def test_entity_volumes(self):
import sfepy
from sfepy.discrete.fem import Mesh, FEDomain
from sfepy.discrete.common import Field
from sfepy.discrete import Integral
mesh = Mesh.from_file('meshes/3d/special/cross3d.mesh',
prefix_dir=sfepy.data_dir)
domain = FEDomain('domain', mesh)
omega = domain.create_region('Omega', 'all')
gamma = domain.create_region('Gamma', 'vertices of surface', 'facet')
top = domain.create_region('Top', 'cell 2')
vfield = Field.from_args('v', nm.float64, 'scalar', omega,
approx_order=1)
sfield = Field.from_args('s', nm.float64, 'scalar', gamma,
approx_order=1)
integral = Integral('i', order=3)
vgeo, _ = vfield.get_mapping(omega, integral, 'volume')
domain.create_surface_group(gamma)
sgeo, _ = sfield.get_mapping(gamma, integral, 'surface')
evols = mesh.cmesh.get_volumes(1)
fvols = mesh.cmesh.get_volumes(2) # Approximate for non-planar faces.
cvols = mesh.cmesh.get_volumes(3)
ok = True
_ok = abs(cvols.sum() - vgeo.volume.sum()) < 1e-15
self.report('total cell volume: %s (ok: %s)' % (cvols.sum(), _ok))
ok = _ok and ok
top_evols = nm.array([ 1. , 1. ,
1. , 1. ,
0.7211102550927979, 0.7211102550927979,
0.7211102550927979, 0.7211102550927979,
1.16619037896906 , 1.16619037896906 ,
1.16619037896906 , 1.16619037896906 ])
_ok = nm.allclose(top_evols, evols[top.edges], rtol=0.0, atol=1e-15)
self.report('total top cell edge length: %s (ok: %s)'
% (evols[top.edges].sum(), _ok))
ok = _ok and ok
i1 = [5, 6, 8, 9]
i2 = nm.setdiff1d(nm.arange(len(gamma.faces)), i1)
aux = fvols[gamma.faces] - sgeo.volume.ravel()
_ok = nm.allclose(aux[i1], 0.10560208437556773, rtol=0.0, atol=1e-15)
ok = _ok and ok
self.report('non-planar faces diff: %s (ok: %s)' % (aux[i1], _ok))
_ok = (nm.abs(aux[i2]) < 1e-15).all()
self.report('max. planar faces diff: %s (ok: %s)'
% (nm.abs(aux[i2]).max(), _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 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 test_entity_volumes(self):
import sfepy
from sfepy.discrete.fem import Mesh, FEDomain
from sfepy.discrete.common import Field
from sfepy.discrete import Integral
mesh = Mesh.from_file('meshes/3d/special/cross3d.mesh',
prefix_dir=sfepy.data_dir)
domain = FEDomain('domain', mesh)
omega = domain.create_region('Omega', 'all')
gamma = domain.create_region('Gamma', 'vertices of surface', 'facet')
top = domain.create_region('Top', 'cell 2')
vfield = Field.from_args('v',
nm.float64,
'scalar',
omega,
approx_order=1)
sfield = Field.from_args('s',
nm.float64,
'scalar',
gamma,
approx_order=1)
integral = Integral('i', order=3)
vgeo, _ = vfield.get_mapping(omega, integral, 'volume')
domain.create_surface_group(gamma)
sgeo, _ = sfield.get_mapping(gamma, integral, 'surface')
evols = mesh.cmesh.get_volumes(1)
fvols = mesh.cmesh.get_volumes(2) # Approximate for non-planar faces.
cvols = mesh.cmesh.get_volumes(3)
ok = True
_ok = abs(cvols.sum() - vgeo.volume.sum()) < 1e-15
self.report('total cell volume: %s (ok: %s)' % (cvols.sum(), _ok))
ok = _ok and ok
top_evols = nm.array([
1., 1., 1., 1., 0.7211102550927979, 0.7211102550927979,
0.7211102550927979, 0.7211102550927979, 1.16619037896906,
1.16619037896906, 1.16619037896906, 1.16619037896906
])
_ok = nm.allclose(top_evols, evols[top.edges], rtol=0.0, atol=1e-15)
self.report('total top cell edge length: %s (ok: %s)' %
(evols[top.edges].sum(), _ok))
ok = _ok and ok
i1 = [5, 6, 8, 9]
i2 = nm.setdiff1d(nm.arange(len(gamma.faces)), i1)
aux = fvols[gamma.faces] - sgeo.volume.ravel()
_ok = nm.allclose(aux[i1], 0.10560208437556773, rtol=0.0, atol=1e-15)
ok = _ok and ok
self.report('non-planar faces diff: %s (ok: %s)' % (aux[i1], _ok))
_ok = (nm.abs(aux[i2]) < 1e-15).all()
self.report('max. planar faces diff: %s (ok: %s)' %
(nm.abs(aux[i2]).max(), _ok))
ok = _ok and ok
return ok
