def injection_matrix(Vc, Vf, fine_mesh, data):
'''Injection mapping from Vc to Vf'''
mesh_c = Vc.mesh()
assert fine_mesh.id() == Vf.mesh().id()
mesh_f = Vf.mesh()
if data['not_nested_method'] == 'interpolate':
return df.PETScDMCollection.create_transfer_matrix(Vc, Vf)
elif data['not_nested_method'] == 'project':
raise ValueError('Missing projection')
# Fallback to our interpolate with lookup, which, however is slower
# to `create_transfer_matrix`
tdim = mesh_f.topology().dim()
# Refine was used to create it
keys, fine_to_coarse = list(
zip(*list(fine_mesh.parent_entity_map[mesh_c.id()][tdim].items())))
fine_to_coarse = np.array(fine_to_coarse, dtype='uintp')
fine_to_coarse[np.argsort(keys)] = fine_to_coarse
# The idea is to evaluate Vf's degrees of freedom at basis functions of Vc
fdmap = Vf.dofmap()
Vf_dof = DegreeOfFreedom(Vf)
cdmap = Vc.dofmap()
Vc_basis_f = FEBasisFunction(Vc)
# Column values
visited_rows = [False] * Vf.dim()
row_values = np.zeros(Vc_basis_f.elm.space_dimension(), dtype='double')
with petsc_serial_matrix(Vf, Vc) as mat:
for f_cell, c_cell in enumerate(fine_to_coarse):
Vc_basis_f.cell = c_cell
# These are the colums
coarse_dofs = cdmap.cell_dofs(c_cell)
Vf_dof.cell = f_cell
fine_dofs = fdmap.cell_dofs(f_cell)
for local, dof in enumerate(fine_dofs):
if visited_rows[dof]:
continue
else:
visited_rows[dof] = True
Vf_dof.dof = local
# Evaluete coarse basis foos here
for local_c, dof_c in enumerate(coarse_dofs):
Vc_basis_f.dof = local_c
row_values[local_c] = Vf_dof.eval(Vc_basis_f)
# Insert
mat.setValues([dof], coarse_dofs, row_values,
PETSc.InsertMode.INSERT_VALUES)
return PETScMatrix(mat)
def restriction_matrix(V, TV, rmesh):
'''The first cell connected to the facet gets to set the values of TV'''
assert TV.mesh().id() == rmesh.id()
mesh = V.mesh()
tdim = mesh.topology().dim()
# Let's get the mapping or cell of TV mesh to V mesh cells
mapping = rmesh.parent_entity_map[mesh.id()][tdim]
# The idea is to evaluate TV's degrees of freedom at basis functions
# of V
Tdmap = TV.dofmap()
TV_dof = DegreeOfFreedom(TV)
dmap = V.dofmap()
V_basis_f = FEBasisFunction(V)
# Rows
visited_dofs = [False] * TV.dim()
# Column values
dof_values = np.zeros(V_basis_f.elm.space_dimension(), dtype='double')
with petsc_serial_matrix(TV, V) as mat:
for trace_cell in range(TV.mesh().num_cells()):
TV_dof.cell = trace_cell
trace_dofs = Tdmap.cell_dofs(trace_cell)
# The corresponding cell in V mesh
cell = mapping[trace_cell]
V_basis_f.cell = cell
dofs = dmap.cell_dofs(cell)
for local_T, dof_T in enumerate(trace_dofs):
if visited_dofs[dof_T]:
continue
else:
visited_dofs[dof_T] = True
# Define trace dof
TV_dof.dof = local_T
# Eval at V basis functions
for local, dof in enumerate(dofs):
# Set which basis foo
V_basis_f.dof = local
dof_values[local] = TV_dof.eval(V_basis_f)
# Can fill the matrix now
col_indices = np.array(dofs, dtype='int32')
# Insert
mat.setValues([dof_T], col_indices, dof_values,
PETSc.InsertMode.INSERT_VALUES)
return mat
def restriction_matrix(V, TV, rmesh):
'''The first cell connected to the facet gets to set the values of TV'''
assert TV.mesh().id() == rmesh.id()
mesh = V.mesh()
tdim = mesh.topology().dim()
# Let's get the mapping or cell of TV mesh to V mesh cells
mapping = rmesh.parent_entity_map[mesh.id()][tdim]
# The idea is to evaluate TV's degrees of freedom at basis functions
# of V
Tdmap = TV.dofmap()
TV_dof = DegreeOfFreedom(TV)
dmap = V.dofmap()
V_basis_f = FEBasisFunction(V)
# Rows
visited_dofs = [False]*TV.dim()
# Column values
dof_values = np.zeros(V_basis_f.elm.space_dimension(), dtype='double')
with petsc_serial_matrix(TV, V) as mat:
for trace_cell in range(TV.mesh().num_cells()):
TV_dof.cell = trace_cell
trace_dofs = Tdmap.cell_dofs(trace_cell)
# The corresponding cell in V mesh
cell = mapping[trace_cell]
V_basis_f.cell = cell
dofs = dmap.cell_dofs(cell)
for local_T, dof_T in enumerate(trace_dofs):
if visited_dofs[dof_T]:
continue
else:
visited_dofs[dof_T] = True
# Define trace dof
TV_dof.dof = local_T
# Eval at V basis functions
for local, dof in enumerate(dofs):
# Set which basis foo
V_basis_f.dof = local
dof_values[local] = TV_dof.eval(V_basis_f)
# Can fill the matrix now
col_indices = np.array(dofs, dtype='int32')
# Insert
mat.setValues([dof_T], col_indices, dof_values, PETSc.InsertMode.INSERT_VALUES)
return mat
def injection_matrix(Vc, Vf):
'''Injection mapping from Vc to Vf'''
mesh_c = Vc.mesh()
mesh_f = Vf.mesh()
assert mesh_f.has_parent() and mesh_c.has_child()
assert mesh_f.parent().id() == mesh_c.id()
fine_to_coarse = mesh_f.data().array('parent_cell',
mesh_f.topology().dim())
# The idea is to evaluate Vf's degrees of freedom at basis functions of Vc
fdmap = Vf.dofmap()
Vf_dof = DegreeOfFreedom(Vf)
cdmap = Vc.dofmap()
Vc_basis_f = FEBasisFunction(Vc)
# Column values
visited_rows = [False] * Vf.dim()
row_values = np.zeros(Vc_basis_f.elm.space_dimension(), dtype='double')
with petsc_serial_matrix(Vf, Vc) as mat:
for f_cell, c_cell in enumerate(fine_to_coarse):
Vc_basis_f.cell = c_cell
# These are the colums
coarse_dofs = cdmap.cell_dofs(c_cell)
Vf_dof.cell = f_cell
fine_dofs = fdmap.cell_dofs(f_cell)
for local, dof in enumerate(fine_dofs):
if visited_rows[dof]:
continue
else:
visited_rows[dof] = True
Vf_dof.dof = local
# Evaluete coarse basis foos here
for local_c, dof_c in enumerate(coarse_dofs):
Vc_basis_f.dof = local_c
row_values[local_c] = Vf_dof.eval(Vc_basis_f)
# Insert
mat.setValues([dof], coarse_dofs, row_values,
PETSc.InsertMode.INSERT_VALUES)
# Transpose
return mat
def interpolation_mat(V, Q):
'''
Matrix representation of interpolation operator from V to Q
'''
# Compatibility of spaces
assert V.dolfin_element().value_rank() == Q.dolfin_element().value_rank()
assert V.ufl_element().value_shape() == Q.ufl_element().value_shape()
# We assume that the spaces are constructed on the same mesh
assert V.mesh().id() == Q.mesh().id()
# The idea is to evaluate Q's degrees of freedom at basis functions of V
V_dm = V.dofmap()
V_basis_f = FEBasisFunction(V)
Q_dm = Q.dofmap()
Q_dof = DegreeOfFreedom(Q)
visited_rows = np.zeros(Q.dim(), dtype=bool)
# Column values for row
column_values = np.zeros(V_basis_f.elm.space_dimension(), dtype='double')
with petsc_serial_matrix(Q, V) as mat:
for cell in xrange(V.mesh().num_cells()):
Q_dof.cell = cell
V_basis_f.cell = cell
cell_rows = Q_dm.cell_dofs(cell)
column_indices = np.array(V_dm.cell_dofs(cell), dtype='int32')
for local_row, row in enumerate(cell_rows):
if visited_rows[row]: continue
visited_rows[row] = True
# Define dof
Q_dof.dof = local_row
# Eval at V basis functions
for local_col, col in enumerate(column_indices):
# Set which basis foo
V_basis_f.dof = local_col
column_values[local_col] = Q_dof.eval(V_basis_f)
# Can fill the matrix now
mat.setValues([row], column_indices, column_values,
PETSc.InsertMode.INSERT_VALUES)
return mat
def trace_mat_no_restrict(V, TV, trace_mesh=None, tag_data=None):
'''The first cell connected to the facet gets to set the values of TV'''
mesh = V.mesh()
if trace_mesh is None: trace_mesh = TV.mesh()
fdim = trace_mesh.topology().dim()
# None means all
if tag_data is None:
tag_data = (MeshFunction('size_t', trace_mesh,
trace_mesh.topology().dim(), 0), set((0, )))
trace_mesh_subdomains, tags = tag_data
# Init/extract the mapping
try:
assert get_entity_map(mesh, trace_mesh, trace_mesh_subdomains, tags)
except (AssertionError, IndexError):
warning('Using non-conforming trace')
# So non-conforming matrix returns PETSc.Mat
return nonconforming_trace_mat(V, TV)
# We can get it
mapping = trace_mesh.parent_entity_map[mesh.id()][
fdim] # Map cell of TV to cells of V
mesh.init(fdim, fdim + 1)
f2c = mesh.topology()(fdim, fdim + 1) # Facets of V to cell of V
# The idea is to evaluate TV's degrees of freedom at basis functions
# of V
Tdmap = TV.dofmap()
TV_dof = DegreeOfFreedom(TV)
dmap = V.dofmap()
V_basis_f = FEBasisFunction(V)
# Only look at tagged cells
trace_cells = itertools.chain(*[
itertools.imap(operator.methodcaller('index'),
SubsetIterator(trace_mesh_subdomains, tag))
for tag in tags
])
# Rows
visited_dofs = [False] * TV.dim()
# Column values
dof_values = np.zeros(V_basis_f.elm.space_dimension(), dtype='double')
with petsc_serial_matrix(TV, V) as mat:
for trace_cell in trace_cells:
# We might
TV_dof.cell = trace_cell
trace_dofs = Tdmap.cell_dofs(trace_cell)
# Figure out the dofs of V to use here. Does not matter which
# cell of the connected ones we pick
cell = f2c(mapping[trace_cell])[0]
V_basis_f.cell = cell
dofs = dmap.cell_dofs(cell)
for local_T, dof_T in enumerate(trace_dofs):
if visited_dofs[dof_T]:
continue
else:
visited_dofs[dof_T] = True
# Define trace dof
TV_dof.dof = local_T
# Eval at V basis functions
for local, dof in enumerate(dofs):
# Set which basis foo
V_basis_f.dof = local
dof_values[local] = TV_dof.eval(V_basis_f)
# Can fill the matrix now
col_indices = np.array(dofs, dtype='int32')
# Insert
mat.setValues([dof_T], col_indices, dof_values,
PETSc.InsertMode.INSERT_VALUES)
return mat
def trace_mat_two_restrict(V, TV, restriction, normal, trace_mesh=None):
'''
Compute the trace values using avg/jump restriction. A + plus is the one
for which the vector cell.midpoint - facet.midpoint agrees in orientation
with the normal on the facet.
'''
mesh = V.mesh()
fdim = mesh.topology().dim() - 1
if trace_mesh is None: trace_mesh = TV.mesh()
# Init/extract entity map
assert get_entity_map(mesh, trace_mesh)
# We can get it
mapping = trace_mesh.parent_entity_map[mesh.id()][
fdim] # Map cell of TV to cells of V
mesh.init(fdim, fdim + 1)
f2c = mesh.topology()(fdim, fdim + 1) # Facets of V to cell of V
# The idea is to evaluate TV's degrees of freedom at basis functions
# of V
Tdmap = TV.dofmap()
TV_dof = DegreeOfFreedom(TV)
dmap = V.dofmap()
V_basis_f = FEBasisFunction(V)
# We define avg as sum(+, -)/2 and jump as sum(+, neg(-))
operator_pieces = {
'avg': (lambda x: x / 2, lambda x: x / 2),
'jump': (lambda x: x, lambda x: -x)
}[restriction]
gdim = mesh.geometry().dim()
# Rows
visited_dofs = [False] * TV.dim()
# Column values
dof_values = np.zeros(V_basis_f.elm.space_dimension(), dtype='double')
with petsc_serial_matrix(TV, V) as mat:
for trace_cell in range(trace_mesh.num_cells()):
TV_dof.cell = trace_cell
trace_dofs = Tdmap.cell_dofs(trace_cell)
# Figure out the dofs of V to use here
facet_cells = f2c(mapping[trace_cell])
assert 0 < len(facet_cells) < 3
# Ignore boundary facets
if len(facet_cells) == 1:
facet_cells = [facet_cells[0]]
modifiers = (lambda x: x, ) # Do nothing
# Search which cell has the right sign
else:
signs = [None, None]
# Order such that '+' is first
t_mp = Cell(trace_mesh, trace_cell).midpoint().array()[:gdim]
mp = Cell(mesh, facet_cells[0]).midpoint().array()[:gdim]
sign = '+' if np.inner(mp - t_mp, normal(t_mp)) > 0 else '-'
# Need to flip
if sign == '-':
facet_cells = facet_cells[::-1]
# As requested
modifiers = operator_pieces
for local_T, dof_T in enumerate(trace_dofs):
if visited_dofs[dof_T]:
continue
else:
visited_dofs[dof_T] = True
# Define trace dof
TV_dof.dof = local_T
# Two sweeps to set the values in the row
ADD_VALUES = False
for modify, cell in zip(modifiers, facet_cells):
V_basis_f.cell = cell
dofs = dmap.cell_dofs(cell)
# Eval at V basis functions
for local, dof in enumerate(dofs):
# Set which basis foo
V_basis_f.dof = local
dof_values[local] = modify(TV_dof.eval(V_basis_f))
# Can fill the matrix now
col_indices = np.array(dofs, dtype='int32')
if not ADD_VALUES:
mat.setValues([dof_T], col_indices, dof_values,
PETSc.InsertMode.INSERT_VALUES)
ADD_VALUES = True
#print 'setting', dof_T, col_indices, dof_values
else:
mat.setValues([dof_T], col_indices, dof_values,
PETSc.InsertMode.ADD_VALUES)
#print 'adding', dof_T, col_indices, dof_values
return mat
def trace_mat_one_restrict(V,
TV,
restriction,
normal,
trace_mesh=None,
tag_data=None):
'''
Compute the trace values using +/- restriction. A + plus is the one
for which the vector cell.midpoint - facet.midpoint agrees in orientation
with the normal on the facet.
'''
mesh = V.mesh()
fdim = mesh.topology().dim() - 1
if trace_mesh is None: trace_mesh = TV.mesh()
# None means all
if tag_data is None:
tag_data = (MeshFunction('size_t', trace_mesh,
trace_mesh.topology().dim(), 0), set((0, )))
trace_mesh_subdomains, tags = tag_data
# Only look at tagged cells
trace_cells = itertools.chain(*[
itertools.imap(operator.methodcaller('index'),
SubsetIterator(trace_mesh_subdomains, tag))
for tag in tags
])
# Init/extract entity map
assert get_entity_map(mesh, trace_mesh, trace_mesh_subdomains, tags)
# We can get it
mapping = trace_mesh.parent_entity_map[mesh.id()][
fdim] # Map cell of TV to cells of V
mesh.init(fdim, fdim + 1)
f2c = mesh.topology()(fdim, fdim + 1) # Facets of V to cell of V
# The idea is to evaluate TV's degrees of freedom at basis functions
# of V
Tdmap = TV.dofmap()
TV_dof = DegreeOfFreedom(TV)
dmap = V.dofmap()
V_basis_f = FEBasisFunction(V)
gdim = mesh.geometry().dim()
# Rows
visited_dofs = [False] * TV.dim()
# Column values
dof_values = np.zeros(V_basis_f.elm.space_dimension(), dtype='double')
with petsc_serial_matrix(TV, V) as mat:
for trace_cell in trace_cells:
TV_dof.cell = trace_cell
trace_dofs = Tdmap.cell_dofs(trace_cell)
# Figure out the dofs of V to use here
facet_cells = f2c(mapping[trace_cell])
assert 0 < len(facet_cells) < 3
# Ignore boundary facets
if len(facet_cells) == 1:
cell = facet_cells[0]
# Search which cell has the right sign
else:
signs = []
for fcell in facet_cells:
t_mp = Cell(trace_mesh,
trace_cell).midpoint().array()[:gdim]
mp = Cell(mesh, fcell).midpoint().array()[:gdim]
sign = '+' if np.inner(mp -
t_mp, normal(t_mp)) > 0 else '-'
signs.append(sign)
cell = facet_cells[signs.index(restriction)]
V_basis_f.cell = cell
dofs = dmap.cell_dofs(cell)
for local_T, dof_T in enumerate(trace_dofs):
if visited_dofs[dof_T]:
continue
else:
visited_dofs[dof_T] = True
# Define trace dof
TV_dof.dof = local_T
# Eval at V basis functions
for local, dof in enumerate(dofs):
# Set which basis foo
V_basis_f.dof = local
dof_values[local] = TV_dof.eval(V_basis_f)
# Can fill the matrix now
col_indices = np.array(dofs, dtype='int32')
# Insert
mat.setValues([dof_T], col_indices, dof_values,
PETSc.InsertMode.INSERT_VALUES)
return mat
def trace_mat_no_restrict(V, TV, trace_mesh=None):
'''The first cell connected to the facet gets to set the values of TV'''
mesh = V.mesh()
if trace_mesh is None: trace_mesh = TV.mesh()
fdim = trace_mesh.topology().dim()
# Init/extract the mapping
assert get_entity_map(mesh, trace_mesh)
# We can get it
mapping = trace_mesh.parent_entity_map[mesh.id()][
fdim] # Map cell of TV to cells of V
mesh.init(fdim, fdim + 1)
f2c = mesh.topology()(fdim, fdim + 1) # Facets of V to cell of V
# The idea is to evaluate TV's degrees of freedom at basis functions
# of V
Tdmap = TV.dofmap()
TV_dof = DegreeOfFreedom(TV)
dmap = V.dofmap()
V_basis_f = FEBasisFunction(V)
# Rows
visited_dofs = [False] * TV.dim()
# Column values
dof_values = np.zeros(V_basis_f.elm.space_dimension(), dtype='double')
with petsc_serial_matrix(TV, V) as mat:
for trace_cell in range(TV.mesh().num_cells()):
TV_dof.cell = trace_cell
trace_dofs = Tdmap.cell_dofs(trace_cell)
# Figure out the dofs of V to use here. Does not matter which
# cell of the connected ones we pick
cell = f2c(mapping[trace_cell])[0]
V_basis_f.cell = cell
dofs = dmap.cell_dofs(cell)
for local_T, dof_T in enumerate(trace_dofs):
if visited_dofs[dof_T]:
continue
else:
visited_dofs[dof_T] = True
# Define trace dof
TV_dof.dof = local_T
# Eval at V basis functions
for local, dof in enumerate(dofs):
# Set which basis foo
V_basis_f.dof = local
dof_values[local] = TV_dof.eval(V_basis_f)
# Can fill the matrix now
col_indices = np.array(dofs, dtype='int32')
# Insert
mat.setValues([dof_T], col_indices, dof_values,
PETSc.InsertMode.INSERT_VALUES)
return mat
def nonconforming_trace_mat(V, T):
'''
Matrix taking function f from d dim space V to g in (d-1) space T.
T(f) ~ g should hold.
'''
# For this to work I only make sure that function values are the same
assert V.ufl_element().value_shape() == T.ufl_element().value_shape()
# I want to evaluate T degrees of freedom at V basis functions, i.e.
# L^T_k{phi^V_l}. The picture is
#
# ------
# \ /\
# ===\==/==\====T
# \/----\
#
# and thus is assume that each dof of T space (row) will involve
# collisions with several cells/basis function of V space. However
# here we only snap to the first one
mesh = V.mesh() # The (d-1)trace mesh
tree = mesh.bounding_box_tree()
limit = mesh.num_entities_global(mesh.topology().dim())
Tdm = T.dofmap()
elm_T = T.element()
# Colliding cells with trace dofs
collisions = []
for Tdof_x in T.tabulate_dof_coordinates().reshape((T.dim(), -1)):
c = tree.compute_first_entity_collision(df.Point(*Tdof_x))
# Contained?
c >= limit and df.warning('Some colliding cells not found')
collisions.append(c)
# So we fill rows by checking basis functions of on the isected cells
Vdm = V.dofmap()
elm_V = V.element()
V_basis_function = FEBasisFunction(V)
T_degree_of_freedom = DegreeOfFreedom(T)
X_T = T.tabulate_dof_coordinates().reshape((T.dim(), -1))
X_V = V.tabulate_dof_coordinates().reshape((V.dim(), -1))
visited_dofs = np.zeros(T.dim(), dtype=bool)
col_values = np.zeros(V_basis_function.elm.space_dimension(),
dtype='double')
with petsc_serial_matrix(T, V) as mat:
for Tcell in range(T.mesh().num_cells()):
# Set for this cell
T_degree_of_freedom.cell = Tcell
Tdofs = Tdm.cell_dofs(Tcell)
for local_T, Tdof in enumerate(Tdofs):
# Seen the row?
if visited_dofs[Tdof]: continue
visited_dofs[Tdof] = True
# Set to current dof
T_degree_of_freedom.dof = local_T
# Now all the V cells and their basis functions
c = collisions[Tdof]
# If we have no reasonable cell leave the row empty
if c >= limit: continue
# Set the dof cell
V_basis_function.cell = c
Vdofs = np.array(Vdm.cell_dofs(c),
dtype='int32') # These are columns
# Fill column
for local_V, Vdof in enumerate(Vdofs):
# Set as basis_function
V_basis_function.dof = local_V
# Evaluate trace dof at basis function
dof_value = T_degree_of_freedom.eval(V_basis_function)
col_values[local_V] = dof_value
mat.setValues([Tdof], Vdofs, col_values,
PETSc.InsertMode.INSERT_VALUES)
return mat
def trace_mat_no_restrict(V, TV, trace_mesh=None, tag_data=None):
'''The first cell connected to the facet gets to set the values of TV'''
mesh = V.mesh()
if trace_mesh is None: trace_mesh = TV.mesh()
fdim = trace_mesh.topology().dim()
# None means all
if tag_data is None:
try:
marking_function = trace_mesh.marking_function
tag_data = (marking_function, set(marking_function.array()))
except AttributeError:
tag_data = (MeshFunction('size_t', trace_mesh,
trace_mesh.topology().dim(), 0), set(
(0, )))
trace_mesh_subdomains, tags = tag_data
# Init/extract the mapping
try:
assert get_entity_map(mesh, trace_mesh, trace_mesh_subdomains, tags)
except (AssertionError, IndexError):
warning('Using non-conforming trace')
# So non-conforming matrix returns PETSc.Mat
return nonconforming_trace_mat(V, TV)
if V.ufl_element().family() == 'HDiv Trace':
assert V.ufl_element().degree() == 0
# In this case
return DLT_trace_mat(V, TV, trace_mesh=trace_mesh, tag_data=tag_data)
# We can get it
mapping = trace_mesh.parent_entity_map[mesh.id()][
fdim] # Map cell of TV to cells of V
mesh.init(fdim, fdim + 1)
f2c = mesh.topology()(fdim, fdim + 1) # Facets of V to cell of V
# The idea is to evaluate TV's degrees of freedom at basis functions of V
Tdmap = TV.dofmap()
TV_dof = DegreeOfFreedom(TV)
dmap = V.dofmap()
V_basis_f = FEBasisFunction(V)
# Only look at tagged cells
trace_cells = list(
itertools.chain(*[
map(operator.methodcaller('index'),
SubsetIterator(trace_mesh_subdomains, tag)) for tag in tags
]))
ndofs_elm, nbasis_elm = TV_dof.elm.space_dimension(
), V_basis_f.elm.space_dimension()
local_values = np.zeros((nbasis_elm, ndofs_elm))
if len(trace_cells) > 10_000:
print(f'Trace mat {TV.ufl_element()} -> {V.ufl_element()}')
trace_cells = tqdm.tqdm(trace_cells, total=len(trace_cells))
rows, cols, values = [], [], []
# DG spaces don't share rows between cells so we take advantage of
# this in special branch
if TV.ufl_element().family() == 'Discontinuous Lagrange':
for trace_cell in trace_cells:
TV_dof.cell = trace_cell
# Many rows at once
trace_dofs = Tdmap.cell_dofs(trace_cell)
# Figure out the dofs of V to use here. Does not matter which
# cell of the connected ones we pick
cell = f2c(mapping[trace_cell])[0]
V_basis_f.cell = cell
# Columns for the rows
dofs = dmap.cell_dofs(cell)
for local, dof in enumerate(dofs):
# Set which basis foo
V_basis_f.dof = local
# Get all rows at once
local_values[local][:] = TV_dof.eval_dofs(V_basis_f)
# Indices for the filled piece
rows_ = np.tile(trace_dofs, nbasis_elm)
cols_ = np.repeat(dofs, ndofs_elm)
rows.extend(rows_)
cols.extend(cols_)
values.extend(local_values.flat)
# FIXME: Othewise we need to take care of duplicate entrieselse:
else:
needs_fill = np.ones(TV.dim(), dtype=bool)
for trace_cell in trace_cells:
TV_dof.cell = trace_cell
# Many rows at once
trace_dofs = Tdmap.cell_dofs(trace_cell)
# Don't add duplicates
unseen = needs_fill[trace_dofs] # Some will be true and
# For the future
needs_fill[trace_dofs[unseen]] = False
# Figure out the dofs of V to use here. Does not matter which
# cell of the connected ones we pick
cell = f2c(mapping[trace_cell])[0]
V_basis_f.cell = cell
# Columns for the rows
dofs = dmap.cell_dofs(cell)
for local, dof in enumerate(dofs):
# Set which basis foo
V_basis_f.dof = local
# Get all rows at once
local_values[local][:] = TV_dof.eval_dofs(V_basis_f)
# Indices for the filled piece
rows_ = np.tile(trace_dofs[unseen], nbasis_elm)
cols_ = np.repeat(dofs, sum(unseen))
rows.extend(rows_)
cols.extend(cols_)
values.extend(local_values[:, unseen].flat)
mat = csr_matrix((values, (rows, cols)), shape=(TV.dim(), V.dim()))
return PETSc.Mat().createAIJ(comm=PETSc.COMM_WORLD,
size=mat.shape,
csr=(mat.indptr, mat.indices, mat.data))
def nonconforming_trace_mat(V, T):
'''
Matrix taking function f from d dim space V to g in (d-1) space T.
T(f) ~ g should hold.
'''
# For this to work I only make sure that function values are the same
assert V.dolfin_element().value_rank() == T.dolfin_element().value_rank()
assert V.ufl_element().value_shape() == T.ufl_element().value_shape()
# I want to evaluate T degrees of freedom at V basis functions, i.e.
# L^T_k{phi^V_l}. The picture is
#
# ------
# \ /\
# ===\==/==\====T
# \/----\
#
# and thus is assume that each dof of T space (row) will involve
# collisions with several cells/basis function of V space
mesh = V.mesh() # The (d-1)trace mesh
tree = mesh.bounding_box_tree()
limit = mesh.topology().size_global(mesh.topology().dim())
Tdm = T.dofmap()
elm_T = T.element()
# Colliding cells with trace dofs
collisions = []
for Tdof_x in T.tabulate_dof_coordinates().reshape((T.dim(), -1)):
cs = tree.compute_entity_collisions(Point(*Tdof_x))
if any(c >= limit for c in cs):
warning('Some colliding cells not found')
cs = filter(lambda c: c < limit, cs)
collisions.append(cs)
# So we fill rows by checking basis functions of on the isected cells
Vdm = V.dofmap()
elm_V = V.element()
V_basis_function = FEBasisFunction(V)
T_degree_of_freedom = DegreeOfFreedom(T)
visited_dofs = [False]*T.dim()
with petsc_serial_matrix(T, V) as mat:
for Tcell in range(T.mesh().num_cells()):
# Set for this cell
T_degree_of_freedom.cell = Tcell
Tdofs = Tdm.cell_dofs(Tcell)
for local_T, Tdof in enumerate(Tdofs):
# Seen the row?
if visited_dofs[Tdof]: continue
visited_dofs[Tdof] = True
# Set to current dof
T_degree_of_freedom.dof = local_T
col_indices, col_values = [], []
# Now all the V cells and their basis functions
for c in collisions[Tdof]:
# Set the dof cell
V_basis_function.cell = c
Vdofs = Vdm.cell_dofs(c)
# Columns
for local_V, Vdof in enumerate(Vdofs):
if Vdof in col_indices:
continue
# Set as basis_function
V_basis_function.dof = local_V
# Evaluate trace dof at basis function
dof_value = T_degree_of_freedom.eval(V_basis_function)
col_indices.append(Vdof)
col_values.append(dof_value)
# Can fill the matrix row
col_indices = np.array(col_indices, dtype='int32')
col_values = np.array(col_values)
mat.setValues([Tdof], col_indices, col_values, PETSc.InsertMode.INSERT_VALUES)
return mat
def trace_mat_no_restrict(V, TV, trace_mesh=None):
'''The first cell connected to the facet gets to set the values of TV'''
mesh = V.mesh()
if trace_mesh is None: trace_mesh = TV.mesh()
fdim = trace_mesh.topology().dim()
# Init/extract the mapping
try:
assert get_entity_map(mesh, trace_mesh)
except AssertionError:
warning('Using non-conforming trace')
return nonconforming_trace_mat(V, TV)
# We can get it
mapping = trace_mesh.parent_entity_map[mesh.id()][fdim] # Map cell of TV to cells of V
mesh.init(fdim, fdim+1)
f2c = mesh.topology()(fdim, fdim+1) # Facets of V to cell of V
# The idea is to evaluate TV's degrees of freedom at basis functions
# of V
Tdmap = TV.dofmap()
TV_dof = DegreeOfFreedom(TV)
dmap = V.dofmap()
V_basis_f = FEBasisFunction(V)
# Rows
visited_dofs = [False]*TV.dim()
# Column values
dof_values = np.zeros(V_basis_f.elm.space_dimension(), dtype='double')
with petsc_serial_matrix(TV, V) as mat:
for trace_cell in range(TV.mesh().num_cells()):
TV_dof.cell = trace_cell
trace_dofs = Tdmap.cell_dofs(trace_cell)
# Figure out the dofs of V to use here. Does not matter which
# cell of the connected ones we pick
cell = f2c(mapping[trace_cell])[0]
V_basis_f.cell = cell
dofs = dmap.cell_dofs(cell)
for local_T, dof_T in enumerate(trace_dofs):
if visited_dofs[dof_T]:
continue
else:
visited_dofs[dof_T] = True
# Define trace dof
TV_dof.dof = local_T
# Eval at V basis functions
for local, dof in enumerate(dofs):
# Set which basis foo
V_basis_f.dof = local
dof_values[local] = TV_dof.eval(V_basis_f)
# Can fill the matrix now
col_indices = np.array(dofs, dtype='int32')
# Insert
mat.setValues([dof_T], col_indices, dof_values, PETSc.InsertMode.INSERT_VALUES)
return mat
def trace_mat_two_restrict(V, TV, restriction, normal, trace_mesh=None):
'''
Compute the trace values using avg/jump restriction. A + plus is the one
for which the vector cell.midpoint - facet.midpoint agrees in orientation
with the normal on the facet.
'''
mesh = V.mesh()
fdim = mesh.topology().dim() - 1
if trace_mesh is None: trace_mesh = TV.mesh()
# Init/extract entity map
assert get_entity_map(mesh, trace_mesh)
# We can get it
mapping = trace_mesh.parent_entity_map[mesh.id()][fdim] # Map cell of TV to cells of V
mesh.init(fdim, fdim+1)
f2c = mesh.topology()(fdim, fdim+1) # Facets of V to cell of V
# The idea is to evaluate TV's degrees of freedom at basis functions
# of V
Tdmap = TV.dofmap()
TV_dof = DegreeOfFreedom(TV)
dmap = V.dofmap()
V_basis_f = FEBasisFunction(V)
# We define avg as sum(+, -)/2 and jump as sum(+, neg(-))
operator_pieces = {'avg': (lambda x: x/2, lambda x: x/2),
'jump': (lambda x: x, lambda x: -x)}[restriction]
gdim = mesh.geometry().dim()
# Rows
visited_dofs = [False]*TV.dim()
# Column values
dof_values = np.zeros(V_basis_f.elm.space_dimension(), dtype='double')
with petsc_serial_matrix(TV, V) as mat:
for trace_cell in range(trace_mesh.num_cells()):
TV_dof.cell = trace_cell
trace_dofs = Tdmap.cell_dofs(trace_cell)
# Figure out the dofs of V to use here
facet_cells = f2c(mapping[trace_cell])
assert 0 < len(facet_cells) < 3
# Ignore boundary facets
if len(facet_cells) == 1:
facet_cells = [facet_cells[0]]
modifiers = (lambda x: x, ) # Do nothing
# Search which cell has the right sign
else:
signs = [None, None]
# Order such that '+' is first
t_mp = Cell(trace_mesh, trace_cell).midpoint().array()[:gdim]
mp = Cell(mesh, facet_cells[0]).midpoint().array()[:gdim]
sign = '+' if np.inner(mp - t_mp, normal(t_mp)) > 0 else '-'
# Need to flip
if sign == '-':
facet_cells = facet_cells[::-1]
# As requested
modifiers = operator_pieces
for local_T, dof_T in enumerate(trace_dofs):
if visited_dofs[dof_T]:
continue
else:
visited_dofs[dof_T] = True
# Define trace dof
TV_dof.dof = local_T
# Two sweeps to set the values in the row
ADD_VALUES = False
for modify, cell in zip(modifiers, facet_cells):
V_basis_f.cell = cell
dofs = dmap.cell_dofs(cell)
# Eval at V basis functions
for local, dof in enumerate(dofs):
# Set which basis foo
V_basis_f.dof = local
dof_values[local] = modify(TV_dof.eval(V_basis_f))
# Can fill the matrix now
col_indices = np.array(dofs, dtype='int32')
if not ADD_VALUES:
mat.setValues([dof_T], col_indices, dof_values, PETSc.InsertMode.INSERT_VALUES)
ADD_VALUES = True
#print 'setting', dof_T, col_indices, dof_values
else:
mat.setValues([dof_T], col_indices, dof_values, PETSc.InsertMode.ADD_VALUES)
#print 'adding', dof_T, col_indices, dof_values
return mat
def trace_mat_one_restrict(V, TV, restriction, normal, trace_mesh=None):
'''
Compute the trace values using +/- restriction. A + plus is the one
for which the vector cell.midpoint - facet.midpoint agrees in orientation
with the normal on the facet.
'''
mesh = V.mesh()
fdim = mesh.topology().dim() - 1
if trace_mesh is None: trace_mesh = TV.mesh()
# Init/extract entity map
assert get_entity_map(mesh, trace_mesh)
# We can get it
mapping = trace_mesh.parent_entity_map[mesh.id()][fdim] # Map cell of TV to cells of V
mesh.init(fdim, fdim+1)
f2c = mesh.topology()(fdim, fdim+1) # Facets of V to cell of V
# The idea is to evaluate TV's degrees of freedom at basis functions
# of V
Tdmap = TV.dofmap()
TV_dof = DegreeOfFreedom(TV)
dmap = V.dofmap()
V_basis_f = FEBasisFunction(V)
gdim = mesh.geometry().dim()
# Rows
visited_dofs = [False]*TV.dim()
# Column values
dof_values = np.zeros(V_basis_f.elm.space_dimension(), dtype='double')
with petsc_serial_matrix(TV, V) as mat:
for trace_cell in range(trace_mesh.num_cells()):
TV_dof.cell = trace_cell
trace_dofs = Tdmap.cell_dofs(trace_cell)
# Figure out the dofs of V to use here
facet_cells = f2c(mapping[trace_cell])
assert 0 < len(facet_cells) < 3
# Ignore boundary facets
if len(facet_cells) == 1:
cell = facet_cells[0]
# Search which cell has the right sign
else:
signs = []
for fcell in facet_cells:
t_mp = Cell(trace_mesh, trace_cell).midpoint().array()[:gdim]
mp = Cell(mesh, fcell).midpoint().array()[:gdim]
sign = '+' if np.inner(mp - t_mp, normal(t_mp)) > 0 else '-'
signs.append(sign)
cell = facet_cells[signs.index(restriction)]
V_basis_f.cell = cell
dofs = dmap.cell_dofs(cell)
for local_T, dof_T in enumerate(trace_dofs):
if visited_dofs[dof_T]:
continue
else:
visited_dofs[dof_T] = True
# Define trace dof
TV_dof.dof = local_T
# Eval at V basis functions
for local, dof in enumerate(dofs):
# Set which basis foo
V_basis_f.dof = local
dof_values[local] = TV_dof.eval(V_basis_f)
# Can fill the matrix now
col_indices = np.array(dofs, dtype='int32')
# Insert
mat.setValues([dof_T], col_indices, dof_values, PETSc.InsertMode.INSERT_VALUES)
return mat