def _setup_global_base( self ):
"""
Setup global DOF/base function indices and connectivity of the field.
"""
self._setup_facet_orientations()
self._init_econn()
n_dof = 0
all_dofs = {}
remaps = {}
for ig, ap in self.aps.iteritems():
ii = self.region.get_cells(ig)
nd = nm.prod(ap.econn.shape)
group = self.domain.groups[ig]
remaps[ig] = prepare_remap(ii, group.shape.n_el)
aux = nm.arange(n_dof, n_dof + nd, dtype=nm.int32)
aux.shape = ap.econn.shape
ap.econn[:] = aux
all_dofs[ig] = aux
n_dof += nd
self.n_nod = n_dof
self.n_bubble_dof = n_dof
self.bubble_dofs = all_dofs
self.bubble_remaps = remaps
self.n_vertex_dof = self.n_edge_dof = self.n_face_dof = 0
self._setup_esurface()
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 = 0
n_dof_per_cell = self.node_desc.bubble.shape[0]
all_dofs = {}
remaps = {}
for ig, ap in self.aps.iteritems():
ii = self.region.get_cells(ig)
n_cell = ii.shape[0]
nd = n_dof_per_cell * n_cell
group = self.domain.groups[ig]
remaps[ig] = prepare_remap(ii, group.shape.n_el)
aux = nm.arange(offset + n_dof, offset + n_dof + nd,
dtype=nm.int32)
aux.shape = (n_cell, n_dof_per_cell)
iep = self.node_desc.bubble[0]
ap.econn[:,iep:] = aux
all_dofs[ig] = aux
n_dof += nd
return n_dof, all_dofs, remaps
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 = 0
n_dof_per_cell = self.node_desc.bubble.shape[0]
all_dofs = {}
remaps = {}
for ig, ap in self.aps.iteritems():
ii = self.region.get_cells(ig)
n_cell = ii.shape[0]
nd = n_dof_per_cell * n_cell
group = self.domain.groups[ig]
remaps[ig] = prepare_remap(ii, group.shape.n_el)
aux = nm.arange(offset + n_dof, offset + n_dof + nd,
dtype=nm.int32)
aux.shape = (n_cell, n_dof_per_cell)
iep = self.node_desc.bubble[0]
ap.econn[:,iep:] = aux
all_dofs[ig] = aux
n_dof += nd
return n_dof, all_dofs, remaps
def _setup_global_base( self ):
"""
Setup global DOF/base function indices and connectivity of the field.
"""
self._setup_facet_orientations()
self._init_econn()
n_dof = 0
all_dofs = {}
remaps = {}
for ig, ap in self.aps.iteritems():
ii = self.region.get_cells(ig)
nd = nm.prod(ap.econn.shape)
group = self.domain.groups[ig]
remaps[ig] = prepare_remap(ii, group.shape.n_el)
aux = nm.arange(n_dof, n_dof + nd, dtype=nm.int32)
aux.shape = ap.econn.shape
ap.econn[:] = aux
all_dofs[ig] = aux
n_dof += nd
self.n_nod = n_dof
self.n_bubble_dof = n_dof
self.bubble_dofs = all_dofs
self.bubble_remaps = remaps
self.n_vertex_dof = self.n_edge_dof = self.n_face_dof = 0
self._setup_esurface()
def _setup_vertex_dofs(self):
"""
Setup vertex DOF connectivity.
"""
if self.node_desc.vertex is None:
return 0, None
region = self.region
vertices = region.get_vertices_of_cells()
remap = prepare_remap(vertices, region.n_v_max)
n_dof = vertices.shape[0]
##
# Remap vertex node connectivity to field-local numbering.
for ig, ap in self.aps.iteritems():
group = self.domain.groups[ig]
offset = group.shape.n_ep
cells = region.get_cells(ig)
ap.econn[:,:offset] = nm.take(remap,
nm.take(group.conn,
cells.astype(nm.int32),
axis=0))
return n_dof, remap
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.domain.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 = self.region.domain.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)
for ig, ap in self.aps.iteritems():
gcells = self.region.get_cells(ig, offset=False)
n_el = gcells.shape[0]
indices = cconn.indices[offs[gcells[0]]:offs[gcells[-1]+1]]
facets_of_cells = remap[indices]
ori = oris[offs[gcells[0]]:offs[gcells[-1]+1]]
perms = facet_perms[ig][ori]
# Define global facet dof numbers.
gdofs = offset + expand_nodes_to_dofs(facets_of_cells,
n_dof_per_facet)
# 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)
# DOF columns in econn for each facet.
iep = facet_desc[ies]
iaux = nm.arange(gdofs.shape[0], dtype=nm.int32)
ap.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_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.domain.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 = self.region.domain.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)
for ig, ap in self.aps.iteritems():
gcells = self.region.get_cells(ig, offset=False)
n_el = gcells.shape[0]
indices = cconn.indices[offs[gcells[0]]:offs[gcells[-1] + 1]]
facets_of_cells = remap[indices]
ori = oris[offs[gcells[0]]:offs[gcells[-1] + 1]]
perms = facet_perms[ig][ori]
# Define global facet dof numbers.
gdofs = offset + expand_nodes_to_dofs(facets_of_cells,
n_dof_per_facet)
# 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)
# DOF columns in econn for each facet.
iep = facet_desc[ies]
iaux = nm.arange(gdofs.shape[0], dtype=nm.int32)
ap.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_facet_dofs(self, facets, facet_desc, facet_perms,
get_facets, 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]
# Prepare global facet id remapping to field-local numbering.
uids = []
for ig, ap in self.aps.iteritems():
ii = get_facets(ig)
uid_i = facets.uid_i[ii]
uids.append(uid_i)
uids = nm.unique(nm.concatenate(uids))
n_uid = uids.shape[0]
lids = nm.arange(n_uid, dtype=nm.int32)
remap = prepare_remap(uids, facets.n_unique)
all_dofs = offset + expand_nodes_to_dofs(lids, n_dof_per_facet)
for ig, ap in self.aps.iteritems():
ori = facets.oris[ig]
perms = facet_perms[ig][ori]
ii = get_facets(ig)
g_uid = facets.uid_i[ii]
uid = remap[g_uid]
# Define global facet dof numbers.
gdofs = offset + expand_nodes_to_dofs(uid, n_dof_per_facet)
# Elements of facets.
iel = facets.indices[ii, 1]
ies = facets.indices[ii, 2]
# DOF columns in econn for each facet.
iep = facet_desc[ies]
iaux = nm.arange(gdofs.shape[0], dtype=nm.int32)
ap.econn[iel[:, None], iep] = gdofs[iaux[:, None], perms]
n_dof = n_dof_per_facet * n_uid
assert_(n_dof == nm.prod(all_dofs.shape))
return n_dof, all_dofs, remap
def __init__(self, name, region, efaces, volume_econn, ig):
"""nodes[leconn] == econn"""
"""nodes are sorted by node number -> same order as region.vertices"""
self.name = get_default(name, 'surface_data_%s' % region.name)
face_indices = region.get_facet_indices(ig)
faces = efaces[face_indices[:,1]]
if faces.size == 0:
raise ValueError('region with group with no faces! (%s)'
% region.name)
try:
ee = volume_econn[face_indices[:,0]]
except:
raise ValueError('missing region face indices! (%s)'
% region.name)
econn = nm.empty(faces.shape, dtype=nm.int32)
for ir, face in enumerate( faces ):
econn[ir] = ee[ir,face]
nodes = nm.unique(econn)
remap = prepare_remap(nodes, nodes.max() + 1)
leconn = remap[econn].copy()
n_fa, n_fp = face_indices.shape[0], faces.shape[1]
face_type = 's%d' % n_fp
# Store bkey in SurfaceData, so that base function can be
# queried later.
bkey = 'b%s' % face_type[1:]
self.ig = ig
self.econn = econn
self.fis = nm.ascontiguousarray(face_indices.astype(nm.int32))
self.n_fa, self.n_fp = n_fa, n_fp
self.nodes = nodes
self.leconn = leconn
self.face_type = face_type
self.bkey = bkey
self.meconn = self.mleconn = None
if self.n_fp <= 4:
self.ori_map, _, _ = build_orientation_map(self.n_fp)
else:
self.ori_map = None
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.all_vertices, region.n_v_max)
n_dof = region.all_vertices.shape[0]
##
# Remap vertex node connectivity to field-local numbering.
for ig, ap in self.aps.iteritems():
group = self.domain.groups[ig]
faces = group.gel.get_surface_entities()
aux = FESurface('aux', region, faces, group.conn, ig)
ap.econn[:,:aux.n_fp] = aux.leconn
ap.surface_data[region.name] = aux
return n_dof, remap
def setup_mirror_connectivity(self, region):
"""
Setup mirror surface connectivity required to integrate over a
mirror region.
1. Get orientation of the faces:
a) for elements in group ig -> ooris (own)
b) for elements in group mig -> moris (mirror)
2. orientation -> permutation.
"""
mregion, ig_map, ig_map_i = region.get_mirror_region()
mig = ig_map_i[self.ig]
oo = self.ori_map
ori_map = nm.zeros((nm.max(oo.keys()) + 1, self.n_fp), dtype=nm.int32)
ori_map[oo.keys()] = nm.array([ii[1] for ii in oo.values()])
conn = region.domain.cmesh.get_conn_as_graph(region.dim, region.dim - 1)
oris = region.domain.cmesh.facet_oris
ofis = region.get_facet_indices(self.ig, offset=False)
ooris = oris[conn.indptr[ofis[:, 0]] + ofis[:, 1]]
mfis = mregion.get_facet_indices(mig, offset=False)
moris = oris[conn.indptr[mfis[:, 0]] + mfis[:, 1]]
omap = ori_map[ooris]
mmap = ori_map[moris]
n_el, n_ep = self.econn.shape
ii = nm.repeat(nm.arange(n_el)[:, None], n_ep, 1)
self.meconn = nm.empty_like(self.econn)
self.meconn[ii, omap] = self.econn[ii, mmap]
nodes = nm.unique(self.meconn)
remap = prepare_remap(nodes, nodes.max() + 1)
self.mleconn = remap[self.meconn].copy()
def _setup_facet_dofs(self, facets, facet_desc, get_facets, 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]
# Prepare global facet id remapping to field-local numbering.
uids = []
for ig, ap in self.aps.iteritems():
ii = get_facets(ig)
uid_i = facets.uid_i[ii]
uids.append(uid_i)
uids = nm.unique(nm.concatenate(uids))
n_uid = uids.shape[0]
lids = nm.arange(n_uid, dtype=nm.int32)
remap = prepare_remap(uids, facets.n_unique)
all_dofs = offset + expand_nodes_to_dofs(lids, n_dof_per_facet)
for ig, ap in self.aps.iteritems():
n_fp = facets.n_fps[ig]
if (n_fp == 2) and (ap.interp.gel.name in ['2_4', '3_8']):
tp_edges = ap.interp.gel.edges
ecs = ap.interp.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()
else:
tp_edge_ori = None
ori = facets.get_orientation(ig, tp_edge_ori)
ii = get_facets(ig)
g_uid = facets.uid_i[ii]
uid = remap[g_uid]
# Define global facet dof numbers.
gdofs = offset + expand_nodes_to_dofs(uid, n_dof_per_facet)
# Elements of facets.
iel = facets.indices[ii, 1]
ies = facets.indices[ii, 2]
# DOF columns in econn for each facet (repeating same values for
# each element.
iep = facet_desc[ies]
ap.econn[iel[:, None], iep] = gdofs
if n_fp == 2: # Edges.
# ori == 1 means the basis has to be multiplied by -1.
ps = ap.interp.poly_spaces['v']
orders = ps.node_orders
eori = nm.repeat(ori[:, None], n_dof_per_facet, 1)
eoo = orders[iep] % 2 # Odd orders.
ap.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 = ap.interp.poly_spaces['v']
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)
ap.ori[iel[:, None], iep] = eori
n_dof = n_dof_per_facet * n_uid
assert_(n_dof == nm.prod(all_dofs.shape))
return n_dof, all_dofs, remap
def _setup_facet_dofs(self, dim, facet_desc, get_facets, 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.domain.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 = self.region.domain.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)
for ig, ap in self.aps.iteritems():
gcells = self.region.get_cells(ig, offset=False)
n_el = gcells.shape[0]
indices = cconn.indices[offs[gcells[0]] : offs[gcells[-1] + 1]]
facets_of_cells = remap[indices]
# Define global facet dof numbers.
gdofs = offset + expand_nodes_to_dofs(facets_of_cells, n_dof_per_facet)
# 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)
# DOF columns in econn for each facet (repeating same values for
# each element.
iep = facet_desc[ies]
ap.econn[iel[:, None], iep] = gdofs
ori = oris[offs[gcells[0]] : offs[gcells[-1] + 1]]
if (n_fp == 2) and (ap.interp.gel.name in ["2_4", "3_8"]):
tp_edges = ap.interp.gel.edges
ecs = ap.interp.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 = ap.interp.poly_spaces["v"]
orders = ps.node_orders
eori = nm.repeat(ori[:, None], n_dof_per_facet, 1)
eoo = orders[iep] % 2 # Odd orders.
ap.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 = ap.interp.poly_spaces["v"]
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)
ap.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