def refine_mesh(filename, level):
"""
Uniformly refine `level`-times a mesh given by `filename`.
The refined mesh is saved to a file with name constructed from base
name of `filename` and `level`-times appended `'_r'` suffix.
Parameters
----------
filename : str
The mesh file name.
level : int
The refinement level.
"""
import os
from sfepy.base.base import output
from sfepy.discrete.fem import Mesh, Domain
if level > 0:
mesh = Mesh.from_file(filename)
domain = Domain(mesh.name, mesh)
for ii in range(level):
output('refine %d...' % ii)
domain = domain.refine()
output('... %d nodes %d elements'
% (domain.shape.n_nod, domain.shape.n_el))
suffix = os.path.splitext(filename)[1]
filename = domain.name + suffix
domain.mesh.write(filename, io='auto')
return filename
def mesh_hook(mesh, mode):
"""
Load and refine a mesh here.
"""
if mode == 'read':
mesh = Mesh.from_file(base_mesh)
domain = Domain(mesh.name, mesh)
for ii in range(3):
output('refine %d...' % ii)
domain = domain.refine()
output('... %d nodes %d elements'
% (domain.shape.n_nod, domain.shape.n_el))
domain.mesh.name = '2_4_2_refined'
return domain.mesh
elif mode == 'write':
pass
def refine_reference(geometry, level):
"""
Refine reference element given by `geometry`.
Notes
-----
The error edges must be generated in the order of the connectivity
of the previous (lower) level.
"""
from sfepy.discrete.fem import Domain
from sfepy.discrete.fem.geometry_element import geometry_data
gcoors, gconn = geometry.coors, geometry.conn
if level == 0:
return gcoors, gconn
gd = geometry_data[geometry.name]
conn = nm.array([gd.conn], dtype=nm.int32)
mat_id = conn[:, 0].copy()
mat_id[:] = 0
mesh = Mesh.from_data('aux', gd.coors, None, [conn],
[mat_id], [geometry.name])
domain = Domain('aux', mesh)
for ii in range(level):
domain = domain.refine()
coors = domain.mesh.coors
conn = domain.mesh.conns[0]
n_el = conn.shape[0]
if geometry.name == '2_3':
aux_conn = conn.reshape((n_el / 4, 4, 3))
ir = [[0, 1, 2], [2, 2, 3], [3, 3, 0]]
ic = [[0, 0, 0], [0, 1, 0], [0, 1, 0]]
elif geometry.name == '2_4':
aux_conn = conn.reshape((n_el / 4, 4, 4))
ir = [[0, 0, 1], [1, 1, 2], [2, 2, 3], [3, 3, 0], [0, 0, 2], [3, 3, 1]]
ic = [[0, 1, 0], [0, 1, 0], [0, 1, 0], [0, 1, 0], [1, 2, 1], [1, 2, 1]]
elif geometry.name == '3_4':
aux_conn = conn.reshape((n_el / 8, 8, 4))
ir = [[0, 0, 1], [1, 1, 2], [2, 0, 0], [3, 1, 1], [3, 2, 2], [3, 0, 0]]
ic = [[0, 1, 1], [1, 2, 2], [2, 2, 0], [3, 3, 1], [3, 3, 2], [3, 3, 0]]
elif geometry.name == '3_8':
aux_conn = conn.reshape((n_el / 8, 8, 8))
ir = [[0, 0, 1], [1, 1, 2], [2, 2, 3], [3, 0, 0], [0, 0, 2], [0, 0, 1],
[0, 0, 1], [1, 1, 2], [2, 2, 3], [3, 0, 0], [0, 0, 2], [0, 0, 1],
[4, 4, 5], [5, 5, 6], [6, 6, 7], [7, 4, 4], [4, 4, 6], [4, 4, 5],
[0, 0, 4], [1, 1, 5], [2, 2, 6], [3, 3, 7],
[0, 0, 4], [1, 1, 5], [2, 2, 6], [0, 0, 4],
[0, 0, 4]]
ic = [[0, 1, 0], [0, 1, 0], [0, 1, 0], [0, 3, 0], [1, 2, 1], [3, 2, 1],
[4, 5, 4], [4, 5, 4], [4, 5, 4], [4, 7, 4], [5, 6, 5], [7, 6, 5],
[0, 3, 0], [0, 3, 0], [0, 3, 0], [0, 1, 0], [3, 2, 3], [1, 2, 3],
[0, 4, 0], [0, 4, 0], [0, 4, 0], [0, 4, 0],
[1, 5, 3], [1, 5, 3], [1, 5, 3], [3, 7, 1],
[2, 6, 2]]
else:
raise ValueError('unsupported geometry! (%s)' % geometry.name)
conn = nm.array(conn, dtype=nm.int32)
error_edges = aux_conn[:, ir, ic]
return coors, conn, error_edges
def test_linearization(self):
from sfepy.base.base import Struct
from sfepy.discrete.fem import Mesh, Domain, Field
from sfepy import data_dir
geometries = ["2_3", "2_4", "3_4", "3_8"]
approx_orders = [1, 2]
funs = [nm.cos, nm.sin, lambda x: x]
ok = True
for geometry in geometries:
name = os.path.join(data_dir, "meshes/elements/%s_1.mesh" % geometry)
mesh = Mesh.from_file(name)
domain = Domain("", mesh)
domain = domain.refine()
domain.mesh.write(self.join("linearizer-%s-0.mesh" % geometry))
omega = domain.create_region("Omega", "all")
for approx_order in approx_orders:
for dpn in [1, mesh.dim]:
self.report("geometry: %s, approx. order: %d, dpn: %d" % (geometry, approx_order, dpn))
field = Field.from_args("fu", nm.float64, dpn, omega, approx_order=approx_order)
cc = field.get_coor()
dofs = nm.zeros((field.n_nod, dpn), dtype=nm.float64)
for ic in range(dpn):
dofs[:, ic] = funs[ic](3 * (cc[:, 0] * cc[:, 1]))
vmesh, vdofs, levels = field.linearize(dofs, min_level=0, max_level=3, eps=1e-2)
level = levels[0]
if approx_order == 1:
_ok = level == 0
else:
_ok = level > 0
self.report("max. refinement level: %d: %s" % (level, _ok))
ok = ok and _ok
rdofs = nm.zeros((vmesh.n_nod, dpn), dtype=nm.float64)
cc = vmesh.coors
for ic in range(dpn):
rdofs[:, ic] = funs[ic](3 * (cc[:, 0] * cc[:, 1]))
_ok = nm.allclose(rdofs, vdofs, rtol=0.0, atol=0.03)
self.report("interpolation: %s" % _ok)
ok = ok and _ok
out = {"u": Struct(name="output_data", mode="vertex", data=vdofs, var_name="u", dofs=None)}
name = self.join("linearizer-%s-%d-%d" % (geometry, approx_order, dpn))
vmesh.write(name + ".mesh")
vmesh.write(name + ".vtk", out=out)
return ok
def main():
parser = OptionParser(usage=usage)
parser.add_option('-s', '--scale', metavar='scale',
action='store', dest='scale',
default=None, help=help['scale'])
parser.add_option('-c', '--center', metavar='center',
action='store', dest='center',
default=None, help=help['center'])
parser.add_option('-r', '--refine', metavar='level',
action='store', type=int, dest='refine',
default=0, help=help['refine'])
parser.add_option('-f', '--format', metavar='format',
action='store', type='string', dest='format',
default=None, help=help['format'])
parser.add_option('-l', '--list', action='store_true',
dest='list', help=help['list'])
(options, args) = parser.parse_args()
if options.list:
output_writable_meshes()
sys.exit(0)
if len(args) != 2:
parser.print_help()
sys.exit(1)
scale = _parse_val_or_vec(options.scale, 'scale', parser)
center = _parse_val_or_vec(options.center, 'center', parser)
filename_in, filename_out = args
mesh = Mesh.from_file(filename_in)
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 = Domain(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
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')