def _la_solve(A, x, b, **kwargs):
"""Solve a linear algebra problem.
:arg A: the assembled bilinear form, a :class:`.Matrix`.
:arg x: the :class:`.Function` to write the solution into.
:arg b: the :class:`.Function` defining the right hand side values.
:kwarg bcs: an optional list of :class:`.DirichletBC`\s to apply.
:kwarg solver_parameters: optional solver parameters.
:kwarg nullspace: an optional :class:`.VectorSpaceBasis` (or
:class:`.MixedVectorSpaceBasis`) spanning the null space of
the operator.
:kwarg transpose_nullspace: as for the nullspace, but used to
make the right hand side consistent.
:kwarg near_nullspace: as for the nullspace, but used to add
the near nullspace.
:kwarg options_prefix: an optional prefix used to distinguish
PETSc options. If not provided a unique prefix will be
created. Use this option if you want to pass options
to the solver from the command line in addition to
through the ``solver_parameters`` dict.
.. note::
Any boundary conditions passed in as an argument here override the
boundary conditions set when the bilinear form was assembled.
That is, in the following example:
.. code-block:: python
A = assemble(a, bcs=[bc1])
solve(A, x, b, bcs=[bc2])
the boundary conditions in `bc2` will be applied to the problem
while `bc1` will be ignored.
Example usage:
.. code-block:: python
_la_solve(A, x, b, solver_parameters=parameters_dict)."""
bcs, solver_parameters, nullspace, nullspace_T, near_nullspace, \
options_prefix = _extract_linear_solver_args(A, x, b, **kwargs)
if bcs is not None:
A.bcs = bcs
solver = ls.LinearSolver(A,
solver_parameters=solver_parameters,
nullspace=nullspace,
transpose_nullspace=nullspace_T,
near_nullspace=near_nullspace,
options_prefix=options_prefix)
solver.solve(x, b)
def _la_solve(A, x, b, **kwargs):
r"""Solve a linear algebra problem.
:arg A: the assembled bilinear form, a :class:`.Matrix`.
:arg x: the :class:`.Function` to write the solution into.
:arg b: the :class:`.Function` defining the right hand side values.
:kwarg solver_parameters: optional solver parameters.
:kwarg nullspace: an optional :class:`.VectorSpaceBasis` (or
:class:`.MixedVectorSpaceBasis`) spanning the null space of
the operator.
:kwarg transpose_nullspace: as for the nullspace, but used to
make the right hand side consistent.
:kwarg near_nullspace: as for the nullspace, but used to add
the near nullspace.
:kwarg options_prefix: an optional prefix used to distinguish
PETSc options. If not provided a unique prefix will be
created. Use this option if you want to pass options
to the solver from the command line in addition to
through the ``solver_parameters`` dict.
.. note::
This function no longer accepts :class:`.DirichletBC`\s or
:class:`.EquationBC`\s as arguments.
Any boundary conditions must be applied when assembling the
bilinear form as:
.. code-block:: python
A = assemble(a, bcs=[bc1])
solve(A, x, b)
Example usage:
.. code-block:: python
_la_solve(A, x, b, solver_parameters=parameters_dict)."""
bcs, solver_parameters, nullspace, nullspace_T, near_nullspace, \
options_prefix = _extract_linear_solver_args(A, x, b, **kwargs)
if bcs is not None:
raise RuntimeError(
"It is no longer possible to apply or change boundary conditions after assembling the matrix `A`; pass any necessary boundary conditions to `assemble` when assembling `A`."
)
solver = ls.LinearSolver(A,
solver_parameters=solver_parameters,
nullspace=nullspace,
transpose_nullspace=nullspace_T,
near_nullspace=near_nullspace,
options_prefix=options_prefix)
if isinstance(x, firedrake.Vector):
x = x.function
# linear MG doesn't need RHS, supply zero.
lvp = vs.LinearVariationalProblem(a=A.a, L=0, u=x, bcs=A.bcs)
mat_type = A.mat_type
appctx = solver_parameters.get("appctx", {})
ctx = solving_utils._SNESContext(lvp,
mat_type=mat_type,
pmat_type=mat_type,
appctx=appctx,
options_prefix=options_prefix)
dm = solver.ksp.dm
with dmhooks.add_hooks(dm, solver, appctx=ctx):
solver.solve(x, b)
def _la_solve(A, x, b, **kwargs):
r"""Solve a linear algebra problem.
:arg A: the assembled bilinear form, a :class:`.Matrix`.
:arg x: the :class:`.Function` to write the solution into.
:arg b: the :class:`.Function` defining the right hand side values.
:kwarg bcs: an optional list of :class:`.DirichletBC`\s to apply.
:kwarg solver_parameters: optional solver parameters.
:kwarg nullspace: an optional :class:`.VectorSpaceBasis` (or
:class:`.MixedVectorSpaceBasis`) spanning the null space of
the operator.
:kwarg transpose_nullspace: as for the nullspace, but used to
make the right hand side consistent.
:kwarg near_nullspace: as for the nullspace, but used to add
the near nullspace.
:kwarg options_prefix: an optional prefix used to distinguish
PETSc options. If not provided a unique prefix will be
created. Use this option if you want to pass options
to the solver from the command line in addition to
through the ``solver_parameters`` dict.
.. note::
Any boundary conditions passed in as an argument here override the
boundary conditions set when the bilinear form was assembled.
That is, in the following example:
.. code-block:: python
A = assemble(a, bcs=[bc1])
solve(A, x, b, bcs=[bc2])
the boundary conditions in `bc2` will be applied to the problem
while `bc1` will be ignored.
Example usage:
.. code-block:: python
_la_solve(A, x, b, solver_parameters=parameters_dict)."""
bcs, solver_parameters, nullspace, nullspace_T, near_nullspace, \
options_prefix = _extract_linear_solver_args(A, x, b, **kwargs)
if bcs is not None:
A.bcs = bcs
solver = ls.LinearSolver(A, solver_parameters=solver_parameters,
nullspace=nullspace,
transpose_nullspace=nullspace_T,
near_nullspace=near_nullspace,
options_prefix=options_prefix)
if isinstance(x, firedrake.Vector):
x = x.function
# linear MG doesn't need RHS, supply zero.
lvp = vs.LinearVariationalProblem(a=A.a, L=0, u=x, bcs=bcs)
mat_type = A.mat_type
appctx = solver_parameters.get("appctx", {})
ctx = solving_utils._SNESContext(lvp,
mat_type=mat_type,
pmat_type=mat_type,
appctx=appctx,
options_prefix=options_prefix)
dm = solver.ksp.dm
with dmhooks.appctx(dm, ctx):
solver.solve(x, b)
