def refine_region(domain0, region0, region1):
"""
Coarse cell sub_cells[ii, 0] in mesh0 is split into sub_cells[ii, 1:] in
mesh1.
The new fine cells are interleaved among the original coarse cells so that
the indices of the coarse cells do not change.
The cell groups are preserved. The vertex groups are preserved only in the
coarse (non-refined) cells.
"""
if region1 is None:
return domain0, None
mesh0 = domain0.mesh
mesh1 = Mesh.from_region(region1, mesh0)
domain1 = FEDomain('d', mesh1)
domain1r = domain1.refine()
mesh1r = domain1r.mesh
n_cell = region1.shape.n_cell
n_sub = 4 if mesh0.cmesh.tdim == 2 else 8
sub_cells = nm.empty((n_cell, n_sub + 1), dtype=nm.uint32)
sub_cells[:, 0] = region1.cells
sub_cells[:, 1] = region1.cells
aux = nm.arange((n_sub - 1) * n_cell, dtype=nm.uint32)
sub_cells[:, 2:] = mesh0.n_el + aux.reshape((n_cell, -1))
coors0, vgs0, conns0, mat_ids0, descs0 = mesh0._get_io_data()
coors, vgs, _conns, _mat_ids, descs = mesh1r._get_io_data()
# Preserve vertex groups of non-refined cells.
vgs[:len(vgs0)] = vgs0
def _interleave_refined(c0, c1):
if c1.ndim == 1:
c0 = c0[:, None]
c1 = c1[:, None]
n_row, n_col = c1.shape
n_new = region0.shape.n_cell + n_row
out = nm.empty((n_new, n_col), dtype=c0.dtype)
out[region0.cells] = c0[region0.cells]
out[region1.cells] = c1[::n_sub]
aux = c1.reshape((-1, n_col * n_sub))
out[mesh0.n_el:] = aux[:, n_col:].reshape((-1, n_col))
return out
conn = _interleave_refined(conns0[0], _conns[0])
mat_id = _interleave_refined(mat_ids0[0], _mat_ids[0]).squeeze()
mesh = Mesh.from_data('a', coors, vgs, [conn], [mat_id], descs)
domain = FEDomain('d', mesh)
return domain, sub_cells
def test_interpolation_two_meshes(self):
from sfepy import data_dir
from sfepy.discrete import Variables
from sfepy.discrete.fem import Mesh, FEDomain, Field
m1 = Mesh.from_file(data_dir + '/meshes/3d/block.mesh')
m2 = Mesh.from_file(data_dir + '/meshes/3d/cube_medium_tetra.mesh')
m2.coors[:] *= 2.0
bbox = m1.get_bounding_box()
dd = bbox[1, :] - bbox[0, :]
data = nm.sin(4.0 * nm.pi * m1.coors[:,0:1] / dd[0]) \
* nm.cos(4.0 * nm.pi * m1.coors[:,1:2] / dd[1])
variables1 = {
'u': ('unknown field', 'scalar_tp', 0),
'v': ('test field', 'scalar_tp', 'u'),
}
variables2 = {
'u': ('unknown field', 'scalar_si', 0),
'v': ('test field', 'scalar_si', 'u'),
}
d1 = FEDomain('d1', m1)
omega1 = d1.create_region('Omega', 'all')
field1 = Field.from_args('scalar_tp',
nm.float64, (1, 1),
omega1,
approx_order=1)
ff1 = {field1.name: field1}
d2 = FEDomain('d2', m2)
omega2 = d2.create_region('Omega', 'all')
field2 = Field.from_args('scalar_si',
nm.float64, (1, 1),
omega2,
approx_order=0)
ff2 = {field2.name: field2}
vv1 = Variables.from_conf(transform_variables(variables1), ff1)
u1 = vv1['u']
u1.set_from_mesh_vertices(data)
vv2 = Variables.from_conf(transform_variables(variables2), ff2)
u2 = vv2['u']
# Performs interpolation, if other field differs from self.field
# or, in particular, is defined on a different mesh.
u2.set_from_other(u1, strategy='interpolation', close_limit=0.1)
fname = in_dir(self.options.out_dir)
u1.save_as_mesh(fname('test_mesh_interp_block_scalar.vtk'))
u2.save_as_mesh(fname('test_mesh_interp_cube_scalar.vtk'))
return True
def do_interpolation(m2, m1, data, field_name, force=False):
"""Interpolate data from m1 to m2. """
from sfepy.discrete import Variables
from sfepy.discrete.fem import FEDomain, Field
fields = {
'scalar_si': ((1, 1), 'Omega', 2),
'vector_si': ((3, 1), 'Omega', 2),
'scalar_tp': ((1, 1), 'Omega', 1),
'vector_tp': ((3, 1), 'Omega', 1),
}
d1 = FEDomain('d1', m1)
omega1 = d1.create_region('Omega', 'all')
f = fields[field_name]
field1 = Field.from_args('f',
nm.float64,
f[0],
d1.regions[f[1]],
approx_order=f[2])
ff = {field1.name: field1}
vv = Variables.from_conf(transform_variables(variables), ff)
u1 = vv['u']
u1.set_from_mesh_vertices(data)
d2 = FEDomain('d2', m2)
omega2 = d2.create_region('Omega', 'all')
field2 = Field.from_args('f',
nm.float64,
f[0],
d2.regions[f[1]],
approx_order=f[2])
ff2 = {field2.name: field2}
vv2 = Variables.from_conf(transform_variables(variables), ff2)
u2 = vv2['u']
if not force:
# Performs interpolation, if other field differs from self.field
# or, in particular, is defined on a different mesh.
u2.set_from_other(u1, strategy='interpolation', close_limit=0.5)
else:
coors = u2.field.get_coor()
vals = u1.evaluate_at(coors, close_limit=0.5)
u2.set_data(vals)
return u1, u2
def prepare_dgfield(approx_order, mesh):
domain = FEDomain("test_domain", mesh)
omega = domain.create_region('Omega', 'all')
regions = {}
if mesh.dim > 1:
left = domain.create_region('left',
'vertices in x == 0',
'edge')
right = domain.create_region('right',
'vertices in x == 1',
'edge')
bottom = domain.create_region('bottom',
'vertices in y == 0',
'edge')
top = domain.create_region('top',
'vertices in y == 1',
'edge')
regions.update({"top": top, "bottom": bottom})
else:
left = domain.create_region('left',
'vertices in x == 0',
'vertex')
right = domain.create_region('right',
'vertices in x == 1',
'vertex')
regions.update({"left": left, "right": right, "omega" : omega})
field = DGField('dgfu', nm.float64, 'scalar', omega,
approx_order=approx_order)
return field, regions
def from_conf(conf, options):
from sfepy.discrete import FieldVariable, Variables, Problem
from sfepy.discrete.fem import Mesh, FEDomain, Field
mesh = Mesh.from_file(data_dir + '/meshes/2d/square_unit_tri.mesh')
domain = FEDomain('domain', mesh)
omega = domain.create_region('Omega', 'all')
domain.create_region('Left', 'vertices in (x < -0.499)', 'facet')
domain.create_region(
'LeftStrip', 'vertices in (x < -0.499)'
' & (y > -0.199) & (y < 0.199)', 'facet')
domain.create_region('LeftFix', 'r.Left -v r.LeftStrip', 'facet')
domain.create_region('Right', 'vertices in (x > 0.499)', 'facet')
domain.create_region(
'RightStrip', 'vertices in (x > 0.499)'
' & (y > -0.199) & (y < 0.199)', 'facet')
domain.create_region('RightFix', 'r.Right -v r.RightStrip', 'facet')
fu = Field.from_args('fu', nm.float64, 'vector', omega, approx_order=2)
u = FieldVariable('u', 'unknown', fu)
fp = Field.from_args('fp', nm.float64, 'scalar', omega, approx_order=2)
p = FieldVariable('p', 'unknown', fp)
pb = Problem('test', domain=domain, fields=[fu, fp], auto_conf=False)
test = Test(problem=pb,
variables=Variables([u, p]),
conf=conf,
options=options)
return test
def from_conf(conf, options):
import sfepy
from sfepy.discrete.fem import Mesh, FEDomain, Field
mesh = Mesh.from_file('meshes/2d/rectangle_tri.mesh',
prefix_dir=sfepy.data_dir)
domain = FEDomain('domain', mesh)
dim = domain.shape.dim
min_x, max_x = domain.get_mesh_bounding_box()[:,0]
eps = 1e-8 * (max_x - min_x)
omega = domain.create_region('Omega', 'all')
gamma1 = domain.create_region('Gamma1',
'vertices in x < %.10f' % (min_x + eps),
'facet')
gamma2 = domain.create_region('Gamma2',
'vertices in x > %.10f' % (max_x - eps),
'facet')
field = Field.from_args('fu', nm.float64, 'vector', omega,
approx_order=2)
test = Test(conf=conf, options=options, dim=dim,
omega=omega, gamma1=gamma1, gamma2=gamma2,
field=field)
return test
def prepare_variable(filename, n_components):
from sfepy.discrete import FieldVariable
from sfepy.discrete.fem import Mesh, FEDomain, Field
mesh = Mesh.from_file(filename)
bbox = mesh.get_bounding_box()
dd = bbox[1, :] - bbox[0, :]
data = (nm.sin(4.0 * nm.pi * mesh.coors[:, 0:1] / dd[0]) *
nm.cos(4.0 * nm.pi * mesh.coors[:, 1:2] / dd[1]))
domain = FEDomain('domain', mesh)
omega = domain.create_region('Omega', 'all')
field = Field.from_args('field',
nm.float64,
n_components,
omega,
approx_order=2)
u = FieldVariable('u',
'parameter',
field,
primary_var_name='(set-to-None)')
u.set_from_mesh_vertices(data * nm.arange(1, n_components + 1)[None, :])
return u
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, FEDomain
if level > 0:
mesh = Mesh.from_file(filename)
domain = FEDomain(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 _get_bqp(geometry, order):
from sfepy.discrete import Integral
from sfepy.discrete.fem.geometry_element import GeometryElement
from sfepy.discrete.fem import Mesh, FEDomain, Field
gel = GeometryElement(geometry)
mesh = Mesh.from_data('aux', gel.coors, None, [gel.conn[None, :]], [[0]],
[geometry])
domain = FEDomain('domain', mesh)
omega = domain.create_region('Omega', 'all')
surf = domain.create_region('Surf', 'vertices of surface', 'facet')
field = Field.from_args('f',
nm.float64,
shape=1,
region=omega,
approx_order=1)
field.setup_surface_data(surf)
integral = Integral('aux', order=order)
field.create_bqp('Surf', integral)
sd = field.surface_data['Surf']
qp = field.qp_coors[(integral.order, sd.bkey)]
output('geometry:', geometry, 'order:', order, 'num. points:',
qp.vals.shape[1], 'true_order:',
integral.qps[gel.surface_facet_name].order)
output('min. weight:', qp.weights.min())
output('max. weight:', qp.weights.max())
return (gel, qp.vals.reshape(
(-1, mesh.dim)), nm.tile(qp.weights, qp.vals.shape[0]))
def test_refine_3_8(self):
mesh = Mesh('3_8', data_dir + '/meshes/elements/3_8_1.mesh')
domain = refine(FEDomain('domain', mesh), self.options.out_dir, 1)
ok = compare_mesh('3_8', domain.mesh.coors, domain.mesh.conns[0])
return ok
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 main():
parser = ArgumentParser(description=__doc__)
parser.add_argument('--version', action='version', version='%(prog)s')
parser.add_argument('filename')
options = parser.parse_args()
filename = options.filename
mesh = Mesh.from_file(filename)
output('Mesh:')
output(' dimension: %d, vertices: %d, elements: %d'
% (mesh.dim, mesh.n_nod, mesh.n_el))
domain = FEDomain('domain', mesh)
output(domain.cmesh)
domain.cmesh.cprint(1)
dim = domain.cmesh.dim
entities_opts = [
{'color' : 'k', 'label_global' : 12, 'label_local' : 8},
{'color' : 'b', 'label_global' : 12, 'label_local' : 8},
{'color' : 'g', 'label_global' : 12, 'label_local' : 8},
{'color' : 'r', 'label_global' : 12},
]
if dim == 2: entities_opts.pop(2)
pc.plot_cmesh(None, domain.cmesh,
wireframe_opts = {'color' : 'k'},
entities_opts=entities_opts)
plt.show()
def solveLaplaceEquationTetrahedral(mesh, meshVTK, boundaryPoints,
boundaryConditions):
"""
mesh: path to a 3D mesh / sfepy mesh
"""
if isinstance(mesh, str):
mesh = Mesh.from_file(mesh)
#Set domains
domain = FEDomain('domain', mesh)
omega = domain.create_region('Omega', 'all')
boundary = domain.create_region(
'gamma',
'vertex %s' % ','.join(map(str, range(meshVTK.GetNumberOfPoints()))),
'facet')
#set fields
field = Field.from_args('fu', np.float64, 1, omega, approx_order=1)
u = FieldVariable('u', 'unknown', field)
v = FieldVariable('v', 'test', field, primary_var_name='u')
m = Material('m', val=[1.])
#Define element integrals
integral = Integral('i', order=3)
#Equations defining
t1 = Term.new('dw_laplace( v, u )', integral, omega, v=v, u=u)
eq = Equation('balance', t1)
eqs = Equations([eq])
heatBoundary = boundaryConditions
points = boundaryPoints
#Boundary conditions
c = ClosestPointStupid(points, heatBoundary, meshVTK)
def u_fun(ts, coors, bc=None, problem=None, c=c):
c.distances = []
v = np.zeros(len(coors))
for i, p in enumerate(coors):
v[i] = c.interpolate(p)
#c.findClosestPoint(p)
return v
bc_fun = Function('u_fun', u_fun)
fix1 = EssentialBC('fix_u', boundary, {'u.all': bc_fun})
#Solve problem
ls = ScipyDirect({})
nls = Newton({}, lin_solver=ls)
pb = Problem('heat', equations=eqs)
pb.set_bcs(ebcs=Conditions([fix1]))
pb.set_solver(nls)
state = pb.solve(verbose=False, save_results=False)
u = state.get_parts()['u']
return u
def test_refine_hexa(self):
mesh = Mesh('mesh_hexa',
data_dir + '/meshes/various_formats/abaqus_hex.inp')
domain = FEDomain('domain', mesh)
refine(domain, self.options.out_dir)
return True
def test_refine_3_4(self):
mesh = Mesh.from_file(data_dir + '/meshes/elements/3_4_1.mesh')
domain = refine(FEDomain('domain', mesh), self.options.out_dir, 1)
ok = compare_mesh('3_4', domain.mesh.coors,
domain.mesh.get_conn('3_4'))
return ok
def test_refine_hexa(self):
filename = data_dir + '/meshes/various_formats/abaqus_hex.inp'
mesh = Mesh.from_file(filename)
domain = FEDomain('domain', mesh)
refine(domain, self.options.out_dir)
return True
def main():
parser = ArgumentParser(description=__doc__,
formatter_class=RawDescriptionHelpFormatter)
parser.add_argument('--version', action='version', version='%(prog)s')
parser.add_argument('-d',
'--dims',
metavar='dims',
action='store',
dest='dims',
default='[1.0, 1.0]',
help=helps['dims'])
parser.add_argument('-c',
'--centre',
metavar='centre',
action='store',
dest='centre',
default='[0.0, 0.0]',
help=helps['centre'])
parser.add_argument('-s',
'--shape',
metavar='shape',
action='store',
dest='shape',
default='[11, 11]',
help=helps['shape'])
parser.add_argument('--show',
action="store_true",
dest='show',
default=False,
help=helps['show'])
options = parser.parse_args()
dims = nm.array(eval(options.dims), dtype=nm.float64)
centre = nm.array(eval(options.centre), dtype=nm.float64)
shape = nm.array(eval(options.shape), dtype=nm.int32)
output('dimensions:', dims)
output('centre: ', centre)
output('shape: ', shape)
mesh = gen_block_mesh(dims, shape, centre, name='block-fem')
fe_domain = FEDomain('domain', mesh)
pb, state = run(fe_domain, 1)
pb.save_state('laplace_shifted_periodic.vtk', state)
if options.show:
from sfepy.postprocess.viewer import Viewer
from sfepy.postprocess.domain_specific import DomainSpecificPlot
view = Viewer('laplace_shifted_periodic.vtk')
view(rel_scaling=1,
domain_specific={
'u': DomainSpecificPlot('plot_warp_scalar', ['rel_scaling=1'])
},
is_scalar_bar=True,
is_wireframe=True,
opacity=0.3)
def test_projection_iga_fem(self):
from sfepy.discrete import FieldVariable
from sfepy.discrete.fem import FEDomain, Field
from sfepy.discrete.iga.domain import IGDomain
from sfepy.mesh.mesh_generators import gen_block_mesh
from sfepy.discrete.iga.domain_generators import gen_patch_block_domain
from sfepy.discrete.projections import (make_l2_projection,
make_l2_projection_data)
shape = [10, 12, 12]
dims = [5, 6, 6]
centre = [0, 0, 0]
degrees = [2, 2, 2]
nurbs, bmesh, regions = gen_patch_block_domain(dims, shape, centre,
degrees,
cp_mode='greville',
name='iga')
ig_domain = IGDomain('iga', nurbs, bmesh, regions=regions)
ig_omega = ig_domain.create_region('Omega', 'all')
ig_field = Field.from_args('iga', nm.float64, 1, ig_omega,
approx_order='iga', poly_space_base='iga')
ig_u = FieldVariable('ig_u', 'parameter', ig_field,
primary_var_name='(set-to-None)')
mesh = gen_block_mesh(dims, shape, centre, name='fem')
fe_domain = FEDomain('fem', mesh)
fe_omega = fe_domain.create_region('Omega', 'all')
fe_field = Field.from_args('fem', nm.float64, 1, fe_omega,
approx_order=2)
fe_u = FieldVariable('fe_u', 'parameter', fe_field,
primary_var_name='(set-to-None)')
def _eval_data(ts, coors, mode, **kwargs):
return nm.prod(coors**2, axis=1)[:, None, None]
make_l2_projection_data(ig_u, _eval_data)
make_l2_projection(fe_u, ig_u) # This calls ig_u.evaluate_at().
coors = 0.5 * nm.random.rand(20, 3) * dims
ig_vals = ig_u.evaluate_at(coors)
fe_vals = fe_u.evaluate_at(coors)
ok = nm.allclose(ig_vals, fe_vals, rtol=0.0, atol=1e-12)
if not ok:
self.report('iga-fem projection failed!')
self.report('coors:')
self.report(coors)
self.report('iga fem diff:')
self.report(nm.c_[ig_vals, fe_vals, nm.abs(ig_vals - fe_vals)])
return ok
def from_conf(conf, options):
mesh = Mesh.from_file('meshes/2d/square_unit_tri.mesh',
prefix_dir=sfepy.data_dir)
domain = FEDomain('domain', mesh)
omega = domain.create_region('Omega', 'all')
field = Field.from_args('linear', nm.float64, 'scalar', omega,
approx_order=1)
test = Test(conf=conf, options=options, omega=omega, field=field)
return test
def test_evaluate_at(self):
from sfepy import data_dir
from sfepy.discrete.fem import Mesh
from sfepy.discrete import Variables
from sfepy.discrete.fem import FEDomain, Field
meshes = {
'tp': Mesh.from_file(data_dir + '/meshes/3d/block.mesh'),
}
datas = gen_datas(meshes)
fields = {
'scalar_tp': ((1, 1), 'Omega', 1),
'vector_tp': ((3, 1), 'Omega', 1),
}
ok = True
for field_name in ['scalar_tp', 'vector_tp']:
d = FEDomain('d', meshes['tp'])
d.create_region('Omega', 'all')
f = fields[field_name]
field = Field.from_args('f',
nm.complex128,
f[0],
d.regions[f[1]],
approx_order=f[2])
ff = {field.name: field}
vv = Variables.from_conf(transform_variables(variables), ff)
u = vv['u']
bbox = d.get_mesh_bounding_box()
t = nm.expand_dims(nm.linspace(0, 1, 100), 1)
coors = nm.expand_dims(bbox[1] - bbox[0], 0) * t + bbox[0]
data_r = datas[field_name]
data_i = 2. / (1 + datas[field_name])
u.set_from_mesh_vertices(data_r)
vals_r = u.evaluate_at(coors)
u.set_from_mesh_vertices(data_i)
vals_i = u.evaluate_at(coors)
u.set_from_mesh_vertices(data_r + data_i * 1j)
vals = u.evaluate_at(coors)
_ok = nm.allclose(vals_r + vals_i * 1j, vals, rtol=0.0, atol=1e-12)
_ok = _ok and nm.abs(vals).sum() > 1
self.report('evaluating complex field %s: %s' % (field_name, _ok))
ok = ok and _ok
return ok
def test_normals(self):
"""
Check orientations of surface normals on the reference elements.
"""
import sfepy
from sfepy.discrete import Integral
from sfepy.discrete.fem import Mesh, FEDomain
from sfepy.discrete.fem.poly_spaces import PolySpace
from sfepy.discrete.fem.mappings import SurfaceMapping
from sfepy.linalg import normalize_vectors
ok = True
for geom in ['2_3', '2_4', '3_4', '3_8']:
mesh = Mesh.from_file('meshes/elements/%s_1.mesh' % geom,
prefix_dir=sfepy.data_dir)
domain = FEDomain('domain', mesh)
surface = domain.create_region('Surface', 'vertices of surface',
'facet')
domain.create_surface_group(surface)
sd = domain.surface_groups[surface.name]
coors = domain.get_mesh_coors()
gel = domain.geom_els[geom].surface_facet
ps = PolySpace.any_from_args('aux', gel, 1)
mapping = SurfaceMapping(coors, sd.get_connectivity(), ps)
integral = Integral('i', order=1)
vals, weights = integral.get_qp(gel.name)
# Evaluate just in the first quadrature point...
geo = mapping.get_mapping(vals[:1], weights[:1])
expected = expected_normals[geom].copy()
normalize_vectors(expected)
_ok = nm.allclose(expected,
geo.normal[:, 0, :, 0],
rtol=0.0,
atol=1e-14)
self.report('%s: %s' % (geom, _ok))
if not _ok:
self.report('expected:')
self.report(expected)
self.report('actual:')
self.report(geo.normal[:, 0, :, 0])
ok = ok and _ok
return ok
def make_domain(dims, shape, transform=None):
"""
Generate a 2D rectangle domain in 3D space, define regions.
"""
xmin = (-0.5 + 1e-12) * dims[0]
xmax = (0.5 - 1e-12) * dims[0]
mesh = make_mesh(dims, shape, transform=transform)
domain = FEDomain('domain', mesh)
domain.create_region('Omega', 'all')
domain.create_region('Gamma1', 'vertices in (x < %.14f)' % xmin, 'facet')
domain.create_region('Gamma2', 'vertices in (x > %.14f)' % xmax, 'facet')
return domain
def main():
parser = OptionParser(usage=usage, version='%prog')
options, args = parser.parse_args()
if len(args) == 1:
filename = args[0]
else:
parser.print_help(),
return
mesh = Mesh.from_file(filename)
output('Mesh:')
output(' dimension: %d, vertices: %d, elements: %d' %
(mesh.dim, mesh.n_nod, mesh.n_el))
domain = FEDomain('domain', mesh)
output(domain.cmesh)
domain.cmesh.cprint(1)
dim = domain.cmesh.dim
entities_opts = [
{
'color': 'k',
'label_global': 12,
'label_local': 8
},
{
'color': 'b',
'label_global': 12,
'label_local': 8
},
{
'color': 'g',
'label_global': 12,
'label_local': 8
},
{
'color': 'r',
'label_global': 12
},
]
if dim == 2: entities_opts.pop(2)
pc.plot_cmesh(None,
domain.cmesh,
wireframe_opts={'color': 'k'},
entities_opts=entities_opts)
plt.show()
def test_projection_tri_quad(self):
from sfepy.discrete.projections import make_l2_projection
source = FieldVariable('us', 'unknown', self.field)
coors = self.field.get_coor()
vals = nm.sin(2.0 * nm.pi * coors[:, 0] * coors[:, 1])
source.set_data(vals)
name = op.join(self.options.out_dir,
'test_projection_tri_quad_source.vtk')
source.save_as_mesh(name)
mesh = Mesh.from_file('meshes/2d/square_quad.mesh',
prefix_dir=sfepy.data_dir)
domain = FEDomain('domain', mesh)
omega = domain.create_region('Omega', 'all')
field = Field.from_args('bilinear',
nm.float64,
'scalar',
omega,
approx_order=1)
target = FieldVariable('ut', 'unknown', field)
make_l2_projection(target, source)
name = op.join(self.options.out_dir,
'test_projection_tri_quad_target.vtk')
target.save_as_mesh(name)
bbox = self.field.domain.get_mesh_bounding_box()
x = nm.linspace(bbox[0, 0] + 0.001, bbox[1, 0] - 0.001, 20)
y = nm.linspace(bbox[0, 1] + 0.001, bbox[1, 1] - 0.001, 20)
xx, yy = nm.meshgrid(x, y)
test_coors = nm.c_[xx.ravel(), yy.ravel()].copy()
vec1 = source.evaluate_at(test_coors)
vec2 = target.evaluate_at(test_coors)
ok = (nm.abs(vec1 - vec2) < 0.01).all()
return ok
def from_conf( conf, options ):
from sfepy import data_dir
from sfepy.discrete.fem import Mesh, FEDomain
from sfepy.discrete import Functions
mesh = Mesh.from_file(data_dir
+ '/meshes/various_formats/abaqus_tet.inp')
mesh.nodal_bcs['set0'] = [0, 7]
domain = FEDomain('test domain', mesh)
conf_functions = {
'get_vertices' : (get_vertices,),
'get_cells' : (get_cells,),
}
functions = Functions.from_conf(transform_functions(conf_functions))
test = Test(conf=conf, options=options,
domain=domain, functions=functions)
return test
def mesh_hook(mesh, mode):
"""
Load and refine a mesh here.
"""
if mode == 'read':
mesh = Mesh.from_file(base_mesh)
domain = FEDomain(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 linear_projection(pb, cval):
from sfepy.discrete import (FieldVariable, Material, Integral, Equation,
Equations, Problem)
from sfepy.discrete.fem import Mesh, FEDomain, Field
from sfepy.terms import Term
from sfepy.solvers.ls import ScipyDirect
from sfepy.solvers.nls import Newton
from sfepy.base.base import IndexedStruct
mesh = Mesh.from_file(pb.conf.filename_mesh)
domain = FEDomain('domain', mesh)
omega = domain.create_region('Omega', 'all')
field = Field.from_args('scf', nm.float64, 'scalar', omega, approx_order=1)
g = FieldVariable('g', 'unknown', field)
f = FieldVariable('f', 'test', field, primary_var_name='g')
integral = Integral('i', order=2)
m = Material('m', function=set_grad)
t1 = Term.new('dw_volume_dot(f, g)', integral, omega, f=f, g=g)
t2 = Term.new('dw_volume_lvf(m.cs, f)', integral, omega, m=m, f=f)
eq = Equation('balance', t1 - t2)
eqs = Equations([eq])
ls = ScipyDirect({})
nls_status = IndexedStruct()
nls = Newton({'eps_a': 1e-15}, lin_solver=ls, status=nls_status)
pb = Problem('elasticity', equations=eqs)
pb.set_solver(nls)
out = nm.empty((g.n_dof, cval.shape[2]), dtype=nm.float64)
for ii in range(cval.shape[2]):
pb.data = nm.ascontiguousarray(cval[:, :, ii, :])
pb.time_update()
state = pb.solve()
out[:, ii] = state.get_parts()['g']
return out
def main():
parser = OptionParser(usage=usage, version='%prog')
options, args = parser.parse_args()
if len(args) == 1:
filename = args[0]
else:
parser.print_help(),
return
mesh = Mesh.from_file(filename)
output('Mesh:')
output(' dimension: %d, vertices: %d, elements: %d' %
(mesh.dim, mesh.n_nod, mesh.n_el))
domain = FEDomain('domain', mesh)
output(domain.cmesh)
domain.cmesh.cprint(1)
dim = domain.cmesh.dim
ax = pc.plot_wireframe(None, domain.cmesh)
ax = pc.plot_entities(ax, domain.cmesh, 0, 'k')
ax = pc.label_global_entities(ax, domain.cmesh, 0, 'k', 12)
ax = pc.label_local_entities(ax, domain.cmesh, 0, 'k', 8)
ax = pc.plot_entities(ax, domain.cmesh, 1, 'b')
ax = pc.label_global_entities(ax, domain.cmesh, 1, 'b', 12)
ax = pc.label_local_entities(ax, domain.cmesh, 1, 'b', 8)
if dim == 3:
ax = pc.plot_entities(ax, domain.cmesh, 2, 'g')
ax = pc.label_global_entities(ax, domain.cmesh, 2, 'g', 12)
ax = pc.label_local_entities(ax, domain.cmesh, 2, 'g', 8)
ax = pc.plot_entities(ax, domain.cmesh, dim, 'r')
ax = pc.label_global_entities(ax, domain.cmesh, dim, 'r', 12)
pc.plt.show()
def test_laplace_shifted_periodic(self):
import numpy as nm
from sfepy.mesh.mesh_generators import gen_block_mesh
from sfepy.discrete.fem import FEDomain
from examples.diffusion.laplace_shifted_periodic import run
dims = [2.0, 1.0]
shape = [21, 11]
centre = [0.0, 0.0]
mesh = gen_block_mesh(dims, shape, centre, name='block-fem')
fe_domain = FEDomain('domain', mesh)
pb, state = run(fe_domain, 3)
gamma3 = pb.domain.regions['Gamma3']
gamma4 = pb.domain.regions['Gamma4']
field = pb.fields['fu']
# Check that the shift equals to one.
i3 = field.get_dofs_in_region(gamma3, merge=True)
i4 = field.get_dofs_in_region(gamma4, merge=True)
i_corners = nm.array([0, shape[0] - 1])
ii = nm.setdiff1d(nm.arange(len(i3)), i_corners)
vals = state()
shift = vals[i3] - vals[i4]
ok = (shift[i_corners] == 0.0).all()
ok = ok and nm.allclose(shift[ii], 1.0, rtol=0.0, atol=1e-14)
if not ok:
self.report('wrong shift:', shift)
return ok
def save_basis_on_mesh(mesh, options, output_dir, lin,
permutations=None, suffix=''):
if permutations is not None:
mesh = mesh.copy()
gel = GeometryElement(mesh.descs[0])
perms = gel.get_conn_permutations()[permutations]
conn = mesh.cmesh.get_cell_conn()
n_el, n_ep = conn.num, gel.n_vertex
offsets = nm.arange(n_el) * n_ep
conn.indices[:] = conn.indices.take((perms + offsets[:, None]).ravel())
domain = FEDomain('domain', mesh)
omega = domain.create_region('Omega', 'all')
field = Field.from_args('f', nm.float64, shape=1, region=omega,
approx_order=options.max_order,
poly_space_base=options.basis)
var = FieldVariable('u', 'unknown', field)
if options.plot_dofs:
import sfepy.postprocess.plot_dofs as pd
import sfepy.postprocess.plot_cmesh as pc
ax = pc.plot_wireframe(None, mesh.cmesh)
ax = pd.plot_global_dofs(ax, field.get_coor(), field.econn)
ax = pd.plot_local_dofs(ax, field.get_coor(), field.econn)
if options.dofs is not None:
ax = pd.plot_nodes(ax, field.get_coor(), field.econn,
field.poly_space.nodes,
get_dofs(options.dofs, var.n_dof))
pd.plt.show()
output('dofs: %d' % var.n_dof)
vec = nm.empty(var.n_dof, dtype=var.dtype)
n_digit, _format = get_print_info(var.n_dof, fill='0')
name_template = os.path.join(output_dir,
'dof_%s%s.vtk' % (_format, suffix))
for ip in get_dofs(options.dofs, var.n_dof):
output('dof %d...' % ip)
vec.fill(0.0)
vec[ip] = 1.0
var.set_data(vec)
if options.derivative == 0:
out = var.create_output(vec, linearization=lin)
else:
out = create_expression_output('ev_grad.ie.Elements(u)',
'u', 'f', {'f' : field}, None,
Variables([var]),
mode='qp', verbose=False,
min_level=lin.min_level,
max_level=lin.max_level,
eps=lin.eps)
name = name_template % ip
ensure_path(name)
out['u'].mesh.write(name, out=out)
output('...done (%s)' % name)
