def _(b: PETSc.Vec,
L: typing.List[FormMetaClass],
a,
bcs: typing.List[DirichletBCMetaClass] = [],
x0: typing.Optional[PETSc.Vec] = None,
scale: float = 1.0,
constants_L=None,
coeffs_L=None,
constants_a=None,
coeffs_a=None) -> PETSc.Vec:
"""Assemble linear forms into a monolithic vector. The vector is not
zeroed and it is not finalised, i.e. ghost values are not
accumulated.
"""
maps = [(form.function_spaces[0].dofmap.index_map,
form.function_spaces[0].dofmap.index_map_bs) for form in L]
if x0 is not None:
x0_local = _cpp.la.petsc.get_local_vectors(x0, maps)
x0_sub = x0_local
else:
x0_local = []
x0_sub = [None] * len(maps)
constants_L = [form and _pack_constants(form)
for form in L] if constants_L is None else constants_L
coeffs_L = [{} if form is None else _pack_coefficients(form)
for form in L] if coeffs_L is None else coeffs_L
constants_a = [[form and _pack_constants(form) for form in forms]
for forms in a] if constants_a is None else constants_a
coeffs_a = [[{} if form is None else _pack_coefficients(form)
for form in forms]
for forms in a] if coeffs_a is None else coeffs_a
bcs1 = _bcs_by_block(_extract_spaces(a, 1), bcs)
b_local = _cpp.la.petsc.get_local_vectors(b, maps)
for b_sub, L_sub, a_sub, const_L, coeff_L, const_a, coeff_a in zip(
b_local, L, a, constants_L, coeffs_L, constants_a, coeffs_a):
_cpp.fem.assemble_vector(b_sub, L_sub, const_L, coeff_L)
_cpp.fem.apply_lifting(b_sub, a_sub, const_a, coeff_a, bcs1, x0_local,
scale)
_cpp.la.petsc.scatter_local_vectors(b, b_local, maps)
b.ghostUpdate(addv=PETSc.InsertMode.ADD, mode=PETSc.ScatterMode.REVERSE)
bcs0 = _bcs_by_block(_extract_spaces(L), bcs)
offset = 0
b_array = b.getArray(readonly=False)
for submap, bc, _x0 in zip(maps, bcs0, x0_sub):
size = submap[0].size_local * submap[1]
_cpp.fem.set_bc(b_array[offset:offset + size], bc, _x0, scale)
offset += size
return b
def _pack(form):
if form is None:
return {}
elif isinstance(form, collections.abc.Iterable):
return list(map(lambda sub_form: _pack(sub_form), form))
else:
return _pack_coefficients(form)
def apply_lifting(b: np.ndarray,
a: typing.List[FormMetaClass],
bcs: typing.List[typing.List[DirichletBCMetaClass]],
x0: typing.Optional[typing.List[np.ndarray]] = None,
scale: float = 1.0,
constants=None,
coeffs=None) -> None:
"""Modify RHS vector b for lifting of Dirichlet boundary conditions.
It modifies b such that:
.. math::
b \\leftarrow b - \\text{scale} * A_j (g_j - x0_j)
where j is a block (nest) index. For a non-blocked problem j = 0.
The boundary conditions bcs are on the trial spaces V_j. The forms
in [a] must have the same test space as L (from which b was built),
but the trial space may differ. If x0 is not supplied, then it is
treated as zero.
Note:
Ghost contributions are not accumulated (not sent to owner).
Caller is responsible for calling VecGhostUpdateBegin/End.
"""
x0 = [] if x0 is None else x0
constants = [form and _pack_constants(form)
for form in a] if constants is None else constants
coeffs = [{} if form is None else _pack_coefficients(form)
for form in a] if coeffs is None else coeffs
_cpp.fem.apply_lifting(b, a, constants, coeffs, bcs, x0, scale)
def _(A: la.MatrixCSRMetaClass,
a: FormMetaClass,
bcs: typing.List[DirichletBCMetaClass] = None,
diagonal: float = 1.0,
constants=None,
coeffs=None) -> la.MatrixCSRMetaClass:
"""Assemble bilinear form into a matrix.
Args:
a: The bilinear form assemble.
bcs: Boundary conditions that affect the assembled matrix.
Degrees-of-freedom constrained by a boundary condition will
have their rows/columns zeroed and the value ``diagonal`` set
on on the matrix diagonal.
constants: Constants that appear in the form. If not provided,
any required constants will be computed.
coeffs: Coefficients that appear in the form. If not provided,
any required coefficients will be computed.
Note:
The returned matrix is not finalised, i.e. ghost values are not
accumulated.
"""
bcs = [] if bcs is None else bcs
constants = _pack_constants(a) if constants is None else constants
coeffs = _pack_coefficients(a) if coeffs is None else coeffs
_cpp.fem.assemble_matrix(A, a, constants, coeffs, bcs)
# If matrix is a 'diagonal'block, set diagonal entry for constrained
# dofs
if a.function_spaces[0] is a.function_spaces[1]:
_cpp.fem.insert_diagonal(A, a.function_spaces[0], bcs, diagonal)
return A
def _(b: np.ndarray, L: FormMetaClass, constants=None, coeffs=None):
"""Assemble linear form into a new Vector.
Args:
b: The array to assemble the contribution from the calling MPI
rank into. It must have the required size.
L: The linear form assemble.
constants: Constants that appear in the form. If not provided,
any required constants will be computed.
coeffs: Coefficients that appear in the form. If not provided,
any required coefficients will be computed.
Note:
Passing `constants` and `coefficients` is a performance
optimisation for when a form is assembled multiple times and
when (some) constants and coefficients are unchanged.
Note:
The returned vector is not finalised, i.e. ghost values are not
accumulated on the owning processes. Calling
:func:`dolfinx.la.VectorMetaClass.scatter_reverse` on the
return vector can accumulate ghost contributions.
"""
constants = _pack_constants(L) if constants is None else constants
coeffs = _pack_coefficients(L) if coeffs is None else coeffs
_cpp.fem.assemble_vector(b, L, constants, coeffs)
return b
def assemble_vector(L: FormMetaClass,
constants=None,
coeffs=None) -> la.VectorMetaClass:
"""Assemble linear form into a new Vector.
Args:
L: The linear form assemble.
constants: Constants that appear in the form. If not provided,
any required constants will be computed.
coeffs: Coefficients that appear in the form. If not provided,
any required coefficients will be computed.
Return:
The assembled vector for the calling rank.
Note:
Passing `constants` and `coefficients` is a performance
optimisation for when a form is assembled multiple times and
when (some) constants and coefficients are unchanged.
Note:
The returned vector is not finalised, i.e. ghost values are not
accumulated on the owning processes. Calling
:func:`dolfinx.la.VectorMetaClass.scatter_reverse` on the
return vector can accumulate ghost contributions.
"""
b = create_vector(L)
b.array[:] = 0
constants = constants or _pack_constants(L)
coeffs = coeffs or _pack_coefficients(L)
_cpp.fem.assemble_vector(b.array, L, constants, coeffs)
return b
def assemble_scalar(M: FormMetaClass, constants=None, coeffs=None):
"""Assemble functional. The returned value is local and not
accumulated across processes.
Args:
M: The functional to compute.
constants: Constants that appear in the form. If not provided,
any required constants will be computed.
coeffs: Coefficients that appear in the form. If not provided,
any required coefficients will be computed.
Return:
The computed scalar on the calling rank.
Note:
Passing `constants` and `coefficients` is a performance
optimisation for when a form is assembled multiple times and
when (some) constants and coefficients are unchanged.
To compute the functional value on the whole domain, the output
of this function is typically summed across all MPI ranks.
"""
constants = constants or _pack_constants(M)
coeffs = coeffs or _pack_coefficients(M)
return _cpp.fem.assemble_scalar(M, constants, coeffs)
def _(A: PETSc.Mat,
a: typing.List[typing.List[FormMetaClass]],
bcs: typing.List[DirichletBCMetaClass] = [],
diagonal: float = 1.0,
constants=None,
coeffs=None) -> PETSc.Mat:
"""Assemble bilinear forms into matrix"""
constants = [[form and _pack_constants(form) for form in forms]
for forms in a] if constants is None else constants
coeffs = [[{} if form is None else _pack_coefficients(form)
for form in forms] for forms in a] if coeffs is None else coeffs
V = _extract_function_spaces(a)
is_rows = _cpp.la.petsc.create_index_sets([
(Vsub.dofmap.index_map, Vsub.dofmap.index_map_bs) for Vsub in V[0]
])
is_cols = _cpp.la.petsc.create_index_sets([
(Vsub.dofmap.index_map, Vsub.dofmap.index_map_bs) for Vsub in V[1]
])
# Assemble form
for i, a_row in enumerate(a):
for j, a_sub in enumerate(a_row):
if a_sub is not None:
Asub = A.getLocalSubMatrix(is_rows[i], is_cols[j])
_cpp.fem.petsc.assemble_matrix(Asub, a_sub, constants[i][j],
coeffs[i][j], bcs, True)
A.restoreLocalSubMatrix(is_rows[i], is_cols[j], Asub)
# Flush to enable switch from add to set in the matrix
A.assemble(PETSc.Mat.AssemblyType.FLUSH)
# Set diagonal
for i, a_row in enumerate(a):
for j, a_sub in enumerate(a_row):
if a_sub is not None:
Asub = A.getLocalSubMatrix(is_rows[i], is_cols[j])
if a_sub.function_spaces[0] is a_sub.function_spaces[1]:
_cpp.fem.petsc.insert_diagonal(Asub,
a_sub.function_spaces[0],
bcs, diagonal)
A.restoreLocalSubMatrix(is_rows[i], is_cols[j], Asub)
return A
def _(A: PETSc.Mat,
a: FormMetaClass,
bcs: typing.List[DirichletBCMetaClass] = [],
diagonal: float = 1.0,
constants=None,
coeffs=None) -> PETSc.Mat:
"""Assemble bilinear form into a matrix. The returned matrix is not
finalised, i.e. ghost values are not accumulated.
"""
constants = _pack_constants(a) if constants is None else constants
coeffs = _pack_coefficients(a) if coeffs is None else coeffs
_cpp.fem.petsc.assemble_matrix(A, a, constants, coeffs, bcs)
if a.function_spaces[0] is a.function_spaces[1]:
A.assemblyBegin(PETSc.Mat.AssemblyType.FLUSH)
A.assemblyEnd(PETSc.Mat.AssemblyType.FLUSH)
_cpp.fem.petsc.insert_diagonal(A, a.function_spaces[0], bcs, diagonal)
return A
def _(A: PETSc.Mat,
a: typing.List[typing.List[FormMetaClass]],
bcs: typing.List[DirichletBCMetaClass] = [],
diagonal: float = 1.0,
constants=None,
coeffs=None) -> PETSc.Mat:
"""Assemble bilinear forms into matrix"""
constants = [[form and _pack_constants(form) for form in forms]
for forms in a] if constants is None else constants
coeffs = [[{} if form is None else _pack_coefficients(form)
for form in forms] for forms in a] if coeffs is None else coeffs
for i, (a_row, const_row,
coeff_row) in enumerate(zip(a, constants, coeffs)):
for j, (a_block, const,
coeff) in enumerate(zip(a_row, const_row, coeff_row)):
if a_block is not None:
Asub = A.getNestSubMatrix(i, j)
assemble_matrix(Asub, a_block, bcs, diagonal, const, coeff)
return A
def apply_lifting_nest(b: PETSc.Vec,
a: typing.List[typing.List[FormMetaClass]],
bcs: typing.List[DirichletBCMetaClass],
x0: typing.Optional[PETSc.Vec] = None,
scale: float = 1.0,
constants=None,
coeffs=None) -> PETSc.Vec:
"""Apply the function :func:`dolfinx.fem.apply_lifting` to each sub-vector in a nested PETSc Vector."""
x0 = [] if x0 is None else x0.getNestSubVecs()
bcs1 = _bcs_by_block(_extract_spaces(a, 1), bcs)
constants = [[form and _pack_constants(form) for form in forms]
for forms in a] if constants is None else constants
coeffs = [[{} if form is None else _pack_coefficients(form)
for form in forms] for forms in a] if coeffs is None else coeffs
for b_sub, a_sub, const, coeff in zip(b.getNestSubVecs(), a, constants,
coeffs):
apply_lifting(b_sub, a_sub, bcs1, x0, scale, const, coeff)
return b