def create_mapping(coors, gel, order):
"""
Create mapping from transformed (in `x-y` plane) element faces to
reference element faces.
Parameters
----------
coors : array
The transformed coordinates of element nodes, shape `(n_el,
n_ep, dim)`. The function verifies that the all `z` components
are zero.
gel : GeometryElement instance
The geometry element corresponding to the faces.
order : int
The polynomial order of the mapping.
Returns
-------
mapping : VolumeMapping instance
The reference element face mapping.
"""
# Strip 'z' component (should be 0 now...).
assert_(nm.allclose(coors[:, :, -1], 0.0, rtol=1e-12, atol=1e-12))
coors = coors[:, :, :-1].copy()
# Mapping from transformed element to reference element.
sh = coors.shape
seq_coors = coors.reshape((sh[0] * sh[1], sh[2]))
seq_conn = nm.arange(seq_coors.shape[0], dtype=nm.int32)
seq_conn.shape = sh[:2]
mapping = VolumeMapping(seq_coors, seq_conn, gel=gel, order=1)
return mapping
def describe_geometry(self, field, gtype, region, integral,
return_mapping=False):
"""
Compute jacobians, element volumes and base function derivatives
for Volume-type geometries (volume mappings), and jacobians,
normals and base function derivatives for Surface-type
geometries (surface mappings).
Notes
-----
- volume mappings can be defined on a part of an element group,
although the field has to be defined always on the whole group.
- surface mappings are defined on the surface region
- surface mappings require field order to be > 0
"""
domain = field.domain
group = domain.groups[self.ig]
coors = domain.get_mesh_coors(actual=True)
if gtype == 'volume':
qp = self.get_qp('v', integral)
iels = region.get_cells(self.ig)
geo_ps = self.interp.get_geom_poly_space('v')
ps = self.interp.poly_spaces['v']
bf = self.get_base('v', 0, integral, iels=iels)
conn = nm.take(group.conn, iels.astype(nm.int32), axis=0)
mapping = VolumeMapping(coors, conn, poly_space=geo_ps)
vg = mapping.get_mapping(qp.vals, qp.weights, poly_space=ps,
ori=self.ori)
out = vg
elif gtype == 'plate':
import sfepy.mechanics.membranes as mm
from sfepy.linalg import dot_sequences
qp = self.get_qp('v', integral)
iels = region.get_cells(self.ig)
ps = self.interp.poly_spaces['v']
bf = self.get_base('v', 0, integral, iels=iels)
conn = nm.take(group.conn, nm.int32(iels), axis=0)
ccoors = coors[conn]
# Coordinate transformation matrix (transposed!).
mtx_t = mm.create_transformation_matrix(ccoors)
# Transform coordinates to the local coordinate system.
coors_loc = dot_sequences((ccoors - ccoors[:, 0:1, :]), mtx_t)
# Mapping from transformed elements to reference elements.
mapping = mm.create_mapping(coors_loc, field.gel, 1)
vg = mapping.get_mapping(qp.vals, qp.weights, poly_space=ps,
ori=self.ori)
vg.mtx_t = mtx_t
out = vg
elif (gtype == 'surface') or (gtype == 'surface_extra'):
assert_(field.approx_order > 0)
if self.ori is not None:
msg = 'surface integrals do not work yet with the' \
' hierarchical basis!'
raise ValueError(msg)
sd = domain.surface_groups[self.ig][region.name]
esd = self.surface_data[region.name]
qp = self.get_qp(sd.face_type, integral)
geo_ps = self.interp.get_geom_poly_space(sd.face_type)
ps = self.interp.poly_spaces[esd.face_type]
bf = self.get_base(esd.face_type, 0, integral)
conn = sd.get_connectivity()
mapping = SurfaceMapping(coors, conn, poly_space=geo_ps)
sg = mapping.get_mapping(qp.vals, qp.weights, poly_space=ps,
mode=gtype)
if gtype == 'surface_extra':
sg.alloc_extra_data(self.n_ep['v'])
self.create_bqp(region.name, integral)
qp = self.qp_coors[(integral.name, esd.bkey)]
v_geo_ps = self.interp.get_geom_poly_space('v')
bf_bg = v_geo_ps.eval_base(qp.vals, diff=True)
ebf_bg = self.get_base(esd.bkey, 1, integral)
sg.evaluate_bfbgm(bf_bg, ebf_bg, coors, sd.fis, group.conn)
out = sg
elif gtype == 'point':
out = mapping = None
else:
raise ValueError('unknown geometry type: %s' % gtype)
if out is not None:
# Store the integral used.
out.integral = integral
out.qp = qp
out.ps = ps
# Update base.
out.bf[:] = bf
if return_mapping:
out = (out, mapping)
return out
def create_mapping(self, region, integral, integration,
return_mapping=True):
"""
Create a new reference mapping.
Compute jacobians, element volumes and base function derivatives
for Volume-type geometries (volume mappings), and jacobians,
normals and base function derivatives for Surface-type
geometries (surface mappings).
Notes
-----
- surface mappings are defined on the surface region
- surface mappings require field order to be > 0
"""
domain = self.domain
coors = domain.get_mesh_coors(actual=True)
dconn = domain.get_conn()
if integration == 'volume':
qp = self.get_qp('v', integral)
iels = region.get_cells()
geo_ps = self.gel.poly_space
ps = self.poly_space
bf = self.get_base('v', 0, integral, iels=iels)
conn = nm.take(dconn, iels.astype(nm.int32), axis=0)
mapping = VolumeMapping(coors, conn, poly_space=geo_ps)
vg = mapping.get_mapping(qp.vals, qp.weights, poly_space=ps,
ori=self.ori)
out = vg
elif integration == 'plate':
import sfepy.mechanics.membranes as mm
from sfepy.linalg import dot_sequences
qp = self.get_qp('v', integral)
iels = region.get_cells()
ps = self.interp.poly_spaces['v']
bf = self.get_base('v', 0, integral, iels=iels)
conn = nm.take(dconn, nm.int32(iels), axis=0)
ccoors = coors[conn]
# Coordinate transformation matrix (transposed!).
mtx_t = mm.create_transformation_matrix(ccoors)
# Transform coordinates to the local coordinate system.
coors_loc = dot_sequences((ccoors - ccoors[:, 0:1, :]), mtx_t)
# Mapping from transformed elements to reference elements.
mapping = mm.create_mapping(coors_loc, self.gel, 1)
vg = mapping.get_mapping(qp.vals, qp.weights, poly_space=ps,
ori=self.ori)
vg.mtx_t = mtx_t
out = vg
elif (integration == 'surface') or (integration == 'surface_extra'):
assert_(self.approx_order > 0)
if self.ori is not None:
msg = 'surface integrals do not work yet with the' \
' hierarchical basis!'
raise ValueError(msg)
sd = domain.surface_groups[region.name]
esd = self.surface_data[region.name]
geo_ps = self.gel.poly_space
ps = self.poly_space
conn = sd.get_connectivity()
mapping = SurfaceMapping(coors, conn, poly_space=geo_ps)
if not self.is_surface:
self.create_bqp(region.name, integral)
qp = self.qp_coors[(integral.order, esd.bkey)]
abf = ps.eval_base(qp.vals[0])
bf = abf[..., self.efaces[0]]
indx = self.gel.get_surface_entities()[0]
# Fix geometry element's 1st facet orientation for gradients.
indx = nm.roll(indx, -1)[::-1]
mapping.set_basis_indices(indx)
sg = mapping.get_mapping(qp.vals[0], qp.weights,
poly_space=Struct(n_nod=bf.shape[-1]),
mode=integration)
if integration == 'surface_extra':
sg.alloc_extra_data(self.econn.shape[1])
bf_bg = geo_ps.eval_base(qp.vals, diff=True)
ebf_bg = self.get_base(esd.bkey, 1, integral)
sg.evaluate_bfbgm(bf_bg, ebf_bg, coors, sd.fis, dconn)
else:
# Do not use BQP for surface fields.
qp = self.get_qp(sd.face_type, integral)
bf = ps.eval_base(qp.vals)
sg = mapping.get_mapping(qp.vals, qp.weights,
poly_space=Struct(n_nod=bf.shape[-1]),
mode=integration)
out = sg
elif integration == 'point':
out = mapping = None
else:
raise ValueError('unknown inegration geometry type: %s'
% integration)
if out is not None:
# Store the integral used.
out.integral = integral
out.qp = qp
out.ps = ps
# Update base.
out.bf[:] = bf
if return_mapping:
out = (out, mapping)
return out
def test_gradients(self):
from sfepy.discrete.fem.mappings import VolumeMapping
ok = True
orders = {'2_3' : 3, '2_4' : 3, '3_4' : 4, '3_8' : 3}
bads = []
bad_families = set()
for (geom, poly_space_base, qp_weights, mesh, ir, ic,
ap, ps, rrc, rcell, crc, ccell, vec,
edofs, fdofs) in _gen_common_data(orders, self.gels, self.report):
gel = self.gels[geom]
conn = mesh.get_conn(gel.name)
geo_ps = ap.interp.get_geom_poly_space('v')
rmapping = VolumeMapping(mesh.coors, conn[rcell:rcell+1],
poly_space=geo_ps)
rori = ap.ori[:1] if ap.ori is not None else None
rvg = rmapping.get_mapping(rrc, qp_weights,
poly_space=ps, ori=rori)
rbfg = rvg.bfg
cmapping = VolumeMapping(mesh.coors, conn[ccell:ccell+1],
poly_space=geo_ps)
cori = ap.ori[1:] if ap.ori is not None else None
cvg = cmapping.get_mapping(crc, qp_weights,
poly_space=ps, ori=cori)
cbfg = cvg.bfg
dofs = nm.r_[edofs, fdofs]
res = nm.zeros((2, dofs.shape[0]), dtype=nm.int32)
res[0, :] = dofs
for ii, ip in enumerate(dofs):
vec.fill(0.0)
vec[ip] = 1.0
evec = vec[ap.econn]
rvals = nm.dot(rbfg, evec[rcell])[0]
cvals = nm.dot(cbfg, evec[ccell])[0]
okx = nm.allclose(rvals[:, 0], cvals[:, 0],
atol=1e-12, rtol=0.0)
if gel.dim == 2:
oky = nm.allclose(rvals[:, 1], -cvals[:, 1],
atol=1e-12, rtol=0.0)
_ok = okx and oky
else:
oky = nm.allclose(rvals[:, 1], cvals[:, 1],
atol=1e-12, rtol=0.0)
okz = nm.allclose(rvals[:, 2], -cvals[:, 2],
atol=1e-12, rtol=0.0)
_ok = okx and oky and okz
res[1, ii] = _ok
if not _ok:
bads.append([geom, poly_space_base, ir, ic, ip])
bad_families.add((geom, poly_space_base))
ok = ok and _ok
self.report('results (dofs, status: 1 ok, 0 failure):\n%s' % res)
if not ok:
self.report('gradient continuity errors:\n', bads)
self.report('%d in total!' % len(bads))
self.report('gradient continuity errors occurred in these'
' spaces:\n', bad_families)
return ok
def create_mapping(self,
region,
integral,
integration,
return_mapping=True):
"""
Create a new reference mapping.
Compute jacobians, element volumes and base function derivatives
for Volume-type geometries (volume mappings), and jacobians,
normals and base function derivatives for Surface-type
geometries (surface mappings).
Notes
-----
- surface mappings are defined on the surface region
- surface mappings require field order to be > 0
"""
domain = self.domain
coors = domain.get_mesh_coors(actual=True)
dconn = domain.get_conn()
if integration == 'volume':
qp = self.get_qp('v', integral)
iels = region.get_cells()
geo_ps = self.gel.poly_space
ps = self.poly_space
bf = self.get_base('v', 0, integral, iels=iels)
conn = nm.take(dconn, iels.astype(nm.int32), axis=0)
mapping = VolumeMapping(coors, conn, poly_space=geo_ps)
vg = mapping.get_mapping(qp.vals,
qp.weights,
poly_space=ps,
ori=self.ori)
out = vg
elif (integration == 'surface') or (integration == 'surface_extra'):
assert_(self.approx_order > 0)
if self.ori is not None:
msg = 'surface integrals do not work yet with the' \
' hierarchical basis!'
raise ValueError(msg)
sd = domain.surface_groups[region.name]
esd = self.surface_data[region.name]
geo_ps = self.gel.poly_space
ps = self.poly_space
conn = sd.get_connectivity()
mapping = SurfaceMapping(coors, conn, poly_space=geo_ps)
if not self.is_surface:
self.create_bqp(region.name, integral)
qp = self.qp_coors[(integral.order, esd.bkey)]
abf = ps.eval_base(qp.vals[0])
bf = abf[..., self.efaces[0]]
indx = self.gel.get_surface_entities()[0]
# Fix geometry element's 1st facet orientation for gradients.
indx = nm.roll(indx, -1)[::-1]
mapping.set_basis_indices(indx)
sg = mapping.get_mapping(qp.vals[0],
qp.weights,
poly_space=Struct(n_nod=bf.shape[-1]),
mode=integration)
if integration == 'surface_extra':
sg.alloc_extra_data(self.econn.shape[1])
bf_bg = geo_ps.eval_base(qp.vals, diff=True)
ebf_bg = self.get_base(esd.bkey, 1, integral)
sg.evaluate_bfbgm(bf_bg, ebf_bg, coors, sd.fis, dconn)
else:
# Do not use BQP for surface fields.
qp = self.get_qp(sd.face_type, integral)
bf = ps.eval_base(qp.vals)
sg = mapping.get_mapping(qp.vals,
qp.weights,
poly_space=Struct(n_nod=bf.shape[-1]),
mode=integration)
out = sg
elif integration == 'point':
out = mapping = None
elif integration == 'custom':
raise ValueError('cannot create custom mapping!')
else:
raise ValueError('unknown integration geometry type: %s' %
integration)
if out is not None:
# Store the integral used.
out.integral = integral
out.qp = qp
out.ps = ps
# Update base.
out.bf[:] = bf
if return_mapping:
out = (out, mapping)
return out
def describe_geometry(self,
field,
gtype,
region,
integral,
return_mapping=False):
"""
Compute jacobians, element volumes and base function derivatives
for Volume-type geometries (volume mappings), and jacobians,
normals and base function derivatives for Surface-type
geometries (surface mappings).
Notes
-----
- volume mappings can be defined on a part of an element group,
although the field has to be defined always on the whole group.
- surface mappings are defined on the surface region
- surface mappings require field order to be > 0
"""
domain = field.domain
group = domain.groups[self.ig]
coors = domain.get_mesh_coors(actual=True)
if gtype == 'volume':
qp = self.get_qp('v', integral)
iels = region.get_cells(self.ig)
geo_ps = self.interp.get_geom_poly_space('v')
ps = self.interp.poly_spaces['v']
bf = self.get_base('v', 0, integral, iels=iels)
conn = nm.take(group.conn, iels.astype(nm.int32), axis=0)
mapping = VolumeMapping(coors, conn, poly_space=geo_ps)
vg = mapping.get_mapping(qp.vals,
qp.weights,
poly_space=ps,
ori=self.ori)
out = vg
elif gtype == 'plate':
import sfepy.mechanics.membranes as mm
from sfepy.linalg import dot_sequences
qp = self.get_qp('v', integral)
iels = region.get_cells(self.ig)
ps = self.interp.poly_spaces['v']
bf = self.get_base('v', 0, integral, iels=iels)
conn = nm.take(group.conn, nm.int32(iels), axis=0)
ccoors = coors[conn]
# Coordinate transformation matrix (transposed!).
mtx_t = mm.create_transformation_matrix(ccoors)
# Transform coordinates to the local coordinate system.
coors_loc = dot_sequences((ccoors - ccoors[:, 0:1, :]), mtx_t)
# Mapping from transformed elements to reference elements.
mapping = mm.create_mapping(coors_loc, field.gel, 1)
vg = mapping.get_mapping(qp.vals,
qp.weights,
poly_space=ps,
ori=self.ori)
vg.mtx_t = mtx_t
out = vg
elif (gtype == 'surface') or (gtype == 'surface_extra'):
assert_(field.approx_order > 0)
if self.ori is not None:
msg = 'surface integrals do not work yet with the' \
' hierarchical basis!'
raise ValueError(msg)
sd = domain.surface_groups[self.ig][region.name]
esd = self.surface_data[region.name]
qp = self.get_qp(sd.face_type, integral)
geo_ps = self.interp.get_geom_poly_space(sd.face_type)
ps = self.interp.poly_spaces[esd.face_type]
bf = self.get_base(esd.face_type, 0, integral)
conn = sd.get_connectivity()
mapping = SurfaceMapping(coors, conn, poly_space=geo_ps)
sg = mapping.get_mapping(qp.vals,
qp.weights,
poly_space=ps,
mode=gtype)
if gtype == 'surface_extra':
sg.alloc_extra_data(self.n_ep['v'])
self.create_bqp(region.name, integral)
qp = self.qp_coors[(integral.order, esd.bkey)]
v_geo_ps = self.interp.get_geom_poly_space('v')
bf_bg = v_geo_ps.eval_base(qp.vals, diff=True)
ebf_bg = self.get_base(esd.bkey, 1, integral)
sg.evaluate_bfbgm(bf_bg, ebf_bg, coors, sd.fis, group.conn)
out = sg
elif gtype == 'point':
out = mapping = None
else:
raise ValueError('unknown geometry type: %s' % gtype)
if out is not None:
# Store the integral used.
out.integral = integral
out.qp = qp
out.ps = ps
# Update base.
out.bf[:] = bf
if return_mapping:
out = (out, mapping)
return out
def create_mapping(self,
region,
integral,
integration,
return_mapping=True):
"""Creates and returns mapping
Parameters
----------
region : sfepy.discrete.common.region.Region
integral : Integral
integration : str
'volume' is only accepted option
return_mapping : default True
(Default value = True)
Returns
-------
mapping : VolumeMapping
"""
domain = self.domain
coors = domain.get_mesh_coors(actual=True)
dconn = domain.get_conn()
# from FEField
if integration == 'volume':
qp = self.get_qp('v', integral)
# qp = self.integral.get_qp(self.gel.name)
iels = region.get_cells()
geo_ps = self.gel.poly_space
ps = self.poly_space
bf = self.get_base('v', 0, integral, iels=iels)
conn = nm.take(dconn, iels.astype(nm.int32), axis=0)
mapping = VolumeMapping(coors, conn, poly_space=geo_ps)
vg = mapping.get_mapping(qp.vals,
qp.weights,
poly_space=ps,
ori=self.ori,
transform=self.basis_transform)
out = vg
else:
raise ValueError('unsupported integration geometry type: %s' %
integration)
if out is not None:
# Store the integral used.
out.integral = integral
out.qp = qp
out.ps = ps
# Update base.
out.bf[:] = bf
if return_mapping:
out = (out, mapping)
return out
def test_gradients(self):
from sfepy.discrete.fem.mappings import VolumeMapping
ok = True
orders = {'2_3': 3, '2_4': 3, '3_4': 4, '3_8': 3}
bads = []
bad_families = set()
for (geom, poly_space_base, qp_weights, mesh, ir, ic, field, ps, rrc,
rcell, crc, ccell, vec, edofs,
fdofs) in _gen_common_data(orders, self.gels, self.report):
gel = self.gels[geom]
conn = mesh.get_conn(gel.name)
geo_ps = field.gel.poly_space
rmapping = VolumeMapping(mesh.coors,
conn[rcell:rcell + 1],
poly_space=geo_ps)
rori = field.ori[:1] if field.ori is not None else None
rvg = rmapping.get_mapping(rrc,
qp_weights,
poly_space=ps,
ori=rori)
rbfg = rvg.bfg
cmapping = VolumeMapping(mesh.coors,
conn[ccell:ccell + 1],
poly_space=geo_ps)
cori = field.ori[1:] if field.ori is not None else None
cvg = cmapping.get_mapping(crc,
qp_weights,
poly_space=ps,
ori=cori)
cbfg = cvg.bfg
dofs = nm.r_[edofs, fdofs]
res = nm.zeros((2, dofs.shape[0]), dtype=nm.int32)
res[0, :] = dofs
for ii, ip in enumerate(dofs):
vec.fill(0.0)
vec[ip] = 1.0
evec = vec[field.econn]
rvals = nm.dot(rbfg, evec[rcell])[0]
cvals = nm.dot(cbfg, evec[ccell])[0]
okx = nm.allclose(rvals[:, 0],
cvals[:, 0],
atol=1e-12,
rtol=0.0)
if gel.dim == 2:
oky = nm.allclose(rvals[:, 1],
-cvals[:, 1],
atol=1e-12,
rtol=0.0)
_ok = okx and oky
else:
oky = nm.allclose(rvals[:, 1],
cvals[:, 1],
atol=1e-12,
rtol=0.0)
okz = nm.allclose(rvals[:, 2],
-cvals[:, 2],
atol=1e-12,
rtol=0.0)
_ok = okx and oky and okz
res[1, ii] = _ok
if not _ok:
bads.append([geom, poly_space_base, ir, ic, ip])
bad_families.add((geom, poly_space_base))
ok = ok and _ok
self.report('results (dofs, status: 1 ok, 0 failure):\n%s' % res)
if not ok:
self.report('gradient continuity errors:\n', bads)
self.report('%d in total!' % len(bads))
self.report(
'gradient continuity errors occurred in these'
' spaces:\n', bad_families)
return ok