def discretize_rhs(f_func, grid, block_space, global_operator, block_ops,
block_op):
logger = getLogger('discretizing_rhs')
logger.debug('...')
local_subdomains, num_local_subdomains, num_global_subdomains = _get_subdomains(
grid)
local_vectors = [None] * num_global_subdomains
rhs_vector = Vector(block_space.mapper.size, 0.)
for ii in range(num_global_subdomains):
local_vectors[ii] = Vector(block_space.local_space(ii).size())
l2_functional = make_l2_volume_vector_functional(
f_func,
local_vectors[ii],
block_space.local_space(ii),
over_integrate=2)
l2_functional.assemble()
block_space.mapper.copy_local_to_global(local_vectors[ii], ii,
rhs_vector)
rhs = VectorFunctional(global_operator.range.make_array([rhs_vector]))
rhss = []
for ii in range(num_global_subdomains):
rhss.append(block_ops[0]._blocks[ii, ii].range.make_array(
[local_vectors[ii]]))
block_rhs = VectorFunctional(block_op.range.make_array(rhss))
return rhs, block_rhs
def thermalblock_vectorfunc_factory(product, xblocks, yblocks, diameter, seed):
from pymor.operators.constructions import VectorFunctional
_, _, U, V, sp, rp = thermalblock_factory(xblocks, yblocks, diameter, seed)
op = VectorFunctional(U.copy(ind=0), product=sp if product else None)
U = V
V = NumpyVectorArray(np.random.random((7, 1)), copy=False)
sp = rp
rp = NumpyMatrixOperator(np.eye(1) * 2)
return op, None, U, V, sp, rp
def action_NumpyMatrixOperator(self, op):
vector = op.source.dim == 1
functional = op.range.dim == 1
if vector and functional:
raise NotImplementedError
if vector:
space = NumpyListVectorSpace(op.range.dim, op.range.id)
return VectorOperator(space.from_numpy(op.matrix.reshape((1, -1))), op.name)
elif functional:
space = NumpyListVectorSpace(op.source.dim, op.source.id)
return VectorFunctional(space.from_numpy(op.matrix.ravel()), op.name)
else:
return op.with_(new_type=NumpyListVectorArrayMatrixOperator)
def discretize(n, nt, blocks):
h = 1. / blocks
ops = [
WrappedDiffusionOperator.create(n, h * i, h * (i + 1))
for i in range(blocks)
]
pfs = [
ProjectionParameterFunctional('diffusion_coefficients', (blocks, ),
(i, )) for i in range(blocks)
]
operator = LincombOperator(ops, pfs)
initial_data = operator.source.zeros()
# use data property of WrappedVector to setup rhs
# note that we cannot use the data property of ListVectorArray,
# since ListVectorArray will always return a copy
rhs_vec = operator.range.zeros()
rhs_data = rhs_vec._list[0].data
rhs_data[:] = np.ones(len(rhs_data))
rhs_data[0] = 0
rhs_data[len(rhs_data) - 1] = 0
rhs = VectorFunctional(rhs_vec)
# hack together a visualizer ...
grid = OnedGrid(domain=(0, 1), num_intervals=n)
visualizer = Matplotlib1DVisualizer(grid)
time_stepper = ExplicitEulerTimeStepper(nt)
parameter_space = CubicParameterSpace(operator.parameter_type, 0.1, 1)
d = InstationaryDiscretization(T=1e-0,
operator=operator,
rhs=rhs,
initial_data=initial_data,
time_stepper=time_stepper,
num_values=20,
parameter_space=parameter_space,
visualizer=visualizer,
name='C++-Discretization',
cache_region=None)
return d
def discretize(grid_and_problem_data, solver_options, mpi_comm):
################ Setup
logger = getLogger('discretize_elliptic_block_swipdg.discretize')
logger.info('discretizing ... ')
grid, boundary_info = grid_and_problem_data['grid'], grid_and_problem_data[
'boundary_info']
local_all_dirichlet_boundary_info = make_subdomain_boundary_info(
grid, {'type': 'xt.grid.boundaryinfo.alldirichlet'})
local_subdomains, num_local_subdomains, num_global_subdomains = _get_subdomains(
grid)
local_all_neumann_boundary_info = make_subdomain_boundary_info(
grid, {'type': 'xt.grid.boundaryinfo.allneumann'})
block_space = make_block_dg_space(grid)
global_rt_space = make_rt_space(grid)
subdomain_rt_spaces = [
global_rt_space.restrict_to_dd_subdomain_view(grid, ii)
for ii in range(num_global_subdomains)
]
local_patterns = [
block_space.local_space(ii).compute_pattern('face_and_volume')
for ii in range(block_space.num_blocks)
]
coupling_patterns = {
'in_in': {},
'out_out': {},
'in_out': {},
'out_in': {}
}
coupling_matrices = {
'in_in': {},
'out_out': {},
'in_out': {},
'out_in': {}
}
for ii in range(num_global_subdomains):
ii_size = block_space.local_space(ii).size()
for jj in grid.neighboring_subdomains(ii):
jj_size = block_space.local_space(jj).size()
if ii < jj: # Assemble primally (visit each coupling only once).
coupling_patterns['in_in'][(ii, jj)] = block_space.local_space(
ii).compute_pattern('face_and_volume')
coupling_patterns['out_out'][(
ii, jj)] = block_space.local_space(jj).compute_pattern(
'face_and_volume')
coupling_patterns['in_out'][(
ii, jj)] = block_space.compute_coupling_pattern(
ii, jj, 'face')
coupling_patterns['out_in'][(
ii, jj)] = block_space.compute_coupling_pattern(
jj, ii, 'face')
coupling_matrices['in_in'][(ii, jj)] = Matrix(
ii_size, ii_size, coupling_patterns['in_in'][(ii, jj)])
coupling_matrices['out_out'][(ii, jj)] = Matrix(
jj_size, jj_size, coupling_patterns['out_out'][(ii, jj)])
coupling_matrices['in_out'][(ii, jj)] = Matrix(
ii_size, jj_size, coupling_patterns['in_out'][(ii, jj)])
coupling_matrices['out_in'][(ii, jj)] = Matrix(
jj_size, ii_size, coupling_patterns['out_in'][(ii, jj)])
boundary_patterns = {}
for ii in grid.boundary_subdomains():
boundary_patterns[ii] = block_space.local_space(ii).compute_pattern(
'face_and_volume')
################ Assemble LHS and RHS
lambda_, kappa = grid_and_problem_data['lambda'], grid_and_problem_data[
'kappa']
if isinstance(lambda_, dict):
lambda_funcs = lambda_['functions']
lambda_coeffs = lambda_['coefficients']
else:
lambda_funcs = [
lambda_,
]
lambda_coeffs = [
1,
]
logger.debug('block op ... ')
ops, block_ops = zip(*(discretize_lhs(
lf, grid, block_space, local_patterns, boundary_patterns,
coupling_matrices, kappa, local_all_neumann_boundary_info,
boundary_info, coupling_patterns, solver_options)
for lf in lambda_funcs))
global_operator = LincombOperator(ops,
lambda_coeffs,
solver_options=solver_options,
name='GlobalOperator')
logger.debug('block op global done ')
block_op = LincombOperator(block_ops,
lambda_coeffs,
name='lhs',
solver_options=solver_options)
logger.debug('block op done ')
f = grid_and_problem_data['f']
if isinstance(f, dict):
f_funcs = f['functions']
f_coeffs = f['coefficients']
else:
f_funcs = [
f,
]
f_coeffs = [
1,
]
rhss, block_rhss = zip(*(discretize_rhs(
ff, grid, block_space, global_operator, block_ops, block_op)
for ff in f_funcs))
global_rhs = LincombOperator(rhss, f_coeffs)
block_rhs = LincombOperator(block_rhss, f_coeffs)
solution_space = block_op.source
################ Assemble interpolation and reconstruction operators
logger.info('discretizing interpolation ')
# Oswald interpolation error operator
oi_op = BlockDiagonalOperator([
OswaldInterpolationErrorOperator(ii, block_op.source, grid,
block_space)
for ii in range(num_global_subdomains)
],
name='oswald_interpolation_error')
# Flux reconstruction operator
fr_op = LincombOperator([
BlockDiagonalOperator([
FluxReconstructionOperator(ii, block_op.source, grid, block_space,
global_rt_space, subdomain_rt_spaces,
lambda_xi, kappa)
for ii in range(num_global_subdomains)
]) for lambda_xi in lambda_funcs
],
lambda_coeffs,
name='flux_reconstruction')
################ Assemble inner products and error estimator operators
logger.info('discretizing inner products ')
lambda_bar, lambda_hat = grid_and_problem_data[
'lambda_bar'], grid_and_problem_data['lambda_hat']
mu_bar, mu_hat = grid_and_problem_data['mu_bar'], grid_and_problem_data[
'mu_hat']
operators = {}
local_projections = []
local_rt_projections = []
local_oi_projections = []
local_div_ops = []
local_l2_products = []
data = dict(grid=grid,
block_space=block_space,
local_projections=local_projections,
local_rt_projections=local_rt_projections,
local_oi_projections=local_oi_projections,
local_div_ops=local_div_ops,
local_l2_products=local_l2_products)
for ii in range(num_global_subdomains):
neighborhood = grid.neighborhood_of(ii)
################ Assemble local inner products
local_dg_space = block_space.local_space(ii)
# we want a larger pattern to allow for axpy with other matrices
tmp_local_matrix = Matrix(
local_dg_space.size(), local_dg_space.size(),
local_dg_space.compute_pattern('face_and_volume'))
local_energy_product_ops = []
local_energy_product_coeffs = []
for func, coeff in zip(lambda_funcs, lambda_coeffs):
local_energy_product_ops.append(
make_elliptic_matrix_operator(func,
kappa,
tmp_local_matrix.copy(),
local_dg_space,
over_integrate=0))
local_energy_product_coeffs.append(coeff)
local_energy_product_ops.append(
make_penalty_product_matrix_operator(
grid,
ii,
local_all_dirichlet_boundary_info,
local_dg_space,
func,
kappa,
over_integrate=0))
local_energy_product_coeffs.append(coeff)
local_l2_product = make_l2_matrix_operator(tmp_local_matrix.copy(),
local_dg_space)
del tmp_local_matrix
local_assembler = make_system_assembler(local_dg_space)
for local_product_op in local_energy_product_ops:
local_assembler.append(local_product_op)
local_assembler.append(local_l2_product)
local_assembler.assemble()
local_energy_product_name = 'local_energy_dg_product_{}'.format(ii)
local_energy_product = LincombOperator([
DuneXTMatrixOperator(op.matrix(),
source_id='domain_{}'.format(ii),
range_id='domain_{}'.format(ii))
for op in local_energy_product_ops
],
local_energy_product_coeffs,
name=local_energy_product_name)
operators[local_energy_product_name] = \
local_energy_product.assemble(mu_bar).with_(name=local_energy_product_name)
local_l2_product = DuneXTMatrixOperator(
local_l2_product.matrix(),
source_id='domain_{}'.format(ii),
range_id='domain_{}'.format(ii))
local_l2_products.append(local_l2_product)
# assemble local elliptic product
matrix = make_local_elliptic_matrix_operator(grid, ii, local_dg_space,
lambda_bar, kappa)
matrix.assemble()
local_elliptic_product = DuneXTMatrixOperator(
matrix.matrix(),
range_id='domain_{}'.format(ii),
source_id='domain_{}'.format(ii))
################ Assemble local to global projections
# assemble projection (solution space) -> (ii space)
local_projection = BlockProjectionOperator(block_op.source, ii)
local_projections.append(local_projection)
# assemble projection (RT spaces on neighborhoods of subdomains) -> (local RT space on ii)
ops = np.full(num_global_subdomains, None)
for kk in neighborhood:
component = grid.neighborhood_of(kk).index(ii)
assert fr_op.range.subspaces[kk].subspaces[
component].id == 'LOCALRT_{}'.format(ii)
ops[kk] = BlockProjectionOperator(fr_op.range.subspaces[kk],
component)
local_rt_projection = BlockRowOperator(
ops,
source_spaces=fr_op.range.subspaces,
name='local_rt_projection_{}'.format(ii))
local_rt_projections.append(local_rt_projection)
# assemble projection (OI spaces on neighborhoods of subdomains) -> (ii space)
ops = np.full(num_global_subdomains, None)
for kk in neighborhood:
component = grid.neighborhood_of(kk).index(ii)
assert oi_op.range.subspaces[kk].subspaces[
component].id == 'domain_{}'.format(ii)
ops[kk] = BlockProjectionOperator(oi_op.range.subspaces[kk],
component)
local_oi_projection = BlockRowOperator(
ops,
source_spaces=oi_op.range.subspaces,
name='local_oi_projection_{}'.format(ii))
local_oi_projections.append(local_oi_projection)
################ Assemble additional operators for error estimation
# assemble local divergence operator
local_rt_space = global_rt_space.restrict_to_dd_subdomain_view(
grid, ii)
local_div_op = make_divergence_matrix_operator_on_subdomain(
grid, ii, local_dg_space, local_rt_space)
local_div_op.assemble()
local_div_op = DuneXTMatrixOperator(
local_div_op.matrix(),
source_id='LOCALRT_{}'.format(ii),
range_id='domain_{}'.format(ii),
name='local_divergence_{}'.format(ii))
local_div_ops.append(local_div_op)
################ Assemble error estimator operators -- Nonconformity
operators['nc_{}'.format(ii)] = \
Concatenation([local_oi_projection.T, local_elliptic_product, local_oi_projection],
name='nonconformity_{}'.format(ii))
################ Assemble error estimator operators -- Residual
if len(f_funcs) == 1:
assert f_coeffs[0] == 1
local_div = Concatenation([local_div_op, local_rt_projection])
local_rhs = VectorFunctional(
block_rhs.operators[0]._array._blocks[ii])
operators['r_fd_{}'.format(ii)] = \
Concatenation([local_rhs, local_div], name='r1_{}'.format(ii))
operators['r_dd_{}'.format(ii)] = \
Concatenation([local_div.T, local_l2_product, local_div], name='r2_{}'.format(ii))
################ Assemble error estimator operators -- Diffusive flux
operators['df_aa_{}'.format(ii)] = LincombOperator(
[
assemble_estimator_diffusive_flux_aa(
lambda_xi, lambda_xi_prime, grid, ii, block_space,
lambda_hat, kappa, solution_space)
for lambda_xi in lambda_funcs
for lambda_xi_prime in lambda_funcs
], [
ProductParameterFunctional([c1, c2]) for c1 in lambda_coeffs
for c2 in lambda_coeffs
],
name='diffusive_flux_aa_{}'.format(ii))
operators['df_bb_{}'.format(
ii)] = assemble_estimator_diffusive_flux_bb(
grid, ii, subdomain_rt_spaces, lambda_hat, kappa,
local_rt_projection)
operators['df_ab_{}'.format(ii)] = LincombOperator(
[
assemble_estimator_diffusive_flux_ab(
lambda_xi, grid, ii, block_space, subdomain_rt_spaces,
lambda_hat, kappa, local_rt_projection, local_projection)
for lambda_xi in lambda_funcs
],
lambda_coeffs,
name='diffusive_flux_ab_{}'.format(ii))
################ Final assembly
logger.info('final assembly ')
# instantiate error estimator
min_diffusion_evs = np.array([
min_diffusion_eigenvalue(grid, ii, lambda_hat, kappa)
for ii in range(num_global_subdomains)
])
subdomain_diameters = np.array(
[subdomain_diameter(grid, ii) for ii in range(num_global_subdomains)])
if len(f_funcs) == 1:
assert f_coeffs[0] == 1
local_eta_rf_squared = np.array([
apply_l2_product(grid,
ii,
f_funcs[0],
f_funcs[0],
over_integrate=2)
for ii in range(num_global_subdomains)
])
else:
local_eta_rf_squared = None
estimator = EllipticEstimator(grid,
min_diffusion_evs,
subdomain_diameters,
local_eta_rf_squared,
lambda_coeffs,
mu_bar,
mu_hat,
fr_op,
oswald_interpolation_error=oi_op,
mpi_comm=mpi_comm)
l2_product = BlockDiagonalOperator(local_l2_products)
# instantiate discretization
neighborhoods = [
grid.neighborhood_of(ii) for ii in range(num_global_subdomains)
]
local_boundary_info = make_subdomain_boundary_info(
grid_and_problem_data['grid'],
{'type': 'xt.grid.boundaryinfo.alldirichlet'})
d = DuneDiscretization(global_operator=global_operator,
global_rhs=global_rhs,
neighborhoods=neighborhoods,
enrichment_data=(grid, local_boundary_info, lambda_,
kappa, f, block_space),
operator=block_op,
rhs=block_rhs,
visualizer=DuneGDTVisualizer(block_space),
operators=operators,
products={'l2': l2_product},
estimator=estimator,
data=data)
parameter_range = grid_and_problem_data['parameter_range']
logger.info('final assembly B')
d = d.with_(parameter_space=CubicParameterSpace(
d.parameter_type, parameter_range[0], parameter_range[1]))
logger.info('final assembly C')
return d, data
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])
def discretize(grid_and_problem_data, polorder=1, solver_options=None):
logger = getLogger('discretize_elliptic_swipdg.discretize')
logger.info('discretizing ... ')
over_integrate = 2
grid, boundary_info = grid_and_problem_data['grid'], grid_and_problem_data[
'boundary_info']
_lambda, kappa, f = (grid_and_problem_data['lambda'],
grid_and_problem_data['kappa'],
grid_and_problem_data['f'])
lambda_bar, lambda_bar = grid_and_problem_data[
'lambda_bar'], grid_and_problem_data['lambda_bar']
mu_bar, mu_hat, parameter_range = (
grid_and_problem_data['mu_bar'], grid_and_problem_data['mu_hat'],
grid_and_problem_data['parameter_range'])
space = make_dg_space(grid)
# prepare operators and functionals
if isinstance(_lambda, dict):
system_ops = [
make_elliptic_swipdg_matrix_operator(lambda_func, kappa,
boundary_info, space,
over_integrate)
for lambda_func in _lambda['functions']
]
elliptic_ops = [
make_elliptic_matrix_operator(lambda_func, kappa, space,
over_integrate)
for lambda_func in _lambda['functions']
]
else:
system_ops = [
make_elliptic_swipdg_matrix_operator(_lambda, kappa, boundary_info,
space, over_integrate),
]
elliptic_ops = [
make_elliptic_matrix_operator(_lambda, kappa, space,
over_integrate),
]
if isinstance(f, dict):
rhs_functionals = [
make_l2_volume_vector_functional(f_func, space, over_integrate)
for f_func in f['functions']
]
else:
rhs_functionals = [
make_l2_volume_vector_functional(f, space, over_integrate),
]
l2_matrix_with_system_pattern = system_ops[0].matrix().copy()
l2_operator = make_l2_matrix_operator(l2_matrix_with_system_pattern, space)
# assemble everything in one grid walk
system_assembler = make_system_assembler(space)
for op in system_ops:
system_assembler.append(op)
for op in elliptic_ops:
system_assembler.append(op)
for func in rhs_functionals:
system_assembler.append(func)
system_assembler.append(l2_operator)
system_assembler.walk()
# wrap everything
if isinstance(_lambda, dict):
op = LincombOperator([
DuneXTMatrixOperator(o.matrix(),
dof_communicator=space.dof_communicator)
for o in system_ops
], _lambda['coefficients'])
elliptic_op = LincombOperator(
[DuneXTMatrixOperator(o.matrix()) for o in elliptic_ops],
_lambda['coefficients'])
else:
op = DuneXTMatrixOperator(system_ops[0].matrix())
elliptic_op = DuneXTMatrixOperator(elliptic_ops[0].matrix())
if isinstance(f, dict):
rhs = LincombOperator([
VectorFunctional(op.range.make_array([func.vector()]))
for func in rhs_functionals
], f['coefficients'])
else:
rhs = VectorFunctional(
op.range.make_array([rhs_functionals[0].vector()]))
operators = {
'l2':
DuneXTMatrixOperator(l2_matrix_with_system_pattern),
'elliptic':
elliptic_op,
'elliptic_mu_bar':
DuneXTMatrixOperator(elliptic_op.assemble(mu=mu_bar).matrix)
}
d = StationaryDiscretization(op,
rhs,
operators=operators,
visualizer=DuneGDTVisualizer(space))
d = d.with_(parameter_space=CubicParameterSpace(
d.parameter_type, parameter_range[0], parameter_range[1]))
return d, {'space': space}
def _discretize_fenics(xblocks, yblocks, grid_num_intervals, element_order):
# assemble system matrices - FEniCS code
########################################
import dolfin as df
mesh = df.UnitSquareMesh(grid_num_intervals, grid_num_intervals, 'crossed')
V = df.FunctionSpace(mesh, 'Lagrange', element_order)
u = df.TrialFunction(V)
v = df.TestFunction(V)
diffusion = df.Expression(
'(lower0 <= x[0]) * (open0 ? (x[0] < upper0) : (x[0] <= upper0)) *' +
'(lower1 <= x[1]) * (open1 ? (x[1] < upper1) : (x[1] <= upper1))',
lower0=0.,
upper0=0.,
open0=0,
lower1=0.,
upper1=0.,
open1=0,
element=df.FunctionSpace(mesh, 'DG', 0).ufl_element())
def assemble_matrix(x, y, nx, ny):
diffusion.user_parameters['lower0'] = x / nx
diffusion.user_parameters['lower1'] = y / ny
diffusion.user_parameters['upper0'] = (x + 1) / nx
diffusion.user_parameters['upper1'] = (y + 1) / ny
diffusion.user_parameters['open0'] = (x + 1 == nx)
diffusion.user_parameters['open1'] = (y + 1 == ny)
return df.assemble(
df.inner(diffusion * df.nabla_grad(u), df.nabla_grad(v)) * df.dx)
mats = [
assemble_matrix(x, y, xblocks, yblocks) for x in range(xblocks)
for y in range(yblocks)
]
mat0 = mats[0].copy()
mat0.zero()
h1_mat = df.assemble(df.inner(df.nabla_grad(u), df.nabla_grad(v)) * df.dx)
l2_mat = df.assemble(u * v * df.dx)
f = df.Constant(1.) * v * df.dx
F = df.assemble(f)
bc = df.DirichletBC(V, 0., df.DomainBoundary())
for m in mats:
bc.zero(m)
bc.apply(mat0)
bc.apply(h1_mat)
bc.apply(F)
# wrap everything as a pyMOR discretization
###########################################
# FEniCS wrappers
from pymor.gui.fenics import FenicsVisualizer
from pymor.operators.fenics import FenicsMatrixOperator
from pymor.vectorarrays.fenics import FenicsVector
# generic pyMOR classes
from pymor.discretizations.basic import StationaryDiscretization
from pymor.operators.constructions import LincombOperator, VectorFunctional
from pymor.parameters.functionals import ProjectionParameterFunctional
from pymor.parameters.spaces import CubicParameterSpace
from pymor.vectorarrays.list import ListVectorArray
# define parameter functionals (same as in pymor.analyticalproblems.thermalblock)
def parameter_functional_factory(x, y):
return ProjectionParameterFunctional(
component_name='diffusion',
component_shape=(yblocks, xblocks),
coordinates=(yblocks - y - 1, x),
name='diffusion_{}_{}'.format(x, y))
parameter_functionals = tuple(
parameter_functional_factory(x, y) for x in range(xblocks)
for y in range(yblocks))
# wrap operators
ops = [FenicsMatrixOperator(mat0, V, V)
] + [FenicsMatrixOperator(m, V, V) for m in mats]
op = LincombOperator(ops, (1., ) + parameter_functionals)
rhs = VectorFunctional(ListVectorArray([FenicsVector(F, V)]))
h1_product = FenicsMatrixOperator(h1_mat, V, V, name='h1_0_semi')
l2_product = FenicsMatrixOperator(l2_mat, V, V, name='l2')
# build discretization
visualizer = FenicsVisualizer(V)
parameter_space = CubicParameterSpace(op.parameter_type, 0.1, 1.)
d = StationaryDiscretization(op,
rhs,
products={
'h1_0_semi': h1_product,
'l2': l2_product
},
parameter_space=parameter_space,
visualizer=visualizer)
return d