def _assemble_and_solve_adj_eq(self, dFdu_adj_form, dJdu, compute_bdy):
dJdu_copy = dJdu.copy()
bcs = self._homogenize_bcs()
solver = self.block_helper.adjoint_solver
if solver is None:
if self.assemble_system:
rhs_bcs_form = backend.inner(
backend.Function(self.function_space),
dFdu_adj_form.arguments()[0]) * backend.dx
A, _ = backend.assemble_system(dFdu_adj_form, rhs_bcs_form,
bcs)
else:
A = compat.assemble_adjoint_value(dFdu_adj_form)
[bc.apply(A) for bc in bcs]
solver = backend.LUSolver(A, self.method)
self.block_helper.adjoint_solver = solver
solver.parameters.update(self.lu_solver_parameters)
[bc.apply(dJdu) for bc in bcs]
adj_sol = backend.Function(self.function_space)
solver.solve(adj_sol.vector(), dJdu)
adj_sol_bdy = None
if compute_bdy:
adj_sol_bdy = compat.function_from_vector(
self.function_space, dJdu_copy - compat.assemble_adjoint_value(
backend.action(dFdu_adj_form, adj_sol)))
return adj_sol, adj_sol_bdy
def _assemble_and_solve_adj_eq(self,
dFdu_adj_form,
dJdu,
compute_bdy=True):
dJdu_copy = dJdu.copy()
dFdu = compat.assemble_adjoint_value(dFdu_adj_form,
**self.assemble_kwargs)
bcs = self._homogenize_bcs()
# Apply boundary conditions on adj_dFdu and dJdu.
for bc in bcs:
bc.apply(dFdu, dJdu)
adj_sol = compat.create_function(self.function_space)
lu_solver_methods = backend.lu_solver_methods()
solver_method = self.adj_args[0] if len(
self.adj_args) >= 1 else "default"
solver_method = "default" if solver_method == "lu" else solver_method
if solver_method in lu_solver_methods:
solver = backend.LUSolver(solver_method)
solver_parameters = self.adj_kwargs.get("lu_solver", {})
else:
solver = backend.KrylovSolver(*self.adj_args)
solver_parameters = self.adj_kwargs.get("krylov_solver", {})
solver.parameters.update(solver_parameters)
solver.solve(dFdu, adj_sol.vector(), dJdu)
adj_sol_bdy = None
if compute_bdy:
adj_sol_bdy = compat.function_from_vector(
self.function_space, dJdu_copy - compat.assemble_adjoint_value(
backend.action(dFdu_adj_form, adj_sol)))
return adj_sol, adj_sol_bdy
def derivative_action(self, dependencies, values, variable,
contraction_vector, hermitian):
idx = dependencies.index(variable)
# If you want to apply boundary conditions symmetrically in the adjoint
# -- and you often do --
# then we need to have a UFL representation of all the terms in the adjoint equation.
# However!
# Since UFL cannot represent the identity map,
# we need to find an f such that when
# assemble(inner(f, v)*dx)
# we get the contraction_vector.data back.
# This involves inverting a mass matrix.
if backend.parameters["adjoint"][
"symmetric_bcs"] and backend.__version__ <= '1.2.0':
backend.info_red(
"Warning: symmetric BC application requested but unavailable in dolfin <= 1.2.0."
)
if backend.parameters["adjoint"][
"symmetric_bcs"] and backend.__version__ > '1.2.0':
V = contraction_vector.data.function_space()
v = backend.TestFunction(V)
if str(V) not in adjglobals.fsp_lu:
u = backend.TrialFunction(V)
A = backend.assemble(backend.inner(u, v) * backend.dx)
solver = "mumps" if "mumps" in backend.lu_solver_methods(
).keys() else "default"
lusolver = backend.LUSolver(A, solver)
lusolver.parameters["symmetric"] = True
lusolver.parameters["reuse_factorization"] = True
adjglobals.fsp_lu[str(V)] = lusolver
else:
lusolver = adjglobals.fsp_lu[str(V)]
riesz = backend.Function(V)
lusolver.solve(
riesz.vector(),
self.weights[idx] * contraction_vector.data.vector())
out = (backend.inner(riesz, v) * backend.dx)
else:
out = backend.Function(self.fn_space)
out.assign(self.weights[idx] * contraction_vector.data)
return adjlinalg.Vector(out)
def _forward_solve(self, lhs, rhs, func, bcs, **kwargs):
solver = self.block_helper.forward_solver
if solver is None:
if self.assemble_system:
A, _ = backend.assemble_system(lhs, rhs, bcs)
else:
A = compat.assemble_adjoint_value(lhs)
[bc.apply(A) for bc in bcs]
solver = backend.LUSolver(A, self.method)
self.block_helper.forward_solver = solver
if self.assemble_system:
system_assembler = backend.SystemAssembler(lhs, rhs, bcs)
b = backend.Function(self.function_space).vector()
system_assembler.assemble(b)
else:
b = compat.assemble_adjoint_value(rhs)
[bc.apply(b) for bc in bcs]
solver.parameters.update(self.lu_solver_parameters)
solver.solve(func.vector(), b)
return func