def _solve_supremizer(self, solution):
N_us = self._supremizer.N
N_usp = solution.N
assert len(
self.inner_product["s"]
) == 1 # the affine expansion storage contains only the inner product matrix
assembled_operator_lhs = self.inner_product["s"][0][:N_us, :N_us]
assembled_operator_bt = sum(
product(self.compute_theta("bt_restricted"),
self.operator["bt_restricted"][:N_us, :N_usp]))
assembled_operator_rhs = assembled_operator_bt * solution
if self.dirichlet_bc[
"u"] and not self.dirichlet_bc_are_homogeneous["u"]:
assembled_dirichlet_bc = dict()
assert self.dirichlet_bc["s"]
assert self.dirichlet_bc_are_homogeneous["s"]
assembled_dirichlet_bc["u"] = self.compute_theta(
"dirichlet_bc_s")
else:
assembled_dirichlet_bc = None
solver = OnlineLinearSolver(assembled_operator_lhs,
self._supremizer,
assembled_operator_rhs,
assembled_dirichlet_bc)
solver.set_parameters(self._linear_solver_parameters)
solver.solve()
def _solve(self, rhs_, N=None):
if N is None:
N = self.N
if N > 0:
self._interpolation_coefficients = OnlineFunction(N)
# Evaluate the parametrized expression at interpolation locations
rhs = evaluate(rhs_, self.interpolation_locations[:N])
(max_abs_rhs, _) = max(abs(rhs))
if max_abs_rhs == 0.:
# If the rhs is zero, then we are interpolating the zero function
# and the default zero coefficients are enough.
pass
else:
# Extract the interpolation matrix
lhs = self.interpolation_matrix[0][:N, :N]
# Solve the interpolation problem
solver = OnlineLinearSolver(lhs,
self._interpolation_coefficients,
rhs)
solver.solve()
else:
self._interpolation_coefficients = None # OnlineFunction
def project(self, snapshot, on_dirichlet_bc=True, N=None, **kwargs):
N, kwargs = self._online_size_from_kwargs(N, **kwargs)
N += self.N_bc
# Get truth and reduced inner product matrices for projection
inner_product = self.truth_problem._combined_projection_inner_product
inner_product_N = self._combined_projection_inner_product[:N, :N]
# Get basis
basis_functions = self.basis_functions[:N]
# Define storage for projected solution
projected_snapshot_N = OnlineFunction(N)
# Project on reduced basis
if on_dirichlet_bc:
solver = OnlineLinearSolver(
inner_product_N, projected_snapshot_N,
transpose(basis_functions) * inner_product * snapshot)
else:
solver = OnlineLinearSolver(
inner_product_N, projected_snapshot_N,
transpose(basis_functions) * inner_product * snapshot,
self._combined_and_homogenized_dirichlet_bc)
solver.set_parameters(self._linear_solver_parameters)
solver.solve()
return projected_snapshot_N
def ic_eval(self):
problem = self.problem
N = self.N
if len(problem.components) > 1:
all_initial_conditions = list()
all_initial_conditions_thetas = list()
for component in problem.components:
if problem.initial_condition[component] and not problem.initial_condition_is_homogeneous[component]:
all_initial_conditions.extend(problem.initial_condition[component][:N])
all_initial_conditions_thetas.extend(problem.compute_theta("initial_condition_" + component))
if len(all_initial_conditions) > 0:
all_initial_conditions = tuple(all_initial_conditions)
all_initial_conditions = OnlineAffineExpansionStorage(all_initial_conditions)
all_initial_conditions_thetas = tuple(all_initial_conditions_thetas)
else:
all_initial_conditions = None
all_initial_conditions_thetas = None
else:
if problem.initial_condition and not problem.initial_condition_is_homogeneous:
all_initial_conditions = problem.initial_condition[:N]
all_initial_conditions_thetas = problem.compute_theta("initial_condition")
else:
all_initial_conditions = None
all_initial_conditions_thetas = None
assert (all_initial_conditions is None) == (all_initial_conditions_thetas is None)
if all_initial_conditions is not None:
inner_product_N = problem._combined_projection_inner_product[:N, :N]
projected_initial_condition = OnlineFunction(N)
solver = OnlineLinearSolver(inner_product_N, projected_initial_condition, sum(product(all_initial_conditions_thetas, all_initial_conditions)))
solver.set_parameters(problem._linear_solver_parameters)
solver.solve()
return projected_initial_condition
else:
return None
def solve(self, mu, c, snapshot):
print("Performing L^2 projection for mu =", mu, "and component", c)
#quit()
projected_snapshot_N = OnlineFunction(self.N)
solver = OnlineLinearSolver(
self.inner_product_N, projected_snapshot_N,
transpose(self.basis_functions) * self.inner_product * snapshot)
solver.solve()
return projected_snapshot_N.vector().__array__()