def apply(self, U, mu=None):
assert U in self.source
result = self.range.empty(reserve=len(U))
local_subdomains, num_local_subdomains, num_global_subdomains = _get_subdomains(
self.grid)
for u_i in range(len(U)):
subdomain_uhs_with_global_support = \
make_discrete_function(
self.block_space,
self.block_space.project_onto_neighborhood(
[U._list[u_i].impl if nn == self.subdomain else
Vector(self.block_space.local_space(nn).size(), 0.)
for nn in range(num_global_subdomains)],
[nn for nn in range(num_global_subdomains)]
)
)
reconstructed_uh_kk_with_global_support = make_discrete_function(
self.global_rt_space)
apply_diffusive_flux_reconstruction_in_neighborhood(
self.grid, self.subdomain, self.lambda_xi, self.kappa,
subdomain_uhs_with_global_support,
reconstructed_uh_kk_with_global_support)
blocks = [
s.make_array([
self.subdomain_rt_spaces[ii].restrict(
reconstructed_uh_kk_with_global_support.vector_copy())
]) # NOQA
for s, ii in zip(self.range.subspaces,
self.grid.neighborhood_of(self.subdomain))
]
result.append(self.range.make_array(blocks))
return result
def apply(self, U, mu=None):
assert U in self.source
results = self.range.empty(reserve=len(U))
for u_i in range(len(U)):
result = self.range.zeros()
result._blocks[self.neighborhood.index(self.subdomain)].axpy(
1, U[u_i])
for i_ii, ii in enumerate(self.neighborhood):
ii_neighborhood = self.grid.neighborhood_of(ii)
ii_neighborhood_space = self.block_space.restricted_to_neighborhood(
ii_neighborhood)
subdomain_uh_with_neighborhood_support = make_discrete_function(
ii_neighborhood_space,
ii_neighborhood_space.project_onto_neighborhood([
U._list[u_i].impl if nn == self.subdomain else Vector(
self.block_space.local_space(nn).size(), 0.)
for nn in ii_neighborhood
], ii_neighborhood))
interpolated_u_vector = ii_neighborhood_space.project_onto_neighborhood(
[
Vector(self.block_space.local_space(nn).size(), 0.)
for nn in ii_neighborhood
], ii_neighborhood)
interpolated_u = make_discrete_function(
ii_neighborhood_space, interpolated_u_vector)
apply_oswald_interpolation_operator(
self.grid, ii,
make_subdomain_boundary_info(
self.grid,
{'type': 'xt.grid.boundaryinfo.alldirichlet'}),
subdomain_uh_with_neighborhood_support, interpolated_u)
local_sizes = np.array([
ii_neighborhood_space.local_space(nn).size()
for nn in ii_neighborhood
])
offsets = np.hstack(([0], np.cumsum(local_sizes)))
ind = ii_neighborhood.index(ii)
result._blocks[i_ii]._list[0].data[:] -= \
np.frombuffer(interpolated_u_vector)[offsets[ind]:offsets[ind+1]]
results.append(result)
return results
def shape_functions(self, subdomain, order=0):
assert 0 <= order <= 1
local_space = self.solution_space.subspaces[subdomain]
U = local_space.make_array([Vector(local_space.dim, 1.)])
if order == 1:
dune_local_space = self.visualizer.space.local_space(subdomain)
tmp_discrete_function = make_discrete_function(dune_local_space)
for expression in ('x[0]', 'x[1]', 'x[0]*x[1]'):
func = make_expression_function_1x1(self.grid,
'x',
expression,
order=2)
dune_project(func, tmp_discrete_function)
U.append(
local_space.make_array(
[tmp_discrete_function.vector_copy()]))
return U
def solve_for_local_correction(self,
subdomain,
Us,
mu=None,
inverse_options=None):
grid, local_boundary_info, affine_lambda, kappa, f, block_space = self.enrichment_data
neighborhood = self.neighborhoods[subdomain]
neighborhood_space = block_space.restricted_to_neighborhood(
neighborhood)
# Compute current solution restricted to the neighborhood to be usable as Dirichlet values for the correction
# problem.
current_solution = [U._list for U in Us]
assert np.all(len(v) == 1 for v in current_solution)
current_solution = [v[0].impl for v in current_solution]
current_solution = neighborhood_space.project_onto_neighborhood(
current_solution, neighborhood)
current_solution = make_discrete_function(neighborhood_space,
current_solution)
# Solve the local corrector problem.
# LHS
ops = []
for lambda_ in affine_lambda['functions']:
ops.append(
make_elliptic_swipdg_matrix_operator_on_neighborhood(
grid,
subdomain,
local_boundary_info,
neighborhood_space,
lambda_,
kappa,
over_integrate=0))
ops_coeffs = affine_lambda['coefficients'].copy()
# RHS
funcs = []
# We don't have any boundary treatment right now. Things will probably
# break in multiple ways in case of non-trivial boundary conditions,
# so we can comment this out for now ..
# for lambda_ in affine_lambda['functions']:
# funcs.append(make_elliptic_swipdg_vector_functional_on_neighborhood(
# grid, subdomain, local_boundary_info,
# neighborhood_space,
# current_solution, lambda_, kappa,
# over_integrate=0))
# funcs_coeffs = affine_lambda['coefficients'].copy()
funcs.append(
make_l2_vector_functional_on_neighborhood(grid,
subdomain,
neighborhood_space,
f,
over_integrate=2))
# funcs_coeffs.append(1.)
funcs_coeffs = [1]
# assemble in one grid walk
neighborhood_assembler = make_neighborhood_system_assembler(
grid, subdomain, neighborhood_space)
for op in ops:
neighborhood_assembler.append(op)
for func in funcs:
neighborhood_assembler.append(func)
neighborhood_assembler.assemble()
# solve
local_space_id = self.solution_space.subspaces[subdomain].id
lhs = LincombOperator([
DuneXTMatrixOperator(
o.matrix(), source_id=local_space_id, range_id=local_space_id)
for o in ops
], ops_coeffs)
rhs = LincombOperator([
VectorFunctional(lhs.range.make_array([v.vector()])) for v in funcs
], funcs_coeffs)
correction = lhs.apply_inverse(rhs.as_source_array(mu),
mu=mu,
inverse_options=inverse_options)
assert len(correction) == 1
# restrict to subdomain
local_sizes = [
block_space.local_space(nn).size() for nn in neighborhood
]
local_starts = [
int(np.sum(local_sizes[:nn])) for nn in range(len(local_sizes))
]
local_starts.append(neighborhood_space.mapper.size)
localized_corrections_as_np = np.array(correction._list[0].impl,
copy=False)
localized_corrections_as_np = [
localized_corrections_as_np[local_starts[nn]:local_starts[nn + 1]]
for nn in range(len(local_sizes))
]
subdomain_index_in_neighborhood = np.where(
np.array(list(neighborhood)) == subdomain)[0]
assert len(subdomain_index_in_neighborhood) == 1
subdomain_index_in_neighborhood = subdomain_index_in_neighborhood[0]
subdomain_correction = Vector(
local_sizes[subdomain_index_in_neighborhood], 0.)
subdomain_correction_as_np = np.array(subdomain_correction, copy=False)
subdomain_correction_as_np[:] = localized_corrections_as_np[
subdomain_index_in_neighborhood][:]
return self.solution_space.subspaces[subdomain].make_array(
[subdomain_correction])
