"""
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.
"""
from __future__ import absolute_import
import numpy as nm
from sfepy.base.base import output, get_default, assert_
from sfepy.base.base import Struct
from sfepy.base.timing import Timer
from sfepy.discrete.common.fields import parse_shape, Field
from sfepy.discrete import PolySpace
from sfepy.discrete.fem.mesh import Mesh
from sfepy.discrete.fem.meshio import convert_complex_output
from sfepy.discrete.fem.utils import (extend_cell_data, prepare_remap,
invert_remap, get_min_value)
from sfepy.discrete.fem.mappings import VolumeMapping, SurfaceMapping
from sfepy.discrete.fem.fe_surface import FESurface
from sfepy.discrete.integrals import Integral
from sfepy.discrete.fem.linearizer import (get_eval_dofs, get_eval_coors,
create_output)
import six
[docs]def set_mesh_coors(domain, fields, coors, update_fields=False, actual=False,
clear_all=True, extra_dofs=False):
if actual:
if not hasattr(domain.mesh, 'coors_act'):
domain.mesh.coors_act = nm.zeros_like(domain.mesh.coors)
domain.mesh.coors_act[:] = coors[:domain.mesh.n_nod]
else:
domain.cmesh.coors[:] = coors[:domain.mesh.n_nod]
if update_fields:
for field in six.itervalues(fields):
field.set_coors(coors, extra_dofs=extra_dofs)
field.clear_mappings(clear_all=clear_all)
[docs]def eval_nodal_coors(coors, mesh_coors, region, poly_space, geom_poly_space,
econn, only_extra=True):
"""
Compute coordinates of nodes corresponding to `poly_space`, given
mesh coordinates and `geom_poly_space`.
"""
if only_extra:
iex = (poly_space.nts[:,0] > 0).nonzero()[0]
if iex.shape[0] == 0: return
qp_coors = poly_space.node_coors[iex, :]
econn = econn[:, iex].copy()
else:
qp_coors = poly_space.node_coors
##
# Evaluate geometry interpolation base functions in (extra) nodes.
bf = geom_poly_space.eval_base(qp_coors)
bf = bf[:,0,:].copy()
##
# Evaluate extra coordinates with 'bf'.
cmesh = region.domain.cmesh
conn = cmesh.get_incident(0, region.cells, region.tdim)
conn.shape = (econn.shape[0], -1)
ecoors = nm.dot(bf, mesh_coors[conn])
coors[econn] = nm.swapaxes(ecoors, 0, 1)
def _interp_to_faces(vertex_vals, bfs, faces):
dim = vertex_vals.shape[1]
n_face = faces.shape[0]
n_qp = bfs.shape[0]
faces_vals = nm.zeros((n_face, n_qp, dim), nm.float64)
for ii, face in enumerate(faces):
vals = vertex_vals[face,:dim]
faces_vals[ii,:,:] = nm.dot(bfs[:,0,:], vals)
return(faces_vals)
[docs]def get_eval_expression(expression,
fields, materials, variables,
functions=None, mode='eval', term_mode=None,
extra_args=None, verbose=True, kwargs=None):
"""
Get the function for evaluating an expression given a list of elements,
and reference element coordinates.
"""
from sfepy.discrete.evaluate import eval_in_els_and_qp
def _eval(iels, coors):
val = eval_in_els_and_qp(expression, iels, coors,
fields, materials, variables,
functions=functions, mode=mode,
term_mode=term_mode,
extra_args=extra_args, verbose=verbose,
kwargs=kwargs)
return val[..., 0]
return _eval
[docs]def create_expression_output(expression, name, primary_field_name,
fields, materials, variables,
functions=None, mode='eval', term_mode=None,
extra_args=None, verbose=True, kwargs=None,
min_level=0, max_level=1, eps=1e-4):
"""
Create output mesh and data for the expression using the adaptive
linearizer.
Parameters
----------
expression : str
The expression to evaluate.
name : str
The name of the data.
primary_field_name : str
The name of field that defines the element groups and polynomial
spaces.
fields : dict
The dictionary of fields used in `variables`.
materials : Materials instance
The materials used in the expression.
variables : Variables instance
The variables used in the expression.
functions : Functions instance, optional
The user functions for materials etc.
mode : one of 'eval', 'el_avg', 'qp'
The evaluation mode - 'qp' requests the values in quadrature points,
'el_avg' element averages and 'eval' means integration over
each term region.
term_mode : str
The term call mode - some terms support different call modes
and depending on the call mode different values are
returned.
extra_args : dict, optional
Extra arguments to be passed to terms in the expression.
verbose : bool
If False, reduce verbosity.
kwargs : dict, optional
The variables (dictionary of (variable name) : (Variable
instance)) to be used in the expression.
min_level : int
The minimum required level of mesh refinement.
max_level : int
The maximum level of mesh refinement.
eps : float
The relative tolerance parameter of mesh adaptivity.
Returns
-------
out : dict
The output dictionary.
"""
field = fields[primary_field_name]
vertex_coors = field.coors[:field.n_vertex_dof, :]
ps = field.poly_space
gps = field.gel.poly_space
vertex_conn = field.econn[:, :field.gel.n_vertex]
eval_dofs = get_eval_expression(expression,
fields, materials, variables,
functions=functions,
mode=mode, extra_args=extra_args,
verbose=verbose, kwargs=kwargs)
eval_coors = get_eval_coors(vertex_coors, vertex_conn, gps)
(level, coors, conn,
vdofs, mat_ids) = create_output(eval_dofs, eval_coors,
vertex_conn.shape[0], ps,
min_level=min_level,
max_level=max_level, eps=eps)
mesh = Mesh.from_data('linearized_mesh', coors, None, [conn], [mat_ids],
field.domain.mesh.descs)
out = {}
out[name] = Struct(name='output_data', mode='vertex',
data=vdofs, var_name=name, dofs=None,
mesh=mesh, level=level)
out = convert_complex_output(out)
return out
[docs]class FEField(Field):
"""
Base class for finite element fields.
Notes
-----
- interps and hence node_descs are per region (must have single
geometry!)
Field shape information:
- ``shape`` - the shape of the base functions in a point
- ``n_components`` - the number of DOFs per FE node
- ``val_shape`` - the shape of field value (the product of DOFs and
base functions) in a point
"""
def __init__(self, name, dtype, shape, region, approx_order=1):
"""
Create a finite element field.
Parameters
----------
name : str
The field name.
dtype : numpy.dtype
The field data type: float64 or complex128.
shape : int/tuple/str
The field shape: 1 or (1,) or 'scalar', space dimension (2, or (2,)
or 3 or (3,)) or 'vector', or a tuple. The field shape determines
the shape of the FE base functions and is related to the number of
components of variables and to the DOF per node count, depending
on the field kind.
region : Region
The region where the field is defined.
approx_order : int or tuple
The FE approximation order. The tuple form is (order, has_bubble),
e.g. (1, True) means order 1 with a bubble function.
Notes
-----
Assumes one cell type for the whole region!
"""
shape = parse_shape(shape, region.domain.shape.dim)
if not self._check_region(region):
raise ValueError('unsuitable region for field %s! (%s)' %
(name, region.name))
Struct.__init__(self, name=name, dtype=dtype, shape=shape,
region=region)
self.domain = self.region.domain
self._set_approx_order(approx_order)
self._setup_geometry()
self._setup_kind()
self._setup_shape()
self.surface_data = {}
self.point_data = {}
self.ori = None
self._create_interpolant()
self._setup_global_base()
self.setup_coors()
self.clear_mappings(clear_all=True)
self.clear_qp_base()
self.basis_transform = None
self.econn0 = None
self.unused_dofs = None
self.stored_subs = None
def _set_approx_order(self, approx_order):
"""
Set a uniform approximation order.
"""
if isinstance(approx_order, tuple):
self.approx_order = approx_order[0]
self.force_bubble = approx_order[1]
else:
self.approx_order = approx_order
self.force_bubble = False
[docs] def get_true_order(self):
"""
Get the true approximation order depending on the reference
element geometry.
For example, for P1 (linear) approximation the true order is 1,
while for Q1 (bilinear) approximation in 2D the true order is 2.
"""
gel = self.gel
if (gel.dim + 1) == gel.n_vertex:
order = self.approx_order
else:
order = gel.dim * self.approx_order
if self.force_bubble:
bubble_order = gel.dim + 1
order = max(order, bubble_order)
return order
[docs] def is_higher_order(self):
"""
Return True, if the field's approximation order is greater than one.
"""
return self.force_bubble or (self.approx_order > 1)
def _setup_global_base(self):
"""
Setup global DOF/base functions, their indices and connectivity of the
field. Called methods implemented in subclasses.
"""
self._setup_facet_orientations()
self._init_econn()
self.n_vertex_dof, self.vertex_remap = self._setup_vertex_dofs()
self.vertex_remap_i = invert_remap(self.vertex_remap)
aux = self._setup_edge_dofs()
self.n_edge_dof, self.edge_dofs, self.edge_remap = aux
aux = self._setup_face_dofs()
self.n_face_dof, self.face_dofs, self.face_remap = aux
aux = self._setup_bubble_dofs()
self.n_bubble_dof, self.bubble_dofs, self.bubble_remap = aux
self.n_nod = self.n_vertex_dof + self.n_edge_dof \
+ self.n_face_dof + self.n_bubble_dof
self._setup_esurface()
def _setup_esurface(self):
"""
Setup extended surface entities (edges in 2D, faces in 3D),
i.e. indices of surface entities into the extended connectivity.
"""
node_desc = self.node_desc
gel = self.gel
self.efaces = gel.get_surface_entities().copy()
nd = node_desc.edge
if nd is not None:
efs = []
for eof in gel.get_edges_per_face():
efs.append(nm.concatenate([nd[ie] for ie in eof]))
efs = nm.array(efs).squeeze()
if efs.ndim < 2:
efs = efs[:,nm.newaxis]
self.efaces = nm.hstack((self.efaces, efs))
efs = node_desc.face
if efs is not None:
efs = nm.array(efs).squeeze()
if efs.ndim < 2:
efs = efs[:,nm.newaxis]
self.efaces = nm.hstack((self.efaces, efs))
if gel.dim == 3:
self.eedges = gel.edges.copy()
efs = node_desc.edge
if efs is not None:
efs = nm.array(efs).squeeze()
if efs.ndim < 2:
efs = efs[:,nm.newaxis]
self.eedges = nm.hstack((self.eedges, efs))
[docs] def set_coors(self, coors, extra_dofs=False):
"""
Set coordinates of field nodes.
"""
# Mesh vertex nodes.
if self.n_vertex_dof:
indx = self.vertex_remap_i
self.coors[:self.n_vertex_dof] = nm.take(coors,
indx.astype(nm.int32),
axis=0)
n_ex_dof = self.n_bubble_dof + self.n_edge_dof + self.n_face_dof
# extra nodes
if n_ex_dof:
if extra_dofs:
if self.n_nod != coors.shape[0]:
raise NotImplementedError
self.coors[:] = coors
else:
gps = self.gel.poly_space
ps = self.poly_space
eval_nodal_coors(self.coors, coors, self.region,
ps, gps, self.econn)
[docs] def setup_coors(self):
"""
Setup coordinates of field nodes.
"""
mesh = self.domain.mesh
self.coors = nm.empty((self.n_nod, mesh.dim), nm.float64)
self.set_coors(mesh.coors)
[docs] def get_vertices(self):
"""
Return indices of vertices belonging to the field region.
"""
return self.vertex_remap_i
def _get_facet_dofs(self, rfacets, remap, dofs):
facets = remap[rfacets]
return dofs[facets[facets >= 0]].ravel()
[docs] def get_data_shape(self, integral, integration='volume', region_name=None):
"""
Get element data dimensions.
Parameters
----------
integral : Integral instance
The integral describing used numerical quadrature.
integration : 'volume', 'surface', 'surface_extra', 'point' or 'custom'
The term integration type.
region_name : str
The name of the region of the integral.
Returns
-------
data_shape : 4 ints
The `(n_el, n_qp, dim, n_en)` for volume shape kind,
`(n_fa, n_qp, dim, n_fn)` for surface shape kind and
`(n_nod, 0, 0, 1)` for point shape kind.
Notes
-----
- `n_el`, `n_fa` = number of elements/facets
- `n_qp` = number of quadrature points per element/facet
- `dim` = spatial dimension
- `n_en`, `n_fn` = number of element/facet nodes
- `n_nod` = number of element nodes
"""
region = self.domain.regions[region_name]
shape = region.shape
dim = region.dim
if integration in ('surface', 'surface_extra'):
if region_name not in self.surface_data:
reg = self.domain.regions[region_name]
self.domain.create_surface_group(reg)
self.setup_surface_data(reg, False, None)
sd = self.surface_data[region_name]
# This works also for surface fields.
key = sd.face_type
weights = self.get_qp(key, integral).weights
n_qp = weights.shape[0]
if integration == 'surface':
data_shape = (sd.n_fa, n_qp, dim, sd.n_fp)
else:
data_shape = (sd.n_fa, n_qp, dim, self.econn.shape[1])
elif integration in ('volume', 'custom'):
_, weights = integral.get_qp(self.gel.name)
n_qp = weights.shape[0]
data_shape = (shape.n_cell, n_qp, dim, self.econn.shape[1])
elif integration == 'point':
dofs = self.get_dofs_in_region(region, merge=True)
data_shape = (dofs.shape[0], 0, 0, 1)
else:
raise NotImplementedError('unsupported integration! (%s)'
% integration)
return data_shape
[docs] def get_dofs_in_region(self, region, merge=True):
"""
Return indices of DOFs that belong to the given region and group.
"""
node_desc = self.node_desc
dofs = []
vdofs = nm.empty((0,), dtype=nm.int32)
if node_desc.vertex is not None:
vdofs = self.vertex_remap[region.vertices]
vdofs = vdofs[vdofs >= 0]
dofs.append(vdofs)
edofs = nm.empty((0,), dtype=nm.int32)
if node_desc.edge is not None:
edofs = self._get_facet_dofs(region.edges,
self.edge_remap,
self.edge_dofs)
dofs.append(edofs)
fdofs = nm.empty((0,), dtype=nm.int32)
if node_desc.face is not None:
fdofs = self._get_facet_dofs(region.faces,
self.face_remap,
self.face_dofs)
dofs.append(fdofs)
bdofs = nm.empty((0,), dtype=nm.int32)
if (node_desc.bubble is not None) and region.has_cells():
els = self.bubble_remap[region.cells]
bdofs = self.bubble_dofs[els[els >= 0]].ravel()
dofs.append(bdofs)
if merge:
dofs = nm.concatenate(dofs)
return dofs
[docs] def clear_qp_base(self):
"""
Remove cached quadrature points and base functions.
"""
self.qp_coors = {}
self.bf = {}
[docs] def get_qp(self, key, integral):
"""
Get quadrature points and weights corresponding to the given key
and integral. The key is 'v' or 's#', where # is the number of
face vertices.
"""
qpkey = (integral.order, key)
if qpkey not in self.qp_coors:
if (key[0] == 's') and not self.is_surface:
dim = self.gel.dim - 1
n_fp = self.gel.surface_facet.n_vertex
geometry = '%d_%d' % (dim, n_fp)
else:
geometry = self.gel.name
vals, weights = integral.get_qp(geometry)
self.qp_coors[qpkey] = Struct(vals=vals, weights=weights)
return self.qp_coors[qpkey]
[docs] def substitute_dofs(self, subs, restore=False):
"""
Perform facet DOF substitutions according to `subs`.
Modifies `self.econn` in-place and sets `self.econn0`,
`self.unused_dofs` and `self.basis_transform`.
"""
if restore and (self.stored_subs is not None):
self.econn0 = self.econn
self.econn, self.unused_dofs, basis_transform = self.stored_subs
else:
if subs is None:
self.econn0 = self.econn
return
else:
self.econn0 = self.econn.copy()
self._substitute_dofs(subs)
self.unused_dofs = nm.setdiff1d(self.econn0, self.econn)
basis_transform = self._eval_basis_transform(subs)
self.set_basis_transform(basis_transform)
[docs] def restore_dofs(self, store=False):
"""
Undoes the effect of :func:`FEField.substitute_dofs()`.
"""
if self.econn0 is None:
raise ValueError('no original DOFs to restore!')
if store:
self.stored_subs = (self.econn,
self.unused_dofs,
self.basis_transform)
else:
self.stored_subs = None
self.econn = self.econn0
self.econn0 = None
self.unused_dofs = None
self.basis_transform = None
[docs] def restore_substituted(self, vec):
"""
Restore values of the unused DOFs using the transpose of the applied
basis transformation.
"""
if (self.econn0 is None) or (self.basis_transform is None):
raise ValueError('no original DOF values to restore!!')
vec = vec.reshape((self.n_nod, self.n_components)).copy()
evec = vec[self.econn]
vec[self.econn0] = nm.einsum('cji,cjk->cik', self.basis_transform, evec)
return vec.ravel()
[docs] def get_base(self, key, derivative, integral, iels=None,
from_geometry=False, base_only=True):
qp = self.get_qp(key, integral)
if from_geometry:
ps = self.gel.poly_space
else:
ps = self.poly_space
_key = key if not from_geometry else 'g' + key
bf_key = (integral.order, _key, derivative)
if bf_key not in self.bf:
ori = self.ori
self.bf[bf_key] = ps.eval_base(qp.vals, diff=derivative, ori=ori,
transform=self.basis_transform)
bf = self.bf[bf_key]
if iels is not None and bf.ndim == 4:
bf = bf[iels]
if base_only:
return bf
else:
return bf, qp.weights
[docs] def create_bqp(self, region_name, integral):
gel = self.gel
sd = self.surface_data[region_name]
bqpkey = (integral.order, sd.bkey)
if not bqpkey in self.qp_coors:
qp = self.get_qp(sd.face_type, integral)
ps_s = self.gel.surface_facet.poly_space
bf_s = ps_s.eval_base(qp.vals)
coors, faces = gel.coors, gel.get_surface_entities()
vals = _interp_to_faces(coors, bf_s, faces)
self.qp_coors[bqpkey] = Struct(name='BQP_%s' % sd.bkey,
vals=vals, weights=qp.weights)
[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 fill_value is None:
if nm.isrealobj(dofs):
fill_value = get_min_value(dofs)
else:
# Complex values - treat real and imaginary parts separately.
fill_value = get_min_value(dofs.real)
fill_value += 1j * get_min_value(dofs.imag)
if self.approx_order != 0:
indx = self.get_vertices()
n_nod = self.domain.shape.n_nod
new_dofs = nm.empty((n_nod, dofs.shape[1]), dtype=self.dtype)
new_dofs.fill(fill_value)
new_dofs[indx] = dofs[:indx.size]
else:
new_dofs = extend_cell_data(dofs, self.domain, self.region,
val=fill_value)
return new_dofs
[docs] def linearize(self, dofs, min_level=0, max_level=1, eps=1e-4):
"""
Linearize the solution for post-processing.
Parameters
----------
dofs : array, shape (n_nod, n_component)
The array of DOFs reshaped so that each column corresponds
to one component.
min_level : int
The minimum required level of mesh refinement.
max_level : int
The maximum level of mesh refinement.
eps : float
The relative tolerance parameter of mesh adaptivity.
Returns
-------
mesh : Mesh instance
The adapted, nonconforming, mesh.
vdofs : array
The DOFs defined in vertices of `mesh`.
levels : array of ints
The refinement level used for each element group.
"""
assert_(dofs.ndim == 2)
n_nod, dpn = dofs.shape
assert_(n_nod == self.n_nod)
assert_(dpn == self.shape[0])
vertex_coors = self.coors[:self.n_vertex_dof, :]
ps = self.poly_space
gps = self.gel.poly_space
vertex_conn = self.econn[:, :self.gel.n_vertex]
eval_dofs = get_eval_dofs(dofs, self.econn, ps, ori=self.ori)
eval_coors = get_eval_coors(vertex_coors, vertex_conn, gps)
(level, coors, conn,
vdofs, mat_ids) = create_output(eval_dofs, eval_coors,
vertex_conn.shape[0], ps,
min_level=min_level,
max_level=max_level, eps=eps)
mesh = Mesh.from_data('linearized_mesh', coors, None, [conn], [mat_ids],
self.domain.mesh.descs)
return mesh, vdofs, level
[docs] def get_output_approx_order(self):
"""
Get the approximation order used in the output file.
"""
return min(self.approx_order, 1)
[docs] def create_output(self, dofs, var_name, dof_names=None,
key=None, extend=True, fill_value=None,
linearization=None):
"""
Convert the DOFs corresponding to the field to a dictionary of
output data usable by Mesh.write().
Parameters
----------
dofs : array, shape (n_nod, n_component)
The array of DOFs reshaped so that each column corresponds
to one component.
var_name : str
The variable name corresponding to `dofs`.
dof_names : tuple of str
The names of DOF components.
key : str, optional
The key to be used in the output dictionary instead of the
variable name.
extend : bool
Extend the DOF values to cover the whole domain.
fill_value : float or complex
The value used to fill the missing DOF values if `extend` is True.
linearization : Struct or None
The linearization configuration for higher order approximations.
Returns
-------
out : dict
The output dictionary.
"""
linearization = get_default(linearization, Struct(kind='strip'))
out = {}
if linearization.kind is None:
out[key] = Struct(name='output_data', mode='full',
data=dofs, var_name=var_name,
dofs=dof_names, field_name=self.name)
elif linearization.kind == 'strip':
if extend:
ext = self.extend_dofs(dofs, fill_value)
else:
ext = self.remove_extra_dofs(dofs)
if ext is not None:
approx_order = self.get_output_approx_order()
if approx_order != 0:
# Has vertex data.
out[key] = Struct(name='output_data', mode='vertex',
data=ext, var_name=var_name,
dofs=dof_names)
else:
ext.shape = (ext.shape[0], 1, ext.shape[1], 1)
out[key] = Struct(name='output_data', mode='cell',
data=ext, var_name=var_name,
dofs=dof_names)
else:
mesh, vdofs, levels = self.linearize(dofs,
linearization.min_level,
linearization.max_level,
linearization.eps)
out[key] = Struct(name='output_data', mode='vertex',
data=vdofs, var_name=var_name, dofs=dof_names,
mesh=mesh, levels=levels)
out = convert_complex_output(out)
return out
[docs] def create_mesh(self, extra_nodes=True):
"""
Create a mesh from the field region, optionally including the field
extra nodes.
"""
mesh = self.domain.mesh
if self.approx_order != 0:
if extra_nodes:
conn = self.econn
else:
conn = self.econn[:, :self.gel.n_vertex]
conns = [conn]
mat_ids = [mesh.cmesh.cell_groups]
descs = mesh.descs[:1]
if extra_nodes:
coors = self.coors
else:
coors = self.coors[:self.n_vertex_dof]
mesh = Mesh.from_data(self.name, coors, None, conns,
mat_ids, descs)
return mesh
[docs] def get_evaluate_cache(self, cache=None, share_geometry=False,
verbose=False):
"""
Get the evaluate cache for :func:`Variable.evaluate_at()
<sfepy.discrete.variables.Variable.evaluate_at()>`.
Parameters
----------
cache : Struct instance, optional
Optionally, use the provided instance to store the cache data.
share_geometry : bool
Set to True to indicate that all the evaluations will work on the
same region. Certain data are then computed only for the first
probe and cached.
verbose : bool
If False, reduce verbosity.
Returns
-------
cache : Struct instance
The evaluate cache.
"""
try:
from scipy.spatial import cKDTree as KDTree
except ImportError:
from scipy.spatial import KDTree
from sfepy.discrete.fem.geometry_element import create_geometry_elements
if cache is None:
cache = Struct(name='evaluate_cache')
timer = Timer(start=True)
if (cache.get('cmesh', None) is None) or not share_geometry:
mesh = self.create_mesh(extra_nodes=False)
cache.cmesh = cmesh = mesh.cmesh
gels = create_geometry_elements()
cmesh.set_local_entities(gels)
cmesh.setup_entities()
cache.centroids = cmesh.get_centroids(cmesh.tdim)
if self.gel.name != '3_8':
cache.normals0 = cmesh.get_facet_normals()
cache.normals1 = None
else:
cache.normals0 = cmesh.get_facet_normals(0)
cache.normals1 = cmesh.get_facet_normals(1)
output('cmesh setup: %f s' % timer.stop(), verbose=verbose)
timer.start()
if (cache.get('kdtree', None) is None) or not share_geometry:
cache.kdtree = KDTree(cmesh.coors)
output('kdtree: %f s' % timer.stop(), verbose=verbose)
return cache
[docs] def interp_to_qp(self, dofs):
"""
Interpolate DOFs into quadrature points.
The quadrature order is given by the field approximation order.
Parameters
----------
dofs : array
The array of DOF values of shape `(n_nod, n_component)`.
Returns
-------
data_qp : array
The values interpolated into the quadrature points.
integral : Integral
The corresponding integral defining the quadrature points.
"""
integral = Integral('i', order=self.approx_order)
bf = self.get_base('v', False, integral)
bf = bf[:,0,:].copy()
data_qp = nm.dot(bf, dofs[self.econn])
data_qp = nm.swapaxes(data_qp, 0, 1)
data_qp.shape = data_qp.shape + (1,)
return data_qp, integral
[docs] def get_coor(self, nods=None):
"""
Get coordinates of the field nodes.
Parameters
----------
nods : array, optional
The indices of the required nodes. If not given, the
coordinates of all the nodes are returned.
"""
if nods is None:
return self.coors
else:
return self.coors[nods]
[docs] def get_connectivity(self, region, integration, is_trace=False):
"""
Convenience alias to `Field.get_econn()`, that is used in some terms.
"""
return self.get_econn(integration, region, is_trace=is_trace)
[docs] 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()
tco = integration in ('volume', 'custom')
iels = region.get_cells(true_cells_only=tco)
transform = (self.basis_transform[iels] if self.basis_transform
is not None else None)
if integration == 'volume':
qp = self.get_qp('v', integral)
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=transform)
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)
if self.basis_transform is not None:
msg = 'surface integrals do not work with the' \
' basis transform!'
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], transform=transform)
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:
if self.basis_transform is not None:
msg = 'surface fields do not work with the' \
' basis transform!'
raise ValueError(msg)
# Do not use BQP for surface fields.
qp = self.get_qp(sd.face_type, integral)
bf = ps.eval_base(qp.vals, transform=transform)
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
[docs]class VolumeField(FEField):
"""
Finite element field base class over volume elements (element dimension
equals space dimension).
"""
def _check_region(self, region):
"""
Check whether the `region` can be used for the
field.
Returns
-------
ok : bool
True if the region is usable for the field.
"""
ok = True
domain = region.domain
if region.kind != 'cell':
output("bad region kind! (is: %r, should be: 'cell')"
% region.kind)
ok = False
elif (region.kind_tdim != domain.shape.tdim):
output('cells with a bad topological dimension! (%d == %d)'
% (region.kind_tdim, domain.shape.tdim))
ok = False
return ok
def _setup_geometry(self):
"""
Setup the field region geometry.
"""
cmesh = self.domain.cmesh
for key, gel in six.iteritems(self.domain.geom_els):
ct = cmesh.cell_types
if (ct[self.region.cells] == cmesh.key_to_index[gel.name]).all():
self.gel = gel
break
else:
raise ValueError('region %s of field %s contains multiple'
' reference geometries!'
% (self.region.name, self.name))
self.is_surface = False
def _create_interpolant(self):
name = '%s_%s_%s_%d%s' % (self.gel.name, self.space,
self.poly_space_base, self.approx_order,
'B' * self.force_bubble)
ps = PolySpace.any_from_args(name, self.gel, self.approx_order,
base=self.poly_space_base,
force_bubble=self.force_bubble)
self.poly_space = ps
def _init_econn(self):
"""
Initialize the extended DOF connectivity.
"""
n_ep = self.poly_space.n_nod
n_cell = self.region.get_n_cells()
self.econn = nm.zeros((n_cell, n_ep), nm.int32)
def _setup_vertex_dofs(self):
"""
Setup vertex DOF connectivity.
"""
if self.node_desc.vertex is None:
return 0, None
region = self.region
cmesh = self.domain.cmesh
conn, offsets = cmesh.get_incident(0, region.cells, region.tdim,
ret_offsets=True)
vertices = nm.unique(conn)
remap = prepare_remap(vertices, region.n_v_max)
n_dof = vertices.shape[0]
aux = nm.unique(nm.diff(offsets))
assert_(len(aux) == 1, 'region with multiple reference geometries!')
offset = aux[0]
# Remap vertex node connectivity to field-local numbering.
aux = conn.reshape((-1, offset)).astype(nm.int32)
self.econn[:, :offset] = nm.take(remap, aux)
return n_dof, remap
[docs] def setup_point_data(self, field, region):
if region.name not in self.point_data:
conn = field.get_dofs_in_region(region, merge=True)
conn.shape += (1,)
self.point_data[region.name] = conn
[docs] def setup_surface_data(self, region, is_trace=False, trace_region=None):
"""nodes[leconn] == econn"""
"""nodes are sorted by node number -> same order as region.vertices"""
if region.name not in self.surface_data:
sd = FESurface('surface_data_%s' % region.name, region,
self.efaces, self.econn, self.region)
self.surface_data[region.name] = sd
if region.name in self.surface_data and is_trace:
sd = self.surface_data[region.name]
sd.setup_mirror_connectivity(region, trace_region)
return self.surface_data[region.name]
[docs] def get_econn(self, conn_type, region, is_trace=False, integration=None,
local=False):
"""
Get extended connectivity of the given type in the given region.
"""
ct = conn_type.type if isinstance(conn_type, Struct) else conn_type
if ct in ('volume', 'custom'):
if region.name == self.region.name:
conn = self.econn
else:
tco = integration in ('volume', 'custom')
cells = region.get_cells(true_cells_only=tco)
ii = self.region.get_cell_indices(cells, true_cells_only=tco)
conn = nm.take(self.econn, ii, axis=0)
elif ct == 'surface':
if region.name not in self.surface_data:
self.domain.create_surface_group(region)
self.setup_surface_data(region)
sd = self.surface_data[region.name]
conn = sd.get_connectivity(local=local, is_trace=is_trace)
elif ct == 'edge':
raise NotImplementedError('connectivity type %s' % ct)
elif ct == 'point':
conn = self.point_data[region.name]
else:
raise ValueError('unknown connectivity type! (%s)' % ct)
return conn
[docs] def average_qp_to_vertices(self, data_qp, integral):
"""
Average data given in quadrature points in region elements into
region vertices.
.. math::
u_n = \sum_e (u_{e,avg} * volume_e) / \sum_e volume_e
= \sum_e \int_{volume_e} u / \sum volume_e
"""
region = self.region
n_cells = region.get_n_cells()
if n_cells != data_qp.shape[0]:
msg = 'incomatible shape! (%d == %d)' % (n_cells,
data_qp.shape[0])
raise ValueError(msg)
n_vertex = self.n_vertex_dof
nc = data_qp.shape[2]
nod_vol = nm.zeros((n_vertex,), dtype=nm.float64)
data_vertex = nm.zeros((n_vertex, nc), dtype=nm.float64)
vg = self.get_mapping(self.region, integral, 'volume')[0]
volume = nm.squeeze(vg.volume)
iels = self.region.get_cells()
data_e = nm.zeros((volume.shape[0], 1, nc, 1), dtype=nm.float64)
vg.integrate(data_e, data_qp[iels])
ir = nm.arange(nc, dtype=nm.int32)
conn = self.econn[:, :self.gel.n_vertex]
for ii, cc in enumerate(conn):
# Assumes unique nodes in cc!
ind2, ind1 = nm.meshgrid(ir, cc)
data_vertex[ind1,ind2] += data_e[iels[ii],0,:,0]
nod_vol[cc] += volume[ii]
data_vertex /= nod_vol[:,nm.newaxis]
return data_vertex
[docs]class SurfaceField(FEField):
"""
Finite element field base class over surface (element dimension is one
less than space dimension).
"""
def _check_region(self, region):
"""
Check whether the `region` can be used for the
field.
Returns
-------
ok : bool
True if the region is usable for the field.
"""
ok1 = ((region.kind_tdim == (region.tdim - 1))
and (region.get_n_cells(True) > 0))
if not ok1:
output('bad region topological dimension and kind! (%d, %s)'
% (region.tdim, region.kind))
n_ns = region.get_facet_indices().shape[0] - region.get_n_cells(True)
ok2 = n_ns == 0
if not ok2:
output('%d region facets are not on the domain surface!' % n_ns)
return ok1 and ok2
def _setup_geometry(self):
"""
Setup the field region geometry.
"""
for key, vgel in six.iteritems(self.domain.geom_els):
self.gel = vgel.surface_facet
break
if self.gel is None:
raise ValueError('cells with no surface!')
self.is_surface = True
def _create_interpolant(self):
name = '%s_%s_%s_%d%s' % (self.gel.name, self.space,
self.poly_space_base, self.approx_order,
'B' * self.force_bubble)
ps = PolySpace.any_from_args(name, self.gel, self.approx_order,
base=self.poly_space_base,
force_bubble=self.force_bubble)
self.poly_space = ps
def _init_econn(self):
"""
Initialize the extended DOF connectivity.
"""
n_ep = self.poly_space.n_nod
n_cell = self.region.get_n_cells(is_surface=self.is_surface)
self.econn = nm.zeros((n_cell, n_ep), nm.int32)
def _setup_vertex_dofs(self):
"""
Setup vertex DOF connectivity.
"""
if self.node_desc.vertex is None:
return 0, None
region = self.region
remap = prepare_remap(region.vertices, region.n_v_max)
n_dof = region.vertices.shape[0]
# Remap vertex node connectivity to field-local numbering.
conn, gel = self.domain.get_conn(ret_gel=True)
faces = gel.get_surface_entities()
aux = FESurface('aux', region, faces, conn)
self.econn[:, :aux.n_fp] = aux.leconn
self.surface_data[region.name] = aux
return n_dof, remap
def _setup_bubble_dofs(self):
"""
Setup bubble DOF connectivity.
"""
return 0, None, None
[docs] def get_econn(self, conn_type, region, is_trace=False,
integration=None):
"""
Get extended connectivity of the given type in the given region.
"""
ct = conn_type.type if isinstance(conn_type, Struct) else conn_type
if ct != 'surface':
msg = 'connectivity type must be "surface"! (%s)' % ct
raise ValueError(msg)
sd = self.surface_data[region.name]
conn = sd.get_connectivity(local=True, is_trace=is_trace)
return conn
[docs] def average_qp_to_vertices(self, data_qp, integral):
"""
Average data given in quadrature points in region elements into
region vertices.
.. math::
u_n = \sum_e (u_{e,avg} * area_e) / \sum_e area_e
= \sum_e \int_{area_e} u / \sum area_e
"""
region = self.region
n_cells = region.get_n_cells(True)
if n_cells != data_qp.shape[0]:
msg = 'incomatible shape! (%d == %d)' % (n_cells,
data_qp.shape[0])
raise ValueError(msg)
n_vertex = len(region.vertices)
nc = data_qp.shape[2]
nod_vol = nm.zeros((n_vertex,), dtype=nm.float64)
data_vertex = nm.zeros((n_vertex, nc), dtype=nm.float64)
sg = self.get_mapping(self.region, integral, 'surface')[0]
area = nm.squeeze(sg.volume)
n_cells = region.get_n_cells(True)
iels = nm.arange(n_cells, dtype=nm.int32)
data_e = nm.zeros((area.shape[0], 1, nc, 1), dtype=nm.float64)
sg.integrate(data_e, data_qp[iels])
ir = nm.arange(nc, dtype=nm.int32)
sd = self.domain.surface_groups[region.name]
# Should be vertex connectivity!
conn = sd.get_connectivity(local=True)
for ii, cc in enumerate(conn):
# Assumes unique nodes in cc!
ind2, ind1 = nm.meshgrid(ir, cc)
data_vertex[ind1,ind2] += data_e[iels[ii],0,:,0]
nod_vol[cc] += area[ii]
data_vertex /= nod_vol[:,nm.newaxis]
return data_vertex
[docs]class H1Mixin(Struct):
"""
Methods of fields specific to H1 space.
"""
def _setup_shape(self):
"""
Setup the field's shape-related attributes, see :class:`Field`.
"""
self.n_components = nm.prod(self.shape)
self.val_shape = self.shape