import numpy as nm
from sfepy.base.base import assert_
from sfepy.discrete.fem.utils import prepare_remap, prepare_translate
from sfepy.discrete.common.dof_info import expand_nodes_to_dofs
from sfepy.discrete.fem.fields_base import FEField, H1Mixin
[docs]class H1HierarchicVolumeField(H1Mixin, FEField):
"""
Hierarchical basis approximation with Lobatto polynomials.
"""
family_name = 'volume_H1_lobatto'
def _init_econn(self):
"""
Initialize the extended DOF connectivity and facet orientation array.
"""
FEField._init_econn(self)
self.ori = nm.zeros_like(self.econn)
def _setup_facet_orientations(self):
self.node_desc = self.poly_space.describe_nodes()
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.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.n_vertex_dof + self.n_edge_dof)
def _setup_facet_dofs(self, dim, facet_desc, 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]
n_fp = 2 if dim == 1 else self.gel.surface_facet.n_vertex
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()
# 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 (repeating same values for
# each element.
iep = facet_desc[ies]
self.econn[iel[:, None], iep] = gdofs
ori = oris[aux].ravel()
if (n_fp == 2) and (self.gel.name in ['2_4', '3_8']):
tp_edges = self.gel.edges
ecs = self.gel.coors[tp_edges]
# True = positive, False = negative edge orientation w.r.t.
# reference tensor product axes.
tp_edge_ori = (nm.diff(ecs, axis=1).sum(axis=2) > 0).squeeze()
aux = nm.tile(tp_edge_ori, n_el)
ori = nm.where(aux, ori, 1 - ori)
if n_fp == 2: # Edges.
# ori == 1 means the basis has to be multiplied by -1.
ps = self.poly_space
orders = ps.node_orders
eori = nm.repeat(ori[:, None], n_dof_per_facet, 1)
eoo = orders[iep] % 2 # Odd orders.
self.ori[iel[:, None], iep] = eori * eoo
elif n_fp == 3: # Triangular faces.
raise NotImplementedError
else: # Quadrilateral faces.
# ori encoding in 3 bits:
# 0: axis swap, 1: axis 1 sign, 2: axis 2 sign
# 0 = + or False, 1 = - or True
# 63 -> 000 = 0
# 0 -> 001 = 1
# 30 -> 010 = 2
# 33 -> 011 = 3
# 11 -> 100 = 4
# 7 -> 101 = 5
# 52 -> 110 = 6
# 56 -> 111 = 7
# Special cases:
# Both orders same and even -> 000
# Both orders same and odd -> 0??
# Bits 1, 2 are multiplied by (swapped) axial order % 2.
new = nm.repeat(nm.arange(8, dtype=nm.int32), 3)
translate = prepare_translate([31, 59, 63,
0, 1, 4,
22, 30, 62,
32, 33, 41,
11, 15, 43,
3, 6, 7,
20, 52, 60,
48, 56, 57], new)
ori = translate[ori]
eori = nm.repeat(ori[:, None], n_dof_per_facet, 1)
ps = self.poly_space
orders = ps.face_axes_nodes[iep - ps.face_indx[0]]
eoo = orders % 2
eoo0, eoo1 = eoo[..., 0], eoo[..., 1]
i0 = nm.where(eori < 4)
i1 = nm.where(eori >= 4)
eori[i0] = nm.bitwise_and(eori[i0], 2*eoo0[i0] + 5)
eori[i0] = nm.bitwise_and(eori[i0], eoo1[i0] + 6)
eori[i1] = nm.bitwise_and(eori[i1], eoo0[i1] + 6)
eori[i1] = nm.bitwise_and(eori[i1], 2*eoo1[i1] + 5)
self.ori[iel[:, None], iep] = eori
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 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
# Hack - use only vertex DOFs.
gnods = self.get_dofs_in_region(region, merge=False)
nods = nm.concatenate(gnods)
n_dof = dpn * nods.shape[0]
if nm.isscalar(fun):
vals = nm.zeros(n_dof, dtype=nm.dtype(type(fun)))
vals[:gnods[0].shape[0] * dpn] = fun
elif callable(fun):
coors = self.get_coor(gnods[0])
vv = nm.asarray(fun(coors))
if (vv.ndim > 1) and (vv.shape != (len(coors), dpn)):
raise ValueError('The projected function return value should be'
' (n_point, dpn) == %s, instead of %s!'
% ((len(coors), dpn), vv.shape))
vals = nm.zeros(n_dof, dtype=vv.dtype)
vals[:gnods[0].shape[0] * dpn] = vv.ravel()
else:
raise ValueError('unknown function/value type! (%s)' % type(fun))
nods, indx = nm.unique(nods, return_index=True)
ii = (nm.tile(dpn * indx, dpn)
+ nm.tile(nm.arange(dpn, dtype=nm.int32), indx.shape[0]))
vals = vals[ii]
vals.shape = (len(nods), -1)
return nods, vals
[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