(default)s]', 'format' : 'output mesh format (overrides filename_out extension)', 'list' : 'list supported readable/writable output mesh formats', 'merge' : 'remove duplicate vertices', 'tri-tetra' : 'convert elements: quad->tri, hexa->tetra', '2d' : 'force a 2D mesh by removing the z coordinates - assumes a 3D mesh' ' in the xy plane', 'save-per-mat': 'extract cells by material id and save them into' ' separate mesh files with a name based on filename_out and the id' ' numbers (preserves original mesh vertices)', 'remesh' : """when given, remesh the given mesh using tetgen. The options can be the following, separated by spaces, in this order: 1. "r" causes remeshing of the mesh volume - if not present the mesh surface is extracted and used for the volume mesh generation. 2. "q[<float>/<float>]" (required) - the two numbers after "q" are a maximum radius-edge ratio bound and a minimum dihedral angle bound. 3. "a<float>" (optional) - the number imposes a maximum volume constraint on all tetrahedra. 4. O[<0-9>/<0-7>] - the two numbers correspond to a mesh optimization level and a choice of optimizing operations. 5. "V" (optional) - if present, mesh statistics are printed. Consult the tetgen documentation for details.""", } def _parse_val_or_vec(option, name, parser): if option is not None: try: try: option = float(option) except ValueError: option = [float(ii) for ii in option.split(',')] option = nm.array(option, dtype=nm.float64, ndmin=1) except: output('bad %s! (%s)' % (name, option)) parser.print_help() sys.exit(1) return option def main(): parser = ArgumentParser(description=__doc__, formatter_class=RawDescriptionHelpFormatter) parser.add_argument('-s', '--scale', metavar='scale', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='scale', default=None, help=helps['scale']) parser.add_argument('-c', '--center', metavar='center', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='center', default=None, help=helps['center']) parser.add_argument('-r', '--refine', metavar='level', action="https://huggingface.co/datasets/luna-code/sfepy/store", type=int, dest='refine', default=0, help=helps['refine']) parser.add_argument('-f', '--format', metavar='format', action="https://huggingface.co/datasets/luna-code/sfepy/store", type=str, dest='format', default=None, help=helps['format']) parser.add_argument('-l', '--list', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='list', help=helps['list']) parser.add_argument('-m', '--merge', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='merge', help=helps['merge']) parser.add_argument('-t', '--tri-tetra', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='tri_tetra', help=helps['tri-tetra']) parser.add_argument('-2', '--2d', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='force_2d', help=helps['2d']) parser.add_argument('--save-per-mat', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='save_per_mat', help=helps['save-per-mat']) parser.add_argument('--remesh', metavar='options', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='remesh', default=None, help=helps['remesh']) parser.add_argument('filename_in') parser.add_argument('filename_out') options = parser.parse_args() if options.list: output('Supported readable mesh formats:') output('--------------------------------') output_mesh_formats('r') output('') output('Supported writable mesh formats:') output('--------------------------------') output_mesh_formats('w') sys.exit(0) scale = _parse_val_or_vec(options.scale, 'scale', parser) center = _parse_val_or_vec(options.center, 'center', parser) filename_in = options.filename_in filename_out = options.filename_out if options.remesh: import tempfile import shlex import subprocess dirname = tempfile.mkdtemp() is_surface = options.remesh.startswith('q') if is_surface: mesh = Mesh.from_file(filename_in) domain = FEDomain(mesh.name, mesh) region = domain.create_region('surf', 'vertices of surface', 'facet') surf_mesh = Mesh.from_region(region, mesh, localize=True, is_surface=True) filename = op.join(dirname, 'surf.mesh') surf_mesh.write(filename, io='auto') else: import shutil shutil.copy(filename_in, dirname) filename = op.join(dirname, op.basename(filename_in)) qopts = ''.join(options.remesh.split()) # Remove spaces. command = 'tetgen -BFENkACp%s %s' % (qopts, filename) args = shlex.split(command) subprocess.call(args) root, ext = op.splitext(filename) mesh = Mesh.from_file(root + '.1.vtk') remove_files(dirname) else: mesh = Mesh.from_file(filename_in) if options.force_2d: data = list(mesh._get_io_data()) data[0] = data[0][:, :2] mesh = Mesh.from_data(mesh.name, *data) if scale is not None: if len(scale) == 1: tr = nm.eye(mesh.dim, dtype=nm.float64) * scale elif len(scale) == mesh.dim: tr = nm.diag(scale) else: raise ValueError('bad scale! (%s)' % scale) mesh.transform_coors(tr) if center is not None: cc = 0.5 * mesh.get_bounding_box().sum(0) shift = center - cc tr = nm.c_[nm.eye(mesh.dim, dtype=nm.float64), shift[:, None]] mesh.transform_coors(tr) if options.refine > 0: domain = FEDomain(mesh.name, mesh) output('initial mesh: %d nodes %d elements' % (domain.shape.n_nod, domain.shape.n_el)) for ii in range(options.refine): output('refine %d...' % ii) domain = domain.refine() output('... %d nodes %d elements' % (domain.shape.n_nod, domain.shape.n_el)) mesh = domain.mesh if options.tri_tetra > 0: conns = None for k, new_desc in [('3_8', '3_4'), ('2_4', '2_3')]: if k in mesh.descs: conns = mesh.get_conn(k) break if conns is not None: nelo = conns.shape[0] output('initial mesh: %d elements' % nelo) new_conns = elems_q2t(conns) nn = new_conns.shape[0] // nelo new_cgroups = nm.repeat(mesh.cmesh.cell_groups, nn) output('new mesh: %d elements' % new_conns.shape[0]) mesh = Mesh.from_data(mesh.name, mesh.coors, mesh.cmesh.vertex_groups, [new_conns], [new_cgroups], [new_desc]) if options.merge: desc = mesh.descs[0] coor, ngroups, conns = fix_double_nodes(mesh.coors, mesh.cmesh.vertex_groups, mesh.get_conn(desc), 1e-9) mesh = Mesh.from_data(mesh.name + '_merged', coor, ngroups, [conns], [mesh.cmesh.cell_groups], [desc]) if options.save_per_mat: desc = mesh.descs[0] conns, cgroups = mesh.get_conn(desc), mesh.cmesh.cell_groups coors, ngroups = mesh.coors, mesh.cmesh.vertex_groups mat_ids = nm.unique(cgroups) for mat_id in mat_ids: idxs =	nm.where(cgroups == mat_id)	sfepy.base.base.nm.where
# This example implements macroscopic homogenized model of Biot-Darcy-Brinkman model of flow in deformable # double porous media. # The mathematical model is described in: # #<NAME>., <NAME>., <NAME>. #The Biot-Darcy-Brinkman model of flow in deformable double porous media; homogenization and numerical modelling. # Computers and Mathematics with applications, 78(9):3044-3066, 2019, # https://doi.org/10.1016/j.camwa.2019.04.004 # # Run simulation: # # ./simple.py example_perfusion_BDB/perf_BDB_mac.py # # The results are stored in `example_perfusion_BDB/results/macro` directory. # import numpy as nm from sfepy.homogenization.micmac import get_homog_coefs_linear from sfepy.homogenization.utils import define_box_regions from sfepy.discrete.fem.mesh import Mesh import os.path as osp material_cache = {} data_dir = 'example_perfusion_BDB' def coefs2qp(coefs, nqp): out = {} for k, v in coefs.items(): if type(v) not in [nm.ndarray, float]: continue if type(v) is nm.ndarray: if len(v.shape) >= 3: out[k] = v out[k] = nm.tile(v, (nqp, 1, 1)) return out # Get raw homogenized coefficients, recalculate them if necessary def get_raw_coefs(problem): if 'raw_coefs' not in material_cache: micro_filename = material_cache['meso_filename'] coefs_filename = 'coefs_meso' coefs_filename = osp.join(problem.conf.options.get('output_dir', '.'), coefs_filename) + '.h5' coefs = get_homog_coefs_linear(0, 0, None, micro_filename=micro_filename, coefs_filename=coefs_filename) coefs['B'] = coefs['B'][:, nm.newaxis] material_cache['raw_coefs'] = coefs return material_cache['raw_coefs'] #Get homogenized coefficients in quadrature points def get_homog(coors,pb, mode, **kwargs): if not (mode == 'qp'): return nqp = coors.shape[0] coefs=get_raw_coefs(pb) for k in coefs.keys(): v = coefs[k] if type(v) is nm.ndarray: if len(v.shape) == 0: coefs[k] = v.reshape((1, 1)) elif len(v.shape) == 1: coefs[k] = v[:, nm.newaxis] elif isinstance(v, float): coefs[k] = nm.array([[v]]) out = coefs2qp(coefs, nqp) return out #Definition of dirichlet boundary conditions def get_ebc( coors, amplitude, cg1, cg2,const=False): """ Define the essential boundary conditions as a function of coordinates `coors` of region nodes. """ y = coors[:, 1] - cg1 z = coors[:, 2] - cg2 val = amplitude*((cg1**2 - (abs(y)**2))+(cg2**2 - (abs(z)**2))) if const: val=nm.ones_like(y) *amplitude return val #Returns value of \phi_c\bar{w}^{mes} as a material function def get_ebc_mat( coors,pb, mode, amplitude, cg1, cg2,konst=False): if mode == 'qp': val = get_ebc( coors, amplitude, cg1, cg2,konst) phic = get_raw_coefs(pb)['vol']["fraction_Zc"] v_w1 = val[:, nm.newaxis, nm.newaxis] return {'val': v_w1*phic} #Definition of boundary conditions for numerical example at http://sfepy.org/sfepy_examples/example_perfusion_BDB/ def define_bc(cg1,cg2, val_in=1e2, val_out=1e2): funs = { 'w_in': (lambda ts, coor, bc, problem, **kwargs: get_ebc( coor, val_in, cg1, cg2),), 'w_out': (lambda ts, coor, bc, problem, **kwargs: get_ebc( coor, val_out, cg1, cg2),), 'w_in_mat': (lambda ts,coor, problem, mode=None, **kwargs: get_ebc_mat( coor, problem, mode, val_in, cg1, cg2),), 'w_out_mat': (lambda ts,coor, problem, mode=None, **kwargs: get_ebc_mat( coor, problem, mode, val_out, cg1, cg2),), } mats = { 'w_in': 'w_in_mat', 'w_out': 'w_out_mat', } ebcs = { 'fix_u_in': ('In', {'u.all': 0.0}), 'fix_u_out': ('Out', {'u.all': 0.0}), 'w_in': ('In', {'w.0': 'w_in','w.[1,2]': 0.0}), 'w_out': ('Out', {'w.0': 'w_out','w.[1,2]': 0.0}), 'wB_dirichlet':('Bottom',{'w.2' :0.0,'u.2':0.0}), 'WT_dirichlet':('Top',{'w.2' :0.0,'u.2':0.0}), 'wN_dirichlet':('Near',{'w.1' :0.0,'u.1':0.0}), 'wF_dirichlet':('Far',{'w.1' :0.0,'u.1':0.0}), } lcbcs = { 'imv': ('Omega', {'ls.all' : None}, None, 'integral_mean_value') } return ebcs, funs, mats, lcbcs #Definition of macroscopic problem def define(filename_mesh=None,cg1=None, cg2=None): if filename_mesh is None: filename_mesh = osp.join(data_dir, 'macro_perf.vtk') cg1, cg2 = 0.0015, 0.0015 # y and z coordinates of center of gravity mesh =	Mesh.from_file(filename_mesh)	sfepy.discrete.fem.mesh.Mesh.from_file
# This example implements macroscopic homogenized model of Biot-Darcy-Brinkman model of flow in deformable # double porous media. # The mathematical model is described in: # #<NAME>., <NAME>., <NAME>. #The Biot-Darcy-Brinkman model of flow in deformable double porous media; homogenization and numerical modelling. # Computers and Mathematics with applications, 78(9):3044-3066, 2019, # https://doi.org/10.1016/j.camwa.2019.04.004 # # Run simulation: # # ./simple.py example_perfusion_BDB/perf_BDB_mac.py # # The results are stored in `example_perfusion_BDB/results/macro` directory. # import numpy as nm from sfepy.homogenization.micmac import get_homog_coefs_linear from sfepy.homogenization.utils import define_box_regions from sfepy.discrete.fem.mesh import Mesh import os.path as osp material_cache = {} data_dir = 'example_perfusion_BDB' def coefs2qp(coefs, nqp): out = {} for k, v in coefs.items(): if type(v) not in [nm.ndarray, float]: continue if type(v) is nm.ndarray: if len(v.shape) >= 3: out[k] = v out[k] = nm.tile(v, (nqp, 1, 1)) return out # Get raw homogenized coefficients, recalculate them if necessary def get_raw_coefs(problem): if 'raw_coefs' not in material_cache: micro_filename = material_cache['meso_filename'] coefs_filename = 'coefs_meso' coefs_filename = osp.join(problem.conf.options.get('output_dir', '.'), coefs_filename) + '.h5' coefs = get_homog_coefs_linear(0, 0, None, micro_filename=micro_filename, coefs_filename=coefs_filename) coefs['B'] = coefs['B'][:, nm.newaxis] material_cache['raw_coefs'] = coefs return material_cache['raw_coefs'] #Get homogenized coefficients in quadrature points def get_homog(coors,pb, mode, **kwargs): if not (mode == 'qp'): return nqp = coors.shape[0] coefs=get_raw_coefs(pb) for k in coefs.keys(): v = coefs[k] if type(v) is nm.ndarray: if len(v.shape) == 0: coefs[k] = v.reshape((1, 1)) elif len(v.shape) == 1: coefs[k] = v[:, nm.newaxis] elif isinstance(v, float): coefs[k] = nm.array([[v]]) out = coefs2qp(coefs, nqp) return out #Definition of dirichlet boundary conditions def get_ebc( coors, amplitude, cg1, cg2,const=False): """ Define the essential boundary conditions as a function of coordinates `coors` of region nodes. """ y = coors[:, 1] - cg1 z = coors[:, 2] - cg2 val = amplitude*((cg1**2 - (abs(y)**2))+(cg2**2 - (abs(z)**2))) if const: val=nm.ones_like(y) *amplitude return val #Returns value of \phi_c\bar{w}^{mes} as a material function def get_ebc_mat( coors,pb, mode, amplitude, cg1, cg2,konst=False): if mode == 'qp': val = get_ebc( coors, amplitude, cg1, cg2,konst) phic = get_raw_coefs(pb)['vol']["fraction_Zc"] v_w1 = val[:, nm.newaxis, nm.newaxis] return {'val': v_w1*phic} #Definition of boundary conditions for numerical example at http://sfepy.org/sfepy_examples/example_perfusion_BDB/ def define_bc(cg1,cg2, val_in=1e2, val_out=1e2): funs = { 'w_in': (lambda ts, coor, bc, problem, **kwargs: get_ebc( coor, val_in, cg1, cg2),), 'w_out': (lambda ts, coor, bc, problem, **kwargs: get_ebc( coor, val_out, cg1, cg2),), 'w_in_mat': (lambda ts,coor, problem, mode=None, **kwargs: get_ebc_mat( coor, problem, mode, val_in, cg1, cg2),), 'w_out_mat': (lambda ts,coor, problem, mode=None, **kwargs: get_ebc_mat( coor, problem, mode, val_out, cg1, cg2),), } mats = { 'w_in': 'w_in_mat', 'w_out': 'w_out_mat', } ebcs = { 'fix_u_in': ('In', {'u.all': 0.0}), 'fix_u_out': ('Out', {'u.all': 0.0}), 'w_in': ('In', {'w.0': 'w_in','w.[1,2]': 0.0}), 'w_out': ('Out', {'w.0': 'w_out','w.[1,2]': 0.0}), 'wB_dirichlet':('Bottom',{'w.2' :0.0,'u.2':0.0}), 'WT_dirichlet':('Top',{'w.2' :0.0,'u.2':0.0}), 'wN_dirichlet':('Near',{'w.1' :0.0,'u.1':0.0}), 'wF_dirichlet':('Far',{'w.1' :0.0,'u.1':0.0}), } lcbcs = { 'imv': ('Omega', {'ls.all' : None}, None, 'integral_mean_value') } return ebcs, funs, mats, lcbcs #Definition of macroscopic problem def define(filename_mesh=None,cg1=None, cg2=None): if filename_mesh is None: filename_mesh = osp.join(data_dir, 'macro_perf.vtk') cg1, cg2 = 0.0015, 0.0015 # y and z coordinates of center of gravity mesh = Mesh.from_file(filename_mesh) poroela_mezo_file = osp.join(data_dir,'perf_BDB_mes.py') material_cache['meso_filename']=poroela_mezo_file bbox = mesh.get_bounding_box() regions =	define_box_regions(mesh.dim, bbox[0], bbox[1], eps=1e-6)	sfepy.homogenization.utils.define_box_regions
#!/usr/bin/env python """ Dispersion analysis of a heterogeneous finite scale periodic cell. The periodic cell mesh has to contain two subdomains Y1 (with the cell ids 1), Y2 (with the cell ids 2), so that different material properties can be defined in each of the subdomains (see ``--pars`` option). The command line parameters can be given in any consistent unit set, for example the basic SI units. The ``--unit-multipliers`` option can be used to rescale the input units to ones more suitable to the simulation, for example to prevent having different matrix blocks with large differences of matrix entries magnitudes. The results are then in the rescaled units. Usage Examples -------------- Default material parameters, a square periodic cell with a spherical inclusion, logs also standard pressure dilatation and shear waves, no eigenvectors:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only As above, with custom eigenvalue solver parameters, and different number of eigenvalues, mesh size and units used in the calculation:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --solver-conf="kind='eig.scipy', method='eigsh', tol=1e-10, maxiter=1000, which='LM', sigma=0" --log-std-waves -n 5 --range=0,640,101 --mode=omega --unit-multipliers=1e-6,1e-2,1e-3 --mesh-size=1e-2 --eigs-only Default material parameters, a square periodic cell with a square inclusion, and a very small mesh to allow comparing the omega and kappa modes (full matrix solver required!):: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.qevp', method='companion', mode='inverted', solver={kind='eig.scipy', method='eig'}" --log-std-waves -n 500 --range=0,4000000,1001 --mesh-size=1e-2 --mode=kappa --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/kappa View/compare the resulting logs:: python script/plot_logs.py output/omega/frequencies.txt --no-legends -g 1 -o mode-omega.png python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends -o mode-kappa.png python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends --swap-axes -o mode-kappa-t.png In contrast to the heterogeneous square periodic cell, a homogeneous square periodic cell (the region Y2 is empty):: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_1m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega-h python script/plot_logs.py output/omega-h/frequencies.txt --no-legends -g 1 -o mode-omega-h.png Use the Brillouin stepper:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves -n=60 --eigs-only --no-legends --stepper=brillouin python script/plot_logs.py output/frequencies.txt -g 0 --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-kappas.png python script/plot_logs.py output/frequencies.txt -g 1 --no-legends --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-omegas.png Additional arguments can be passed to the problem configuration's :func:`define()` function using the ``--define-kwargs`` option. In this file, only the mesh vertex separation parameter `mesh_eps` can be used:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only --define-kwargs="mesh_eps=1e-10" --save-regions """ from __future__ import absolute_import import os import sys sys.path.append('.') import gc from copy import copy from argparse import ArgumentParser, RawDescriptionHelpFormatter import numpy as nm import matplotlib.pyplot as plt from sfepy.base.base import import_file, output, Struct from sfepy.base.conf import dict_from_string, ProblemConf from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options from sfepy.base.log import Log from sfepy.discrete.fem import MeshIO from sfepy.mechanics.matcoefs import stiffness_from_youngpoisson as stiffness import sfepy.mechanics.matcoefs as mc from sfepy.mechanics.units import apply_unit_multipliers import sfepy.discrete.fem.periodic as per from sfepy.discrete.fem.meshio import convert_complex_output from sfepy.homogenization.utils import define_box_regions from sfepy.discrete import Problem from sfepy.mechanics.tensors import get_von_mises_stress from sfepy.solvers import Solver from sfepy.solvers.ts import get_print_info, TimeStepper from sfepy.linalg.utils import output_array_stats, max_diff_csr def apply_units(pars, unit_multipliers): new_pars = apply_unit_multipliers(pars, ['stress', 'one', 'density', 'stress', 'one' ,'density'], unit_multipliers) return new_pars def compute_von_mises(out, pb, state, extend=False, wmag=None, wdir=None): """ Calculate the von Mises stress. """ stress = pb.evaluate('ev_cauchy_stress.i.Omega(m.D, u)', mode='el_avg') vms = get_von_mises_stress(stress.squeeze()) vms.shape = (vms.shape[0], 1, 1, 1) out['von_mises_stress'] = Struct(name='output_data', mode='cell', data=vms) return out def define(filename_mesh, pars, approx_order, refinement_level, solver_conf, plane='strain', post_process=False, mesh_eps=1e-8): io =	MeshIO.any_from_filename(filename_mesh)	sfepy.discrete.fem.MeshIO.any_from_filename
#!/usr/bin/env python """ Dispersion analysis of a heterogeneous finite scale periodic cell. The periodic cell mesh has to contain two subdomains Y1 (with the cell ids 1), Y2 (with the cell ids 2), so that different material properties can be defined in each of the subdomains (see ``--pars`` option). The command line parameters can be given in any consistent unit set, for example the basic SI units. The ``--unit-multipliers`` option can be used to rescale the input units to ones more suitable to the simulation, for example to prevent having different matrix blocks with large differences of matrix entries magnitudes. The results are then in the rescaled units. Usage Examples -------------- Default material parameters, a square periodic cell with a spherical inclusion, logs also standard pressure dilatation and shear waves, no eigenvectors:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only As above, with custom eigenvalue solver parameters, and different number of eigenvalues, mesh size and units used in the calculation:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --solver-conf="kind='eig.scipy', method='eigsh', tol=1e-10, maxiter=1000, which='LM', sigma=0" --log-std-waves -n 5 --range=0,640,101 --mode=omega --unit-multipliers=1e-6,1e-2,1e-3 --mesh-size=1e-2 --eigs-only Default material parameters, a square periodic cell with a square inclusion, and a very small mesh to allow comparing the omega and kappa modes (full matrix solver required!):: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.qevp', method='companion', mode='inverted', solver={kind='eig.scipy', method='eig'}" --log-std-waves -n 500 --range=0,4000000,1001 --mesh-size=1e-2 --mode=kappa --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/kappa View/compare the resulting logs:: python script/plot_logs.py output/omega/frequencies.txt --no-legends -g 1 -o mode-omega.png python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends -o mode-kappa.png python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends --swap-axes -o mode-kappa-t.png In contrast to the heterogeneous square periodic cell, a homogeneous square periodic cell (the region Y2 is empty):: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_1m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega-h python script/plot_logs.py output/omega-h/frequencies.txt --no-legends -g 1 -o mode-omega-h.png Use the Brillouin stepper:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves -n=60 --eigs-only --no-legends --stepper=brillouin python script/plot_logs.py output/frequencies.txt -g 0 --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-kappas.png python script/plot_logs.py output/frequencies.txt -g 1 --no-legends --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-omegas.png Additional arguments can be passed to the problem configuration's :func:`define()` function using the ``--define-kwargs`` option. In this file, only the mesh vertex separation parameter `mesh_eps` can be used:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only --define-kwargs="mesh_eps=1e-10" --save-regions """ from __future__ import absolute_import import os import sys sys.path.append('.') import gc from copy import copy from argparse import ArgumentParser, RawDescriptionHelpFormatter import numpy as nm import matplotlib.pyplot as plt from sfepy.base.base import import_file, output, Struct from sfepy.base.conf import dict_from_string, ProblemConf from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options from sfepy.base.log import Log from sfepy.discrete.fem import MeshIO from sfepy.mechanics.matcoefs import stiffness_from_youngpoisson as stiffness import sfepy.mechanics.matcoefs as mc from sfepy.mechanics.units import apply_unit_multipliers import sfepy.discrete.fem.periodic as per from sfepy.discrete.fem.meshio import convert_complex_output from sfepy.homogenization.utils import define_box_regions from sfepy.discrete import Problem from sfepy.mechanics.tensors import get_von_mises_stress from sfepy.solvers import Solver from sfepy.solvers.ts import get_print_info, TimeStepper from sfepy.linalg.utils import output_array_stats, max_diff_csr def apply_units(pars, unit_multipliers): new_pars = apply_unit_multipliers(pars, ['stress', 'one', 'density', 'stress', 'one' ,'density'], unit_multipliers) return new_pars def compute_von_mises(out, pb, state, extend=False, wmag=None, wdir=None): """ Calculate the von Mises stress. """ stress = pb.evaluate('ev_cauchy_stress.i.Omega(m.D, u)', mode='el_avg') vms = get_von_mises_stress(stress.squeeze()) vms.shape = (vms.shape[0], 1, 1, 1) out['von_mises_stress'] = Struct(name='output_data', mode='cell', data=vms) return out def define(filename_mesh, pars, approx_order, refinement_level, solver_conf, plane='strain', post_process=False, mesh_eps=1e-8): io = MeshIO.any_from_filename(filename_mesh) bbox = io.read_bounding_box() dim = bbox.shape[1] options = { 'absolute_mesh_path' : True, 'refinement_level' : refinement_level, 'allow_empty_regions' : True, 'post_process_hook' : 'compute_von_mises' if post_process else None, } fields = { 'displacement': ('complex', dim, 'Omega', approx_order), } young1, poisson1, density1, young2, poisson2, density2 = pars materials = { 'm' : ({ 'D' : {'Y1' : stiffness(dim, young=young1, poisson=poisson1, plane=plane), 'Y2' : stiffness(dim, young=young2, poisson=poisson2, plane=plane)}, 'density' : {'Y1' : density1, 'Y2' : density2}, },), 'wave' : 'get_wdir', } variables = { 'u' : ('unknown field', 'displacement', 0), 'v' : ('test field', 'displacement', 'u'), } regions = { 'Omega' : 'all', 'Y1': 'cells of group 1', 'Y2': 'cells of group 2', } regions.update(define_box_regions(dim, bbox[0], bbox[1], mesh_eps)) ebcs = { } if dim == 3: epbcs = { 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'}, 'match_x_plane'), 'periodic_y' : (['Near', 'Far'], {'u.all' : 'u.all'}, 'match_y_plane'), 'periodic_z' : (['Top', 'Bottom'], {'u.all' : 'u.all'}, 'match_z_plane'), } else: epbcs = { 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'}, 'match_y_line'), 'periodic_y' : (['Bottom', 'Top'], {'u.all' : 'u.all'}, 'match_x_line'), }	per.set_accuracy(mesh_eps)	sfepy.discrete.fem.periodic.set_accuracy
#!/usr/bin/env python """ Dispersion analysis of a heterogeneous finite scale periodic cell. The periodic cell mesh has to contain two subdomains Y1 (with the cell ids 1), Y2 (with the cell ids 2), so that different material properties can be defined in each of the subdomains (see ``--pars`` option). The command line parameters can be given in any consistent unit set, for example the basic SI units. The ``--unit-multipliers`` option can be used to rescale the input units to ones more suitable to the simulation, for example to prevent having different matrix blocks with large differences of matrix entries magnitudes. The results are then in the rescaled units. Usage Examples -------------- Default material parameters, a square periodic cell with a spherical inclusion, logs also standard pressure dilatation and shear waves, no eigenvectors:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only As above, with custom eigenvalue solver parameters, and different number of eigenvalues, mesh size and units used in the calculation:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --solver-conf="kind='eig.scipy', method='eigsh', tol=1e-10, maxiter=1000, which='LM', sigma=0" --log-std-waves -n 5 --range=0,640,101 --mode=omega --unit-multipliers=1e-6,1e-2,1e-3 --mesh-size=1e-2 --eigs-only Default material parameters, a square periodic cell with a square inclusion, and a very small mesh to allow comparing the omega and kappa modes (full matrix solver required!):: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.qevp', method='companion', mode='inverted', solver={kind='eig.scipy', method='eig'}" --log-std-waves -n 500 --range=0,4000000,1001 --mesh-size=1e-2 --mode=kappa --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/kappa View/compare the resulting logs:: python script/plot_logs.py output/omega/frequencies.txt --no-legends -g 1 -o mode-omega.png python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends -o mode-kappa.png python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends --swap-axes -o mode-kappa-t.png In contrast to the heterogeneous square periodic cell, a homogeneous square periodic cell (the region Y2 is empty):: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_1m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega-h python script/plot_logs.py output/omega-h/frequencies.txt --no-legends -g 1 -o mode-omega-h.png Use the Brillouin stepper:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves -n=60 --eigs-only --no-legends --stepper=brillouin python script/plot_logs.py output/frequencies.txt -g 0 --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-kappas.png python script/plot_logs.py output/frequencies.txt -g 1 --no-legends --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-omegas.png Additional arguments can be passed to the problem configuration's :func:`define()` function using the ``--define-kwargs`` option. In this file, only the mesh vertex separation parameter `mesh_eps` can be used:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only --define-kwargs="mesh_eps=1e-10" --save-regions """ from __future__ import absolute_import import os import sys sys.path.append('.') import gc from copy import copy from argparse import ArgumentParser, RawDescriptionHelpFormatter import numpy as nm import matplotlib.pyplot as plt from sfepy.base.base import import_file, output, Struct from sfepy.base.conf import dict_from_string, ProblemConf from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options from sfepy.base.log import Log from sfepy.discrete.fem import MeshIO from sfepy.mechanics.matcoefs import stiffness_from_youngpoisson as stiffness import sfepy.mechanics.matcoefs as mc from sfepy.mechanics.units import apply_unit_multipliers import sfepy.discrete.fem.periodic as per from sfepy.discrete.fem.meshio import convert_complex_output from sfepy.homogenization.utils import define_box_regions from sfepy.discrete import Problem from sfepy.mechanics.tensors import get_von_mises_stress from sfepy.solvers import Solver from sfepy.solvers.ts import get_print_info, TimeStepper from sfepy.linalg.utils import output_array_stats, max_diff_csr def apply_units(pars, unit_multipliers): new_pars = apply_unit_multipliers(pars, ['stress', 'one', 'density', 'stress', 'one' ,'density'], unit_multipliers) return new_pars def compute_von_mises(out, pb, state, extend=False, wmag=None, wdir=None): """ Calculate the von Mises stress. """ stress = pb.evaluate('ev_cauchy_stress.i.Omega(m.D, u)', mode='el_avg') vms = get_von_mises_stress(stress.squeeze()) vms.shape = (vms.shape[0], 1, 1, 1) out['von_mises_stress'] = Struct(name='output_data', mode='cell', data=vms) return out def define(filename_mesh, pars, approx_order, refinement_level, solver_conf, plane='strain', post_process=False, mesh_eps=1e-8): io = MeshIO.any_from_filename(filename_mesh) bbox = io.read_bounding_box() dim = bbox.shape[1] options = { 'absolute_mesh_path' : True, 'refinement_level' : refinement_level, 'allow_empty_regions' : True, 'post_process_hook' : 'compute_von_mises' if post_process else None, } fields = { 'displacement': ('complex', dim, 'Omega', approx_order), } young1, poisson1, density1, young2, poisson2, density2 = pars materials = { 'm' : ({ 'D' : {'Y1' : stiffness(dim, young=young1, poisson=poisson1, plane=plane), 'Y2' : stiffness(dim, young=young2, poisson=poisson2, plane=plane)}, 'density' : {'Y1' : density1, 'Y2' : density2}, },), 'wave' : 'get_wdir', } variables = { 'u' : ('unknown field', 'displacement', 0), 'v' : ('test field', 'displacement', 'u'), } regions = { 'Omega' : 'all', 'Y1': 'cells of group 1', 'Y2': 'cells of group 2', } regions.update(define_box_regions(dim, bbox[0], bbox[1], mesh_eps)) ebcs = { } if dim == 3: epbcs = { 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'}, 'match_x_plane'), 'periodic_y' : (['Near', 'Far'], {'u.all' : 'u.all'}, 'match_y_plane'), 'periodic_z' : (['Top', 'Bottom'], {'u.all' : 'u.all'}, 'match_z_plane'), } else: epbcs = { 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'}, 'match_y_line'), 'periodic_y' : (['Bottom', 'Top'], {'u.all' : 'u.all'}, 'match_x_line'), } per.set_accuracy(mesh_eps) functions = { 'match_x_plane' : (per.match_x_plane,), 'match_y_plane' : (per.match_y_plane,), 'match_z_plane' : (per.match_z_plane,), 'match_x_line' : (per.match_x_line,), 'match_y_line' : (per.match_y_line,), 'get_wdir' : (get_wdir,), } integrals = { 'i' : 2 * approx_order, } equations = { 'K' : 'dw_lin_elastic.i.Omega(m.D, v, u)', 'S' : 'dw_elastic_wave.i.Omega(m.D, wave.vec, v, u)', 'R' : """1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, u, v) - 1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, v, u)""", 'M' : 'dw_volume_dot.i.Omega(m.density, v, u)', } solver_0 = solver_conf.copy() solver_0['name'] = 'eig' return locals() def get_wdir(ts, coors, mode=None, equations=None, term=None, problem=None, wdir=None, **kwargs): if mode == 'special': return {'vec' : wdir} def set_wave_dir(pb, wdir): materials = pb.get_materials() wave_mat = materials['wave'] wave_mat.set_extra_args(wdir=wdir) def save_materials(output_dir, pb, options): stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)', mode='el_avg', copy_materials=False, verbose=False) young, poisson = mc.youngpoisson_from_stiffness(stiffness, plane=options.plane) density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)', mode='el_avg', copy_materials=False, verbose=False) out = {} out['young'] = Struct(name='young', mode='cell', data=young[..., None, None]) out['poisson'] = Struct(name='poisson', mode='cell', data=poisson[..., None, None]) out['density'] =	Struct(name='density', mode='cell', data=density)	sfepy.base.base.Struct
#!/usr/bin/env python """ Dispersion analysis of a heterogeneous finite scale periodic cell. The periodic cell mesh has to contain two subdomains Y1 (with the cell ids 1), Y2 (with the cell ids 2), so that different material properties can be defined in each of the subdomains (see ``--pars`` option). The command line parameters can be given in any consistent unit set, for example the basic SI units. The ``--unit-multipliers`` option can be used to rescale the input units to ones more suitable to the simulation, for example to prevent having different matrix blocks with large differences of matrix entries magnitudes. The results are then in the rescaled units. Usage Examples -------------- Default material parameters, a square periodic cell with a spherical inclusion, logs also standard pressure dilatation and shear waves, no eigenvectors:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only As above, with custom eigenvalue solver parameters, and different number of eigenvalues, mesh size and units used in the calculation:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --solver-conf="kind='eig.scipy', method='eigsh', tol=1e-10, maxiter=1000, which='LM', sigma=0" --log-std-waves -n 5 --range=0,640,101 --mode=omega --unit-multipliers=1e-6,1e-2,1e-3 --mesh-size=1e-2 --eigs-only Default material parameters, a square periodic cell with a square inclusion, and a very small mesh to allow comparing the omega and kappa modes (full matrix solver required!):: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.qevp', method='companion', mode='inverted', solver={kind='eig.scipy', method='eig'}" --log-std-waves -n 500 --range=0,4000000,1001 --mesh-size=1e-2 --mode=kappa --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/kappa View/compare the resulting logs:: python script/plot_logs.py output/omega/frequencies.txt --no-legends -g 1 -o mode-omega.png python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends -o mode-kappa.png python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends --swap-axes -o mode-kappa-t.png In contrast to the heterogeneous square periodic cell, a homogeneous square periodic cell (the region Y2 is empty):: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_1m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega-h python script/plot_logs.py output/omega-h/frequencies.txt --no-legends -g 1 -o mode-omega-h.png Use the Brillouin stepper:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves -n=60 --eigs-only --no-legends --stepper=brillouin python script/plot_logs.py output/frequencies.txt -g 0 --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-kappas.png python script/plot_logs.py output/frequencies.txt -g 1 --no-legends --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-omegas.png Additional arguments can be passed to the problem configuration's :func:`define()` function using the ``--define-kwargs`` option. In this file, only the mesh vertex separation parameter `mesh_eps` can be used:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only --define-kwargs="mesh_eps=1e-10" --save-regions """ from __future__ import absolute_import import os import sys sys.path.append('.') import gc from copy import copy from argparse import ArgumentParser, RawDescriptionHelpFormatter import numpy as nm import matplotlib.pyplot as plt from sfepy.base.base import import_file, output, Struct from sfepy.base.conf import dict_from_string, ProblemConf from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options from sfepy.base.log import Log from sfepy.discrete.fem import MeshIO from sfepy.mechanics.matcoefs import stiffness_from_youngpoisson as stiffness import sfepy.mechanics.matcoefs as mc from sfepy.mechanics.units import apply_unit_multipliers import sfepy.discrete.fem.periodic as per from sfepy.discrete.fem.meshio import convert_complex_output from sfepy.homogenization.utils import define_box_regions from sfepy.discrete import Problem from sfepy.mechanics.tensors import get_von_mises_stress from sfepy.solvers import Solver from sfepy.solvers.ts import get_print_info, TimeStepper from sfepy.linalg.utils import output_array_stats, max_diff_csr def apply_units(pars, unit_multipliers): new_pars = apply_unit_multipliers(pars, ['stress', 'one', 'density', 'stress', 'one' ,'density'], unit_multipliers) return new_pars def compute_von_mises(out, pb, state, extend=False, wmag=None, wdir=None): """ Calculate the von Mises stress. """ stress = pb.evaluate('ev_cauchy_stress.i.Omega(m.D, u)', mode='el_avg') vms = get_von_mises_stress(stress.squeeze()) vms.shape = (vms.shape[0], 1, 1, 1) out['von_mises_stress'] = Struct(name='output_data', mode='cell', data=vms) return out def define(filename_mesh, pars, approx_order, refinement_level, solver_conf, plane='strain', post_process=False, mesh_eps=1e-8): io = MeshIO.any_from_filename(filename_mesh) bbox = io.read_bounding_box() dim = bbox.shape[1] options = { 'absolute_mesh_path' : True, 'refinement_level' : refinement_level, 'allow_empty_regions' : True, 'post_process_hook' : 'compute_von_mises' if post_process else None, } fields = { 'displacement': ('complex', dim, 'Omega', approx_order), } young1, poisson1, density1, young2, poisson2, density2 = pars materials = { 'm' : ({ 'D' : {'Y1' : stiffness(dim, young=young1, poisson=poisson1, plane=plane), 'Y2' : stiffness(dim, young=young2, poisson=poisson2, plane=plane)}, 'density' : {'Y1' : density1, 'Y2' : density2}, },), 'wave' : 'get_wdir', } variables = { 'u' : ('unknown field', 'displacement', 0), 'v' : ('test field', 'displacement', 'u'), } regions = { 'Omega' : 'all', 'Y1': 'cells of group 1', 'Y2': 'cells of group 2', } regions.update(define_box_regions(dim, bbox[0], bbox[1], mesh_eps)) ebcs = { } if dim == 3: epbcs = { 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'}, 'match_x_plane'), 'periodic_y' : (['Near', 'Far'], {'u.all' : 'u.all'}, 'match_y_plane'), 'periodic_z' : (['Top', 'Bottom'], {'u.all' : 'u.all'}, 'match_z_plane'), } else: epbcs = { 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'}, 'match_y_line'), 'periodic_y' : (['Bottom', 'Top'], {'u.all' : 'u.all'}, 'match_x_line'), } per.set_accuracy(mesh_eps) functions = { 'match_x_plane' : (per.match_x_plane,), 'match_y_plane' : (per.match_y_plane,), 'match_z_plane' : (per.match_z_plane,), 'match_x_line' : (per.match_x_line,), 'match_y_line' : (per.match_y_line,), 'get_wdir' : (get_wdir,), } integrals = { 'i' : 2 * approx_order, } equations = { 'K' : 'dw_lin_elastic.i.Omega(m.D, v, u)', 'S' : 'dw_elastic_wave.i.Omega(m.D, wave.vec, v, u)', 'R' : """1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, u, v) - 1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, v, u)""", 'M' : 'dw_volume_dot.i.Omega(m.density, v, u)', } solver_0 = solver_conf.copy() solver_0['name'] = 'eig' return locals() def get_wdir(ts, coors, mode=None, equations=None, term=None, problem=None, wdir=None, **kwargs): if mode == 'special': return {'vec' : wdir} def set_wave_dir(pb, wdir): materials = pb.get_materials() wave_mat = materials['wave'] wave_mat.set_extra_args(wdir=wdir) def save_materials(output_dir, pb, options): stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)', mode='el_avg', copy_materials=False, verbose=False) young, poisson = mc.youngpoisson_from_stiffness(stiffness, plane=options.plane) density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)', mode='el_avg', copy_materials=False, verbose=False) out = {} out['young'] = Struct(name='young', mode='cell', data=young[..., None, None]) out['poisson'] = Struct(name='poisson', mode='cell', data=poisson[..., None, None]) out['density'] = Struct(name='density', mode='cell', data=density) materials_filename = os.path.join(output_dir, 'materials.vtk') pb.save_state(materials_filename, out=out) def get_std_wave_fun(pb, options): stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)', mode='el_avg', copy_materials=False, verbose=False) young, poisson = mc.youngpoisson_from_stiffness(stiffness, plane=options.plane) density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)', mode='el_avg', copy_materials=False, verbose=False) lam, mu = mc.lame_from_youngpoisson(young, poisson, plane=options.plane) alam = nm.average(lam) amu = nm.average(mu) adensity = nm.average(density) cp = nm.sqrt((alam + 2.0 * amu) / adensity) cs = nm.sqrt(amu / adensity)	output('average p-wave speed:', cp)	sfepy.base.base.output
#!/usr/bin/env python """ Dispersion analysis of a heterogeneous finite scale periodic cell. The periodic cell mesh has to contain two subdomains Y1 (with the cell ids 1), Y2 (with the cell ids 2), so that different material properties can be defined in each of the subdomains (see ``--pars`` option). The command line parameters can be given in any consistent unit set, for example the basic SI units. The ``--unit-multipliers`` option can be used to rescale the input units to ones more suitable to the simulation, for example to prevent having different matrix blocks with large differences of matrix entries magnitudes. The results are then in the rescaled units. Usage Examples -------------- Default material parameters, a square periodic cell with a spherical inclusion, logs also standard pressure dilatation and shear waves, no eigenvectors:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only As above, with custom eigenvalue solver parameters, and different number of eigenvalues, mesh size and units used in the calculation:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --solver-conf="kind='eig.scipy', method='eigsh', tol=1e-10, maxiter=1000, which='LM', sigma=0" --log-std-waves -n 5 --range=0,640,101 --mode=omega --unit-multipliers=1e-6,1e-2,1e-3 --mesh-size=1e-2 --eigs-only Default material parameters, a square periodic cell with a square inclusion, and a very small mesh to allow comparing the omega and kappa modes (full matrix solver required!):: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.qevp', method='companion', mode='inverted', solver={kind='eig.scipy', method='eig'}" --log-std-waves -n 500 --range=0,4000000,1001 --mesh-size=1e-2 --mode=kappa --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/kappa View/compare the resulting logs:: python script/plot_logs.py output/omega/frequencies.txt --no-legends -g 1 -o mode-omega.png python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends -o mode-kappa.png python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends --swap-axes -o mode-kappa-t.png In contrast to the heterogeneous square periodic cell, a homogeneous square periodic cell (the region Y2 is empty):: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_1m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega-h python script/plot_logs.py output/omega-h/frequencies.txt --no-legends -g 1 -o mode-omega-h.png Use the Brillouin stepper:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves -n=60 --eigs-only --no-legends --stepper=brillouin python script/plot_logs.py output/frequencies.txt -g 0 --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-kappas.png python script/plot_logs.py output/frequencies.txt -g 1 --no-legends --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-omegas.png Additional arguments can be passed to the problem configuration's :func:`define()` function using the ``--define-kwargs`` option. In this file, only the mesh vertex separation parameter `mesh_eps` can be used:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only --define-kwargs="mesh_eps=1e-10" --save-regions """ from __future__ import absolute_import import os import sys sys.path.append('.') import gc from copy import copy from argparse import ArgumentParser, RawDescriptionHelpFormatter import numpy as nm import matplotlib.pyplot as plt from sfepy.base.base import import_file, output, Struct from sfepy.base.conf import dict_from_string, ProblemConf from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options from sfepy.base.log import Log from sfepy.discrete.fem import MeshIO from sfepy.mechanics.matcoefs import stiffness_from_youngpoisson as stiffness import sfepy.mechanics.matcoefs as mc from sfepy.mechanics.units import apply_unit_multipliers import sfepy.discrete.fem.periodic as per from sfepy.discrete.fem.meshio import convert_complex_output from sfepy.homogenization.utils import define_box_regions from sfepy.discrete import Problem from sfepy.mechanics.tensors import get_von_mises_stress from sfepy.solvers import Solver from sfepy.solvers.ts import get_print_info, TimeStepper from sfepy.linalg.utils import output_array_stats, max_diff_csr def apply_units(pars, unit_multipliers): new_pars = apply_unit_multipliers(pars, ['stress', 'one', 'density', 'stress', 'one' ,'density'], unit_multipliers) return new_pars def compute_von_mises(out, pb, state, extend=False, wmag=None, wdir=None): """ Calculate the von Mises stress. """ stress = pb.evaluate('ev_cauchy_stress.i.Omega(m.D, u)', mode='el_avg') vms = get_von_mises_stress(stress.squeeze()) vms.shape = (vms.shape[0], 1, 1, 1) out['von_mises_stress'] = Struct(name='output_data', mode='cell', data=vms) return out def define(filename_mesh, pars, approx_order, refinement_level, solver_conf, plane='strain', post_process=False, mesh_eps=1e-8): io = MeshIO.any_from_filename(filename_mesh) bbox = io.read_bounding_box() dim = bbox.shape[1] options = { 'absolute_mesh_path' : True, 'refinement_level' : refinement_level, 'allow_empty_regions' : True, 'post_process_hook' : 'compute_von_mises' if post_process else None, } fields = { 'displacement': ('complex', dim, 'Omega', approx_order), } young1, poisson1, density1, young2, poisson2, density2 = pars materials = { 'm' : ({ 'D' : {'Y1' : stiffness(dim, young=young1, poisson=poisson1, plane=plane), 'Y2' : stiffness(dim, young=young2, poisson=poisson2, plane=plane)}, 'density' : {'Y1' : density1, 'Y2' : density2}, },), 'wave' : 'get_wdir', } variables = { 'u' : ('unknown field', 'displacement', 0), 'v' : ('test field', 'displacement', 'u'), } regions = { 'Omega' : 'all', 'Y1': 'cells of group 1', 'Y2': 'cells of group 2', } regions.update(define_box_regions(dim, bbox[0], bbox[1], mesh_eps)) ebcs = { } if dim == 3: epbcs = { 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'}, 'match_x_plane'), 'periodic_y' : (['Near', 'Far'], {'u.all' : 'u.all'}, 'match_y_plane'), 'periodic_z' : (['Top', 'Bottom'], {'u.all' : 'u.all'}, 'match_z_plane'), } else: epbcs = { 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'}, 'match_y_line'), 'periodic_y' : (['Bottom', 'Top'], {'u.all' : 'u.all'}, 'match_x_line'), } per.set_accuracy(mesh_eps) functions = { 'match_x_plane' : (per.match_x_plane,), 'match_y_plane' : (per.match_y_plane,), 'match_z_plane' : (per.match_z_plane,), 'match_x_line' : (per.match_x_line,), 'match_y_line' : (per.match_y_line,), 'get_wdir' : (get_wdir,), } integrals = { 'i' : 2 * approx_order, } equations = { 'K' : 'dw_lin_elastic.i.Omega(m.D, v, u)', 'S' : 'dw_elastic_wave.i.Omega(m.D, wave.vec, v, u)', 'R' : """1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, u, v) - 1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, v, u)""", 'M' : 'dw_volume_dot.i.Omega(m.density, v, u)', } solver_0 = solver_conf.copy() solver_0['name'] = 'eig' return locals() def get_wdir(ts, coors, mode=None, equations=None, term=None, problem=None, wdir=None, **kwargs): if mode == 'special': return {'vec' : wdir} def set_wave_dir(pb, wdir): materials = pb.get_materials() wave_mat = materials['wave'] wave_mat.set_extra_args(wdir=wdir) def save_materials(output_dir, pb, options): stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)', mode='el_avg', copy_materials=False, verbose=False) young, poisson = mc.youngpoisson_from_stiffness(stiffness, plane=options.plane) density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)', mode='el_avg', copy_materials=False, verbose=False) out = {} out['young'] = Struct(name='young', mode='cell', data=young[..., None, None]) out['poisson'] = Struct(name='poisson', mode='cell', data=poisson[..., None, None]) out['density'] = Struct(name='density', mode='cell', data=density) materials_filename = os.path.join(output_dir, 'materials.vtk') pb.save_state(materials_filename, out=out) def get_std_wave_fun(pb, options): stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)', mode='el_avg', copy_materials=False, verbose=False) young, poisson = mc.youngpoisson_from_stiffness(stiffness, plane=options.plane) density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)', mode='el_avg', copy_materials=False, verbose=False) lam, mu = mc.lame_from_youngpoisson(young, poisson, plane=options.plane) alam = nm.average(lam) amu = nm.average(mu) adensity = nm.average(density) cp = nm.sqrt((alam + 2.0 * amu) / adensity) cs = nm.sqrt(amu / adensity) output('average p-wave speed:', cp)	output('average shear wave speed:', cs)	sfepy.base.base.output
#!/usr/bin/env python """ Dispersion analysis of a heterogeneous finite scale periodic cell. The periodic cell mesh has to contain two subdomains Y1 (with the cell ids 1), Y2 (with the cell ids 2), so that different material properties can be defined in each of the subdomains (see ``--pars`` option). The command line parameters can be given in any consistent unit set, for example the basic SI units. The ``--unit-multipliers`` option can be used to rescale the input units to ones more suitable to the simulation, for example to prevent having different matrix blocks with large differences of matrix entries magnitudes. The results are then in the rescaled units. Usage Examples -------------- Default material parameters, a square periodic cell with a spherical inclusion, logs also standard pressure dilatation and shear waves, no eigenvectors:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only As above, with custom eigenvalue solver parameters, and different number of eigenvalues, mesh size and units used in the calculation:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --solver-conf="kind='eig.scipy', method='eigsh', tol=1e-10, maxiter=1000, which='LM', sigma=0" --log-std-waves -n 5 --range=0,640,101 --mode=omega --unit-multipliers=1e-6,1e-2,1e-3 --mesh-size=1e-2 --eigs-only Default material parameters, a square periodic cell with a square inclusion, and a very small mesh to allow comparing the omega and kappa modes (full matrix solver required!):: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.qevp', method='companion', mode='inverted', solver={kind='eig.scipy', method='eig'}" --log-std-waves -n 500 --range=0,4000000,1001 --mesh-size=1e-2 --mode=kappa --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/kappa View/compare the resulting logs:: python script/plot_logs.py output/omega/frequencies.txt --no-legends -g 1 -o mode-omega.png python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends -o mode-kappa.png python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends --swap-axes -o mode-kappa-t.png In contrast to the heterogeneous square periodic cell, a homogeneous square periodic cell (the region Y2 is empty):: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_1m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega-h python script/plot_logs.py output/omega-h/frequencies.txt --no-legends -g 1 -o mode-omega-h.png Use the Brillouin stepper:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves -n=60 --eigs-only --no-legends --stepper=brillouin python script/plot_logs.py output/frequencies.txt -g 0 --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-kappas.png python script/plot_logs.py output/frequencies.txt -g 1 --no-legends --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-omegas.png Additional arguments can be passed to the problem configuration's :func:`define()` function using the ``--define-kwargs`` option. In this file, only the mesh vertex separation parameter `mesh_eps` can be used:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only --define-kwargs="mesh_eps=1e-10" --save-regions """ from __future__ import absolute_import import os import sys sys.path.append('.') import gc from copy import copy from argparse import ArgumentParser, RawDescriptionHelpFormatter import numpy as nm import matplotlib.pyplot as plt from sfepy.base.base import import_file, output, Struct from sfepy.base.conf import dict_from_string, ProblemConf from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options from sfepy.base.log import Log from sfepy.discrete.fem import MeshIO from sfepy.mechanics.matcoefs import stiffness_from_youngpoisson as stiffness import sfepy.mechanics.matcoefs as mc from sfepy.mechanics.units import apply_unit_multipliers import sfepy.discrete.fem.periodic as per from sfepy.discrete.fem.meshio import convert_complex_output from sfepy.homogenization.utils import define_box_regions from sfepy.discrete import Problem from sfepy.mechanics.tensors import get_von_mises_stress from sfepy.solvers import Solver from sfepy.solvers.ts import get_print_info, TimeStepper from sfepy.linalg.utils import output_array_stats, max_diff_csr def apply_units(pars, unit_multipliers): new_pars = apply_unit_multipliers(pars, ['stress', 'one', 'density', 'stress', 'one' ,'density'], unit_multipliers) return new_pars def compute_von_mises(out, pb, state, extend=False, wmag=None, wdir=None): """ Calculate the von Mises stress. """ stress = pb.evaluate('ev_cauchy_stress.i.Omega(m.D, u)', mode='el_avg') vms = get_von_mises_stress(stress.squeeze()) vms.shape = (vms.shape[0], 1, 1, 1) out['von_mises_stress'] = Struct(name='output_data', mode='cell', data=vms) return out def define(filename_mesh, pars, approx_order, refinement_level, solver_conf, plane='strain', post_process=False, mesh_eps=1e-8): io = MeshIO.any_from_filename(filename_mesh) bbox = io.read_bounding_box() dim = bbox.shape[1] options = { 'absolute_mesh_path' : True, 'refinement_level' : refinement_level, 'allow_empty_regions' : True, 'post_process_hook' : 'compute_von_mises' if post_process else None, } fields = { 'displacement': ('complex', dim, 'Omega', approx_order), } young1, poisson1, density1, young2, poisson2, density2 = pars materials = { 'm' : ({ 'D' : {'Y1' : stiffness(dim, young=young1, poisson=poisson1, plane=plane), 'Y2' : stiffness(dim, young=young2, poisson=poisson2, plane=plane)}, 'density' : {'Y1' : density1, 'Y2' : density2}, },), 'wave' : 'get_wdir', } variables = { 'u' : ('unknown field', 'displacement', 0), 'v' : ('test field', 'displacement', 'u'), } regions = { 'Omega' : 'all', 'Y1': 'cells of group 1', 'Y2': 'cells of group 2', } regions.update(define_box_regions(dim, bbox[0], bbox[1], mesh_eps)) ebcs = { } if dim == 3: epbcs = { 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'}, 'match_x_plane'), 'periodic_y' : (['Near', 'Far'], {'u.all' : 'u.all'}, 'match_y_plane'), 'periodic_z' : (['Top', 'Bottom'], {'u.all' : 'u.all'}, 'match_z_plane'), } else: epbcs = { 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'}, 'match_y_line'), 'periodic_y' : (['Bottom', 'Top'], {'u.all' : 'u.all'}, 'match_x_line'), } per.set_accuracy(mesh_eps) functions = { 'match_x_plane' : (per.match_x_plane,), 'match_y_plane' : (per.match_y_plane,), 'match_z_plane' : (per.match_z_plane,), 'match_x_line' : (per.match_x_line,), 'match_y_line' : (per.match_y_line,), 'get_wdir' : (get_wdir,), } integrals = { 'i' : 2 * approx_order, } equations = { 'K' : 'dw_lin_elastic.i.Omega(m.D, v, u)', 'S' : 'dw_elastic_wave.i.Omega(m.D, wave.vec, v, u)', 'R' : """1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, u, v) - 1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, v, u)""", 'M' : 'dw_volume_dot.i.Omega(m.density, v, u)', } solver_0 = solver_conf.copy() solver_0['name'] = 'eig' return locals() def get_wdir(ts, coors, mode=None, equations=None, term=None, problem=None, wdir=None, **kwargs): if mode == 'special': return {'vec' : wdir} def set_wave_dir(pb, wdir): materials = pb.get_materials() wave_mat = materials['wave'] wave_mat.set_extra_args(wdir=wdir) def save_materials(output_dir, pb, options): stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)', mode='el_avg', copy_materials=False, verbose=False) young, poisson = mc.youngpoisson_from_stiffness(stiffness, plane=options.plane) density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)', mode='el_avg', copy_materials=False, verbose=False) out = {} out['young'] = Struct(name='young', mode='cell', data=young[..., None, None]) out['poisson'] = Struct(name='poisson', mode='cell', data=poisson[..., None, None]) out['density'] = Struct(name='density', mode='cell', data=density) materials_filename = os.path.join(output_dir, 'materials.vtk') pb.save_state(materials_filename, out=out) def get_std_wave_fun(pb, options): stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)', mode='el_avg', copy_materials=False, verbose=False) young, poisson = mc.youngpoisson_from_stiffness(stiffness, plane=options.plane) density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)', mode='el_avg', copy_materials=False, verbose=False) lam, mu = mc.lame_from_youngpoisson(young, poisson, plane=options.plane) alam = nm.average(lam) amu = nm.average(mu) adensity = nm.average(density) cp = nm.sqrt((alam + 2.0 * amu) / adensity) cs = nm.sqrt(amu / adensity) output('average p-wave speed:', cp) output('average shear wave speed:', cs) log_names = [r'$\omega_p$', r'$\omega_s$'] log_plot_kwargs = [{'ls' : '--', 'color' : 'k'}, {'ls' : '--', 'color' : 'gray'}] if options.mode == 'omega': fun = lambda wmag, wdir: (cp * wmag, cs * wmag) else: fun = lambda wmag, wdir: (wmag / cp, wmag / cs) return fun, log_names, log_plot_kwargs def get_stepper(rng, pb, options): if options.stepper == 'linear': stepper = TimeStepper(rng[0], rng[1], dt=None, n_step=rng[2]) return stepper bbox = pb.domain.mesh.get_bounding_box() bzone = 2.0 * nm.pi / (bbox[1] - bbox[0]) num = rng[2] // 3 class BrillouinStepper(Struct): """ Step over 1. Brillouin zone in xy plane. """ def __init__(self, t0, t1, dt=None, n_step=None, step=None, **kwargs): Struct.__init__(self, t0=t0, t1=t1, dt=dt, n_step=n_step, step=step) self.n_digit, self.format, self.suffix = get_print_info(self.n_step) def __iter__(self): ts = TimeStepper(0, bzone[0], dt=None, n_step=num) for ii, val in ts: yield ii, val, nm.array([1.0, 0.0]) if ii == (num-2): break ts = TimeStepper(0, bzone[1], dt=None, n_step=num) for ii, k1 in ts: wdir = nm.array([bzone[0], k1]) val = nm.linalg.norm(wdir) wdir = wdir / val yield num + ii, val, wdir if ii == (num-2): break wdir = nm.array([bzone[0], bzone[1]]) val = nm.linalg.norm(wdir) wdir = wdir / val ts = TimeStepper(0, 1, dt=None, n_step=num) for ii, _ in ts: yield 2 * num + ii, val * (1.0 - float(ii)/(num-1)), wdir stepper = BrillouinStepper(0, 1, n_step=rng[2]) return stepper def save_eigenvectors(filename, svecs, wmag, wdir, pb): if svecs is None: return variables = pb.get_variables() # Make full eigenvectors (add DOFs fixed by boundary conditions). vecs = nm.empty((variables.di.ptr[-1], svecs.shape[1]), dtype=svecs.dtype) for ii in range(svecs.shape[1]): vecs[:, ii] = variables.make_full_vec(svecs[:, ii]) # Save the eigenvectors. out = {} state = pb.create_state() pp_name = pb.conf.options.get('post_process_hook') pp = getattr(pb.conf.funmod, pp_name if pp_name is not None else '', lambda out, *args, **kwargs: out) for ii in range(svecs.shape[1]): state.set_full(vecs[:, ii]) aux = state.create_output_dict() aux2 = {} pp(aux2, pb, state, wmag=wmag, wdir=wdir) aux.update(convert_complex_output(aux2)) out.update({key + '%03d' % ii : aux[key] for key in aux}) pb.save_state(filename, out=out) def assemble_matrices(define, mod, pars, set_wave_dir, options, wdir=None): """ Assemble the blocks of dispersion eigenvalue problem matrices. """ define_dict = define(filename_mesh=options.mesh_filename, pars=pars, approx_order=options.order, refinement_level=options.refine, solver_conf=options.solver_conf, plane=options.plane, post_process=options.post_process, **options.define_kwargs) conf =	ProblemConf.from_dict(define_dict, mod)	sfepy.base.conf.ProblemConf.from_dict
#!/usr/bin/env python """ Dispersion analysis of a heterogeneous finite scale periodic cell. The periodic cell mesh has to contain two subdomains Y1 (with the cell ids 1), Y2 (with the cell ids 2), so that different material properties can be defined in each of the subdomains (see ``--pars`` option). The command line parameters can be given in any consistent unit set, for example the basic SI units. The ``--unit-multipliers`` option can be used to rescale the input units to ones more suitable to the simulation, for example to prevent having different matrix blocks with large differences of matrix entries magnitudes. The results are then in the rescaled units. Usage Examples -------------- Default material parameters, a square periodic cell with a spherical inclusion, logs also standard pressure dilatation and shear waves, no eigenvectors:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only As above, with custom eigenvalue solver parameters, and different number of eigenvalues, mesh size and units used in the calculation:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --solver-conf="kind='eig.scipy', method='eigsh', tol=1e-10, maxiter=1000, which='LM', sigma=0" --log-std-waves -n 5 --range=0,640,101 --mode=omega --unit-multipliers=1e-6,1e-2,1e-3 --mesh-size=1e-2 --eigs-only Default material parameters, a square periodic cell with a square inclusion, and a very small mesh to allow comparing the omega and kappa modes (full matrix solver required!):: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.qevp', method='companion', mode='inverted', solver={kind='eig.scipy', method='eig'}" --log-std-waves -n 500 --range=0,4000000,1001 --mesh-size=1e-2 --mode=kappa --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/kappa View/compare the resulting logs:: python script/plot_logs.py output/omega/frequencies.txt --no-legends -g 1 -o mode-omega.png python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends -o mode-kappa.png python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends --swap-axes -o mode-kappa-t.png In contrast to the heterogeneous square periodic cell, a homogeneous square periodic cell (the region Y2 is empty):: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_1m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega-h python script/plot_logs.py output/omega-h/frequencies.txt --no-legends -g 1 -o mode-omega-h.png Use the Brillouin stepper:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves -n=60 --eigs-only --no-legends --stepper=brillouin python script/plot_logs.py output/frequencies.txt -g 0 --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-kappas.png python script/plot_logs.py output/frequencies.txt -g 1 --no-legends --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-omegas.png Additional arguments can be passed to the problem configuration's :func:`define()` function using the ``--define-kwargs`` option. In this file, only the mesh vertex separation parameter `mesh_eps` can be used:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only --define-kwargs="mesh_eps=1e-10" --save-regions """ from __future__ import absolute_import import os import sys sys.path.append('.') import gc from copy import copy from argparse import ArgumentParser, RawDescriptionHelpFormatter import numpy as nm import matplotlib.pyplot as plt from sfepy.base.base import import_file, output, Struct from sfepy.base.conf import dict_from_string, ProblemConf from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options from sfepy.base.log import Log from sfepy.discrete.fem import MeshIO from sfepy.mechanics.matcoefs import stiffness_from_youngpoisson as stiffness import sfepy.mechanics.matcoefs as mc from sfepy.mechanics.units import apply_unit_multipliers import sfepy.discrete.fem.periodic as per from sfepy.discrete.fem.meshio import convert_complex_output from sfepy.homogenization.utils import define_box_regions from sfepy.discrete import Problem from sfepy.mechanics.tensors import get_von_mises_stress from sfepy.solvers import Solver from sfepy.solvers.ts import get_print_info, TimeStepper from sfepy.linalg.utils import output_array_stats, max_diff_csr def apply_units(pars, unit_multipliers): new_pars = apply_unit_multipliers(pars, ['stress', 'one', 'density', 'stress', 'one' ,'density'], unit_multipliers) return new_pars def compute_von_mises(out, pb, state, extend=False, wmag=None, wdir=None): """ Calculate the von Mises stress. """ stress = pb.evaluate('ev_cauchy_stress.i.Omega(m.D, u)', mode='el_avg') vms = get_von_mises_stress(stress.squeeze()) vms.shape = (vms.shape[0], 1, 1, 1) out['von_mises_stress'] = Struct(name='output_data', mode='cell', data=vms) return out def define(filename_mesh, pars, approx_order, refinement_level, solver_conf, plane='strain', post_process=False, mesh_eps=1e-8): io = MeshIO.any_from_filename(filename_mesh) bbox = io.read_bounding_box() dim = bbox.shape[1] options = { 'absolute_mesh_path' : True, 'refinement_level' : refinement_level, 'allow_empty_regions' : True, 'post_process_hook' : 'compute_von_mises' if post_process else None, } fields = { 'displacement': ('complex', dim, 'Omega', approx_order), } young1, poisson1, density1, young2, poisson2, density2 = pars materials = { 'm' : ({ 'D' : {'Y1' : stiffness(dim, young=young1, poisson=poisson1, plane=plane), 'Y2' : stiffness(dim, young=young2, poisson=poisson2, plane=plane)}, 'density' : {'Y1' : density1, 'Y2' : density2}, },), 'wave' : 'get_wdir', } variables = { 'u' : ('unknown field', 'displacement', 0), 'v' : ('test field', 'displacement', 'u'), } regions = { 'Omega' : 'all', 'Y1': 'cells of group 1', 'Y2': 'cells of group 2', } regions.update(define_box_regions(dim, bbox[0], bbox[1], mesh_eps)) ebcs = { } if dim == 3: epbcs = { 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'}, 'match_x_plane'), 'periodic_y' : (['Near', 'Far'], {'u.all' : 'u.all'}, 'match_y_plane'), 'periodic_z' : (['Top', 'Bottom'], {'u.all' : 'u.all'}, 'match_z_plane'), } else: epbcs = { 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'}, 'match_y_line'), 'periodic_y' : (['Bottom', 'Top'], {'u.all' : 'u.all'}, 'match_x_line'), } per.set_accuracy(mesh_eps) functions = { 'match_x_plane' : (per.match_x_plane,), 'match_y_plane' : (per.match_y_plane,), 'match_z_plane' : (per.match_z_plane,), 'match_x_line' : (per.match_x_line,), 'match_y_line' : (per.match_y_line,), 'get_wdir' : (get_wdir,), } integrals = { 'i' : 2 * approx_order, } equations = { 'K' : 'dw_lin_elastic.i.Omega(m.D, v, u)', 'S' : 'dw_elastic_wave.i.Omega(m.D, wave.vec, v, u)', 'R' : """1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, u, v) - 1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, v, u)""", 'M' : 'dw_volume_dot.i.Omega(m.density, v, u)', } solver_0 = solver_conf.copy() solver_0['name'] = 'eig' return locals() def get_wdir(ts, coors, mode=None, equations=None, term=None, problem=None, wdir=None, **kwargs): if mode == 'special': return {'vec' : wdir} def set_wave_dir(pb, wdir): materials = pb.get_materials() wave_mat = materials['wave'] wave_mat.set_extra_args(wdir=wdir) def save_materials(output_dir, pb, options): stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)', mode='el_avg', copy_materials=False, verbose=False) young, poisson = mc.youngpoisson_from_stiffness(stiffness, plane=options.plane) density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)', mode='el_avg', copy_materials=False, verbose=False) out = {} out['young'] = Struct(name='young', mode='cell', data=young[..., None, None]) out['poisson'] = Struct(name='poisson', mode='cell', data=poisson[..., None, None]) out['density'] = Struct(name='density', mode='cell', data=density) materials_filename = os.path.join(output_dir, 'materials.vtk') pb.save_state(materials_filename, out=out) def get_std_wave_fun(pb, options): stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)', mode='el_avg', copy_materials=False, verbose=False) young, poisson = mc.youngpoisson_from_stiffness(stiffness, plane=options.plane) density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)', mode='el_avg', copy_materials=False, verbose=False) lam, mu = mc.lame_from_youngpoisson(young, poisson, plane=options.plane) alam = nm.average(lam) amu = nm.average(mu) adensity = nm.average(density) cp = nm.sqrt((alam + 2.0 * amu) / adensity) cs = nm.sqrt(amu / adensity) output('average p-wave speed:', cp) output('average shear wave speed:', cs) log_names = [r'$\omega_p$', r'$\omega_s$'] log_plot_kwargs = [{'ls' : '--', 'color' : 'k'}, {'ls' : '--', 'color' : 'gray'}] if options.mode == 'omega': fun = lambda wmag, wdir: (cp * wmag, cs * wmag) else: fun = lambda wmag, wdir: (wmag / cp, wmag / cs) return fun, log_names, log_plot_kwargs def get_stepper(rng, pb, options): if options.stepper == 'linear': stepper = TimeStepper(rng[0], rng[1], dt=None, n_step=rng[2]) return stepper bbox = pb.domain.mesh.get_bounding_box() bzone = 2.0 * nm.pi / (bbox[1] - bbox[0]) num = rng[2] // 3 class BrillouinStepper(Struct): """ Step over 1. Brillouin zone in xy plane. """ def __init__(self, t0, t1, dt=None, n_step=None, step=None, **kwargs): Struct.__init__(self, t0=t0, t1=t1, dt=dt, n_step=n_step, step=step) self.n_digit, self.format, self.suffix = get_print_info(self.n_step) def __iter__(self): ts = TimeStepper(0, bzone[0], dt=None, n_step=num) for ii, val in ts: yield ii, val, nm.array([1.0, 0.0]) if ii == (num-2): break ts = TimeStepper(0, bzone[1], dt=None, n_step=num) for ii, k1 in ts: wdir = nm.array([bzone[0], k1]) val = nm.linalg.norm(wdir) wdir = wdir / val yield num + ii, val, wdir if ii == (num-2): break wdir = nm.array([bzone[0], bzone[1]]) val = nm.linalg.norm(wdir) wdir = wdir / val ts = TimeStepper(0, 1, dt=None, n_step=num) for ii, _ in ts: yield 2 * num + ii, val * (1.0 - float(ii)/(num-1)), wdir stepper = BrillouinStepper(0, 1, n_step=rng[2]) return stepper def save_eigenvectors(filename, svecs, wmag, wdir, pb): if svecs is None: return variables = pb.get_variables() # Make full eigenvectors (add DOFs fixed by boundary conditions). vecs = nm.empty((variables.di.ptr[-1], svecs.shape[1]), dtype=svecs.dtype) for ii in range(svecs.shape[1]): vecs[:, ii] = variables.make_full_vec(svecs[:, ii]) # Save the eigenvectors. out = {} state = pb.create_state() pp_name = pb.conf.options.get('post_process_hook') pp = getattr(pb.conf.funmod, pp_name if pp_name is not None else '', lambda out, *args, **kwargs: out) for ii in range(svecs.shape[1]): state.set_full(vecs[:, ii]) aux = state.create_output_dict() aux2 = {} pp(aux2, pb, state, wmag=wmag, wdir=wdir) aux.update(convert_complex_output(aux2)) out.update({key + '%03d' % ii : aux[key] for key in aux}) pb.save_state(filename, out=out) def assemble_matrices(define, mod, pars, set_wave_dir, options, wdir=None): """ Assemble the blocks of dispersion eigenvalue problem matrices. """ define_dict = define(filename_mesh=options.mesh_filename, pars=pars, approx_order=options.order, refinement_level=options.refine, solver_conf=options.solver_conf, plane=options.plane, post_process=options.post_process, **options.define_kwargs) conf = ProblemConf.from_dict(define_dict, mod) pb =	Problem.from_conf(conf)	sfepy.discrete.Problem.from_conf
#!/usr/bin/env python """ Dispersion analysis of a heterogeneous finite scale periodic cell. The periodic cell mesh has to contain two subdomains Y1 (with the cell ids 1), Y2 (with the cell ids 2), so that different material properties can be defined in each of the subdomains (see ``--pars`` option). The command line parameters can be given in any consistent unit set, for example the basic SI units. The ``--unit-multipliers`` option can be used to rescale the input units to ones more suitable to the simulation, for example to prevent having different matrix blocks with large differences of matrix entries magnitudes. The results are then in the rescaled units. Usage Examples -------------- Default material parameters, a square periodic cell with a spherical inclusion, logs also standard pressure dilatation and shear waves, no eigenvectors:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only As above, with custom eigenvalue solver parameters, and different number of eigenvalues, mesh size and units used in the calculation:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --solver-conf="kind='eig.scipy', method='eigsh', tol=1e-10, maxiter=1000, which='LM', sigma=0" --log-std-waves -n 5 --range=0,640,101 --mode=omega --unit-multipliers=1e-6,1e-2,1e-3 --mesh-size=1e-2 --eigs-only Default material parameters, a square periodic cell with a square inclusion, and a very small mesh to allow comparing the omega and kappa modes (full matrix solver required!):: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.qevp', method='companion', mode='inverted', solver={kind='eig.scipy', method='eig'}" --log-std-waves -n 500 --range=0,4000000,1001 --mesh-size=1e-2 --mode=kappa --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/kappa View/compare the resulting logs:: python script/plot_logs.py output/omega/frequencies.txt --no-legends -g 1 -o mode-omega.png python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends -o mode-kappa.png python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends --swap-axes -o mode-kappa-t.png In contrast to the heterogeneous square periodic cell, a homogeneous square periodic cell (the region Y2 is empty):: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_1m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega-h python script/plot_logs.py output/omega-h/frequencies.txt --no-legends -g 1 -o mode-omega-h.png Use the Brillouin stepper:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves -n=60 --eigs-only --no-legends --stepper=brillouin python script/plot_logs.py output/frequencies.txt -g 0 --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-kappas.png python script/plot_logs.py output/frequencies.txt -g 1 --no-legends --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-omegas.png Additional arguments can be passed to the problem configuration's :func:`define()` function using the ``--define-kwargs`` option. In this file, only the mesh vertex separation parameter `mesh_eps` can be used:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only --define-kwargs="mesh_eps=1e-10" --save-regions """ from __future__ import absolute_import import os import sys sys.path.append('.') import gc from copy import copy from argparse import ArgumentParser, RawDescriptionHelpFormatter import numpy as nm import matplotlib.pyplot as plt from sfepy.base.base import import_file, output, Struct from sfepy.base.conf import dict_from_string, ProblemConf from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options from sfepy.base.log import Log from sfepy.discrete.fem import MeshIO from sfepy.mechanics.matcoefs import stiffness_from_youngpoisson as stiffness import sfepy.mechanics.matcoefs as mc from sfepy.mechanics.units import apply_unit_multipliers import sfepy.discrete.fem.periodic as per from sfepy.discrete.fem.meshio import convert_complex_output from sfepy.homogenization.utils import define_box_regions from sfepy.discrete import Problem from sfepy.mechanics.tensors import get_von_mises_stress from sfepy.solvers import Solver from sfepy.solvers.ts import get_print_info, TimeStepper from sfepy.linalg.utils import output_array_stats, max_diff_csr def apply_units(pars, unit_multipliers): new_pars = apply_unit_multipliers(pars, ['stress', 'one', 'density', 'stress', 'one' ,'density'], unit_multipliers) return new_pars def compute_von_mises(out, pb, state, extend=False, wmag=None, wdir=None): """ Calculate the von Mises stress. """ stress = pb.evaluate('ev_cauchy_stress.i.Omega(m.D, u)', mode='el_avg') vms = get_von_mises_stress(stress.squeeze()) vms.shape = (vms.shape[0], 1, 1, 1) out['von_mises_stress'] = Struct(name='output_data', mode='cell', data=vms) return out def define(filename_mesh, pars, approx_order, refinement_level, solver_conf, plane='strain', post_process=False, mesh_eps=1e-8): io = MeshIO.any_from_filename(filename_mesh) bbox = io.read_bounding_box() dim = bbox.shape[1] options = { 'absolute_mesh_path' : True, 'refinement_level' : refinement_level, 'allow_empty_regions' : True, 'post_process_hook' : 'compute_von_mises' if post_process else None, } fields = { 'displacement': ('complex', dim, 'Omega', approx_order), } young1, poisson1, density1, young2, poisson2, density2 = pars materials = { 'm' : ({ 'D' : {'Y1' : stiffness(dim, young=young1, poisson=poisson1, plane=plane), 'Y2' : stiffness(dim, young=young2, poisson=poisson2, plane=plane)}, 'density' : {'Y1' : density1, 'Y2' : density2}, },), 'wave' : 'get_wdir', } variables = { 'u' : ('unknown field', 'displacement', 0), 'v' : ('test field', 'displacement', 'u'), } regions = { 'Omega' : 'all', 'Y1': 'cells of group 1', 'Y2': 'cells of group 2', } regions.update(define_box_regions(dim, bbox[0], bbox[1], mesh_eps)) ebcs = { } if dim == 3: epbcs = { 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'}, 'match_x_plane'), 'periodic_y' : (['Near', 'Far'], {'u.all' : 'u.all'}, 'match_y_plane'), 'periodic_z' : (['Top', 'Bottom'], {'u.all' : 'u.all'}, 'match_z_plane'), } else: epbcs = { 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'}, 'match_y_line'), 'periodic_y' : (['Bottom', 'Top'], {'u.all' : 'u.all'}, 'match_x_line'), } per.set_accuracy(mesh_eps) functions = { 'match_x_plane' : (per.match_x_plane,), 'match_y_plane' : (per.match_y_plane,), 'match_z_plane' : (per.match_z_plane,), 'match_x_line' : (per.match_x_line,), 'match_y_line' : (per.match_y_line,), 'get_wdir' : (get_wdir,), } integrals = { 'i' : 2 * approx_order, } equations = { 'K' : 'dw_lin_elastic.i.Omega(m.D, v, u)', 'S' : 'dw_elastic_wave.i.Omega(m.D, wave.vec, v, u)', 'R' : """1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, u, v) - 1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, v, u)""", 'M' : 'dw_volume_dot.i.Omega(m.density, v, u)', } solver_0 = solver_conf.copy() solver_0['name'] = 'eig' return locals() def get_wdir(ts, coors, mode=None, equations=None, term=None, problem=None, wdir=None, **kwargs): if mode == 'special': return {'vec' : wdir} def set_wave_dir(pb, wdir): materials = pb.get_materials() wave_mat = materials['wave'] wave_mat.set_extra_args(wdir=wdir) def save_materials(output_dir, pb, options): stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)', mode='el_avg', copy_materials=False, verbose=False) young, poisson = mc.youngpoisson_from_stiffness(stiffness, plane=options.plane) density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)', mode='el_avg', copy_materials=False, verbose=False) out = {} out['young'] = Struct(name='young', mode='cell', data=young[..., None, None]) out['poisson'] = Struct(name='poisson', mode='cell', data=poisson[..., None, None]) out['density'] = Struct(name='density', mode='cell', data=density) materials_filename = os.path.join(output_dir, 'materials.vtk') pb.save_state(materials_filename, out=out) def get_std_wave_fun(pb, options): stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)', mode='el_avg', copy_materials=False, verbose=False) young, poisson = mc.youngpoisson_from_stiffness(stiffness, plane=options.plane) density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)', mode='el_avg', copy_materials=False, verbose=False) lam, mu = mc.lame_from_youngpoisson(young, poisson, plane=options.plane) alam = nm.average(lam) amu = nm.average(mu) adensity = nm.average(density) cp = nm.sqrt((alam + 2.0 * amu) / adensity) cs = nm.sqrt(amu / adensity) output('average p-wave speed:', cp) output('average shear wave speed:', cs) log_names = [r'$\omega_p$', r'$\omega_s$'] log_plot_kwargs = [{'ls' : '--', 'color' : 'k'}, {'ls' : '--', 'color' : 'gray'}] if options.mode == 'omega': fun = lambda wmag, wdir: (cp * wmag, cs * wmag) else: fun = lambda wmag, wdir: (wmag / cp, wmag / cs) return fun, log_names, log_plot_kwargs def get_stepper(rng, pb, options): if options.stepper == 'linear': stepper = TimeStepper(rng[0], rng[1], dt=None, n_step=rng[2]) return stepper bbox = pb.domain.mesh.get_bounding_box() bzone = 2.0 * nm.pi / (bbox[1] - bbox[0]) num = rng[2] // 3 class BrillouinStepper(Struct): """ Step over 1. Brillouin zone in xy plane. """ def __init__(self, t0, t1, dt=None, n_step=None, step=None, **kwargs): Struct.__init__(self, t0=t0, t1=t1, dt=dt, n_step=n_step, step=step) self.n_digit, self.format, self.suffix = get_print_info(self.n_step) def __iter__(self): ts = TimeStepper(0, bzone[0], dt=None, n_step=num) for ii, val in ts: yield ii, val, nm.array([1.0, 0.0]) if ii == (num-2): break ts = TimeStepper(0, bzone[1], dt=None, n_step=num) for ii, k1 in ts: wdir = nm.array([bzone[0], k1]) val = nm.linalg.norm(wdir) wdir = wdir / val yield num + ii, val, wdir if ii == (num-2): break wdir = nm.array([bzone[0], bzone[1]]) val = nm.linalg.norm(wdir) wdir = wdir / val ts = TimeStepper(0, 1, dt=None, n_step=num) for ii, _ in ts: yield 2 * num + ii, val * (1.0 - float(ii)/(num-1)), wdir stepper = BrillouinStepper(0, 1, n_step=rng[2]) return stepper def save_eigenvectors(filename, svecs, wmag, wdir, pb): if svecs is None: return variables = pb.get_variables() # Make full eigenvectors (add DOFs fixed by boundary conditions). vecs = nm.empty((variables.di.ptr[-1], svecs.shape[1]), dtype=svecs.dtype) for ii in range(svecs.shape[1]): vecs[:, ii] = variables.make_full_vec(svecs[:, ii]) # Save the eigenvectors. out = {} state = pb.create_state() pp_name = pb.conf.options.get('post_process_hook') pp = getattr(pb.conf.funmod, pp_name if pp_name is not None else '', lambda out, *args, **kwargs: out) for ii in range(svecs.shape[1]): state.set_full(vecs[:, ii]) aux = state.create_output_dict() aux2 = {} pp(aux2, pb, state, wmag=wmag, wdir=wdir) aux.update(convert_complex_output(aux2)) out.update({key + '%03d' % ii : aux[key] for key in aux}) pb.save_state(filename, out=out) def assemble_matrices(define, mod, pars, set_wave_dir, options, wdir=None): """ Assemble the blocks of dispersion eigenvalue problem matrices. """ define_dict = define(filename_mesh=options.mesh_filename, pars=pars, approx_order=options.order, refinement_level=options.refine, solver_conf=options.solver_conf, plane=options.plane, post_process=options.post_process, **options.define_kwargs) conf = ProblemConf.from_dict(define_dict, mod) pb = Problem.from_conf(conf) pb.dispersion_options = options pb.set_output_dir(options.output_dir) dim = pb.domain.shape.dim # Set the normalized wave vector direction to the material(s). if wdir is None: wdir = nm.asarray(options.wave_dir[:dim], dtype=nm.float64) wdir = wdir / nm.linalg.norm(wdir) set_wave_dir(pb, wdir) bbox = pb.domain.mesh.get_bounding_box() size = (bbox[1] - bbox[0]).max() scaling0 = apply_unit_multipliers([1.0], ['length'], options.unit_multipliers)[0] scaling = scaling0 if options.mesh_size is not None: scaling *= options.mesh_size / size	output('scaling factor of periodic cell mesh coordinates:', scaling)	sfepy.base.base.output
#!/usr/bin/env python """ Dispersion analysis of a heterogeneous finite scale periodic cell. The periodic cell mesh has to contain two subdomains Y1 (with the cell ids 1), Y2 (with the cell ids 2), so that different material properties can be defined in each of the subdomains (see ``--pars`` option). The command line parameters can be given in any consistent unit set, for example the basic SI units. The ``--unit-multipliers`` option can be used to rescale the input units to ones more suitable to the simulation, for example to prevent having different matrix blocks with large differences of matrix entries magnitudes. The results are then in the rescaled units. Usage Examples -------------- Default material parameters, a square periodic cell with a spherical inclusion, logs also standard pressure dilatation and shear waves, no eigenvectors:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only As above, with custom eigenvalue solver parameters, and different number of eigenvalues, mesh size and units used in the calculation:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --solver-conf="kind='eig.scipy', method='eigsh', tol=1e-10, maxiter=1000, which='LM', sigma=0" --log-std-waves -n 5 --range=0,640,101 --mode=omega --unit-multipliers=1e-6,1e-2,1e-3 --mesh-size=1e-2 --eigs-only Default material parameters, a square periodic cell with a square inclusion, and a very small mesh to allow comparing the omega and kappa modes (full matrix solver required!):: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.qevp', method='companion', mode='inverted', solver={kind='eig.scipy', method='eig'}" --log-std-waves -n 500 --range=0,4000000,1001 --mesh-size=1e-2 --mode=kappa --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/kappa View/compare the resulting logs:: python script/plot_logs.py output/omega/frequencies.txt --no-legends -g 1 -o mode-omega.png python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends -o mode-kappa.png python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends --swap-axes -o mode-kappa-t.png In contrast to the heterogeneous square periodic cell, a homogeneous square periodic cell (the region Y2 is empty):: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_1m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega-h python script/plot_logs.py output/omega-h/frequencies.txt --no-legends -g 1 -o mode-omega-h.png Use the Brillouin stepper:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves -n=60 --eigs-only --no-legends --stepper=brillouin python script/plot_logs.py output/frequencies.txt -g 0 --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-kappas.png python script/plot_logs.py output/frequencies.txt -g 1 --no-legends --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-omegas.png Additional arguments can be passed to the problem configuration's :func:`define()` function using the ``--define-kwargs`` option. In this file, only the mesh vertex separation parameter `mesh_eps` can be used:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only --define-kwargs="mesh_eps=1e-10" --save-regions """ from __future__ import absolute_import import os import sys sys.path.append('.') import gc from copy import copy from argparse import ArgumentParser, RawDescriptionHelpFormatter import numpy as nm import matplotlib.pyplot as plt from sfepy.base.base import import_file, output, Struct from sfepy.base.conf import dict_from_string, ProblemConf from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options from sfepy.base.log import Log from sfepy.discrete.fem import MeshIO from sfepy.mechanics.matcoefs import stiffness_from_youngpoisson as stiffness import sfepy.mechanics.matcoefs as mc from sfepy.mechanics.units import apply_unit_multipliers import sfepy.discrete.fem.periodic as per from sfepy.discrete.fem.meshio import convert_complex_output from sfepy.homogenization.utils import define_box_regions from sfepy.discrete import Problem from sfepy.mechanics.tensors import get_von_mises_stress from sfepy.solvers import Solver from sfepy.solvers.ts import get_print_info, TimeStepper from sfepy.linalg.utils import output_array_stats, max_diff_csr def apply_units(pars, unit_multipliers): new_pars = apply_unit_multipliers(pars, ['stress', 'one', 'density', 'stress', 'one' ,'density'], unit_multipliers) return new_pars def compute_von_mises(out, pb, state, extend=False, wmag=None, wdir=None): """ Calculate the von Mises stress. """ stress = pb.evaluate('ev_cauchy_stress.i.Omega(m.D, u)', mode='el_avg') vms = get_von_mises_stress(stress.squeeze()) vms.shape = (vms.shape[0], 1, 1, 1) out['von_mises_stress'] = Struct(name='output_data', mode='cell', data=vms) return out def define(filename_mesh, pars, approx_order, refinement_level, solver_conf, plane='strain', post_process=False, mesh_eps=1e-8): io = MeshIO.any_from_filename(filename_mesh) bbox = io.read_bounding_box() dim = bbox.shape[1] options = { 'absolute_mesh_path' : True, 'refinement_level' : refinement_level, 'allow_empty_regions' : True, 'post_process_hook' : 'compute_von_mises' if post_process else None, } fields = { 'displacement': ('complex', dim, 'Omega', approx_order), } young1, poisson1, density1, young2, poisson2, density2 = pars materials = { 'm' : ({ 'D' : {'Y1' : stiffness(dim, young=young1, poisson=poisson1, plane=plane), 'Y2' : stiffness(dim, young=young2, poisson=poisson2, plane=plane)}, 'density' : {'Y1' : density1, 'Y2' : density2}, },), 'wave' : 'get_wdir', } variables = { 'u' : ('unknown field', 'displacement', 0), 'v' : ('test field', 'displacement', 'u'), } regions = { 'Omega' : 'all', 'Y1': 'cells of group 1', 'Y2': 'cells of group 2', } regions.update(define_box_regions(dim, bbox[0], bbox[1], mesh_eps)) ebcs = { } if dim == 3: epbcs = { 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'}, 'match_x_plane'), 'periodic_y' : (['Near', 'Far'], {'u.all' : 'u.all'}, 'match_y_plane'), 'periodic_z' : (['Top', 'Bottom'], {'u.all' : 'u.all'}, 'match_z_plane'), } else: epbcs = { 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'}, 'match_y_line'), 'periodic_y' : (['Bottom', 'Top'], {'u.all' : 'u.all'}, 'match_x_line'), } per.set_accuracy(mesh_eps) functions = { 'match_x_plane' : (per.match_x_plane,), 'match_y_plane' : (per.match_y_plane,), 'match_z_plane' : (per.match_z_plane,), 'match_x_line' : (per.match_x_line,), 'match_y_line' : (per.match_y_line,), 'get_wdir' : (get_wdir,), } integrals = { 'i' : 2 * approx_order, } equations = { 'K' : 'dw_lin_elastic.i.Omega(m.D, v, u)', 'S' : 'dw_elastic_wave.i.Omega(m.D, wave.vec, v, u)', 'R' : """1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, u, v) - 1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, v, u)""", 'M' : 'dw_volume_dot.i.Omega(m.density, v, u)', } solver_0 = solver_conf.copy() solver_0['name'] = 'eig' return locals() def get_wdir(ts, coors, mode=None, equations=None, term=None, problem=None, wdir=None, **kwargs): if mode == 'special': return {'vec' : wdir} def set_wave_dir(pb, wdir): materials = pb.get_materials() wave_mat = materials['wave'] wave_mat.set_extra_args(wdir=wdir) def save_materials(output_dir, pb, options): stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)', mode='el_avg', copy_materials=False, verbose=False) young, poisson = mc.youngpoisson_from_stiffness(stiffness, plane=options.plane) density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)', mode='el_avg', copy_materials=False, verbose=False) out = {} out['young'] = Struct(name='young', mode='cell', data=young[..., None, None]) out['poisson'] = Struct(name='poisson', mode='cell', data=poisson[..., None, None]) out['density'] = Struct(name='density', mode='cell', data=density) materials_filename = os.path.join(output_dir, 'materials.vtk') pb.save_state(materials_filename, out=out) def get_std_wave_fun(pb, options): stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)', mode='el_avg', copy_materials=False, verbose=False) young, poisson = mc.youngpoisson_from_stiffness(stiffness, plane=options.plane) density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)', mode='el_avg', copy_materials=False, verbose=False) lam, mu = mc.lame_from_youngpoisson(young, poisson, plane=options.plane) alam = nm.average(lam) amu = nm.average(mu) adensity = nm.average(density) cp = nm.sqrt((alam + 2.0 * amu) / adensity) cs = nm.sqrt(amu / adensity) output('average p-wave speed:', cp) output('average shear wave speed:', cs) log_names = [r'$\omega_p$', r'$\omega_s$'] log_plot_kwargs = [{'ls' : '--', 'color' : 'k'}, {'ls' : '--', 'color' : 'gray'}] if options.mode == 'omega': fun = lambda wmag, wdir: (cp * wmag, cs * wmag) else: fun = lambda wmag, wdir: (wmag / cp, wmag / cs) return fun, log_names, log_plot_kwargs def get_stepper(rng, pb, options): if options.stepper == 'linear': stepper = TimeStepper(rng[0], rng[1], dt=None, n_step=rng[2]) return stepper bbox = pb.domain.mesh.get_bounding_box() bzone = 2.0 * nm.pi / (bbox[1] - bbox[0]) num = rng[2] // 3 class BrillouinStepper(Struct): """ Step over 1. Brillouin zone in xy plane. """ def __init__(self, t0, t1, dt=None, n_step=None, step=None, **kwargs): Struct.__init__(self, t0=t0, t1=t1, dt=dt, n_step=n_step, step=step) self.n_digit, self.format, self.suffix = get_print_info(self.n_step) def __iter__(self): ts = TimeStepper(0, bzone[0], dt=None, n_step=num) for ii, val in ts: yield ii, val, nm.array([1.0, 0.0]) if ii == (num-2): break ts = TimeStepper(0, bzone[1], dt=None, n_step=num) for ii, k1 in ts: wdir = nm.array([bzone[0], k1]) val = nm.linalg.norm(wdir) wdir = wdir / val yield num + ii, val, wdir if ii == (num-2): break wdir = nm.array([bzone[0], bzone[1]]) val = nm.linalg.norm(wdir) wdir = wdir / val ts = TimeStepper(0, 1, dt=None, n_step=num) for ii, _ in ts: yield 2 * num + ii, val * (1.0 - float(ii)/(num-1)), wdir stepper = BrillouinStepper(0, 1, n_step=rng[2]) return stepper def save_eigenvectors(filename, svecs, wmag, wdir, pb): if svecs is None: return variables = pb.get_variables() # Make full eigenvectors (add DOFs fixed by boundary conditions). vecs = nm.empty((variables.di.ptr[-1], svecs.shape[1]), dtype=svecs.dtype) for ii in range(svecs.shape[1]): vecs[:, ii] = variables.make_full_vec(svecs[:, ii]) # Save the eigenvectors. out = {} state = pb.create_state() pp_name = pb.conf.options.get('post_process_hook') pp = getattr(pb.conf.funmod, pp_name if pp_name is not None else '', lambda out, *args, **kwargs: out) for ii in range(svecs.shape[1]): state.set_full(vecs[:, ii]) aux = state.create_output_dict() aux2 = {} pp(aux2, pb, state, wmag=wmag, wdir=wdir) aux.update(convert_complex_output(aux2)) out.update({key + '%03d' % ii : aux[key] for key in aux}) pb.save_state(filename, out=out) def assemble_matrices(define, mod, pars, set_wave_dir, options, wdir=None): """ Assemble the blocks of dispersion eigenvalue problem matrices. """ define_dict = define(filename_mesh=options.mesh_filename, pars=pars, approx_order=options.order, refinement_level=options.refine, solver_conf=options.solver_conf, plane=options.plane, post_process=options.post_process, **options.define_kwargs) conf = ProblemConf.from_dict(define_dict, mod) pb = Problem.from_conf(conf) pb.dispersion_options = options pb.set_output_dir(options.output_dir) dim = pb.domain.shape.dim # Set the normalized wave vector direction to the material(s). if wdir is None: wdir = nm.asarray(options.wave_dir[:dim], dtype=nm.float64) wdir = wdir / nm.linalg.norm(wdir) set_wave_dir(pb, wdir) bbox = pb.domain.mesh.get_bounding_box() size = (bbox[1] - bbox[0]).max() scaling0 = apply_unit_multipliers([1.0], ['length'], options.unit_multipliers)[0] scaling = scaling0 if options.mesh_size is not None: scaling *= options.mesh_size / size output('scaling factor of periodic cell mesh coordinates:', scaling)	output('new mesh size with applied unit multipliers:', scaling * size)	sfepy.base.base.output
#!/usr/bin/env python """ Dispersion analysis of a heterogeneous finite scale periodic cell. The periodic cell mesh has to contain two subdomains Y1 (with the cell ids 1), Y2 (with the cell ids 2), so that different material properties can be defined in each of the subdomains (see ``--pars`` option). The command line parameters can be given in any consistent unit set, for example the basic SI units. The ``--unit-multipliers`` option can be used to rescale the input units to ones more suitable to the simulation, for example to prevent having different matrix blocks with large differences of matrix entries magnitudes. The results are then in the rescaled units. Usage Examples -------------- Default material parameters, a square periodic cell with a spherical inclusion, logs also standard pressure dilatation and shear waves, no eigenvectors:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only As above, with custom eigenvalue solver parameters, and different number of eigenvalues, mesh size and units used in the calculation:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --solver-conf="kind='eig.scipy', method='eigsh', tol=1e-10, maxiter=1000, which='LM', sigma=0" --log-std-waves -n 5 --range=0,640,101 --mode=omega --unit-multipliers=1e-6,1e-2,1e-3 --mesh-size=1e-2 --eigs-only Default material parameters, a square periodic cell with a square inclusion, and a very small mesh to allow comparing the omega and kappa modes (full matrix solver required!):: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.qevp', method='companion', mode='inverted', solver={kind='eig.scipy', method='eig'}" --log-std-waves -n 500 --range=0,4000000,1001 --mesh-size=1e-2 --mode=kappa --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/kappa View/compare the resulting logs:: python script/plot_logs.py output/omega/frequencies.txt --no-legends -g 1 -o mode-omega.png python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends -o mode-kappa.png python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends --swap-axes -o mode-kappa-t.png In contrast to the heterogeneous square periodic cell, a homogeneous square periodic cell (the region Y2 is empty):: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_1m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega-h python script/plot_logs.py output/omega-h/frequencies.txt --no-legends -g 1 -o mode-omega-h.png Use the Brillouin stepper:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves -n=60 --eigs-only --no-legends --stepper=brillouin python script/plot_logs.py output/frequencies.txt -g 0 --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-kappas.png python script/plot_logs.py output/frequencies.txt -g 1 --no-legends --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-omegas.png Additional arguments can be passed to the problem configuration's :func:`define()` function using the ``--define-kwargs`` option. In this file, only the mesh vertex separation parameter `mesh_eps` can be used:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only --define-kwargs="mesh_eps=1e-10" --save-regions """ from __future__ import absolute_import import os import sys sys.path.append('.') import gc from copy import copy from argparse import ArgumentParser, RawDescriptionHelpFormatter import numpy as nm import matplotlib.pyplot as plt from sfepy.base.base import import_file, output, Struct from sfepy.base.conf import dict_from_string, ProblemConf from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options from sfepy.base.log import Log from sfepy.discrete.fem import MeshIO from sfepy.mechanics.matcoefs import stiffness_from_youngpoisson as stiffness import sfepy.mechanics.matcoefs as mc from sfepy.mechanics.units import apply_unit_multipliers import sfepy.discrete.fem.periodic as per from sfepy.discrete.fem.meshio import convert_complex_output from sfepy.homogenization.utils import define_box_regions from sfepy.discrete import Problem from sfepy.mechanics.tensors import get_von_mises_stress from sfepy.solvers import Solver from sfepy.solvers.ts import get_print_info, TimeStepper from sfepy.linalg.utils import output_array_stats, max_diff_csr def apply_units(pars, unit_multipliers): new_pars = apply_unit_multipliers(pars, ['stress', 'one', 'density', 'stress', 'one' ,'density'], unit_multipliers) return new_pars def compute_von_mises(out, pb, state, extend=False, wmag=None, wdir=None): """ Calculate the von Mises stress. """ stress = pb.evaluate('ev_cauchy_stress.i.Omega(m.D, u)', mode='el_avg') vms = get_von_mises_stress(stress.squeeze()) vms.shape = (vms.shape[0], 1, 1, 1) out['von_mises_stress'] = Struct(name='output_data', mode='cell', data=vms) return out def define(filename_mesh, pars, approx_order, refinement_level, solver_conf, plane='strain', post_process=False, mesh_eps=1e-8): io = MeshIO.any_from_filename(filename_mesh) bbox = io.read_bounding_box() dim = bbox.shape[1] options = { 'absolute_mesh_path' : True, 'refinement_level' : refinement_level, 'allow_empty_regions' : True, 'post_process_hook' : 'compute_von_mises' if post_process else None, } fields = { 'displacement': ('complex', dim, 'Omega', approx_order), } young1, poisson1, density1, young2, poisson2, density2 = pars materials = { 'm' : ({ 'D' : {'Y1' : stiffness(dim, young=young1, poisson=poisson1, plane=plane), 'Y2' : stiffness(dim, young=young2, poisson=poisson2, plane=plane)}, 'density' : {'Y1' : density1, 'Y2' : density2}, },), 'wave' : 'get_wdir', } variables = { 'u' : ('unknown field', 'displacement', 0), 'v' : ('test field', 'displacement', 'u'), } regions = { 'Omega' : 'all', 'Y1': 'cells of group 1', 'Y2': 'cells of group 2', } regions.update(define_box_regions(dim, bbox[0], bbox[1], mesh_eps)) ebcs = { } if dim == 3: epbcs = { 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'}, 'match_x_plane'), 'periodic_y' : (['Near', 'Far'], {'u.all' : 'u.all'}, 'match_y_plane'), 'periodic_z' : (['Top', 'Bottom'], {'u.all' : 'u.all'}, 'match_z_plane'), } else: epbcs = { 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'}, 'match_y_line'), 'periodic_y' : (['Bottom', 'Top'], {'u.all' : 'u.all'}, 'match_x_line'), } per.set_accuracy(mesh_eps) functions = { 'match_x_plane' : (per.match_x_plane,), 'match_y_plane' : (per.match_y_plane,), 'match_z_plane' : (per.match_z_plane,), 'match_x_line' : (per.match_x_line,), 'match_y_line' : (per.match_y_line,), 'get_wdir' : (get_wdir,), } integrals = { 'i' : 2 * approx_order, } equations = { 'K' : 'dw_lin_elastic.i.Omega(m.D, v, u)', 'S' : 'dw_elastic_wave.i.Omega(m.D, wave.vec, v, u)', 'R' : """1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, u, v) - 1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, v, u)""", 'M' : 'dw_volume_dot.i.Omega(m.density, v, u)', } solver_0 = solver_conf.copy() solver_0['name'] = 'eig' return locals() def get_wdir(ts, coors, mode=None, equations=None, term=None, problem=None, wdir=None, **kwargs): if mode == 'special': return {'vec' : wdir} def set_wave_dir(pb, wdir): materials = pb.get_materials() wave_mat = materials['wave'] wave_mat.set_extra_args(wdir=wdir) def save_materials(output_dir, pb, options): stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)', mode='el_avg', copy_materials=False, verbose=False) young, poisson = mc.youngpoisson_from_stiffness(stiffness, plane=options.plane) density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)', mode='el_avg', copy_materials=False, verbose=False) out = {} out['young'] = Struct(name='young', mode='cell', data=young[..., None, None]) out['poisson'] = Struct(name='poisson', mode='cell', data=poisson[..., None, None]) out['density'] = Struct(name='density', mode='cell', data=density) materials_filename = os.path.join(output_dir, 'materials.vtk') pb.save_state(materials_filename, out=out) def get_std_wave_fun(pb, options): stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)', mode='el_avg', copy_materials=False, verbose=False) young, poisson = mc.youngpoisson_from_stiffness(stiffness, plane=options.plane) density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)', mode='el_avg', copy_materials=False, verbose=False) lam, mu = mc.lame_from_youngpoisson(young, poisson, plane=options.plane) alam = nm.average(lam) amu = nm.average(mu) adensity = nm.average(density) cp = nm.sqrt((alam + 2.0 * amu) / adensity) cs = nm.sqrt(amu / adensity) output('average p-wave speed:', cp) output('average shear wave speed:', cs) log_names = [r'$\omega_p$', r'$\omega_s$'] log_plot_kwargs = [{'ls' : '--', 'color' : 'k'}, {'ls' : '--', 'color' : 'gray'}] if options.mode == 'omega': fun = lambda wmag, wdir: (cp * wmag, cs * wmag) else: fun = lambda wmag, wdir: (wmag / cp, wmag / cs) return fun, log_names, log_plot_kwargs def get_stepper(rng, pb, options): if options.stepper == 'linear': stepper = TimeStepper(rng[0], rng[1], dt=None, n_step=rng[2]) return stepper bbox = pb.domain.mesh.get_bounding_box() bzone = 2.0 * nm.pi / (bbox[1] - bbox[0]) num = rng[2] // 3 class BrillouinStepper(Struct): """ Step over 1. Brillouin zone in xy plane. """ def __init__(self, t0, t1, dt=None, n_step=None, step=None, **kwargs): Struct.__init__(self, t0=t0, t1=t1, dt=dt, n_step=n_step, step=step) self.n_digit, self.format, self.suffix = get_print_info(self.n_step) def __iter__(self): ts = TimeStepper(0, bzone[0], dt=None, n_step=num) for ii, val in ts: yield ii, val, nm.array([1.0, 0.0]) if ii == (num-2): break ts = TimeStepper(0, bzone[1], dt=None, n_step=num) for ii, k1 in ts: wdir = nm.array([bzone[0], k1]) val = nm.linalg.norm(wdir) wdir = wdir / val yield num + ii, val, wdir if ii == (num-2): break wdir = nm.array([bzone[0], bzone[1]]) val = nm.linalg.norm(wdir) wdir = wdir / val ts = TimeStepper(0, 1, dt=None, n_step=num) for ii, _ in ts: yield 2 * num + ii, val * (1.0 - float(ii)/(num-1)), wdir stepper = BrillouinStepper(0, 1, n_step=rng[2]) return stepper def save_eigenvectors(filename, svecs, wmag, wdir, pb): if svecs is None: return variables = pb.get_variables() # Make full eigenvectors (add DOFs fixed by boundary conditions). vecs = nm.empty((variables.di.ptr[-1], svecs.shape[1]), dtype=svecs.dtype) for ii in range(svecs.shape[1]): vecs[:, ii] = variables.make_full_vec(svecs[:, ii]) # Save the eigenvectors. out = {} state = pb.create_state() pp_name = pb.conf.options.get('post_process_hook') pp = getattr(pb.conf.funmod, pp_name if pp_name is not None else '', lambda out, *args, **kwargs: out) for ii in range(svecs.shape[1]): state.set_full(vecs[:, ii]) aux = state.create_output_dict() aux2 = {} pp(aux2, pb, state, wmag=wmag, wdir=wdir) aux.update(convert_complex_output(aux2)) out.update({key + '%03d' % ii : aux[key] for key in aux}) pb.save_state(filename, out=out) def assemble_matrices(define, mod, pars, set_wave_dir, options, wdir=None): """ Assemble the blocks of dispersion eigenvalue problem matrices. """ define_dict = define(filename_mesh=options.mesh_filename, pars=pars, approx_order=options.order, refinement_level=options.refine, solver_conf=options.solver_conf, plane=options.plane, post_process=options.post_process, **options.define_kwargs) conf = ProblemConf.from_dict(define_dict, mod) pb = Problem.from_conf(conf) pb.dispersion_options = options pb.set_output_dir(options.output_dir) dim = pb.domain.shape.dim # Set the normalized wave vector direction to the material(s). if wdir is None: wdir = nm.asarray(options.wave_dir[:dim], dtype=nm.float64) wdir = wdir / nm.linalg.norm(wdir) set_wave_dir(pb, wdir) bbox = pb.domain.mesh.get_bounding_box() size = (bbox[1] - bbox[0]).max() scaling0 = apply_unit_multipliers([1.0], ['length'], options.unit_multipliers)[0] scaling = scaling0 if options.mesh_size is not None: scaling *= options.mesh_size / size output('scaling factor of periodic cell mesh coordinates:', scaling) output('new mesh size with applied unit multipliers:', scaling * size) pb.domain.mesh.coors[:] *= scaling pb.set_mesh_coors(pb.domain.mesh.coors, update_fields=True) bzone = 2.0 * nm.pi / (scaling * size)	output('1. Brillouin zone size:', bzone * scaling0)	sfepy.base.base.output
#!/usr/bin/env python """ Dispersion analysis of a heterogeneous finite scale periodic cell. The periodic cell mesh has to contain two subdomains Y1 (with the cell ids 1), Y2 (with the cell ids 2), so that different material properties can be defined in each of the subdomains (see ``--pars`` option). The command line parameters can be given in any consistent unit set, for example the basic SI units. The ``--unit-multipliers`` option can be used to rescale the input units to ones more suitable to the simulation, for example to prevent having different matrix blocks with large differences of matrix entries magnitudes. The results are then in the rescaled units. Usage Examples -------------- Default material parameters, a square periodic cell with a spherical inclusion, logs also standard pressure dilatation and shear waves, no eigenvectors:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only As above, with custom eigenvalue solver parameters, and different number of eigenvalues, mesh size and units used in the calculation:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --solver-conf="kind='eig.scipy', method='eigsh', tol=1e-10, maxiter=1000, which='LM', sigma=0" --log-std-waves -n 5 --range=0,640,101 --mode=omega --unit-multipliers=1e-6,1e-2,1e-3 --mesh-size=1e-2 --eigs-only Default material parameters, a square periodic cell with a square inclusion, and a very small mesh to allow comparing the omega and kappa modes (full matrix solver required!):: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.qevp', method='companion', mode='inverted', solver={kind='eig.scipy', method='eig'}" --log-std-waves -n 500 --range=0,4000000,1001 --mesh-size=1e-2 --mode=kappa --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/kappa View/compare the resulting logs:: python script/plot_logs.py output/omega/frequencies.txt --no-legends -g 1 -o mode-omega.png python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends -o mode-kappa.png python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends --swap-axes -o mode-kappa-t.png In contrast to the heterogeneous square periodic cell, a homogeneous square periodic cell (the region Y2 is empty):: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_1m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega-h python script/plot_logs.py output/omega-h/frequencies.txt --no-legends -g 1 -o mode-omega-h.png Use the Brillouin stepper:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves -n=60 --eigs-only --no-legends --stepper=brillouin python script/plot_logs.py output/frequencies.txt -g 0 --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-kappas.png python script/plot_logs.py output/frequencies.txt -g 1 --no-legends --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-omegas.png Additional arguments can be passed to the problem configuration's :func:`define()` function using the ``--define-kwargs`` option. In this file, only the mesh vertex separation parameter `mesh_eps` can be used:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only --define-kwargs="mesh_eps=1e-10" --save-regions """ from __future__ import absolute_import import os import sys sys.path.append('.') import gc from copy import copy from argparse import ArgumentParser, RawDescriptionHelpFormatter import numpy as nm import matplotlib.pyplot as plt from sfepy.base.base import import_file, output, Struct from sfepy.base.conf import dict_from_string, ProblemConf from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options from sfepy.base.log import Log from sfepy.discrete.fem import MeshIO from sfepy.mechanics.matcoefs import stiffness_from_youngpoisson as stiffness import sfepy.mechanics.matcoefs as mc from sfepy.mechanics.units import apply_unit_multipliers import sfepy.discrete.fem.periodic as per from sfepy.discrete.fem.meshio import convert_complex_output from sfepy.homogenization.utils import define_box_regions from sfepy.discrete import Problem from sfepy.mechanics.tensors import get_von_mises_stress from sfepy.solvers import Solver from sfepy.solvers.ts import get_print_info, TimeStepper from sfepy.linalg.utils import output_array_stats, max_diff_csr def apply_units(pars, unit_multipliers): new_pars = apply_unit_multipliers(pars, ['stress', 'one', 'density', 'stress', 'one' ,'density'], unit_multipliers) return new_pars def compute_von_mises(out, pb, state, extend=False, wmag=None, wdir=None): """ Calculate the von Mises stress. """ stress = pb.evaluate('ev_cauchy_stress.i.Omega(m.D, u)', mode='el_avg') vms = get_von_mises_stress(stress.squeeze()) vms.shape = (vms.shape[0], 1, 1, 1) out['von_mises_stress'] = Struct(name='output_data', mode='cell', data=vms) return out def define(filename_mesh, pars, approx_order, refinement_level, solver_conf, plane='strain', post_process=False, mesh_eps=1e-8): io = MeshIO.any_from_filename(filename_mesh) bbox = io.read_bounding_box() dim = bbox.shape[1] options = { 'absolute_mesh_path' : True, 'refinement_level' : refinement_level, 'allow_empty_regions' : True, 'post_process_hook' : 'compute_von_mises' if post_process else None, } fields = { 'displacement': ('complex', dim, 'Omega', approx_order), } young1, poisson1, density1, young2, poisson2, density2 = pars materials = { 'm' : ({ 'D' : {'Y1' : stiffness(dim, young=young1, poisson=poisson1, plane=plane), 'Y2' : stiffness(dim, young=young2, poisson=poisson2, plane=plane)}, 'density' : {'Y1' : density1, 'Y2' : density2}, },), 'wave' : 'get_wdir', } variables = { 'u' : ('unknown field', 'displacement', 0), 'v' : ('test field', 'displacement', 'u'), } regions = { 'Omega' : 'all', 'Y1': 'cells of group 1', 'Y2': 'cells of group 2', } regions.update(define_box_regions(dim, bbox[0], bbox[1], mesh_eps)) ebcs = { } if dim == 3: epbcs = { 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'}, 'match_x_plane'), 'periodic_y' : (['Near', 'Far'], {'u.all' : 'u.all'}, 'match_y_plane'), 'periodic_z' : (['Top', 'Bottom'], {'u.all' : 'u.all'}, 'match_z_plane'), } else: epbcs = { 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'}, 'match_y_line'), 'periodic_y' : (['Bottom', 'Top'], {'u.all' : 'u.all'}, 'match_x_line'), } per.set_accuracy(mesh_eps) functions = { 'match_x_plane' : (per.match_x_plane,), 'match_y_plane' : (per.match_y_plane,), 'match_z_plane' : (per.match_z_plane,), 'match_x_line' : (per.match_x_line,), 'match_y_line' : (per.match_y_line,), 'get_wdir' : (get_wdir,), } integrals = { 'i' : 2 * approx_order, } equations = { 'K' : 'dw_lin_elastic.i.Omega(m.D, v, u)', 'S' : 'dw_elastic_wave.i.Omega(m.D, wave.vec, v, u)', 'R' : """1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, u, v) - 1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, v, u)""", 'M' : 'dw_volume_dot.i.Omega(m.density, v, u)', } solver_0 = solver_conf.copy() solver_0['name'] = 'eig' return locals() def get_wdir(ts, coors, mode=None, equations=None, term=None, problem=None, wdir=None, **kwargs): if mode == 'special': return {'vec' : wdir} def set_wave_dir(pb, wdir): materials = pb.get_materials() wave_mat = materials['wave'] wave_mat.set_extra_args(wdir=wdir) def save_materials(output_dir, pb, options): stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)', mode='el_avg', copy_materials=False, verbose=False) young, poisson = mc.youngpoisson_from_stiffness(stiffness, plane=options.plane) density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)', mode='el_avg', copy_materials=False, verbose=False) out = {} out['young'] = Struct(name='young', mode='cell', data=young[..., None, None]) out['poisson'] = Struct(name='poisson', mode='cell', data=poisson[..., None, None]) out['density'] = Struct(name='density', mode='cell', data=density) materials_filename = os.path.join(output_dir, 'materials.vtk') pb.save_state(materials_filename, out=out) def get_std_wave_fun(pb, options): stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)', mode='el_avg', copy_materials=False, verbose=False) young, poisson = mc.youngpoisson_from_stiffness(stiffness, plane=options.plane) density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)', mode='el_avg', copy_materials=False, verbose=False) lam, mu = mc.lame_from_youngpoisson(young, poisson, plane=options.plane) alam = nm.average(lam) amu = nm.average(mu) adensity = nm.average(density) cp = nm.sqrt((alam + 2.0 * amu) / adensity) cs = nm.sqrt(amu / adensity) output('average p-wave speed:', cp) output('average shear wave speed:', cs) log_names = [r'$\omega_p$', r'$\omega_s$'] log_plot_kwargs = [{'ls' : '--', 'color' : 'k'}, {'ls' : '--', 'color' : 'gray'}] if options.mode == 'omega': fun = lambda wmag, wdir: (cp * wmag, cs * wmag) else: fun = lambda wmag, wdir: (wmag / cp, wmag / cs) return fun, log_names, log_plot_kwargs def get_stepper(rng, pb, options): if options.stepper == 'linear': stepper = TimeStepper(rng[0], rng[1], dt=None, n_step=rng[2]) return stepper bbox = pb.domain.mesh.get_bounding_box() bzone = 2.0 * nm.pi / (bbox[1] - bbox[0]) num = rng[2] // 3 class BrillouinStepper(Struct): """ Step over 1. Brillouin zone in xy plane. """ def __init__(self, t0, t1, dt=None, n_step=None, step=None, **kwargs): Struct.__init__(self, t0=t0, t1=t1, dt=dt, n_step=n_step, step=step) self.n_digit, self.format, self.suffix = get_print_info(self.n_step) def __iter__(self): ts = TimeStepper(0, bzone[0], dt=None, n_step=num) for ii, val in ts: yield ii, val, nm.array([1.0, 0.0]) if ii == (num-2): break ts = TimeStepper(0, bzone[1], dt=None, n_step=num) for ii, k1 in ts: wdir = nm.array([bzone[0], k1]) val = nm.linalg.norm(wdir) wdir = wdir / val yield num + ii, val, wdir if ii == (num-2): break wdir = nm.array([bzone[0], bzone[1]]) val = nm.linalg.norm(wdir) wdir = wdir / val ts = TimeStepper(0, 1, dt=None, n_step=num) for ii, _ in ts: yield 2 * num + ii, val * (1.0 - float(ii)/(num-1)), wdir stepper = BrillouinStepper(0, 1, n_step=rng[2]) return stepper def save_eigenvectors(filename, svecs, wmag, wdir, pb): if svecs is None: return variables = pb.get_variables() # Make full eigenvectors (add DOFs fixed by boundary conditions). vecs = nm.empty((variables.di.ptr[-1], svecs.shape[1]), dtype=svecs.dtype) for ii in range(svecs.shape[1]): vecs[:, ii] = variables.make_full_vec(svecs[:, ii]) # Save the eigenvectors. out = {} state = pb.create_state() pp_name = pb.conf.options.get('post_process_hook') pp = getattr(pb.conf.funmod, pp_name if pp_name is not None else '', lambda out, *args, **kwargs: out) for ii in range(svecs.shape[1]): state.set_full(vecs[:, ii]) aux = state.create_output_dict() aux2 = {} pp(aux2, pb, state, wmag=wmag, wdir=wdir) aux.update(convert_complex_output(aux2)) out.update({key + '%03d' % ii : aux[key] for key in aux}) pb.save_state(filename, out=out) def assemble_matrices(define, mod, pars, set_wave_dir, options, wdir=None): """ Assemble the blocks of dispersion eigenvalue problem matrices. """ define_dict = define(filename_mesh=options.mesh_filename, pars=pars, approx_order=options.order, refinement_level=options.refine, solver_conf=options.solver_conf, plane=options.plane, post_process=options.post_process, **options.define_kwargs) conf = ProblemConf.from_dict(define_dict, mod) pb = Problem.from_conf(conf) pb.dispersion_options = options pb.set_output_dir(options.output_dir) dim = pb.domain.shape.dim # Set the normalized wave vector direction to the material(s). if wdir is None: wdir = nm.asarray(options.wave_dir[:dim], dtype=nm.float64) wdir = wdir / nm.linalg.norm(wdir) set_wave_dir(pb, wdir) bbox = pb.domain.mesh.get_bounding_box() size = (bbox[1] - bbox[0]).max() scaling0 = apply_unit_multipliers([1.0], ['length'], options.unit_multipliers)[0] scaling = scaling0 if options.mesh_size is not None: scaling *= options.mesh_size / size output('scaling factor of periodic cell mesh coordinates:', scaling) output('new mesh size with applied unit multipliers:', scaling * size) pb.domain.mesh.coors[:] *= scaling pb.set_mesh_coors(pb.domain.mesh.coors, update_fields=True) bzone = 2.0 * nm.pi / (scaling * size) output('1. Brillouin zone size:', bzone * scaling0)	output('1. Brillouin zone size with applied unit multipliers:', bzone)	sfepy.base.base.output
#!/usr/bin/env python """ Dispersion analysis of a heterogeneous finite scale periodic cell. The periodic cell mesh has to contain two subdomains Y1 (with the cell ids 1), Y2 (with the cell ids 2), so that different material properties can be defined in each of the subdomains (see ``--pars`` option). The command line parameters can be given in any consistent unit set, for example the basic SI units. The ``--unit-multipliers`` option can be used to rescale the input units to ones more suitable to the simulation, for example to prevent having different matrix blocks with large differences of matrix entries magnitudes. The results are then in the rescaled units. Usage Examples -------------- Default material parameters, a square periodic cell with a spherical inclusion, logs also standard pressure dilatation and shear waves, no eigenvectors:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only As above, with custom eigenvalue solver parameters, and different number of eigenvalues, mesh size and units used in the calculation:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --solver-conf="kind='eig.scipy', method='eigsh', tol=1e-10, maxiter=1000, which='LM', sigma=0" --log-std-waves -n 5 --range=0,640,101 --mode=omega --unit-multipliers=1e-6,1e-2,1e-3 --mesh-size=1e-2 --eigs-only Default material parameters, a square periodic cell with a square inclusion, and a very small mesh to allow comparing the omega and kappa modes (full matrix solver required!):: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.qevp', method='companion', mode='inverted', solver={kind='eig.scipy', method='eig'}" --log-std-waves -n 500 --range=0,4000000,1001 --mesh-size=1e-2 --mode=kappa --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/kappa View/compare the resulting logs:: python script/plot_logs.py output/omega/frequencies.txt --no-legends -g 1 -o mode-omega.png python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends -o mode-kappa.png python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends --swap-axes -o mode-kappa-t.png In contrast to the heterogeneous square periodic cell, a homogeneous square periodic cell (the region Y2 is empty):: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_1m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega-h python script/plot_logs.py output/omega-h/frequencies.txt --no-legends -g 1 -o mode-omega-h.png Use the Brillouin stepper:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves -n=60 --eigs-only --no-legends --stepper=brillouin python script/plot_logs.py output/frequencies.txt -g 0 --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-kappas.png python script/plot_logs.py output/frequencies.txt -g 1 --no-legends --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-omegas.png Additional arguments can be passed to the problem configuration's :func:`define()` function using the ``--define-kwargs`` option. In this file, only the mesh vertex separation parameter `mesh_eps` can be used:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only --define-kwargs="mesh_eps=1e-10" --save-regions """ from __future__ import absolute_import import os import sys sys.path.append('.') import gc from copy import copy from argparse import ArgumentParser, RawDescriptionHelpFormatter import numpy as nm import matplotlib.pyplot as plt from sfepy.base.base import import_file, output, Struct from sfepy.base.conf import dict_from_string, ProblemConf from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options from sfepy.base.log import Log from sfepy.discrete.fem import MeshIO from sfepy.mechanics.matcoefs import stiffness_from_youngpoisson as stiffness import sfepy.mechanics.matcoefs as mc from sfepy.mechanics.units import apply_unit_multipliers import sfepy.discrete.fem.periodic as per from sfepy.discrete.fem.meshio import convert_complex_output from sfepy.homogenization.utils import define_box_regions from sfepy.discrete import Problem from sfepy.mechanics.tensors import get_von_mises_stress from sfepy.solvers import Solver from sfepy.solvers.ts import get_print_info, TimeStepper from sfepy.linalg.utils import output_array_stats, max_diff_csr def apply_units(pars, unit_multipliers): new_pars = apply_unit_multipliers(pars, ['stress', 'one', 'density', 'stress', 'one' ,'density'], unit_multipliers) return new_pars def compute_von_mises(out, pb, state, extend=False, wmag=None, wdir=None): """ Calculate the von Mises stress. """ stress = pb.evaluate('ev_cauchy_stress.i.Omega(m.D, u)', mode='el_avg') vms = get_von_mises_stress(stress.squeeze()) vms.shape = (vms.shape[0], 1, 1, 1) out['von_mises_stress'] = Struct(name='output_data', mode='cell', data=vms) return out def define(filename_mesh, pars, approx_order, refinement_level, solver_conf, plane='strain', post_process=False, mesh_eps=1e-8): io = MeshIO.any_from_filename(filename_mesh) bbox = io.read_bounding_box() dim = bbox.shape[1] options = { 'absolute_mesh_path' : True, 'refinement_level' : refinement_level, 'allow_empty_regions' : True, 'post_process_hook' : 'compute_von_mises' if post_process else None, } fields = { 'displacement': ('complex', dim, 'Omega', approx_order), } young1, poisson1, density1, young2, poisson2, density2 = pars materials = { 'm' : ({ 'D' : {'Y1' : stiffness(dim, young=young1, poisson=poisson1, plane=plane), 'Y2' : stiffness(dim, young=young2, poisson=poisson2, plane=plane)}, 'density' : {'Y1' : density1, 'Y2' : density2}, },), 'wave' : 'get_wdir', } variables = { 'u' : ('unknown field', 'displacement', 0), 'v' : ('test field', 'displacement', 'u'), } regions = { 'Omega' : 'all', 'Y1': 'cells of group 1', 'Y2': 'cells of group 2', } regions.update(define_box_regions(dim, bbox[0], bbox[1], mesh_eps)) ebcs = { } if dim == 3: epbcs = { 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'}, 'match_x_plane'), 'periodic_y' : (['Near', 'Far'], {'u.all' : 'u.all'}, 'match_y_plane'), 'periodic_z' : (['Top', 'Bottom'], {'u.all' : 'u.all'}, 'match_z_plane'), } else: epbcs = { 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'}, 'match_y_line'), 'periodic_y' : (['Bottom', 'Top'], {'u.all' : 'u.all'}, 'match_x_line'), } per.set_accuracy(mesh_eps) functions = { 'match_x_plane' : (per.match_x_plane,), 'match_y_plane' : (per.match_y_plane,), 'match_z_plane' : (per.match_z_plane,), 'match_x_line' : (per.match_x_line,), 'match_y_line' : (per.match_y_line,), 'get_wdir' : (get_wdir,), } integrals = { 'i' : 2 * approx_order, } equations = { 'K' : 'dw_lin_elastic.i.Omega(m.D, v, u)', 'S' : 'dw_elastic_wave.i.Omega(m.D, wave.vec, v, u)', 'R' : """1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, u, v) - 1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, v, u)""", 'M' : 'dw_volume_dot.i.Omega(m.density, v, u)', } solver_0 = solver_conf.copy() solver_0['name'] = 'eig' return locals() def get_wdir(ts, coors, mode=None, equations=None, term=None, problem=None, wdir=None, **kwargs): if mode == 'special': return {'vec' : wdir} def set_wave_dir(pb, wdir): materials = pb.get_materials() wave_mat = materials['wave'] wave_mat.set_extra_args(wdir=wdir) def save_materials(output_dir, pb, options): stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)', mode='el_avg', copy_materials=False, verbose=False) young, poisson = mc.youngpoisson_from_stiffness(stiffness, plane=options.plane) density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)', mode='el_avg', copy_materials=False, verbose=False) out = {} out['young'] = Struct(name='young', mode='cell', data=young[..., None, None]) out['poisson'] = Struct(name='poisson', mode='cell', data=poisson[..., None, None]) out['density'] = Struct(name='density', mode='cell', data=density) materials_filename = os.path.join(output_dir, 'materials.vtk') pb.save_state(materials_filename, out=out) def get_std_wave_fun(pb, options): stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)', mode='el_avg', copy_materials=False, verbose=False) young, poisson = mc.youngpoisson_from_stiffness(stiffness, plane=options.plane) density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)', mode='el_avg', copy_materials=False, verbose=False) lam, mu = mc.lame_from_youngpoisson(young, poisson, plane=options.plane) alam = nm.average(lam) amu = nm.average(mu) adensity = nm.average(density) cp = nm.sqrt((alam + 2.0 * amu) / adensity) cs = nm.sqrt(amu / adensity) output('average p-wave speed:', cp) output('average shear wave speed:', cs) log_names = [r'$\omega_p$', r'$\omega_s$'] log_plot_kwargs = [{'ls' : '--', 'color' : 'k'}, {'ls' : '--', 'color' : 'gray'}] if options.mode == 'omega': fun = lambda wmag, wdir: (cp * wmag, cs * wmag) else: fun = lambda wmag, wdir: (wmag / cp, wmag / cs) return fun, log_names, log_plot_kwargs def get_stepper(rng, pb, options): if options.stepper == 'linear': stepper = TimeStepper(rng[0], rng[1], dt=None, n_step=rng[2]) return stepper bbox = pb.domain.mesh.get_bounding_box() bzone = 2.0 * nm.pi / (bbox[1] - bbox[0]) num = rng[2] // 3 class BrillouinStepper(Struct): """ Step over 1. Brillouin zone in xy plane. """ def __init__(self, t0, t1, dt=None, n_step=None, step=None, **kwargs): Struct.__init__(self, t0=t0, t1=t1, dt=dt, n_step=n_step, step=step) self.n_digit, self.format, self.suffix = get_print_info(self.n_step) def __iter__(self): ts = TimeStepper(0, bzone[0], dt=None, n_step=num) for ii, val in ts: yield ii, val, nm.array([1.0, 0.0]) if ii == (num-2): break ts = TimeStepper(0, bzone[1], dt=None, n_step=num) for ii, k1 in ts: wdir = nm.array([bzone[0], k1]) val = nm.linalg.norm(wdir) wdir = wdir / val yield num + ii, val, wdir if ii == (num-2): break wdir = nm.array([bzone[0], bzone[1]]) val = nm.linalg.norm(wdir) wdir = wdir / val ts = TimeStepper(0, 1, dt=None, n_step=num) for ii, _ in ts: yield 2 * num + ii, val * (1.0 - float(ii)/(num-1)), wdir stepper = BrillouinStepper(0, 1, n_step=rng[2]) return stepper def save_eigenvectors(filename, svecs, wmag, wdir, pb): if svecs is None: return variables = pb.get_variables() # Make full eigenvectors (add DOFs fixed by boundary conditions). vecs = nm.empty((variables.di.ptr[-1], svecs.shape[1]), dtype=svecs.dtype) for ii in range(svecs.shape[1]): vecs[:, ii] = variables.make_full_vec(svecs[:, ii]) # Save the eigenvectors. out = {} state = pb.create_state() pp_name = pb.conf.options.get('post_process_hook') pp = getattr(pb.conf.funmod, pp_name if pp_name is not None else '', lambda out, *args, **kwargs: out) for ii in range(svecs.shape[1]): state.set_full(vecs[:, ii]) aux = state.create_output_dict() aux2 = {} pp(aux2, pb, state, wmag=wmag, wdir=wdir) aux.update(convert_complex_output(aux2)) out.update({key + '%03d' % ii : aux[key] for key in aux}) pb.save_state(filename, out=out) def assemble_matrices(define, mod, pars, set_wave_dir, options, wdir=None): """ Assemble the blocks of dispersion eigenvalue problem matrices. """ define_dict = define(filename_mesh=options.mesh_filename, pars=pars, approx_order=options.order, refinement_level=options.refine, solver_conf=options.solver_conf, plane=options.plane, post_process=options.post_process, **options.define_kwargs) conf = ProblemConf.from_dict(define_dict, mod) pb = Problem.from_conf(conf) pb.dispersion_options = options pb.set_output_dir(options.output_dir) dim = pb.domain.shape.dim # Set the normalized wave vector direction to the material(s). if wdir is None: wdir = nm.asarray(options.wave_dir[:dim], dtype=nm.float64) wdir = wdir / nm.linalg.norm(wdir) set_wave_dir(pb, wdir) bbox = pb.domain.mesh.get_bounding_box() size = (bbox[1] - bbox[0]).max() scaling0 = apply_unit_multipliers([1.0], ['length'], options.unit_multipliers)[0] scaling = scaling0 if options.mesh_size is not None: scaling *= options.mesh_size / size output('scaling factor of periodic cell mesh coordinates:', scaling) output('new mesh size with applied unit multipliers:', scaling * size) pb.domain.mesh.coors[:] *= scaling pb.set_mesh_coors(pb.domain.mesh.coors, update_fields=True) bzone = 2.0 * nm.pi / (scaling * size) output('1. Brillouin zone size:', bzone * scaling0) output('1. Brillouin zone size with applied unit multipliers:', bzone) pb.time_update() pb.update_materials() # Assemble the matrices. mtxs = {} for key, eq in pb.equations.iteritems(): mtxs[key] = mtx = pb.mtx_a.copy() mtx = eq.evaluate(mode='weak', dw_mode='matrix', asm_obj=mtx) mtx.eliminate_zeros() output_array_stats(mtx.data, 'nonzeros in %s' % key) output('symmetry checks:') output('%s - %s^T:' % (key, key), max_diff_csr(mtx, mtx.T)) output('%s - %s^H:' % (key, key), max_diff_csr(mtx, mtx.H)) return pb, wdir, bzone, mtxs def setup_n_eigs(options, pb, mtxs): """ Setup the numbers of eigenvalues based on options and numbers of DOFs. """ solver_n_eigs = n_eigs = options.n_eigs n_dof = mtxs['K'].shape[0] if options.mode == 'omega': if options.n_eigs > n_dof: n_eigs = n_dof solver_n_eigs = None else: if options.n_eigs > 2 * n_dof: n_eigs = 2 * n_dof solver_n_eigs = None return solver_n_eigs, n_eigs def build_evp_matrices(mtxs, val, mode, pb): """ Build the matrices of the dispersion eigenvalue problem. """ if mode == 'omega': mtx_a = mtxs['K'] + val**2 * mtxs['S'] + val * mtxs['R'] output('A - A^H:', max_diff_csr(mtx_a, mtx_a.H)) evp_mtxs = (mtx_a, mtxs['M']) else: evp_mtxs = (mtxs['S'], mtxs['R'], mtxs['K'] - val**2 * mtxs['M']) return evp_mtxs def process_evp_results(eigs, svecs, val, wdir, bzone, pb, mtxs, options, std_wave_fun=None): """ Transform eigenvalues to either omegas or kappas, depending on `mode`. Transform eigenvectors, if available, depending on `mode`. Return also the values to log. """ if options.mode == 'omega': omegas = nm.sqrt(eigs) output('eigs, omegas:') for ii, om in enumerate(omegas): output('{:>3}. {: .10e}, {:.10e}'.format(ii, eigs[ii], om)) if options.stepper == 'linear': out = tuple(eigs) + tuple(omegas) else: out = tuple(val * wdir) + tuple(omegas) if std_wave_fun is not None: out = out + std_wave_fun(val, wdir) return omegas, svecs, out else: kappas = eigs.copy() rks = kappas.copy() # Mask modes far from 1. Brillouin zone. max_kappa = 1.2 * bzone kappas[kappas.real > max_kappa] = nm.nan # Mask non-physical modes. kappas[kappas.real < 0] = nm.nan kappas[nm.abs(kappas.imag) > 1e-10] = nm.nan out = tuple(kappas.real) output('raw kappas, masked real part:',) for ii, kr in enumerate(kappas.real): output('{:>3}. {: 23.5e}, {:.10e}'.format(ii, rks[ii], kr)) if svecs is not None: n_dof = mtxs['K'].shape[0] # Select only vectors corresponding to physical modes. ii = nm.isfinite(kappas.real) svecs = svecs[:n_dof, ii] if std_wave_fun is not None: out = out + tuple(ii if ii <= max_kappa else nm.nan for ii in std_wave_fun(val, wdir)) return kappas, svecs, out helps = { 'pars' : 'material parameters in Y1, Y2 subdomains in basic units' ' [default: %(default)s]', 'conf' : 'if given, an alternative problem description file with apply_units() and' ' define() functions [default: %(default)s]', 'define_kwargs' : 'additional keyword arguments passed to define()', 'mesh_size' : 'desired mesh size (max. of bounding box dimensions) in basic units' ' - the input periodic cell mesh is rescaled to this size' ' [default: %(default)s]', 'unit_multipliers' : 'basic unit multipliers (time, length, mass) [default: %(default)s]', 'plane' : 'for 2D problems, plane strain or stress hypothesis selection' ' [default: %(default)s]', 'wave_dir' : 'the wave vector direction (will be normalized)' ' [default: %(default)s]', 'mode' : 'solution mode: omega = solve a generalized EVP for omega,' ' kappa = solve a quadratic generalized EVP for kappa' ' [default: %(default)s]', 'stepper' : 'the range stepper. For "brillouin", only the number' ' of items from --range is used' ' [default: %(default)s]', 'range' : 'the wave vector magnitude / frequency range' ' (like numpy.linspace) depending on the mode option' ' [default: %(default)s]', 'order' : 'displacement field approximation order [default: %(default)s]', 'refine' : 'number of uniform mesh refinements [default: %(default)s]', 'n_eigs' : 'the number of eigenvalues to compute [default: %(default)s]', 'eigs_only' : 'compute only eigenvalues, not eigenvectors', 'post_process' : 'post-process eigenvectors', 'solver_conf' : 'eigenvalue problem solver configuration options' ' [default: %(default)s]', 'save_regions' : 'save defined regions into' ' <output_directory>/regions.vtk', 'save_materials' : 'save material parameters into' ' <output_directory>/materials.vtk', 'log_std_waves' : 'log also standard pressure dilatation and shear waves', 'no_legends' : 'do not show legends in the log plots', 'no_show' : 'do not show the log figure', 'silent' : 'do not print messages to screen', 'clear' : 'clear old solution files from output directory', 'output_dir' : 'output directory [default: %(default)s]', 'mesh_filename' : 'input periodic cell mesh file name [default: %(default)s]', } def main(): # Aluminium and epoxy. default_pars = '70e9,0.35,2.799e3, 3.8e9,0.27,1.142e3' default_solver_conf = ("kind='eig.scipy',method='eigsh',tol=1.0e-5," "maxiter=1000,which='LM',sigma=0.0") parser = ArgumentParser(description=__doc__, formatter_class=RawDescriptionHelpFormatter) parser.add_argument('--pars', metavar='young1,poisson1,density1' ',young2,poisson2,density2', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='pars', default=default_pars, help=helps['pars']) parser.add_argument('--conf', metavar='filename', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='conf', default=None, help=helps['conf']) parser.add_argument('--define-kwargs', metavar='dict-like', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='define_kwargs', default=None, help=helps['define_kwargs']) parser.add_argument('--mesh-size', type=float, metavar='float', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='mesh_size', default=None, help=helps['mesh_size']) parser.add_argument('--unit-multipliers', metavar='c_time,c_length,c_mass', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='unit_multipliers', default='1.0,1.0,1.0', help=helps['unit_multipliers']) parser.add_argument('--plane', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='plane', choices=['strain', 'stress'], default='strain', help=helps['plane']) parser.add_argument('--wave-dir', metavar='float,float[,float]', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='wave_dir', default='1.0,0.0,0.0', help=helps['wave_dir']) parser.add_argument('--mode', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='mode', choices=['omega', 'kappa'], default='omega', help=helps['mode']) parser.add_argument('--stepper', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='stepper', choices=['linear', 'brillouin'], default='linear', help=helps['stepper']) parser.add_argument('--range', metavar='start,stop,count', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='range', default='0,6.4,33', help=helps['range']) parser.add_argument('--order', metavar='int', type=int, action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='order', default=1, help=helps['order']) parser.add_argument('--refine', metavar='int', type=int, action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='refine', default=0, help=helps['refine']) parser.add_argument('-n', '--n-eigs', metavar='int', type=int, action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='n_eigs', default=6, help=helps['n_eigs']) group = parser.add_mutually_exclusive_group() group.add_argument('--eigs-only', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='eigs_only', default=False, help=helps['eigs_only']) group.add_argument('--post-process', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='post_process', default=False, help=helps['post_process']) parser.add_argument('--solver-conf', metavar='dict-like', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='solver_conf', default=default_solver_conf, help=helps['solver_conf']) parser.add_argument('--save-regions', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='save_regions', default=False, help=helps['save_regions']) parser.add_argument('--save-materials', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='save_materials', default=False, help=helps['save_materials']) parser.add_argument('--log-std-waves', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='log_std_waves', default=False, help=helps['log_std_waves']) parser.add_argument('--no-legends', action="https://huggingface.co/datasets/luna-code/sfepy/store_false", dest='show_legends', default=True, help=helps['no_legends']) parser.add_argument('--no-show', action="https://huggingface.co/datasets/luna-code/sfepy/store_false", dest='show', default=True, help=helps['no_show']) parser.add_argument('--silent', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='silent', default=False, help=helps['silent']) parser.add_argument('-c', '--clear', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='clear', default=False, help=helps['clear']) parser.add_argument('-o', '--output-dir', metavar='path', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='output_dir', default='output', help=helps['output_dir']) parser.add_argument('mesh_filename', default='', help=helps['mesh_filename']) options = parser.parse_args() output_dir = options.output_dir output.set_output(filename=os.path.join(output_dir,'output_log.txt'), combined=options.silent == False) if options.conf is not None: mod = import_file(options.conf) else: mod = sys.modules[__name__] apply_units = mod.apply_units define = mod.define set_wave_dir = mod.set_wave_dir setup_n_eigs = mod.setup_n_eigs build_evp_matrices = mod.build_evp_matrices save_materials = mod.save_materials get_std_wave_fun = mod.get_std_wave_fun get_stepper = mod.get_stepper process_evp_results = mod.process_evp_results options.pars = [float(ii) for ii in options.pars.split(',')] options.unit_multipliers = [float(ii) for ii in options.unit_multipliers.split(',')] options.wave_dir = [float(ii) for ii in options.wave_dir.split(',')] aux = options.range.split(',') options.range = [float(aux[0]), float(aux[1]), int(aux[2])] options.solver_conf =	dict_from_string(options.solver_conf)	sfepy.base.conf.dict_from_string
#!/usr/bin/env python """ Dispersion analysis of a heterogeneous finite scale periodic cell. The periodic cell mesh has to contain two subdomains Y1 (with the cell ids 1), Y2 (with the cell ids 2), so that different material properties can be defined in each of the subdomains (see ``--pars`` option). The command line parameters can be given in any consistent unit set, for example the basic SI units. The ``--unit-multipliers`` option can be used to rescale the input units to ones more suitable to the simulation, for example to prevent having different matrix blocks with large differences of matrix entries magnitudes. The results are then in the rescaled units. Usage Examples -------------- Default material parameters, a square periodic cell with a spherical inclusion, logs also standard pressure dilatation and shear waves, no eigenvectors:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only As above, with custom eigenvalue solver parameters, and different number of eigenvalues, mesh size and units used in the calculation:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --solver-conf="kind='eig.scipy', method='eigsh', tol=1e-10, maxiter=1000, which='LM', sigma=0" --log-std-waves -n 5 --range=0,640,101 --mode=omega --unit-multipliers=1e-6,1e-2,1e-3 --mesh-size=1e-2 --eigs-only Default material parameters, a square periodic cell with a square inclusion, and a very small mesh to allow comparing the omega and kappa modes (full matrix solver required!):: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.qevp', method='companion', mode='inverted', solver={kind='eig.scipy', method='eig'}" --log-std-waves -n 500 --range=0,4000000,1001 --mesh-size=1e-2 --mode=kappa --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/kappa View/compare the resulting logs:: python script/plot_logs.py output/omega/frequencies.txt --no-legends -g 1 -o mode-omega.png python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends -o mode-kappa.png python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends --swap-axes -o mode-kappa-t.png In contrast to the heterogeneous square periodic cell, a homogeneous square periodic cell (the region Y2 is empty):: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_1m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega-h python script/plot_logs.py output/omega-h/frequencies.txt --no-legends -g 1 -o mode-omega-h.png Use the Brillouin stepper:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves -n=60 --eigs-only --no-legends --stepper=brillouin python script/plot_logs.py output/frequencies.txt -g 0 --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-kappas.png python script/plot_logs.py output/frequencies.txt -g 1 --no-legends --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-omegas.png Additional arguments can be passed to the problem configuration's :func:`define()` function using the ``--define-kwargs`` option. In this file, only the mesh vertex separation parameter `mesh_eps` can be used:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only --define-kwargs="mesh_eps=1e-10" --save-regions """ from __future__ import absolute_import import os import sys sys.path.append('.') import gc from copy import copy from argparse import ArgumentParser, RawDescriptionHelpFormatter import numpy as nm import matplotlib.pyplot as plt from sfepy.base.base import import_file, output, Struct from sfepy.base.conf import dict_from_string, ProblemConf from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options from sfepy.base.log import Log from sfepy.discrete.fem import MeshIO from sfepy.mechanics.matcoefs import stiffness_from_youngpoisson as stiffness import sfepy.mechanics.matcoefs as mc from sfepy.mechanics.units import apply_unit_multipliers import sfepy.discrete.fem.periodic as per from sfepy.discrete.fem.meshio import convert_complex_output from sfepy.homogenization.utils import define_box_regions from sfepy.discrete import Problem from sfepy.mechanics.tensors import get_von_mises_stress from sfepy.solvers import Solver from sfepy.solvers.ts import get_print_info, TimeStepper from sfepy.linalg.utils import output_array_stats, max_diff_csr def apply_units(pars, unit_multipliers): new_pars = apply_unit_multipliers(pars, ['stress', 'one', 'density', 'stress', 'one' ,'density'], unit_multipliers) return new_pars def compute_von_mises(out, pb, state, extend=False, wmag=None, wdir=None): """ Calculate the von Mises stress. """ stress = pb.evaluate('ev_cauchy_stress.i.Omega(m.D, u)', mode='el_avg') vms = get_von_mises_stress(stress.squeeze()) vms.shape = (vms.shape[0], 1, 1, 1) out['von_mises_stress'] = Struct(name='output_data', mode='cell', data=vms) return out def define(filename_mesh, pars, approx_order, refinement_level, solver_conf, plane='strain', post_process=False, mesh_eps=1e-8): io = MeshIO.any_from_filename(filename_mesh) bbox = io.read_bounding_box() dim = bbox.shape[1] options = { 'absolute_mesh_path' : True, 'refinement_level' : refinement_level, 'allow_empty_regions' : True, 'post_process_hook' : 'compute_von_mises' if post_process else None, } fields = { 'displacement': ('complex', dim, 'Omega', approx_order), } young1, poisson1, density1, young2, poisson2, density2 = pars materials = { 'm' : ({ 'D' : {'Y1' : stiffness(dim, young=young1, poisson=poisson1, plane=plane), 'Y2' : stiffness(dim, young=young2, poisson=poisson2, plane=plane)}, 'density' : {'Y1' : density1, 'Y2' : density2}, },), 'wave' : 'get_wdir', } variables = { 'u' : ('unknown field', 'displacement', 0), 'v' : ('test field', 'displacement', 'u'), } regions = { 'Omega' : 'all', 'Y1': 'cells of group 1', 'Y2': 'cells of group 2', } regions.update(define_box_regions(dim, bbox[0], bbox[1], mesh_eps)) ebcs = { } if dim == 3: epbcs = { 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'}, 'match_x_plane'), 'periodic_y' : (['Near', 'Far'], {'u.all' : 'u.all'}, 'match_y_plane'), 'periodic_z' : (['Top', 'Bottom'], {'u.all' : 'u.all'}, 'match_z_plane'), } else: epbcs = { 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'}, 'match_y_line'), 'periodic_y' : (['Bottom', 'Top'], {'u.all' : 'u.all'}, 'match_x_line'), } per.set_accuracy(mesh_eps) functions = { 'match_x_plane' : (per.match_x_plane,), 'match_y_plane' : (per.match_y_plane,), 'match_z_plane' : (per.match_z_plane,), 'match_x_line' : (per.match_x_line,), 'match_y_line' : (per.match_y_line,), 'get_wdir' : (get_wdir,), } integrals = { 'i' : 2 * approx_order, } equations = { 'K' : 'dw_lin_elastic.i.Omega(m.D, v, u)', 'S' : 'dw_elastic_wave.i.Omega(m.D, wave.vec, v, u)', 'R' : """1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, u, v) - 1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, v, u)""", 'M' : 'dw_volume_dot.i.Omega(m.density, v, u)', } solver_0 = solver_conf.copy() solver_0['name'] = 'eig' return locals() def get_wdir(ts, coors, mode=None, equations=None, term=None, problem=None, wdir=None, **kwargs): if mode == 'special': return {'vec' : wdir} def set_wave_dir(pb, wdir): materials = pb.get_materials() wave_mat = materials['wave'] wave_mat.set_extra_args(wdir=wdir) def save_materials(output_dir, pb, options): stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)', mode='el_avg', copy_materials=False, verbose=False) young, poisson = mc.youngpoisson_from_stiffness(stiffness, plane=options.plane) density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)', mode='el_avg', copy_materials=False, verbose=False) out = {} out['young'] = Struct(name='young', mode='cell', data=young[..., None, None]) out['poisson'] = Struct(name='poisson', mode='cell', data=poisson[..., None, None]) out['density'] = Struct(name='density', mode='cell', data=density) materials_filename = os.path.join(output_dir, 'materials.vtk') pb.save_state(materials_filename, out=out) def get_std_wave_fun(pb, options): stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)', mode='el_avg', copy_materials=False, verbose=False) young, poisson = mc.youngpoisson_from_stiffness(stiffness, plane=options.plane) density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)', mode='el_avg', copy_materials=False, verbose=False) lam, mu = mc.lame_from_youngpoisson(young, poisson, plane=options.plane) alam = nm.average(lam) amu = nm.average(mu) adensity = nm.average(density) cp = nm.sqrt((alam + 2.0 * amu) / adensity) cs = nm.sqrt(amu / adensity) output('average p-wave speed:', cp) output('average shear wave speed:', cs) log_names = [r'$\omega_p$', r'$\omega_s$'] log_plot_kwargs = [{'ls' : '--', 'color' : 'k'}, {'ls' : '--', 'color' : 'gray'}] if options.mode == 'omega': fun = lambda wmag, wdir: (cp * wmag, cs * wmag) else: fun = lambda wmag, wdir: (wmag / cp, wmag / cs) return fun, log_names, log_plot_kwargs def get_stepper(rng, pb, options): if options.stepper == 'linear': stepper = TimeStepper(rng[0], rng[1], dt=None, n_step=rng[2]) return stepper bbox = pb.domain.mesh.get_bounding_box() bzone = 2.0 * nm.pi / (bbox[1] - bbox[0]) num = rng[2] // 3 class BrillouinStepper(Struct): """ Step over 1. Brillouin zone in xy plane. """ def __init__(self, t0, t1, dt=None, n_step=None, step=None, **kwargs): Struct.__init__(self, t0=t0, t1=t1, dt=dt, n_step=n_step, step=step) self.n_digit, self.format, self.suffix = get_print_info(self.n_step) def __iter__(self): ts = TimeStepper(0, bzone[0], dt=None, n_step=num) for ii, val in ts: yield ii, val, nm.array([1.0, 0.0]) if ii == (num-2): break ts = TimeStepper(0, bzone[1], dt=None, n_step=num) for ii, k1 in ts: wdir = nm.array([bzone[0], k1]) val = nm.linalg.norm(wdir) wdir = wdir / val yield num + ii, val, wdir if ii == (num-2): break wdir = nm.array([bzone[0], bzone[1]]) val = nm.linalg.norm(wdir) wdir = wdir / val ts = TimeStepper(0, 1, dt=None, n_step=num) for ii, _ in ts: yield 2 * num + ii, val * (1.0 - float(ii)/(num-1)), wdir stepper = BrillouinStepper(0, 1, n_step=rng[2]) return stepper def save_eigenvectors(filename, svecs, wmag, wdir, pb): if svecs is None: return variables = pb.get_variables() # Make full eigenvectors (add DOFs fixed by boundary conditions). vecs = nm.empty((variables.di.ptr[-1], svecs.shape[1]), dtype=svecs.dtype) for ii in range(svecs.shape[1]): vecs[:, ii] = variables.make_full_vec(svecs[:, ii]) # Save the eigenvectors. out = {} state = pb.create_state() pp_name = pb.conf.options.get('post_process_hook') pp = getattr(pb.conf.funmod, pp_name if pp_name is not None else '', lambda out, *args, **kwargs: out) for ii in range(svecs.shape[1]): state.set_full(vecs[:, ii]) aux = state.create_output_dict() aux2 = {} pp(aux2, pb, state, wmag=wmag, wdir=wdir) aux.update(convert_complex_output(aux2)) out.update({key + '%03d' % ii : aux[key] for key in aux}) pb.save_state(filename, out=out) def assemble_matrices(define, mod, pars, set_wave_dir, options, wdir=None): """ Assemble the blocks of dispersion eigenvalue problem matrices. """ define_dict = define(filename_mesh=options.mesh_filename, pars=pars, approx_order=options.order, refinement_level=options.refine, solver_conf=options.solver_conf, plane=options.plane, post_process=options.post_process, **options.define_kwargs) conf = ProblemConf.from_dict(define_dict, mod) pb = Problem.from_conf(conf) pb.dispersion_options = options pb.set_output_dir(options.output_dir) dim = pb.domain.shape.dim # Set the normalized wave vector direction to the material(s). if wdir is None: wdir = nm.asarray(options.wave_dir[:dim], dtype=nm.float64) wdir = wdir / nm.linalg.norm(wdir) set_wave_dir(pb, wdir) bbox = pb.domain.mesh.get_bounding_box() size = (bbox[1] - bbox[0]).max() scaling0 = apply_unit_multipliers([1.0], ['length'], options.unit_multipliers)[0] scaling = scaling0 if options.mesh_size is not None: scaling *= options.mesh_size / size output('scaling factor of periodic cell mesh coordinates:', scaling) output('new mesh size with applied unit multipliers:', scaling * size) pb.domain.mesh.coors[:] *= scaling pb.set_mesh_coors(pb.domain.mesh.coors, update_fields=True) bzone = 2.0 * nm.pi / (scaling * size) output('1. Brillouin zone size:', bzone * scaling0) output('1. Brillouin zone size with applied unit multipliers:', bzone) pb.time_update() pb.update_materials() # Assemble the matrices. mtxs = {} for key, eq in pb.equations.iteritems(): mtxs[key] = mtx = pb.mtx_a.copy() mtx = eq.evaluate(mode='weak', dw_mode='matrix', asm_obj=mtx) mtx.eliminate_zeros() output_array_stats(mtx.data, 'nonzeros in %s' % key) output('symmetry checks:') output('%s - %s^T:' % (key, key), max_diff_csr(mtx, mtx.T)) output('%s - %s^H:' % (key, key), max_diff_csr(mtx, mtx.H)) return pb, wdir, bzone, mtxs def setup_n_eigs(options, pb, mtxs): """ Setup the numbers of eigenvalues based on options and numbers of DOFs. """ solver_n_eigs = n_eigs = options.n_eigs n_dof = mtxs['K'].shape[0] if options.mode == 'omega': if options.n_eigs > n_dof: n_eigs = n_dof solver_n_eigs = None else: if options.n_eigs > 2 * n_dof: n_eigs = 2 * n_dof solver_n_eigs = None return solver_n_eigs, n_eigs def build_evp_matrices(mtxs, val, mode, pb): """ Build the matrices of the dispersion eigenvalue problem. """ if mode == 'omega': mtx_a = mtxs['K'] + val**2 * mtxs['S'] + val * mtxs['R'] output('A - A^H:', max_diff_csr(mtx_a, mtx_a.H)) evp_mtxs = (mtx_a, mtxs['M']) else: evp_mtxs = (mtxs['S'], mtxs['R'], mtxs['K'] - val**2 * mtxs['M']) return evp_mtxs def process_evp_results(eigs, svecs, val, wdir, bzone, pb, mtxs, options, std_wave_fun=None): """ Transform eigenvalues to either omegas or kappas, depending on `mode`. Transform eigenvectors, if available, depending on `mode`. Return also the values to log. """ if options.mode == 'omega': omegas = nm.sqrt(eigs) output('eigs, omegas:') for ii, om in enumerate(omegas): output('{:>3}. {: .10e}, {:.10e}'.format(ii, eigs[ii], om)) if options.stepper == 'linear': out = tuple(eigs) + tuple(omegas) else: out = tuple(val * wdir) + tuple(omegas) if std_wave_fun is not None: out = out + std_wave_fun(val, wdir) return omegas, svecs, out else: kappas = eigs.copy() rks = kappas.copy() # Mask modes far from 1. Brillouin zone. max_kappa = 1.2 * bzone kappas[kappas.real > max_kappa] = nm.nan # Mask non-physical modes. kappas[kappas.real < 0] = nm.nan kappas[nm.abs(kappas.imag) > 1e-10] = nm.nan out = tuple(kappas.real) output('raw kappas, masked real part:',) for ii, kr in enumerate(kappas.real): output('{:>3}. {: 23.5e}, {:.10e}'.format(ii, rks[ii], kr)) if svecs is not None: n_dof = mtxs['K'].shape[0] # Select only vectors corresponding to physical modes. ii = nm.isfinite(kappas.real) svecs = svecs[:n_dof, ii] if std_wave_fun is not None: out = out + tuple(ii if ii <= max_kappa else nm.nan for ii in std_wave_fun(val, wdir)) return kappas, svecs, out helps = { 'pars' : 'material parameters in Y1, Y2 subdomains in basic units' ' [default: %(default)s]', 'conf' : 'if given, an alternative problem description file with apply_units() and' ' define() functions [default: %(default)s]', 'define_kwargs' : 'additional keyword arguments passed to define()', 'mesh_size' : 'desired mesh size (max. of bounding box dimensions) in basic units' ' - the input periodic cell mesh is rescaled to this size' ' [default: %(default)s]', 'unit_multipliers' : 'basic unit multipliers (time, length, mass) [default: %(default)s]', 'plane' : 'for 2D problems, plane strain or stress hypothesis selection' ' [default: %(default)s]', 'wave_dir' : 'the wave vector direction (will be normalized)' ' [default: %(default)s]', 'mode' : 'solution mode: omega = solve a generalized EVP for omega,' ' kappa = solve a quadratic generalized EVP for kappa' ' [default: %(default)s]', 'stepper' : 'the range stepper. For "brillouin", only the number' ' of items from --range is used' ' [default: %(default)s]', 'range' : 'the wave vector magnitude / frequency range' ' (like numpy.linspace) depending on the mode option' ' [default: %(default)s]', 'order' : 'displacement field approximation order [default: %(default)s]', 'refine' : 'number of uniform mesh refinements [default: %(default)s]', 'n_eigs' : 'the number of eigenvalues to compute [default: %(default)s]', 'eigs_only' : 'compute only eigenvalues, not eigenvectors', 'post_process' : 'post-process eigenvectors', 'solver_conf' : 'eigenvalue problem solver configuration options' ' [default: %(default)s]', 'save_regions' : 'save defined regions into' ' <output_directory>/regions.vtk', 'save_materials' : 'save material parameters into' ' <output_directory>/materials.vtk', 'log_std_waves' : 'log also standard pressure dilatation and shear waves', 'no_legends' : 'do not show legends in the log plots', 'no_show' : 'do not show the log figure', 'silent' : 'do not print messages to screen', 'clear' : 'clear old solution files from output directory', 'output_dir' : 'output directory [default: %(default)s]', 'mesh_filename' : 'input periodic cell mesh file name [default: %(default)s]', } def main(): # Aluminium and epoxy. default_pars = '70e9,0.35,2.799e3, 3.8e9,0.27,1.142e3' default_solver_conf = ("kind='eig.scipy',method='eigsh',tol=1.0e-5," "maxiter=1000,which='LM',sigma=0.0") parser = ArgumentParser(description=__doc__, formatter_class=RawDescriptionHelpFormatter) parser.add_argument('--pars', metavar='young1,poisson1,density1' ',young2,poisson2,density2', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='pars', default=default_pars, help=helps['pars']) parser.add_argument('--conf', metavar='filename', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='conf', default=None, help=helps['conf']) parser.add_argument('--define-kwargs', metavar='dict-like', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='define_kwargs', default=None, help=helps['define_kwargs']) parser.add_argument('--mesh-size', type=float, metavar='float', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='mesh_size', default=None, help=helps['mesh_size']) parser.add_argument('--unit-multipliers', metavar='c_time,c_length,c_mass', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='unit_multipliers', default='1.0,1.0,1.0', help=helps['unit_multipliers']) parser.add_argument('--plane', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='plane', choices=['strain', 'stress'], default='strain', help=helps['plane']) parser.add_argument('--wave-dir', metavar='float,float[,float]', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='wave_dir', default='1.0,0.0,0.0', help=helps['wave_dir']) parser.add_argument('--mode', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='mode', choices=['omega', 'kappa'], default='omega', help=helps['mode']) parser.add_argument('--stepper', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='stepper', choices=['linear', 'brillouin'], default='linear', help=helps['stepper']) parser.add_argument('--range', metavar='start,stop,count', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='range', default='0,6.4,33', help=helps['range']) parser.add_argument('--order', metavar='int', type=int, action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='order', default=1, help=helps['order']) parser.add_argument('--refine', metavar='int', type=int, action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='refine', default=0, help=helps['refine']) parser.add_argument('-n', '--n-eigs', metavar='int', type=int, action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='n_eigs', default=6, help=helps['n_eigs']) group = parser.add_mutually_exclusive_group() group.add_argument('--eigs-only', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='eigs_only', default=False, help=helps['eigs_only']) group.add_argument('--post-process', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='post_process', default=False, help=helps['post_process']) parser.add_argument('--solver-conf', metavar='dict-like', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='solver_conf', default=default_solver_conf, help=helps['solver_conf']) parser.add_argument('--save-regions', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='save_regions', default=False, help=helps['save_regions']) parser.add_argument('--save-materials', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='save_materials', default=False, help=helps['save_materials']) parser.add_argument('--log-std-waves', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='log_std_waves', default=False, help=helps['log_std_waves']) parser.add_argument('--no-legends', action="https://huggingface.co/datasets/luna-code/sfepy/store_false", dest='show_legends', default=True, help=helps['no_legends']) parser.add_argument('--no-show', action="https://huggingface.co/datasets/luna-code/sfepy/store_false", dest='show', default=True, help=helps['no_show']) parser.add_argument('--silent', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='silent', default=False, help=helps['silent']) parser.add_argument('-c', '--clear', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='clear', default=False, help=helps['clear']) parser.add_argument('-o', '--output-dir', metavar='path', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='output_dir', default='output', help=helps['output_dir']) parser.add_argument('mesh_filename', default='', help=helps['mesh_filename']) options = parser.parse_args() output_dir = options.output_dir output.set_output(filename=os.path.join(output_dir,'output_log.txt'), combined=options.silent == False) if options.conf is not None: mod = import_file(options.conf) else: mod = sys.modules[__name__] apply_units = mod.apply_units define = mod.define set_wave_dir = mod.set_wave_dir setup_n_eigs = mod.setup_n_eigs build_evp_matrices = mod.build_evp_matrices save_materials = mod.save_materials get_std_wave_fun = mod.get_std_wave_fun get_stepper = mod.get_stepper process_evp_results = mod.process_evp_results options.pars = [float(ii) for ii in options.pars.split(',')] options.unit_multipliers = [float(ii) for ii in options.unit_multipliers.split(',')] options.wave_dir = [float(ii) for ii in options.wave_dir.split(',')] aux = options.range.split(',') options.range = [float(aux[0]), float(aux[1]), int(aux[2])] options.solver_conf = dict_from_string(options.solver_conf) options.define_kwargs =	dict_from_string(options.define_kwargs)	sfepy.base.conf.dict_from_string
#!/usr/bin/env python """ Dispersion analysis of a heterogeneous finite scale periodic cell. The periodic cell mesh has to contain two subdomains Y1 (with the cell ids 1), Y2 (with the cell ids 2), so that different material properties can be defined in each of the subdomains (see ``--pars`` option). The command line parameters can be given in any consistent unit set, for example the basic SI units. The ``--unit-multipliers`` option can be used to rescale the input units to ones more suitable to the simulation, for example to prevent having different matrix blocks with large differences of matrix entries magnitudes. The results are then in the rescaled units. Usage Examples -------------- Default material parameters, a square periodic cell with a spherical inclusion, logs also standard pressure dilatation and shear waves, no eigenvectors:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only As above, with custom eigenvalue solver parameters, and different number of eigenvalues, mesh size and units used in the calculation:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --solver-conf="kind='eig.scipy', method='eigsh', tol=1e-10, maxiter=1000, which='LM', sigma=0" --log-std-waves -n 5 --range=0,640,101 --mode=omega --unit-multipliers=1e-6,1e-2,1e-3 --mesh-size=1e-2 --eigs-only Default material parameters, a square periodic cell with a square inclusion, and a very small mesh to allow comparing the omega and kappa modes (full matrix solver required!):: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.qevp', method='companion', mode='inverted', solver={kind='eig.scipy', method='eig'}" --log-std-waves -n 500 --range=0,4000000,1001 --mesh-size=1e-2 --mode=kappa --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/kappa View/compare the resulting logs:: python script/plot_logs.py output/omega/frequencies.txt --no-legends -g 1 -o mode-omega.png python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends -o mode-kappa.png python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends --swap-axes -o mode-kappa-t.png In contrast to the heterogeneous square periodic cell, a homogeneous square periodic cell (the region Y2 is empty):: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_1m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega-h python script/plot_logs.py output/omega-h/frequencies.txt --no-legends -g 1 -o mode-omega-h.png Use the Brillouin stepper:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves -n=60 --eigs-only --no-legends --stepper=brillouin python script/plot_logs.py output/frequencies.txt -g 0 --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-kappas.png python script/plot_logs.py output/frequencies.txt -g 1 --no-legends --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-omegas.png Additional arguments can be passed to the problem configuration's :func:`define()` function using the ``--define-kwargs`` option. In this file, only the mesh vertex separation parameter `mesh_eps` can be used:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only --define-kwargs="mesh_eps=1e-10" --save-regions """ from __future__ import absolute_import import os import sys sys.path.append('.') import gc from copy import copy from argparse import ArgumentParser, RawDescriptionHelpFormatter import numpy as nm import matplotlib.pyplot as plt from sfepy.base.base import import_file, output, Struct from sfepy.base.conf import dict_from_string, ProblemConf from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options from sfepy.base.log import Log from sfepy.discrete.fem import MeshIO from sfepy.mechanics.matcoefs import stiffness_from_youngpoisson as stiffness import sfepy.mechanics.matcoefs as mc from sfepy.mechanics.units import apply_unit_multipliers import sfepy.discrete.fem.periodic as per from sfepy.discrete.fem.meshio import convert_complex_output from sfepy.homogenization.utils import define_box_regions from sfepy.discrete import Problem from sfepy.mechanics.tensors import get_von_mises_stress from sfepy.solvers import Solver from sfepy.solvers.ts import get_print_info, TimeStepper from sfepy.linalg.utils import output_array_stats, max_diff_csr def apply_units(pars, unit_multipliers): new_pars = apply_unit_multipliers(pars, ['stress', 'one', 'density', 'stress', 'one' ,'density'], unit_multipliers) return new_pars def compute_von_mises(out, pb, state, extend=False, wmag=None, wdir=None): """ Calculate the von Mises stress. """ stress = pb.evaluate('ev_cauchy_stress.i.Omega(m.D, u)', mode='el_avg') vms = get_von_mises_stress(stress.squeeze()) vms.shape = (vms.shape[0], 1, 1, 1) out['von_mises_stress'] = Struct(name='output_data', mode='cell', data=vms) return out def define(filename_mesh, pars, approx_order, refinement_level, solver_conf, plane='strain', post_process=False, mesh_eps=1e-8): io = MeshIO.any_from_filename(filename_mesh) bbox = io.read_bounding_box() dim = bbox.shape[1] options = { 'absolute_mesh_path' : True, 'refinement_level' : refinement_level, 'allow_empty_regions' : True, 'post_process_hook' : 'compute_von_mises' if post_process else None, } fields = { 'displacement': ('complex', dim, 'Omega', approx_order), } young1, poisson1, density1, young2, poisson2, density2 = pars materials = { 'm' : ({ 'D' : {'Y1' : stiffness(dim, young=young1, poisson=poisson1, plane=plane), 'Y2' : stiffness(dim, young=young2, poisson=poisson2, plane=plane)}, 'density' : {'Y1' : density1, 'Y2' : density2}, },), 'wave' : 'get_wdir', } variables = { 'u' : ('unknown field', 'displacement', 0), 'v' : ('test field', 'displacement', 'u'), } regions = { 'Omega' : 'all', 'Y1': 'cells of group 1', 'Y2': 'cells of group 2', } regions.update(define_box_regions(dim, bbox[0], bbox[1], mesh_eps)) ebcs = { } if dim == 3: epbcs = { 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'}, 'match_x_plane'), 'periodic_y' : (['Near', 'Far'], {'u.all' : 'u.all'}, 'match_y_plane'), 'periodic_z' : (['Top', 'Bottom'], {'u.all' : 'u.all'}, 'match_z_plane'), } else: epbcs = { 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'}, 'match_y_line'), 'periodic_y' : (['Bottom', 'Top'], {'u.all' : 'u.all'}, 'match_x_line'), } per.set_accuracy(mesh_eps) functions = { 'match_x_plane' : (per.match_x_plane,), 'match_y_plane' : (per.match_y_plane,), 'match_z_plane' : (per.match_z_plane,), 'match_x_line' : (per.match_x_line,), 'match_y_line' : (per.match_y_line,), 'get_wdir' : (get_wdir,), } integrals = { 'i' : 2 * approx_order, } equations = { 'K' : 'dw_lin_elastic.i.Omega(m.D, v, u)', 'S' : 'dw_elastic_wave.i.Omega(m.D, wave.vec, v, u)', 'R' : """1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, u, v) - 1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, v, u)""", 'M' : 'dw_volume_dot.i.Omega(m.density, v, u)', } solver_0 = solver_conf.copy() solver_0['name'] = 'eig' return locals() def get_wdir(ts, coors, mode=None, equations=None, term=None, problem=None, wdir=None, **kwargs): if mode == 'special': return {'vec' : wdir} def set_wave_dir(pb, wdir): materials = pb.get_materials() wave_mat = materials['wave'] wave_mat.set_extra_args(wdir=wdir) def save_materials(output_dir, pb, options): stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)', mode='el_avg', copy_materials=False, verbose=False) young, poisson = mc.youngpoisson_from_stiffness(stiffness, plane=options.plane) density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)', mode='el_avg', copy_materials=False, verbose=False) out = {} out['young'] = Struct(name='young', mode='cell', data=young[..., None, None]) out['poisson'] = Struct(name='poisson', mode='cell', data=poisson[..., None, None]) out['density'] = Struct(name='density', mode='cell', data=density) materials_filename = os.path.join(output_dir, 'materials.vtk') pb.save_state(materials_filename, out=out) def get_std_wave_fun(pb, options): stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)', mode='el_avg', copy_materials=False, verbose=False) young, poisson = mc.youngpoisson_from_stiffness(stiffness, plane=options.plane) density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)', mode='el_avg', copy_materials=False, verbose=False) lam, mu = mc.lame_from_youngpoisson(young, poisson, plane=options.plane) alam = nm.average(lam) amu = nm.average(mu) adensity = nm.average(density) cp = nm.sqrt((alam + 2.0 * amu) / adensity) cs = nm.sqrt(amu / adensity) output('average p-wave speed:', cp) output('average shear wave speed:', cs) log_names = [r'$\omega_p$', r'$\omega_s$'] log_plot_kwargs = [{'ls' : '--', 'color' : 'k'}, {'ls' : '--', 'color' : 'gray'}] if options.mode == 'omega': fun = lambda wmag, wdir: (cp * wmag, cs * wmag) else: fun = lambda wmag, wdir: (wmag / cp, wmag / cs) return fun, log_names, log_plot_kwargs def get_stepper(rng, pb, options): if options.stepper == 'linear': stepper = TimeStepper(rng[0], rng[1], dt=None, n_step=rng[2]) return stepper bbox = pb.domain.mesh.get_bounding_box() bzone = 2.0 * nm.pi / (bbox[1] - bbox[0]) num = rng[2] // 3 class BrillouinStepper(Struct): """ Step over 1. Brillouin zone in xy plane. """ def __init__(self, t0, t1, dt=None, n_step=None, step=None, **kwargs): Struct.__init__(self, t0=t0, t1=t1, dt=dt, n_step=n_step, step=step) self.n_digit, self.format, self.suffix = get_print_info(self.n_step) def __iter__(self): ts = TimeStepper(0, bzone[0], dt=None, n_step=num) for ii, val in ts: yield ii, val, nm.array([1.0, 0.0]) if ii == (num-2): break ts = TimeStepper(0, bzone[1], dt=None, n_step=num) for ii, k1 in ts: wdir = nm.array([bzone[0], k1]) val = nm.linalg.norm(wdir) wdir = wdir / val yield num + ii, val, wdir if ii == (num-2): break wdir = nm.array([bzone[0], bzone[1]]) val = nm.linalg.norm(wdir) wdir = wdir / val ts = TimeStepper(0, 1, dt=None, n_step=num) for ii, _ in ts: yield 2 * num + ii, val * (1.0 - float(ii)/(num-1)), wdir stepper = BrillouinStepper(0, 1, n_step=rng[2]) return stepper def save_eigenvectors(filename, svecs, wmag, wdir, pb): if svecs is None: return variables = pb.get_variables() # Make full eigenvectors (add DOFs fixed by boundary conditions). vecs = nm.empty((variables.di.ptr[-1], svecs.shape[1]), dtype=svecs.dtype) for ii in range(svecs.shape[1]): vecs[:, ii] = variables.make_full_vec(svecs[:, ii]) # Save the eigenvectors. out = {} state = pb.create_state() pp_name = pb.conf.options.get('post_process_hook') pp = getattr(pb.conf.funmod, pp_name if pp_name is not None else '', lambda out, *args, **kwargs: out) for ii in range(svecs.shape[1]): state.set_full(vecs[:, ii]) aux = state.create_output_dict() aux2 = {} pp(aux2, pb, state, wmag=wmag, wdir=wdir) aux.update(convert_complex_output(aux2)) out.update({key + '%03d' % ii : aux[key] for key in aux}) pb.save_state(filename, out=out) def assemble_matrices(define, mod, pars, set_wave_dir, options, wdir=None): """ Assemble the blocks of dispersion eigenvalue problem matrices. """ define_dict = define(filename_mesh=options.mesh_filename, pars=pars, approx_order=options.order, refinement_level=options.refine, solver_conf=options.solver_conf, plane=options.plane, post_process=options.post_process, **options.define_kwargs) conf = ProblemConf.from_dict(define_dict, mod) pb = Problem.from_conf(conf) pb.dispersion_options = options pb.set_output_dir(options.output_dir) dim = pb.domain.shape.dim # Set the normalized wave vector direction to the material(s). if wdir is None: wdir = nm.asarray(options.wave_dir[:dim], dtype=nm.float64) wdir = wdir / nm.linalg.norm(wdir) set_wave_dir(pb, wdir) bbox = pb.domain.mesh.get_bounding_box() size = (bbox[1] - bbox[0]).max() scaling0 = apply_unit_multipliers([1.0], ['length'], options.unit_multipliers)[0] scaling = scaling0 if options.mesh_size is not None: scaling *= options.mesh_size / size output('scaling factor of periodic cell mesh coordinates:', scaling) output('new mesh size with applied unit multipliers:', scaling * size) pb.domain.mesh.coors[:] *= scaling pb.set_mesh_coors(pb.domain.mesh.coors, update_fields=True) bzone = 2.0 * nm.pi / (scaling * size) output('1. Brillouin zone size:', bzone * scaling0) output('1. Brillouin zone size with applied unit multipliers:', bzone) pb.time_update() pb.update_materials() # Assemble the matrices. mtxs = {} for key, eq in pb.equations.iteritems(): mtxs[key] = mtx = pb.mtx_a.copy() mtx = eq.evaluate(mode='weak', dw_mode='matrix', asm_obj=mtx) mtx.eliminate_zeros() output_array_stats(mtx.data, 'nonzeros in %s' % key) output('symmetry checks:') output('%s - %s^T:' % (key, key), max_diff_csr(mtx, mtx.T)) output('%s - %s^H:' % (key, key), max_diff_csr(mtx, mtx.H)) return pb, wdir, bzone, mtxs def setup_n_eigs(options, pb, mtxs): """ Setup the numbers of eigenvalues based on options and numbers of DOFs. """ solver_n_eigs = n_eigs = options.n_eigs n_dof = mtxs['K'].shape[0] if options.mode == 'omega': if options.n_eigs > n_dof: n_eigs = n_dof solver_n_eigs = None else: if options.n_eigs > 2 * n_dof: n_eigs = 2 * n_dof solver_n_eigs = None return solver_n_eigs, n_eigs def build_evp_matrices(mtxs, val, mode, pb): """ Build the matrices of the dispersion eigenvalue problem. """ if mode == 'omega': mtx_a = mtxs['K'] + val**2 * mtxs['S'] + val * mtxs['R'] output('A - A^H:', max_diff_csr(mtx_a, mtx_a.H)) evp_mtxs = (mtx_a, mtxs['M']) else: evp_mtxs = (mtxs['S'], mtxs['R'], mtxs['K'] - val**2 * mtxs['M']) return evp_mtxs def process_evp_results(eigs, svecs, val, wdir, bzone, pb, mtxs, options, std_wave_fun=None): """ Transform eigenvalues to either omegas or kappas, depending on `mode`. Transform eigenvectors, if available, depending on `mode`. Return also the values to log. """ if options.mode == 'omega': omegas = nm.sqrt(eigs) output('eigs, omegas:') for ii, om in enumerate(omegas): output('{:>3}. {: .10e}, {:.10e}'.format(ii, eigs[ii], om)) if options.stepper == 'linear': out = tuple(eigs) + tuple(omegas) else: out = tuple(val * wdir) + tuple(omegas) if std_wave_fun is not None: out = out + std_wave_fun(val, wdir) return omegas, svecs, out else: kappas = eigs.copy() rks = kappas.copy() # Mask modes far from 1. Brillouin zone. max_kappa = 1.2 * bzone kappas[kappas.real > max_kappa] = nm.nan # Mask non-physical modes. kappas[kappas.real < 0] = nm.nan kappas[nm.abs(kappas.imag) > 1e-10] = nm.nan out = tuple(kappas.real) output('raw kappas, masked real part:',) for ii, kr in enumerate(kappas.real): output('{:>3}. {: 23.5e}, {:.10e}'.format(ii, rks[ii], kr)) if svecs is not None: n_dof = mtxs['K'].shape[0] # Select only vectors corresponding to physical modes. ii = nm.isfinite(kappas.real) svecs = svecs[:n_dof, ii] if std_wave_fun is not None: out = out + tuple(ii if ii <= max_kappa else nm.nan for ii in std_wave_fun(val, wdir)) return kappas, svecs, out helps = { 'pars' : 'material parameters in Y1, Y2 subdomains in basic units' ' [default: %(default)s]', 'conf' : 'if given, an alternative problem description file with apply_units() and' ' define() functions [default: %(default)s]', 'define_kwargs' : 'additional keyword arguments passed to define()', 'mesh_size' : 'desired mesh size (max. of bounding box dimensions) in basic units' ' - the input periodic cell mesh is rescaled to this size' ' [default: %(default)s]', 'unit_multipliers' : 'basic unit multipliers (time, length, mass) [default: %(default)s]', 'plane' : 'for 2D problems, plane strain or stress hypothesis selection' ' [default: %(default)s]', 'wave_dir' : 'the wave vector direction (will be normalized)' ' [default: %(default)s]', 'mode' : 'solution mode: omega = solve a generalized EVP for omega,' ' kappa = solve a quadratic generalized EVP for kappa' ' [default: %(default)s]', 'stepper' : 'the range stepper. For "brillouin", only the number' ' of items from --range is used' ' [default: %(default)s]', 'range' : 'the wave vector magnitude / frequency range' ' (like numpy.linspace) depending on the mode option' ' [default: %(default)s]', 'order' : 'displacement field approximation order [default: %(default)s]', 'refine' : 'number of uniform mesh refinements [default: %(default)s]', 'n_eigs' : 'the number of eigenvalues to compute [default: %(default)s]', 'eigs_only' : 'compute only eigenvalues, not eigenvectors', 'post_process' : 'post-process eigenvectors', 'solver_conf' : 'eigenvalue problem solver configuration options' ' [default: %(default)s]', 'save_regions' : 'save defined regions into' ' <output_directory>/regions.vtk', 'save_materials' : 'save material parameters into' ' <output_directory>/materials.vtk', 'log_std_waves' : 'log also standard pressure dilatation and shear waves', 'no_legends' : 'do not show legends in the log plots', 'no_show' : 'do not show the log figure', 'silent' : 'do not print messages to screen', 'clear' : 'clear old solution files from output directory', 'output_dir' : 'output directory [default: %(default)s]', 'mesh_filename' : 'input periodic cell mesh file name [default: %(default)s]', } def main(): # Aluminium and epoxy. default_pars = '70e9,0.35,2.799e3, 3.8e9,0.27,1.142e3' default_solver_conf = ("kind='eig.scipy',method='eigsh',tol=1.0e-5," "maxiter=1000,which='LM',sigma=0.0") parser = ArgumentParser(description=__doc__, formatter_class=RawDescriptionHelpFormatter) parser.add_argument('--pars', metavar='young1,poisson1,density1' ',young2,poisson2,density2', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='pars', default=default_pars, help=helps['pars']) parser.add_argument('--conf', metavar='filename', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='conf', default=None, help=helps['conf']) parser.add_argument('--define-kwargs', metavar='dict-like', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='define_kwargs', default=None, help=helps['define_kwargs']) parser.add_argument('--mesh-size', type=float, metavar='float', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='mesh_size', default=None, help=helps['mesh_size']) parser.add_argument('--unit-multipliers', metavar='c_time,c_length,c_mass', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='unit_multipliers', default='1.0,1.0,1.0', help=helps['unit_multipliers']) parser.add_argument('--plane', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='plane', choices=['strain', 'stress'], default='strain', help=helps['plane']) parser.add_argument('--wave-dir', metavar='float,float[,float]', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='wave_dir', default='1.0,0.0,0.0', help=helps['wave_dir']) parser.add_argument('--mode', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='mode', choices=['omega', 'kappa'], default='omega', help=helps['mode']) parser.add_argument('--stepper', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='stepper', choices=['linear', 'brillouin'], default='linear', help=helps['stepper']) parser.add_argument('--range', metavar='start,stop,count', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='range', default='0,6.4,33', help=helps['range']) parser.add_argument('--order', metavar='int', type=int, action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='order', default=1, help=helps['order']) parser.add_argument('--refine', metavar='int', type=int, action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='refine', default=0, help=helps['refine']) parser.add_argument('-n', '--n-eigs', metavar='int', type=int, action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='n_eigs', default=6, help=helps['n_eigs']) group = parser.add_mutually_exclusive_group() group.add_argument('--eigs-only', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='eigs_only', default=False, help=helps['eigs_only']) group.add_argument('--post-process', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='post_process', default=False, help=helps['post_process']) parser.add_argument('--solver-conf', metavar='dict-like', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='solver_conf', default=default_solver_conf, help=helps['solver_conf']) parser.add_argument('--save-regions', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='save_regions', default=False, help=helps['save_regions']) parser.add_argument('--save-materials', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='save_materials', default=False, help=helps['save_materials']) parser.add_argument('--log-std-waves', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='log_std_waves', default=False, help=helps['log_std_waves']) parser.add_argument('--no-legends', action="https://huggingface.co/datasets/luna-code/sfepy/store_false", dest='show_legends', default=True, help=helps['no_legends']) parser.add_argument('--no-show', action="https://huggingface.co/datasets/luna-code/sfepy/store_false", dest='show', default=True, help=helps['no_show']) parser.add_argument('--silent', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='silent', default=False, help=helps['silent']) parser.add_argument('-c', '--clear', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='clear', default=False, help=helps['clear']) parser.add_argument('-o', '--output-dir', metavar='path', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='output_dir', default='output', help=helps['output_dir']) parser.add_argument('mesh_filename', default='', help=helps['mesh_filename']) options = parser.parse_args() output_dir = options.output_dir output.set_output(filename=os.path.join(output_dir,'output_log.txt'), combined=options.silent == False) if options.conf is not None: mod = import_file(options.conf) else: mod = sys.modules[__name__] apply_units = mod.apply_units define = mod.define set_wave_dir = mod.set_wave_dir setup_n_eigs = mod.setup_n_eigs build_evp_matrices = mod.build_evp_matrices save_materials = mod.save_materials get_std_wave_fun = mod.get_std_wave_fun get_stepper = mod.get_stepper process_evp_results = mod.process_evp_results options.pars = [float(ii) for ii in options.pars.split(',')] options.unit_multipliers = [float(ii) for ii in options.unit_multipliers.split(',')] options.wave_dir = [float(ii) for ii in options.wave_dir.split(',')] aux = options.range.split(',') options.range = [float(aux[0]), float(aux[1]), int(aux[2])] options.solver_conf = dict_from_string(options.solver_conf) options.define_kwargs = dict_from_string(options.define_kwargs) if options.clear: remove_files_patterns(output_dir, ['*.h5', '*.vtk', '*.txt'], ignores=['output_log.txt'], verbose=True) filename = os.path.join(output_dir, 'options.txt')	ensure_path(filename)	sfepy.base.ioutils.ensure_path
#!/usr/bin/env python """ Dispersion analysis of a heterogeneous finite scale periodic cell. The periodic cell mesh has to contain two subdomains Y1 (with the cell ids 1), Y2 (with the cell ids 2), so that different material properties can be defined in each of the subdomains (see ``--pars`` option). The command line parameters can be given in any consistent unit set, for example the basic SI units. The ``--unit-multipliers`` option can be used to rescale the input units to ones more suitable to the simulation, for example to prevent having different matrix blocks with large differences of matrix entries magnitudes. The results are then in the rescaled units. Usage Examples -------------- Default material parameters, a square periodic cell with a spherical inclusion, logs also standard pressure dilatation and shear waves, no eigenvectors:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only As above, with custom eigenvalue solver parameters, and different number of eigenvalues, mesh size and units used in the calculation:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --solver-conf="kind='eig.scipy', method='eigsh', tol=1e-10, maxiter=1000, which='LM', sigma=0" --log-std-waves -n 5 --range=0,640,101 --mode=omega --unit-multipliers=1e-6,1e-2,1e-3 --mesh-size=1e-2 --eigs-only Default material parameters, a square periodic cell with a square inclusion, and a very small mesh to allow comparing the omega and kappa modes (full matrix solver required!):: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.qevp', method='companion', mode='inverted', solver={kind='eig.scipy', method='eig'}" --log-std-waves -n 500 --range=0,4000000,1001 --mesh-size=1e-2 --mode=kappa --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/kappa View/compare the resulting logs:: python script/plot_logs.py output/omega/frequencies.txt --no-legends -g 1 -o mode-omega.png python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends -o mode-kappa.png python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends --swap-axes -o mode-kappa-t.png In contrast to the heterogeneous square periodic cell, a homogeneous square periodic cell (the region Y2 is empty):: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_1m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega-h python script/plot_logs.py output/omega-h/frequencies.txt --no-legends -g 1 -o mode-omega-h.png Use the Brillouin stepper:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves -n=60 --eigs-only --no-legends --stepper=brillouin python script/plot_logs.py output/frequencies.txt -g 0 --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-kappas.png python script/plot_logs.py output/frequencies.txt -g 1 --no-legends --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-omegas.png Additional arguments can be passed to the problem configuration's :func:`define()` function using the ``--define-kwargs`` option. In this file, only the mesh vertex separation parameter `mesh_eps` can be used:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only --define-kwargs="mesh_eps=1e-10" --save-regions """ from __future__ import absolute_import import os import sys sys.path.append('.') import gc from copy import copy from argparse import ArgumentParser, RawDescriptionHelpFormatter import numpy as nm import matplotlib.pyplot as plt from sfepy.base.base import import_file, output, Struct from sfepy.base.conf import dict_from_string, ProblemConf from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options from sfepy.base.log import Log from sfepy.discrete.fem import MeshIO from sfepy.mechanics.matcoefs import stiffness_from_youngpoisson as stiffness import sfepy.mechanics.matcoefs as mc from sfepy.mechanics.units import apply_unit_multipliers import sfepy.discrete.fem.periodic as per from sfepy.discrete.fem.meshio import convert_complex_output from sfepy.homogenization.utils import define_box_regions from sfepy.discrete import Problem from sfepy.mechanics.tensors import get_von_mises_stress from sfepy.solvers import Solver from sfepy.solvers.ts import get_print_info, TimeStepper from sfepy.linalg.utils import output_array_stats, max_diff_csr def apply_units(pars, unit_multipliers): new_pars = apply_unit_multipliers(pars, ['stress', 'one', 'density', 'stress', 'one' ,'density'], unit_multipliers) return new_pars def compute_von_mises(out, pb, state, extend=False, wmag=None, wdir=None): """ Calculate the von Mises stress. """ stress = pb.evaluate('ev_cauchy_stress.i.Omega(m.D, u)', mode='el_avg') vms = get_von_mises_stress(stress.squeeze()) vms.shape = (vms.shape[0], 1, 1, 1) out['von_mises_stress'] = Struct(name='output_data', mode='cell', data=vms) return out def define(filename_mesh, pars, approx_order, refinement_level, solver_conf, plane='strain', post_process=False, mesh_eps=1e-8): io = MeshIO.any_from_filename(filename_mesh) bbox = io.read_bounding_box() dim = bbox.shape[1] options = { 'absolute_mesh_path' : True, 'refinement_level' : refinement_level, 'allow_empty_regions' : True, 'post_process_hook' : 'compute_von_mises' if post_process else None, } fields = { 'displacement': ('complex', dim, 'Omega', approx_order), } young1, poisson1, density1, young2, poisson2, density2 = pars materials = { 'm' : ({ 'D' : {'Y1' : stiffness(dim, young=young1, poisson=poisson1, plane=plane), 'Y2' : stiffness(dim, young=young2, poisson=poisson2, plane=plane)}, 'density' : {'Y1' : density1, 'Y2' : density2}, },), 'wave' : 'get_wdir', } variables = { 'u' : ('unknown field', 'displacement', 0), 'v' : ('test field', 'displacement', 'u'), } regions = { 'Omega' : 'all', 'Y1': 'cells of group 1', 'Y2': 'cells of group 2', } regions.update(define_box_regions(dim, bbox[0], bbox[1], mesh_eps)) ebcs = { } if dim == 3: epbcs = { 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'}, 'match_x_plane'), 'periodic_y' : (['Near', 'Far'], {'u.all' : 'u.all'}, 'match_y_plane'), 'periodic_z' : (['Top', 'Bottom'], {'u.all' : 'u.all'}, 'match_z_plane'), } else: epbcs = { 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'}, 'match_y_line'), 'periodic_y' : (['Bottom', 'Top'], {'u.all' : 'u.all'}, 'match_x_line'), } per.set_accuracy(mesh_eps) functions = { 'match_x_plane' : (per.match_x_plane,), 'match_y_plane' : (per.match_y_plane,), 'match_z_plane' : (per.match_z_plane,), 'match_x_line' : (per.match_x_line,), 'match_y_line' : (per.match_y_line,), 'get_wdir' : (get_wdir,), } integrals = { 'i' : 2 * approx_order, } equations = { 'K' : 'dw_lin_elastic.i.Omega(m.D, v, u)', 'S' : 'dw_elastic_wave.i.Omega(m.D, wave.vec, v, u)', 'R' : """1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, u, v) - 1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, v, u)""", 'M' : 'dw_volume_dot.i.Omega(m.density, v, u)', } solver_0 = solver_conf.copy() solver_0['name'] = 'eig' return locals() def get_wdir(ts, coors, mode=None, equations=None, term=None, problem=None, wdir=None, **kwargs): if mode == 'special': return {'vec' : wdir} def set_wave_dir(pb, wdir): materials = pb.get_materials() wave_mat = materials['wave'] wave_mat.set_extra_args(wdir=wdir) def save_materials(output_dir, pb, options): stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)', mode='el_avg', copy_materials=False, verbose=False) young, poisson = mc.youngpoisson_from_stiffness(stiffness, plane=options.plane) density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)', mode='el_avg', copy_materials=False, verbose=False) out = {} out['young'] = Struct(name='young', mode='cell', data=young[..., None, None]) out['poisson'] = Struct(name='poisson', mode='cell', data=poisson[..., None, None]) out['density'] = Struct(name='density', mode='cell', data=density) materials_filename = os.path.join(output_dir, 'materials.vtk') pb.save_state(materials_filename, out=out) def get_std_wave_fun(pb, options): stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)', mode='el_avg', copy_materials=False, verbose=False) young, poisson = mc.youngpoisson_from_stiffness(stiffness, plane=options.plane) density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)', mode='el_avg', copy_materials=False, verbose=False) lam, mu = mc.lame_from_youngpoisson(young, poisson, plane=options.plane) alam = nm.average(lam) amu = nm.average(mu) adensity = nm.average(density) cp = nm.sqrt((alam + 2.0 * amu) / adensity) cs = nm.sqrt(amu / adensity) output('average p-wave speed:', cp) output('average shear wave speed:', cs) log_names = [r'$\omega_p$', r'$\omega_s$'] log_plot_kwargs = [{'ls' : '--', 'color' : 'k'}, {'ls' : '--', 'color' : 'gray'}] if options.mode == 'omega': fun = lambda wmag, wdir: (cp * wmag, cs * wmag) else: fun = lambda wmag, wdir: (wmag / cp, wmag / cs) return fun, log_names, log_plot_kwargs def get_stepper(rng, pb, options): if options.stepper == 'linear': stepper = TimeStepper(rng[0], rng[1], dt=None, n_step=rng[2]) return stepper bbox = pb.domain.mesh.get_bounding_box() bzone = 2.0 * nm.pi / (bbox[1] - bbox[0]) num = rng[2] // 3 class BrillouinStepper(Struct): """ Step over 1. Brillouin zone in xy plane. """ def __init__(self, t0, t1, dt=None, n_step=None, step=None, **kwargs): Struct.__init__(self, t0=t0, t1=t1, dt=dt, n_step=n_step, step=step) self.n_digit, self.format, self.suffix = get_print_info(self.n_step) def __iter__(self): ts = TimeStepper(0, bzone[0], dt=None, n_step=num) for ii, val in ts: yield ii, val, nm.array([1.0, 0.0]) if ii == (num-2): break ts = TimeStepper(0, bzone[1], dt=None, n_step=num) for ii, k1 in ts: wdir = nm.array([bzone[0], k1]) val = nm.linalg.norm(wdir) wdir = wdir / val yield num + ii, val, wdir if ii == (num-2): break wdir = nm.array([bzone[0], bzone[1]]) val = nm.linalg.norm(wdir) wdir = wdir / val ts = TimeStepper(0, 1, dt=None, n_step=num) for ii, _ in ts: yield 2 * num + ii, val * (1.0 - float(ii)/(num-1)), wdir stepper = BrillouinStepper(0, 1, n_step=rng[2]) return stepper def save_eigenvectors(filename, svecs, wmag, wdir, pb): if svecs is None: return variables = pb.get_variables() # Make full eigenvectors (add DOFs fixed by boundary conditions). vecs = nm.empty((variables.di.ptr[-1], svecs.shape[1]), dtype=svecs.dtype) for ii in range(svecs.shape[1]): vecs[:, ii] = variables.make_full_vec(svecs[:, ii]) # Save the eigenvectors. out = {} state = pb.create_state() pp_name = pb.conf.options.get('post_process_hook') pp = getattr(pb.conf.funmod, pp_name if pp_name is not None else '', lambda out, *args, **kwargs: out) for ii in range(svecs.shape[1]): state.set_full(vecs[:, ii]) aux = state.create_output_dict() aux2 = {} pp(aux2, pb, state, wmag=wmag, wdir=wdir) aux.update(convert_complex_output(aux2)) out.update({key + '%03d' % ii : aux[key] for key in aux}) pb.save_state(filename, out=out) def assemble_matrices(define, mod, pars, set_wave_dir, options, wdir=None): """ Assemble the blocks of dispersion eigenvalue problem matrices. """ define_dict = define(filename_mesh=options.mesh_filename, pars=pars, approx_order=options.order, refinement_level=options.refine, solver_conf=options.solver_conf, plane=options.plane, post_process=options.post_process, **options.define_kwargs) conf = ProblemConf.from_dict(define_dict, mod) pb = Problem.from_conf(conf) pb.dispersion_options = options pb.set_output_dir(options.output_dir) dim = pb.domain.shape.dim # Set the normalized wave vector direction to the material(s). if wdir is None: wdir = nm.asarray(options.wave_dir[:dim], dtype=nm.float64) wdir = wdir / nm.linalg.norm(wdir) set_wave_dir(pb, wdir) bbox = pb.domain.mesh.get_bounding_box() size = (bbox[1] - bbox[0]).max() scaling0 = apply_unit_multipliers([1.0], ['length'], options.unit_multipliers)[0] scaling = scaling0 if options.mesh_size is not None: scaling *= options.mesh_size / size output('scaling factor of periodic cell mesh coordinates:', scaling) output('new mesh size with applied unit multipliers:', scaling * size) pb.domain.mesh.coors[:] *= scaling pb.set_mesh_coors(pb.domain.mesh.coors, update_fields=True) bzone = 2.0 * nm.pi / (scaling * size) output('1. Brillouin zone size:', bzone * scaling0) output('1. Brillouin zone size with applied unit multipliers:', bzone) pb.time_update() pb.update_materials() # Assemble the matrices. mtxs = {} for key, eq in pb.equations.iteritems(): mtxs[key] = mtx = pb.mtx_a.copy() mtx = eq.evaluate(mode='weak', dw_mode='matrix', asm_obj=mtx) mtx.eliminate_zeros() output_array_stats(mtx.data, 'nonzeros in %s' % key) output('symmetry checks:') output('%s - %s^T:' % (key, key), max_diff_csr(mtx, mtx.T)) output('%s - %s^H:' % (key, key), max_diff_csr(mtx, mtx.H)) return pb, wdir, bzone, mtxs def setup_n_eigs(options, pb, mtxs): """ Setup the numbers of eigenvalues based on options and numbers of DOFs. """ solver_n_eigs = n_eigs = options.n_eigs n_dof = mtxs['K'].shape[0] if options.mode == 'omega': if options.n_eigs > n_dof: n_eigs = n_dof solver_n_eigs = None else: if options.n_eigs > 2 * n_dof: n_eigs = 2 * n_dof solver_n_eigs = None return solver_n_eigs, n_eigs def build_evp_matrices(mtxs, val, mode, pb): """ Build the matrices of the dispersion eigenvalue problem. """ if mode == 'omega': mtx_a = mtxs['K'] + val**2 * mtxs['S'] + val * mtxs['R'] output('A - A^H:', max_diff_csr(mtx_a, mtx_a.H)) evp_mtxs = (mtx_a, mtxs['M']) else: evp_mtxs = (mtxs['S'], mtxs['R'], mtxs['K'] - val**2 * mtxs['M']) return evp_mtxs def process_evp_results(eigs, svecs, val, wdir, bzone, pb, mtxs, options, std_wave_fun=None): """ Transform eigenvalues to either omegas or kappas, depending on `mode`. Transform eigenvectors, if available, depending on `mode`. Return also the values to log. """ if options.mode == 'omega': omegas = nm.sqrt(eigs) output('eigs, omegas:') for ii, om in enumerate(omegas): output('{:>3}. {: .10e}, {:.10e}'.format(ii, eigs[ii], om)) if options.stepper == 'linear': out = tuple(eigs) + tuple(omegas) else: out = tuple(val * wdir) + tuple(omegas) if std_wave_fun is not None: out = out + std_wave_fun(val, wdir) return omegas, svecs, out else: kappas = eigs.copy() rks = kappas.copy() # Mask modes far from 1. Brillouin zone. max_kappa = 1.2 * bzone kappas[kappas.real > max_kappa] = nm.nan # Mask non-physical modes. kappas[kappas.real < 0] = nm.nan kappas[nm.abs(kappas.imag) > 1e-10] = nm.nan out = tuple(kappas.real) output('raw kappas, masked real part:',) for ii, kr in enumerate(kappas.real): output('{:>3}. {: 23.5e}, {:.10e}'.format(ii, rks[ii], kr)) if svecs is not None: n_dof = mtxs['K'].shape[0] # Select only vectors corresponding to physical modes. ii = nm.isfinite(kappas.real) svecs = svecs[:n_dof, ii] if std_wave_fun is not None: out = out + tuple(ii if ii <= max_kappa else nm.nan for ii in std_wave_fun(val, wdir)) return kappas, svecs, out helps = { 'pars' : 'material parameters in Y1, Y2 subdomains in basic units' ' [default: %(default)s]', 'conf' : 'if given, an alternative problem description file with apply_units() and' ' define() functions [default: %(default)s]', 'define_kwargs' : 'additional keyword arguments passed to define()', 'mesh_size' : 'desired mesh size (max. of bounding box dimensions) in basic units' ' - the input periodic cell mesh is rescaled to this size' ' [default: %(default)s]', 'unit_multipliers' : 'basic unit multipliers (time, length, mass) [default: %(default)s]', 'plane' : 'for 2D problems, plane strain or stress hypothesis selection' ' [default: %(default)s]', 'wave_dir' : 'the wave vector direction (will be normalized)' ' [default: %(default)s]', 'mode' : 'solution mode: omega = solve a generalized EVP for omega,' ' kappa = solve a quadratic generalized EVP for kappa' ' [default: %(default)s]', 'stepper' : 'the range stepper. For "brillouin", only the number' ' of items from --range is used' ' [default: %(default)s]', 'range' : 'the wave vector magnitude / frequency range' ' (like numpy.linspace) depending on the mode option' ' [default: %(default)s]', 'order' : 'displacement field approximation order [default: %(default)s]', 'refine' : 'number of uniform mesh refinements [default: %(default)s]', 'n_eigs' : 'the number of eigenvalues to compute [default: %(default)s]', 'eigs_only' : 'compute only eigenvalues, not eigenvectors', 'post_process' : 'post-process eigenvectors', 'solver_conf' : 'eigenvalue problem solver configuration options' ' [default: %(default)s]', 'save_regions' : 'save defined regions into' ' <output_directory>/regions.vtk', 'save_materials' : 'save material parameters into' ' <output_directory>/materials.vtk', 'log_std_waves' : 'log also standard pressure dilatation and shear waves', 'no_legends' : 'do not show legends in the log plots', 'no_show' : 'do not show the log figure', 'silent' : 'do not print messages to screen', 'clear' : 'clear old solution files from output directory', 'output_dir' : 'output directory [default: %(default)s]', 'mesh_filename' : 'input periodic cell mesh file name [default: %(default)s]', } def main(): # Aluminium and epoxy. default_pars = '70e9,0.35,2.799e3, 3.8e9,0.27,1.142e3' default_solver_conf = ("kind='eig.scipy',method='eigsh',tol=1.0e-5," "maxiter=1000,which='LM',sigma=0.0") parser = ArgumentParser(description=__doc__, formatter_class=RawDescriptionHelpFormatter) parser.add_argument('--pars', metavar='young1,poisson1,density1' ',young2,poisson2,density2', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='pars', default=default_pars, help=helps['pars']) parser.add_argument('--conf', metavar='filename', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='conf', default=None, help=helps['conf']) parser.add_argument('--define-kwargs', metavar='dict-like', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='define_kwargs', default=None, help=helps['define_kwargs']) parser.add_argument('--mesh-size', type=float, metavar='float', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='mesh_size', default=None, help=helps['mesh_size']) parser.add_argument('--unit-multipliers', metavar='c_time,c_length,c_mass', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='unit_multipliers', default='1.0,1.0,1.0', help=helps['unit_multipliers']) parser.add_argument('--plane', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='plane', choices=['strain', 'stress'], default='strain', help=helps['plane']) parser.add_argument('--wave-dir', metavar='float,float[,float]', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='wave_dir', default='1.0,0.0,0.0', help=helps['wave_dir']) parser.add_argument('--mode', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='mode', choices=['omega', 'kappa'], default='omega', help=helps['mode']) parser.add_argument('--stepper', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='stepper', choices=['linear', 'brillouin'], default='linear', help=helps['stepper']) parser.add_argument('--range', metavar='start,stop,count', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='range', default='0,6.4,33', help=helps['range']) parser.add_argument('--order', metavar='int', type=int, action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='order', default=1, help=helps['order']) parser.add_argument('--refine', metavar='int', type=int, action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='refine', default=0, help=helps['refine']) parser.add_argument('-n', '--n-eigs', metavar='int', type=int, action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='n_eigs', default=6, help=helps['n_eigs']) group = parser.add_mutually_exclusive_group() group.add_argument('--eigs-only', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='eigs_only', default=False, help=helps['eigs_only']) group.add_argument('--post-process', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='post_process', default=False, help=helps['post_process']) parser.add_argument('--solver-conf', metavar='dict-like', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='solver_conf', default=default_solver_conf, help=helps['solver_conf']) parser.add_argument('--save-regions', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='save_regions', default=False, help=helps['save_regions']) parser.add_argument('--save-materials', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='save_materials', default=False, help=helps['save_materials']) parser.add_argument('--log-std-waves', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='log_std_waves', default=False, help=helps['log_std_waves']) parser.add_argument('--no-legends', action="https://huggingface.co/datasets/luna-code/sfepy/store_false", dest='show_legends', default=True, help=helps['no_legends']) parser.add_argument('--no-show', action="https://huggingface.co/datasets/luna-code/sfepy/store_false", dest='show', default=True, help=helps['no_show']) parser.add_argument('--silent', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='silent', default=False, help=helps['silent']) parser.add_argument('-c', '--clear', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='clear', default=False, help=helps['clear']) parser.add_argument('-o', '--output-dir', metavar='path', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='output_dir', default='output', help=helps['output_dir']) parser.add_argument('mesh_filename', default='', help=helps['mesh_filename']) options = parser.parse_args() output_dir = options.output_dir output.set_output(filename=os.path.join(output_dir,'output_log.txt'), combined=options.silent == False) if options.conf is not None: mod = import_file(options.conf) else: mod = sys.modules[__name__] apply_units = mod.apply_units define = mod.define set_wave_dir = mod.set_wave_dir setup_n_eigs = mod.setup_n_eigs build_evp_matrices = mod.build_evp_matrices save_materials = mod.save_materials get_std_wave_fun = mod.get_std_wave_fun get_stepper = mod.get_stepper process_evp_results = mod.process_evp_results options.pars = [float(ii) for ii in options.pars.split(',')] options.unit_multipliers = [float(ii) for ii in options.unit_multipliers.split(',')] options.wave_dir = [float(ii) for ii in options.wave_dir.split(',')] aux = options.range.split(',') options.range = [float(aux[0]), float(aux[1]), int(aux[2])] options.solver_conf = dict_from_string(options.solver_conf) options.define_kwargs = dict_from_string(options.define_kwargs) if options.clear: remove_files_patterns(output_dir, ['*.h5', '*.vtk', '*.txt'], ignores=['output_log.txt'], verbose=True) filename = os.path.join(output_dir, 'options.txt') ensure_path(filename) save_options(filename, [('options', vars(options))], quote_command_line=True) pars = apply_units(options.pars, options.unit_multipliers)	output('material parameters with applied unit multipliers:')	sfepy.base.base.output
#!/usr/bin/env python """ Dispersion analysis of a heterogeneous finite scale periodic cell. The periodic cell mesh has to contain two subdomains Y1 (with the cell ids 1), Y2 (with the cell ids 2), so that different material properties can be defined in each of the subdomains (see ``--pars`` option). The command line parameters can be given in any consistent unit set, for example the basic SI units. The ``--unit-multipliers`` option can be used to rescale the input units to ones more suitable to the simulation, for example to prevent having different matrix blocks with large differences of matrix entries magnitudes. The results are then in the rescaled units. Usage Examples -------------- Default material parameters, a square periodic cell with a spherical inclusion, logs also standard pressure dilatation and shear waves, no eigenvectors:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only As above, with custom eigenvalue solver parameters, and different number of eigenvalues, mesh size and units used in the calculation:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --solver-conf="kind='eig.scipy', method='eigsh', tol=1e-10, maxiter=1000, which='LM', sigma=0" --log-std-waves -n 5 --range=0,640,101 --mode=omega --unit-multipliers=1e-6,1e-2,1e-3 --mesh-size=1e-2 --eigs-only Default material parameters, a square periodic cell with a square inclusion, and a very small mesh to allow comparing the omega and kappa modes (full matrix solver required!):: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.qevp', method='companion', mode='inverted', solver={kind='eig.scipy', method='eig'}" --log-std-waves -n 500 --range=0,4000000,1001 --mesh-size=1e-2 --mode=kappa --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/kappa View/compare the resulting logs:: python script/plot_logs.py output/omega/frequencies.txt --no-legends -g 1 -o mode-omega.png python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends -o mode-kappa.png python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends --swap-axes -o mode-kappa-t.png In contrast to the heterogeneous square periodic cell, a homogeneous square periodic cell (the region Y2 is empty):: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_1m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega-h python script/plot_logs.py output/omega-h/frequencies.txt --no-legends -g 1 -o mode-omega-h.png Use the Brillouin stepper:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves -n=60 --eigs-only --no-legends --stepper=brillouin python script/plot_logs.py output/frequencies.txt -g 0 --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-kappas.png python script/plot_logs.py output/frequencies.txt -g 1 --no-legends --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-omegas.png Additional arguments can be passed to the problem configuration's :func:`define()` function using the ``--define-kwargs`` option. In this file, only the mesh vertex separation parameter `mesh_eps` can be used:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only --define-kwargs="mesh_eps=1e-10" --save-regions """ from __future__ import absolute_import import os import sys sys.path.append('.') import gc from copy import copy from argparse import ArgumentParser, RawDescriptionHelpFormatter import numpy as nm import matplotlib.pyplot as plt from sfepy.base.base import import_file, output, Struct from sfepy.base.conf import dict_from_string, ProblemConf from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options from sfepy.base.log import Log from sfepy.discrete.fem import MeshIO from sfepy.mechanics.matcoefs import stiffness_from_youngpoisson as stiffness import sfepy.mechanics.matcoefs as mc from sfepy.mechanics.units import apply_unit_multipliers import sfepy.discrete.fem.periodic as per from sfepy.discrete.fem.meshio import convert_complex_output from sfepy.homogenization.utils import define_box_regions from sfepy.discrete import Problem from sfepy.mechanics.tensors import get_von_mises_stress from sfepy.solvers import Solver from sfepy.solvers.ts import get_print_info, TimeStepper from sfepy.linalg.utils import output_array_stats, max_diff_csr def apply_units(pars, unit_multipliers): new_pars = apply_unit_multipliers(pars, ['stress', 'one', 'density', 'stress', 'one' ,'density'], unit_multipliers) return new_pars def compute_von_mises(out, pb, state, extend=False, wmag=None, wdir=None): """ Calculate the von Mises stress. """ stress = pb.evaluate('ev_cauchy_stress.i.Omega(m.D, u)', mode='el_avg') vms = get_von_mises_stress(stress.squeeze()) vms.shape = (vms.shape[0], 1, 1, 1) out['von_mises_stress'] = Struct(name='output_data', mode='cell', data=vms) return out def define(filename_mesh, pars, approx_order, refinement_level, solver_conf, plane='strain', post_process=False, mesh_eps=1e-8): io = MeshIO.any_from_filename(filename_mesh) bbox = io.read_bounding_box() dim = bbox.shape[1] options = { 'absolute_mesh_path' : True, 'refinement_level' : refinement_level, 'allow_empty_regions' : True, 'post_process_hook' : 'compute_von_mises' if post_process else None, } fields = { 'displacement': ('complex', dim, 'Omega', approx_order), } young1, poisson1, density1, young2, poisson2, density2 = pars materials = { 'm' : ({ 'D' : {'Y1' : stiffness(dim, young=young1, poisson=poisson1, plane=plane), 'Y2' : stiffness(dim, young=young2, poisson=poisson2, plane=plane)}, 'density' : {'Y1' : density1, 'Y2' : density2}, },), 'wave' : 'get_wdir', } variables = { 'u' : ('unknown field', 'displacement', 0), 'v' : ('test field', 'displacement', 'u'), } regions = { 'Omega' : 'all', 'Y1': 'cells of group 1', 'Y2': 'cells of group 2', } regions.update(define_box_regions(dim, bbox[0], bbox[1], mesh_eps)) ebcs = { } if dim == 3: epbcs = { 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'}, 'match_x_plane'), 'periodic_y' : (['Near', 'Far'], {'u.all' : 'u.all'}, 'match_y_plane'), 'periodic_z' : (['Top', 'Bottom'], {'u.all' : 'u.all'}, 'match_z_plane'), } else: epbcs = { 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'}, 'match_y_line'), 'periodic_y' : (['Bottom', 'Top'], {'u.all' : 'u.all'}, 'match_x_line'), } per.set_accuracy(mesh_eps) functions = { 'match_x_plane' : (per.match_x_plane,), 'match_y_plane' : (per.match_y_plane,), 'match_z_plane' : (per.match_z_plane,), 'match_x_line' : (per.match_x_line,), 'match_y_line' : (per.match_y_line,), 'get_wdir' : (get_wdir,), } integrals = { 'i' : 2 * approx_order, } equations = { 'K' : 'dw_lin_elastic.i.Omega(m.D, v, u)', 'S' : 'dw_elastic_wave.i.Omega(m.D, wave.vec, v, u)', 'R' : """1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, u, v) - 1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, v, u)""", 'M' : 'dw_volume_dot.i.Omega(m.density, v, u)', } solver_0 = solver_conf.copy() solver_0['name'] = 'eig' return locals() def get_wdir(ts, coors, mode=None, equations=None, term=None, problem=None, wdir=None, **kwargs): if mode == 'special': return {'vec' : wdir} def set_wave_dir(pb, wdir): materials = pb.get_materials() wave_mat = materials['wave'] wave_mat.set_extra_args(wdir=wdir) def save_materials(output_dir, pb, options): stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)', mode='el_avg', copy_materials=False, verbose=False) young, poisson = mc.youngpoisson_from_stiffness(stiffness, plane=options.plane) density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)', mode='el_avg', copy_materials=False, verbose=False) out = {} out['young'] = Struct(name='young', mode='cell', data=young[..., None, None]) out['poisson'] = Struct(name='poisson', mode='cell', data=poisson[..., None, None]) out['density'] = Struct(name='density', mode='cell', data=density) materials_filename = os.path.join(output_dir, 'materials.vtk') pb.save_state(materials_filename, out=out) def get_std_wave_fun(pb, options): stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)', mode='el_avg', copy_materials=False, verbose=False) young, poisson = mc.youngpoisson_from_stiffness(stiffness, plane=options.plane) density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)', mode='el_avg', copy_materials=False, verbose=False) lam, mu = mc.lame_from_youngpoisson(young, poisson, plane=options.plane) alam = nm.average(lam) amu = nm.average(mu) adensity = nm.average(density) cp = nm.sqrt((alam + 2.0 * amu) / adensity) cs = nm.sqrt(amu / adensity) output('average p-wave speed:', cp) output('average shear wave speed:', cs) log_names = [r'$\omega_p$', r'$\omega_s$'] log_plot_kwargs = [{'ls' : '--', 'color' : 'k'}, {'ls' : '--', 'color' : 'gray'}] if options.mode == 'omega': fun = lambda wmag, wdir: (cp * wmag, cs * wmag) else: fun = lambda wmag, wdir: (wmag / cp, wmag / cs) return fun, log_names, log_plot_kwargs def get_stepper(rng, pb, options): if options.stepper == 'linear': stepper = TimeStepper(rng[0], rng[1], dt=None, n_step=rng[2]) return stepper bbox = pb.domain.mesh.get_bounding_box() bzone = 2.0 * nm.pi / (bbox[1] - bbox[0]) num = rng[2] // 3 class BrillouinStepper(Struct): """ Step over 1. Brillouin zone in xy plane. """ def __init__(self, t0, t1, dt=None, n_step=None, step=None, **kwargs): Struct.__init__(self, t0=t0, t1=t1, dt=dt, n_step=n_step, step=step) self.n_digit, self.format, self.suffix = get_print_info(self.n_step) def __iter__(self): ts = TimeStepper(0, bzone[0], dt=None, n_step=num) for ii, val in ts: yield ii, val, nm.array([1.0, 0.0]) if ii == (num-2): break ts = TimeStepper(0, bzone[1], dt=None, n_step=num) for ii, k1 in ts: wdir = nm.array([bzone[0], k1]) val = nm.linalg.norm(wdir) wdir = wdir / val yield num + ii, val, wdir if ii == (num-2): break wdir = nm.array([bzone[0], bzone[1]]) val = nm.linalg.norm(wdir) wdir = wdir / val ts = TimeStepper(0, 1, dt=None, n_step=num) for ii, _ in ts: yield 2 * num + ii, val * (1.0 - float(ii)/(num-1)), wdir stepper = BrillouinStepper(0, 1, n_step=rng[2]) return stepper def save_eigenvectors(filename, svecs, wmag, wdir, pb): if svecs is None: return variables = pb.get_variables() # Make full eigenvectors (add DOFs fixed by boundary conditions). vecs = nm.empty((variables.di.ptr[-1], svecs.shape[1]), dtype=svecs.dtype) for ii in range(svecs.shape[1]): vecs[:, ii] = variables.make_full_vec(svecs[:, ii]) # Save the eigenvectors. out = {} state = pb.create_state() pp_name = pb.conf.options.get('post_process_hook') pp = getattr(pb.conf.funmod, pp_name if pp_name is not None else '', lambda out, *args, **kwargs: out) for ii in range(svecs.shape[1]): state.set_full(vecs[:, ii]) aux = state.create_output_dict() aux2 = {} pp(aux2, pb, state, wmag=wmag, wdir=wdir) aux.update(convert_complex_output(aux2)) out.update({key + '%03d' % ii : aux[key] for key in aux}) pb.save_state(filename, out=out) def assemble_matrices(define, mod, pars, set_wave_dir, options, wdir=None): """ Assemble the blocks of dispersion eigenvalue problem matrices. """ define_dict = define(filename_mesh=options.mesh_filename, pars=pars, approx_order=options.order, refinement_level=options.refine, solver_conf=options.solver_conf, plane=options.plane, post_process=options.post_process, **options.define_kwargs) conf = ProblemConf.from_dict(define_dict, mod) pb = Problem.from_conf(conf) pb.dispersion_options = options pb.set_output_dir(options.output_dir) dim = pb.domain.shape.dim # Set the normalized wave vector direction to the material(s). if wdir is None: wdir = nm.asarray(options.wave_dir[:dim], dtype=nm.float64) wdir = wdir / nm.linalg.norm(wdir) set_wave_dir(pb, wdir) bbox = pb.domain.mesh.get_bounding_box() size = (bbox[1] - bbox[0]).max() scaling0 = apply_unit_multipliers([1.0], ['length'], options.unit_multipliers)[0] scaling = scaling0 if options.mesh_size is not None: scaling *= options.mesh_size / size output('scaling factor of periodic cell mesh coordinates:', scaling) output('new mesh size with applied unit multipliers:', scaling * size) pb.domain.mesh.coors[:] *= scaling pb.set_mesh_coors(pb.domain.mesh.coors, update_fields=True) bzone = 2.0 * nm.pi / (scaling * size) output('1. Brillouin zone size:', bzone * scaling0) output('1. Brillouin zone size with applied unit multipliers:', bzone) pb.time_update() pb.update_materials() # Assemble the matrices. mtxs = {} for key, eq in pb.equations.iteritems(): mtxs[key] = mtx = pb.mtx_a.copy() mtx = eq.evaluate(mode='weak', dw_mode='matrix', asm_obj=mtx) mtx.eliminate_zeros() output_array_stats(mtx.data, 'nonzeros in %s' % key) output('symmetry checks:') output('%s - %s^T:' % (key, key), max_diff_csr(mtx, mtx.T)) output('%s - %s^H:' % (key, key), max_diff_csr(mtx, mtx.H)) return pb, wdir, bzone, mtxs def setup_n_eigs(options, pb, mtxs): """ Setup the numbers of eigenvalues based on options and numbers of DOFs. """ solver_n_eigs = n_eigs = options.n_eigs n_dof = mtxs['K'].shape[0] if options.mode == 'omega': if options.n_eigs > n_dof: n_eigs = n_dof solver_n_eigs = None else: if options.n_eigs > 2 * n_dof: n_eigs = 2 * n_dof solver_n_eigs = None return solver_n_eigs, n_eigs def build_evp_matrices(mtxs, val, mode, pb): """ Build the matrices of the dispersion eigenvalue problem. """ if mode == 'omega': mtx_a = mtxs['K'] + val**2 * mtxs['S'] + val * mtxs['R'] output('A - A^H:', max_diff_csr(mtx_a, mtx_a.H)) evp_mtxs = (mtx_a, mtxs['M']) else: evp_mtxs = (mtxs['S'], mtxs['R'], mtxs['K'] - val**2 * mtxs['M']) return evp_mtxs def process_evp_results(eigs, svecs, val, wdir, bzone, pb, mtxs, options, std_wave_fun=None): """ Transform eigenvalues to either omegas or kappas, depending on `mode`. Transform eigenvectors, if available, depending on `mode`. Return also the values to log. """ if options.mode == 'omega': omegas = nm.sqrt(eigs) output('eigs, omegas:') for ii, om in enumerate(omegas): output('{:>3}. {: .10e}, {:.10e}'.format(ii, eigs[ii], om)) if options.stepper == 'linear': out = tuple(eigs) + tuple(omegas) else: out = tuple(val * wdir) + tuple(omegas) if std_wave_fun is not None: out = out + std_wave_fun(val, wdir) return omegas, svecs, out else: kappas = eigs.copy() rks = kappas.copy() # Mask modes far from 1. Brillouin zone. max_kappa = 1.2 * bzone kappas[kappas.real > max_kappa] = nm.nan # Mask non-physical modes. kappas[kappas.real < 0] = nm.nan kappas[nm.abs(kappas.imag) > 1e-10] = nm.nan out = tuple(kappas.real) output('raw kappas, masked real part:',) for ii, kr in enumerate(kappas.real): output('{:>3}. {: 23.5e}, {:.10e}'.format(ii, rks[ii], kr)) if svecs is not None: n_dof = mtxs['K'].shape[0] # Select only vectors corresponding to physical modes. ii = nm.isfinite(kappas.real) svecs = svecs[:n_dof, ii] if std_wave_fun is not None: out = out + tuple(ii if ii <= max_kappa else nm.nan for ii in std_wave_fun(val, wdir)) return kappas, svecs, out helps = { 'pars' : 'material parameters in Y1, Y2 subdomains in basic units' ' [default: %(default)s]', 'conf' : 'if given, an alternative problem description file with apply_units() and' ' define() functions [default: %(default)s]', 'define_kwargs' : 'additional keyword arguments passed to define()', 'mesh_size' : 'desired mesh size (max. of bounding box dimensions) in basic units' ' - the input periodic cell mesh is rescaled to this size' ' [default: %(default)s]', 'unit_multipliers' : 'basic unit multipliers (time, length, mass) [default: %(default)s]', 'plane' : 'for 2D problems, plane strain or stress hypothesis selection' ' [default: %(default)s]', 'wave_dir' : 'the wave vector direction (will be normalized)' ' [default: %(default)s]', 'mode' : 'solution mode: omega = solve a generalized EVP for omega,' ' kappa = solve a quadratic generalized EVP for kappa' ' [default: %(default)s]', 'stepper' : 'the range stepper. For "brillouin", only the number' ' of items from --range is used' ' [default: %(default)s]', 'range' : 'the wave vector magnitude / frequency range' ' (like numpy.linspace) depending on the mode option' ' [default: %(default)s]', 'order' : 'displacement field approximation order [default: %(default)s]', 'refine' : 'number of uniform mesh refinements [default: %(default)s]', 'n_eigs' : 'the number of eigenvalues to compute [default: %(default)s]', 'eigs_only' : 'compute only eigenvalues, not eigenvectors', 'post_process' : 'post-process eigenvectors', 'solver_conf' : 'eigenvalue problem solver configuration options' ' [default: %(default)s]', 'save_regions' : 'save defined regions into' ' <output_directory>/regions.vtk', 'save_materials' : 'save material parameters into' ' <output_directory>/materials.vtk', 'log_std_waves' : 'log also standard pressure dilatation and shear waves', 'no_legends' : 'do not show legends in the log plots', 'no_show' : 'do not show the log figure', 'silent' : 'do not print messages to screen', 'clear' : 'clear old solution files from output directory', 'output_dir' : 'output directory [default: %(default)s]', 'mesh_filename' : 'input periodic cell mesh file name [default: %(default)s]', } def main(): # Aluminium and epoxy. default_pars = '70e9,0.35,2.799e3, 3.8e9,0.27,1.142e3' default_solver_conf = ("kind='eig.scipy',method='eigsh',tol=1.0e-5," "maxiter=1000,which='LM',sigma=0.0") parser = ArgumentParser(description=__doc__, formatter_class=RawDescriptionHelpFormatter) parser.add_argument('--pars', metavar='young1,poisson1,density1' ',young2,poisson2,density2', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='pars', default=default_pars, help=helps['pars']) parser.add_argument('--conf', metavar='filename', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='conf', default=None, help=helps['conf']) parser.add_argument('--define-kwargs', metavar='dict-like', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='define_kwargs', default=None, help=helps['define_kwargs']) parser.add_argument('--mesh-size', type=float, metavar='float', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='mesh_size', default=None, help=helps['mesh_size']) parser.add_argument('--unit-multipliers', metavar='c_time,c_length,c_mass', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='unit_multipliers', default='1.0,1.0,1.0', help=helps['unit_multipliers']) parser.add_argument('--plane', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='plane', choices=['strain', 'stress'], default='strain', help=helps['plane']) parser.add_argument('--wave-dir', metavar='float,float[,float]', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='wave_dir', default='1.0,0.0,0.0', help=helps['wave_dir']) parser.add_argument('--mode', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='mode', choices=['omega', 'kappa'], default='omega', help=helps['mode']) parser.add_argument('--stepper', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='stepper', choices=['linear', 'brillouin'], default='linear', help=helps['stepper']) parser.add_argument('--range', metavar='start,stop,count', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='range', default='0,6.4,33', help=helps['range']) parser.add_argument('--order', metavar='int', type=int, action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='order', default=1, help=helps['order']) parser.add_argument('--refine', metavar='int', type=int, action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='refine', default=0, help=helps['refine']) parser.add_argument('-n', '--n-eigs', metavar='int', type=int, action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='n_eigs', default=6, help=helps['n_eigs']) group = parser.add_mutually_exclusive_group() group.add_argument('--eigs-only', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='eigs_only', default=False, help=helps['eigs_only']) group.add_argument('--post-process', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='post_process', default=False, help=helps['post_process']) parser.add_argument('--solver-conf', metavar='dict-like', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='solver_conf', default=default_solver_conf, help=helps['solver_conf']) parser.add_argument('--save-regions', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='save_regions', default=False, help=helps['save_regions']) parser.add_argument('--save-materials', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='save_materials', default=False, help=helps['save_materials']) parser.add_argument('--log-std-waves', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='log_std_waves', default=False, help=helps['log_std_waves']) parser.add_argument('--no-legends', action="https://huggingface.co/datasets/luna-code/sfepy/store_false", dest='show_legends', default=True, help=helps['no_legends']) parser.add_argument('--no-show', action="https://huggingface.co/datasets/luna-code/sfepy/store_false", dest='show', default=True, help=helps['no_show']) parser.add_argument('--silent', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='silent', default=False, help=helps['silent']) parser.add_argument('-c', '--clear', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='clear', default=False, help=helps['clear']) parser.add_argument('-o', '--output-dir', metavar='path', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='output_dir', default='output', help=helps['output_dir']) parser.add_argument('mesh_filename', default='', help=helps['mesh_filename']) options = parser.parse_args() output_dir = options.output_dir output.set_output(filename=os.path.join(output_dir,'output_log.txt'), combined=options.silent == False) if options.conf is not None: mod = import_file(options.conf) else: mod = sys.modules[__name__] apply_units = mod.apply_units define = mod.define set_wave_dir = mod.set_wave_dir setup_n_eigs = mod.setup_n_eigs build_evp_matrices = mod.build_evp_matrices save_materials = mod.save_materials get_std_wave_fun = mod.get_std_wave_fun get_stepper = mod.get_stepper process_evp_results = mod.process_evp_results options.pars = [float(ii) for ii in options.pars.split(',')] options.unit_multipliers = [float(ii) for ii in options.unit_multipliers.split(',')] options.wave_dir = [float(ii) for ii in options.wave_dir.split(',')] aux = options.range.split(',') options.range = [float(aux[0]), float(aux[1]), int(aux[2])] options.solver_conf = dict_from_string(options.solver_conf) options.define_kwargs = dict_from_string(options.define_kwargs) if options.clear: remove_files_patterns(output_dir, ['*.h5', '*.vtk', '*.txt'], ignores=['output_log.txt'], verbose=True) filename = os.path.join(output_dir, 'options.txt') ensure_path(filename) save_options(filename, [('options', vars(options))], quote_command_line=True) pars = apply_units(options.pars, options.unit_multipliers) output('material parameters with applied unit multipliers:')	output(pars)	sfepy.base.base.output
#!/usr/bin/env python """ Dispersion analysis of a heterogeneous finite scale periodic cell. The periodic cell mesh has to contain two subdomains Y1 (with the cell ids 1), Y2 (with the cell ids 2), so that different material properties can be defined in each of the subdomains (see ``--pars`` option). The command line parameters can be given in any consistent unit set, for example the basic SI units. The ``--unit-multipliers`` option can be used to rescale the input units to ones more suitable to the simulation, for example to prevent having different matrix blocks with large differences of matrix entries magnitudes. The results are then in the rescaled units. Usage Examples -------------- Default material parameters, a square periodic cell with a spherical inclusion, logs also standard pressure dilatation and shear waves, no eigenvectors:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only As above, with custom eigenvalue solver parameters, and different number of eigenvalues, mesh size and units used in the calculation:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --solver-conf="kind='eig.scipy', method='eigsh', tol=1e-10, maxiter=1000, which='LM', sigma=0" --log-std-waves -n 5 --range=0,640,101 --mode=omega --unit-multipliers=1e-6,1e-2,1e-3 --mesh-size=1e-2 --eigs-only Default material parameters, a square periodic cell with a square inclusion, and a very small mesh to allow comparing the omega and kappa modes (full matrix solver required!):: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.qevp', method='companion', mode='inverted', solver={kind='eig.scipy', method='eig'}" --log-std-waves -n 500 --range=0,4000000,1001 --mesh-size=1e-2 --mode=kappa --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/kappa View/compare the resulting logs:: python script/plot_logs.py output/omega/frequencies.txt --no-legends -g 1 -o mode-omega.png python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends -o mode-kappa.png python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends --swap-axes -o mode-kappa-t.png In contrast to the heterogeneous square periodic cell, a homogeneous square periodic cell (the region Y2 is empty):: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_1m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega-h python script/plot_logs.py output/omega-h/frequencies.txt --no-legends -g 1 -o mode-omega-h.png Use the Brillouin stepper:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves -n=60 --eigs-only --no-legends --stepper=brillouin python script/plot_logs.py output/frequencies.txt -g 0 --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-kappas.png python script/plot_logs.py output/frequencies.txt -g 1 --no-legends --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-omegas.png Additional arguments can be passed to the problem configuration's :func:`define()` function using the ``--define-kwargs`` option. In this file, only the mesh vertex separation parameter `mesh_eps` can be used:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only --define-kwargs="mesh_eps=1e-10" --save-regions """ from __future__ import absolute_import import os import sys sys.path.append('.') import gc from copy import copy from argparse import ArgumentParser, RawDescriptionHelpFormatter import numpy as nm import matplotlib.pyplot as plt from sfepy.base.base import import_file, output, Struct from sfepy.base.conf import dict_from_string, ProblemConf from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options from sfepy.base.log import Log from sfepy.discrete.fem import MeshIO from sfepy.mechanics.matcoefs import stiffness_from_youngpoisson as stiffness import sfepy.mechanics.matcoefs as mc from sfepy.mechanics.units import apply_unit_multipliers import sfepy.discrete.fem.periodic as per from sfepy.discrete.fem.meshio import convert_complex_output from sfepy.homogenization.utils import define_box_regions from sfepy.discrete import Problem from sfepy.mechanics.tensors import get_von_mises_stress from sfepy.solvers import Solver from sfepy.solvers.ts import get_print_info, TimeStepper from sfepy.linalg.utils import output_array_stats, max_diff_csr def apply_units(pars, unit_multipliers): new_pars = apply_unit_multipliers(pars, ['stress', 'one', 'density', 'stress', 'one' ,'density'], unit_multipliers) return new_pars def compute_von_mises(out, pb, state, extend=False, wmag=None, wdir=None): """ Calculate the von Mises stress. """ stress = pb.evaluate('ev_cauchy_stress.i.Omega(m.D, u)', mode='el_avg') vms = get_von_mises_stress(stress.squeeze()) vms.shape = (vms.shape[0], 1, 1, 1) out['von_mises_stress'] = Struct(name='output_data', mode='cell', data=vms) return out def define(filename_mesh, pars, approx_order, refinement_level, solver_conf, plane='strain', post_process=False, mesh_eps=1e-8): io = MeshIO.any_from_filename(filename_mesh) bbox = io.read_bounding_box() dim = bbox.shape[1] options = { 'absolute_mesh_path' : True, 'refinement_level' : refinement_level, 'allow_empty_regions' : True, 'post_process_hook' : 'compute_von_mises' if post_process else None, } fields = { 'displacement': ('complex', dim, 'Omega', approx_order), } young1, poisson1, density1, young2, poisson2, density2 = pars materials = { 'm' : ({ 'D' : {'Y1' : stiffness(dim, young=young1, poisson=poisson1, plane=plane), 'Y2' : stiffness(dim, young=young2, poisson=poisson2, plane=plane)}, 'density' : {'Y1' : density1, 'Y2' : density2}, },), 'wave' : 'get_wdir', } variables = { 'u' : ('unknown field', 'displacement', 0), 'v' : ('test field', 'displacement', 'u'), } regions = { 'Omega' : 'all', 'Y1': 'cells of group 1', 'Y2': 'cells of group 2', } regions.update(define_box_regions(dim, bbox[0], bbox[1], mesh_eps)) ebcs = { } if dim == 3: epbcs = { 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'}, 'match_x_plane'), 'periodic_y' : (['Near', 'Far'], {'u.all' : 'u.all'}, 'match_y_plane'), 'periodic_z' : (['Top', 'Bottom'], {'u.all' : 'u.all'}, 'match_z_plane'), } else: epbcs = { 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'}, 'match_y_line'), 'periodic_y' : (['Bottom', 'Top'], {'u.all' : 'u.all'}, 'match_x_line'), } per.set_accuracy(mesh_eps) functions = { 'match_x_plane' : (per.match_x_plane,), 'match_y_plane' : (per.match_y_plane,), 'match_z_plane' : (per.match_z_plane,), 'match_x_line' : (per.match_x_line,), 'match_y_line' : (per.match_y_line,), 'get_wdir' : (get_wdir,), } integrals = { 'i' : 2 * approx_order, } equations = { 'K' : 'dw_lin_elastic.i.Omega(m.D, v, u)', 'S' : 'dw_elastic_wave.i.Omega(m.D, wave.vec, v, u)', 'R' : """1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, u, v) - 1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, v, u)""", 'M' : 'dw_volume_dot.i.Omega(m.density, v, u)', } solver_0 = solver_conf.copy() solver_0['name'] = 'eig' return locals() def get_wdir(ts, coors, mode=None, equations=None, term=None, problem=None, wdir=None, **kwargs): if mode == 'special': return {'vec' : wdir} def set_wave_dir(pb, wdir): materials = pb.get_materials() wave_mat = materials['wave'] wave_mat.set_extra_args(wdir=wdir) def save_materials(output_dir, pb, options): stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)', mode='el_avg', copy_materials=False, verbose=False) young, poisson = mc.youngpoisson_from_stiffness(stiffness, plane=options.plane) density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)', mode='el_avg', copy_materials=False, verbose=False) out = {} out['young'] = Struct(name='young', mode='cell', data=young[..., None, None]) out['poisson'] = Struct(name='poisson', mode='cell', data=poisson[..., None, None]) out['density'] = Struct(name='density', mode='cell', data=density) materials_filename = os.path.join(output_dir, 'materials.vtk') pb.save_state(materials_filename, out=out) def get_std_wave_fun(pb, options): stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)', mode='el_avg', copy_materials=False, verbose=False) young, poisson = mc.youngpoisson_from_stiffness(stiffness, plane=options.plane) density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)', mode='el_avg', copy_materials=False, verbose=False) lam, mu = mc.lame_from_youngpoisson(young, poisson, plane=options.plane) alam = nm.average(lam) amu = nm.average(mu) adensity = nm.average(density) cp = nm.sqrt((alam + 2.0 * amu) / adensity) cs = nm.sqrt(amu / adensity) output('average p-wave speed:', cp) output('average shear wave speed:', cs) log_names = [r'$\omega_p$', r'$\omega_s$'] log_plot_kwargs = [{'ls' : '--', 'color' : 'k'}, {'ls' : '--', 'color' : 'gray'}] if options.mode == 'omega': fun = lambda wmag, wdir: (cp * wmag, cs * wmag) else: fun = lambda wmag, wdir: (wmag / cp, wmag / cs) return fun, log_names, log_plot_kwargs def get_stepper(rng, pb, options): if options.stepper == 'linear': stepper = TimeStepper(rng[0], rng[1], dt=None, n_step=rng[2]) return stepper bbox = pb.domain.mesh.get_bounding_box() bzone = 2.0 * nm.pi / (bbox[1] - bbox[0]) num = rng[2] // 3 class BrillouinStepper(Struct): """ Step over 1. Brillouin zone in xy plane. """ def __init__(self, t0, t1, dt=None, n_step=None, step=None, **kwargs): Struct.__init__(self, t0=t0, t1=t1, dt=dt, n_step=n_step, step=step) self.n_digit, self.format, self.suffix = get_print_info(self.n_step) def __iter__(self): ts = TimeStepper(0, bzone[0], dt=None, n_step=num) for ii, val in ts: yield ii, val, nm.array([1.0, 0.0]) if ii == (num-2): break ts = TimeStepper(0, bzone[1], dt=None, n_step=num) for ii, k1 in ts: wdir = nm.array([bzone[0], k1]) val = nm.linalg.norm(wdir) wdir = wdir / val yield num + ii, val, wdir if ii == (num-2): break wdir = nm.array([bzone[0], bzone[1]]) val = nm.linalg.norm(wdir) wdir = wdir / val ts = TimeStepper(0, 1, dt=None, n_step=num) for ii, _ in ts: yield 2 * num + ii, val * (1.0 - float(ii)/(num-1)), wdir stepper = BrillouinStepper(0, 1, n_step=rng[2]) return stepper def save_eigenvectors(filename, svecs, wmag, wdir, pb): if svecs is None: return variables = pb.get_variables() # Make full eigenvectors (add DOFs fixed by boundary conditions). vecs = nm.empty((variables.di.ptr[-1], svecs.shape[1]), dtype=svecs.dtype) for ii in range(svecs.shape[1]): vecs[:, ii] = variables.make_full_vec(svecs[:, ii]) # Save the eigenvectors. out = {} state = pb.create_state() pp_name = pb.conf.options.get('post_process_hook') pp = getattr(pb.conf.funmod, pp_name if pp_name is not None else '', lambda out, *args, **kwargs: out) for ii in range(svecs.shape[1]): state.set_full(vecs[:, ii]) aux = state.create_output_dict() aux2 = {} pp(aux2, pb, state, wmag=wmag, wdir=wdir) aux.update(convert_complex_output(aux2)) out.update({key + '%03d' % ii : aux[key] for key in aux}) pb.save_state(filename, out=out) def assemble_matrices(define, mod, pars, set_wave_dir, options, wdir=None): """ Assemble the blocks of dispersion eigenvalue problem matrices. """ define_dict = define(filename_mesh=options.mesh_filename, pars=pars, approx_order=options.order, refinement_level=options.refine, solver_conf=options.solver_conf, plane=options.plane, post_process=options.post_process, **options.define_kwargs) conf = ProblemConf.from_dict(define_dict, mod) pb = Problem.from_conf(conf) pb.dispersion_options = options pb.set_output_dir(options.output_dir) dim = pb.domain.shape.dim # Set the normalized wave vector direction to the material(s). if wdir is None: wdir = nm.asarray(options.wave_dir[:dim], dtype=nm.float64) wdir = wdir / nm.linalg.norm(wdir) set_wave_dir(pb, wdir) bbox = pb.domain.mesh.get_bounding_box() size = (bbox[1] - bbox[0]).max() scaling0 = apply_unit_multipliers([1.0], ['length'], options.unit_multipliers)[0] scaling = scaling0 if options.mesh_size is not None: scaling *= options.mesh_size / size output('scaling factor of periodic cell mesh coordinates:', scaling) output('new mesh size with applied unit multipliers:', scaling * size) pb.domain.mesh.coors[:] *= scaling pb.set_mesh_coors(pb.domain.mesh.coors, update_fields=True) bzone = 2.0 * nm.pi / (scaling * size) output('1. Brillouin zone size:', bzone * scaling0) output('1. Brillouin zone size with applied unit multipliers:', bzone) pb.time_update() pb.update_materials() # Assemble the matrices. mtxs = {} for key, eq in pb.equations.iteritems(): mtxs[key] = mtx = pb.mtx_a.copy() mtx = eq.evaluate(mode='weak', dw_mode='matrix', asm_obj=mtx) mtx.eliminate_zeros() output_array_stats(mtx.data, 'nonzeros in %s' % key) output('symmetry checks:') output('%s - %s^T:' % (key, key), max_diff_csr(mtx, mtx.T)) output('%s - %s^H:' % (key, key), max_diff_csr(mtx, mtx.H)) return pb, wdir, bzone, mtxs def setup_n_eigs(options, pb, mtxs): """ Setup the numbers of eigenvalues based on options and numbers of DOFs. """ solver_n_eigs = n_eigs = options.n_eigs n_dof = mtxs['K'].shape[0] if options.mode == 'omega': if options.n_eigs > n_dof: n_eigs = n_dof solver_n_eigs = None else: if options.n_eigs > 2 * n_dof: n_eigs = 2 * n_dof solver_n_eigs = None return solver_n_eigs, n_eigs def build_evp_matrices(mtxs, val, mode, pb): """ Build the matrices of the dispersion eigenvalue problem. """ if mode == 'omega': mtx_a = mtxs['K'] + val**2 * mtxs['S'] + val * mtxs['R'] output('A - A^H:', max_diff_csr(mtx_a, mtx_a.H)) evp_mtxs = (mtx_a, mtxs['M']) else: evp_mtxs = (mtxs['S'], mtxs['R'], mtxs['K'] - val**2 * mtxs['M']) return evp_mtxs def process_evp_results(eigs, svecs, val, wdir, bzone, pb, mtxs, options, std_wave_fun=None): """ Transform eigenvalues to either omegas or kappas, depending on `mode`. Transform eigenvectors, if available, depending on `mode`. Return also the values to log. """ if options.mode == 'omega': omegas = nm.sqrt(eigs) output('eigs, omegas:') for ii, om in enumerate(omegas): output('{:>3}. {: .10e}, {:.10e}'.format(ii, eigs[ii], om)) if options.stepper == 'linear': out = tuple(eigs) + tuple(omegas) else: out = tuple(val * wdir) + tuple(omegas) if std_wave_fun is not None: out = out + std_wave_fun(val, wdir) return omegas, svecs, out else: kappas = eigs.copy() rks = kappas.copy() # Mask modes far from 1. Brillouin zone. max_kappa = 1.2 * bzone kappas[kappas.real > max_kappa] = nm.nan # Mask non-physical modes. kappas[kappas.real < 0] = nm.nan kappas[nm.abs(kappas.imag) > 1e-10] = nm.nan out = tuple(kappas.real) output('raw kappas, masked real part:',) for ii, kr in enumerate(kappas.real): output('{:>3}. {: 23.5e}, {:.10e}'.format(ii, rks[ii], kr)) if svecs is not None: n_dof = mtxs['K'].shape[0] # Select only vectors corresponding to physical modes. ii = nm.isfinite(kappas.real) svecs = svecs[:n_dof, ii] if std_wave_fun is not None: out = out + tuple(ii if ii <= max_kappa else nm.nan for ii in std_wave_fun(val, wdir)) return kappas, svecs, out helps = { 'pars' : 'material parameters in Y1, Y2 subdomains in basic units' ' [default: %(default)s]', 'conf' : 'if given, an alternative problem description file with apply_units() and' ' define() functions [default: %(default)s]', 'define_kwargs' : 'additional keyword arguments passed to define()', 'mesh_size' : 'desired mesh size (max. of bounding box dimensions) in basic units' ' - the input periodic cell mesh is rescaled to this size' ' [default: %(default)s]', 'unit_multipliers' : 'basic unit multipliers (time, length, mass) [default: %(default)s]', 'plane' : 'for 2D problems, plane strain or stress hypothesis selection' ' [default: %(default)s]', 'wave_dir' : 'the wave vector direction (will be normalized)' ' [default: %(default)s]', 'mode' : 'solution mode: omega = solve a generalized EVP for omega,' ' kappa = solve a quadratic generalized EVP for kappa' ' [default: %(default)s]', 'stepper' : 'the range stepper. For "brillouin", only the number' ' of items from --range is used' ' [default: %(default)s]', 'range' : 'the wave vector magnitude / frequency range' ' (like numpy.linspace) depending on the mode option' ' [default: %(default)s]', 'order' : 'displacement field approximation order [default: %(default)s]', 'refine' : 'number of uniform mesh refinements [default: %(default)s]', 'n_eigs' : 'the number of eigenvalues to compute [default: %(default)s]', 'eigs_only' : 'compute only eigenvalues, not eigenvectors', 'post_process' : 'post-process eigenvectors', 'solver_conf' : 'eigenvalue problem solver configuration options' ' [default: %(default)s]', 'save_regions' : 'save defined regions into' ' <output_directory>/regions.vtk', 'save_materials' : 'save material parameters into' ' <output_directory>/materials.vtk', 'log_std_waves' : 'log also standard pressure dilatation and shear waves', 'no_legends' : 'do not show legends in the log plots', 'no_show' : 'do not show the log figure', 'silent' : 'do not print messages to screen', 'clear' : 'clear old solution files from output directory', 'output_dir' : 'output directory [default: %(default)s]', 'mesh_filename' : 'input periodic cell mesh file name [default: %(default)s]', } def main(): # Aluminium and epoxy. default_pars = '70e9,0.35,2.799e3, 3.8e9,0.27,1.142e3' default_solver_conf = ("kind='eig.scipy',method='eigsh',tol=1.0e-5," "maxiter=1000,which='LM',sigma=0.0") parser = ArgumentParser(description=__doc__, formatter_class=RawDescriptionHelpFormatter) parser.add_argument('--pars', metavar='young1,poisson1,density1' ',young2,poisson2,density2', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='pars', default=default_pars, help=helps['pars']) parser.add_argument('--conf', metavar='filename', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='conf', default=None, help=helps['conf']) parser.add_argument('--define-kwargs', metavar='dict-like', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='define_kwargs', default=None, help=helps['define_kwargs']) parser.add_argument('--mesh-size', type=float, metavar='float', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='mesh_size', default=None, help=helps['mesh_size']) parser.add_argument('--unit-multipliers', metavar='c_time,c_length,c_mass', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='unit_multipliers', default='1.0,1.0,1.0', help=helps['unit_multipliers']) parser.add_argument('--plane', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='plane', choices=['strain', 'stress'], default='strain', help=helps['plane']) parser.add_argument('--wave-dir', metavar='float,float[,float]', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='wave_dir', default='1.0,0.0,0.0', help=helps['wave_dir']) parser.add_argument('--mode', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='mode', choices=['omega', 'kappa'], default='omega', help=helps['mode']) parser.add_argument('--stepper', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='stepper', choices=['linear', 'brillouin'], default='linear', help=helps['stepper']) parser.add_argument('--range', metavar='start,stop,count', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='range', default='0,6.4,33', help=helps['range']) parser.add_argument('--order', metavar='int', type=int, action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='order', default=1, help=helps['order']) parser.add_argument('--refine', metavar='int', type=int, action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='refine', default=0, help=helps['refine']) parser.add_argument('-n', '--n-eigs', metavar='int', type=int, action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='n_eigs', default=6, help=helps['n_eigs']) group = parser.add_mutually_exclusive_group() group.add_argument('--eigs-only', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='eigs_only', default=False, help=helps['eigs_only']) group.add_argument('--post-process', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='post_process', default=False, help=helps['post_process']) parser.add_argument('--solver-conf', metavar='dict-like', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='solver_conf', default=default_solver_conf, help=helps['solver_conf']) parser.add_argument('--save-regions', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='save_regions', default=False, help=helps['save_regions']) parser.add_argument('--save-materials', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='save_materials', default=False, help=helps['save_materials']) parser.add_argument('--log-std-waves', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='log_std_waves', default=False, help=helps['log_std_waves']) parser.add_argument('--no-legends', action="https://huggingface.co/datasets/luna-code/sfepy/store_false", dest='show_legends', default=True, help=helps['no_legends']) parser.add_argument('--no-show', action="https://huggingface.co/datasets/luna-code/sfepy/store_false", dest='show', default=True, help=helps['no_show']) parser.add_argument('--silent', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='silent', default=False, help=helps['silent']) parser.add_argument('-c', '--clear', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='clear', default=False, help=helps['clear']) parser.add_argument('-o', '--output-dir', metavar='path', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='output_dir', default='output', help=helps['output_dir']) parser.add_argument('mesh_filename', default='', help=helps['mesh_filename']) options = parser.parse_args() output_dir = options.output_dir output.set_output(filename=os.path.join(output_dir,'output_log.txt'), combined=options.silent == False) if options.conf is not None: mod = import_file(options.conf) else: mod = sys.modules[__name__] apply_units = mod.apply_units define = mod.define set_wave_dir = mod.set_wave_dir setup_n_eigs = mod.setup_n_eigs build_evp_matrices = mod.build_evp_matrices save_materials = mod.save_materials get_std_wave_fun = mod.get_std_wave_fun get_stepper = mod.get_stepper process_evp_results = mod.process_evp_results options.pars = [float(ii) for ii in options.pars.split(',')] options.unit_multipliers = [float(ii) for ii in options.unit_multipliers.split(',')] options.wave_dir = [float(ii) for ii in options.wave_dir.split(',')] aux = options.range.split(',') options.range = [float(aux[0]), float(aux[1]), int(aux[2])] options.solver_conf = dict_from_string(options.solver_conf) options.define_kwargs = dict_from_string(options.define_kwargs) if options.clear: remove_files_patterns(output_dir, ['*.h5', '*.vtk', '*.txt'], ignores=['output_log.txt'], verbose=True) filename = os.path.join(output_dir, 'options.txt') ensure_path(filename) save_options(filename, [('options', vars(options))], quote_command_line=True) pars = apply_units(options.pars, options.unit_multipliers) output('material parameters with applied unit multipliers:') output(pars) if options.mode == 'omega': rng = copy(options.range) rng[:2] = apply_unit_multipliers(options.range[:2], ['wave_number', 'wave_number'], options.unit_multipliers) output('wave number range with applied unit multipliers:', rng) else: if options.stepper == 'brillouin': raise ValueError('Cannot use "brillouin" stepper in kappa mode!') rng = copy(options.range) rng[:2] = apply_unit_multipliers(options.range[:2], ['frequency', 'frequency'], options.unit_multipliers) output('frequency range with applied unit multipliers:', rng) pb, wdir, bzone, mtxs = assemble_matrices(define, mod, pars, set_wave_dir, options) dim = pb.domain.shape.dim if dim != 2: options.plane = 'strain' if options.save_regions: pb.save_regions_as_groups(os.path.join(output_dir, 'regions')) if options.save_materials: save_materials(output_dir, pb, options) conf = pb.solver_confs['eig'] eig_solver =	Solver.any_from_conf(conf)	sfepy.solvers.Solver.any_from_conf
#!/usr/bin/env python """ Dispersion analysis of a heterogeneous finite scale periodic cell. The periodic cell mesh has to contain two subdomains Y1 (with the cell ids 1), Y2 (with the cell ids 2), so that different material properties can be defined in each of the subdomains (see ``--pars`` option). The command line parameters can be given in any consistent unit set, for example the basic SI units. The ``--unit-multipliers`` option can be used to rescale the input units to ones more suitable to the simulation, for example to prevent having different matrix blocks with large differences of matrix entries magnitudes. The results are then in the rescaled units. Usage Examples -------------- Default material parameters, a square periodic cell with a spherical inclusion, logs also standard pressure dilatation and shear waves, no eigenvectors:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only As above, with custom eigenvalue solver parameters, and different number of eigenvalues, mesh size and units used in the calculation:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --solver-conf="kind='eig.scipy', method='eigsh', tol=1e-10, maxiter=1000, which='LM', sigma=0" --log-std-waves -n 5 --range=0,640,101 --mode=omega --unit-multipliers=1e-6,1e-2,1e-3 --mesh-size=1e-2 --eigs-only Default material parameters, a square periodic cell with a square inclusion, and a very small mesh to allow comparing the omega and kappa modes (full matrix solver required!):: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.qevp', method='companion', mode='inverted', solver={kind='eig.scipy', method='eig'}" --log-std-waves -n 500 --range=0,4000000,1001 --mesh-size=1e-2 --mode=kappa --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/kappa View/compare the resulting logs:: python script/plot_logs.py output/omega/frequencies.txt --no-legends -g 1 -o mode-omega.png python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends -o mode-kappa.png python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends --swap-axes -o mode-kappa-t.png In contrast to the heterogeneous square periodic cell, a homogeneous square periodic cell (the region Y2 is empty):: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_1m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega-h python script/plot_logs.py output/omega-h/frequencies.txt --no-legends -g 1 -o mode-omega-h.png Use the Brillouin stepper:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves -n=60 --eigs-only --no-legends --stepper=brillouin python script/plot_logs.py output/frequencies.txt -g 0 --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-kappas.png python script/plot_logs.py output/frequencies.txt -g 1 --no-legends --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-omegas.png Additional arguments can be passed to the problem configuration's :func:`define()` function using the ``--define-kwargs`` option. In this file, only the mesh vertex separation parameter `mesh_eps` can be used:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only --define-kwargs="mesh_eps=1e-10" --save-regions """ from __future__ import absolute_import import os import sys sys.path.append('.') import gc from copy import copy from argparse import ArgumentParser, RawDescriptionHelpFormatter import numpy as nm import matplotlib.pyplot as plt from sfepy.base.base import import_file, output, Struct from sfepy.base.conf import dict_from_string, ProblemConf from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options from sfepy.base.log import Log from sfepy.discrete.fem import MeshIO from sfepy.mechanics.matcoefs import stiffness_from_youngpoisson as stiffness import sfepy.mechanics.matcoefs as mc from sfepy.mechanics.units import apply_unit_multipliers import sfepy.discrete.fem.periodic as per from sfepy.discrete.fem.meshio import convert_complex_output from sfepy.homogenization.utils import define_box_regions from sfepy.discrete import Problem from sfepy.mechanics.tensors import get_von_mises_stress from sfepy.solvers import Solver from sfepy.solvers.ts import get_print_info, TimeStepper from sfepy.linalg.utils import output_array_stats, max_diff_csr def apply_units(pars, unit_multipliers): new_pars = apply_unit_multipliers(pars, ['stress', 'one', 'density', 'stress', 'one' ,'density'], unit_multipliers) return new_pars def compute_von_mises(out, pb, state, extend=False, wmag=None, wdir=None): """ Calculate the von Mises stress. """ stress = pb.evaluate('ev_cauchy_stress.i.Omega(m.D, u)', mode='el_avg') vms = get_von_mises_stress(stress.squeeze()) vms.shape = (vms.shape[0], 1, 1, 1) out['von_mises_stress'] = Struct(name='output_data', mode='cell', data=vms) return out def define(filename_mesh, pars, approx_order, refinement_level, solver_conf, plane='strain', post_process=False, mesh_eps=1e-8): io = MeshIO.any_from_filename(filename_mesh) bbox = io.read_bounding_box() dim = bbox.shape[1] options = { 'absolute_mesh_path' : True, 'refinement_level' : refinement_level, 'allow_empty_regions' : True, 'post_process_hook' : 'compute_von_mises' if post_process else None, } fields = { 'displacement': ('complex', dim, 'Omega', approx_order), } young1, poisson1, density1, young2, poisson2, density2 = pars materials = { 'm' : ({ 'D' : {'Y1' : stiffness(dim, young=young1, poisson=poisson1, plane=plane), 'Y2' : stiffness(dim, young=young2, poisson=poisson2, plane=plane)}, 'density' : {'Y1' : density1, 'Y2' : density2}, },), 'wave' : 'get_wdir', } variables = { 'u' : ('unknown field', 'displacement', 0), 'v' : ('test field', 'displacement', 'u'), } regions = { 'Omega' : 'all', 'Y1': 'cells of group 1', 'Y2': 'cells of group 2', } regions.update(define_box_regions(dim, bbox[0], bbox[1], mesh_eps)) ebcs = { } if dim == 3: epbcs = { 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'}, 'match_x_plane'), 'periodic_y' : (['Near', 'Far'], {'u.all' : 'u.all'}, 'match_y_plane'), 'periodic_z' : (['Top', 'Bottom'], {'u.all' : 'u.all'}, 'match_z_plane'), } else: epbcs = { 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'}, 'match_y_line'), 'periodic_y' : (['Bottom', 'Top'], {'u.all' : 'u.all'}, 'match_x_line'), } per.set_accuracy(mesh_eps) functions = { 'match_x_plane' : (per.match_x_plane,), 'match_y_plane' : (per.match_y_plane,), 'match_z_plane' : (per.match_z_plane,), 'match_x_line' : (per.match_x_line,), 'match_y_line' : (per.match_y_line,), 'get_wdir' : (get_wdir,), } integrals = { 'i' : 2 * approx_order, } equations = { 'K' : 'dw_lin_elastic.i.Omega(m.D, v, u)', 'S' : 'dw_elastic_wave.i.Omega(m.D, wave.vec, v, u)', 'R' : """1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, u, v) - 1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, v, u)""", 'M' : 'dw_volume_dot.i.Omega(m.density, v, u)', } solver_0 = solver_conf.copy() solver_0['name'] = 'eig' return locals() def get_wdir(ts, coors, mode=None, equations=None, term=None, problem=None, wdir=None, **kwargs): if mode == 'special': return {'vec' : wdir} def set_wave_dir(pb, wdir): materials = pb.get_materials() wave_mat = materials['wave'] wave_mat.set_extra_args(wdir=wdir) def save_materials(output_dir, pb, options): stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)', mode='el_avg', copy_materials=False, verbose=False) young, poisson = mc.youngpoisson_from_stiffness(stiffness, plane=options.plane) density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)', mode='el_avg', copy_materials=False, verbose=False) out = {} out['young'] = Struct(name='young', mode='cell', data=young[..., None, None]) out['poisson'] = Struct(name='poisson', mode='cell', data=poisson[..., None, None]) out['density'] = Struct(name='density', mode='cell', data=density) materials_filename = os.path.join(output_dir, 'materials.vtk') pb.save_state(materials_filename, out=out) def get_std_wave_fun(pb, options): stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)', mode='el_avg', copy_materials=False, verbose=False) young, poisson = mc.youngpoisson_from_stiffness(stiffness, plane=options.plane) density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)', mode='el_avg', copy_materials=False, verbose=False) lam, mu = mc.lame_from_youngpoisson(young, poisson, plane=options.plane) alam = nm.average(lam) amu = nm.average(mu) adensity = nm.average(density) cp = nm.sqrt((alam + 2.0 * amu) / adensity) cs = nm.sqrt(amu / adensity) output('average p-wave speed:', cp) output('average shear wave speed:', cs) log_names = [r'$\omega_p$', r'$\omega_s$'] log_plot_kwargs = [{'ls' : '--', 'color' : 'k'}, {'ls' : '--', 'color' : 'gray'}] if options.mode == 'omega': fun = lambda wmag, wdir: (cp * wmag, cs * wmag) else: fun = lambda wmag, wdir: (wmag / cp, wmag / cs) return fun, log_names, log_plot_kwargs def get_stepper(rng, pb, options): if options.stepper == 'linear': stepper =	TimeStepper(rng[0], rng[1], dt=None, n_step=rng[2])	sfepy.solvers.ts.TimeStepper
#!/usr/bin/env python """ Dispersion analysis of a heterogeneous finite scale periodic cell. The periodic cell mesh has to contain two subdomains Y1 (with the cell ids 1), Y2 (with the cell ids 2), so that different material properties can be defined in each of the subdomains (see ``--pars`` option). The command line parameters can be given in any consistent unit set, for example the basic SI units. The ``--unit-multipliers`` option can be used to rescale the input units to ones more suitable to the simulation, for example to prevent having different matrix blocks with large differences of matrix entries magnitudes. The results are then in the rescaled units. Usage Examples -------------- Default material parameters, a square periodic cell with a spherical inclusion, logs also standard pressure dilatation and shear waves, no eigenvectors:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only As above, with custom eigenvalue solver parameters, and different number of eigenvalues, mesh size and units used in the calculation:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --solver-conf="kind='eig.scipy', method='eigsh', tol=1e-10, maxiter=1000, which='LM', sigma=0" --log-std-waves -n 5 --range=0,640,101 --mode=omega --unit-multipliers=1e-6,1e-2,1e-3 --mesh-size=1e-2 --eigs-only Default material parameters, a square periodic cell with a square inclusion, and a very small mesh to allow comparing the omega and kappa modes (full matrix solver required!):: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.qevp', method='companion', mode='inverted', solver={kind='eig.scipy', method='eig'}" --log-std-waves -n 500 --range=0,4000000,1001 --mesh-size=1e-2 --mode=kappa --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/kappa View/compare the resulting logs:: python script/plot_logs.py output/omega/frequencies.txt --no-legends -g 1 -o mode-omega.png python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends -o mode-kappa.png python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends --swap-axes -o mode-kappa-t.png In contrast to the heterogeneous square periodic cell, a homogeneous square periodic cell (the region Y2 is empty):: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_1m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega-h python script/plot_logs.py output/omega-h/frequencies.txt --no-legends -g 1 -o mode-omega-h.png Use the Brillouin stepper:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves -n=60 --eigs-only --no-legends --stepper=brillouin python script/plot_logs.py output/frequencies.txt -g 0 --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-kappas.png python script/plot_logs.py output/frequencies.txt -g 1 --no-legends --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-omegas.png Additional arguments can be passed to the problem configuration's :func:`define()` function using the ``--define-kwargs`` option. In this file, only the mesh vertex separation parameter `mesh_eps` can be used:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only --define-kwargs="mesh_eps=1e-10" --save-regions """ from __future__ import absolute_import import os import sys sys.path.append('.') import gc from copy import copy from argparse import ArgumentParser, RawDescriptionHelpFormatter import numpy as nm import matplotlib.pyplot as plt from sfepy.base.base import import_file, output, Struct from sfepy.base.conf import dict_from_string, ProblemConf from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options from sfepy.base.log import Log from sfepy.discrete.fem import MeshIO from sfepy.mechanics.matcoefs import stiffness_from_youngpoisson as stiffness import sfepy.mechanics.matcoefs as mc from sfepy.mechanics.units import apply_unit_multipliers import sfepy.discrete.fem.periodic as per from sfepy.discrete.fem.meshio import convert_complex_output from sfepy.homogenization.utils import define_box_regions from sfepy.discrete import Problem from sfepy.mechanics.tensors import get_von_mises_stress from sfepy.solvers import Solver from sfepy.solvers.ts import get_print_info, TimeStepper from sfepy.linalg.utils import output_array_stats, max_diff_csr def apply_units(pars, unit_multipliers): new_pars = apply_unit_multipliers(pars, ['stress', 'one', 'density', 'stress', 'one' ,'density'], unit_multipliers) return new_pars def compute_von_mises(out, pb, state, extend=False, wmag=None, wdir=None): """ Calculate the von Mises stress. """ stress = pb.evaluate('ev_cauchy_stress.i.Omega(m.D, u)', mode='el_avg') vms = get_von_mises_stress(stress.squeeze()) vms.shape = (vms.shape[0], 1, 1, 1) out['von_mises_stress'] = Struct(name='output_data', mode='cell', data=vms) return out def define(filename_mesh, pars, approx_order, refinement_level, solver_conf, plane='strain', post_process=False, mesh_eps=1e-8): io = MeshIO.any_from_filename(filename_mesh) bbox = io.read_bounding_box() dim = bbox.shape[1] options = { 'absolute_mesh_path' : True, 'refinement_level' : refinement_level, 'allow_empty_regions' : True, 'post_process_hook' : 'compute_von_mises' if post_process else None, } fields = { 'displacement': ('complex', dim, 'Omega', approx_order), } young1, poisson1, density1, young2, poisson2, density2 = pars materials = { 'm' : ({ 'D' : {'Y1' : stiffness(dim, young=young1, poisson=poisson1, plane=plane), 'Y2' : stiffness(dim, young=young2, poisson=poisson2, plane=plane)}, 'density' : {'Y1' : density1, 'Y2' : density2}, },), 'wave' : 'get_wdir', } variables = { 'u' : ('unknown field', 'displacement', 0), 'v' : ('test field', 'displacement', 'u'), } regions = { 'Omega' : 'all', 'Y1': 'cells of group 1', 'Y2': 'cells of group 2', } regions.update(define_box_regions(dim, bbox[0], bbox[1], mesh_eps)) ebcs = { } if dim == 3: epbcs = { 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'}, 'match_x_plane'), 'periodic_y' : (['Near', 'Far'], {'u.all' : 'u.all'}, 'match_y_plane'), 'periodic_z' : (['Top', 'Bottom'], {'u.all' : 'u.all'}, 'match_z_plane'), } else: epbcs = { 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'}, 'match_y_line'), 'periodic_y' : (['Bottom', 'Top'], {'u.all' : 'u.all'}, 'match_x_line'), } per.set_accuracy(mesh_eps) functions = { 'match_x_plane' : (per.match_x_plane,), 'match_y_plane' : (per.match_y_plane,), 'match_z_plane' : (per.match_z_plane,), 'match_x_line' : (per.match_x_line,), 'match_y_line' : (per.match_y_line,), 'get_wdir' : (get_wdir,), } integrals = { 'i' : 2 * approx_order, } equations = { 'K' : 'dw_lin_elastic.i.Omega(m.D, v, u)', 'S' : 'dw_elastic_wave.i.Omega(m.D, wave.vec, v, u)', 'R' : """1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, u, v) - 1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, v, u)""", 'M' : 'dw_volume_dot.i.Omega(m.density, v, u)', } solver_0 = solver_conf.copy() solver_0['name'] = 'eig' return locals() def get_wdir(ts, coors, mode=None, equations=None, term=None, problem=None, wdir=None, **kwargs): if mode == 'special': return {'vec' : wdir} def set_wave_dir(pb, wdir): materials = pb.get_materials() wave_mat = materials['wave'] wave_mat.set_extra_args(wdir=wdir) def save_materials(output_dir, pb, options): stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)', mode='el_avg', copy_materials=False, verbose=False) young, poisson = mc.youngpoisson_from_stiffness(stiffness, plane=options.plane) density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)', mode='el_avg', copy_materials=False, verbose=False) out = {} out['young'] = Struct(name='young', mode='cell', data=young[..., None, None]) out['poisson'] = Struct(name='poisson', mode='cell', data=poisson[..., None, None]) out['density'] = Struct(name='density', mode='cell', data=density) materials_filename = os.path.join(output_dir, 'materials.vtk') pb.save_state(materials_filename, out=out) def get_std_wave_fun(pb, options): stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)', mode='el_avg', copy_materials=False, verbose=False) young, poisson = mc.youngpoisson_from_stiffness(stiffness, plane=options.plane) density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)', mode='el_avg', copy_materials=False, verbose=False) lam, mu = mc.lame_from_youngpoisson(young, poisson, plane=options.plane) alam = nm.average(lam) amu = nm.average(mu) adensity = nm.average(density) cp = nm.sqrt((alam + 2.0 * amu) / adensity) cs = nm.sqrt(amu / adensity) output('average p-wave speed:', cp) output('average shear wave speed:', cs) log_names = [r'$\omega_p$', r'$\omega_s$'] log_plot_kwargs = [{'ls' : '--', 'color' : 'k'}, {'ls' : '--', 'color' : 'gray'}] if options.mode == 'omega': fun = lambda wmag, wdir: (cp * wmag, cs * wmag) else: fun = lambda wmag, wdir: (wmag / cp, wmag / cs) return fun, log_names, log_plot_kwargs def get_stepper(rng, pb, options): if options.stepper == 'linear': stepper = TimeStepper(rng[0], rng[1], dt=None, n_step=rng[2]) return stepper bbox = pb.domain.mesh.get_bounding_box() bzone = 2.0 * nm.pi / (bbox[1] - bbox[0]) num = rng[2] // 3 class BrillouinStepper(Struct): """ Step over 1. Brillouin zone in xy plane. """ def __init__(self, t0, t1, dt=None, n_step=None, step=None, **kwargs): Struct.__init__(self, t0=t0, t1=t1, dt=dt, n_step=n_step, step=step) self.n_digit, self.format, self.suffix = get_print_info(self.n_step) def __iter__(self): ts = TimeStepper(0, bzone[0], dt=None, n_step=num) for ii, val in ts: yield ii, val, nm.array([1.0, 0.0]) if ii == (num-2): break ts = TimeStepper(0, bzone[1], dt=None, n_step=num) for ii, k1 in ts: wdir = nm.array([bzone[0], k1]) val = nm.linalg.norm(wdir) wdir = wdir / val yield num + ii, val, wdir if ii == (num-2): break wdir = nm.array([bzone[0], bzone[1]]) val = nm.linalg.norm(wdir) wdir = wdir / val ts = TimeStepper(0, 1, dt=None, n_step=num) for ii, _ in ts: yield 2 * num + ii, val * (1.0 - float(ii)/(num-1)), wdir stepper = BrillouinStepper(0, 1, n_step=rng[2]) return stepper def save_eigenvectors(filename, svecs, wmag, wdir, pb): if svecs is None: return variables = pb.get_variables() # Make full eigenvectors (add DOFs fixed by boundary conditions). vecs = nm.empty((variables.di.ptr[-1], svecs.shape[1]), dtype=svecs.dtype) for ii in range(svecs.shape[1]): vecs[:, ii] = variables.make_full_vec(svecs[:, ii]) # Save the eigenvectors. out = {} state = pb.create_state() pp_name = pb.conf.options.get('post_process_hook') pp = getattr(pb.conf.funmod, pp_name if pp_name is not None else '', lambda out, *args, **kwargs: out) for ii in range(svecs.shape[1]): state.set_full(vecs[:, ii]) aux = state.create_output_dict() aux2 = {} pp(aux2, pb, state, wmag=wmag, wdir=wdir) aux.update(convert_complex_output(aux2)) out.update({key + '%03d' % ii : aux[key] for key in aux}) pb.save_state(filename, out=out) def assemble_matrices(define, mod, pars, set_wave_dir, options, wdir=None): """ Assemble the blocks of dispersion eigenvalue problem matrices. """ define_dict = define(filename_mesh=options.mesh_filename, pars=pars, approx_order=options.order, refinement_level=options.refine, solver_conf=options.solver_conf, plane=options.plane, post_process=options.post_process, **options.define_kwargs) conf = ProblemConf.from_dict(define_dict, mod) pb = Problem.from_conf(conf) pb.dispersion_options = options pb.set_output_dir(options.output_dir) dim = pb.domain.shape.dim # Set the normalized wave vector direction to the material(s). if wdir is None: wdir = nm.asarray(options.wave_dir[:dim], dtype=nm.float64) wdir = wdir / nm.linalg.norm(wdir) set_wave_dir(pb, wdir) bbox = pb.domain.mesh.get_bounding_box() size = (bbox[1] - bbox[0]).max() scaling0 = apply_unit_multipliers([1.0], ['length'], options.unit_multipliers)[0] scaling = scaling0 if options.mesh_size is not None: scaling *= options.mesh_size / size output('scaling factor of periodic cell mesh coordinates:', scaling) output('new mesh size with applied unit multipliers:', scaling * size) pb.domain.mesh.coors[:] *= scaling pb.set_mesh_coors(pb.domain.mesh.coors, update_fields=True) bzone = 2.0 * nm.pi / (scaling * size) output('1. Brillouin zone size:', bzone * scaling0) output('1. Brillouin zone size with applied unit multipliers:', bzone) pb.time_update() pb.update_materials() # Assemble the matrices. mtxs = {} for key, eq in pb.equations.iteritems(): mtxs[key] = mtx = pb.mtx_a.copy() mtx = eq.evaluate(mode='weak', dw_mode='matrix', asm_obj=mtx) mtx.eliminate_zeros()	output_array_stats(mtx.data, 'nonzeros in %s' % key)	sfepy.linalg.utils.output_array_stats
#!/usr/bin/env python """ Dispersion analysis of a heterogeneous finite scale periodic cell. The periodic cell mesh has to contain two subdomains Y1 (with the cell ids 1), Y2 (with the cell ids 2), so that different material properties can be defined in each of the subdomains (see ``--pars`` option). The command line parameters can be given in any consistent unit set, for example the basic SI units. The ``--unit-multipliers`` option can be used to rescale the input units to ones more suitable to the simulation, for example to prevent having different matrix blocks with large differences of matrix entries magnitudes. The results are then in the rescaled units. Usage Examples -------------- Default material parameters, a square periodic cell with a spherical inclusion, logs also standard pressure dilatation and shear waves, no eigenvectors:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only As above, with custom eigenvalue solver parameters, and different number of eigenvalues, mesh size and units used in the calculation:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --solver-conf="kind='eig.scipy', method='eigsh', tol=1e-10, maxiter=1000, which='LM', sigma=0" --log-std-waves -n 5 --range=0,640,101 --mode=omega --unit-multipliers=1e-6,1e-2,1e-3 --mesh-size=1e-2 --eigs-only Default material parameters, a square periodic cell with a square inclusion, and a very small mesh to allow comparing the omega and kappa modes (full matrix solver required!):: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.qevp', method='companion', mode='inverted', solver={kind='eig.scipy', method='eig'}" --log-std-waves -n 500 --range=0,4000000,1001 --mesh-size=1e-2 --mode=kappa --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/kappa View/compare the resulting logs:: python script/plot_logs.py output/omega/frequencies.txt --no-legends -g 1 -o mode-omega.png python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends -o mode-kappa.png python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends --swap-axes -o mode-kappa-t.png In contrast to the heterogeneous square periodic cell, a homogeneous square periodic cell (the region Y2 is empty):: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_1m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega-h python script/plot_logs.py output/omega-h/frequencies.txt --no-legends -g 1 -o mode-omega-h.png Use the Brillouin stepper:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves -n=60 --eigs-only --no-legends --stepper=brillouin python script/plot_logs.py output/frequencies.txt -g 0 --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-kappas.png python script/plot_logs.py output/frequencies.txt -g 1 --no-legends --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-omegas.png Additional arguments can be passed to the problem configuration's :func:`define()` function using the ``--define-kwargs`` option. In this file, only the mesh vertex separation parameter `mesh_eps` can be used:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only --define-kwargs="mesh_eps=1e-10" --save-regions """ from __future__ import absolute_import import os import sys sys.path.append('.') import gc from copy import copy from argparse import ArgumentParser, RawDescriptionHelpFormatter import numpy as nm import matplotlib.pyplot as plt from sfepy.base.base import import_file, output, Struct from sfepy.base.conf import dict_from_string, ProblemConf from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options from sfepy.base.log import Log from sfepy.discrete.fem import MeshIO from sfepy.mechanics.matcoefs import stiffness_from_youngpoisson as stiffness import sfepy.mechanics.matcoefs as mc from sfepy.mechanics.units import apply_unit_multipliers import sfepy.discrete.fem.periodic as per from sfepy.discrete.fem.meshio import convert_complex_output from sfepy.homogenization.utils import define_box_regions from sfepy.discrete import Problem from sfepy.mechanics.tensors import get_von_mises_stress from sfepy.solvers import Solver from sfepy.solvers.ts import get_print_info, TimeStepper from sfepy.linalg.utils import output_array_stats, max_diff_csr def apply_units(pars, unit_multipliers): new_pars = apply_unit_multipliers(pars, ['stress', 'one', 'density', 'stress', 'one' ,'density'], unit_multipliers) return new_pars def compute_von_mises(out, pb, state, extend=False, wmag=None, wdir=None): """ Calculate the von Mises stress. """ stress = pb.evaluate('ev_cauchy_stress.i.Omega(m.D, u)', mode='el_avg') vms = get_von_mises_stress(stress.squeeze()) vms.shape = (vms.shape[0], 1, 1, 1) out['von_mises_stress'] = Struct(name='output_data', mode='cell', data=vms) return out def define(filename_mesh, pars, approx_order, refinement_level, solver_conf, plane='strain', post_process=False, mesh_eps=1e-8): io = MeshIO.any_from_filename(filename_mesh) bbox = io.read_bounding_box() dim = bbox.shape[1] options = { 'absolute_mesh_path' : True, 'refinement_level' : refinement_level, 'allow_empty_regions' : True, 'post_process_hook' : 'compute_von_mises' if post_process else None, } fields = { 'displacement': ('complex', dim, 'Omega', approx_order), } young1, poisson1, density1, young2, poisson2, density2 = pars materials = { 'm' : ({ 'D' : {'Y1' : stiffness(dim, young=young1, poisson=poisson1, plane=plane), 'Y2' : stiffness(dim, young=young2, poisson=poisson2, plane=plane)}, 'density' : {'Y1' : density1, 'Y2' : density2}, },), 'wave' : 'get_wdir', } variables = { 'u' : ('unknown field', 'displacement', 0), 'v' : ('test field', 'displacement', 'u'), } regions = { 'Omega' : 'all', 'Y1': 'cells of group 1', 'Y2': 'cells of group 2', } regions.update(define_box_regions(dim, bbox[0], bbox[1], mesh_eps)) ebcs = { } if dim == 3: epbcs = { 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'}, 'match_x_plane'), 'periodic_y' : (['Near', 'Far'], {'u.all' : 'u.all'}, 'match_y_plane'), 'periodic_z' : (['Top', 'Bottom'], {'u.all' : 'u.all'}, 'match_z_plane'), } else: epbcs = { 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'}, 'match_y_line'), 'periodic_y' : (['Bottom', 'Top'], {'u.all' : 'u.all'}, 'match_x_line'), } per.set_accuracy(mesh_eps) functions = { 'match_x_plane' : (per.match_x_plane,), 'match_y_plane' : (per.match_y_plane,), 'match_z_plane' : (per.match_z_plane,), 'match_x_line' : (per.match_x_line,), 'match_y_line' : (per.match_y_line,), 'get_wdir' : (get_wdir,), } integrals = { 'i' : 2 * approx_order, } equations = { 'K' : 'dw_lin_elastic.i.Omega(m.D, v, u)', 'S' : 'dw_elastic_wave.i.Omega(m.D, wave.vec, v, u)', 'R' : """1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, u, v) - 1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, v, u)""", 'M' : 'dw_volume_dot.i.Omega(m.density, v, u)', } solver_0 = solver_conf.copy() solver_0['name'] = 'eig' return locals() def get_wdir(ts, coors, mode=None, equations=None, term=None, problem=None, wdir=None, **kwargs): if mode == 'special': return {'vec' : wdir} def set_wave_dir(pb, wdir): materials = pb.get_materials() wave_mat = materials['wave'] wave_mat.set_extra_args(wdir=wdir) def save_materials(output_dir, pb, options): stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)', mode='el_avg', copy_materials=False, verbose=False) young, poisson = mc.youngpoisson_from_stiffness(stiffness, plane=options.plane) density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)', mode='el_avg', copy_materials=False, verbose=False) out = {} out['young'] = Struct(name='young', mode='cell', data=young[..., None, None]) out['poisson'] = Struct(name='poisson', mode='cell', data=poisson[..., None, None]) out['density'] = Struct(name='density', mode='cell', data=density) materials_filename = os.path.join(output_dir, 'materials.vtk') pb.save_state(materials_filename, out=out) def get_std_wave_fun(pb, options): stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)', mode='el_avg', copy_materials=False, verbose=False) young, poisson = mc.youngpoisson_from_stiffness(stiffness, plane=options.plane) density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)', mode='el_avg', copy_materials=False, verbose=False) lam, mu = mc.lame_from_youngpoisson(young, poisson, plane=options.plane) alam = nm.average(lam) amu = nm.average(mu) adensity = nm.average(density) cp = nm.sqrt((alam + 2.0 * amu) / adensity) cs = nm.sqrt(amu / adensity) output('average p-wave speed:', cp) output('average shear wave speed:', cs) log_names = [r'$\omega_p$', r'$\omega_s$'] log_plot_kwargs = [{'ls' : '--', 'color' : 'k'}, {'ls' : '--', 'color' : 'gray'}] if options.mode == 'omega': fun = lambda wmag, wdir: (cp * wmag, cs * wmag) else: fun = lambda wmag, wdir: (wmag / cp, wmag / cs) return fun, log_names, log_plot_kwargs def get_stepper(rng, pb, options): if options.stepper == 'linear': stepper = TimeStepper(rng[0], rng[1], dt=None, n_step=rng[2]) return stepper bbox = pb.domain.mesh.get_bounding_box() bzone = 2.0 * nm.pi / (bbox[1] - bbox[0]) num = rng[2] // 3 class BrillouinStepper(Struct): """ Step over 1. Brillouin zone in xy plane. """ def __init__(self, t0, t1, dt=None, n_step=None, step=None, **kwargs): Struct.__init__(self, t0=t0, t1=t1, dt=dt, n_step=n_step, step=step) self.n_digit, self.format, self.suffix = get_print_info(self.n_step) def __iter__(self): ts = TimeStepper(0, bzone[0], dt=None, n_step=num) for ii, val in ts: yield ii, val, nm.array([1.0, 0.0]) if ii == (num-2): break ts = TimeStepper(0, bzone[1], dt=None, n_step=num) for ii, k1 in ts: wdir = nm.array([bzone[0], k1]) val = nm.linalg.norm(wdir) wdir = wdir / val yield num + ii, val, wdir if ii == (num-2): break wdir = nm.array([bzone[0], bzone[1]]) val = nm.linalg.norm(wdir) wdir = wdir / val ts = TimeStepper(0, 1, dt=None, n_step=num) for ii, _ in ts: yield 2 * num + ii, val * (1.0 - float(ii)/(num-1)), wdir stepper = BrillouinStepper(0, 1, n_step=rng[2]) return stepper def save_eigenvectors(filename, svecs, wmag, wdir, pb): if svecs is None: return variables = pb.get_variables() # Make full eigenvectors (add DOFs fixed by boundary conditions). vecs = nm.empty((variables.di.ptr[-1], svecs.shape[1]), dtype=svecs.dtype) for ii in range(svecs.shape[1]): vecs[:, ii] = variables.make_full_vec(svecs[:, ii]) # Save the eigenvectors. out = {} state = pb.create_state() pp_name = pb.conf.options.get('post_process_hook') pp = getattr(pb.conf.funmod, pp_name if pp_name is not None else '', lambda out, *args, **kwargs: out) for ii in range(svecs.shape[1]): state.set_full(vecs[:, ii]) aux = state.create_output_dict() aux2 = {} pp(aux2, pb, state, wmag=wmag, wdir=wdir) aux.update(convert_complex_output(aux2)) out.update({key + '%03d' % ii : aux[key] for key in aux}) pb.save_state(filename, out=out) def assemble_matrices(define, mod, pars, set_wave_dir, options, wdir=None): """ Assemble the blocks of dispersion eigenvalue problem matrices. """ define_dict = define(filename_mesh=options.mesh_filename, pars=pars, approx_order=options.order, refinement_level=options.refine, solver_conf=options.solver_conf, plane=options.plane, post_process=options.post_process, **options.define_kwargs) conf = ProblemConf.from_dict(define_dict, mod) pb = Problem.from_conf(conf) pb.dispersion_options = options pb.set_output_dir(options.output_dir) dim = pb.domain.shape.dim # Set the normalized wave vector direction to the material(s). if wdir is None: wdir = nm.asarray(options.wave_dir[:dim], dtype=nm.float64) wdir = wdir / nm.linalg.norm(wdir) set_wave_dir(pb, wdir) bbox = pb.domain.mesh.get_bounding_box() size = (bbox[1] - bbox[0]).max() scaling0 = apply_unit_multipliers([1.0], ['length'], options.unit_multipliers)[0] scaling = scaling0 if options.mesh_size is not None: scaling *= options.mesh_size / size output('scaling factor of periodic cell mesh coordinates:', scaling) output('new mesh size with applied unit multipliers:', scaling * size) pb.domain.mesh.coors[:] *= scaling pb.set_mesh_coors(pb.domain.mesh.coors, update_fields=True) bzone = 2.0 * nm.pi / (scaling * size) output('1. Brillouin zone size:', bzone * scaling0) output('1. Brillouin zone size with applied unit multipliers:', bzone) pb.time_update() pb.update_materials() # Assemble the matrices. mtxs = {} for key, eq in pb.equations.iteritems(): mtxs[key] = mtx = pb.mtx_a.copy() mtx = eq.evaluate(mode='weak', dw_mode='matrix', asm_obj=mtx) mtx.eliminate_zeros() output_array_stats(mtx.data, 'nonzeros in %s' % key)	output('symmetry checks:')	sfepy.base.base.output
#!/usr/bin/env python """ Dispersion analysis of a heterogeneous finite scale periodic cell. The periodic cell mesh has to contain two subdomains Y1 (with the cell ids 1), Y2 (with the cell ids 2), so that different material properties can be defined in each of the subdomains (see ``--pars`` option). The command line parameters can be given in any consistent unit set, for example the basic SI units. The ``--unit-multipliers`` option can be used to rescale the input units to ones more suitable to the simulation, for example to prevent having different matrix blocks with large differences of matrix entries magnitudes. The results are then in the rescaled units. Usage Examples -------------- Default material parameters, a square periodic cell with a spherical inclusion, logs also standard pressure dilatation and shear waves, no eigenvectors:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only As above, with custom eigenvalue solver parameters, and different number of eigenvalues, mesh size and units used in the calculation:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --solver-conf="kind='eig.scipy', method='eigsh', tol=1e-10, maxiter=1000, which='LM', sigma=0" --log-std-waves -n 5 --range=0,640,101 --mode=omega --unit-multipliers=1e-6,1e-2,1e-3 --mesh-size=1e-2 --eigs-only Default material parameters, a square periodic cell with a square inclusion, and a very small mesh to allow comparing the omega and kappa modes (full matrix solver required!):: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.qevp', method='companion', mode='inverted', solver={kind='eig.scipy', method='eig'}" --log-std-waves -n 500 --range=0,4000000,1001 --mesh-size=1e-2 --mode=kappa --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/kappa View/compare the resulting logs:: python script/plot_logs.py output/omega/frequencies.txt --no-legends -g 1 -o mode-omega.png python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends -o mode-kappa.png python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends --swap-axes -o mode-kappa-t.png In contrast to the heterogeneous square periodic cell, a homogeneous square periodic cell (the region Y2 is empty):: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_1m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega-h python script/plot_logs.py output/omega-h/frequencies.txt --no-legends -g 1 -o mode-omega-h.png Use the Brillouin stepper:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves -n=60 --eigs-only --no-legends --stepper=brillouin python script/plot_logs.py output/frequencies.txt -g 0 --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-kappas.png python script/plot_logs.py output/frequencies.txt -g 1 --no-legends --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-omegas.png Additional arguments can be passed to the problem configuration's :func:`define()` function using the ``--define-kwargs`` option. In this file, only the mesh vertex separation parameter `mesh_eps` can be used:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only --define-kwargs="mesh_eps=1e-10" --save-regions """ from __future__ import absolute_import import os import sys sys.path.append('.') import gc from copy import copy from argparse import ArgumentParser, RawDescriptionHelpFormatter import numpy as nm import matplotlib.pyplot as plt from sfepy.base.base import import_file, output, Struct from sfepy.base.conf import dict_from_string, ProblemConf from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options from sfepy.base.log import Log from sfepy.discrete.fem import MeshIO from sfepy.mechanics.matcoefs import stiffness_from_youngpoisson as stiffness import sfepy.mechanics.matcoefs as mc from sfepy.mechanics.units import apply_unit_multipliers import sfepy.discrete.fem.periodic as per from sfepy.discrete.fem.meshio import convert_complex_output from sfepy.homogenization.utils import define_box_regions from sfepy.discrete import Problem from sfepy.mechanics.tensors import get_von_mises_stress from sfepy.solvers import Solver from sfepy.solvers.ts import get_print_info, TimeStepper from sfepy.linalg.utils import output_array_stats, max_diff_csr def apply_units(pars, unit_multipliers): new_pars = apply_unit_multipliers(pars, ['stress', 'one', 'density', 'stress', 'one' ,'density'], unit_multipliers) return new_pars def compute_von_mises(out, pb, state, extend=False, wmag=None, wdir=None): """ Calculate the von Mises stress. """ stress = pb.evaluate('ev_cauchy_stress.i.Omega(m.D, u)', mode='el_avg') vms = get_von_mises_stress(stress.squeeze()) vms.shape = (vms.shape[0], 1, 1, 1) out['von_mises_stress'] = Struct(name='output_data', mode='cell', data=vms) return out def define(filename_mesh, pars, approx_order, refinement_level, solver_conf, plane='strain', post_process=False, mesh_eps=1e-8): io = MeshIO.any_from_filename(filename_mesh) bbox = io.read_bounding_box() dim = bbox.shape[1] options = { 'absolute_mesh_path' : True, 'refinement_level' : refinement_level, 'allow_empty_regions' : True, 'post_process_hook' : 'compute_von_mises' if post_process else None, } fields = { 'displacement': ('complex', dim, 'Omega', approx_order), } young1, poisson1, density1, young2, poisson2, density2 = pars materials = { 'm' : ({ 'D' : {'Y1' : stiffness(dim, young=young1, poisson=poisson1, plane=plane), 'Y2' : stiffness(dim, young=young2, poisson=poisson2, plane=plane)}, 'density' : {'Y1' : density1, 'Y2' : density2}, },), 'wave' : 'get_wdir', } variables = { 'u' : ('unknown field', 'displacement', 0), 'v' : ('test field', 'displacement', 'u'), } regions = { 'Omega' : 'all', 'Y1': 'cells of group 1', 'Y2': 'cells of group 2', } regions.update(define_box_regions(dim, bbox[0], bbox[1], mesh_eps)) ebcs = { } if dim == 3: epbcs = { 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'}, 'match_x_plane'), 'periodic_y' : (['Near', 'Far'], {'u.all' : 'u.all'}, 'match_y_plane'), 'periodic_z' : (['Top', 'Bottom'], {'u.all' : 'u.all'}, 'match_z_plane'), } else: epbcs = { 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'}, 'match_y_line'), 'periodic_y' : (['Bottom', 'Top'], {'u.all' : 'u.all'}, 'match_x_line'), } per.set_accuracy(mesh_eps) functions = { 'match_x_plane' : (per.match_x_plane,), 'match_y_plane' : (per.match_y_plane,), 'match_z_plane' : (per.match_z_plane,), 'match_x_line' : (per.match_x_line,), 'match_y_line' : (per.match_y_line,), 'get_wdir' : (get_wdir,), } integrals = { 'i' : 2 * approx_order, } equations = { 'K' : 'dw_lin_elastic.i.Omega(m.D, v, u)', 'S' : 'dw_elastic_wave.i.Omega(m.D, wave.vec, v, u)', 'R' : """1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, u, v) - 1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, v, u)""", 'M' : 'dw_volume_dot.i.Omega(m.density, v, u)', } solver_0 = solver_conf.copy() solver_0['name'] = 'eig' return locals() def get_wdir(ts, coors, mode=None, equations=None, term=None, problem=None, wdir=None, **kwargs): if mode == 'special': return {'vec' : wdir} def set_wave_dir(pb, wdir): materials = pb.get_materials() wave_mat = materials['wave'] wave_mat.set_extra_args(wdir=wdir) def save_materials(output_dir, pb, options): stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)', mode='el_avg', copy_materials=False, verbose=False) young, poisson = mc.youngpoisson_from_stiffness(stiffness, plane=options.plane) density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)', mode='el_avg', copy_materials=False, verbose=False) out = {} out['young'] = Struct(name='young', mode='cell', data=young[..., None, None]) out['poisson'] = Struct(name='poisson', mode='cell', data=poisson[..., None, None]) out['density'] = Struct(name='density', mode='cell', data=density) materials_filename = os.path.join(output_dir, 'materials.vtk') pb.save_state(materials_filename, out=out) def get_std_wave_fun(pb, options): stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)', mode='el_avg', copy_materials=False, verbose=False) young, poisson = mc.youngpoisson_from_stiffness(stiffness, plane=options.plane) density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)', mode='el_avg', copy_materials=False, verbose=False) lam, mu = mc.lame_from_youngpoisson(young, poisson, plane=options.plane) alam = nm.average(lam) amu = nm.average(mu) adensity = nm.average(density) cp = nm.sqrt((alam + 2.0 * amu) / adensity) cs = nm.sqrt(amu / adensity) output('average p-wave speed:', cp) output('average shear wave speed:', cs) log_names = [r'$\omega_p$', r'$\omega_s$'] log_plot_kwargs = [{'ls' : '--', 'color' : 'k'}, {'ls' : '--', 'color' : 'gray'}] if options.mode == 'omega': fun = lambda wmag, wdir: (cp * wmag, cs * wmag) else: fun = lambda wmag, wdir: (wmag / cp, wmag / cs) return fun, log_names, log_plot_kwargs def get_stepper(rng, pb, options): if options.stepper == 'linear': stepper = TimeStepper(rng[0], rng[1], dt=None, n_step=rng[2]) return stepper bbox = pb.domain.mesh.get_bounding_box() bzone = 2.0 * nm.pi / (bbox[1] - bbox[0]) num = rng[2] // 3 class BrillouinStepper(Struct): """ Step over 1. Brillouin zone in xy plane. """ def __init__(self, t0, t1, dt=None, n_step=None, step=None, **kwargs): Struct.__init__(self, t0=t0, t1=t1, dt=dt, n_step=n_step, step=step) self.n_digit, self.format, self.suffix = get_print_info(self.n_step) def __iter__(self): ts = TimeStepper(0, bzone[0], dt=None, n_step=num) for ii, val in ts: yield ii, val, nm.array([1.0, 0.0]) if ii == (num-2): break ts = TimeStepper(0, bzone[1], dt=None, n_step=num) for ii, k1 in ts: wdir = nm.array([bzone[0], k1]) val = nm.linalg.norm(wdir) wdir = wdir / val yield num + ii, val, wdir if ii == (num-2): break wdir = nm.array([bzone[0], bzone[1]]) val = nm.linalg.norm(wdir) wdir = wdir / val ts = TimeStepper(0, 1, dt=None, n_step=num) for ii, _ in ts: yield 2 * num + ii, val * (1.0 - float(ii)/(num-1)), wdir stepper = BrillouinStepper(0, 1, n_step=rng[2]) return stepper def save_eigenvectors(filename, svecs, wmag, wdir, pb): if svecs is None: return variables = pb.get_variables() # Make full eigenvectors (add DOFs fixed by boundary conditions). vecs = nm.empty((variables.di.ptr[-1], svecs.shape[1]), dtype=svecs.dtype) for ii in range(svecs.shape[1]): vecs[:, ii] = variables.make_full_vec(svecs[:, ii]) # Save the eigenvectors. out = {} state = pb.create_state() pp_name = pb.conf.options.get('post_process_hook') pp = getattr(pb.conf.funmod, pp_name if pp_name is not None else '', lambda out, *args, **kwargs: out) for ii in range(svecs.shape[1]): state.set_full(vecs[:, ii]) aux = state.create_output_dict() aux2 = {} pp(aux2, pb, state, wmag=wmag, wdir=wdir) aux.update(convert_complex_output(aux2)) out.update({key + '%03d' % ii : aux[key] for key in aux}) pb.save_state(filename, out=out) def assemble_matrices(define, mod, pars, set_wave_dir, options, wdir=None): """ Assemble the blocks of dispersion eigenvalue problem matrices. """ define_dict = define(filename_mesh=options.mesh_filename, pars=pars, approx_order=options.order, refinement_level=options.refine, solver_conf=options.solver_conf, plane=options.plane, post_process=options.post_process, **options.define_kwargs) conf = ProblemConf.from_dict(define_dict, mod) pb = Problem.from_conf(conf) pb.dispersion_options = options pb.set_output_dir(options.output_dir) dim = pb.domain.shape.dim # Set the normalized wave vector direction to the material(s). if wdir is None: wdir = nm.asarray(options.wave_dir[:dim], dtype=nm.float64) wdir = wdir / nm.linalg.norm(wdir) set_wave_dir(pb, wdir) bbox = pb.domain.mesh.get_bounding_box() size = (bbox[1] - bbox[0]).max() scaling0 = apply_unit_multipliers([1.0], ['length'], options.unit_multipliers)[0] scaling = scaling0 if options.mesh_size is not None: scaling *= options.mesh_size / size output('scaling factor of periodic cell mesh coordinates:', scaling) output('new mesh size with applied unit multipliers:', scaling * size) pb.domain.mesh.coors[:] *= scaling pb.set_mesh_coors(pb.domain.mesh.coors, update_fields=True) bzone = 2.0 * nm.pi / (scaling * size) output('1. Brillouin zone size:', bzone * scaling0) output('1. Brillouin zone size with applied unit multipliers:', bzone) pb.time_update() pb.update_materials() # Assemble the matrices. mtxs = {} for key, eq in pb.equations.iteritems(): mtxs[key] = mtx = pb.mtx_a.copy() mtx = eq.evaluate(mode='weak', dw_mode='matrix', asm_obj=mtx) mtx.eliminate_zeros() output_array_stats(mtx.data, 'nonzeros in %s' % key) output('symmetry checks:') output('%s - %s^T:' % (key, key), max_diff_csr(mtx, mtx.T)) output('%s - %s^H:' % (key, key), max_diff_csr(mtx, mtx.H)) return pb, wdir, bzone, mtxs def setup_n_eigs(options, pb, mtxs): """ Setup the numbers of eigenvalues based on options and numbers of DOFs. """ solver_n_eigs = n_eigs = options.n_eigs n_dof = mtxs['K'].shape[0] if options.mode == 'omega': if options.n_eigs > n_dof: n_eigs = n_dof solver_n_eigs = None else: if options.n_eigs > 2 * n_dof: n_eigs = 2 * n_dof solver_n_eigs = None return solver_n_eigs, n_eigs def build_evp_matrices(mtxs, val, mode, pb): """ Build the matrices of the dispersion eigenvalue problem. """ if mode == 'omega': mtx_a = mtxs['K'] + val**2 * mtxs['S'] + val * mtxs['R'] output('A - A^H:', max_diff_csr(mtx_a, mtx_a.H)) evp_mtxs = (mtx_a, mtxs['M']) else: evp_mtxs = (mtxs['S'], mtxs['R'], mtxs['K'] - val**2 * mtxs['M']) return evp_mtxs def process_evp_results(eigs, svecs, val, wdir, bzone, pb, mtxs, options, std_wave_fun=None): """ Transform eigenvalues to either omegas or kappas, depending on `mode`. Transform eigenvectors, if available, depending on `mode`. Return also the values to log. """ if options.mode == 'omega': omegas = nm.sqrt(eigs)	output('eigs, omegas:')	sfepy.base.base.output
#!/usr/bin/env python """ Dispersion analysis of a heterogeneous finite scale periodic cell. The periodic cell mesh has to contain two subdomains Y1 (with the cell ids 1), Y2 (with the cell ids 2), so that different material properties can be defined in each of the subdomains (see ``--pars`` option). The command line parameters can be given in any consistent unit set, for example the basic SI units. The ``--unit-multipliers`` option can be used to rescale the input units to ones more suitable to the simulation, for example to prevent having different matrix blocks with large differences of matrix entries magnitudes. The results are then in the rescaled units. Usage Examples -------------- Default material parameters, a square periodic cell with a spherical inclusion, logs also standard pressure dilatation and shear waves, no eigenvectors:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only As above, with custom eigenvalue solver parameters, and different number of eigenvalues, mesh size and units used in the calculation:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --solver-conf="kind='eig.scipy', method='eigsh', tol=1e-10, maxiter=1000, which='LM', sigma=0" --log-std-waves -n 5 --range=0,640,101 --mode=omega --unit-multipliers=1e-6,1e-2,1e-3 --mesh-size=1e-2 --eigs-only Default material parameters, a square periodic cell with a square inclusion, and a very small mesh to allow comparing the omega and kappa modes (full matrix solver required!):: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.qevp', method='companion', mode='inverted', solver={kind='eig.scipy', method='eig'}" --log-std-waves -n 500 --range=0,4000000,1001 --mesh-size=1e-2 --mode=kappa --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/kappa View/compare the resulting logs:: python script/plot_logs.py output/omega/frequencies.txt --no-legends -g 1 -o mode-omega.png python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends -o mode-kappa.png python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends --swap-axes -o mode-kappa-t.png In contrast to the heterogeneous square periodic cell, a homogeneous square periodic cell (the region Y2 is empty):: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_1m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega-h python script/plot_logs.py output/omega-h/frequencies.txt --no-legends -g 1 -o mode-omega-h.png Use the Brillouin stepper:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves -n=60 --eigs-only --no-legends --stepper=brillouin python script/plot_logs.py output/frequencies.txt -g 0 --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-kappas.png python script/plot_logs.py output/frequencies.txt -g 1 --no-legends --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-omegas.png Additional arguments can be passed to the problem configuration's :func:`define()` function using the ``--define-kwargs`` option. In this file, only the mesh vertex separation parameter `mesh_eps` can be used:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only --define-kwargs="mesh_eps=1e-10" --save-regions """ from __future__ import absolute_import import os import sys sys.path.append('.') import gc from copy import copy from argparse import ArgumentParser, RawDescriptionHelpFormatter import numpy as nm import matplotlib.pyplot as plt from sfepy.base.base import import_file, output, Struct from sfepy.base.conf import dict_from_string, ProblemConf from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options from sfepy.base.log import Log from sfepy.discrete.fem import MeshIO from sfepy.mechanics.matcoefs import stiffness_from_youngpoisson as stiffness import sfepy.mechanics.matcoefs as mc from sfepy.mechanics.units import apply_unit_multipliers import sfepy.discrete.fem.periodic as per from sfepy.discrete.fem.meshio import convert_complex_output from sfepy.homogenization.utils import define_box_regions from sfepy.discrete import Problem from sfepy.mechanics.tensors import get_von_mises_stress from sfepy.solvers import Solver from sfepy.solvers.ts import get_print_info, TimeStepper from sfepy.linalg.utils import output_array_stats, max_diff_csr def apply_units(pars, unit_multipliers): new_pars = apply_unit_multipliers(pars, ['stress', 'one', 'density', 'stress', 'one' ,'density'], unit_multipliers) return new_pars def compute_von_mises(out, pb, state, extend=False, wmag=None, wdir=None): """ Calculate the von Mises stress. """ stress = pb.evaluate('ev_cauchy_stress.i.Omega(m.D, u)', mode='el_avg') vms = get_von_mises_stress(stress.squeeze()) vms.shape = (vms.shape[0], 1, 1, 1) out['von_mises_stress'] = Struct(name='output_data', mode='cell', data=vms) return out def define(filename_mesh, pars, approx_order, refinement_level, solver_conf, plane='strain', post_process=False, mesh_eps=1e-8): io = MeshIO.any_from_filename(filename_mesh) bbox = io.read_bounding_box() dim = bbox.shape[1] options = { 'absolute_mesh_path' : True, 'refinement_level' : refinement_level, 'allow_empty_regions' : True, 'post_process_hook' : 'compute_von_mises' if post_process else None, } fields = { 'displacement': ('complex', dim, 'Omega', approx_order), } young1, poisson1, density1, young2, poisson2, density2 = pars materials = { 'm' : ({ 'D' : {'Y1' : stiffness(dim, young=young1, poisson=poisson1, plane=plane), 'Y2' : stiffness(dim, young=young2, poisson=poisson2, plane=plane)}, 'density' : {'Y1' : density1, 'Y2' : density2}, },), 'wave' : 'get_wdir', } variables = { 'u' : ('unknown field', 'displacement', 0), 'v' : ('test field', 'displacement', 'u'), } regions = { 'Omega' : 'all', 'Y1': 'cells of group 1', 'Y2': 'cells of group 2', } regions.update(define_box_regions(dim, bbox[0], bbox[1], mesh_eps)) ebcs = { } if dim == 3: epbcs = { 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'}, 'match_x_plane'), 'periodic_y' : (['Near', 'Far'], {'u.all' : 'u.all'}, 'match_y_plane'), 'periodic_z' : (['Top', 'Bottom'], {'u.all' : 'u.all'}, 'match_z_plane'), } else: epbcs = { 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'}, 'match_y_line'), 'periodic_y' : (['Bottom', 'Top'], {'u.all' : 'u.all'}, 'match_x_line'), } per.set_accuracy(mesh_eps) functions = { 'match_x_plane' : (per.match_x_plane,), 'match_y_plane' : (per.match_y_plane,), 'match_z_plane' : (per.match_z_plane,), 'match_x_line' : (per.match_x_line,), 'match_y_line' : (per.match_y_line,), 'get_wdir' : (get_wdir,), } integrals = { 'i' : 2 * approx_order, } equations = { 'K' : 'dw_lin_elastic.i.Omega(m.D, v, u)', 'S' : 'dw_elastic_wave.i.Omega(m.D, wave.vec, v, u)', 'R' : """1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, u, v) - 1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, v, u)""", 'M' : 'dw_volume_dot.i.Omega(m.density, v, u)', } solver_0 = solver_conf.copy() solver_0['name'] = 'eig' return locals() def get_wdir(ts, coors, mode=None, equations=None, term=None, problem=None, wdir=None, **kwargs): if mode == 'special': return {'vec' : wdir} def set_wave_dir(pb, wdir): materials = pb.get_materials() wave_mat = materials['wave'] wave_mat.set_extra_args(wdir=wdir) def save_materials(output_dir, pb, options): stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)', mode='el_avg', copy_materials=False, verbose=False) young, poisson = mc.youngpoisson_from_stiffness(stiffness, plane=options.plane) density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)', mode='el_avg', copy_materials=False, verbose=False) out = {} out['young'] = Struct(name='young', mode='cell', data=young[..., None, None]) out['poisson'] = Struct(name='poisson', mode='cell', data=poisson[..., None, None]) out['density'] = Struct(name='density', mode='cell', data=density) materials_filename = os.path.join(output_dir, 'materials.vtk') pb.save_state(materials_filename, out=out) def get_std_wave_fun(pb, options): stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)', mode='el_avg', copy_materials=False, verbose=False) young, poisson = mc.youngpoisson_from_stiffness(stiffness, plane=options.plane) density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)', mode='el_avg', copy_materials=False, verbose=False) lam, mu = mc.lame_from_youngpoisson(young, poisson, plane=options.plane) alam = nm.average(lam) amu = nm.average(mu) adensity = nm.average(density) cp = nm.sqrt((alam + 2.0 * amu) / adensity) cs = nm.sqrt(amu / adensity) output('average p-wave speed:', cp) output('average shear wave speed:', cs) log_names = [r'$\omega_p$', r'$\omega_s$'] log_plot_kwargs = [{'ls' : '--', 'color' : 'k'}, {'ls' : '--', 'color' : 'gray'}] if options.mode == 'omega': fun = lambda wmag, wdir: (cp * wmag, cs * wmag) else: fun = lambda wmag, wdir: (wmag / cp, wmag / cs) return fun, log_names, log_plot_kwargs def get_stepper(rng, pb, options): if options.stepper == 'linear': stepper = TimeStepper(rng[0], rng[1], dt=None, n_step=rng[2]) return stepper bbox = pb.domain.mesh.get_bounding_box() bzone = 2.0 * nm.pi / (bbox[1] - bbox[0]) num = rng[2] // 3 class BrillouinStepper(Struct): """ Step over 1. Brillouin zone in xy plane. """ def __init__(self, t0, t1, dt=None, n_step=None, step=None, **kwargs): Struct.__init__(self, t0=t0, t1=t1, dt=dt, n_step=n_step, step=step) self.n_digit, self.format, self.suffix = get_print_info(self.n_step) def __iter__(self): ts = TimeStepper(0, bzone[0], dt=None, n_step=num) for ii, val in ts: yield ii, val, nm.array([1.0, 0.0]) if ii == (num-2): break ts = TimeStepper(0, bzone[1], dt=None, n_step=num) for ii, k1 in ts: wdir = nm.array([bzone[0], k1]) val = nm.linalg.norm(wdir) wdir = wdir / val yield num + ii, val, wdir if ii == (num-2): break wdir = nm.array([bzone[0], bzone[1]]) val = nm.linalg.norm(wdir) wdir = wdir / val ts = TimeStepper(0, 1, dt=None, n_step=num) for ii, _ in ts: yield 2 * num + ii, val * (1.0 - float(ii)/(num-1)), wdir stepper = BrillouinStepper(0, 1, n_step=rng[2]) return stepper def save_eigenvectors(filename, svecs, wmag, wdir, pb): if svecs is None: return variables = pb.get_variables() # Make full eigenvectors (add DOFs fixed by boundary conditions). vecs = nm.empty((variables.di.ptr[-1], svecs.shape[1]), dtype=svecs.dtype) for ii in range(svecs.shape[1]): vecs[:, ii] = variables.make_full_vec(svecs[:, ii]) # Save the eigenvectors. out = {} state = pb.create_state() pp_name = pb.conf.options.get('post_process_hook') pp = getattr(pb.conf.funmod, pp_name if pp_name is not None else '', lambda out, *args, **kwargs: out) for ii in range(svecs.shape[1]): state.set_full(vecs[:, ii]) aux = state.create_output_dict() aux2 = {} pp(aux2, pb, state, wmag=wmag, wdir=wdir) aux.update(convert_complex_output(aux2)) out.update({key + '%03d' % ii : aux[key] for key in aux}) pb.save_state(filename, out=out) def assemble_matrices(define, mod, pars, set_wave_dir, options, wdir=None): """ Assemble the blocks of dispersion eigenvalue problem matrices. """ define_dict = define(filename_mesh=options.mesh_filename, pars=pars, approx_order=options.order, refinement_level=options.refine, solver_conf=options.solver_conf, plane=options.plane, post_process=options.post_process, **options.define_kwargs) conf = ProblemConf.from_dict(define_dict, mod) pb = Problem.from_conf(conf) pb.dispersion_options = options pb.set_output_dir(options.output_dir) dim = pb.domain.shape.dim # Set the normalized wave vector direction to the material(s). if wdir is None: wdir = nm.asarray(options.wave_dir[:dim], dtype=nm.float64) wdir = wdir / nm.linalg.norm(wdir) set_wave_dir(pb, wdir) bbox = pb.domain.mesh.get_bounding_box() size = (bbox[1] - bbox[0]).max() scaling0 = apply_unit_multipliers([1.0], ['length'], options.unit_multipliers)[0] scaling = scaling0 if options.mesh_size is not None: scaling *= options.mesh_size / size output('scaling factor of periodic cell mesh coordinates:', scaling) output('new mesh size with applied unit multipliers:', scaling * size) pb.domain.mesh.coors[:] *= scaling pb.set_mesh_coors(pb.domain.mesh.coors, update_fields=True) bzone = 2.0 * nm.pi / (scaling * size) output('1. Brillouin zone size:', bzone * scaling0) output('1. Brillouin zone size with applied unit multipliers:', bzone) pb.time_update() pb.update_materials() # Assemble the matrices. mtxs = {} for key, eq in pb.equations.iteritems(): mtxs[key] = mtx = pb.mtx_a.copy() mtx = eq.evaluate(mode='weak', dw_mode='matrix', asm_obj=mtx) mtx.eliminate_zeros() output_array_stats(mtx.data, 'nonzeros in %s' % key) output('symmetry checks:') output('%s - %s^T:' % (key, key), max_diff_csr(mtx, mtx.T)) output('%s - %s^H:' % (key, key), max_diff_csr(mtx, mtx.H)) return pb, wdir, bzone, mtxs def setup_n_eigs(options, pb, mtxs): """ Setup the numbers of eigenvalues based on options and numbers of DOFs. """ solver_n_eigs = n_eigs = options.n_eigs n_dof = mtxs['K'].shape[0] if options.mode == 'omega': if options.n_eigs > n_dof: n_eigs = n_dof solver_n_eigs = None else: if options.n_eigs > 2 * n_dof: n_eigs = 2 * n_dof solver_n_eigs = None return solver_n_eigs, n_eigs def build_evp_matrices(mtxs, val, mode, pb): """ Build the matrices of the dispersion eigenvalue problem. """ if mode == 'omega': mtx_a = mtxs['K'] + val**2 * mtxs['S'] + val * mtxs['R'] output('A - A^H:', max_diff_csr(mtx_a, mtx_a.H)) evp_mtxs = (mtx_a, mtxs['M']) else: evp_mtxs = (mtxs['S'], mtxs['R'], mtxs['K'] - val**2 * mtxs['M']) return evp_mtxs def process_evp_results(eigs, svecs, val, wdir, bzone, pb, mtxs, options, std_wave_fun=None): """ Transform eigenvalues to either omegas or kappas, depending on `mode`. Transform eigenvectors, if available, depending on `mode`. Return also the values to log. """ if options.mode == 'omega': omegas = nm.sqrt(eigs) output('eigs, omegas:') for ii, om in enumerate(omegas): output('{:>3}. {: .10e}, {:.10e}'.format(ii, eigs[ii], om)) if options.stepper == 'linear': out = tuple(eigs) + tuple(omegas) else: out = tuple(val * wdir) + tuple(omegas) if std_wave_fun is not None: out = out + std_wave_fun(val, wdir) return omegas, svecs, out else: kappas = eigs.copy() rks = kappas.copy() # Mask modes far from 1. Brillouin zone. max_kappa = 1.2 * bzone kappas[kappas.real > max_kappa] = nm.nan # Mask non-physical modes. kappas[kappas.real < 0] = nm.nan kappas[nm.abs(kappas.imag) > 1e-10] = nm.nan out = tuple(kappas.real) output('raw kappas, masked real part:',) for ii, kr in enumerate(kappas.real): output('{:>3}. {: 23.5e}, {:.10e}'.format(ii, rks[ii], kr)) if svecs is not None: n_dof = mtxs['K'].shape[0] # Select only vectors corresponding to physical modes. ii = nm.isfinite(kappas.real) svecs = svecs[:n_dof, ii] if std_wave_fun is not None: out = out + tuple(ii if ii <= max_kappa else nm.nan for ii in std_wave_fun(val, wdir)) return kappas, svecs, out helps = { 'pars' : 'material parameters in Y1, Y2 subdomains in basic units' ' [default: %(default)s]', 'conf' : 'if given, an alternative problem description file with apply_units() and' ' define() functions [default: %(default)s]', 'define_kwargs' : 'additional keyword arguments passed to define()', 'mesh_size' : 'desired mesh size (max. of bounding box dimensions) in basic units' ' - the input periodic cell mesh is rescaled to this size' ' [default: %(default)s]', 'unit_multipliers' : 'basic unit multipliers (time, length, mass) [default: %(default)s]', 'plane' : 'for 2D problems, plane strain or stress hypothesis selection' ' [default: %(default)s]', 'wave_dir' : 'the wave vector direction (will be normalized)' ' [default: %(default)s]', 'mode' : 'solution mode: omega = solve a generalized EVP for omega,' ' kappa = solve a quadratic generalized EVP for kappa' ' [default: %(default)s]', 'stepper' : 'the range stepper. For "brillouin", only the number' ' of items from --range is used' ' [default: %(default)s]', 'range' : 'the wave vector magnitude / frequency range' ' (like numpy.linspace) depending on the mode option' ' [default: %(default)s]', 'order' : 'displacement field approximation order [default: %(default)s]', 'refine' : 'number of uniform mesh refinements [default: %(default)s]', 'n_eigs' : 'the number of eigenvalues to compute [default: %(default)s]', 'eigs_only' : 'compute only eigenvalues, not eigenvectors', 'post_process' : 'post-process eigenvectors', 'solver_conf' : 'eigenvalue problem solver configuration options' ' [default: %(default)s]', 'save_regions' : 'save defined regions into' ' <output_directory>/regions.vtk', 'save_materials' : 'save material parameters into' ' <output_directory>/materials.vtk', 'log_std_waves' : 'log also standard pressure dilatation and shear waves', 'no_legends' : 'do not show legends in the log plots', 'no_show' : 'do not show the log figure', 'silent' : 'do not print messages to screen', 'clear' : 'clear old solution files from output directory', 'output_dir' : 'output directory [default: %(default)s]', 'mesh_filename' : 'input periodic cell mesh file name [default: %(default)s]', } def main(): # Aluminium and epoxy. default_pars = '70e9,0.35,2.799e3, 3.8e9,0.27,1.142e3' default_solver_conf = ("kind='eig.scipy',method='eigsh',tol=1.0e-5," "maxiter=1000,which='LM',sigma=0.0") parser = ArgumentParser(description=__doc__, formatter_class=RawDescriptionHelpFormatter) parser.add_argument('--pars', metavar='young1,poisson1,density1' ',young2,poisson2,density2', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='pars', default=default_pars, help=helps['pars']) parser.add_argument('--conf', metavar='filename', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='conf', default=None, help=helps['conf']) parser.add_argument('--define-kwargs', metavar='dict-like', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='define_kwargs', default=None, help=helps['define_kwargs']) parser.add_argument('--mesh-size', type=float, metavar='float', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='mesh_size', default=None, help=helps['mesh_size']) parser.add_argument('--unit-multipliers', metavar='c_time,c_length,c_mass', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='unit_multipliers', default='1.0,1.0,1.0', help=helps['unit_multipliers']) parser.add_argument('--plane', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='plane', choices=['strain', 'stress'], default='strain', help=helps['plane']) parser.add_argument('--wave-dir', metavar='float,float[,float]', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='wave_dir', default='1.0,0.0,0.0', help=helps['wave_dir']) parser.add_argument('--mode', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='mode', choices=['omega', 'kappa'], default='omega', help=helps['mode']) parser.add_argument('--stepper', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='stepper', choices=['linear', 'brillouin'], default='linear', help=helps['stepper']) parser.add_argument('--range', metavar='start,stop,count', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='range', default='0,6.4,33', help=helps['range']) parser.add_argument('--order', metavar='int', type=int, action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='order', default=1, help=helps['order']) parser.add_argument('--refine', metavar='int', type=int, action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='refine', default=0, help=helps['refine']) parser.add_argument('-n', '--n-eigs', metavar='int', type=int, action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='n_eigs', default=6, help=helps['n_eigs']) group = parser.add_mutually_exclusive_group() group.add_argument('--eigs-only', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='eigs_only', default=False, help=helps['eigs_only']) group.add_argument('--post-process', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='post_process', default=False, help=helps['post_process']) parser.add_argument('--solver-conf', metavar='dict-like', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='solver_conf', default=default_solver_conf, help=helps['solver_conf']) parser.add_argument('--save-regions', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='save_regions', default=False, help=helps['save_regions']) parser.add_argument('--save-materials', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='save_materials', default=False, help=helps['save_materials']) parser.add_argument('--log-std-waves', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='log_std_waves', default=False, help=helps['log_std_waves']) parser.add_argument('--no-legends', action="https://huggingface.co/datasets/luna-code/sfepy/store_false", dest='show_legends', default=True, help=helps['no_legends']) parser.add_argument('--no-show', action="https://huggingface.co/datasets/luna-code/sfepy/store_false", dest='show', default=True, help=helps['no_show']) parser.add_argument('--silent', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='silent', default=False, help=helps['silent']) parser.add_argument('-c', '--clear', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='clear', default=False, help=helps['clear']) parser.add_argument('-o', '--output-dir', metavar='path', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='output_dir', default='output', help=helps['output_dir']) parser.add_argument('mesh_filename', default='', help=helps['mesh_filename']) options = parser.parse_args() output_dir = options.output_dir output.set_output(filename=os.path.join(output_dir,'output_log.txt'), combined=options.silent == False) if options.conf is not None: mod =	import_file(options.conf)	sfepy.base.base.import_file
#!/usr/bin/env python """ Dispersion analysis of a heterogeneous finite scale periodic cell. The periodic cell mesh has to contain two subdomains Y1 (with the cell ids 1), Y2 (with the cell ids 2), so that different material properties can be defined in each of the subdomains (see ``--pars`` option). The command line parameters can be given in any consistent unit set, for example the basic SI units. The ``--unit-multipliers`` option can be used to rescale the input units to ones more suitable to the simulation, for example to prevent having different matrix blocks with large differences of matrix entries magnitudes. The results are then in the rescaled units. Usage Examples -------------- Default material parameters, a square periodic cell with a spherical inclusion, logs also standard pressure dilatation and shear waves, no eigenvectors:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only As above, with custom eigenvalue solver parameters, and different number of eigenvalues, mesh size and units used in the calculation:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --solver-conf="kind='eig.scipy', method='eigsh', tol=1e-10, maxiter=1000, which='LM', sigma=0" --log-std-waves -n 5 --range=0,640,101 --mode=omega --unit-multipliers=1e-6,1e-2,1e-3 --mesh-size=1e-2 --eigs-only Default material parameters, a square periodic cell with a square inclusion, and a very small mesh to allow comparing the omega and kappa modes (full matrix solver required!):: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.qevp', method='companion', mode='inverted', solver={kind='eig.scipy', method='eig'}" --log-std-waves -n 500 --range=0,4000000,1001 --mesh-size=1e-2 --mode=kappa --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/kappa View/compare the resulting logs:: python script/plot_logs.py output/omega/frequencies.txt --no-legends -g 1 -o mode-omega.png python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends -o mode-kappa.png python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends --swap-axes -o mode-kappa-t.png In contrast to the heterogeneous square periodic cell, a homogeneous square periodic cell (the region Y2 is empty):: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_1m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega-h python script/plot_logs.py output/omega-h/frequencies.txt --no-legends -g 1 -o mode-omega-h.png Use the Brillouin stepper:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves -n=60 --eigs-only --no-legends --stepper=brillouin python script/plot_logs.py output/frequencies.txt -g 0 --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-kappas.png python script/plot_logs.py output/frequencies.txt -g 1 --no-legends --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-omegas.png Additional arguments can be passed to the problem configuration's :func:`define()` function using the ``--define-kwargs`` option. In this file, only the mesh vertex separation parameter `mesh_eps` can be used:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only --define-kwargs="mesh_eps=1e-10" --save-regions """ from __future__ import absolute_import import os import sys sys.path.append('.') import gc from copy import copy from argparse import ArgumentParser, RawDescriptionHelpFormatter import numpy as nm import matplotlib.pyplot as plt from sfepy.base.base import import_file, output, Struct from sfepy.base.conf import dict_from_string, ProblemConf from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options from sfepy.base.log import Log from sfepy.discrete.fem import MeshIO from sfepy.mechanics.matcoefs import stiffness_from_youngpoisson as stiffness import sfepy.mechanics.matcoefs as mc from sfepy.mechanics.units import apply_unit_multipliers import sfepy.discrete.fem.periodic as per from sfepy.discrete.fem.meshio import convert_complex_output from sfepy.homogenization.utils import define_box_regions from sfepy.discrete import Problem from sfepy.mechanics.tensors import get_von_mises_stress from sfepy.solvers import Solver from sfepy.solvers.ts import get_print_info, TimeStepper from sfepy.linalg.utils import output_array_stats, max_diff_csr def apply_units(pars, unit_multipliers): new_pars = apply_unit_multipliers(pars, ['stress', 'one', 'density', 'stress', 'one' ,'density'], unit_multipliers) return new_pars def compute_von_mises(out, pb, state, extend=False, wmag=None, wdir=None): """ Calculate the von Mises stress. """ stress = pb.evaluate('ev_cauchy_stress.i.Omega(m.D, u)', mode='el_avg') vms = get_von_mises_stress(stress.squeeze()) vms.shape = (vms.shape[0], 1, 1, 1) out['von_mises_stress'] = Struct(name='output_data', mode='cell', data=vms) return out def define(filename_mesh, pars, approx_order, refinement_level, solver_conf, plane='strain', post_process=False, mesh_eps=1e-8): io = MeshIO.any_from_filename(filename_mesh) bbox = io.read_bounding_box() dim = bbox.shape[1] options = { 'absolute_mesh_path' : True, 'refinement_level' : refinement_level, 'allow_empty_regions' : True, 'post_process_hook' : 'compute_von_mises' if post_process else None, } fields = { 'displacement': ('complex', dim, 'Omega', approx_order), } young1, poisson1, density1, young2, poisson2, density2 = pars materials = { 'm' : ({ 'D' : {'Y1' : stiffness(dim, young=young1, poisson=poisson1, plane=plane), 'Y2' : stiffness(dim, young=young2, poisson=poisson2, plane=plane)}, 'density' : {'Y1' : density1, 'Y2' : density2}, },), 'wave' : 'get_wdir', } variables = { 'u' : ('unknown field', 'displacement', 0), 'v' : ('test field', 'displacement', 'u'), } regions = { 'Omega' : 'all', 'Y1': 'cells of group 1', 'Y2': 'cells of group 2', } regions.update(define_box_regions(dim, bbox[0], bbox[1], mesh_eps)) ebcs = { } if dim == 3: epbcs = { 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'}, 'match_x_plane'), 'periodic_y' : (['Near', 'Far'], {'u.all' : 'u.all'}, 'match_y_plane'), 'periodic_z' : (['Top', 'Bottom'], {'u.all' : 'u.all'}, 'match_z_plane'), } else: epbcs = { 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'}, 'match_y_line'), 'periodic_y' : (['Bottom', 'Top'], {'u.all' : 'u.all'}, 'match_x_line'), } per.set_accuracy(mesh_eps) functions = { 'match_x_plane' : (per.match_x_plane,), 'match_y_plane' : (per.match_y_plane,), 'match_z_plane' : (per.match_z_plane,), 'match_x_line' : (per.match_x_line,), 'match_y_line' : (per.match_y_line,), 'get_wdir' : (get_wdir,), } integrals = { 'i' : 2 * approx_order, } equations = { 'K' : 'dw_lin_elastic.i.Omega(m.D, v, u)', 'S' : 'dw_elastic_wave.i.Omega(m.D, wave.vec, v, u)', 'R' : """1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, u, v) - 1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, v, u)""", 'M' : 'dw_volume_dot.i.Omega(m.density, v, u)', } solver_0 = solver_conf.copy() solver_0['name'] = 'eig' return locals() def get_wdir(ts, coors, mode=None, equations=None, term=None, problem=None, wdir=None, **kwargs): if mode == 'special': return {'vec' : wdir} def set_wave_dir(pb, wdir): materials = pb.get_materials() wave_mat = materials['wave'] wave_mat.set_extra_args(wdir=wdir) def save_materials(output_dir, pb, options): stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)', mode='el_avg', copy_materials=False, verbose=False) young, poisson = mc.youngpoisson_from_stiffness(stiffness, plane=options.plane) density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)', mode='el_avg', copy_materials=False, verbose=False) out = {} out['young'] = Struct(name='young', mode='cell', data=young[..., None, None]) out['poisson'] = Struct(name='poisson', mode='cell', data=poisson[..., None, None]) out['density'] = Struct(name='density', mode='cell', data=density) materials_filename = os.path.join(output_dir, 'materials.vtk') pb.save_state(materials_filename, out=out) def get_std_wave_fun(pb, options): stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)', mode='el_avg', copy_materials=False, verbose=False) young, poisson = mc.youngpoisson_from_stiffness(stiffness, plane=options.plane) density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)', mode='el_avg', copy_materials=False, verbose=False) lam, mu = mc.lame_from_youngpoisson(young, poisson, plane=options.plane) alam = nm.average(lam) amu = nm.average(mu) adensity = nm.average(density) cp = nm.sqrt((alam + 2.0 * amu) / adensity) cs = nm.sqrt(amu / adensity) output('average p-wave speed:', cp) output('average shear wave speed:', cs) log_names = [r'$\omega_p$', r'$\omega_s$'] log_plot_kwargs = [{'ls' : '--', 'color' : 'k'}, {'ls' : '--', 'color' : 'gray'}] if options.mode == 'omega': fun = lambda wmag, wdir: (cp * wmag, cs * wmag) else: fun = lambda wmag, wdir: (wmag / cp, wmag / cs) return fun, log_names, log_plot_kwargs def get_stepper(rng, pb, options): if options.stepper == 'linear': stepper = TimeStepper(rng[0], rng[1], dt=None, n_step=rng[2]) return stepper bbox = pb.domain.mesh.get_bounding_box() bzone = 2.0 * nm.pi / (bbox[1] - bbox[0]) num = rng[2] // 3 class BrillouinStepper(Struct): """ Step over 1. Brillouin zone in xy plane. """ def __init__(self, t0, t1, dt=None, n_step=None, step=None, **kwargs): Struct.__init__(self, t0=t0, t1=t1, dt=dt, n_step=n_step, step=step) self.n_digit, self.format, self.suffix = get_print_info(self.n_step) def __iter__(self): ts = TimeStepper(0, bzone[0], dt=None, n_step=num) for ii, val in ts: yield ii, val, nm.array([1.0, 0.0]) if ii == (num-2): break ts = TimeStepper(0, bzone[1], dt=None, n_step=num) for ii, k1 in ts: wdir = nm.array([bzone[0], k1]) val = nm.linalg.norm(wdir) wdir = wdir / val yield num + ii, val, wdir if ii == (num-2): break wdir = nm.array([bzone[0], bzone[1]]) val = nm.linalg.norm(wdir) wdir = wdir / val ts = TimeStepper(0, 1, dt=None, n_step=num) for ii, _ in ts: yield 2 * num + ii, val * (1.0 - float(ii)/(num-1)), wdir stepper = BrillouinStepper(0, 1, n_step=rng[2]) return stepper def save_eigenvectors(filename, svecs, wmag, wdir, pb): if svecs is None: return variables = pb.get_variables() # Make full eigenvectors (add DOFs fixed by boundary conditions). vecs = nm.empty((variables.di.ptr[-1], svecs.shape[1]), dtype=svecs.dtype) for ii in range(svecs.shape[1]): vecs[:, ii] = variables.make_full_vec(svecs[:, ii]) # Save the eigenvectors. out = {} state = pb.create_state() pp_name = pb.conf.options.get('post_process_hook') pp = getattr(pb.conf.funmod, pp_name if pp_name is not None else '', lambda out, *args, **kwargs: out) for ii in range(svecs.shape[1]): state.set_full(vecs[:, ii]) aux = state.create_output_dict() aux2 = {} pp(aux2, pb, state, wmag=wmag, wdir=wdir) aux.update(convert_complex_output(aux2)) out.update({key + '%03d' % ii : aux[key] for key in aux}) pb.save_state(filename, out=out) def assemble_matrices(define, mod, pars, set_wave_dir, options, wdir=None): """ Assemble the blocks of dispersion eigenvalue problem matrices. """ define_dict = define(filename_mesh=options.mesh_filename, pars=pars, approx_order=options.order, refinement_level=options.refine, solver_conf=options.solver_conf, plane=options.plane, post_process=options.post_process, **options.define_kwargs) conf = ProblemConf.from_dict(define_dict, mod) pb = Problem.from_conf(conf) pb.dispersion_options = options pb.set_output_dir(options.output_dir) dim = pb.domain.shape.dim # Set the normalized wave vector direction to the material(s). if wdir is None: wdir = nm.asarray(options.wave_dir[:dim], dtype=nm.float64) wdir = wdir / nm.linalg.norm(wdir) set_wave_dir(pb, wdir) bbox = pb.domain.mesh.get_bounding_box() size = (bbox[1] - bbox[0]).max() scaling0 = apply_unit_multipliers([1.0], ['length'], options.unit_multipliers)[0] scaling = scaling0 if options.mesh_size is not None: scaling *= options.mesh_size / size output('scaling factor of periodic cell mesh coordinates:', scaling) output('new mesh size with applied unit multipliers:', scaling * size) pb.domain.mesh.coors[:] *= scaling pb.set_mesh_coors(pb.domain.mesh.coors, update_fields=True) bzone = 2.0 * nm.pi / (scaling * size) output('1. Brillouin zone size:', bzone * scaling0) output('1. Brillouin zone size with applied unit multipliers:', bzone) pb.time_update() pb.update_materials() # Assemble the matrices. mtxs = {} for key, eq in pb.equations.iteritems(): mtxs[key] = mtx = pb.mtx_a.copy() mtx = eq.evaluate(mode='weak', dw_mode='matrix', asm_obj=mtx) mtx.eliminate_zeros() output_array_stats(mtx.data, 'nonzeros in %s' % key) output('symmetry checks:') output('%s - %s^T:' % (key, key), max_diff_csr(mtx, mtx.T)) output('%s - %s^H:' % (key, key), max_diff_csr(mtx, mtx.H)) return pb, wdir, bzone, mtxs def setup_n_eigs(options, pb, mtxs): """ Setup the numbers of eigenvalues based on options and numbers of DOFs. """ solver_n_eigs = n_eigs = options.n_eigs n_dof = mtxs['K'].shape[0] if options.mode == 'omega': if options.n_eigs > n_dof: n_eigs = n_dof solver_n_eigs = None else: if options.n_eigs > 2 * n_dof: n_eigs = 2 * n_dof solver_n_eigs = None return solver_n_eigs, n_eigs def build_evp_matrices(mtxs, val, mode, pb): """ Build the matrices of the dispersion eigenvalue problem. """ if mode == 'omega': mtx_a = mtxs['K'] + val**2 * mtxs['S'] + val * mtxs['R'] output('A - A^H:', max_diff_csr(mtx_a, mtx_a.H)) evp_mtxs = (mtx_a, mtxs['M']) else: evp_mtxs = (mtxs['S'], mtxs['R'], mtxs['K'] - val**2 * mtxs['M']) return evp_mtxs def process_evp_results(eigs, svecs, val, wdir, bzone, pb, mtxs, options, std_wave_fun=None): """ Transform eigenvalues to either omegas or kappas, depending on `mode`. Transform eigenvectors, if available, depending on `mode`. Return also the values to log. """ if options.mode == 'omega': omegas = nm.sqrt(eigs) output('eigs, omegas:') for ii, om in enumerate(omegas): output('{:>3}. {: .10e}, {:.10e}'.format(ii, eigs[ii], om)) if options.stepper == 'linear': out = tuple(eigs) + tuple(omegas) else: out = tuple(val * wdir) + tuple(omegas) if std_wave_fun is not None: out = out + std_wave_fun(val, wdir) return omegas, svecs, out else: kappas = eigs.copy() rks = kappas.copy() # Mask modes far from 1. Brillouin zone. max_kappa = 1.2 * bzone kappas[kappas.real > max_kappa] = nm.nan # Mask non-physical modes. kappas[kappas.real < 0] = nm.nan kappas[nm.abs(kappas.imag) > 1e-10] = nm.nan out = tuple(kappas.real) output('raw kappas, masked real part:',) for ii, kr in enumerate(kappas.real): output('{:>3}. {: 23.5e}, {:.10e}'.format(ii, rks[ii], kr)) if svecs is not None: n_dof = mtxs['K'].shape[0] # Select only vectors corresponding to physical modes. ii = nm.isfinite(kappas.real) svecs = svecs[:n_dof, ii] if std_wave_fun is not None: out = out + tuple(ii if ii <= max_kappa else nm.nan for ii in std_wave_fun(val, wdir)) return kappas, svecs, out helps = { 'pars' : 'material parameters in Y1, Y2 subdomains in basic units' ' [default: %(default)s]', 'conf' : 'if given, an alternative problem description file with apply_units() and' ' define() functions [default: %(default)s]', 'define_kwargs' : 'additional keyword arguments passed to define()', 'mesh_size' : 'desired mesh size (max. of bounding box dimensions) in basic units' ' - the input periodic cell mesh is rescaled to this size' ' [default: %(default)s]', 'unit_multipliers' : 'basic unit multipliers (time, length, mass) [default: %(default)s]', 'plane' : 'for 2D problems, plane strain or stress hypothesis selection' ' [default: %(default)s]', 'wave_dir' : 'the wave vector direction (will be normalized)' ' [default: %(default)s]', 'mode' : 'solution mode: omega = solve a generalized EVP for omega,' ' kappa = solve a quadratic generalized EVP for kappa' ' [default: %(default)s]', 'stepper' : 'the range stepper. For "brillouin", only the number' ' of items from --range is used' ' [default: %(default)s]', 'range' : 'the wave vector magnitude / frequency range' ' (like numpy.linspace) depending on the mode option' ' [default: %(default)s]', 'order' : 'displacement field approximation order [default: %(default)s]', 'refine' : 'number of uniform mesh refinements [default: %(default)s]', 'n_eigs' : 'the number of eigenvalues to compute [default: %(default)s]', 'eigs_only' : 'compute only eigenvalues, not eigenvectors', 'post_process' : 'post-process eigenvectors', 'solver_conf' : 'eigenvalue problem solver configuration options' ' [default: %(default)s]', 'save_regions' : 'save defined regions into' ' <output_directory>/regions.vtk', 'save_materials' : 'save material parameters into' ' <output_directory>/materials.vtk', 'log_std_waves' : 'log also standard pressure dilatation and shear waves', 'no_legends' : 'do not show legends in the log plots', 'no_show' : 'do not show the log figure', 'silent' : 'do not print messages to screen', 'clear' : 'clear old solution files from output directory', 'output_dir' : 'output directory [default: %(default)s]', 'mesh_filename' : 'input periodic cell mesh file name [default: %(default)s]', } def main(): # Aluminium and epoxy. default_pars = '70e9,0.35,2.799e3, 3.8e9,0.27,1.142e3' default_solver_conf = ("kind='eig.scipy',method='eigsh',tol=1.0e-5," "maxiter=1000,which='LM',sigma=0.0") parser = ArgumentParser(description=__doc__, formatter_class=RawDescriptionHelpFormatter) parser.add_argument('--pars', metavar='young1,poisson1,density1' ',young2,poisson2,density2', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='pars', default=default_pars, help=helps['pars']) parser.add_argument('--conf', metavar='filename', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='conf', default=None, help=helps['conf']) parser.add_argument('--define-kwargs', metavar='dict-like', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='define_kwargs', default=None, help=helps['define_kwargs']) parser.add_argument('--mesh-size', type=float, metavar='float', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='mesh_size', default=None, help=helps['mesh_size']) parser.add_argument('--unit-multipliers', metavar='c_time,c_length,c_mass', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='unit_multipliers', default='1.0,1.0,1.0', help=helps['unit_multipliers']) parser.add_argument('--plane', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='plane', choices=['strain', 'stress'], default='strain', help=helps['plane']) parser.add_argument('--wave-dir', metavar='float,float[,float]', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='wave_dir', default='1.0,0.0,0.0', help=helps['wave_dir']) parser.add_argument('--mode', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='mode', choices=['omega', 'kappa'], default='omega', help=helps['mode']) parser.add_argument('--stepper', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='stepper', choices=['linear', 'brillouin'], default='linear', help=helps['stepper']) parser.add_argument('--range', metavar='start,stop,count', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='range', default='0,6.4,33', help=helps['range']) parser.add_argument('--order', metavar='int', type=int, action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='order', default=1, help=helps['order']) parser.add_argument('--refine', metavar='int', type=int, action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='refine', default=0, help=helps['refine']) parser.add_argument('-n', '--n-eigs', metavar='int', type=int, action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='n_eigs', default=6, help=helps['n_eigs']) group = parser.add_mutually_exclusive_group() group.add_argument('--eigs-only', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='eigs_only', default=False, help=helps['eigs_only']) group.add_argument('--post-process', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='post_process', default=False, help=helps['post_process']) parser.add_argument('--solver-conf', metavar='dict-like', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='solver_conf', default=default_solver_conf, help=helps['solver_conf']) parser.add_argument('--save-regions', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='save_regions', default=False, help=helps['save_regions']) parser.add_argument('--save-materials', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='save_materials', default=False, help=helps['save_materials']) parser.add_argument('--log-std-waves', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='log_std_waves', default=False, help=helps['log_std_waves']) parser.add_argument('--no-legends', action="https://huggingface.co/datasets/luna-code/sfepy/store_false", dest='show_legends', default=True, help=helps['no_legends']) parser.add_argument('--no-show', action="https://huggingface.co/datasets/luna-code/sfepy/store_false", dest='show', default=True, help=helps['no_show']) parser.add_argument('--silent', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='silent', default=False, help=helps['silent']) parser.add_argument('-c', '--clear', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='clear', default=False, help=helps['clear']) parser.add_argument('-o', '--output-dir', metavar='path', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='output_dir', default='output', help=helps['output_dir']) parser.add_argument('mesh_filename', default='', help=helps['mesh_filename']) options = parser.parse_args() output_dir = options.output_dir output.set_output(filename=os.path.join(output_dir,'output_log.txt'), combined=options.silent == False) if options.conf is not None: mod = import_file(options.conf) else: mod = sys.modules[__name__] apply_units = mod.apply_units define = mod.define set_wave_dir = mod.set_wave_dir setup_n_eigs = mod.setup_n_eigs build_evp_matrices = mod.build_evp_matrices save_materials = mod.save_materials get_std_wave_fun = mod.get_std_wave_fun get_stepper = mod.get_stepper process_evp_results = mod.process_evp_results options.pars = [float(ii) for ii in options.pars.split(',')] options.unit_multipliers = [float(ii) for ii in options.unit_multipliers.split(',')] options.wave_dir = [float(ii) for ii in options.wave_dir.split(',')] aux = options.range.split(',') options.range = [float(aux[0]), float(aux[1]), int(aux[2])] options.solver_conf = dict_from_string(options.solver_conf) options.define_kwargs = dict_from_string(options.define_kwargs) if options.clear: remove_files_patterns(output_dir, ['*.h5', '*.vtk', '*.txt'], ignores=['output_log.txt'], verbose=True) filename = os.path.join(output_dir, 'options.txt') ensure_path(filename) save_options(filename, [('options', vars(options))], quote_command_line=True) pars = apply_units(options.pars, options.unit_multipliers) output('material parameters with applied unit multipliers:') output(pars) if options.mode == 'omega': rng = copy(options.range) rng[:2] = apply_unit_multipliers(options.range[:2], ['wave_number', 'wave_number'], options.unit_multipliers)	output('wave number range with applied unit multipliers:', rng)	sfepy.base.base.output
#!/usr/bin/env python """ Dispersion analysis of a heterogeneous finite scale periodic cell. The periodic cell mesh has to contain two subdomains Y1 (with the cell ids 1), Y2 (with the cell ids 2), so that different material properties can be defined in each of the subdomains (see ``--pars`` option). The command line parameters can be given in any consistent unit set, for example the basic SI units. The ``--unit-multipliers`` option can be used to rescale the input units to ones more suitable to the simulation, for example to prevent having different matrix blocks with large differences of matrix entries magnitudes. The results are then in the rescaled units. Usage Examples -------------- Default material parameters, a square periodic cell with a spherical inclusion, logs also standard pressure dilatation and shear waves, no eigenvectors:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only As above, with custom eigenvalue solver parameters, and different number of eigenvalues, mesh size and units used in the calculation:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --solver-conf="kind='eig.scipy', method='eigsh', tol=1e-10, maxiter=1000, which='LM', sigma=0" --log-std-waves -n 5 --range=0,640,101 --mode=omega --unit-multipliers=1e-6,1e-2,1e-3 --mesh-size=1e-2 --eigs-only Default material parameters, a square periodic cell with a square inclusion, and a very small mesh to allow comparing the omega and kappa modes (full matrix solver required!):: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.qevp', method='companion', mode='inverted', solver={kind='eig.scipy', method='eig'}" --log-std-waves -n 500 --range=0,4000000,1001 --mesh-size=1e-2 --mode=kappa --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/kappa View/compare the resulting logs:: python script/plot_logs.py output/omega/frequencies.txt --no-legends -g 1 -o mode-omega.png python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends -o mode-kappa.png python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends --swap-axes -o mode-kappa-t.png In contrast to the heterogeneous square periodic cell, a homogeneous square periodic cell (the region Y2 is empty):: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_1m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega-h python script/plot_logs.py output/omega-h/frequencies.txt --no-legends -g 1 -o mode-omega-h.png Use the Brillouin stepper:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves -n=60 --eigs-only --no-legends --stepper=brillouin python script/plot_logs.py output/frequencies.txt -g 0 --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-kappas.png python script/plot_logs.py output/frequencies.txt -g 1 --no-legends --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-omegas.png Additional arguments can be passed to the problem configuration's :func:`define()` function using the ``--define-kwargs`` option. In this file, only the mesh vertex separation parameter `mesh_eps` can be used:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only --define-kwargs="mesh_eps=1e-10" --save-regions """ from __future__ import absolute_import import os import sys sys.path.append('.') import gc from copy import copy from argparse import ArgumentParser, RawDescriptionHelpFormatter import numpy as nm import matplotlib.pyplot as plt from sfepy.base.base import import_file, output, Struct from sfepy.base.conf import dict_from_string, ProblemConf from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options from sfepy.base.log import Log from sfepy.discrete.fem import MeshIO from sfepy.mechanics.matcoefs import stiffness_from_youngpoisson as stiffness import sfepy.mechanics.matcoefs as mc from sfepy.mechanics.units import apply_unit_multipliers import sfepy.discrete.fem.periodic as per from sfepy.discrete.fem.meshio import convert_complex_output from sfepy.homogenization.utils import define_box_regions from sfepy.discrete import Problem from sfepy.mechanics.tensors import get_von_mises_stress from sfepy.solvers import Solver from sfepy.solvers.ts import get_print_info, TimeStepper from sfepy.linalg.utils import output_array_stats, max_diff_csr def apply_units(pars, unit_multipliers): new_pars = apply_unit_multipliers(pars, ['stress', 'one', 'density', 'stress', 'one' ,'density'], unit_multipliers) return new_pars def compute_von_mises(out, pb, state, extend=False, wmag=None, wdir=None): """ Calculate the von Mises stress. """ stress = pb.evaluate('ev_cauchy_stress.i.Omega(m.D, u)', mode='el_avg') vms = get_von_mises_stress(stress.squeeze()) vms.shape = (vms.shape[0], 1, 1, 1) out['von_mises_stress'] = Struct(name='output_data', mode='cell', data=vms) return out def define(filename_mesh, pars, approx_order, refinement_level, solver_conf, plane='strain', post_process=False, mesh_eps=1e-8): io = MeshIO.any_from_filename(filename_mesh) bbox = io.read_bounding_box() dim = bbox.shape[1] options = { 'absolute_mesh_path' : True, 'refinement_level' : refinement_level, 'allow_empty_regions' : True, 'post_process_hook' : 'compute_von_mises' if post_process else None, } fields = { 'displacement': ('complex', dim, 'Omega', approx_order), } young1, poisson1, density1, young2, poisson2, density2 = pars materials = { 'm' : ({ 'D' : {'Y1' : stiffness(dim, young=young1, poisson=poisson1, plane=plane), 'Y2' : stiffness(dim, young=young2, poisson=poisson2, plane=plane)}, 'density' : {'Y1' : density1, 'Y2' : density2}, },), 'wave' : 'get_wdir', } variables = { 'u' : ('unknown field', 'displacement', 0), 'v' : ('test field', 'displacement', 'u'), } regions = { 'Omega' : 'all', 'Y1': 'cells of group 1', 'Y2': 'cells of group 2', } regions.update(define_box_regions(dim, bbox[0], bbox[1], mesh_eps)) ebcs = { } if dim == 3: epbcs = { 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'}, 'match_x_plane'), 'periodic_y' : (['Near', 'Far'], {'u.all' : 'u.all'}, 'match_y_plane'), 'periodic_z' : (['Top', 'Bottom'], {'u.all' : 'u.all'}, 'match_z_plane'), } else: epbcs = { 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'}, 'match_y_line'), 'periodic_y' : (['Bottom', 'Top'], {'u.all' : 'u.all'}, 'match_x_line'), } per.set_accuracy(mesh_eps) functions = { 'match_x_plane' : (per.match_x_plane,), 'match_y_plane' : (per.match_y_plane,), 'match_z_plane' : (per.match_z_plane,), 'match_x_line' : (per.match_x_line,), 'match_y_line' : (per.match_y_line,), 'get_wdir' : (get_wdir,), } integrals = { 'i' : 2 * approx_order, } equations = { 'K' : 'dw_lin_elastic.i.Omega(m.D, v, u)', 'S' : 'dw_elastic_wave.i.Omega(m.D, wave.vec, v, u)', 'R' : """1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, u, v) - 1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, v, u)""", 'M' : 'dw_volume_dot.i.Omega(m.density, v, u)', } solver_0 = solver_conf.copy() solver_0['name'] = 'eig' return locals() def get_wdir(ts, coors, mode=None, equations=None, term=None, problem=None, wdir=None, **kwargs): if mode == 'special': return {'vec' : wdir} def set_wave_dir(pb, wdir): materials = pb.get_materials() wave_mat = materials['wave'] wave_mat.set_extra_args(wdir=wdir) def save_materials(output_dir, pb, options): stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)', mode='el_avg', copy_materials=False, verbose=False) young, poisson = mc.youngpoisson_from_stiffness(stiffness, plane=options.plane) density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)', mode='el_avg', copy_materials=False, verbose=False) out = {} out['young'] = Struct(name='young', mode='cell', data=young[..., None, None]) out['poisson'] = Struct(name='poisson', mode='cell', data=poisson[..., None, None]) out['density'] = Struct(name='density', mode='cell', data=density) materials_filename = os.path.join(output_dir, 'materials.vtk') pb.save_state(materials_filename, out=out) def get_std_wave_fun(pb, options): stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)', mode='el_avg', copy_materials=False, verbose=False) young, poisson = mc.youngpoisson_from_stiffness(stiffness, plane=options.plane) density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)', mode='el_avg', copy_materials=False, verbose=False) lam, mu = mc.lame_from_youngpoisson(young, poisson, plane=options.plane) alam = nm.average(lam) amu = nm.average(mu) adensity = nm.average(density) cp = nm.sqrt((alam + 2.0 * amu) / adensity) cs = nm.sqrt(amu / adensity) output('average p-wave speed:', cp) output('average shear wave speed:', cs) log_names = [r'$\omega_p$', r'$\omega_s$'] log_plot_kwargs = [{'ls' : '--', 'color' : 'k'}, {'ls' : '--', 'color' : 'gray'}] if options.mode == 'omega': fun = lambda wmag, wdir: (cp * wmag, cs * wmag) else: fun = lambda wmag, wdir: (wmag / cp, wmag / cs) return fun, log_names, log_plot_kwargs def get_stepper(rng, pb, options): if options.stepper == 'linear': stepper = TimeStepper(rng[0], rng[1], dt=None, n_step=rng[2]) return stepper bbox = pb.domain.mesh.get_bounding_box() bzone = 2.0 * nm.pi / (bbox[1] - bbox[0]) num = rng[2] // 3 class BrillouinStepper(Struct): """ Step over 1. Brillouin zone in xy plane. """ def __init__(self, t0, t1, dt=None, n_step=None, step=None, **kwargs): Struct.__init__(self, t0=t0, t1=t1, dt=dt, n_step=n_step, step=step) self.n_digit, self.format, self.suffix = get_print_info(self.n_step) def __iter__(self): ts = TimeStepper(0, bzone[0], dt=None, n_step=num) for ii, val in ts: yield ii, val, nm.array([1.0, 0.0]) if ii == (num-2): break ts = TimeStepper(0, bzone[1], dt=None, n_step=num) for ii, k1 in ts: wdir = nm.array([bzone[0], k1]) val = nm.linalg.norm(wdir) wdir = wdir / val yield num + ii, val, wdir if ii == (num-2): break wdir = nm.array([bzone[0], bzone[1]]) val = nm.linalg.norm(wdir) wdir = wdir / val ts = TimeStepper(0, 1, dt=None, n_step=num) for ii, _ in ts: yield 2 * num + ii, val * (1.0 - float(ii)/(num-1)), wdir stepper = BrillouinStepper(0, 1, n_step=rng[2]) return stepper def save_eigenvectors(filename, svecs, wmag, wdir, pb): if svecs is None: return variables = pb.get_variables() # Make full eigenvectors (add DOFs fixed by boundary conditions). vecs = nm.empty((variables.di.ptr[-1], svecs.shape[1]), dtype=svecs.dtype) for ii in range(svecs.shape[1]): vecs[:, ii] = variables.make_full_vec(svecs[:, ii]) # Save the eigenvectors. out = {} state = pb.create_state() pp_name = pb.conf.options.get('post_process_hook') pp = getattr(pb.conf.funmod, pp_name if pp_name is not None else '', lambda out, *args, **kwargs: out) for ii in range(svecs.shape[1]): state.set_full(vecs[:, ii]) aux = state.create_output_dict() aux2 = {} pp(aux2, pb, state, wmag=wmag, wdir=wdir) aux.update(convert_complex_output(aux2)) out.update({key + '%03d' % ii : aux[key] for key in aux}) pb.save_state(filename, out=out) def assemble_matrices(define, mod, pars, set_wave_dir, options, wdir=None): """ Assemble the blocks of dispersion eigenvalue problem matrices. """ define_dict = define(filename_mesh=options.mesh_filename, pars=pars, approx_order=options.order, refinement_level=options.refine, solver_conf=options.solver_conf, plane=options.plane, post_process=options.post_process, **options.define_kwargs) conf = ProblemConf.from_dict(define_dict, mod) pb = Problem.from_conf(conf) pb.dispersion_options = options pb.set_output_dir(options.output_dir) dim = pb.domain.shape.dim # Set the normalized wave vector direction to the material(s). if wdir is None: wdir = nm.asarray(options.wave_dir[:dim], dtype=nm.float64) wdir = wdir / nm.linalg.norm(wdir) set_wave_dir(pb, wdir) bbox = pb.domain.mesh.get_bounding_box() size = (bbox[1] - bbox[0]).max() scaling0 = apply_unit_multipliers([1.0], ['length'], options.unit_multipliers)[0] scaling = scaling0 if options.mesh_size is not None: scaling *= options.mesh_size / size output('scaling factor of periodic cell mesh coordinates:', scaling) output('new mesh size with applied unit multipliers:', scaling * size) pb.domain.mesh.coors[:] *= scaling pb.set_mesh_coors(pb.domain.mesh.coors, update_fields=True) bzone = 2.0 * nm.pi / (scaling * size) output('1. Brillouin zone size:', bzone * scaling0) output('1. Brillouin zone size with applied unit multipliers:', bzone) pb.time_update() pb.update_materials() # Assemble the matrices. mtxs = {} for key, eq in pb.equations.iteritems(): mtxs[key] = mtx = pb.mtx_a.copy() mtx = eq.evaluate(mode='weak', dw_mode='matrix', asm_obj=mtx) mtx.eliminate_zeros() output_array_stats(mtx.data, 'nonzeros in %s' % key) output('symmetry checks:') output('%s - %s^T:' % (key, key), max_diff_csr(mtx, mtx.T)) output('%s - %s^H:' % (key, key), max_diff_csr(mtx, mtx.H)) return pb, wdir, bzone, mtxs def setup_n_eigs(options, pb, mtxs): """ Setup the numbers of eigenvalues based on options and numbers of DOFs. """ solver_n_eigs = n_eigs = options.n_eigs n_dof = mtxs['K'].shape[0] if options.mode == 'omega': if options.n_eigs > n_dof: n_eigs = n_dof solver_n_eigs = None else: if options.n_eigs > 2 * n_dof: n_eigs = 2 * n_dof solver_n_eigs = None return solver_n_eigs, n_eigs def build_evp_matrices(mtxs, val, mode, pb): """ Build the matrices of the dispersion eigenvalue problem. """ if mode == 'omega': mtx_a = mtxs['K'] + val**2 * mtxs['S'] + val * mtxs['R'] output('A - A^H:', max_diff_csr(mtx_a, mtx_a.H)) evp_mtxs = (mtx_a, mtxs['M']) else: evp_mtxs = (mtxs['S'], mtxs['R'], mtxs['K'] - val**2 * mtxs['M']) return evp_mtxs def process_evp_results(eigs, svecs, val, wdir, bzone, pb, mtxs, options, std_wave_fun=None): """ Transform eigenvalues to either omegas or kappas, depending on `mode`. Transform eigenvectors, if available, depending on `mode`. Return also the values to log. """ if options.mode == 'omega': omegas = nm.sqrt(eigs) output('eigs, omegas:') for ii, om in enumerate(omegas): output('{:>3}. {: .10e}, {:.10e}'.format(ii, eigs[ii], om)) if options.stepper == 'linear': out = tuple(eigs) + tuple(omegas) else: out = tuple(val * wdir) + tuple(omegas) if std_wave_fun is not None: out = out + std_wave_fun(val, wdir) return omegas, svecs, out else: kappas = eigs.copy() rks = kappas.copy() # Mask modes far from 1. Brillouin zone. max_kappa = 1.2 * bzone kappas[kappas.real > max_kappa] = nm.nan # Mask non-physical modes. kappas[kappas.real < 0] = nm.nan kappas[nm.abs(kappas.imag) > 1e-10] = nm.nan out = tuple(kappas.real) output('raw kappas, masked real part:',) for ii, kr in enumerate(kappas.real): output('{:>3}. {: 23.5e}, {:.10e}'.format(ii, rks[ii], kr)) if svecs is not None: n_dof = mtxs['K'].shape[0] # Select only vectors corresponding to physical modes. ii = nm.isfinite(kappas.real) svecs = svecs[:n_dof, ii] if std_wave_fun is not None: out = out + tuple(ii if ii <= max_kappa else nm.nan for ii in std_wave_fun(val, wdir)) return kappas, svecs, out helps = { 'pars' : 'material parameters in Y1, Y2 subdomains in basic units' ' [default: %(default)s]', 'conf' : 'if given, an alternative problem description file with apply_units() and' ' define() functions [default: %(default)s]', 'define_kwargs' : 'additional keyword arguments passed to define()', 'mesh_size' : 'desired mesh size (max. of bounding box dimensions) in basic units' ' - the input periodic cell mesh is rescaled to this size' ' [default: %(default)s]', 'unit_multipliers' : 'basic unit multipliers (time, length, mass) [default: %(default)s]', 'plane' : 'for 2D problems, plane strain or stress hypothesis selection' ' [default: %(default)s]', 'wave_dir' : 'the wave vector direction (will be normalized)' ' [default: %(default)s]', 'mode' : 'solution mode: omega = solve a generalized EVP for omega,' ' kappa = solve a quadratic generalized EVP for kappa' ' [default: %(default)s]', 'stepper' : 'the range stepper. For "brillouin", only the number' ' of items from --range is used' ' [default: %(default)s]', 'range' : 'the wave vector magnitude / frequency range' ' (like numpy.linspace) depending on the mode option' ' [default: %(default)s]', 'order' : 'displacement field approximation order [default: %(default)s]', 'refine' : 'number of uniform mesh refinements [default: %(default)s]', 'n_eigs' : 'the number of eigenvalues to compute [default: %(default)s]', 'eigs_only' : 'compute only eigenvalues, not eigenvectors', 'post_process' : 'post-process eigenvectors', 'solver_conf' : 'eigenvalue problem solver configuration options' ' [default: %(default)s]', 'save_regions' : 'save defined regions into' ' <output_directory>/regions.vtk', 'save_materials' : 'save material parameters into' ' <output_directory>/materials.vtk', 'log_std_waves' : 'log also standard pressure dilatation and shear waves', 'no_legends' : 'do not show legends in the log plots', 'no_show' : 'do not show the log figure', 'silent' : 'do not print messages to screen', 'clear' : 'clear old solution files from output directory', 'output_dir' : 'output directory [default: %(default)s]', 'mesh_filename' : 'input periodic cell mesh file name [default: %(default)s]', } def main(): # Aluminium and epoxy. default_pars = '70e9,0.35,2.799e3, 3.8e9,0.27,1.142e3' default_solver_conf = ("kind='eig.scipy',method='eigsh',tol=1.0e-5," "maxiter=1000,which='LM',sigma=0.0") parser = ArgumentParser(description=__doc__, formatter_class=RawDescriptionHelpFormatter) parser.add_argument('--pars', metavar='young1,poisson1,density1' ',young2,poisson2,density2', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='pars', default=default_pars, help=helps['pars']) parser.add_argument('--conf', metavar='filename', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='conf', default=None, help=helps['conf']) parser.add_argument('--define-kwargs', metavar='dict-like', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='define_kwargs', default=None, help=helps['define_kwargs']) parser.add_argument('--mesh-size', type=float, metavar='float', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='mesh_size', default=None, help=helps['mesh_size']) parser.add_argument('--unit-multipliers', metavar='c_time,c_length,c_mass', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='unit_multipliers', default='1.0,1.0,1.0', help=helps['unit_multipliers']) parser.add_argument('--plane', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='plane', choices=['strain', 'stress'], default='strain', help=helps['plane']) parser.add_argument('--wave-dir', metavar='float,float[,float]', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='wave_dir', default='1.0,0.0,0.0', help=helps['wave_dir']) parser.add_argument('--mode', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='mode', choices=['omega', 'kappa'], default='omega', help=helps['mode']) parser.add_argument('--stepper', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='stepper', choices=['linear', 'brillouin'], default='linear', help=helps['stepper']) parser.add_argument('--range', metavar='start,stop,count', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='range', default='0,6.4,33', help=helps['range']) parser.add_argument('--order', metavar='int', type=int, action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='order', default=1, help=helps['order']) parser.add_argument('--refine', metavar='int', type=int, action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='refine', default=0, help=helps['refine']) parser.add_argument('-n', '--n-eigs', metavar='int', type=int, action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='n_eigs', default=6, help=helps['n_eigs']) group = parser.add_mutually_exclusive_group() group.add_argument('--eigs-only', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='eigs_only', default=False, help=helps['eigs_only']) group.add_argument('--post-process', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='post_process', default=False, help=helps['post_process']) parser.add_argument('--solver-conf', metavar='dict-like', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='solver_conf', default=default_solver_conf, help=helps['solver_conf']) parser.add_argument('--save-regions', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='save_regions', default=False, help=helps['save_regions']) parser.add_argument('--save-materials', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='save_materials', default=False, help=helps['save_materials']) parser.add_argument('--log-std-waves', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='log_std_waves', default=False, help=helps['log_std_waves']) parser.add_argument('--no-legends', action="https://huggingface.co/datasets/luna-code/sfepy/store_false", dest='show_legends', default=True, help=helps['no_legends']) parser.add_argument('--no-show', action="https://huggingface.co/datasets/luna-code/sfepy/store_false", dest='show', default=True, help=helps['no_show']) parser.add_argument('--silent', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='silent', default=False, help=helps['silent']) parser.add_argument('-c', '--clear', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='clear', default=False, help=helps['clear']) parser.add_argument('-o', '--output-dir', metavar='path', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='output_dir', default='output', help=helps['output_dir']) parser.add_argument('mesh_filename', default='', help=helps['mesh_filename']) options = parser.parse_args() output_dir = options.output_dir output.set_output(filename=os.path.join(output_dir,'output_log.txt'), combined=options.silent == False) if options.conf is not None: mod = import_file(options.conf) else: mod = sys.modules[__name__] apply_units = mod.apply_units define = mod.define set_wave_dir = mod.set_wave_dir setup_n_eigs = mod.setup_n_eigs build_evp_matrices = mod.build_evp_matrices save_materials = mod.save_materials get_std_wave_fun = mod.get_std_wave_fun get_stepper = mod.get_stepper process_evp_results = mod.process_evp_results options.pars = [float(ii) for ii in options.pars.split(',')] options.unit_multipliers = [float(ii) for ii in options.unit_multipliers.split(',')] options.wave_dir = [float(ii) for ii in options.wave_dir.split(',')] aux = options.range.split(',') options.range = [float(aux[0]), float(aux[1]), int(aux[2])] options.solver_conf = dict_from_string(options.solver_conf) options.define_kwargs = dict_from_string(options.define_kwargs) if options.clear: remove_files_patterns(output_dir, ['*.h5', '*.vtk', '*.txt'], ignores=['output_log.txt'], verbose=True) filename = os.path.join(output_dir, 'options.txt') ensure_path(filename) save_options(filename, [('options', vars(options))], quote_command_line=True) pars = apply_units(options.pars, options.unit_multipliers) output('material parameters with applied unit multipliers:') output(pars) if options.mode == 'omega': rng = copy(options.range) rng[:2] = apply_unit_multipliers(options.range[:2], ['wave_number', 'wave_number'], options.unit_multipliers) output('wave number range with applied unit multipliers:', rng) else: if options.stepper == 'brillouin': raise ValueError('Cannot use "brillouin" stepper in kappa mode!') rng = copy(options.range) rng[:2] = apply_unit_multipliers(options.range[:2], ['frequency', 'frequency'], options.unit_multipliers)	output('frequency range with applied unit multipliers:', rng)	sfepy.base.base.output
#!/usr/bin/env python """ Dispersion analysis of a heterogeneous finite scale periodic cell. The periodic cell mesh has to contain two subdomains Y1 (with the cell ids 1), Y2 (with the cell ids 2), so that different material properties can be defined in each of the subdomains (see ``--pars`` option). The command line parameters can be given in any consistent unit set, for example the basic SI units. The ``--unit-multipliers`` option can be used to rescale the input units to ones more suitable to the simulation, for example to prevent having different matrix blocks with large differences of matrix entries magnitudes. The results are then in the rescaled units. Usage Examples -------------- Default material parameters, a square periodic cell with a spherical inclusion, logs also standard pressure dilatation and shear waves, no eigenvectors:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only As above, with custom eigenvalue solver parameters, and different number of eigenvalues, mesh size and units used in the calculation:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --solver-conf="kind='eig.scipy', method='eigsh', tol=1e-10, maxiter=1000, which='LM', sigma=0" --log-std-waves -n 5 --range=0,640,101 --mode=omega --unit-multipliers=1e-6,1e-2,1e-3 --mesh-size=1e-2 --eigs-only Default material parameters, a square periodic cell with a square inclusion, and a very small mesh to allow comparing the omega and kappa modes (full matrix solver required!):: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.qevp', method='companion', mode='inverted', solver={kind='eig.scipy', method='eig'}" --log-std-waves -n 500 --range=0,4000000,1001 --mesh-size=1e-2 --mode=kappa --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/kappa View/compare the resulting logs:: python script/plot_logs.py output/omega/frequencies.txt --no-legends -g 1 -o mode-omega.png python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends -o mode-kappa.png python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends --swap-axes -o mode-kappa-t.png In contrast to the heterogeneous square periodic cell, a homogeneous square periodic cell (the region Y2 is empty):: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_1m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega-h python script/plot_logs.py output/omega-h/frequencies.txt --no-legends -g 1 -o mode-omega-h.png Use the Brillouin stepper:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves -n=60 --eigs-only --no-legends --stepper=brillouin python script/plot_logs.py output/frequencies.txt -g 0 --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-kappas.png python script/plot_logs.py output/frequencies.txt -g 1 --no-legends --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-omegas.png Additional arguments can be passed to the problem configuration's :func:`define()` function using the ``--define-kwargs`` option. In this file, only the mesh vertex separation parameter `mesh_eps` can be used:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only --define-kwargs="mesh_eps=1e-10" --save-regions """ from __future__ import absolute_import import os import sys sys.path.append('.') import gc from copy import copy from argparse import ArgumentParser, RawDescriptionHelpFormatter import numpy as nm import matplotlib.pyplot as plt from sfepy.base.base import import_file, output, Struct from sfepy.base.conf import dict_from_string, ProblemConf from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options from sfepy.base.log import Log from sfepy.discrete.fem import MeshIO from sfepy.mechanics.matcoefs import stiffness_from_youngpoisson as stiffness import sfepy.mechanics.matcoefs as mc from sfepy.mechanics.units import apply_unit_multipliers import sfepy.discrete.fem.periodic as per from sfepy.discrete.fem.meshio import convert_complex_output from sfepy.homogenization.utils import define_box_regions from sfepy.discrete import Problem from sfepy.mechanics.tensors import get_von_mises_stress from sfepy.solvers import Solver from sfepy.solvers.ts import get_print_info, TimeStepper from sfepy.linalg.utils import output_array_stats, max_diff_csr def apply_units(pars, unit_multipliers): new_pars = apply_unit_multipliers(pars, ['stress', 'one', 'density', 'stress', 'one' ,'density'], unit_multipliers) return new_pars def compute_von_mises(out, pb, state, extend=False, wmag=None, wdir=None): """ Calculate the von Mises stress. """ stress = pb.evaluate('ev_cauchy_stress.i.Omega(m.D, u)', mode='el_avg') vms = get_von_mises_stress(stress.squeeze()) vms.shape = (vms.shape[0], 1, 1, 1) out['von_mises_stress'] = Struct(name='output_data', mode='cell', data=vms) return out def define(filename_mesh, pars, approx_order, refinement_level, solver_conf, plane='strain', post_process=False, mesh_eps=1e-8): io = MeshIO.any_from_filename(filename_mesh) bbox = io.read_bounding_box() dim = bbox.shape[1] options = { 'absolute_mesh_path' : True, 'refinement_level' : refinement_level, 'allow_empty_regions' : True, 'post_process_hook' : 'compute_von_mises' if post_process else None, } fields = { 'displacement': ('complex', dim, 'Omega', approx_order), } young1, poisson1, density1, young2, poisson2, density2 = pars materials = { 'm' : ({ 'D' : {'Y1' : stiffness(dim, young=young1, poisson=poisson1, plane=plane), 'Y2' : stiffness(dim, young=young2, poisson=poisson2, plane=plane)}, 'density' : {'Y1' : density1, 'Y2' : density2}, },), 'wave' : 'get_wdir', } variables = { 'u' : ('unknown field', 'displacement', 0), 'v' : ('test field', 'displacement', 'u'), } regions = { 'Omega' : 'all', 'Y1': 'cells of group 1', 'Y2': 'cells of group 2', } regions.update(define_box_regions(dim, bbox[0], bbox[1], mesh_eps)) ebcs = { } if dim == 3: epbcs = { 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'}, 'match_x_plane'), 'periodic_y' : (['Near', 'Far'], {'u.all' : 'u.all'}, 'match_y_plane'), 'periodic_z' : (['Top', 'Bottom'], {'u.all' : 'u.all'}, 'match_z_plane'), } else: epbcs = { 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'}, 'match_y_line'), 'periodic_y' : (['Bottom', 'Top'], {'u.all' : 'u.all'}, 'match_x_line'), } per.set_accuracy(mesh_eps) functions = { 'match_x_plane' : (per.match_x_plane,), 'match_y_plane' : (per.match_y_plane,), 'match_z_plane' : (per.match_z_plane,), 'match_x_line' : (per.match_x_line,), 'match_y_line' : (per.match_y_line,), 'get_wdir' : (get_wdir,), } integrals = { 'i' : 2 * approx_order, } equations = { 'K' : 'dw_lin_elastic.i.Omega(m.D, v, u)', 'S' : 'dw_elastic_wave.i.Omega(m.D, wave.vec, v, u)', 'R' : """1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, u, v) - 1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, v, u)""", 'M' : 'dw_volume_dot.i.Omega(m.density, v, u)', } solver_0 = solver_conf.copy() solver_0['name'] = 'eig' return locals() def get_wdir(ts, coors, mode=None, equations=None, term=None, problem=None, wdir=None, **kwargs): if mode == 'special': return {'vec' : wdir} def set_wave_dir(pb, wdir): materials = pb.get_materials() wave_mat = materials['wave'] wave_mat.set_extra_args(wdir=wdir) def save_materials(output_dir, pb, options): stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)', mode='el_avg', copy_materials=False, verbose=False) young, poisson = mc.youngpoisson_from_stiffness(stiffness, plane=options.plane) density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)', mode='el_avg', copy_materials=False, verbose=False) out = {} out['young'] = Struct(name='young', mode='cell', data=young[..., None, None]) out['poisson'] = Struct(name='poisson', mode='cell', data=poisson[..., None, None]) out['density'] = Struct(name='density', mode='cell', data=density) materials_filename = os.path.join(output_dir, 'materials.vtk') pb.save_state(materials_filename, out=out) def get_std_wave_fun(pb, options): stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)', mode='el_avg', copy_materials=False, verbose=False) young, poisson = mc.youngpoisson_from_stiffness(stiffness, plane=options.plane) density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)', mode='el_avg', copy_materials=False, verbose=False) lam, mu = mc.lame_from_youngpoisson(young, poisson, plane=options.plane) alam = nm.average(lam) amu = nm.average(mu) adensity = nm.average(density) cp = nm.sqrt((alam + 2.0 * amu) / adensity) cs = nm.sqrt(amu / adensity) output('average p-wave speed:', cp) output('average shear wave speed:', cs) log_names = [r'$\omega_p$', r'$\omega_s$'] log_plot_kwargs = [{'ls' : '--', 'color' : 'k'}, {'ls' : '--', 'color' : 'gray'}] if options.mode == 'omega': fun = lambda wmag, wdir: (cp * wmag, cs * wmag) else: fun = lambda wmag, wdir: (wmag / cp, wmag / cs) return fun, log_names, log_plot_kwargs def get_stepper(rng, pb, options): if options.stepper == 'linear': stepper = TimeStepper(rng[0], rng[1], dt=None, n_step=rng[2]) return stepper bbox = pb.domain.mesh.get_bounding_box() bzone = 2.0 * nm.pi / (bbox[1] - bbox[0]) num = rng[2] // 3 class BrillouinStepper(Struct): """ Step over 1. Brillouin zone in xy plane. """ def __init__(self, t0, t1, dt=None, n_step=None, step=None, **kwargs):	Struct.__init__(self, t0=t0, t1=t1, dt=dt, n_step=n_step, step=step)	sfepy.base.base.Struct.__init__
#!/usr/bin/env python """ Dispersion analysis of a heterogeneous finite scale periodic cell. The periodic cell mesh has to contain two subdomains Y1 (with the cell ids 1), Y2 (with the cell ids 2), so that different material properties can be defined in each of the subdomains (see ``--pars`` option). The command line parameters can be given in any consistent unit set, for example the basic SI units. The ``--unit-multipliers`` option can be used to rescale the input units to ones more suitable to the simulation, for example to prevent having different matrix blocks with large differences of matrix entries magnitudes. The results are then in the rescaled units. Usage Examples -------------- Default material parameters, a square periodic cell with a spherical inclusion, logs also standard pressure dilatation and shear waves, no eigenvectors:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only As above, with custom eigenvalue solver parameters, and different number of eigenvalues, mesh size and units used in the calculation:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --solver-conf="kind='eig.scipy', method='eigsh', tol=1e-10, maxiter=1000, which='LM', sigma=0" --log-std-waves -n 5 --range=0,640,101 --mode=omega --unit-multipliers=1e-6,1e-2,1e-3 --mesh-size=1e-2 --eigs-only Default material parameters, a square periodic cell with a square inclusion, and a very small mesh to allow comparing the omega and kappa modes (full matrix solver required!):: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.qevp', method='companion', mode='inverted', solver={kind='eig.scipy', method='eig'}" --log-std-waves -n 500 --range=0,4000000,1001 --mesh-size=1e-2 --mode=kappa --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/kappa View/compare the resulting logs:: python script/plot_logs.py output/omega/frequencies.txt --no-legends -g 1 -o mode-omega.png python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends -o mode-kappa.png python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends --swap-axes -o mode-kappa-t.png In contrast to the heterogeneous square periodic cell, a homogeneous square periodic cell (the region Y2 is empty):: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_1m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega-h python script/plot_logs.py output/omega-h/frequencies.txt --no-legends -g 1 -o mode-omega-h.png Use the Brillouin stepper:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves -n=60 --eigs-only --no-legends --stepper=brillouin python script/plot_logs.py output/frequencies.txt -g 0 --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-kappas.png python script/plot_logs.py output/frequencies.txt -g 1 --no-legends --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-omegas.png Additional arguments can be passed to the problem configuration's :func:`define()` function using the ``--define-kwargs`` option. In this file, only the mesh vertex separation parameter `mesh_eps` can be used:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only --define-kwargs="mesh_eps=1e-10" --save-regions """ from __future__ import absolute_import import os import sys sys.path.append('.') import gc from copy import copy from argparse import ArgumentParser, RawDescriptionHelpFormatter import numpy as nm import matplotlib.pyplot as plt from sfepy.base.base import import_file, output, Struct from sfepy.base.conf import dict_from_string, ProblemConf from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options from sfepy.base.log import Log from sfepy.discrete.fem import MeshIO from sfepy.mechanics.matcoefs import stiffness_from_youngpoisson as stiffness import sfepy.mechanics.matcoefs as mc from sfepy.mechanics.units import apply_unit_multipliers import sfepy.discrete.fem.periodic as per from sfepy.discrete.fem.meshio import convert_complex_output from sfepy.homogenization.utils import define_box_regions from sfepy.discrete import Problem from sfepy.mechanics.tensors import get_von_mises_stress from sfepy.solvers import Solver from sfepy.solvers.ts import get_print_info, TimeStepper from sfepy.linalg.utils import output_array_stats, max_diff_csr def apply_units(pars, unit_multipliers): new_pars = apply_unit_multipliers(pars, ['stress', 'one', 'density', 'stress', 'one' ,'density'], unit_multipliers) return new_pars def compute_von_mises(out, pb, state, extend=False, wmag=None, wdir=None): """ Calculate the von Mises stress. """ stress = pb.evaluate('ev_cauchy_stress.i.Omega(m.D, u)', mode='el_avg') vms = get_von_mises_stress(stress.squeeze()) vms.shape = (vms.shape[0], 1, 1, 1) out['von_mises_stress'] = Struct(name='output_data', mode='cell', data=vms) return out def define(filename_mesh, pars, approx_order, refinement_level, solver_conf, plane='strain', post_process=False, mesh_eps=1e-8): io = MeshIO.any_from_filename(filename_mesh) bbox = io.read_bounding_box() dim = bbox.shape[1] options = { 'absolute_mesh_path' : True, 'refinement_level' : refinement_level, 'allow_empty_regions' : True, 'post_process_hook' : 'compute_von_mises' if post_process else None, } fields = { 'displacement': ('complex', dim, 'Omega', approx_order), } young1, poisson1, density1, young2, poisson2, density2 = pars materials = { 'm' : ({ 'D' : {'Y1' : stiffness(dim, young=young1, poisson=poisson1, plane=plane), 'Y2' : stiffness(dim, young=young2, poisson=poisson2, plane=plane)}, 'density' : {'Y1' : density1, 'Y2' : density2}, },), 'wave' : 'get_wdir', } variables = { 'u' : ('unknown field', 'displacement', 0), 'v' : ('test field', 'displacement', 'u'), } regions = { 'Omega' : 'all', 'Y1': 'cells of group 1', 'Y2': 'cells of group 2', } regions.update(define_box_regions(dim, bbox[0], bbox[1], mesh_eps)) ebcs = { } if dim == 3: epbcs = { 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'}, 'match_x_plane'), 'periodic_y' : (['Near', 'Far'], {'u.all' : 'u.all'}, 'match_y_plane'), 'periodic_z' : (['Top', 'Bottom'], {'u.all' : 'u.all'}, 'match_z_plane'), } else: epbcs = { 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'}, 'match_y_line'), 'periodic_y' : (['Bottom', 'Top'], {'u.all' : 'u.all'}, 'match_x_line'), } per.set_accuracy(mesh_eps) functions = { 'match_x_plane' : (per.match_x_plane,), 'match_y_plane' : (per.match_y_plane,), 'match_z_plane' : (per.match_z_plane,), 'match_x_line' : (per.match_x_line,), 'match_y_line' : (per.match_y_line,), 'get_wdir' : (get_wdir,), } integrals = { 'i' : 2 * approx_order, } equations = { 'K' : 'dw_lin_elastic.i.Omega(m.D, v, u)', 'S' : 'dw_elastic_wave.i.Omega(m.D, wave.vec, v, u)', 'R' : """1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, u, v) - 1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, v, u)""", 'M' : 'dw_volume_dot.i.Omega(m.density, v, u)', } solver_0 = solver_conf.copy() solver_0['name'] = 'eig' return locals() def get_wdir(ts, coors, mode=None, equations=None, term=None, problem=None, wdir=None, **kwargs): if mode == 'special': return {'vec' : wdir} def set_wave_dir(pb, wdir): materials = pb.get_materials() wave_mat = materials['wave'] wave_mat.set_extra_args(wdir=wdir) def save_materials(output_dir, pb, options): stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)', mode='el_avg', copy_materials=False, verbose=False) young, poisson = mc.youngpoisson_from_stiffness(stiffness, plane=options.plane) density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)', mode='el_avg', copy_materials=False, verbose=False) out = {} out['young'] = Struct(name='young', mode='cell', data=young[..., None, None]) out['poisson'] = Struct(name='poisson', mode='cell', data=poisson[..., None, None]) out['density'] = Struct(name='density', mode='cell', data=density) materials_filename = os.path.join(output_dir, 'materials.vtk') pb.save_state(materials_filename, out=out) def get_std_wave_fun(pb, options): stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)', mode='el_avg', copy_materials=False, verbose=False) young, poisson = mc.youngpoisson_from_stiffness(stiffness, plane=options.plane) density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)', mode='el_avg', copy_materials=False, verbose=False) lam, mu = mc.lame_from_youngpoisson(young, poisson, plane=options.plane) alam = nm.average(lam) amu = nm.average(mu) adensity = nm.average(density) cp = nm.sqrt((alam + 2.0 * amu) / adensity) cs = nm.sqrt(amu / adensity) output('average p-wave speed:', cp) output('average shear wave speed:', cs) log_names = [r'$\omega_p$', r'$\omega_s$'] log_plot_kwargs = [{'ls' : '--', 'color' : 'k'}, {'ls' : '--', 'color' : 'gray'}] if options.mode == 'omega': fun = lambda wmag, wdir: (cp * wmag, cs * wmag) else: fun = lambda wmag, wdir: (wmag / cp, wmag / cs) return fun, log_names, log_plot_kwargs def get_stepper(rng, pb, options): if options.stepper == 'linear': stepper = TimeStepper(rng[0], rng[1], dt=None, n_step=rng[2]) return stepper bbox = pb.domain.mesh.get_bounding_box() bzone = 2.0 * nm.pi / (bbox[1] - bbox[0]) num = rng[2] // 3 class BrillouinStepper(Struct): """ Step over 1. Brillouin zone in xy plane. """ def __init__(self, t0, t1, dt=None, n_step=None, step=None, **kwargs): Struct.__init__(self, t0=t0, t1=t1, dt=dt, n_step=n_step, step=step) self.n_digit, self.format, self.suffix =	get_print_info(self.n_step)	sfepy.solvers.ts.get_print_info
#!/usr/bin/env python """ Dispersion analysis of a heterogeneous finite scale periodic cell. The periodic cell mesh has to contain two subdomains Y1 (with the cell ids 1), Y2 (with the cell ids 2), so that different material properties can be defined in each of the subdomains (see ``--pars`` option). The command line parameters can be given in any consistent unit set, for example the basic SI units. The ``--unit-multipliers`` option can be used to rescale the input units to ones more suitable to the simulation, for example to prevent having different matrix blocks with large differences of matrix entries magnitudes. The results are then in the rescaled units. Usage Examples -------------- Default material parameters, a square periodic cell with a spherical inclusion, logs also standard pressure dilatation and shear waves, no eigenvectors:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only As above, with custom eigenvalue solver parameters, and different number of eigenvalues, mesh size and units used in the calculation:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --solver-conf="kind='eig.scipy', method='eigsh', tol=1e-10, maxiter=1000, which='LM', sigma=0" --log-std-waves -n 5 --range=0,640,101 --mode=omega --unit-multipliers=1e-6,1e-2,1e-3 --mesh-size=1e-2 --eigs-only Default material parameters, a square periodic cell with a square inclusion, and a very small mesh to allow comparing the omega and kappa modes (full matrix solver required!):: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.qevp', method='companion', mode='inverted', solver={kind='eig.scipy', method='eig'}" --log-std-waves -n 500 --range=0,4000000,1001 --mesh-size=1e-2 --mode=kappa --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/kappa View/compare the resulting logs:: python script/plot_logs.py output/omega/frequencies.txt --no-legends -g 1 -o mode-omega.png python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends -o mode-kappa.png python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends --swap-axes -o mode-kappa-t.png In contrast to the heterogeneous square periodic cell, a homogeneous square periodic cell (the region Y2 is empty):: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_1m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega-h python script/plot_logs.py output/omega-h/frequencies.txt --no-legends -g 1 -o mode-omega-h.png Use the Brillouin stepper:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves -n=60 --eigs-only --no-legends --stepper=brillouin python script/plot_logs.py output/frequencies.txt -g 0 --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-kappas.png python script/plot_logs.py output/frequencies.txt -g 1 --no-legends --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-omegas.png Additional arguments can be passed to the problem configuration's :func:`define()` function using the ``--define-kwargs`` option. In this file, only the mesh vertex separation parameter `mesh_eps` can be used:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only --define-kwargs="mesh_eps=1e-10" --save-regions """ from __future__ import absolute_import import os import sys sys.path.append('.') import gc from copy import copy from argparse import ArgumentParser, RawDescriptionHelpFormatter import numpy as nm import matplotlib.pyplot as plt from sfepy.base.base import import_file, output, Struct from sfepy.base.conf import dict_from_string, ProblemConf from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options from sfepy.base.log import Log from sfepy.discrete.fem import MeshIO from sfepy.mechanics.matcoefs import stiffness_from_youngpoisson as stiffness import sfepy.mechanics.matcoefs as mc from sfepy.mechanics.units import apply_unit_multipliers import sfepy.discrete.fem.periodic as per from sfepy.discrete.fem.meshio import convert_complex_output from sfepy.homogenization.utils import define_box_regions from sfepy.discrete import Problem from sfepy.mechanics.tensors import get_von_mises_stress from sfepy.solvers import Solver from sfepy.solvers.ts import get_print_info, TimeStepper from sfepy.linalg.utils import output_array_stats, max_diff_csr def apply_units(pars, unit_multipliers): new_pars = apply_unit_multipliers(pars, ['stress', 'one', 'density', 'stress', 'one' ,'density'], unit_multipliers) return new_pars def compute_von_mises(out, pb, state, extend=False, wmag=None, wdir=None): """ Calculate the von Mises stress. """ stress = pb.evaluate('ev_cauchy_stress.i.Omega(m.D, u)', mode='el_avg') vms = get_von_mises_stress(stress.squeeze()) vms.shape = (vms.shape[0], 1, 1, 1) out['von_mises_stress'] = Struct(name='output_data', mode='cell', data=vms) return out def define(filename_mesh, pars, approx_order, refinement_level, solver_conf, plane='strain', post_process=False, mesh_eps=1e-8): io = MeshIO.any_from_filename(filename_mesh) bbox = io.read_bounding_box() dim = bbox.shape[1] options = { 'absolute_mesh_path' : True, 'refinement_level' : refinement_level, 'allow_empty_regions' : True, 'post_process_hook' : 'compute_von_mises' if post_process else None, } fields = { 'displacement': ('complex', dim, 'Omega', approx_order), } young1, poisson1, density1, young2, poisson2, density2 = pars materials = { 'm' : ({ 'D' : {'Y1' : stiffness(dim, young=young1, poisson=poisson1, plane=plane), 'Y2' : stiffness(dim, young=young2, poisson=poisson2, plane=plane)}, 'density' : {'Y1' : density1, 'Y2' : density2}, },), 'wave' : 'get_wdir', } variables = { 'u' : ('unknown field', 'displacement', 0), 'v' : ('test field', 'displacement', 'u'), } regions = { 'Omega' : 'all', 'Y1': 'cells of group 1', 'Y2': 'cells of group 2', } regions.update(define_box_regions(dim, bbox[0], bbox[1], mesh_eps)) ebcs = { } if dim == 3: epbcs = { 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'}, 'match_x_plane'), 'periodic_y' : (['Near', 'Far'], {'u.all' : 'u.all'}, 'match_y_plane'), 'periodic_z' : (['Top', 'Bottom'], {'u.all' : 'u.all'}, 'match_z_plane'), } else: epbcs = { 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'}, 'match_y_line'), 'periodic_y' : (['Bottom', 'Top'], {'u.all' : 'u.all'}, 'match_x_line'), } per.set_accuracy(mesh_eps) functions = { 'match_x_plane' : (per.match_x_plane,), 'match_y_plane' : (per.match_y_plane,), 'match_z_plane' : (per.match_z_plane,), 'match_x_line' : (per.match_x_line,), 'match_y_line' : (per.match_y_line,), 'get_wdir' : (get_wdir,), } integrals = { 'i' : 2 * approx_order, } equations = { 'K' : 'dw_lin_elastic.i.Omega(m.D, v, u)', 'S' : 'dw_elastic_wave.i.Omega(m.D, wave.vec, v, u)', 'R' : """1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, u, v) - 1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, v, u)""", 'M' : 'dw_volume_dot.i.Omega(m.density, v, u)', } solver_0 = solver_conf.copy() solver_0['name'] = 'eig' return locals() def get_wdir(ts, coors, mode=None, equations=None, term=None, problem=None, wdir=None, **kwargs): if mode == 'special': return {'vec' : wdir} def set_wave_dir(pb, wdir): materials = pb.get_materials() wave_mat = materials['wave'] wave_mat.set_extra_args(wdir=wdir) def save_materials(output_dir, pb, options): stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)', mode='el_avg', copy_materials=False, verbose=False) young, poisson = mc.youngpoisson_from_stiffness(stiffness, plane=options.plane) density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)', mode='el_avg', copy_materials=False, verbose=False) out = {} out['young'] = Struct(name='young', mode='cell', data=young[..., None, None]) out['poisson'] = Struct(name='poisson', mode='cell', data=poisson[..., None, None]) out['density'] = Struct(name='density', mode='cell', data=density) materials_filename = os.path.join(output_dir, 'materials.vtk') pb.save_state(materials_filename, out=out) def get_std_wave_fun(pb, options): stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)', mode='el_avg', copy_materials=False, verbose=False) young, poisson = mc.youngpoisson_from_stiffness(stiffness, plane=options.plane) density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)', mode='el_avg', copy_materials=False, verbose=False) lam, mu = mc.lame_from_youngpoisson(young, poisson, plane=options.plane) alam = nm.average(lam) amu = nm.average(mu) adensity = nm.average(density) cp = nm.sqrt((alam + 2.0 * amu) / adensity) cs = nm.sqrt(amu / adensity) output('average p-wave speed:', cp) output('average shear wave speed:', cs) log_names = [r'$\omega_p$', r'$\omega_s$'] log_plot_kwargs = [{'ls' : '--', 'color' : 'k'}, {'ls' : '--', 'color' : 'gray'}] if options.mode == 'omega': fun = lambda wmag, wdir: (cp * wmag, cs * wmag) else: fun = lambda wmag, wdir: (wmag / cp, wmag / cs) return fun, log_names, log_plot_kwargs def get_stepper(rng, pb, options): if options.stepper == 'linear': stepper = TimeStepper(rng[0], rng[1], dt=None, n_step=rng[2]) return stepper bbox = pb.domain.mesh.get_bounding_box() bzone = 2.0 * nm.pi / (bbox[1] - bbox[0]) num = rng[2] // 3 class BrillouinStepper(Struct): """ Step over 1. Brillouin zone in xy plane. """ def __init__(self, t0, t1, dt=None, n_step=None, step=None, **kwargs): Struct.__init__(self, t0=t0, t1=t1, dt=dt, n_step=n_step, step=step) self.n_digit, self.format, self.suffix = get_print_info(self.n_step) def __iter__(self): ts =	TimeStepper(0, bzone[0], dt=None, n_step=num)	sfepy.solvers.ts.TimeStepper
#!/usr/bin/env python """ Dispersion analysis of a heterogeneous finite scale periodic cell. The periodic cell mesh has to contain two subdomains Y1 (with the cell ids 1), Y2 (with the cell ids 2), so that different material properties can be defined in each of the subdomains (see ``--pars`` option). The command line parameters can be given in any consistent unit set, for example the basic SI units. The ``--unit-multipliers`` option can be used to rescale the input units to ones more suitable to the simulation, for example to prevent having different matrix blocks with large differences of matrix entries magnitudes. The results are then in the rescaled units. Usage Examples -------------- Default material parameters, a square periodic cell with a spherical inclusion, logs also standard pressure dilatation and shear waves, no eigenvectors:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only As above, with custom eigenvalue solver parameters, and different number of eigenvalues, mesh size and units used in the calculation:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --solver-conf="kind='eig.scipy', method='eigsh', tol=1e-10, maxiter=1000, which='LM', sigma=0" --log-std-waves -n 5 --range=0,640,101 --mode=omega --unit-multipliers=1e-6,1e-2,1e-3 --mesh-size=1e-2 --eigs-only Default material parameters, a square periodic cell with a square inclusion, and a very small mesh to allow comparing the omega and kappa modes (full matrix solver required!):: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.qevp', method='companion', mode='inverted', solver={kind='eig.scipy', method='eig'}" --log-std-waves -n 500 --range=0,4000000,1001 --mesh-size=1e-2 --mode=kappa --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/kappa View/compare the resulting logs:: python script/plot_logs.py output/omega/frequencies.txt --no-legends -g 1 -o mode-omega.png python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends -o mode-kappa.png python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends --swap-axes -o mode-kappa-t.png In contrast to the heterogeneous square periodic cell, a homogeneous square periodic cell (the region Y2 is empty):: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_1m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega-h python script/plot_logs.py output/omega-h/frequencies.txt --no-legends -g 1 -o mode-omega-h.png Use the Brillouin stepper:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves -n=60 --eigs-only --no-legends --stepper=brillouin python script/plot_logs.py output/frequencies.txt -g 0 --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-kappas.png python script/plot_logs.py output/frequencies.txt -g 1 --no-legends --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-omegas.png Additional arguments can be passed to the problem configuration's :func:`define()` function using the ``--define-kwargs`` option. In this file, only the mesh vertex separation parameter `mesh_eps` can be used:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only --define-kwargs="mesh_eps=1e-10" --save-regions """ from __future__ import absolute_import import os import sys sys.path.append('.') import gc from copy import copy from argparse import ArgumentParser, RawDescriptionHelpFormatter import numpy as nm import matplotlib.pyplot as plt from sfepy.base.base import import_file, output, Struct from sfepy.base.conf import dict_from_string, ProblemConf from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options from sfepy.base.log import Log from sfepy.discrete.fem import MeshIO from sfepy.mechanics.matcoefs import stiffness_from_youngpoisson as stiffness import sfepy.mechanics.matcoefs as mc from sfepy.mechanics.units import apply_unit_multipliers import sfepy.discrete.fem.periodic as per from sfepy.discrete.fem.meshio import convert_complex_output from sfepy.homogenization.utils import define_box_regions from sfepy.discrete import Problem from sfepy.mechanics.tensors import get_von_mises_stress from sfepy.solvers import Solver from sfepy.solvers.ts import get_print_info, TimeStepper from sfepy.linalg.utils import output_array_stats, max_diff_csr def apply_units(pars, unit_multipliers): new_pars = apply_unit_multipliers(pars, ['stress', 'one', 'density', 'stress', 'one' ,'density'], unit_multipliers) return new_pars def compute_von_mises(out, pb, state, extend=False, wmag=None, wdir=None): """ Calculate the von Mises stress. """ stress = pb.evaluate('ev_cauchy_stress.i.Omega(m.D, u)', mode='el_avg') vms = get_von_mises_stress(stress.squeeze()) vms.shape = (vms.shape[0], 1, 1, 1) out['von_mises_stress'] = Struct(name='output_data', mode='cell', data=vms) return out def define(filename_mesh, pars, approx_order, refinement_level, solver_conf, plane='strain', post_process=False, mesh_eps=1e-8): io = MeshIO.any_from_filename(filename_mesh) bbox = io.read_bounding_box() dim = bbox.shape[1] options = { 'absolute_mesh_path' : True, 'refinement_level' : refinement_level, 'allow_empty_regions' : True, 'post_process_hook' : 'compute_von_mises' if post_process else None, } fields = { 'displacement': ('complex', dim, 'Omega', approx_order), } young1, poisson1, density1, young2, poisson2, density2 = pars materials = { 'm' : ({ 'D' : {'Y1' : stiffness(dim, young=young1, poisson=poisson1, plane=plane), 'Y2' : stiffness(dim, young=young2, poisson=poisson2, plane=plane)}, 'density' : {'Y1' : density1, 'Y2' : density2}, },), 'wave' : 'get_wdir', } variables = { 'u' : ('unknown field', 'displacement', 0), 'v' : ('test field', 'displacement', 'u'), } regions = { 'Omega' : 'all', 'Y1': 'cells of group 1', 'Y2': 'cells of group 2', } regions.update(define_box_regions(dim, bbox[0], bbox[1], mesh_eps)) ebcs = { } if dim == 3: epbcs = { 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'}, 'match_x_plane'), 'periodic_y' : (['Near', 'Far'], {'u.all' : 'u.all'}, 'match_y_plane'), 'periodic_z' : (['Top', 'Bottom'], {'u.all' : 'u.all'}, 'match_z_plane'), } else: epbcs = { 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'}, 'match_y_line'), 'periodic_y' : (['Bottom', 'Top'], {'u.all' : 'u.all'}, 'match_x_line'), } per.set_accuracy(mesh_eps) functions = { 'match_x_plane' : (per.match_x_plane,), 'match_y_plane' : (per.match_y_plane,), 'match_z_plane' : (per.match_z_plane,), 'match_x_line' : (per.match_x_line,), 'match_y_line' : (per.match_y_line,), 'get_wdir' : (get_wdir,), } integrals = { 'i' : 2 * approx_order, } equations = { 'K' : 'dw_lin_elastic.i.Omega(m.D, v, u)', 'S' : 'dw_elastic_wave.i.Omega(m.D, wave.vec, v, u)', 'R' : """1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, u, v) - 1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, v, u)""", 'M' : 'dw_volume_dot.i.Omega(m.density, v, u)', } solver_0 = solver_conf.copy() solver_0['name'] = 'eig' return locals() def get_wdir(ts, coors, mode=None, equations=None, term=None, problem=None, wdir=None, **kwargs): if mode == 'special': return {'vec' : wdir} def set_wave_dir(pb, wdir): materials = pb.get_materials() wave_mat = materials['wave'] wave_mat.set_extra_args(wdir=wdir) def save_materials(output_dir, pb, options): stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)', mode='el_avg', copy_materials=False, verbose=False) young, poisson = mc.youngpoisson_from_stiffness(stiffness, plane=options.plane) density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)', mode='el_avg', copy_materials=False, verbose=False) out = {} out['young'] = Struct(name='young', mode='cell', data=young[..., None, None]) out['poisson'] = Struct(name='poisson', mode='cell', data=poisson[..., None, None]) out['density'] = Struct(name='density', mode='cell', data=density) materials_filename = os.path.join(output_dir, 'materials.vtk') pb.save_state(materials_filename, out=out) def get_std_wave_fun(pb, options): stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)', mode='el_avg', copy_materials=False, verbose=False) young, poisson = mc.youngpoisson_from_stiffness(stiffness, plane=options.plane) density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)', mode='el_avg', copy_materials=False, verbose=False) lam, mu = mc.lame_from_youngpoisson(young, poisson, plane=options.plane) alam = nm.average(lam) amu = nm.average(mu) adensity = nm.average(density) cp = nm.sqrt((alam + 2.0 * amu) / adensity) cs = nm.sqrt(amu / adensity) output('average p-wave speed:', cp) output('average shear wave speed:', cs) log_names = [r'$\omega_p$', r'$\omega_s$'] log_plot_kwargs = [{'ls' : '--', 'color' : 'k'}, {'ls' : '--', 'color' : 'gray'}] if options.mode == 'omega': fun = lambda wmag, wdir: (cp * wmag, cs * wmag) else: fun = lambda wmag, wdir: (wmag / cp, wmag / cs) return fun, log_names, log_plot_kwargs def get_stepper(rng, pb, options): if options.stepper == 'linear': stepper = TimeStepper(rng[0], rng[1], dt=None, n_step=rng[2]) return stepper bbox = pb.domain.mesh.get_bounding_box() bzone = 2.0 * nm.pi / (bbox[1] - bbox[0]) num = rng[2] // 3 class BrillouinStepper(Struct): """ Step over 1. Brillouin zone in xy plane. """ def __init__(self, t0, t1, dt=None, n_step=None, step=None, **kwargs): Struct.__init__(self, t0=t0, t1=t1, dt=dt, n_step=n_step, step=step) self.n_digit, self.format, self.suffix = get_print_info(self.n_step) def __iter__(self): ts = TimeStepper(0, bzone[0], dt=None, n_step=num) for ii, val in ts: yield ii, val, nm.array([1.0, 0.0]) if ii == (num-2): break ts =	TimeStepper(0, bzone[1], dt=None, n_step=num)	sfepy.solvers.ts.TimeStepper
#!/usr/bin/env python """ Dispersion analysis of a heterogeneous finite scale periodic cell. The periodic cell mesh has to contain two subdomains Y1 (with the cell ids 1), Y2 (with the cell ids 2), so that different material properties can be defined in each of the subdomains (see ``--pars`` option). The command line parameters can be given in any consistent unit set, for example the basic SI units. The ``--unit-multipliers`` option can be used to rescale the input units to ones more suitable to the simulation, for example to prevent having different matrix blocks with large differences of matrix entries magnitudes. The results are then in the rescaled units. Usage Examples -------------- Default material parameters, a square periodic cell with a spherical inclusion, logs also standard pressure dilatation and shear waves, no eigenvectors:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only As above, with custom eigenvalue solver parameters, and different number of eigenvalues, mesh size and units used in the calculation:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --solver-conf="kind='eig.scipy', method='eigsh', tol=1e-10, maxiter=1000, which='LM', sigma=0" --log-std-waves -n 5 --range=0,640,101 --mode=omega --unit-multipliers=1e-6,1e-2,1e-3 --mesh-size=1e-2 --eigs-only Default material parameters, a square periodic cell with a square inclusion, and a very small mesh to allow comparing the omega and kappa modes (full matrix solver required!):: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.qevp', method='companion', mode='inverted', solver={kind='eig.scipy', method='eig'}" --log-std-waves -n 500 --range=0,4000000,1001 --mesh-size=1e-2 --mode=kappa --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/kappa View/compare the resulting logs:: python script/plot_logs.py output/omega/frequencies.txt --no-legends -g 1 -o mode-omega.png python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends -o mode-kappa.png python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends --swap-axes -o mode-kappa-t.png In contrast to the heterogeneous square periodic cell, a homogeneous square periodic cell (the region Y2 is empty):: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_1m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega-h python script/plot_logs.py output/omega-h/frequencies.txt --no-legends -g 1 -o mode-omega-h.png Use the Brillouin stepper:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves -n=60 --eigs-only --no-legends --stepper=brillouin python script/plot_logs.py output/frequencies.txt -g 0 --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-kappas.png python script/plot_logs.py output/frequencies.txt -g 1 --no-legends --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-omegas.png Additional arguments can be passed to the problem configuration's :func:`define()` function using the ``--define-kwargs`` option. In this file, only the mesh vertex separation parameter `mesh_eps` can be used:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only --define-kwargs="mesh_eps=1e-10" --save-regions """ from __future__ import absolute_import import os import sys sys.path.append('.') import gc from copy import copy from argparse import ArgumentParser, RawDescriptionHelpFormatter import numpy as nm import matplotlib.pyplot as plt from sfepy.base.base import import_file, output, Struct from sfepy.base.conf import dict_from_string, ProblemConf from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options from sfepy.base.log import Log from sfepy.discrete.fem import MeshIO from sfepy.mechanics.matcoefs import stiffness_from_youngpoisson as stiffness import sfepy.mechanics.matcoefs as mc from sfepy.mechanics.units import apply_unit_multipliers import sfepy.discrete.fem.periodic as per from sfepy.discrete.fem.meshio import convert_complex_output from sfepy.homogenization.utils import define_box_regions from sfepy.discrete import Problem from sfepy.mechanics.tensors import get_von_mises_stress from sfepy.solvers import Solver from sfepy.solvers.ts import get_print_info, TimeStepper from sfepy.linalg.utils import output_array_stats, max_diff_csr def apply_units(pars, unit_multipliers): new_pars = apply_unit_multipliers(pars, ['stress', 'one', 'density', 'stress', 'one' ,'density'], unit_multipliers) return new_pars def compute_von_mises(out, pb, state, extend=False, wmag=None, wdir=None): """ Calculate the von Mises stress. """ stress = pb.evaluate('ev_cauchy_stress.i.Omega(m.D, u)', mode='el_avg') vms = get_von_mises_stress(stress.squeeze()) vms.shape = (vms.shape[0], 1, 1, 1) out['von_mises_stress'] = Struct(name='output_data', mode='cell', data=vms) return out def define(filename_mesh, pars, approx_order, refinement_level, solver_conf, plane='strain', post_process=False, mesh_eps=1e-8): io = MeshIO.any_from_filename(filename_mesh) bbox = io.read_bounding_box() dim = bbox.shape[1] options = { 'absolute_mesh_path' : True, 'refinement_level' : refinement_level, 'allow_empty_regions' : True, 'post_process_hook' : 'compute_von_mises' if post_process else None, } fields = { 'displacement': ('complex', dim, 'Omega', approx_order), } young1, poisson1, density1, young2, poisson2, density2 = pars materials = { 'm' : ({ 'D' : {'Y1' : stiffness(dim, young=young1, poisson=poisson1, plane=plane), 'Y2' : stiffness(dim, young=young2, poisson=poisson2, plane=plane)}, 'density' : {'Y1' : density1, 'Y2' : density2}, },), 'wave' : 'get_wdir', } variables = { 'u' : ('unknown field', 'displacement', 0), 'v' : ('test field', 'displacement', 'u'), } regions = { 'Omega' : 'all', 'Y1': 'cells of group 1', 'Y2': 'cells of group 2', } regions.update(define_box_regions(dim, bbox[0], bbox[1], mesh_eps)) ebcs = { } if dim == 3: epbcs = { 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'}, 'match_x_plane'), 'periodic_y' : (['Near', 'Far'], {'u.all' : 'u.all'}, 'match_y_plane'), 'periodic_z' : (['Top', 'Bottom'], {'u.all' : 'u.all'}, 'match_z_plane'), } else: epbcs = { 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'}, 'match_y_line'), 'periodic_y' : (['Bottom', 'Top'], {'u.all' : 'u.all'}, 'match_x_line'), } per.set_accuracy(mesh_eps) functions = { 'match_x_plane' : (per.match_x_plane,), 'match_y_plane' : (per.match_y_plane,), 'match_z_plane' : (per.match_z_plane,), 'match_x_line' : (per.match_x_line,), 'match_y_line' : (per.match_y_line,), 'get_wdir' : (get_wdir,), } integrals = { 'i' : 2 * approx_order, } equations = { 'K' : 'dw_lin_elastic.i.Omega(m.D, v, u)', 'S' : 'dw_elastic_wave.i.Omega(m.D, wave.vec, v, u)', 'R' : """1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, u, v) - 1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, v, u)""", 'M' : 'dw_volume_dot.i.Omega(m.density, v, u)', } solver_0 = solver_conf.copy() solver_0['name'] = 'eig' return locals() def get_wdir(ts, coors, mode=None, equations=None, term=None, problem=None, wdir=None, **kwargs): if mode == 'special': return {'vec' : wdir} def set_wave_dir(pb, wdir): materials = pb.get_materials() wave_mat = materials['wave'] wave_mat.set_extra_args(wdir=wdir) def save_materials(output_dir, pb, options): stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)', mode='el_avg', copy_materials=False, verbose=False) young, poisson = mc.youngpoisson_from_stiffness(stiffness, plane=options.plane) density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)', mode='el_avg', copy_materials=False, verbose=False) out = {} out['young'] = Struct(name='young', mode='cell', data=young[..., None, None]) out['poisson'] = Struct(name='poisson', mode='cell', data=poisson[..., None, None]) out['density'] = Struct(name='density', mode='cell', data=density) materials_filename = os.path.join(output_dir, 'materials.vtk') pb.save_state(materials_filename, out=out) def get_std_wave_fun(pb, options): stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)', mode='el_avg', copy_materials=False, verbose=False) young, poisson = mc.youngpoisson_from_stiffness(stiffness, plane=options.plane) density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)', mode='el_avg', copy_materials=False, verbose=False) lam, mu = mc.lame_from_youngpoisson(young, poisson, plane=options.plane) alam = nm.average(lam) amu = nm.average(mu) adensity = nm.average(density) cp = nm.sqrt((alam + 2.0 * amu) / adensity) cs = nm.sqrt(amu / adensity) output('average p-wave speed:', cp) output('average shear wave speed:', cs) log_names = [r'$\omega_p$', r'$\omega_s$'] log_plot_kwargs = [{'ls' : '--', 'color' : 'k'}, {'ls' : '--', 'color' : 'gray'}] if options.mode == 'omega': fun = lambda wmag, wdir: (cp * wmag, cs * wmag) else: fun = lambda wmag, wdir: (wmag / cp, wmag / cs) return fun, log_names, log_plot_kwargs def get_stepper(rng, pb, options): if options.stepper == 'linear': stepper = TimeStepper(rng[0], rng[1], dt=None, n_step=rng[2]) return stepper bbox = pb.domain.mesh.get_bounding_box() bzone = 2.0 * nm.pi / (bbox[1] - bbox[0]) num = rng[2] // 3 class BrillouinStepper(Struct): """ Step over 1. Brillouin zone in xy plane. """ def __init__(self, t0, t1, dt=None, n_step=None, step=None, **kwargs): Struct.__init__(self, t0=t0, t1=t1, dt=dt, n_step=n_step, step=step) self.n_digit, self.format, self.suffix = get_print_info(self.n_step) def __iter__(self): ts = TimeStepper(0, bzone[0], dt=None, n_step=num) for ii, val in ts: yield ii, val, nm.array([1.0, 0.0]) if ii == (num-2): break ts = TimeStepper(0, bzone[1], dt=None, n_step=num) for ii, k1 in ts: wdir = nm.array([bzone[0], k1]) val = nm.linalg.norm(wdir) wdir = wdir / val yield num + ii, val, wdir if ii == (num-2): break wdir = nm.array([bzone[0], bzone[1]]) val = nm.linalg.norm(wdir) wdir = wdir / val ts =	TimeStepper(0, 1, dt=None, n_step=num)	sfepy.solvers.ts.TimeStepper
#!/usr/bin/env python """ Dispersion analysis of a heterogeneous finite scale periodic cell. The periodic cell mesh has to contain two subdomains Y1 (with the cell ids 1), Y2 (with the cell ids 2), so that different material properties can be defined in each of the subdomains (see ``--pars`` option). The command line parameters can be given in any consistent unit set, for example the basic SI units. The ``--unit-multipliers`` option can be used to rescale the input units to ones more suitable to the simulation, for example to prevent having different matrix blocks with large differences of matrix entries magnitudes. The results are then in the rescaled units. Usage Examples -------------- Default material parameters, a square periodic cell with a spherical inclusion, logs also standard pressure dilatation and shear waves, no eigenvectors:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only As above, with custom eigenvalue solver parameters, and different number of eigenvalues, mesh size and units used in the calculation:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --solver-conf="kind='eig.scipy', method='eigsh', tol=1e-10, maxiter=1000, which='LM', sigma=0" --log-std-waves -n 5 --range=0,640,101 --mode=omega --unit-multipliers=1e-6,1e-2,1e-3 --mesh-size=1e-2 --eigs-only Default material parameters, a square periodic cell with a square inclusion, and a very small mesh to allow comparing the omega and kappa modes (full matrix solver required!):: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.qevp', method='companion', mode='inverted', solver={kind='eig.scipy', method='eig'}" --log-std-waves -n 500 --range=0,4000000,1001 --mesh-size=1e-2 --mode=kappa --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/kappa View/compare the resulting logs:: python script/plot_logs.py output/omega/frequencies.txt --no-legends -g 1 -o mode-omega.png python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends -o mode-kappa.png python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends --swap-axes -o mode-kappa-t.png In contrast to the heterogeneous square periodic cell, a homogeneous square periodic cell (the region Y2 is empty):: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_1m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega-h python script/plot_logs.py output/omega-h/frequencies.txt --no-legends -g 1 -o mode-omega-h.png Use the Brillouin stepper:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves -n=60 --eigs-only --no-legends --stepper=brillouin python script/plot_logs.py output/frequencies.txt -g 0 --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-kappas.png python script/plot_logs.py output/frequencies.txt -g 1 --no-legends --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-omegas.png Additional arguments can be passed to the problem configuration's :func:`define()` function using the ``--define-kwargs`` option. In this file, only the mesh vertex separation parameter `mesh_eps` can be used:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only --define-kwargs="mesh_eps=1e-10" --save-regions """ from __future__ import absolute_import import os import sys sys.path.append('.') import gc from copy import copy from argparse import ArgumentParser, RawDescriptionHelpFormatter import numpy as nm import matplotlib.pyplot as plt from sfepy.base.base import import_file, output, Struct from sfepy.base.conf import dict_from_string, ProblemConf from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options from sfepy.base.log import Log from sfepy.discrete.fem import MeshIO from sfepy.mechanics.matcoefs import stiffness_from_youngpoisson as stiffness import sfepy.mechanics.matcoefs as mc from sfepy.mechanics.units import apply_unit_multipliers import sfepy.discrete.fem.periodic as per from sfepy.discrete.fem.meshio import convert_complex_output from sfepy.homogenization.utils import define_box_regions from sfepy.discrete import Problem from sfepy.mechanics.tensors import get_von_mises_stress from sfepy.solvers import Solver from sfepy.solvers.ts import get_print_info, TimeStepper from sfepy.linalg.utils import output_array_stats, max_diff_csr def apply_units(pars, unit_multipliers): new_pars = apply_unit_multipliers(pars, ['stress', 'one', 'density', 'stress', 'one' ,'density'], unit_multipliers) return new_pars def compute_von_mises(out, pb, state, extend=False, wmag=None, wdir=None): """ Calculate the von Mises stress. """ stress = pb.evaluate('ev_cauchy_stress.i.Omega(m.D, u)', mode='el_avg') vms = get_von_mises_stress(stress.squeeze()) vms.shape = (vms.shape[0], 1, 1, 1) out['von_mises_stress'] = Struct(name='output_data', mode='cell', data=vms) return out def define(filename_mesh, pars, approx_order, refinement_level, solver_conf, plane='strain', post_process=False, mesh_eps=1e-8): io = MeshIO.any_from_filename(filename_mesh) bbox = io.read_bounding_box() dim = bbox.shape[1] options = { 'absolute_mesh_path' : True, 'refinement_level' : refinement_level, 'allow_empty_regions' : True, 'post_process_hook' : 'compute_von_mises' if post_process else None, } fields = { 'displacement': ('complex', dim, 'Omega', approx_order), } young1, poisson1, density1, young2, poisson2, density2 = pars materials = { 'm' : ({ 'D' : {'Y1' : stiffness(dim, young=young1, poisson=poisson1, plane=plane), 'Y2' : stiffness(dim, young=young2, poisson=poisson2, plane=plane)}, 'density' : {'Y1' : density1, 'Y2' : density2}, },), 'wave' : 'get_wdir', } variables = { 'u' : ('unknown field', 'displacement', 0), 'v' : ('test field', 'displacement', 'u'), } regions = { 'Omega' : 'all', 'Y1': 'cells of group 1', 'Y2': 'cells of group 2', } regions.update(define_box_regions(dim, bbox[0], bbox[1], mesh_eps)) ebcs = { } if dim == 3: epbcs = { 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'}, 'match_x_plane'), 'periodic_y' : (['Near', 'Far'], {'u.all' : 'u.all'}, 'match_y_plane'), 'periodic_z' : (['Top', 'Bottom'], {'u.all' : 'u.all'}, 'match_z_plane'), } else: epbcs = { 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'}, 'match_y_line'), 'periodic_y' : (['Bottom', 'Top'], {'u.all' : 'u.all'}, 'match_x_line'), } per.set_accuracy(mesh_eps) functions = { 'match_x_plane' : (per.match_x_plane,), 'match_y_plane' : (per.match_y_plane,), 'match_z_plane' : (per.match_z_plane,), 'match_x_line' : (per.match_x_line,), 'match_y_line' : (per.match_y_line,), 'get_wdir' : (get_wdir,), } integrals = { 'i' : 2 * approx_order, } equations = { 'K' : 'dw_lin_elastic.i.Omega(m.D, v, u)', 'S' : 'dw_elastic_wave.i.Omega(m.D, wave.vec, v, u)', 'R' : """1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, u, v) - 1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, v, u)""", 'M' : 'dw_volume_dot.i.Omega(m.density, v, u)', } solver_0 = solver_conf.copy() solver_0['name'] = 'eig' return locals() def get_wdir(ts, coors, mode=None, equations=None, term=None, problem=None, wdir=None, **kwargs): if mode == 'special': return {'vec' : wdir} def set_wave_dir(pb, wdir): materials = pb.get_materials() wave_mat = materials['wave'] wave_mat.set_extra_args(wdir=wdir) def save_materials(output_dir, pb, options): stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)', mode='el_avg', copy_materials=False, verbose=False) young, poisson = mc.youngpoisson_from_stiffness(stiffness, plane=options.plane) density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)', mode='el_avg', copy_materials=False, verbose=False) out = {} out['young'] = Struct(name='young', mode='cell', data=young[..., None, None]) out['poisson'] = Struct(name='poisson', mode='cell', data=poisson[..., None, None]) out['density'] = Struct(name='density', mode='cell', data=density) materials_filename = os.path.join(output_dir, 'materials.vtk') pb.save_state(materials_filename, out=out) def get_std_wave_fun(pb, options): stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)', mode='el_avg', copy_materials=False, verbose=False) young, poisson = mc.youngpoisson_from_stiffness(stiffness, plane=options.plane) density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)', mode='el_avg', copy_materials=False, verbose=False) lam, mu = mc.lame_from_youngpoisson(young, poisson, plane=options.plane) alam = nm.average(lam) amu = nm.average(mu) adensity = nm.average(density) cp = nm.sqrt((alam + 2.0 * amu) / adensity) cs = nm.sqrt(amu / adensity) output('average p-wave speed:', cp) output('average shear wave speed:', cs) log_names = [r'$\omega_p$', r'$\omega_s$'] log_plot_kwargs = [{'ls' : '--', 'color' : 'k'}, {'ls' : '--', 'color' : 'gray'}] if options.mode == 'omega': fun = lambda wmag, wdir: (cp * wmag, cs * wmag) else: fun = lambda wmag, wdir: (wmag / cp, wmag / cs) return fun, log_names, log_plot_kwargs def get_stepper(rng, pb, options): if options.stepper == 'linear': stepper = TimeStepper(rng[0], rng[1], dt=None, n_step=rng[2]) return stepper bbox = pb.domain.mesh.get_bounding_box() bzone = 2.0 * nm.pi / (bbox[1] - bbox[0]) num = rng[2] // 3 class BrillouinStepper(Struct): """ Step over 1. Brillouin zone in xy plane. """ def __init__(self, t0, t1, dt=None, n_step=None, step=None, **kwargs): Struct.__init__(self, t0=t0, t1=t1, dt=dt, n_step=n_step, step=step) self.n_digit, self.format, self.suffix = get_print_info(self.n_step) def __iter__(self): ts = TimeStepper(0, bzone[0], dt=None, n_step=num) for ii, val in ts: yield ii, val, nm.array([1.0, 0.0]) if ii == (num-2): break ts = TimeStepper(0, bzone[1], dt=None, n_step=num) for ii, k1 in ts: wdir = nm.array([bzone[0], k1]) val = nm.linalg.norm(wdir) wdir = wdir / val yield num + ii, val, wdir if ii == (num-2): break wdir = nm.array([bzone[0], bzone[1]]) val = nm.linalg.norm(wdir) wdir = wdir / val ts = TimeStepper(0, 1, dt=None, n_step=num) for ii, _ in ts: yield 2 * num + ii, val * (1.0 - float(ii)/(num-1)), wdir stepper = BrillouinStepper(0, 1, n_step=rng[2]) return stepper def save_eigenvectors(filename, svecs, wmag, wdir, pb): if svecs is None: return variables = pb.get_variables() # Make full eigenvectors (add DOFs fixed by boundary conditions). vecs = nm.empty((variables.di.ptr[-1], svecs.shape[1]), dtype=svecs.dtype) for ii in range(svecs.shape[1]): vecs[:, ii] = variables.make_full_vec(svecs[:, ii]) # Save the eigenvectors. out = {} state = pb.create_state() pp_name = pb.conf.options.get('post_process_hook') pp = getattr(pb.conf.funmod, pp_name if pp_name is not None else '', lambda out, *args, **kwargs: out) for ii in range(svecs.shape[1]): state.set_full(vecs[:, ii]) aux = state.create_output_dict() aux2 = {} pp(aux2, pb, state, wmag=wmag, wdir=wdir) aux.update(	convert_complex_output(aux2)	sfepy.discrete.fem.meshio.convert_complex_output
#!/usr/bin/env python """ Dispersion analysis of a heterogeneous finite scale periodic cell. The periodic cell mesh has to contain two subdomains Y1 (with the cell ids 1), Y2 (with the cell ids 2), so that different material properties can be defined in each of the subdomains (see ``--pars`` option). The command line parameters can be given in any consistent unit set, for example the basic SI units. The ``--unit-multipliers`` option can be used to rescale the input units to ones more suitable to the simulation, for example to prevent having different matrix blocks with large differences of matrix entries magnitudes. The results are then in the rescaled units. Usage Examples -------------- Default material parameters, a square periodic cell with a spherical inclusion, logs also standard pressure dilatation and shear waves, no eigenvectors:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only As above, with custom eigenvalue solver parameters, and different number of eigenvalues, mesh size and units used in the calculation:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --solver-conf="kind='eig.scipy', method='eigsh', tol=1e-10, maxiter=1000, which='LM', sigma=0" --log-std-waves -n 5 --range=0,640,101 --mode=omega --unit-multipliers=1e-6,1e-2,1e-3 --mesh-size=1e-2 --eigs-only Default material parameters, a square periodic cell with a square inclusion, and a very small mesh to allow comparing the omega and kappa modes (full matrix solver required!):: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.qevp', method='companion', mode='inverted', solver={kind='eig.scipy', method='eig'}" --log-std-waves -n 500 --range=0,4000000,1001 --mesh-size=1e-2 --mode=kappa --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/kappa View/compare the resulting logs:: python script/plot_logs.py output/omega/frequencies.txt --no-legends -g 1 -o mode-omega.png python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends -o mode-kappa.png python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends --swap-axes -o mode-kappa-t.png In contrast to the heterogeneous square periodic cell, a homogeneous square periodic cell (the region Y2 is empty):: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_1m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega-h python script/plot_logs.py output/omega-h/frequencies.txt --no-legends -g 1 -o mode-omega-h.png Use the Brillouin stepper:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves -n=60 --eigs-only --no-legends --stepper=brillouin python script/plot_logs.py output/frequencies.txt -g 0 --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-kappas.png python script/plot_logs.py output/frequencies.txt -g 1 --no-legends --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-omegas.png Additional arguments can be passed to the problem configuration's :func:`define()` function using the ``--define-kwargs`` option. In this file, only the mesh vertex separation parameter `mesh_eps` can be used:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only --define-kwargs="mesh_eps=1e-10" --save-regions """ from __future__ import absolute_import import os import sys sys.path.append('.') import gc from copy import copy from argparse import ArgumentParser, RawDescriptionHelpFormatter import numpy as nm import matplotlib.pyplot as plt from sfepy.base.base import import_file, output, Struct from sfepy.base.conf import dict_from_string, ProblemConf from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options from sfepy.base.log import Log from sfepy.discrete.fem import MeshIO from sfepy.mechanics.matcoefs import stiffness_from_youngpoisson as stiffness import sfepy.mechanics.matcoefs as mc from sfepy.mechanics.units import apply_unit_multipliers import sfepy.discrete.fem.periodic as per from sfepy.discrete.fem.meshio import convert_complex_output from sfepy.homogenization.utils import define_box_regions from sfepy.discrete import Problem from sfepy.mechanics.tensors import get_von_mises_stress from sfepy.solvers import Solver from sfepy.solvers.ts import get_print_info, TimeStepper from sfepy.linalg.utils import output_array_stats, max_diff_csr def apply_units(pars, unit_multipliers): new_pars = apply_unit_multipliers(pars, ['stress', 'one', 'density', 'stress', 'one' ,'density'], unit_multipliers) return new_pars def compute_von_mises(out, pb, state, extend=False, wmag=None, wdir=None): """ Calculate the von Mises stress. """ stress = pb.evaluate('ev_cauchy_stress.i.Omega(m.D, u)', mode='el_avg') vms = get_von_mises_stress(stress.squeeze()) vms.shape = (vms.shape[0], 1, 1, 1) out['von_mises_stress'] = Struct(name='output_data', mode='cell', data=vms) return out def define(filename_mesh, pars, approx_order, refinement_level, solver_conf, plane='strain', post_process=False, mesh_eps=1e-8): io = MeshIO.any_from_filename(filename_mesh) bbox = io.read_bounding_box() dim = bbox.shape[1] options = { 'absolute_mesh_path' : True, 'refinement_level' : refinement_level, 'allow_empty_regions' : True, 'post_process_hook' : 'compute_von_mises' if post_process else None, } fields = { 'displacement': ('complex', dim, 'Omega', approx_order), } young1, poisson1, density1, young2, poisson2, density2 = pars materials = { 'm' : ({ 'D' : {'Y1' : stiffness(dim, young=young1, poisson=poisson1, plane=plane), 'Y2' : stiffness(dim, young=young2, poisson=poisson2, plane=plane)}, 'density' : {'Y1' : density1, 'Y2' : density2}, },), 'wave' : 'get_wdir', } variables = { 'u' : ('unknown field', 'displacement', 0), 'v' : ('test field', 'displacement', 'u'), } regions = { 'Omega' : 'all', 'Y1': 'cells of group 1', 'Y2': 'cells of group 2', } regions.update(define_box_regions(dim, bbox[0], bbox[1], mesh_eps)) ebcs = { } if dim == 3: epbcs = { 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'}, 'match_x_plane'), 'periodic_y' : (['Near', 'Far'], {'u.all' : 'u.all'}, 'match_y_plane'), 'periodic_z' : (['Top', 'Bottom'], {'u.all' : 'u.all'}, 'match_z_plane'), } else: epbcs = { 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'}, 'match_y_line'), 'periodic_y' : (['Bottom', 'Top'], {'u.all' : 'u.all'}, 'match_x_line'), } per.set_accuracy(mesh_eps) functions = { 'match_x_plane' : (per.match_x_plane,), 'match_y_plane' : (per.match_y_plane,), 'match_z_plane' : (per.match_z_plane,), 'match_x_line' : (per.match_x_line,), 'match_y_line' : (per.match_y_line,), 'get_wdir' : (get_wdir,), } integrals = { 'i' : 2 * approx_order, } equations = { 'K' : 'dw_lin_elastic.i.Omega(m.D, v, u)', 'S' : 'dw_elastic_wave.i.Omega(m.D, wave.vec, v, u)', 'R' : """1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, u, v) - 1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, v, u)""", 'M' : 'dw_volume_dot.i.Omega(m.density, v, u)', } solver_0 = solver_conf.copy() solver_0['name'] = 'eig' return locals() def get_wdir(ts, coors, mode=None, equations=None, term=None, problem=None, wdir=None, **kwargs): if mode == 'special': return {'vec' : wdir} def set_wave_dir(pb, wdir): materials = pb.get_materials() wave_mat = materials['wave'] wave_mat.set_extra_args(wdir=wdir) def save_materials(output_dir, pb, options): stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)', mode='el_avg', copy_materials=False, verbose=False) young, poisson = mc.youngpoisson_from_stiffness(stiffness, plane=options.plane) density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)', mode='el_avg', copy_materials=False, verbose=False) out = {} out['young'] = Struct(name='young', mode='cell', data=young[..., None, None]) out['poisson'] = Struct(name='poisson', mode='cell', data=poisson[..., None, None]) out['density'] = Struct(name='density', mode='cell', data=density) materials_filename = os.path.join(output_dir, 'materials.vtk') pb.save_state(materials_filename, out=out) def get_std_wave_fun(pb, options): stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)', mode='el_avg', copy_materials=False, verbose=False) young, poisson = mc.youngpoisson_from_stiffness(stiffness, plane=options.plane) density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)', mode='el_avg', copy_materials=False, verbose=False) lam, mu = mc.lame_from_youngpoisson(young, poisson, plane=options.plane) alam = nm.average(lam) amu = nm.average(mu) adensity = nm.average(density) cp = nm.sqrt((alam + 2.0 * amu) / adensity) cs = nm.sqrt(amu / adensity) output('average p-wave speed:', cp) output('average shear wave speed:', cs) log_names = [r'$\omega_p$', r'$\omega_s$'] log_plot_kwargs = [{'ls' : '--', 'color' : 'k'}, {'ls' : '--', 'color' : 'gray'}] if options.mode == 'omega': fun = lambda wmag, wdir: (cp * wmag, cs * wmag) else: fun = lambda wmag, wdir: (wmag / cp, wmag / cs) return fun, log_names, log_plot_kwargs def get_stepper(rng, pb, options): if options.stepper == 'linear': stepper = TimeStepper(rng[0], rng[1], dt=None, n_step=rng[2]) return stepper bbox = pb.domain.mesh.get_bounding_box() bzone = 2.0 * nm.pi / (bbox[1] - bbox[0]) num = rng[2] // 3 class BrillouinStepper(Struct): """ Step over 1. Brillouin zone in xy plane. """ def __init__(self, t0, t1, dt=None, n_step=None, step=None, **kwargs): Struct.__init__(self, t0=t0, t1=t1, dt=dt, n_step=n_step, step=step) self.n_digit, self.format, self.suffix = get_print_info(self.n_step) def __iter__(self): ts = TimeStepper(0, bzone[0], dt=None, n_step=num) for ii, val in ts: yield ii, val, nm.array([1.0, 0.0]) if ii == (num-2): break ts = TimeStepper(0, bzone[1], dt=None, n_step=num) for ii, k1 in ts: wdir = nm.array([bzone[0], k1]) val = nm.linalg.norm(wdir) wdir = wdir / val yield num + ii, val, wdir if ii == (num-2): break wdir = nm.array([bzone[0], bzone[1]]) val = nm.linalg.norm(wdir) wdir = wdir / val ts = TimeStepper(0, 1, dt=None, n_step=num) for ii, _ in ts: yield 2 * num + ii, val * (1.0 - float(ii)/(num-1)), wdir stepper = BrillouinStepper(0, 1, n_step=rng[2]) return stepper def save_eigenvectors(filename, svecs, wmag, wdir, pb): if svecs is None: return variables = pb.get_variables() # Make full eigenvectors (add DOFs fixed by boundary conditions). vecs = nm.empty((variables.di.ptr[-1], svecs.shape[1]), dtype=svecs.dtype) for ii in range(svecs.shape[1]): vecs[:, ii] = variables.make_full_vec(svecs[:, ii]) # Save the eigenvectors. out = {} state = pb.create_state() pp_name = pb.conf.options.get('post_process_hook') pp = getattr(pb.conf.funmod, pp_name if pp_name is not None else '', lambda out, *args, **kwargs: out) for ii in range(svecs.shape[1]): state.set_full(vecs[:, ii]) aux = state.create_output_dict() aux2 = {} pp(aux2, pb, state, wmag=wmag, wdir=wdir) aux.update(convert_complex_output(aux2)) out.update({key + '%03d' % ii : aux[key] for key in aux}) pb.save_state(filename, out=out) def assemble_matrices(define, mod, pars, set_wave_dir, options, wdir=None): """ Assemble the blocks of dispersion eigenvalue problem matrices. """ define_dict = define(filename_mesh=options.mesh_filename, pars=pars, approx_order=options.order, refinement_level=options.refine, solver_conf=options.solver_conf, plane=options.plane, post_process=options.post_process, **options.define_kwargs) conf = ProblemConf.from_dict(define_dict, mod) pb = Problem.from_conf(conf) pb.dispersion_options = options pb.set_output_dir(options.output_dir) dim = pb.domain.shape.dim # Set the normalized wave vector direction to the material(s). if wdir is None: wdir = nm.asarray(options.wave_dir[:dim], dtype=nm.float64) wdir = wdir / nm.linalg.norm(wdir) set_wave_dir(pb, wdir) bbox = pb.domain.mesh.get_bounding_box() size = (bbox[1] - bbox[0]).max() scaling0 = apply_unit_multipliers([1.0], ['length'], options.unit_multipliers)[0] scaling = scaling0 if options.mesh_size is not None: scaling *= options.mesh_size / size output('scaling factor of periodic cell mesh coordinates:', scaling) output('new mesh size with applied unit multipliers:', scaling * size) pb.domain.mesh.coors[:] *= scaling pb.set_mesh_coors(pb.domain.mesh.coors, update_fields=True) bzone = 2.0 * nm.pi / (scaling * size) output('1. Brillouin zone size:', bzone * scaling0) output('1. Brillouin zone size with applied unit multipliers:', bzone) pb.time_update() pb.update_materials() # Assemble the matrices. mtxs = {} for key, eq in pb.equations.iteritems(): mtxs[key] = mtx = pb.mtx_a.copy() mtx = eq.evaluate(mode='weak', dw_mode='matrix', asm_obj=mtx) mtx.eliminate_zeros() output_array_stats(mtx.data, 'nonzeros in %s' % key) output('symmetry checks:') output('%s - %s^T:' % (key, key),	max_diff_csr(mtx, mtx.T)	sfepy.linalg.utils.max_diff_csr
#!/usr/bin/env python """ Dispersion analysis of a heterogeneous finite scale periodic cell. The periodic cell mesh has to contain two subdomains Y1 (with the cell ids 1), Y2 (with the cell ids 2), so that different material properties can be defined in each of the subdomains (see ``--pars`` option). The command line parameters can be given in any consistent unit set, for example the basic SI units. The ``--unit-multipliers`` option can be used to rescale the input units to ones more suitable to the simulation, for example to prevent having different matrix blocks with large differences of matrix entries magnitudes. The results are then in the rescaled units. Usage Examples -------------- Default material parameters, a square periodic cell with a spherical inclusion, logs also standard pressure dilatation and shear waves, no eigenvectors:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only As above, with custom eigenvalue solver parameters, and different number of eigenvalues, mesh size and units used in the calculation:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --solver-conf="kind='eig.scipy', method='eigsh', tol=1e-10, maxiter=1000, which='LM', sigma=0" --log-std-waves -n 5 --range=0,640,101 --mode=omega --unit-multipliers=1e-6,1e-2,1e-3 --mesh-size=1e-2 --eigs-only Default material parameters, a square periodic cell with a square inclusion, and a very small mesh to allow comparing the omega and kappa modes (full matrix solver required!):: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.qevp', method='companion', mode='inverted', solver={kind='eig.scipy', method='eig'}" --log-std-waves -n 500 --range=0,4000000,1001 --mesh-size=1e-2 --mode=kappa --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/kappa View/compare the resulting logs:: python script/plot_logs.py output/omega/frequencies.txt --no-legends -g 1 -o mode-omega.png python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends -o mode-kappa.png python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends --swap-axes -o mode-kappa-t.png In contrast to the heterogeneous square periodic cell, a homogeneous square periodic cell (the region Y2 is empty):: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_1m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega-h python script/plot_logs.py output/omega-h/frequencies.txt --no-legends -g 1 -o mode-omega-h.png Use the Brillouin stepper:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves -n=60 --eigs-only --no-legends --stepper=brillouin python script/plot_logs.py output/frequencies.txt -g 0 --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-kappas.png python script/plot_logs.py output/frequencies.txt -g 1 --no-legends --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-omegas.png Additional arguments can be passed to the problem configuration's :func:`define()` function using the ``--define-kwargs`` option. In this file, only the mesh vertex separation parameter `mesh_eps` can be used:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only --define-kwargs="mesh_eps=1e-10" --save-regions """ from __future__ import absolute_import import os import sys sys.path.append('.') import gc from copy import copy from argparse import ArgumentParser, RawDescriptionHelpFormatter import numpy as nm import matplotlib.pyplot as plt from sfepy.base.base import import_file, output, Struct from sfepy.base.conf import dict_from_string, ProblemConf from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options from sfepy.base.log import Log from sfepy.discrete.fem import MeshIO from sfepy.mechanics.matcoefs import stiffness_from_youngpoisson as stiffness import sfepy.mechanics.matcoefs as mc from sfepy.mechanics.units import apply_unit_multipliers import sfepy.discrete.fem.periodic as per from sfepy.discrete.fem.meshio import convert_complex_output from sfepy.homogenization.utils import define_box_regions from sfepy.discrete import Problem from sfepy.mechanics.tensors import get_von_mises_stress from sfepy.solvers import Solver from sfepy.solvers.ts import get_print_info, TimeStepper from sfepy.linalg.utils import output_array_stats, max_diff_csr def apply_units(pars, unit_multipliers): new_pars = apply_unit_multipliers(pars, ['stress', 'one', 'density', 'stress', 'one' ,'density'], unit_multipliers) return new_pars def compute_von_mises(out, pb, state, extend=False, wmag=None, wdir=None): """ Calculate the von Mises stress. """ stress = pb.evaluate('ev_cauchy_stress.i.Omega(m.D, u)', mode='el_avg') vms = get_von_mises_stress(stress.squeeze()) vms.shape = (vms.shape[0], 1, 1, 1) out['von_mises_stress'] = Struct(name='output_data', mode='cell', data=vms) return out def define(filename_mesh, pars, approx_order, refinement_level, solver_conf, plane='strain', post_process=False, mesh_eps=1e-8): io = MeshIO.any_from_filename(filename_mesh) bbox = io.read_bounding_box() dim = bbox.shape[1] options = { 'absolute_mesh_path' : True, 'refinement_level' : refinement_level, 'allow_empty_regions' : True, 'post_process_hook' : 'compute_von_mises' if post_process else None, } fields = { 'displacement': ('complex', dim, 'Omega', approx_order), } young1, poisson1, density1, young2, poisson2, density2 = pars materials = { 'm' : ({ 'D' : {'Y1' : stiffness(dim, young=young1, poisson=poisson1, plane=plane), 'Y2' : stiffness(dim, young=young2, poisson=poisson2, plane=plane)}, 'density' : {'Y1' : density1, 'Y2' : density2}, },), 'wave' : 'get_wdir', } variables = { 'u' : ('unknown field', 'displacement', 0), 'v' : ('test field', 'displacement', 'u'), } regions = { 'Omega' : 'all', 'Y1': 'cells of group 1', 'Y2': 'cells of group 2', } regions.update(define_box_regions(dim, bbox[0], bbox[1], mesh_eps)) ebcs = { } if dim == 3: epbcs = { 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'}, 'match_x_plane'), 'periodic_y' : (['Near', 'Far'], {'u.all' : 'u.all'}, 'match_y_plane'), 'periodic_z' : (['Top', 'Bottom'], {'u.all' : 'u.all'}, 'match_z_plane'), } else: epbcs = { 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'}, 'match_y_line'), 'periodic_y' : (['Bottom', 'Top'], {'u.all' : 'u.all'}, 'match_x_line'), } per.set_accuracy(mesh_eps) functions = { 'match_x_plane' : (per.match_x_plane,), 'match_y_plane' : (per.match_y_plane,), 'match_z_plane' : (per.match_z_plane,), 'match_x_line' : (per.match_x_line,), 'match_y_line' : (per.match_y_line,), 'get_wdir' : (get_wdir,), } integrals = { 'i' : 2 * approx_order, } equations = { 'K' : 'dw_lin_elastic.i.Omega(m.D, v, u)', 'S' : 'dw_elastic_wave.i.Omega(m.D, wave.vec, v, u)', 'R' : """1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, u, v) - 1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, v, u)""", 'M' : 'dw_volume_dot.i.Omega(m.density, v, u)', } solver_0 = solver_conf.copy() solver_0['name'] = 'eig' return locals() def get_wdir(ts, coors, mode=None, equations=None, term=None, problem=None, wdir=None, **kwargs): if mode == 'special': return {'vec' : wdir} def set_wave_dir(pb, wdir): materials = pb.get_materials() wave_mat = materials['wave'] wave_mat.set_extra_args(wdir=wdir) def save_materials(output_dir, pb, options): stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)', mode='el_avg', copy_materials=False, verbose=False) young, poisson = mc.youngpoisson_from_stiffness(stiffness, plane=options.plane) density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)', mode='el_avg', copy_materials=False, verbose=False) out = {} out['young'] = Struct(name='young', mode='cell', data=young[..., None, None]) out['poisson'] = Struct(name='poisson', mode='cell', data=poisson[..., None, None]) out['density'] = Struct(name='density', mode='cell', data=density) materials_filename = os.path.join(output_dir, 'materials.vtk') pb.save_state(materials_filename, out=out) def get_std_wave_fun(pb, options): stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)', mode='el_avg', copy_materials=False, verbose=False) young, poisson = mc.youngpoisson_from_stiffness(stiffness, plane=options.plane) density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)', mode='el_avg', copy_materials=False, verbose=False) lam, mu = mc.lame_from_youngpoisson(young, poisson, plane=options.plane) alam = nm.average(lam) amu = nm.average(mu) adensity = nm.average(density) cp = nm.sqrt((alam + 2.0 * amu) / adensity) cs = nm.sqrt(amu / adensity) output('average p-wave speed:', cp) output('average shear wave speed:', cs) log_names = [r'$\omega_p$', r'$\omega_s$'] log_plot_kwargs = [{'ls' : '--', 'color' : 'k'}, {'ls' : '--', 'color' : 'gray'}] if options.mode == 'omega': fun = lambda wmag, wdir: (cp * wmag, cs * wmag) else: fun = lambda wmag, wdir: (wmag / cp, wmag / cs) return fun, log_names, log_plot_kwargs def get_stepper(rng, pb, options): if options.stepper == 'linear': stepper = TimeStepper(rng[0], rng[1], dt=None, n_step=rng[2]) return stepper bbox = pb.domain.mesh.get_bounding_box() bzone = 2.0 * nm.pi / (bbox[1] - bbox[0]) num = rng[2] // 3 class BrillouinStepper(Struct): """ Step over 1. Brillouin zone in xy plane. """ def __init__(self, t0, t1, dt=None, n_step=None, step=None, **kwargs): Struct.__init__(self, t0=t0, t1=t1, dt=dt, n_step=n_step, step=step) self.n_digit, self.format, self.suffix = get_print_info(self.n_step) def __iter__(self): ts = TimeStepper(0, bzone[0], dt=None, n_step=num) for ii, val in ts: yield ii, val, nm.array([1.0, 0.0]) if ii == (num-2): break ts = TimeStepper(0, bzone[1], dt=None, n_step=num) for ii, k1 in ts: wdir = nm.array([bzone[0], k1]) val = nm.linalg.norm(wdir) wdir = wdir / val yield num + ii, val, wdir if ii == (num-2): break wdir = nm.array([bzone[0], bzone[1]]) val = nm.linalg.norm(wdir) wdir = wdir / val ts = TimeStepper(0, 1, dt=None, n_step=num) for ii, _ in ts: yield 2 * num + ii, val * (1.0 - float(ii)/(num-1)), wdir stepper = BrillouinStepper(0, 1, n_step=rng[2]) return stepper def save_eigenvectors(filename, svecs, wmag, wdir, pb): if svecs is None: return variables = pb.get_variables() # Make full eigenvectors (add DOFs fixed by boundary conditions). vecs = nm.empty((variables.di.ptr[-1], svecs.shape[1]), dtype=svecs.dtype) for ii in range(svecs.shape[1]): vecs[:, ii] = variables.make_full_vec(svecs[:, ii]) # Save the eigenvectors. out = {} state = pb.create_state() pp_name = pb.conf.options.get('post_process_hook') pp = getattr(pb.conf.funmod, pp_name if pp_name is not None else '', lambda out, *args, **kwargs: out) for ii in range(svecs.shape[1]): state.set_full(vecs[:, ii]) aux = state.create_output_dict() aux2 = {} pp(aux2, pb, state, wmag=wmag, wdir=wdir) aux.update(convert_complex_output(aux2)) out.update({key + '%03d' % ii : aux[key] for key in aux}) pb.save_state(filename, out=out) def assemble_matrices(define, mod, pars, set_wave_dir, options, wdir=None): """ Assemble the blocks of dispersion eigenvalue problem matrices. """ define_dict = define(filename_mesh=options.mesh_filename, pars=pars, approx_order=options.order, refinement_level=options.refine, solver_conf=options.solver_conf, plane=options.plane, post_process=options.post_process, **options.define_kwargs) conf = ProblemConf.from_dict(define_dict, mod) pb = Problem.from_conf(conf) pb.dispersion_options = options pb.set_output_dir(options.output_dir) dim = pb.domain.shape.dim # Set the normalized wave vector direction to the material(s). if wdir is None: wdir = nm.asarray(options.wave_dir[:dim], dtype=nm.float64) wdir = wdir / nm.linalg.norm(wdir) set_wave_dir(pb, wdir) bbox = pb.domain.mesh.get_bounding_box() size = (bbox[1] - bbox[0]).max() scaling0 = apply_unit_multipliers([1.0], ['length'], options.unit_multipliers)[0] scaling = scaling0 if options.mesh_size is not None: scaling *= options.mesh_size / size output('scaling factor of periodic cell mesh coordinates:', scaling) output('new mesh size with applied unit multipliers:', scaling * size) pb.domain.mesh.coors[:] *= scaling pb.set_mesh_coors(pb.domain.mesh.coors, update_fields=True) bzone = 2.0 * nm.pi / (scaling * size) output('1. Brillouin zone size:', bzone * scaling0) output('1. Brillouin zone size with applied unit multipliers:', bzone) pb.time_update() pb.update_materials() # Assemble the matrices. mtxs = {} for key, eq in pb.equations.iteritems(): mtxs[key] = mtx = pb.mtx_a.copy() mtx = eq.evaluate(mode='weak', dw_mode='matrix', asm_obj=mtx) mtx.eliminate_zeros() output_array_stats(mtx.data, 'nonzeros in %s' % key) output('symmetry checks:') output('%s - %s^T:' % (key, key), max_diff_csr(mtx, mtx.T)) output('%s - %s^H:' % (key, key),	max_diff_csr(mtx, mtx.H)	sfepy.linalg.utils.max_diff_csr
#!/usr/bin/env python """ Dispersion analysis of a heterogeneous finite scale periodic cell. The periodic cell mesh has to contain two subdomains Y1 (with the cell ids 1), Y2 (with the cell ids 2), so that different material properties can be defined in each of the subdomains (see ``--pars`` option). The command line parameters can be given in any consistent unit set, for example the basic SI units. The ``--unit-multipliers`` option can be used to rescale the input units to ones more suitable to the simulation, for example to prevent having different matrix blocks with large differences of matrix entries magnitudes. The results are then in the rescaled units. Usage Examples -------------- Default material parameters, a square periodic cell with a spherical inclusion, logs also standard pressure dilatation and shear waves, no eigenvectors:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only As above, with custom eigenvalue solver parameters, and different number of eigenvalues, mesh size and units used in the calculation:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --solver-conf="kind='eig.scipy', method='eigsh', tol=1e-10, maxiter=1000, which='LM', sigma=0" --log-std-waves -n 5 --range=0,640,101 --mode=omega --unit-multipliers=1e-6,1e-2,1e-3 --mesh-size=1e-2 --eigs-only Default material parameters, a square periodic cell with a square inclusion, and a very small mesh to allow comparing the omega and kappa modes (full matrix solver required!):: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.qevp', method='companion', mode='inverted', solver={kind='eig.scipy', method='eig'}" --log-std-waves -n 500 --range=0,4000000,1001 --mesh-size=1e-2 --mode=kappa --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/kappa View/compare the resulting logs:: python script/plot_logs.py output/omega/frequencies.txt --no-legends -g 1 -o mode-omega.png python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends -o mode-kappa.png python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends --swap-axes -o mode-kappa-t.png In contrast to the heterogeneous square periodic cell, a homogeneous square periodic cell (the region Y2 is empty):: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_1m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega-h python script/plot_logs.py output/omega-h/frequencies.txt --no-legends -g 1 -o mode-omega-h.png Use the Brillouin stepper:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves -n=60 --eigs-only --no-legends --stepper=brillouin python script/plot_logs.py output/frequencies.txt -g 0 --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-kappas.png python script/plot_logs.py output/frequencies.txt -g 1 --no-legends --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-omegas.png Additional arguments can be passed to the problem configuration's :func:`define()` function using the ``--define-kwargs`` option. In this file, only the mesh vertex separation parameter `mesh_eps` can be used:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only --define-kwargs="mesh_eps=1e-10" --save-regions """ from __future__ import absolute_import import os import sys sys.path.append('.') import gc from copy import copy from argparse import ArgumentParser, RawDescriptionHelpFormatter import numpy as nm import matplotlib.pyplot as plt from sfepy.base.base import import_file, output, Struct from sfepy.base.conf import dict_from_string, ProblemConf from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options from sfepy.base.log import Log from sfepy.discrete.fem import MeshIO from sfepy.mechanics.matcoefs import stiffness_from_youngpoisson as stiffness import sfepy.mechanics.matcoefs as mc from sfepy.mechanics.units import apply_unit_multipliers import sfepy.discrete.fem.periodic as per from sfepy.discrete.fem.meshio import convert_complex_output from sfepy.homogenization.utils import define_box_regions from sfepy.discrete import Problem from sfepy.mechanics.tensors import get_von_mises_stress from sfepy.solvers import Solver from sfepy.solvers.ts import get_print_info, TimeStepper from sfepy.linalg.utils import output_array_stats, max_diff_csr def apply_units(pars, unit_multipliers): new_pars = apply_unit_multipliers(pars, ['stress', 'one', 'density', 'stress', 'one' ,'density'], unit_multipliers) return new_pars def compute_von_mises(out, pb, state, extend=False, wmag=None, wdir=None): """ Calculate the von Mises stress. """ stress = pb.evaluate('ev_cauchy_stress.i.Omega(m.D, u)', mode='el_avg') vms = get_von_mises_stress(stress.squeeze()) vms.shape = (vms.shape[0], 1, 1, 1) out['von_mises_stress'] = Struct(name='output_data', mode='cell', data=vms) return out def define(filename_mesh, pars, approx_order, refinement_level, solver_conf, plane='strain', post_process=False, mesh_eps=1e-8): io = MeshIO.any_from_filename(filename_mesh) bbox = io.read_bounding_box() dim = bbox.shape[1] options = { 'absolute_mesh_path' : True, 'refinement_level' : refinement_level, 'allow_empty_regions' : True, 'post_process_hook' : 'compute_von_mises' if post_process else None, } fields = { 'displacement': ('complex', dim, 'Omega', approx_order), } young1, poisson1, density1, young2, poisson2, density2 = pars materials = { 'm' : ({ 'D' : {'Y1' : stiffness(dim, young=young1, poisson=poisson1, plane=plane), 'Y2' : stiffness(dim, young=young2, poisson=poisson2, plane=plane)}, 'density' : {'Y1' : density1, 'Y2' : density2}, },), 'wave' : 'get_wdir', } variables = { 'u' : ('unknown field', 'displacement', 0), 'v' : ('test field', 'displacement', 'u'), } regions = { 'Omega' : 'all', 'Y1': 'cells of group 1', 'Y2': 'cells of group 2', } regions.update(define_box_regions(dim, bbox[0], bbox[1], mesh_eps)) ebcs = { } if dim == 3: epbcs = { 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'}, 'match_x_plane'), 'periodic_y' : (['Near', 'Far'], {'u.all' : 'u.all'}, 'match_y_plane'), 'periodic_z' : (['Top', 'Bottom'], {'u.all' : 'u.all'}, 'match_z_plane'), } else: epbcs = { 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'}, 'match_y_line'), 'periodic_y' : (['Bottom', 'Top'], {'u.all' : 'u.all'}, 'match_x_line'), } per.set_accuracy(mesh_eps) functions = { 'match_x_plane' : (per.match_x_plane,), 'match_y_plane' : (per.match_y_plane,), 'match_z_plane' : (per.match_z_plane,), 'match_x_line' : (per.match_x_line,), 'match_y_line' : (per.match_y_line,), 'get_wdir' : (get_wdir,), } integrals = { 'i' : 2 * approx_order, } equations = { 'K' : 'dw_lin_elastic.i.Omega(m.D, v, u)', 'S' : 'dw_elastic_wave.i.Omega(m.D, wave.vec, v, u)', 'R' : """1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, u, v) - 1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, v, u)""", 'M' : 'dw_volume_dot.i.Omega(m.density, v, u)', } solver_0 = solver_conf.copy() solver_0['name'] = 'eig' return locals() def get_wdir(ts, coors, mode=None, equations=None, term=None, problem=None, wdir=None, **kwargs): if mode == 'special': return {'vec' : wdir} def set_wave_dir(pb, wdir): materials = pb.get_materials() wave_mat = materials['wave'] wave_mat.set_extra_args(wdir=wdir) def save_materials(output_dir, pb, options): stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)', mode='el_avg', copy_materials=False, verbose=False) young, poisson = mc.youngpoisson_from_stiffness(stiffness, plane=options.plane) density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)', mode='el_avg', copy_materials=False, verbose=False) out = {} out['young'] = Struct(name='young', mode='cell', data=young[..., None, None]) out['poisson'] = Struct(name='poisson', mode='cell', data=poisson[..., None, None]) out['density'] = Struct(name='density', mode='cell', data=density) materials_filename = os.path.join(output_dir, 'materials.vtk') pb.save_state(materials_filename, out=out) def get_std_wave_fun(pb, options): stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)', mode='el_avg', copy_materials=False, verbose=False) young, poisson = mc.youngpoisson_from_stiffness(stiffness, plane=options.plane) density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)', mode='el_avg', copy_materials=False, verbose=False) lam, mu = mc.lame_from_youngpoisson(young, poisson, plane=options.plane) alam = nm.average(lam) amu = nm.average(mu) adensity = nm.average(density) cp = nm.sqrt((alam + 2.0 * amu) / adensity) cs = nm.sqrt(amu / adensity) output('average p-wave speed:', cp) output('average shear wave speed:', cs) log_names = [r'$\omega_p$', r'$\omega_s$'] log_plot_kwargs = [{'ls' : '--', 'color' : 'k'}, {'ls' : '--', 'color' : 'gray'}] if options.mode == 'omega': fun = lambda wmag, wdir: (cp * wmag, cs * wmag) else: fun = lambda wmag, wdir: (wmag / cp, wmag / cs) return fun, log_names, log_plot_kwargs def get_stepper(rng, pb, options): if options.stepper == 'linear': stepper = TimeStepper(rng[0], rng[1], dt=None, n_step=rng[2]) return stepper bbox = pb.domain.mesh.get_bounding_box() bzone = 2.0 * nm.pi / (bbox[1] - bbox[0]) num = rng[2] // 3 class BrillouinStepper(Struct): """ Step over 1. Brillouin zone in xy plane. """ def __init__(self, t0, t1, dt=None, n_step=None, step=None, **kwargs): Struct.__init__(self, t0=t0, t1=t1, dt=dt, n_step=n_step, step=step) self.n_digit, self.format, self.suffix = get_print_info(self.n_step) def __iter__(self): ts = TimeStepper(0, bzone[0], dt=None, n_step=num) for ii, val in ts: yield ii, val, nm.array([1.0, 0.0]) if ii == (num-2): break ts = TimeStepper(0, bzone[1], dt=None, n_step=num) for ii, k1 in ts: wdir = nm.array([bzone[0], k1]) val = nm.linalg.norm(wdir) wdir = wdir / val yield num + ii, val, wdir if ii == (num-2): break wdir = nm.array([bzone[0], bzone[1]]) val = nm.linalg.norm(wdir) wdir = wdir / val ts = TimeStepper(0, 1, dt=None, n_step=num) for ii, _ in ts: yield 2 * num + ii, val * (1.0 - float(ii)/(num-1)), wdir stepper = BrillouinStepper(0, 1, n_step=rng[2]) return stepper def save_eigenvectors(filename, svecs, wmag, wdir, pb): if svecs is None: return variables = pb.get_variables() # Make full eigenvectors (add DOFs fixed by boundary conditions). vecs = nm.empty((variables.di.ptr[-1], svecs.shape[1]), dtype=svecs.dtype) for ii in range(svecs.shape[1]): vecs[:, ii] = variables.make_full_vec(svecs[:, ii]) # Save the eigenvectors. out = {} state = pb.create_state() pp_name = pb.conf.options.get('post_process_hook') pp = getattr(pb.conf.funmod, pp_name if pp_name is not None else '', lambda out, *args, **kwargs: out) for ii in range(svecs.shape[1]): state.set_full(vecs[:, ii]) aux = state.create_output_dict() aux2 = {} pp(aux2, pb, state, wmag=wmag, wdir=wdir) aux.update(convert_complex_output(aux2)) out.update({key + '%03d' % ii : aux[key] for key in aux}) pb.save_state(filename, out=out) def assemble_matrices(define, mod, pars, set_wave_dir, options, wdir=None): """ Assemble the blocks of dispersion eigenvalue problem matrices. """ define_dict = define(filename_mesh=options.mesh_filename, pars=pars, approx_order=options.order, refinement_level=options.refine, solver_conf=options.solver_conf, plane=options.plane, post_process=options.post_process, **options.define_kwargs) conf = ProblemConf.from_dict(define_dict, mod) pb = Problem.from_conf(conf) pb.dispersion_options = options pb.set_output_dir(options.output_dir) dim = pb.domain.shape.dim # Set the normalized wave vector direction to the material(s). if wdir is None: wdir = nm.asarray(options.wave_dir[:dim], dtype=nm.float64) wdir = wdir / nm.linalg.norm(wdir) set_wave_dir(pb, wdir) bbox = pb.domain.mesh.get_bounding_box() size = (bbox[1] - bbox[0]).max() scaling0 = apply_unit_multipliers([1.0], ['length'], options.unit_multipliers)[0] scaling = scaling0 if options.mesh_size is not None: scaling *= options.mesh_size / size output('scaling factor of periodic cell mesh coordinates:', scaling) output('new mesh size with applied unit multipliers:', scaling * size) pb.domain.mesh.coors[:] *= scaling pb.set_mesh_coors(pb.domain.mesh.coors, update_fields=True) bzone = 2.0 * nm.pi / (scaling * size) output('1. Brillouin zone size:', bzone * scaling0) output('1. Brillouin zone size with applied unit multipliers:', bzone) pb.time_update() pb.update_materials() # Assemble the matrices. mtxs = {} for key, eq in pb.equations.iteritems(): mtxs[key] = mtx = pb.mtx_a.copy() mtx = eq.evaluate(mode='weak', dw_mode='matrix', asm_obj=mtx) mtx.eliminate_zeros() output_array_stats(mtx.data, 'nonzeros in %s' % key) output('symmetry checks:') output('%s - %s^T:' % (key, key), max_diff_csr(mtx, mtx.T)) output('%s - %s^H:' % (key, key), max_diff_csr(mtx, mtx.H)) return pb, wdir, bzone, mtxs def setup_n_eigs(options, pb, mtxs): """ Setup the numbers of eigenvalues based on options and numbers of DOFs. """ solver_n_eigs = n_eigs = options.n_eigs n_dof = mtxs['K'].shape[0] if options.mode == 'omega': if options.n_eigs > n_dof: n_eigs = n_dof solver_n_eigs = None else: if options.n_eigs > 2 * n_dof: n_eigs = 2 * n_dof solver_n_eigs = None return solver_n_eigs, n_eigs def build_evp_matrices(mtxs, val, mode, pb): """ Build the matrices of the dispersion eigenvalue problem. """ if mode == 'omega': mtx_a = mtxs['K'] + val**2 * mtxs['S'] + val * mtxs['R'] output('A - A^H:',	max_diff_csr(mtx_a, mtx_a.H)	sfepy.linalg.utils.max_diff_csr
#!/usr/bin/env python """ Dispersion analysis of a heterogeneous finite scale periodic cell. The periodic cell mesh has to contain two subdomains Y1 (with the cell ids 1), Y2 (with the cell ids 2), so that different material properties can be defined in each of the subdomains (see ``--pars`` option). The command line parameters can be given in any consistent unit set, for example the basic SI units. The ``--unit-multipliers`` option can be used to rescale the input units to ones more suitable to the simulation, for example to prevent having different matrix blocks with large differences of matrix entries magnitudes. The results are then in the rescaled units. Usage Examples -------------- Default material parameters, a square periodic cell with a spherical inclusion, logs also standard pressure dilatation and shear waves, no eigenvectors:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only As above, with custom eigenvalue solver parameters, and different number of eigenvalues, mesh size and units used in the calculation:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --solver-conf="kind='eig.scipy', method='eigsh', tol=1e-10, maxiter=1000, which='LM', sigma=0" --log-std-waves -n 5 --range=0,640,101 --mode=omega --unit-multipliers=1e-6,1e-2,1e-3 --mesh-size=1e-2 --eigs-only Default material parameters, a square periodic cell with a square inclusion, and a very small mesh to allow comparing the omega and kappa modes (full matrix solver required!):: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.qevp', method='companion', mode='inverted', solver={kind='eig.scipy', method='eig'}" --log-std-waves -n 500 --range=0,4000000,1001 --mesh-size=1e-2 --mode=kappa --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/kappa View/compare the resulting logs:: python script/plot_logs.py output/omega/frequencies.txt --no-legends -g 1 -o mode-omega.png python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends -o mode-kappa.png python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends --swap-axes -o mode-kappa-t.png In contrast to the heterogeneous square periodic cell, a homogeneous square periodic cell (the region Y2 is empty):: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_1m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega-h python script/plot_logs.py output/omega-h/frequencies.txt --no-legends -g 1 -o mode-omega-h.png Use the Brillouin stepper:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves -n=60 --eigs-only --no-legends --stepper=brillouin python script/plot_logs.py output/frequencies.txt -g 0 --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-kappas.png python script/plot_logs.py output/frequencies.txt -g 1 --no-legends --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-omegas.png Additional arguments can be passed to the problem configuration's :func:`define()` function using the ``--define-kwargs`` option. In this file, only the mesh vertex separation parameter `mesh_eps` can be used:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only --define-kwargs="mesh_eps=1e-10" --save-regions """ from __future__ import absolute_import import os import sys sys.path.append('.') import gc from copy import copy from argparse import ArgumentParser, RawDescriptionHelpFormatter import numpy as nm import matplotlib.pyplot as plt from sfepy.base.base import import_file, output, Struct from sfepy.base.conf import dict_from_string, ProblemConf from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options from sfepy.base.log import Log from sfepy.discrete.fem import MeshIO from sfepy.mechanics.matcoefs import stiffness_from_youngpoisson as stiffness import sfepy.mechanics.matcoefs as mc from sfepy.mechanics.units import apply_unit_multipliers import sfepy.discrete.fem.periodic as per from sfepy.discrete.fem.meshio import convert_complex_output from sfepy.homogenization.utils import define_box_regions from sfepy.discrete import Problem from sfepy.mechanics.tensors import get_von_mises_stress from sfepy.solvers import Solver from sfepy.solvers.ts import get_print_info, TimeStepper from sfepy.linalg.utils import output_array_stats, max_diff_csr def apply_units(pars, unit_multipliers): new_pars = apply_unit_multipliers(pars, ['stress', 'one', 'density', 'stress', 'one' ,'density'], unit_multipliers) return new_pars def compute_von_mises(out, pb, state, extend=False, wmag=None, wdir=None): """ Calculate the von Mises stress. """ stress = pb.evaluate('ev_cauchy_stress.i.Omega(m.D, u)', mode='el_avg') vms = get_von_mises_stress(stress.squeeze()) vms.shape = (vms.shape[0], 1, 1, 1) out['von_mises_stress'] = Struct(name='output_data', mode='cell', data=vms) return out def define(filename_mesh, pars, approx_order, refinement_level, solver_conf, plane='strain', post_process=False, mesh_eps=1e-8): io = MeshIO.any_from_filename(filename_mesh) bbox = io.read_bounding_box() dim = bbox.shape[1] options = { 'absolute_mesh_path' : True, 'refinement_level' : refinement_level, 'allow_empty_regions' : True, 'post_process_hook' : 'compute_von_mises' if post_process else None, } fields = { 'displacement': ('complex', dim, 'Omega', approx_order), } young1, poisson1, density1, young2, poisson2, density2 = pars materials = { 'm' : ({ 'D' : {'Y1' : stiffness(dim, young=young1, poisson=poisson1, plane=plane), 'Y2' : stiffness(dim, young=young2, poisson=poisson2, plane=plane)}, 'density' : {'Y1' : density1, 'Y2' : density2}, },), 'wave' : 'get_wdir', } variables = { 'u' : ('unknown field', 'displacement', 0), 'v' : ('test field', 'displacement', 'u'), } regions = { 'Omega' : 'all', 'Y1': 'cells of group 1', 'Y2': 'cells of group 2', } regions.update(define_box_regions(dim, bbox[0], bbox[1], mesh_eps)) ebcs = { } if dim == 3: epbcs = { 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'}, 'match_x_plane'), 'periodic_y' : (['Near', 'Far'], {'u.all' : 'u.all'}, 'match_y_plane'), 'periodic_z' : (['Top', 'Bottom'], {'u.all' : 'u.all'}, 'match_z_plane'), } else: epbcs = { 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'}, 'match_y_line'), 'periodic_y' : (['Bottom', 'Top'], {'u.all' : 'u.all'}, 'match_x_line'), } per.set_accuracy(mesh_eps) functions = { 'match_x_plane' : (per.match_x_plane,), 'match_y_plane' : (per.match_y_plane,), 'match_z_plane' : (per.match_z_plane,), 'match_x_line' : (per.match_x_line,), 'match_y_line' : (per.match_y_line,), 'get_wdir' : (get_wdir,), } integrals = { 'i' : 2 * approx_order, } equations = { 'K' : 'dw_lin_elastic.i.Omega(m.D, v, u)', 'S' : 'dw_elastic_wave.i.Omega(m.D, wave.vec, v, u)', 'R' : """1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, u, v) - 1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, v, u)""", 'M' : 'dw_volume_dot.i.Omega(m.density, v, u)', } solver_0 = solver_conf.copy() solver_0['name'] = 'eig' return locals() def get_wdir(ts, coors, mode=None, equations=None, term=None, problem=None, wdir=None, **kwargs): if mode == 'special': return {'vec' : wdir} def set_wave_dir(pb, wdir): materials = pb.get_materials() wave_mat = materials['wave'] wave_mat.set_extra_args(wdir=wdir) def save_materials(output_dir, pb, options): stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)', mode='el_avg', copy_materials=False, verbose=False) young, poisson = mc.youngpoisson_from_stiffness(stiffness, plane=options.plane) density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)', mode='el_avg', copy_materials=False, verbose=False) out = {} out['young'] = Struct(name='young', mode='cell', data=young[..., None, None]) out['poisson'] = Struct(name='poisson', mode='cell', data=poisson[..., None, None]) out['density'] = Struct(name='density', mode='cell', data=density) materials_filename = os.path.join(output_dir, 'materials.vtk') pb.save_state(materials_filename, out=out) def get_std_wave_fun(pb, options): stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)', mode='el_avg', copy_materials=False, verbose=False) young, poisson = mc.youngpoisson_from_stiffness(stiffness, plane=options.plane) density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)', mode='el_avg', copy_materials=False, verbose=False) lam, mu = mc.lame_from_youngpoisson(young, poisson, plane=options.plane) alam = nm.average(lam) amu = nm.average(mu) adensity = nm.average(density) cp = nm.sqrt((alam + 2.0 * amu) / adensity) cs = nm.sqrt(amu / adensity) output('average p-wave speed:', cp) output('average shear wave speed:', cs) log_names = [r'$\omega_p$', r'$\omega_s$'] log_plot_kwargs = [{'ls' : '--', 'color' : 'k'}, {'ls' : '--', 'color' : 'gray'}] if options.mode == 'omega': fun = lambda wmag, wdir: (cp * wmag, cs * wmag) else: fun = lambda wmag, wdir: (wmag / cp, wmag / cs) return fun, log_names, log_plot_kwargs def get_stepper(rng, pb, options): if options.stepper == 'linear': stepper = TimeStepper(rng[0], rng[1], dt=None, n_step=rng[2]) return stepper bbox = pb.domain.mesh.get_bounding_box() bzone = 2.0 * nm.pi / (bbox[1] - bbox[0]) num = rng[2] // 3 class BrillouinStepper(Struct): """ Step over 1. Brillouin zone in xy plane. """ def __init__(self, t0, t1, dt=None, n_step=None, step=None, **kwargs): Struct.__init__(self, t0=t0, t1=t1, dt=dt, n_step=n_step, step=step) self.n_digit, self.format, self.suffix = get_print_info(self.n_step) def __iter__(self): ts = TimeStepper(0, bzone[0], dt=None, n_step=num) for ii, val in ts: yield ii, val, nm.array([1.0, 0.0]) if ii == (num-2): break ts = TimeStepper(0, bzone[1], dt=None, n_step=num) for ii, k1 in ts: wdir = nm.array([bzone[0], k1]) val = nm.linalg.norm(wdir) wdir = wdir / val yield num + ii, val, wdir if ii == (num-2): break wdir = nm.array([bzone[0], bzone[1]]) val = nm.linalg.norm(wdir) wdir = wdir / val ts = TimeStepper(0, 1, dt=None, n_step=num) for ii, _ in ts: yield 2 * num + ii, val * (1.0 - float(ii)/(num-1)), wdir stepper = BrillouinStepper(0, 1, n_step=rng[2]) return stepper def save_eigenvectors(filename, svecs, wmag, wdir, pb): if svecs is None: return variables = pb.get_variables() # Make full eigenvectors (add DOFs fixed by boundary conditions). vecs = nm.empty((variables.di.ptr[-1], svecs.shape[1]), dtype=svecs.dtype) for ii in range(svecs.shape[1]): vecs[:, ii] = variables.make_full_vec(svecs[:, ii]) # Save the eigenvectors. out = {} state = pb.create_state() pp_name = pb.conf.options.get('post_process_hook') pp = getattr(pb.conf.funmod, pp_name if pp_name is not None else '', lambda out, *args, **kwargs: out) for ii in range(svecs.shape[1]): state.set_full(vecs[:, ii]) aux = state.create_output_dict() aux2 = {} pp(aux2, pb, state, wmag=wmag, wdir=wdir) aux.update(convert_complex_output(aux2)) out.update({key + '%03d' % ii : aux[key] for key in aux}) pb.save_state(filename, out=out) def assemble_matrices(define, mod, pars, set_wave_dir, options, wdir=None): """ Assemble the blocks of dispersion eigenvalue problem matrices. """ define_dict = define(filename_mesh=options.mesh_filename, pars=pars, approx_order=options.order, refinement_level=options.refine, solver_conf=options.solver_conf, plane=options.plane, post_process=options.post_process, **options.define_kwargs) conf = ProblemConf.from_dict(define_dict, mod) pb = Problem.from_conf(conf) pb.dispersion_options = options pb.set_output_dir(options.output_dir) dim = pb.domain.shape.dim # Set the normalized wave vector direction to the material(s). if wdir is None: wdir = nm.asarray(options.wave_dir[:dim], dtype=nm.float64) wdir = wdir / nm.linalg.norm(wdir) set_wave_dir(pb, wdir) bbox = pb.domain.mesh.get_bounding_box() size = (bbox[1] - bbox[0]).max() scaling0 = apply_unit_multipliers([1.0], ['length'], options.unit_multipliers)[0] scaling = scaling0 if options.mesh_size is not None: scaling *= options.mesh_size / size output('scaling factor of periodic cell mesh coordinates:', scaling) output('new mesh size with applied unit multipliers:', scaling * size) pb.domain.mesh.coors[:] *= scaling pb.set_mesh_coors(pb.domain.mesh.coors, update_fields=True) bzone = 2.0 * nm.pi / (scaling * size) output('1. Brillouin zone size:', bzone * scaling0) output('1. Brillouin zone size with applied unit multipliers:', bzone) pb.time_update() pb.update_materials() # Assemble the matrices. mtxs = {} for key, eq in pb.equations.iteritems(): mtxs[key] = mtx = pb.mtx_a.copy() mtx = eq.evaluate(mode='weak', dw_mode='matrix', asm_obj=mtx) mtx.eliminate_zeros() output_array_stats(mtx.data, 'nonzeros in %s' % key) output('symmetry checks:') output('%s - %s^T:' % (key, key), max_diff_csr(mtx, mtx.T)) output('%s - %s^H:' % (key, key), max_diff_csr(mtx, mtx.H)) return pb, wdir, bzone, mtxs def setup_n_eigs(options, pb, mtxs): """ Setup the numbers of eigenvalues based on options and numbers of DOFs. """ solver_n_eigs = n_eigs = options.n_eigs n_dof = mtxs['K'].shape[0] if options.mode == 'omega': if options.n_eigs > n_dof: n_eigs = n_dof solver_n_eigs = None else: if options.n_eigs > 2 * n_dof: n_eigs = 2 * n_dof solver_n_eigs = None return solver_n_eigs, n_eigs def build_evp_matrices(mtxs, val, mode, pb): """ Build the matrices of the dispersion eigenvalue problem. """ if mode == 'omega': mtx_a = mtxs['K'] + val**2 * mtxs['S'] + val * mtxs['R'] output('A - A^H:', max_diff_csr(mtx_a, mtx_a.H)) evp_mtxs = (mtx_a, mtxs['M']) else: evp_mtxs = (mtxs['S'], mtxs['R'], mtxs['K'] - val**2 * mtxs['M']) return evp_mtxs def process_evp_results(eigs, svecs, val, wdir, bzone, pb, mtxs, options, std_wave_fun=None): """ Transform eigenvalues to either omegas or kappas, depending on `mode`. Transform eigenvectors, if available, depending on `mode`. Return also the values to log. """ if options.mode == 'omega': omegas = nm.sqrt(eigs) output('eigs, omegas:') for ii, om in enumerate(omegas): output('{:>3}. {: .10e}, {:.10e}'.format(ii, eigs[ii], om)) if options.stepper == 'linear': out = tuple(eigs) + tuple(omegas) else: out = tuple(val * wdir) + tuple(omegas) if std_wave_fun is not None: out = out + std_wave_fun(val, wdir) return omegas, svecs, out else: kappas = eigs.copy() rks = kappas.copy() # Mask modes far from 1. Brillouin zone. max_kappa = 1.2 * bzone kappas[kappas.real > max_kappa] = nm.nan # Mask non-physical modes. kappas[kappas.real < 0] = nm.nan kappas[nm.abs(kappas.imag) > 1e-10] = nm.nan out = tuple(kappas.real) output('raw kappas, masked real part:',) for ii, kr in enumerate(kappas.real): output('{:>3}. {: 23.5e}, {:.10e}'.format(ii, rks[ii], kr)) if svecs is not None: n_dof = mtxs['K'].shape[0] # Select only vectors corresponding to physical modes. ii = nm.isfinite(kappas.real) svecs = svecs[:n_dof, ii] if std_wave_fun is not None: out = out + tuple(ii if ii <= max_kappa else nm.nan for ii in std_wave_fun(val, wdir)) return kappas, svecs, out helps = { 'pars' : 'material parameters in Y1, Y2 subdomains in basic units' ' [default: %(default)s]', 'conf' : 'if given, an alternative problem description file with apply_units() and' ' define() functions [default: %(default)s]', 'define_kwargs' : 'additional keyword arguments passed to define()', 'mesh_size' : 'desired mesh size (max. of bounding box dimensions) in basic units' ' - the input periodic cell mesh is rescaled to this size' ' [default: %(default)s]', 'unit_multipliers' : 'basic unit multipliers (time, length, mass) [default: %(default)s]', 'plane' : 'for 2D problems, plane strain or stress hypothesis selection' ' [default: %(default)s]', 'wave_dir' : 'the wave vector direction (will be normalized)' ' [default: %(default)s]', 'mode' : 'solution mode: omega = solve a generalized EVP for omega,' ' kappa = solve a quadratic generalized EVP for kappa' ' [default: %(default)s]', 'stepper' : 'the range stepper. For "brillouin", only the number' ' of items from --range is used' ' [default: %(default)s]', 'range' : 'the wave vector magnitude / frequency range' ' (like numpy.linspace) depending on the mode option' ' [default: %(default)s]', 'order' : 'displacement field approximation order [default: %(default)s]', 'refine' : 'number of uniform mesh refinements [default: %(default)s]', 'n_eigs' : 'the number of eigenvalues to compute [default: %(default)s]', 'eigs_only' : 'compute only eigenvalues, not eigenvectors', 'post_process' : 'post-process eigenvectors', 'solver_conf' : 'eigenvalue problem solver configuration options' ' [default: %(default)s]', 'save_regions' : 'save defined regions into' ' <output_directory>/regions.vtk', 'save_materials' : 'save material parameters into' ' <output_directory>/materials.vtk', 'log_std_waves' : 'log also standard pressure dilatation and shear waves', 'no_legends' : 'do not show legends in the log plots', 'no_show' : 'do not show the log figure', 'silent' : 'do not print messages to screen', 'clear' : 'clear old solution files from output directory', 'output_dir' : 'output directory [default: %(default)s]', 'mesh_filename' : 'input periodic cell mesh file name [default: %(default)s]', } def main(): # Aluminium and epoxy. default_pars = '70e9,0.35,2.799e3, 3.8e9,0.27,1.142e3' default_solver_conf = ("kind='eig.scipy',method='eigsh',tol=1.0e-5," "maxiter=1000,which='LM',sigma=0.0") parser = ArgumentParser(description=__doc__, formatter_class=RawDescriptionHelpFormatter) parser.add_argument('--pars', metavar='young1,poisson1,density1' ',young2,poisson2,density2', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='pars', default=default_pars, help=helps['pars']) parser.add_argument('--conf', metavar='filename', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='conf', default=None, help=helps['conf']) parser.add_argument('--define-kwargs', metavar='dict-like', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='define_kwargs', default=None, help=helps['define_kwargs']) parser.add_argument('--mesh-size', type=float, metavar='float', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='mesh_size', default=None, help=helps['mesh_size']) parser.add_argument('--unit-multipliers', metavar='c_time,c_length,c_mass', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='unit_multipliers', default='1.0,1.0,1.0', help=helps['unit_multipliers']) parser.add_argument('--plane', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='plane', choices=['strain', 'stress'], default='strain', help=helps['plane']) parser.add_argument('--wave-dir', metavar='float,float[,float]', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='wave_dir', default='1.0,0.0,0.0', help=helps['wave_dir']) parser.add_argument('--mode', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='mode', choices=['omega', 'kappa'], default='omega', help=helps['mode']) parser.add_argument('--stepper', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='stepper', choices=['linear', 'brillouin'], default='linear', help=helps['stepper']) parser.add_argument('--range', metavar='start,stop,count', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='range', default='0,6.4,33', help=helps['range']) parser.add_argument('--order', metavar='int', type=int, action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='order', default=1, help=helps['order']) parser.add_argument('--refine', metavar='int', type=int, action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='refine', default=0, help=helps['refine']) parser.add_argument('-n', '--n-eigs', metavar='int', type=int, action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='n_eigs', default=6, help=helps['n_eigs']) group = parser.add_mutually_exclusive_group() group.add_argument('--eigs-only', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='eigs_only', default=False, help=helps['eigs_only']) group.add_argument('--post-process', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='post_process', default=False, help=helps['post_process']) parser.add_argument('--solver-conf', metavar='dict-like', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='solver_conf', default=default_solver_conf, help=helps['solver_conf']) parser.add_argument('--save-regions', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='save_regions', default=False, help=helps['save_regions']) parser.add_argument('--save-materials', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='save_materials', default=False, help=helps['save_materials']) parser.add_argument('--log-std-waves', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='log_std_waves', default=False, help=helps['log_std_waves']) parser.add_argument('--no-legends', action="https://huggingface.co/datasets/luna-code/sfepy/store_false", dest='show_legends', default=True, help=helps['no_legends']) parser.add_argument('--no-show', action="https://huggingface.co/datasets/luna-code/sfepy/store_false", dest='show', default=True, help=helps['no_show']) parser.add_argument('--silent', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='silent', default=False, help=helps['silent']) parser.add_argument('-c', '--clear', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='clear', default=False, help=helps['clear']) parser.add_argument('-o', '--output-dir', metavar='path', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='output_dir', default='output', help=helps['output_dir']) parser.add_argument('mesh_filename', default='', help=helps['mesh_filename']) options = parser.parse_args() output_dir = options.output_dir output.set_output(filename=os.path.join(output_dir,'output_log.txt'), combined=options.silent == False) if options.conf is not None: mod = import_file(options.conf) else: mod = sys.modules[__name__] apply_units = mod.apply_units define = mod.define set_wave_dir = mod.set_wave_dir setup_n_eigs = mod.setup_n_eigs build_evp_matrices = mod.build_evp_matrices save_materials = mod.save_materials get_std_wave_fun = mod.get_std_wave_fun get_stepper = mod.get_stepper process_evp_results = mod.process_evp_results options.pars = [float(ii) for ii in options.pars.split(',')] options.unit_multipliers = [float(ii) for ii in options.unit_multipliers.split(',')] options.wave_dir = [float(ii) for ii in options.wave_dir.split(',')] aux = options.range.split(',') options.range = [float(aux[0]), float(aux[1]), int(aux[2])] options.solver_conf = dict_from_string(options.solver_conf) options.define_kwargs = dict_from_string(options.define_kwargs) if options.clear: remove_files_patterns(output_dir, ['*.h5', '*.vtk', '*.txt'], ignores=['output_log.txt'], verbose=True) filename = os.path.join(output_dir, 'options.txt') ensure_path(filename) save_options(filename, [('options', vars(options))], quote_command_line=True) pars = apply_units(options.pars, options.unit_multipliers) output('material parameters with applied unit multipliers:') output(pars) if options.mode == 'omega': rng = copy(options.range) rng[:2] = apply_unit_multipliers(options.range[:2], ['wave_number', 'wave_number'], options.unit_multipliers) output('wave number range with applied unit multipliers:', rng) else: if options.stepper == 'brillouin': raise ValueError('Cannot use "brillouin" stepper in kappa mode!') rng = copy(options.range) rng[:2] = apply_unit_multipliers(options.range[:2], ['frequency', 'frequency'], options.unit_multipliers) output('frequency range with applied unit multipliers:', rng) pb, wdir, bzone, mtxs = assemble_matrices(define, mod, pars, set_wave_dir, options) dim = pb.domain.shape.dim if dim != 2: options.plane = 'strain' if options.save_regions: pb.save_regions_as_groups(os.path.join(output_dir, 'regions')) if options.save_materials: save_materials(output_dir, pb, options) conf = pb.solver_confs['eig'] eig_solver = Solver.any_from_conf(conf) n_eigs, options.n_eigs = setup_n_eigs(options, pb, mtxs) get_color = lambda ii: plt.cm.viridis((float(ii) / (options.n_eigs - 1))) plot_kwargs = [{'color' : get_color(ii), 'ls' : '', 'marker' : 'o'} for ii in range(options.n_eigs)] get_color_dim = lambda ii: plt.cm.viridis((float(ii) / (dim-1))) plot_kwargs_dim = [{'color' : get_color_dim(ii), 'ls' : '', 'marker' : 'o'} for ii in range(dim)] log_names = [] log_plot_kwargs = [] if options.log_std_waves: std_wave_fun, log_names, log_plot_kwargs = get_std_wave_fun( pb, options) else: std_wave_fun = None stepper = get_stepper(rng, pb, options) if options.mode == 'omega': eigenshapes_filename = os.path.join(output_dir, 'frequency-eigenshapes-%s.vtk' % stepper.suffix) if options.stepper == 'linear': log = Log([[r'$\lambda_{%d}$' % ii for ii in range(options.n_eigs)], [r'$\omega_{%d}$' % ii for ii in range(options.n_eigs)] + log_names], plot_kwargs=[plot_kwargs, plot_kwargs + log_plot_kwargs], formats=[['{:.5e}'] * options.n_eigs, ['{:.5e}'] * (options.n_eigs + len(log_names))], yscales=['linear', 'linear'], xlabels=[r'$\kappa$', r'$\kappa$'], ylabels=[r'eigenvalues $\lambda_i$', r'frequencies $\omega_i$'], show_legends=options.show_legends, is_plot=options.show, log_filename=os.path.join(output_dir, 'frequencies.txt'), aggregate=1000, sleep=0.1) else: log = Log([[r'$\kappa_{%d}$'% ii for ii in range(dim)], [r'$\omega_{%d}$' % ii for ii in range(options.n_eigs)] + log_names], plot_kwargs=[plot_kwargs_dim, plot_kwargs + log_plot_kwargs], formats=[['{:.5e}'] * dim, ['{:.5e}'] * (options.n_eigs + len(log_names))], yscales=['linear', 'linear'], xlabels=[r'', r''], ylabels=[r'wave vector $\kappa$', r'frequencies $\omega_i$'], show_legends=options.show_legends, is_plot=options.show, log_filename=os.path.join(output_dir, 'frequencies.txt'), aggregate=1000, sleep=0.1) for aux in stepper: if options.stepper == 'linear': iv, wmag = aux else: iv, wmag, wdir = aux	output('step %d: wave vector %s' % (iv, wmag * wdir))	sfepy.base.base.output
#!/usr/bin/env python """ Dispersion analysis of a heterogeneous finite scale periodic cell. The periodic cell mesh has to contain two subdomains Y1 (with the cell ids 1), Y2 (with the cell ids 2), so that different material properties can be defined in each of the subdomains (see ``--pars`` option). The command line parameters can be given in any consistent unit set, for example the basic SI units. The ``--unit-multipliers`` option can be used to rescale the input units to ones more suitable to the simulation, for example to prevent having different matrix blocks with large differences of matrix entries magnitudes. The results are then in the rescaled units. Usage Examples -------------- Default material parameters, a square periodic cell with a spherical inclusion, logs also standard pressure dilatation and shear waves, no eigenvectors:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only As above, with custom eigenvalue solver parameters, and different number of eigenvalues, mesh size and units used in the calculation:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --solver-conf="kind='eig.scipy', method='eigsh', tol=1e-10, maxiter=1000, which='LM', sigma=0" --log-std-waves -n 5 --range=0,640,101 --mode=omega --unit-multipliers=1e-6,1e-2,1e-3 --mesh-size=1e-2 --eigs-only Default material parameters, a square periodic cell with a square inclusion, and a very small mesh to allow comparing the omega and kappa modes (full matrix solver required!):: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.qevp', method='companion', mode='inverted', solver={kind='eig.scipy', method='eig'}" --log-std-waves -n 500 --range=0,4000000,1001 --mesh-size=1e-2 --mode=kappa --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/kappa View/compare the resulting logs:: python script/plot_logs.py output/omega/frequencies.txt --no-legends -g 1 -o mode-omega.png python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends -o mode-kappa.png python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends --swap-axes -o mode-kappa-t.png In contrast to the heterogeneous square periodic cell, a homogeneous square periodic cell (the region Y2 is empty):: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_1m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega-h python script/plot_logs.py output/omega-h/frequencies.txt --no-legends -g 1 -o mode-omega-h.png Use the Brillouin stepper:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves -n=60 --eigs-only --no-legends --stepper=brillouin python script/plot_logs.py output/frequencies.txt -g 0 --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-kappas.png python script/plot_logs.py output/frequencies.txt -g 1 --no-legends --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-omegas.png Additional arguments can be passed to the problem configuration's :func:`define()` function using the ``--define-kwargs`` option. In this file, only the mesh vertex separation parameter `mesh_eps` can be used:: python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only --define-kwargs="mesh_eps=1e-10" --save-regions """ from __future__ import absolute_import import os import sys sys.path.append('.') import gc from copy import copy from argparse import ArgumentParser, RawDescriptionHelpFormatter import numpy as nm import matplotlib.pyplot as plt from sfepy.base.base import import_file, output, Struct from sfepy.base.conf import dict_from_string, ProblemConf from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options from sfepy.base.log import Log from sfepy.discrete.fem import MeshIO from sfepy.mechanics.matcoefs import stiffness_from_youngpoisson as stiffness import sfepy.mechanics.matcoefs as mc from sfepy.mechanics.units import apply_unit_multipliers import sfepy.discrete.fem.periodic as per from sfepy.discrete.fem.meshio import convert_complex_output from sfepy.homogenization.utils import define_box_regions from sfepy.discrete import Problem from sfepy.mechanics.tensors import get_von_mises_stress from sfepy.solvers import Solver from sfepy.solvers.ts import get_print_info, TimeStepper from sfepy.linalg.utils import output_array_stats, max_diff_csr def apply_units(pars, unit_multipliers): new_pars = apply_unit_multipliers(pars, ['stress', 'one', 'density', 'stress', 'one' ,'density'], unit_multipliers) return new_pars def compute_von_mises(out, pb, state, extend=False, wmag=None, wdir=None): """ Calculate the von Mises stress. """ stress = pb.evaluate('ev_cauchy_stress.i.Omega(m.D, u)', mode='el_avg') vms = get_von_mises_stress(stress.squeeze()) vms.shape = (vms.shape[0], 1, 1, 1) out['von_mises_stress'] = Struct(name='output_data', mode='cell', data=vms) return out def define(filename_mesh, pars, approx_order, refinement_level, solver_conf, plane='strain', post_process=False, mesh_eps=1e-8): io = MeshIO.any_from_filename(filename_mesh) bbox = io.read_bounding_box() dim = bbox.shape[1] options = { 'absolute_mesh_path' : True, 'refinement_level' : refinement_level, 'allow_empty_regions' : True, 'post_process_hook' : 'compute_von_mises' if post_process else None, } fields = { 'displacement': ('complex', dim, 'Omega', approx_order), } young1, poisson1, density1, young2, poisson2, density2 = pars materials = { 'm' : ({ 'D' : {'Y1' : stiffness(dim, young=young1, poisson=poisson1, plane=plane), 'Y2' : stiffness(dim, young=young2, poisson=poisson2, plane=plane)}, 'density' : {'Y1' : density1, 'Y2' : density2}, },), 'wave' : 'get_wdir', } variables = { 'u' : ('unknown field', 'displacement', 0), 'v' : ('test field', 'displacement', 'u'), } regions = { 'Omega' : 'all', 'Y1': 'cells of group 1', 'Y2': 'cells of group 2', } regions.update(define_box_regions(dim, bbox[0], bbox[1], mesh_eps)) ebcs = { } if dim == 3: epbcs = { 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'}, 'match_x_plane'), 'periodic_y' : (['Near', 'Far'], {'u.all' : 'u.all'}, 'match_y_plane'), 'periodic_z' : (['Top', 'Bottom'], {'u.all' : 'u.all'}, 'match_z_plane'), } else: epbcs = { 'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'}, 'match_y_line'), 'periodic_y' : (['Bottom', 'Top'], {'u.all' : 'u.all'}, 'match_x_line'), } per.set_accuracy(mesh_eps) functions = { 'match_x_plane' : (per.match_x_plane,), 'match_y_plane' : (per.match_y_plane,), 'match_z_plane' : (per.match_z_plane,), 'match_x_line' : (per.match_x_line,), 'match_y_line' : (per.match_y_line,), 'get_wdir' : (get_wdir,), } integrals = { 'i' : 2 * approx_order, } equations = { 'K' : 'dw_lin_elastic.i.Omega(m.D, v, u)', 'S' : 'dw_elastic_wave.i.Omega(m.D, wave.vec, v, u)', 'R' : """1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, u, v) - 1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, v, u)""", 'M' : 'dw_volume_dot.i.Omega(m.density, v, u)', } solver_0 = solver_conf.copy() solver_0['name'] = 'eig' return locals() def get_wdir(ts, coors, mode=None, equations=None, term=None, problem=None, wdir=None, **kwargs): if mode == 'special': return {'vec' : wdir} def set_wave_dir(pb, wdir): materials = pb.get_materials() wave_mat = materials['wave'] wave_mat.set_extra_args(wdir=wdir) def save_materials(output_dir, pb, options): stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)', mode='el_avg', copy_materials=False, verbose=False) young, poisson = mc.youngpoisson_from_stiffness(stiffness, plane=options.plane) density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)', mode='el_avg', copy_materials=False, verbose=False) out = {} out['young'] = Struct(name='young', mode='cell', data=young[..., None, None]) out['poisson'] = Struct(name='poisson', mode='cell', data=poisson[..., None, None]) out['density'] = Struct(name='density', mode='cell', data=density) materials_filename = os.path.join(output_dir, 'materials.vtk') pb.save_state(materials_filename, out=out) def get_std_wave_fun(pb, options): stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)', mode='el_avg', copy_materials=False, verbose=False) young, poisson = mc.youngpoisson_from_stiffness(stiffness, plane=options.plane) density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)', mode='el_avg', copy_materials=False, verbose=False) lam, mu = mc.lame_from_youngpoisson(young, poisson, plane=options.plane) alam = nm.average(lam) amu = nm.average(mu) adensity = nm.average(density) cp = nm.sqrt((alam + 2.0 * amu) / adensity) cs = nm.sqrt(amu / adensity) output('average p-wave speed:', cp) output('average shear wave speed:', cs) log_names = [r'$\omega_p$', r'$\omega_s$'] log_plot_kwargs = [{'ls' : '--', 'color' : 'k'}, {'ls' : '--', 'color' : 'gray'}] if options.mode == 'omega': fun = lambda wmag, wdir: (cp * wmag, cs * wmag) else: fun = lambda wmag, wdir: (wmag / cp, wmag / cs) return fun, log_names, log_plot_kwargs def get_stepper(rng, pb, options): if options.stepper == 'linear': stepper = TimeStepper(rng[0], rng[1], dt=None, n_step=rng[2]) return stepper bbox = pb.domain.mesh.get_bounding_box() bzone = 2.0 * nm.pi / (bbox[1] - bbox[0]) num = rng[2] // 3 class BrillouinStepper(Struct): """ Step over 1. Brillouin zone in xy plane. """ def __init__(self, t0, t1, dt=None, n_step=None, step=None, **kwargs): Struct.__init__(self, t0=t0, t1=t1, dt=dt, n_step=n_step, step=step) self.n_digit, self.format, self.suffix = get_print_info(self.n_step) def __iter__(self): ts = TimeStepper(0, bzone[0], dt=None, n_step=num) for ii, val in ts: yield ii, val, nm.array([1.0, 0.0]) if ii == (num-2): break ts = TimeStepper(0, bzone[1], dt=None, n_step=num) for ii, k1 in ts: wdir = nm.array([bzone[0], k1]) val = nm.linalg.norm(wdir) wdir = wdir / val yield num + ii, val, wdir if ii == (num-2): break wdir = nm.array([bzone[0], bzone[1]]) val = nm.linalg.norm(wdir) wdir = wdir / val ts = TimeStepper(0, 1, dt=None, n_step=num) for ii, _ in ts: yield 2 * num + ii, val * (1.0 - float(ii)/(num-1)), wdir stepper = BrillouinStepper(0, 1, n_step=rng[2]) return stepper def save_eigenvectors(filename, svecs, wmag, wdir, pb): if svecs is None: return variables = pb.get_variables() # Make full eigenvectors (add DOFs fixed by boundary conditions). vecs = nm.empty((variables.di.ptr[-1], svecs.shape[1]), dtype=svecs.dtype) for ii in range(svecs.shape[1]): vecs[:, ii] = variables.make_full_vec(svecs[:, ii]) # Save the eigenvectors. out = {} state = pb.create_state() pp_name = pb.conf.options.get('post_process_hook') pp = getattr(pb.conf.funmod, pp_name if pp_name is not None else '', lambda out, *args, **kwargs: out) for ii in range(svecs.shape[1]): state.set_full(vecs[:, ii]) aux = state.create_output_dict() aux2 = {} pp(aux2, pb, state, wmag=wmag, wdir=wdir) aux.update(convert_complex_output(aux2)) out.update({key + '%03d' % ii : aux[key] for key in aux}) pb.save_state(filename, out=out) def assemble_matrices(define, mod, pars, set_wave_dir, options, wdir=None): """ Assemble the blocks of dispersion eigenvalue problem matrices. """ define_dict = define(filename_mesh=options.mesh_filename, pars=pars, approx_order=options.order, refinement_level=options.refine, solver_conf=options.solver_conf, plane=options.plane, post_process=options.post_process, **options.define_kwargs) conf = ProblemConf.from_dict(define_dict, mod) pb = Problem.from_conf(conf) pb.dispersion_options = options pb.set_output_dir(options.output_dir) dim = pb.domain.shape.dim # Set the normalized wave vector direction to the material(s). if wdir is None: wdir = nm.asarray(options.wave_dir[:dim], dtype=nm.float64) wdir = wdir / nm.linalg.norm(wdir) set_wave_dir(pb, wdir) bbox = pb.domain.mesh.get_bounding_box() size = (bbox[1] - bbox[0]).max() scaling0 = apply_unit_multipliers([1.0], ['length'], options.unit_multipliers)[0] scaling = scaling0 if options.mesh_size is not None: scaling *= options.mesh_size / size output('scaling factor of periodic cell mesh coordinates:', scaling) output('new mesh size with applied unit multipliers:', scaling * size) pb.domain.mesh.coors[:] *= scaling pb.set_mesh_coors(pb.domain.mesh.coors, update_fields=True) bzone = 2.0 * nm.pi / (scaling * size) output('1. Brillouin zone size:', bzone * scaling0) output('1. Brillouin zone size with applied unit multipliers:', bzone) pb.time_update() pb.update_materials() # Assemble the matrices. mtxs = {} for key, eq in pb.equations.iteritems(): mtxs[key] = mtx = pb.mtx_a.copy() mtx = eq.evaluate(mode='weak', dw_mode='matrix', asm_obj=mtx) mtx.eliminate_zeros() output_array_stats(mtx.data, 'nonzeros in %s' % key) output('symmetry checks:') output('%s - %s^T:' % (key, key), max_diff_csr(mtx, mtx.T)) output('%s - %s^H:' % (key, key), max_diff_csr(mtx, mtx.H)) return pb, wdir, bzone, mtxs def setup_n_eigs(options, pb, mtxs): """ Setup the numbers of eigenvalues based on options and numbers of DOFs. """ solver_n_eigs = n_eigs = options.n_eigs n_dof = mtxs['K'].shape[0] if options.mode == 'omega': if options.n_eigs > n_dof: n_eigs = n_dof solver_n_eigs = None else: if options.n_eigs > 2 * n_dof: n_eigs = 2 * n_dof solver_n_eigs = None return solver_n_eigs, n_eigs def build_evp_matrices(mtxs, val, mode, pb): """ Build the matrices of the dispersion eigenvalue problem. """ if mode == 'omega': mtx_a = mtxs['K'] + val**2 * mtxs['S'] + val * mtxs['R'] output('A - A^H:', max_diff_csr(mtx_a, mtx_a.H)) evp_mtxs = (mtx_a, mtxs['M']) else: evp_mtxs = (mtxs['S'], mtxs['R'], mtxs['K'] - val**2 * mtxs['M']) return evp_mtxs def process_evp_results(eigs, svecs, val, wdir, bzone, pb, mtxs, options, std_wave_fun=None): """ Transform eigenvalues to either omegas or kappas, depending on `mode`. Transform eigenvectors, if available, depending on `mode`. Return also the values to log. """ if options.mode == 'omega': omegas = nm.sqrt(eigs) output('eigs, omegas:') for ii, om in enumerate(omegas): output('{:>3}. {: .10e}, {:.10e}'.format(ii, eigs[ii], om)) if options.stepper == 'linear': out = tuple(eigs) + tuple(omegas) else: out = tuple(val * wdir) + tuple(omegas) if std_wave_fun is not None: out = out + std_wave_fun(val, wdir) return omegas, svecs, out else: kappas = eigs.copy() rks = kappas.copy() # Mask modes far from 1. Brillouin zone. max_kappa = 1.2 * bzone kappas[kappas.real > max_kappa] = nm.nan # Mask non-physical modes. kappas[kappas.real < 0] = nm.nan kappas[nm.abs(kappas.imag) > 1e-10] = nm.nan out = tuple(kappas.real) output('raw kappas, masked real part:',) for ii, kr in enumerate(kappas.real): output('{:>3}. {: 23.5e}, {:.10e}'.format(ii, rks[ii], kr)) if svecs is not None: n_dof = mtxs['K'].shape[0] # Select only vectors corresponding to physical modes. ii = nm.isfinite(kappas.real) svecs = svecs[:n_dof, ii] if std_wave_fun is not None: out = out + tuple(ii if ii <= max_kappa else nm.nan for ii in std_wave_fun(val, wdir)) return kappas, svecs, out helps = { 'pars' : 'material parameters in Y1, Y2 subdomains in basic units' ' [default: %(default)s]', 'conf' : 'if given, an alternative problem description file with apply_units() and' ' define() functions [default: %(default)s]', 'define_kwargs' : 'additional keyword arguments passed to define()', 'mesh_size' : 'desired mesh size (max. of bounding box dimensions) in basic units' ' - the input periodic cell mesh is rescaled to this size' ' [default: %(default)s]', 'unit_multipliers' : 'basic unit multipliers (time, length, mass) [default: %(default)s]', 'plane' : 'for 2D problems, plane strain or stress hypothesis selection' ' [default: %(default)s]', 'wave_dir' : 'the wave vector direction (will be normalized)' ' [default: %(default)s]', 'mode' : 'solution mode: omega = solve a generalized EVP for omega,' ' kappa = solve a quadratic generalized EVP for kappa' ' [default: %(default)s]', 'stepper' : 'the range stepper. For "brillouin", only the number' ' of items from --range is used' ' [default: %(default)s]', 'range' : 'the wave vector magnitude / frequency range' ' (like numpy.linspace) depending on the mode option' ' [default: %(default)s]', 'order' : 'displacement field approximation order [default: %(default)s]', 'refine' : 'number of uniform mesh refinements [default: %(default)s]', 'n_eigs' : 'the number of eigenvalues to compute [default: %(default)s]', 'eigs_only' : 'compute only eigenvalues, not eigenvectors', 'post_process' : 'post-process eigenvectors', 'solver_conf' : 'eigenvalue problem solver configuration options' ' [default: %(default)s]', 'save_regions' : 'save defined regions into' ' <output_directory>/regions.vtk', 'save_materials' : 'save material parameters into' ' <output_directory>/materials.vtk', 'log_std_waves' : 'log also standard pressure dilatation and shear waves', 'no_legends' : 'do not show legends in the log plots', 'no_show' : 'do not show the log figure', 'silent' : 'do not print messages to screen', 'clear' : 'clear old solution files from output directory', 'output_dir' : 'output directory [default: %(default)s]', 'mesh_filename' : 'input periodic cell mesh file name [default: %(default)s]', } def main(): # Aluminium and epoxy. default_pars = '70e9,0.35,2.799e3, 3.8e9,0.27,1.142e3' default_solver_conf = ("kind='eig.scipy',method='eigsh',tol=1.0e-5," "maxiter=1000,which='LM',sigma=0.0") parser = ArgumentParser(description=__doc__, formatter_class=RawDescriptionHelpFormatter) parser.add_argument('--pars', metavar='young1,poisson1,density1' ',young2,poisson2,density2', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='pars', default=default_pars, help=helps['pars']) parser.add_argument('--conf', metavar='filename', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='conf', default=None, help=helps['conf']) parser.add_argument('--define-kwargs', metavar='dict-like', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='define_kwargs', default=None, help=helps['define_kwargs']) parser.add_argument('--mesh-size', type=float, metavar='float', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='mesh_size', default=None, help=helps['mesh_size']) parser.add_argument('--unit-multipliers', metavar='c_time,c_length,c_mass', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='unit_multipliers', default='1.0,1.0,1.0', help=helps['unit_multipliers']) parser.add_argument('--plane', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='plane', choices=['strain', 'stress'], default='strain', help=helps['plane']) parser.add_argument('--wave-dir', metavar='float,float[,float]', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='wave_dir', default='1.0,0.0,0.0', help=helps['wave_dir']) parser.add_argument('--mode', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='mode', choices=['omega', 'kappa'], default='omega', help=helps['mode']) parser.add_argument('--stepper', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='stepper', choices=['linear', 'brillouin'], default='linear', help=helps['stepper']) parser.add_argument('--range', metavar='start,stop,count', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='range', default='0,6.4,33', help=helps['range']) parser.add_argument('--order', metavar='int', type=int, action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='order', default=1, help=helps['order']) parser.add_argument('--refine', metavar='int', type=int, action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='refine', default=0, help=helps['refine']) parser.add_argument('-n', '--n-eigs', metavar='int', type=int, action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='n_eigs', default=6, help=helps['n_eigs']) group = parser.add_mutually_exclusive_group() group.add_argument('--eigs-only', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='eigs_only', default=False, help=helps['eigs_only']) group.add_argument('--post-process', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='post_process', default=False, help=helps['post_process']) parser.add_argument('--solver-conf', metavar='dict-like', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='solver_conf', default=default_solver_conf, help=helps['solver_conf']) parser.add_argument('--save-regions', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='save_regions', default=False, help=helps['save_regions']) parser.add_argument('--save-materials', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='save_materials', default=False, help=helps['save_materials']) parser.add_argument('--log-std-waves', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='log_std_waves', default=False, help=helps['log_std_waves']) parser.add_argument('--no-legends', action="https://huggingface.co/datasets/luna-code/sfepy/store_false", dest='show_legends', default=True, help=helps['no_legends']) parser.add_argument('--no-show', action="https://huggingface.co/datasets/luna-code/sfepy/store_false", dest='show', default=True, help=helps['no_show']) parser.add_argument('--silent', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='silent', default=False, help=helps['silent']) parser.add_argument('-c', '--clear', action="https://huggingface.co/datasets/luna-code/sfepy/store_true", dest='clear', default=False, help=helps['clear']) parser.add_argument('-o', '--output-dir', metavar='path', action="https://huggingface.co/datasets/luna-code/sfepy/store", dest='output_dir', default='output', help=helps['output_dir']) parser.add_argument('mesh_filename', default='', help=helps['mesh_filename']) options = parser.parse_args() output_dir = options.output_dir output.set_output(filename=os.path.join(output_dir,'output_log.txt'), combined=options.silent == False) if options.conf is not None: mod = import_file(options.conf) else: mod = sys.modules[__name__] apply_units = mod.apply_units define = mod.define set_wave_dir = mod.set_wave_dir setup_n_eigs = mod.setup_n_eigs build_evp_matrices = mod.build_evp_matrices save_materials = mod.save_materials get_std_wave_fun = mod.get_std_wave_fun get_stepper = mod.get_stepper process_evp_results = mod.process_evp_results options.pars = [float(ii) for ii in options.pars.split(',')] options.unit_multipliers = [float(ii) for ii in options.unit_multipliers.split(',')] options.wave_dir = [float(ii) for ii in options.wave_dir.split(',')] aux = options.range.split(',') options.range = [float(aux[0]), float(aux[1]), int(aux[2])] options.solver_conf = dict_from_string(options.solver_conf) options.define_kwargs = dict_from_string(options.define_kwargs) if options.clear: remove_files_patterns(output_dir, ['*.h5', '*.vtk', '*.txt'], ignores=['output_log.txt'], verbose=True) filename = os.path.join(output_dir, 'options.txt') ensure_path(filename) save_options(filename, [('options', vars(options))], quote_command_line=True) pars = apply_units(options.pars, options.unit_multipliers) output('material parameters with applied unit multipliers:') output(pars) if options.mode == 'omega': rng = copy(options.range) rng[:2] = apply_unit_multipliers(options.range[:2], ['wave_number', 'wave_number'], options.unit_multipliers) output('wave number range with applied unit multipliers:', rng) else: if options.stepper == 'brillouin': raise ValueError('Cannot use "brillouin" stepper in kappa mode!') rng = copy(options.range) rng[:2] = apply_unit_multipliers(options.range[:2], ['frequency', 'frequency'], options.unit_multipliers) output('frequency range with applied unit multipliers:', rng) pb, wdir, bzone, mtxs = assemble_matrices(define, mod, pars, set_wave_dir, options) dim = pb.domain.shape.dim if dim != 2: options.plane = 'strain' if options.save_regions: pb.save_regions_as_groups(os.path.join(output_dir, 'regions')) if options.save_materials: save_materials(output_dir, pb, options) conf = pb.solver_confs['eig'] eig_solver = Solver.any_from_conf(conf) n_eigs, options.n_eigs = setup_n_eigs(options, pb, mtxs) get_color = lambda ii: plt.cm.viridis((float(ii) / (options.n_eigs - 1))) plot_kwargs = [{'color' : get_color(ii), 'ls' : '', 'marker' : 'o'} for ii in range(options.n_eigs)] get_color_dim = lambda ii: plt.cm.viridis((float(ii) / (dim-1))) plot_kwargs_dim = [{'color' : get_color_dim(ii), 'ls' : '', 'marker' : 'o'} for ii in range(dim)] log_names = [] log_plot_kwargs = [] if options.log_std_waves: std_wave_fun, log_names, log_plot_kwargs = get_std_wave_fun( pb, options) else: std_wave_fun = None stepper = get_stepper(rng, pb, options) if options.mode == 'omega': eigenshapes_filename = os.path.join(output_dir, 'frequency-eigenshapes-%s.vtk' % stepper.suffix) if options.stepper == 'linear': log = Log([[r'$\lambda_{%d}$' % ii for ii in range(options.n_eigs)], [r'$\omega_{%d}$' % ii for ii in range(options.n_eigs)] + log_names], plot_kwargs=[plot_kwargs, plot_kwargs + log_plot_kwargs], formats=[['{:.5e}'] * options.n_eigs, ['{:.5e}'] * (options.n_eigs + len(log_names))], yscales=['linear', 'linear'], xlabels=[r'$\kappa$', r'$\kappa$'], ylabels=[r'eigenvalues $\lambda_i$', r'frequencies $\omega_i$'], show_legends=options.show_legends, is_plot=options.show, log_filename=os.path.join(output_dir, 'frequencies.txt'), aggregate=1000, sleep=0.1) else: log = Log([[r'$\kappa_{%d}$'% ii for ii in range(dim)], [r'$\omega_{%d}$' % ii for ii in range(options.n_eigs)] + log_names], plot_kwargs=[plot_kwargs_dim, plot_kwargs + log_plot_kwargs], formats=[['{:.5e}'] * dim, ['{:.5e}'] * (options.n_eigs + len(log_names))], yscales=['linear', 'linear'], xlabels=[r'', r''], ylabels=[r'wave vector $\kappa$', r'frequencies $\omega_i$'], show_legends=options.show_legends, is_plot=options.show, log_filename=os.path.join(output_dir, 'frequencies.txt'), aggregate=1000, sleep=0.1) for aux in stepper: if options.stepper == 'linear': iv, wmag = aux else: iv, wmag, wdir = aux output('step %d: wave vector %s' % (iv, wmag * wdir)) if options.stepper == 'brillouin': pb, _, bzone, mtxs = assemble_matrices( define, mod, pars, set_wave_dir, options, wdir=wdir) evp_mtxs = build_evp_matrices(mtxs, wmag, options.mode, pb) if options.eigs_only: eigs = eig_solver(*evp_mtxs, n_eigs=n_eigs, eigenvectors=False) svecs = None else: eigs, svecs = eig_solver(*evp_mtxs, n_eigs=n_eigs, eigenvectors=True) omegas, svecs, out = process_evp_results( eigs, svecs, wmag, wdir, bzone, pb, mtxs, options, std_wave_fun=std_wave_fun ) if options.stepper == 'linear': log(*out, x=[wmag, wmag]) else: log(*out, x=[iv, iv]) save_eigenvectors(eigenshapes_filename % iv, svecs, wmag, wdir, pb) gc.collect() log(save_figure=os.path.join(output_dir, 'frequencies.png')) log(finished=True) else: eigenshapes_filename = os.path.join(output_dir, 'wave-number-eigenshapes-%s.vtk' % stepper.suffix) log = Log([[r'$\kappa_{%d}$' % ii for ii in range(options.n_eigs)] + log_names], plot_kwargs=[plot_kwargs + log_plot_kwargs], formats=[['{:.5e}'] * (options.n_eigs + len(log_names))], yscales=['linear'], xlabels=[r'$\omega$'], ylabels=[r'wave numbers $\kappa_i$'], show_legends=options.show_legends, is_plot=options.show, log_filename=os.path.join(output_dir, 'wave-numbers.txt'), aggregate=1000, sleep=0.1) for io, omega in stepper:	output('step %d: frequency %s' % (io, omega))	sfepy.base.base.output
from __future__ import absolute_import from copy import copy import numpy as nm from sfepy.base.testing import TestCommon from sfepy.base.base import ordered_iteritems from sfepy import data_dir filename_meshes = [data_dir + '/meshes/elements/%s_2.mesh' % geom for geom in ['1_2', '2_3', '2_4', '3_4', '3_8', '3_2_4']] def make_term_args(arg_shapes, arg_kinds, arg_types, ats_mode, domain, material_value=None, poly_space_base=None): from sfepy.base.base import basestr from sfepy.discrete import FieldVariable, Material, Variables, Materials from sfepy.discrete.fem import Field from sfepy.solvers.ts import TimeStepper from sfepy.mechanics.tensors import dim2sym omega = domain.regions['Omega'] dim = domain.shape.dim sym =	dim2sym(dim)	sfepy.mechanics.tensors.dim2sym
from __future__ import absolute_import from copy import copy import numpy as nm from sfepy.base.testing import TestCommon from sfepy.base.base import ordered_iteritems from sfepy import data_dir filename_meshes = [data_dir + '/meshes/elements/%s_2.mesh' % geom for geom in ['1_2', '2_3', '2_4', '3_4', '3_8', '3_2_4']] def make_term_args(arg_shapes, arg_kinds, arg_types, ats_mode, domain, material_value=None, poly_space_base=None): from sfepy.base.base import basestr from sfepy.discrete import FieldVariable, Material, Variables, Materials from sfepy.discrete.fem import Field from sfepy.solvers.ts import TimeStepper from sfepy.mechanics.tensors import dim2sym omega = domain.regions['Omega'] dim = domain.shape.dim sym = dim2sym(dim) def _parse_scalar_shape(sh): if isinstance(sh, basestr): if sh == 'D': return dim elif sh == 'D2': return dim**2 elif sh == 'S': return sym elif sh == 'N': # General number ;) return 1 else: return int(sh) else: return sh def _parse_tuple_shape(sh): if isinstance(sh, basestr): return [_parse_scalar_shape(ii.strip()) for ii in sh.split(',')] else: return (int(sh),) args = {} str_args = [] materials = [] variables = [] for ii, arg_kind in enumerate(arg_kinds): if arg_kind != 'ts': if ats_mode is not None: extended_ats = arg_types[ii] + ('/%s' % ats_mode) else: extended_ats = arg_types[ii] try: sh = arg_shapes[arg_types[ii]] except KeyError: sh = arg_shapes[extended_ats] if arg_kind.endswith('variable'): shape = _parse_scalar_shape(sh[0] if isinstance(sh, tuple) else sh) field = Field.from_args('f%d' % ii, nm.float64, shape, omega, approx_order=1, poly_space_base=poly_space_base) if arg_kind == 'virtual_variable': if sh[1] is not None: istate = arg_types.index(sh[1]) else: # Only virtual variable in arguments. istate = -1 # -> Make fake variable. var = FieldVariable('u-1', 'unknown', field) var.set_constant(0.0) variables.append(var) var = FieldVariable('v', 'test', field, primary_var_name='u%d' % istate) elif arg_kind == 'state_variable': var = FieldVariable('u%d' % ii, 'unknown', field) var.set_constant(0.0) elif arg_kind == 'parameter_variable': var = FieldVariable('p%d' % ii, 'parameter', field, primary_var_name='(set-to-None)') var.set_constant(0.0) variables.append(var) str_args.append(var.name) args[var.name] = var elif arg_kind.endswith('material'): if sh is None: # Switched-off opt_material. continue prefix = '' if isinstance(sh, basestr): aux = sh.split(':') if len(aux) == 2: prefix, sh = aux if material_value is None: material_value = 1.0 shape = _parse_tuple_shape(sh) if (len(shape) > 1) or (shape[0] > 1): if ((len(shape) == 2) and (shape[0] == shape[1]) and (material_value != 0.0)): # Identity matrix. val = nm.eye(shape[0], dtype=nm.float64) else: # Array. val = nm.empty(shape, dtype=nm.float64) val.fill(material_value) values = {'%sc%d' % (prefix, ii) : val} elif (len(shape) == 1) and (shape[0] == 1): # Single scalar as a special value. values = {'.c%d' % ii : material_value} else: raise ValueError('wrong material shape! (%s)' % shape) mat = Material('m%d' % ii, values=values) materials.append(mat) str_args.append(mat.name + '.' + 'c%d' % ii) args[mat.name] = mat elif arg_kind == 'ts': ts = TimeStepper(0.0, 1.0, 1.0, 5) str_args.append('ts') args['ts'] = ts else: str_args.append('user%d' % ii) args[str_args[-1]] = None materials =	Materials(materials)	sfepy.discrete.Materials
from __future__ import absolute_import from copy import copy import numpy as nm from sfepy.base.testing import TestCommon from sfepy.base.base import ordered_iteritems from sfepy import data_dir filename_meshes = [data_dir + '/meshes/elements/%s_2.mesh' % geom for geom in ['1_2', '2_3', '2_4', '3_4', '3_8', '3_2_4']] def make_term_args(arg_shapes, arg_kinds, arg_types, ats_mode, domain, material_value=None, poly_space_base=None): from sfepy.base.base import basestr from sfepy.discrete import FieldVariable, Material, Variables, Materials from sfepy.discrete.fem import Field from sfepy.solvers.ts import TimeStepper from sfepy.mechanics.tensors import dim2sym omega = domain.regions['Omega'] dim = domain.shape.dim sym = dim2sym(dim) def _parse_scalar_shape(sh): if isinstance(sh, basestr): if sh == 'D': return dim elif sh == 'D2': return dim**2 elif sh == 'S': return sym elif sh == 'N': # General number ;) return 1 else: return int(sh) else: return sh def _parse_tuple_shape(sh): if isinstance(sh, basestr): return [_parse_scalar_shape(ii.strip()) for ii in sh.split(',')] else: return (int(sh),) args = {} str_args = [] materials = [] variables = [] for ii, arg_kind in enumerate(arg_kinds): if arg_kind != 'ts': if ats_mode is not None: extended_ats = arg_types[ii] + ('/%s' % ats_mode) else: extended_ats = arg_types[ii] try: sh = arg_shapes[arg_types[ii]] except KeyError: sh = arg_shapes[extended_ats] if arg_kind.endswith('variable'): shape = _parse_scalar_shape(sh[0] if isinstance(sh, tuple) else sh) field = Field.from_args('f%d' % ii, nm.float64, shape, omega, approx_order=1, poly_space_base=poly_space_base) if arg_kind == 'virtual_variable': if sh[1] is not None: istate = arg_types.index(sh[1]) else: # Only virtual variable in arguments. istate = -1 # -> Make fake variable. var = FieldVariable('u-1', 'unknown', field) var.set_constant(0.0) variables.append(var) var = FieldVariable('v', 'test', field, primary_var_name='u%d' % istate) elif arg_kind == 'state_variable': var = FieldVariable('u%d' % ii, 'unknown', field) var.set_constant(0.0) elif arg_kind == 'parameter_variable': var = FieldVariable('p%d' % ii, 'parameter', field, primary_var_name='(set-to-None)') var.set_constant(0.0) variables.append(var) str_args.append(var.name) args[var.name] = var elif arg_kind.endswith('material'): if sh is None: # Switched-off opt_material. continue prefix = '' if isinstance(sh, basestr): aux = sh.split(':') if len(aux) == 2: prefix, sh = aux if material_value is None: material_value = 1.0 shape = _parse_tuple_shape(sh) if (len(shape) > 1) or (shape[0] > 1): if ((len(shape) == 2) and (shape[0] == shape[1]) and (material_value != 0.0)): # Identity matrix. val = nm.eye(shape[0], dtype=nm.float64) else: # Array. val = nm.empty(shape, dtype=nm.float64) val.fill(material_value) values = {'%sc%d' % (prefix, ii) : val} elif (len(shape) == 1) and (shape[0] == 1): # Single scalar as a special value. values = {'.c%d' % ii : material_value} else: raise ValueError('wrong material shape! (%s)' % shape) mat = Material('m%d' % ii, values=values) materials.append(mat) str_args.append(mat.name + '.' + 'c%d' % ii) args[mat.name] = mat elif arg_kind == 'ts': ts = TimeStepper(0.0, 1.0, 1.0, 5) str_args.append('ts') args['ts'] = ts else: str_args.append('user%d' % ii) args[str_args[-1]] = None materials = Materials(materials) variables =	Variables(variables)	sfepy.discrete.Variables
from __future__ import absolute_import from copy import copy import numpy as nm from sfepy.base.testing import TestCommon from sfepy.base.base import ordered_iteritems from sfepy import data_dir filename_meshes = [data_dir + '/meshes/elements/%s_2.mesh' % geom for geom in ['1_2', '2_3', '2_4', '3_4', '3_8', '3_2_4']] def make_term_args(arg_shapes, arg_kinds, arg_types, ats_mode, domain, material_value=None, poly_space_base=None): from sfepy.base.base import basestr from sfepy.discrete import FieldVariable, Material, Variables, Materials from sfepy.discrete.fem import Field from sfepy.solvers.ts import TimeStepper from sfepy.mechanics.tensors import dim2sym omega = domain.regions['Omega'] dim = domain.shape.dim sym = dim2sym(dim) def _parse_scalar_shape(sh): if isinstance(sh, basestr): if sh == 'D': return dim elif sh == 'D2': return dim**2 elif sh == 'S': return sym elif sh == 'N': # General number ;) return 1 else: return int(sh) else: return sh def _parse_tuple_shape(sh): if isinstance(sh, basestr): return [_parse_scalar_shape(ii.strip()) for ii in sh.split(',')] else: return (int(sh),) args = {} str_args = [] materials = [] variables = [] for ii, arg_kind in enumerate(arg_kinds): if arg_kind != 'ts': if ats_mode is not None: extended_ats = arg_types[ii] + ('/%s' % ats_mode) else: extended_ats = arg_types[ii] try: sh = arg_shapes[arg_types[ii]] except KeyError: sh = arg_shapes[extended_ats] if arg_kind.endswith('variable'): shape = _parse_scalar_shape(sh[0] if isinstance(sh, tuple) else sh) field = Field.from_args('f%d' % ii, nm.float64, shape, omega, approx_order=1, poly_space_base=poly_space_base) if arg_kind == 'virtual_variable': if sh[1] is not None: istate = arg_types.index(sh[1]) else: # Only virtual variable in arguments. istate = -1 # -> Make fake variable. var = FieldVariable('u-1', 'unknown', field) var.set_constant(0.0) variables.append(var) var = FieldVariable('v', 'test', field, primary_var_name='u%d' % istate) elif arg_kind == 'state_variable': var = FieldVariable('u%d' % ii, 'unknown', field) var.set_constant(0.0) elif arg_kind == 'parameter_variable': var = FieldVariable('p%d' % ii, 'parameter', field, primary_var_name='(set-to-None)') var.set_constant(0.0) variables.append(var) str_args.append(var.name) args[var.name] = var elif arg_kind.endswith('material'): if sh is None: # Switched-off opt_material. continue prefix = '' if isinstance(sh, basestr): aux = sh.split(':') if len(aux) == 2: prefix, sh = aux if material_value is None: material_value = 1.0 shape = _parse_tuple_shape(sh) if (len(shape) > 1) or (shape[0] > 1): if ((len(shape) == 2) and (shape[0] == shape[1]) and (material_value != 0.0)): # Identity matrix. val = nm.eye(shape[0], dtype=nm.float64) else: # Array. val = nm.empty(shape, dtype=nm.float64) val.fill(material_value) values = {'%sc%d' % (prefix, ii) : val} elif (len(shape) == 1) and (shape[0] == 1): # Single scalar as a special value. values = {'.c%d' % ii : material_value} else: raise ValueError('wrong material shape! (%s)' % shape) mat = Material('m%d' % ii, values=values) materials.append(mat) str_args.append(mat.name + '.' + 'c%d' % ii) args[mat.name] = mat elif arg_kind == 'ts': ts = TimeStepper(0.0, 1.0, 1.0, 5) str_args.append('ts') args['ts'] = ts else: str_args.append('user%d' % ii) args[str_args[-1]] = None materials = Materials(materials) variables = Variables(variables) return args, str_args, materials, variables class Test(TestCommon): @staticmethod def from_conf(conf, options): from sfepy.discrete import Integral from sfepy.discrete.fem import Mesh, FEDomain domains = [] for filename in filename_meshes: mesh = Mesh.from_file(filename) domain = FEDomain('domain_%s' % mesh.name.replace(data_dir, ''), mesh) domain.create_region('Omega', 'all') domain.create_region('Gamma', 'vertices of surface', 'facet') domains.append(domain) integral =	Integral('i', order=3)	sfepy.discrete.Integral
from __future__ import absolute_import from copy import copy import numpy as nm from sfepy.base.testing import TestCommon from sfepy.base.base import ordered_iteritems from sfepy import data_dir filename_meshes = [data_dir + '/meshes/elements/%s_2.mesh' % geom for geom in ['1_2', '2_3', '2_4', '3_4', '3_8', '3_2_4']] def make_term_args(arg_shapes, arg_kinds, arg_types, ats_mode, domain, material_value=None, poly_space_base=None): from sfepy.base.base import basestr from sfepy.discrete import FieldVariable, Material, Variables, Materials from sfepy.discrete.fem import Field from sfepy.solvers.ts import TimeStepper from sfepy.mechanics.tensors import dim2sym omega = domain.regions['Omega'] dim = domain.shape.dim sym = dim2sym(dim) def _parse_scalar_shape(sh): if isinstance(sh, basestr): if sh == 'D': return dim elif sh == 'D2': return dim**2 elif sh == 'S': return sym elif sh == 'N': # General number ;) return 1 else: return int(sh) else: return sh def _parse_tuple_shape(sh): if isinstance(sh, basestr): return [_parse_scalar_shape(ii.strip()) for ii in sh.split(',')] else: return (int(sh),) args = {} str_args = [] materials = [] variables = [] for ii, arg_kind in enumerate(arg_kinds): if arg_kind != 'ts': if ats_mode is not None: extended_ats = arg_types[ii] + ('/%s' % ats_mode) else: extended_ats = arg_types[ii] try: sh = arg_shapes[arg_types[ii]] except KeyError: sh = arg_shapes[extended_ats] if arg_kind.endswith('variable'): shape = _parse_scalar_shape(sh[0] if isinstance(sh, tuple) else sh) field = Field.from_args('f%d' % ii, nm.float64, shape, omega, approx_order=1, poly_space_base=poly_space_base) if arg_kind == 'virtual_variable': if sh[1] is not None: istate = arg_types.index(sh[1]) else: # Only virtual variable in arguments. istate = -1 # -> Make fake variable. var = FieldVariable('u-1', 'unknown', field) var.set_constant(0.0) variables.append(var) var = FieldVariable('v', 'test', field, primary_var_name='u%d' % istate) elif arg_kind == 'state_variable': var = FieldVariable('u%d' % ii, 'unknown', field) var.set_constant(0.0) elif arg_kind == 'parameter_variable': var = FieldVariable('p%d' % ii, 'parameter', field, primary_var_name='(set-to-None)') var.set_constant(0.0) variables.append(var) str_args.append(var.name) args[var.name] = var elif arg_kind.endswith('material'): if sh is None: # Switched-off opt_material. continue prefix = '' if isinstance(sh, basestr): aux = sh.split(':') if len(aux) == 2: prefix, sh = aux if material_value is None: material_value = 1.0 shape = _parse_tuple_shape(sh) if (len(shape) > 1) or (shape[0] > 1): if ((len(shape) == 2) and (shape[0] == shape[1]) and (material_value != 0.0)): # Identity matrix. val = nm.eye(shape[0], dtype=nm.float64) else: # Array. val = nm.empty(shape, dtype=nm.float64) val.fill(material_value) values = {'%sc%d' % (prefix, ii) : val} elif (len(shape) == 1) and (shape[0] == 1): # Single scalar as a special value. values = {'.c%d' % ii : material_value} else: raise ValueError('wrong material shape! (%s)' % shape) mat = Material('m%d' % ii, values=values) materials.append(mat) str_args.append(mat.name + '.' + 'c%d' % ii) args[mat.name] = mat elif arg_kind == 'ts': ts = TimeStepper(0.0, 1.0, 1.0, 5) str_args.append('ts') args['ts'] = ts else: str_args.append('user%d' % ii) args[str_args[-1]] = None materials = Materials(materials) variables = Variables(variables) return args, str_args, materials, variables class Test(TestCommon): @staticmethod def from_conf(conf, options): from sfepy.discrete import Integral from sfepy.discrete.fem import Mesh, FEDomain domains = [] for filename in filename_meshes: mesh =	Mesh.from_file(filename)	sfepy.discrete.fem.Mesh.from_file
from __future__ import absolute_import from copy import copy import numpy as nm from sfepy.base.testing import TestCommon from sfepy.base.base import ordered_iteritems from sfepy import data_dir filename_meshes = [data_dir + '/meshes/elements/%s_2.mesh' % geom for geom in ['1_2', '2_3', '2_4', '3_4', '3_8', '3_2_4']] def make_term_args(arg_shapes, arg_kinds, arg_types, ats_mode, domain, material_value=None, poly_space_base=None): from sfepy.base.base import basestr from sfepy.discrete import FieldVariable, Material, Variables, Materials from sfepy.discrete.fem import Field from sfepy.solvers.ts import TimeStepper from sfepy.mechanics.tensors import dim2sym omega = domain.regions['Omega'] dim = domain.shape.dim sym = dim2sym(dim) def _parse_scalar_shape(sh): if isinstance(sh, basestr): if sh == 'D': return dim elif sh == 'D2': return dim**2 elif sh == 'S': return sym elif sh == 'N': # General number ;) return 1 else: return int(sh) else: return sh def _parse_tuple_shape(sh): if isinstance(sh, basestr): return [_parse_scalar_shape(ii.strip()) for ii in sh.split(',')] else: return (int(sh),) args = {} str_args = [] materials = [] variables = [] for ii, arg_kind in enumerate(arg_kinds): if arg_kind != 'ts': if ats_mode is not None: extended_ats = arg_types[ii] + ('/%s' % ats_mode) else: extended_ats = arg_types[ii] try: sh = arg_shapes[arg_types[ii]] except KeyError: sh = arg_shapes[extended_ats] if arg_kind.endswith('variable'): shape = _parse_scalar_shape(sh[0] if isinstance(sh, tuple) else sh) field = Field.from_args('f%d' % ii, nm.float64, shape, omega, approx_order=1, poly_space_base=poly_space_base) if arg_kind == 'virtual_variable': if sh[1] is not None: istate = arg_types.index(sh[1]) else: # Only virtual variable in arguments. istate = -1 # -> Make fake variable. var = FieldVariable('u-1', 'unknown', field) var.set_constant(0.0) variables.append(var) var = FieldVariable('v', 'test', field, primary_var_name='u%d' % istate) elif arg_kind == 'state_variable': var = FieldVariable('u%d' % ii, 'unknown', field) var.set_constant(0.0) elif arg_kind == 'parameter_variable': var = FieldVariable('p%d' % ii, 'parameter', field, primary_var_name='(set-to-None)') var.set_constant(0.0) variables.append(var) str_args.append(var.name) args[var.name] = var elif arg_kind.endswith('material'): if sh is None: # Switched-off opt_material. continue prefix = '' if isinstance(sh, basestr): aux = sh.split(':') if len(aux) == 2: prefix, sh = aux if material_value is None: material_value = 1.0 shape = _parse_tuple_shape(sh) if (len(shape) > 1) or (shape[0] > 1): if ((len(shape) == 2) and (shape[0] == shape[1]) and (material_value != 0.0)): # Identity matrix. val = nm.eye(shape[0], dtype=nm.float64) else: # Array. val = nm.empty(shape, dtype=nm.float64) val.fill(material_value) values = {'%sc%d' % (prefix, ii) : val} elif (len(shape) == 1) and (shape[0] == 1): # Single scalar as a special value. values = {'.c%d' % ii : material_value} else: raise ValueError('wrong material shape! (%s)' % shape) mat = Material('m%d' % ii, values=values) materials.append(mat) str_args.append(mat.name + '.' + 'c%d' % ii) args[mat.name] = mat elif arg_kind == 'ts': ts = TimeStepper(0.0, 1.0, 1.0, 5) str_args.append('ts') args['ts'] = ts else: str_args.append('user%d' % ii) args[str_args[-1]] = None materials = Materials(materials) variables = Variables(variables) return args, str_args, materials, variables class Test(TestCommon): @staticmethod def from_conf(conf, options): from sfepy.discrete import Integral from sfepy.discrete.fem import Mesh, FEDomain domains = [] for filename in filename_meshes: mesh = Mesh.from_file(filename) domain = FEDomain('domain_%s' % mesh.name.replace(data_dir, ''), mesh) domain.create_region('Omega', 'all') domain.create_region('Gamma', 'vertices of surface', 'facet') domains.append(domain) integral = Integral('i', order=3) qp_coors, qp_weights = integral.get_qp('3_8') custom_integral = Integral('i', coors=qp_coors, weights=qp_weights, order='custom') test = Test(domains=domains, integral=integral, custom_integral=custom_integral, conf=conf, options=options) return test def test_term_call_modes(self): from sfepy.terms import term_table ok = True failed = [] for domain in self.domains: self.report('domain: %s' % domain.name) domain_geometry = list(domain.geom_els.values())[0].name if domain.shape.dim != domain.shape.tdim: domain_geometry = '%d_%s' % (domain.shape.dim, domain_geometry) for _, term_cls in	ordered_iteritems(term_table)	sfepy.base.base.ordered_iteritems
from __future__ import absolute_import from copy import copy import numpy as nm from sfepy.base.testing import TestCommon from sfepy.base.base import ordered_iteritems from sfepy import data_dir filename_meshes = [data_dir + '/meshes/elements/%s_2.mesh' % geom for geom in ['1_2', '2_3', '2_4', '3_4', '3_8', '3_2_4']] def make_term_args(arg_shapes, arg_kinds, arg_types, ats_mode, domain, material_value=None, poly_space_base=None): from sfepy.base.base import basestr from sfepy.discrete import FieldVariable, Material, Variables, Materials from sfepy.discrete.fem import Field from sfepy.solvers.ts import TimeStepper from sfepy.mechanics.tensors import dim2sym omega = domain.regions['Omega'] dim = domain.shape.dim sym = dim2sym(dim) def _parse_scalar_shape(sh): if isinstance(sh, basestr): if sh == 'D': return dim elif sh == 'D2': return dim**2 elif sh == 'S': return sym elif sh == 'N': # General number ;) return 1 else: return int(sh) else: return sh def _parse_tuple_shape(sh): if isinstance(sh, basestr): return [_parse_scalar_shape(ii.strip()) for ii in sh.split(',')] else: return (int(sh),) args = {} str_args = [] materials = [] variables = [] for ii, arg_kind in enumerate(arg_kinds): if arg_kind != 'ts': if ats_mode is not None: extended_ats = arg_types[ii] + ('/%s' % ats_mode) else: extended_ats = arg_types[ii] try: sh = arg_shapes[arg_types[ii]] except KeyError: sh = arg_shapes[extended_ats] if arg_kind.endswith('variable'): shape = _parse_scalar_shape(sh[0] if isinstance(sh, tuple) else sh) field = Field.from_args('f%d' % ii, nm.float64, shape, omega, approx_order=1, poly_space_base=poly_space_base) if arg_kind == 'virtual_variable': if sh[1] is not None: istate = arg_types.index(sh[1]) else: # Only virtual variable in arguments. istate = -1 # -> Make fake variable. var = FieldVariable('u-1', 'unknown', field) var.set_constant(0.0) variables.append(var) var = FieldVariable('v', 'test', field, primary_var_name='u%d' % istate) elif arg_kind == 'state_variable': var = FieldVariable('u%d' % ii, 'unknown', field) var.set_constant(0.0) elif arg_kind == 'parameter_variable': var = FieldVariable('p%d' % ii, 'parameter', field, primary_var_name='(set-to-None)') var.set_constant(0.0) variables.append(var) str_args.append(var.name) args[var.name] = var elif arg_kind.endswith('material'): if sh is None: # Switched-off opt_material. continue prefix = '' if isinstance(sh, basestr): aux = sh.split(':') if len(aux) == 2: prefix, sh = aux if material_value is None: material_value = 1.0 shape = _parse_tuple_shape(sh) if (len(shape) > 1) or (shape[0] > 1): if ((len(shape) == 2) and (shape[0] == shape[1]) and (material_value != 0.0)): # Identity matrix. val = nm.eye(shape[0], dtype=nm.float64) else: # Array. val = nm.empty(shape, dtype=nm.float64) val.fill(material_value) values = {'%sc%d' % (prefix, ii) : val} elif (len(shape) == 1) and (shape[0] == 1): # Single scalar as a special value. values = {'.c%d' % ii : material_value} else: raise ValueError('wrong material shape! (%s)' % shape) mat =	Material('m%d' % ii, values=values)	sfepy.discrete.Material
from __future__ import absolute_import from copy import copy import numpy as nm from sfepy.base.testing import TestCommon from sfepy.base.base import ordered_iteritems from sfepy import data_dir filename_meshes = [data_dir + '/meshes/elements/%s_2.mesh' % geom for geom in ['1_2', '2_3', '2_4', '3_4', '3_8', '3_2_4']] def make_term_args(arg_shapes, arg_kinds, arg_types, ats_mode, domain, material_value=None, poly_space_base=None): from sfepy.base.base import basestr from sfepy.discrete import FieldVariable, Material, Variables, Materials from sfepy.discrete.fem import Field from sfepy.solvers.ts import TimeStepper from sfepy.mechanics.tensors import dim2sym omega = domain.regions['Omega'] dim = domain.shape.dim sym = dim2sym(dim) def _parse_scalar_shape(sh): if isinstance(sh, basestr): if sh == 'D': return dim elif sh == 'D2': return dim**2 elif sh == 'S': return sym elif sh == 'N': # General number ;) return 1 else: return int(sh) else: return sh def _parse_tuple_shape(sh): if isinstance(sh, basestr): return [_parse_scalar_shape(ii.strip()) for ii in sh.split(',')] else: return (int(sh),) args = {} str_args = [] materials = [] variables = [] for ii, arg_kind in enumerate(arg_kinds): if arg_kind != 'ts': if ats_mode is not None: extended_ats = arg_types[ii] + ('/%s' % ats_mode) else: extended_ats = arg_types[ii] try: sh = arg_shapes[arg_types[ii]] except KeyError: sh = arg_shapes[extended_ats] if arg_kind.endswith('variable'): shape = _parse_scalar_shape(sh[0] if isinstance(sh, tuple) else sh) field = Field.from_args('f%d' % ii, nm.float64, shape, omega, approx_order=1, poly_space_base=poly_space_base) if arg_kind == 'virtual_variable': if sh[1] is not None: istate = arg_types.index(sh[1]) else: # Only virtual variable in arguments. istate = -1 # -> Make fake variable. var = FieldVariable('u-1', 'unknown', field) var.set_constant(0.0) variables.append(var) var = FieldVariable('v', 'test', field, primary_var_name='u%d' % istate) elif arg_kind == 'state_variable': var = FieldVariable('u%d' % ii, 'unknown', field) var.set_constant(0.0) elif arg_kind == 'parameter_variable': var = FieldVariable('p%d' % ii, 'parameter', field, primary_var_name='(set-to-None)') var.set_constant(0.0) variables.append(var) str_args.append(var.name) args[var.name] = var elif arg_kind.endswith('material'): if sh is None: # Switched-off opt_material. continue prefix = '' if isinstance(sh, basestr): aux = sh.split(':') if len(aux) == 2: prefix, sh = aux if material_value is None: material_value = 1.0 shape = _parse_tuple_shape(sh) if (len(shape) > 1) or (shape[0] > 1): if ((len(shape) == 2) and (shape[0] == shape[1]) and (material_value != 0.0)): # Identity matrix. val = nm.eye(shape[0], dtype=nm.float64) else: # Array. val = nm.empty(shape, dtype=nm.float64) val.fill(material_value) values = {'%sc%d' % (prefix, ii) : val} elif (len(shape) == 1) and (shape[0] == 1): # Single scalar as a special value. values = {'.c%d' % ii : material_value} else: raise ValueError('wrong material shape! (%s)' % shape) mat = Material('m%d' % ii, values=values) materials.append(mat) str_args.append(mat.name + '.' + 'c%d' % ii) args[mat.name] = mat elif arg_kind == 'ts': ts = TimeStepper(0.0, 1.0, 1.0, 5) str_args.append('ts') args['ts'] = ts else: str_args.append('user%d' % ii) args[str_args[-1]] = None materials = Materials(materials) variables = Variables(variables) return args, str_args, materials, variables class Test(TestCommon): @staticmethod def from_conf(conf, options): from sfepy.discrete import Integral from sfepy.discrete.fem import Mesh, FEDomain domains = [] for filename in filename_meshes: mesh = Mesh.from_file(filename) domain = FEDomain('domain_%s' % mesh.name.replace(data_dir, ''), mesh) domain.create_region('Omega', 'all') domain.create_region('Gamma', 'vertices of surface', 'facet') domains.append(domain) integral = Integral('i', order=3) qp_coors, qp_weights = integral.get_qp('3_8') custom_integral = Integral('i', coors=qp_coors, weights=qp_weights, order='custom') test = Test(domains=domains, integral=integral, custom_integral=custom_integral, conf=conf, options=options) return test def test_term_call_modes(self): from sfepy.terms import term_table ok = True failed = [] for domain in self.domains: self.report('domain: %s' % domain.name) domain_geometry = list(domain.geom_els.values())[0].name if domain.shape.dim != domain.shape.tdim: domain_geometry = '%d_%s' % (domain.shape.dim, domain_geometry) for _, term_cls in ordered_iteritems(term_table): if (domain_geometry not in term_cls.geometries) \ or ("dg" in term_cls.name) \ or (term_cls.name == "dw_ns_dot_grad_s"): continue vint = ('volume', 'point', 'custom') rname = 'Omega' if term_cls.integration in vint else 'Gamma' self.report('<-- %s ...' % term_cls.name) if rname == 'Gamma' and domain.mesh.dim == 1: self.report('--> 1D Gamma region: not tested!') elif term_cls.arg_shapes: try: _ok = self._test_single_term(term_cls, domain, rname) except: _ok = False if not _ok: failed.append((domain.name, term_cls.name)) ok = ok and _ok self.report('--> ok: %s' % _ok) else: self.report('--> not tested!') self.report('failed:', failed) return ok def _test_single_term(self, term_cls, domain, rname): from sfepy.terms import Term from sfepy.terms.terms import get_arg_kinds ok = True term_call = term_cls.name + '(%s)' arg_shapes_list = term_cls.arg_shapes if not isinstance(arg_shapes_list, list): arg_shapes_list = [arg_shapes_list] if term_cls.integration != 'custom': integral = self.integral else: integral = self.custom_integral poly_space_base = getattr(term_cls, 'poly_space_base', 'lagrange') prev_shapes = {} for _arg_shapes in arg_shapes_list: # Unset shapes are taken from the previous iteration. arg_shapes = copy(prev_shapes) arg_shapes.update(_arg_shapes) prev_shapes = arg_shapes self.report('arg_shapes:', arg_shapes) arg_types = term_cls.arg_types if not isinstance(arg_types[0], tuple): arg_types = (arg_types,) for iat, ats in enumerate(arg_types): self.report('arg_types:', ats) arg_kinds =	get_arg_kinds(ats)	sfepy.terms.terms.get_arg_kinds
from __future__ import absolute_import from copy import copy import numpy as nm from sfepy.base.testing import TestCommon from sfepy.base.base import ordered_iteritems from sfepy import data_dir filename_meshes = [data_dir + '/meshes/elements/%s_2.mesh' % geom for geom in ['1_2', '2_3', '2_4', '3_4', '3_8', '3_2_4']] def make_term_args(arg_shapes, arg_kinds, arg_types, ats_mode, domain, material_value=None, poly_space_base=None): from sfepy.base.base import basestr from sfepy.discrete import FieldVariable, Material, Variables, Materials from sfepy.discrete.fem import Field from sfepy.solvers.ts import TimeStepper from sfepy.mechanics.tensors import dim2sym omega = domain.regions['Omega'] dim = domain.shape.dim sym = dim2sym(dim) def _parse_scalar_shape(sh): if isinstance(sh, basestr): if sh == 'D': return dim elif sh == 'D2': return dim**2 elif sh == 'S': return sym elif sh == 'N': # General number ;) return 1 else: return int(sh) else: return sh def _parse_tuple_shape(sh): if isinstance(sh, basestr): return [_parse_scalar_shape(ii.strip()) for ii in sh.split(',')] else: return (int(sh),) args = {} str_args = [] materials = [] variables = [] for ii, arg_kind in enumerate(arg_kinds): if arg_kind != 'ts': if ats_mode is not None: extended_ats = arg_types[ii] + ('/%s' % ats_mode) else: extended_ats = arg_types[ii] try: sh = arg_shapes[arg_types[ii]] except KeyError: sh = arg_shapes[extended_ats] if arg_kind.endswith('variable'): shape = _parse_scalar_shape(sh[0] if isinstance(sh, tuple) else sh) field = Field.from_args('f%d' % ii, nm.float64, shape, omega, approx_order=1, poly_space_base=poly_space_base) if arg_kind == 'virtual_variable': if sh[1] is not None: istate = arg_types.index(sh[1]) else: # Only virtual variable in arguments. istate = -1 # -> Make fake variable. var = FieldVariable('u-1', 'unknown', field) var.set_constant(0.0) variables.append(var) var = FieldVariable('v', 'test', field, primary_var_name='u%d' % istate) elif arg_kind == 'state_variable': var = FieldVariable('u%d' % ii, 'unknown', field) var.set_constant(0.0) elif arg_kind == 'parameter_variable': var = FieldVariable('p%d' % ii, 'parameter', field, primary_var_name='(set-to-None)') var.set_constant(0.0) variables.append(var) str_args.append(var.name) args[var.name] = var elif arg_kind.endswith('material'): if sh is None: # Switched-off opt_material. continue prefix = '' if isinstance(sh, basestr): aux = sh.split(':') if len(aux) == 2: prefix, sh = aux if material_value is None: material_value = 1.0 shape = _parse_tuple_shape(sh) if (len(shape) > 1) or (shape[0] > 1): if ((len(shape) == 2) and (shape[0] == shape[1]) and (material_value != 0.0)): # Identity matrix. val = nm.eye(shape[0], dtype=nm.float64) else: # Array. val = nm.empty(shape, dtype=nm.float64) val.fill(material_value) values = {'%sc%d' % (prefix, ii) : val} elif (len(shape) == 1) and (shape[0] == 1): # Single scalar as a special value. values = {'.c%d' % ii : material_value} else: raise ValueError('wrong material shape! (%s)' % shape) mat = Material('m%d' % ii, values=values) materials.append(mat) str_args.append(mat.name + '.' + 'c%d' % ii) args[mat.name] = mat elif arg_kind == 'ts': ts = TimeStepper(0.0, 1.0, 1.0, 5) str_args.append('ts') args['ts'] = ts else: str_args.append('user%d' % ii) args[str_args[-1]] = None materials = Materials(materials) variables = Variables(variables) return args, str_args, materials, variables class Test(TestCommon): @staticmethod def from_conf(conf, options): from sfepy.discrete import Integral from sfepy.discrete.fem import Mesh, FEDomain domains = [] for filename in filename_meshes: mesh = Mesh.from_file(filename) domain = FEDomain('domain_%s' % mesh.name.replace(data_dir, ''), mesh) domain.create_region('Omega', 'all') domain.create_region('Gamma', 'vertices of surface', 'facet') domains.append(domain) integral = Integral('i', order=3) qp_coors, qp_weights = integral.get_qp('3_8') custom_integral = Integral('i', coors=qp_coors, weights=qp_weights, order='custom') test = Test(domains=domains, integral=integral, custom_integral=custom_integral, conf=conf, options=options) return test def test_term_call_modes(self): from sfepy.terms import term_table ok = True failed = [] for domain in self.domains: self.report('domain: %s' % domain.name) domain_geometry = list(domain.geom_els.values())[0].name if domain.shape.dim != domain.shape.tdim: domain_geometry = '%d_%s' % (domain.shape.dim, domain_geometry) for _, term_cls in ordered_iteritems(term_table): if (domain_geometry not in term_cls.geometries) \ or ("dg" in term_cls.name) \ or (term_cls.name == "dw_ns_dot_grad_s"): continue vint = ('volume', 'point', 'custom') rname = 'Omega' if term_cls.integration in vint else 'Gamma' self.report('<-- %s ...' % term_cls.name) if rname == 'Gamma' and domain.mesh.dim == 1: self.report('--> 1D Gamma region: not tested!') elif term_cls.arg_shapes: try: _ok = self._test_single_term(term_cls, domain, rname) except: _ok = False if not _ok: failed.append((domain.name, term_cls.name)) ok = ok and _ok self.report('--> ok: %s' % _ok) else: self.report('--> not tested!') self.report('failed:', failed) return ok def _test_single_term(self, term_cls, domain, rname): from sfepy.terms import Term from sfepy.terms.terms import get_arg_kinds ok = True term_call = term_cls.name + '(%s)' arg_shapes_list = term_cls.arg_shapes if not isinstance(arg_shapes_list, list): arg_shapes_list = [arg_shapes_list] if term_cls.integration != 'custom': integral = self.integral else: integral = self.custom_integral poly_space_base = getattr(term_cls, 'poly_space_base', 'lagrange') prev_shapes = {} for _arg_shapes in arg_shapes_list: # Unset shapes are taken from the previous iteration. arg_shapes = copy(prev_shapes) arg_shapes.update(_arg_shapes) prev_shapes = arg_shapes self.report('arg_shapes:', arg_shapes) arg_types = term_cls.arg_types if not isinstance(arg_types[0], tuple): arg_types = (arg_types,) for iat, ats in enumerate(arg_types): self.report('arg_types:', ats) arg_kinds = get_arg_kinds(ats) modes = getattr(term_cls, 'modes', None) mode = modes[iat] if modes is not None else None if 'dw_s_dot_grad_i_s' in term_cls.name: material_value = 0.0 else: material_value = 1.0 aux = make_term_args(arg_shapes, arg_kinds, ats, mode, domain, material_value=material_value, poly_space_base=poly_space_base) args, str_args, materials, variables = aux self.report('args:', str_args) name = term_call % (', '.join(str_args)) term =	Term.new(name, integral, domain.regions[rname], **args)	sfepy.terms.Term.new

---

Subsets and Splits

Run Query Ctrl+↵

• Saved Queries
• Top Community Queries

No community queries yet

The top public SQL queries from the community will appear here once available.