def plot_partitioning(axs, field, cell_tasks, gfd, output_dir, size):
"""
Plot the partitioning of the domain and field DOFs.
"""
mesh = field.domain.mesh
ax = pc.plot_wireframe(axs[0], mesh.cmesh)
coors = field.get_coor()
econn = field.econn
ax = pd.plot_global_dofs(ax, coors, econn)
ax.set_title('global DOFs')
ax.figure.savefig(os.path.join(output_dir, 'global_dofs.png'),
bbox_inches='tight')
ax = pc.plot_wireframe(axs[1], mesh.cmesh)
fig = ax.figure
coors = field.get_coor()
econn = field.econn
id_map = gfd.id_map
colors = nm.zeros((field.n_nod, 4))
for ir, dof_map in ordered_iteritems(gfd.dof_maps):
aux = id_map[dof_map[0]]
colors[aux] = [0, 0, float(ir + 1) / size, 0.6]
for aux in dof_map[1]:
colors[id_map[aux]] = [0, 0, float(ir + 1) / size, 0.9]
from sfepy.discrete.fem.utils import prepare_translate
aux = prepare_translate(id_map[econn], econn)
ax = label_dofs(ax, coors[aux], id_map, colors)
mark_subdomains(ax, mesh.cmesh, cell_tasks, size, 0, 0.7)
ax.set_title('subdomains of tasks and PETSc DOFs')
fig.savefig(os.path.join(output_dir, 'petsc_dofs.png'),
bbox_inches='tight')
ax.set_title('')
axis = ax.axis()
for ir, ocells in enumerate(gfd.overlap_cells):
aux = nm.zeros_like(cell_tasks)
aux[ocells] = 10
aux[gfd.cell_parts[ir]] = 1
ax = fig.add_axes(ax.get_position(), frameon=False, label='aux')
mark_subdomains(ax, mesh.cmesh, aux, 11, 1, 0.3, True)
ax.axis(axis)
ax.set_title('overlap cells on task %d' % ir)
fig.savefig(os.path.join(output_dir,
'petsc_overlaps_%02d.png' % ir),
bbox_inches='tight')
fig.delaxes(ax)
def plot_partitioning(axs, field, cell_tasks, gfd, output_dir, size):
"""
Plot the partitioning of the domain and field DOFs.
"""
mesh = field.domain.mesh
ax = pc.plot_wireframe(axs[0], mesh.cmesh)
coors = field.get_coor()
econn = field.econn
ax = pd.plot_global_dofs(ax, coors, econn)
ax.set_title('global DOFs')
ax.figure.savefig(os.path.join(output_dir, 'global_dofs.png'),
bbox_inches='tight')
ax = pc.plot_wireframe(axs[1], mesh.cmesh)
fig = ax.figure
coors = field.get_coor()
econn = field.econn
id_map = gfd.id_map
colors = nm.zeros((field.n_nod, 4))
for ir, dof_map in ordered_iteritems(gfd.dof_maps):
aux = id_map[dof_map[0]]
colors[aux] = [0, 0, float(ir + 1) / size, 0.6]
for aux in dof_map[1]:
colors[id_map[aux]] = [0, 0, float(ir + 1) / size, 0.9]
from sfepy.discrete.fem.utils import prepare_translate
aux = prepare_translate(id_map[econn], econn)
ax = label_dofs(ax, coors[aux], id_map, colors)
mark_subdomains(ax, mesh.cmesh, cell_tasks, size, 0, 0.7)
ax.set_title('subdomains of tasks and PETSc DOFs')
fig.savefig(os.path.join(output_dir, 'petsc_dofs.png'),
bbox_inches='tight')
ax.set_title('')
axis = ax.axis()
for ir, ocells in enumerate(gfd.overlap_cells):
aux = nm.zeros_like(cell_tasks)
aux[ocells] = 10
aux[gfd.cell_parts[ir]] = 1
ax = fig.add_axes(ax.get_position(), frameon=False, label='aux')
mark_subdomains(ax, mesh.cmesh, aux, 11, 1, 0.3, True)
ax.axis(axis)
ax.set_title('overlap cells on task %d' % ir)
fig.savefig(os.path.join(output_dir, 'petsc_overlaps_%02d.png' % ir),
bbox_inches='tight')
fig.delaxes(ax)
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.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)
ap = self.ap
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]
ap.econn[iel[:, None], iep] = gdofs
ori = oris[aux].ravel()
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
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.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)
ap = self.ap
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]
ap.econn[iel[:, None], iep] = gdofs
ori = oris[aux].ravel()
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
