"""
Notes
-----
Important attributes of continuous (order > 0) :class:`Field` and
:class:`SurfaceField` instances:
- `vertex_remap` : `econn[:, :n_vertex] = vertex_remap[conn]`
- `vertex_remap_i` : `conn = vertex_remap_i[econn[:, :n_vertex]]`
where `conn` is the mesh vertex connectivity, `econn` is the
region-local field connectivity.
"""
import numpy as nm
from sfepy.base.base import assert_, Struct
from sfepy.discrete.integrals import Integral
from sfepy.discrete.fem.utils import prepare_remap
from sfepy.discrete.common.dof_info import expand_nodes_to_dofs
from sfepy.discrete.common.mappings import get_physical_qps
from sfepy.discrete.fem.facets import get_facet_dof_permutations
from sfepy.discrete.fem.fields_base import FEField, H1Mixin
[docs]class GlobalNodalLikeBasis(Struct):
def _setup_facet_orientations(self):
order = self.approx_order
self.node_desc = self.poly_space.describe_nodes()
edge_nodes = self.node_desc.edge_nodes
if edge_nodes is not None:
n_fp = self.gel.edges.shape[1]
self.edge_dof_perms = get_facet_dof_permutations(n_fp, order)
face_nodes = self.node_desc.face_nodes
if face_nodes is not None:
n_fp = self.gel.faces.shape[1]
self.face_dof_perms = get_facet_dof_permutations(n_fp, order)
def _setup_edge_dofs(self):
"""
Setup edge DOF connectivity.
"""
if self.node_desc.edge is None:
return 0, None, None
return self._setup_facet_dofs(1, self.node_desc.edge,
self.edge_dof_perms,
self.n_vertex_dof)
def _setup_face_dofs(self):
"""
Setup face DOF connectivity.
"""
if self.node_desc.face is None:
return 0, None, None
return self._setup_facet_dofs(self.domain.shape.tdim - 1,
self.node_desc.face,
self.face_dof_perms,
self.n_vertex_dof + self.n_edge_dof)
def _setup_facet_dofs(self, dim, facet_desc, facet_perms, offset):
"""
Helper function to setup facet DOF connectivity, works for both
edges and faces.
"""
facet_desc = nm.array(facet_desc)
n_dof_per_facet = facet_desc.shape[1]
cmesh = self.cmesh
facets = self.region.entities[dim]
ii = nm.arange(facets.shape[0], dtype=nm.int32)
all_dofs = offset + expand_nodes_to_dofs(ii, n_dof_per_facet)
# Prepare global facet id remapping to field-local numbering.
remap = prepare_remap(facets, cmesh.num[dim])
cconn = cmesh.get_conn(self.region.tdim, dim)
offs = cconn.offsets
n_f = self.gel.edges.shape[0] if dim == 1 else self.gel.faces.shape[0]
oris = cmesh.get_orientations(dim)
gcells = self.region.get_cells()
n_el = gcells.shape[0]
# Elements of facets.
iel = nm.arange(n_el, dtype=nm.int32).repeat(n_f)
ies = nm.tile(nm.arange(n_f, dtype=nm.int32), n_el)
aux = offs[gcells][:, None] + ies.reshape((n_el, n_f))
indices = cconn.indices[aux]
facets_of_cells = remap[indices].ravel()
ori = oris[aux].ravel()
perms = facet_perms[ori]
# Define global facet dof numbers.
gdofs = offset + expand_nodes_to_dofs(facets_of_cells,
n_dof_per_facet)
# DOF columns in econn for each facet.
iep = facet_desc[ies]
iaux = nm.arange(gdofs.shape[0], dtype=nm.int32)
self.econn[iel[:, None], iep] = gdofs[iaux[:, None], perms]
n_dof = n_dof_per_facet * facets.shape[0]
assert_(n_dof == nm.prod(all_dofs.shape))
return n_dof, all_dofs, remap
def _setup_bubble_dofs(self):
"""
Setup bubble DOF connectivity.
"""
if self.node_desc.bubble is None:
return 0, None, None
offset = self.n_vertex_dof + self.n_edge_dof + self.n_face_dof
n_dof_per_cell = self.node_desc.bubble.shape[0]
ii = self.region.get_cells()
remap = prepare_remap(ii, self.cmesh.n_el)
n_cell = ii.shape[0]
n_dof = n_dof_per_cell * n_cell
all_dofs = nm.arange(offset, offset + n_dof, dtype=nm.int32)
all_dofs.shape = (n_cell, n_dof_per_cell)
iep = self.node_desc.bubble[0]
self.econn[:,iep:] = all_dofs
return n_dof, all_dofs, remap
[docs] def get_surface_basis(self, region):
"""
Get basis for projections to region's facets.
Notes
-----
Cannot be uses for all fields because IGA does not support surface
mappings.
"""
order = self.approx_order
integral = Integral('i', order=2*order)
geo, mapping = self.get_mapping(region, integral, 'surface')
pqps = get_physical_qps(region, integral)
qps = pqps.values.reshape(pqps.shape)
bfs = nm.broadcast_to(
geo.bf[..., 0, :],
(qps.shape[0], qps.shape[1], geo.bf.shape[3]),
)
return qps, bfs, geo.det[..., 0]
[docs]class H1NodalMixin(H1Mixin, GlobalNodalLikeBasis):
def _substitute_dofs(self, subs):
"""
Perform facet DOF substitutions according to `subs`.
Modifies `self.econn` in-place.
"""
if self.gel.name == '2_4':
ef = self.efaces
for ii, sub in enumerate(subs):
# 2_4 edges always in opposite orientation.
ee = ef[sub[1]].copy()
ee[0], ee[1] = ee[1], ee[0] # Swap vertex DOFs.
ee[2:] = ee[-1:1:-1] # Swap edge DOFs.
master = self.econn[sub[0], ee]
self.econn[sub[2], ef[sub[3]]] = master
self.econn[sub[4], ef[sub[5]]] = master
elif self.gel.name == '3_8':
def _sort4(p):
key = 0
if (p[0] < p[1]): key += 1
if (p[0] < p[2]): key += 2
if (p[1] < p[2]): key += 4
if (p[0] < p[3]): key += 8
if (p[1] < p[3]): key += 16
if (p[2] < p[3]): key += 32
return key
if subs[0] is not None:
ef = self.efaces
epf = self.gel.get_edges_per_face()
nde = self.node_desc.edge
ndf = self.node_desc.face
gedges = self.gel.edges
gfaces = self.gel.faces
for ii, sub in enumerate(subs[0]):
master = self.econn[sub[0]]
fmaster = master[ef[sub[1]]]
lmaster = fmaster.tolist()
for ic in range(4):
ia, ib = 2 + 2 * ic, 2 + 2 * ic + 1
cell = self.econn[sub[ia]]
# Corner vertex is always the first for faces 0, 1, 2.
iv = cell[ef[sub[ib]][0]]
i0 = lmaster.index(iv)
for ik in range(4):
cell[ef[sub[ib]][ik]] = fmaster[:4][i0 - ik]
# Treat edge DOFs.
if nde is not None:
sedges = epf[sub[ib]]
medges = epf[sub[1]]
for ie, sedge in enumerate(sedges):
iim = i0 - 1 - ie
ies = nde[sedge]
medge = medges[iim]
iem = nde[medge]
vm = master[gedges[medge]][0]
vs = cell[gedges[sedge]][0]
if vm == vs:
cell[ies] = self.econn[sub[0], iem]
else:
cell[ies] = self.econn[sub[0], iem[::-1]]
# Treat face DOFs.
if ndf is not None:
new_ori = _sort4(cell[gfaces[sub[ib]]])
smaster = nm.sort(master[ndf[sub[1]]])
aux = self.face_dof_perms[new_ori]
cell[ndf[sub[ib]]] = smaster[aux]
if subs[1] is not None:
ef = self.eedges
for ii, sub in enumerate(subs[1]):
master = self.econn[sub[0]]
me = master[gedges[sub[1]]]
for ic in range(2):
ia, ib = 2 + 2 * ic, 2 + 2 * ic + 1
cell = self.econn[sub[ia]]
ce = cell[gedges[sub[ib]]]
if (me[0] == ce[0]) or (me[1] == ce[1]):
cell[ef[sub[ib]]] = master[ef[sub[1]]]
else:
ee = ef[sub[1]].copy()
ee[0], ee[1] = ee[1], ee[0] # Swap vertex DOFs.
ee[2:] = ee[-1:1:-1] # Swap edge DOFs.
cell[ef[sub[ib]]] = master[ee]
else:
raise ValueError('unsupported reference element type! (%s)'
% self.gel.name)
def _eval_basis_transform(self, subs):
"""
"""
from sfepy.discrete import Integral
from sfepy.discrete.fem import Mesh, FEDomain, Field
transform = nm.tile(nm.eye(self.econn.shape[1]),
(self.econn.shape[0], 1, 1))
if subs is None:
return transform
gel = self.gel
ao = self.approx_order
conn = [gel.conn]
mesh = Mesh.from_data('a', gel.coors, None, [conn], [nm.array([0])],
[gel.name])
cdomain = FEDomain('d', mesh)
comega = cdomain.create_region('Omega', 'all')
rcfield = Field.from_args('rc', self.dtype, 1, comega, approx_order=ao)
fdomain = cdomain.refine()
fomega = fdomain.create_region('Omega', 'all')
rffield = Field.from_args('rf', self.dtype, 1, fomega, approx_order=ao)
def assign_transform(transform, bf, subs, ef):
if not len(subs): return
n_sub = (subs.shape[1] - 2) // 2
for ii, sub in enumerate(subs):
for ij in range(n_sub):
ik = 2 * (ij + 1)
fface = ef[sub[ik+1]]
mtx = transform[sub[ik]]
ix, iy = nm.meshgrid(fface, fface)
cbf = bf[iy, 0, ix]
mtx[ix, iy] = cbf
fcoors = rffield.get_coor()
coors = fcoors[rffield.econn[0]]
integral = Integral('i', coors=coors, weights=nm.ones_like(coors[:, 0]))
rcfield.clear_qp_base()
bf = rcfield.get_base('v', False, integral)
if gel.name == '2_4':
fsubs = subs
esubs = None
assign_transform(transform, bf, fsubs, rffield.efaces)
else:
fsubs = subs[0]
esubs = subs[1]
assign_transform(transform, bf, fsubs, rffield.efaces)
if esubs is not None:
assign_transform(transform, bf, esubs, rffield.eedges)
assert_((nm.abs(transform.sum(1) - 1.0) < 1e-15).all())
return transform
[docs] def set_dofs(self, fun=0.0, region=None, dpn=None, warn=None):
"""
Set the values of DOFs in a given `region` using a function of space
coordinates or value `fun`.
"""
if region is None:
region = self.region
if dpn is None:
dpn = self.n_components
aux = self.get_dofs_in_region(region)
nods = nm.unique(aux)
if callable(fun):
coors = self.get_coor(nods)
vals = nm.asarray(fun(coors))
if (vals.ndim > 1) and (vals.shape != (len(coors), dpn)):
raise ValueError('The projected function return value should be'
' (n_point, dpn) == %s, instead of %s!'
% ((len(coors), dpn), vals.shape))
elif nm.isscalar(fun):
vals = nm.repeat([fun], nods.shape[0] * dpn)
elif isinstance(fun, nm.ndarray):
try:
assert_(len(fun) == dpn)
except (TypeError, ValueError):
msg = ('wrong array value shape for setting'
' DOFs of "%s" field!'
' (shape %s should be %s)'
% (self.name, fun.shape, (dpn,)))
raise ValueError(msg)
vals = nm.repeat(fun, nods.shape[0])
else:
raise ValueError('unknown function/value type! (%s)' % type(fun))
vals.shape = (len(nods), -1)
return nods, vals
[docs] def create_basis_context(self):
"""
Create the context required for evaluating the field basis.
"""
ps = self.poly_space
gps = self.gel.poly_space
mesh = self.create_mesh(extra_nodes=False)
ctx = ps.create_context(None, 0, 1e-15, 100, 1e-8,
tdim=mesh.cmesh.tdim)
geo_ctx = gps.create_context(mesh.cmesh, 0, 1e-15, 100, 1e-8)
ctx.geo_ctx = geo_ctx
return ctx
[docs]class H1NodalVolumeField(H1NodalMixin, FEField):
"""
Lagrange basis nodal approximation.
"""
family_name = 'volume_H1_lagrange'
[docs] def interp_v_vals_to_n_vals(self, vec):
"""
Interpolate a function defined by vertex DOF values using the FE
geometry base (P1 or Q1) into the extra nodes, i.e. define the
extra DOF values.
"""
if not self.node_desc.has_extra_nodes():
enod_vol_val = vec.copy()
else:
dim = vec.shape[1]
enod_vol_val = nm.zeros((self.n_nod, dim), dtype=nm.float64)
coors = self.poly_space.node_coors
bf = self.gel.poly_space.eval_base(coors)
bf = bf[:,0,:].copy()
conn = self.econn[:, :self.gel.n_vertex]
evec = nm.dot(bf, vec[conn])
enod_vol_val[self.econn] = nm.swapaxes(evec, 0, 1)
return enod_vol_val
[docs]class H1SNodalVolumeField(H1NodalVolumeField):
"""
Lagrange basis nodal serendipity approximation with order <= 3.
"""
family_name = 'volume_H1_serendipity'
[docs] def create_basis_context(self):
"""
Create the context required for evaluating the field basis.
"""
# Hack for tests to pass - the reference coordinates are determined
# from vertices only - we can use the Lagrange basis context for the
# moment. The true context for Field.evaluate_at() is not implemented.
gps = self.gel.poly_space
mesh = self.create_mesh(extra_nodes=False)
ctx = geo_ctx = gps.create_context(self.cmesh, 0, 1e-15, 100, 1e-8)
ctx.geo_ctx = geo_ctx
return ctx
[docs]class H1SEMVolumeField(H1NodalVolumeField):
"""
Spectral element method approximation.
Uses the Lagrange basis with Legendre-Gauss-Lobatto nodes and quadrature.
"""
family_name = 'volume_H1_sem'
[docs] def create_basis_context(self):
"""
Create the context required for evaluating the field basis.
"""
# Hack for tests to pass - the reference coordinates are determined
# from vertices only - we can use the Lagrange basis context for the
# moment. The true context for Field.evaluate_at() is not implemented.
gps = self.gel.poly_space
mesh = self.create_mesh(extra_nodes=False)
ctx = geo_ctx = gps.create_context(self.cmesh, 0, 1e-15, 100, 1e-8)
ctx.geo_ctx = geo_ctx
return ctx
[docs]class H1DiscontinuousField(H1NodalMixin, FEField):
"""
The C0 constant-per-cell approximation.
"""
family_name = 'volume_H1_lagrange_discontinuous'
def _setup_global_base(self):
"""
Setup global DOF/base function indices and connectivity of the field.
"""
self._setup_facet_orientations()
self._init_econn()
ii = self.region.get_cells()
self.bubble_remap = prepare_remap(ii, self.cmesh.n_el)
n_dof = nm.prod(self.econn.shape)
all_dofs = nm.arange(n_dof, dtype=nm.int32)
all_dofs.shape = self.econn.shape
self.econn[:] = all_dofs
self.n_nod = n_dof
self.n_bubble_dof = n_dof
self.bubble_dofs = all_dofs
self.n_vertex_dof = self.n_edge_dof = self.n_face_dof = 0
self._setup_esurface()
[docs] def extend_dofs(self, dofs, fill_value=None):
"""
Extend DOFs to the whole domain using the `fill_value`, or the
smallest value in `dofs` if `fill_value` is None.
"""
if self.approx_order != 0:
dofs = self.average_to_vertices(dofs)
new_dofs = FEField.extend_dofs(self, dofs)
return new_dofs
[docs] def average_to_vertices(self, dofs):
"""
Average DOFs of the discontinuous field into the field region
vertices.
"""
data_qp, integral = self.interp_to_qp(dofs)
vertex_dofs = self.average_qp_to_vertices(data_qp, integral)
return vertex_dofs
[docs]class H1NodalSurfaceField(H1NodalMixin, FEField):
"""
A field defined on a surface region.
"""
family_name = 'surface_H1_lagrange'
[docs] def interp_v_vals_to_n_vals(self, vec):
"""
Interpolate a function defined by vertex DOF values using the FE
surface geometry base (P1 or Q1) into the extra nodes, i.e. define the
extra DOF values.
"""
if not self.node_desc.has_extra_nodes():
enod_vol_val = vec.copy()
else:
msg = 'surface nodal fields do not support higher order nodes yet!'
raise NotImplementedError(msg)
return enod_vol_val
[docs]class H1SNodalSurfaceField(H1NodalSurfaceField):
family_name = 'surface_H1_serendipity'
[docs]class H1SEMSurfaceField(H1NodalSurfaceField):
family_name = 'surface_H1_sem'