def discretize(num_refinements, polorder=1):
grid = GridProvider(
[0, 0], [5, 1],
[100, 20]) # The OS2015 test is [0, 5]x[0, 1], 100x20 elements, ...
grid.refine(num_refinements)
dg_space = DiscontinuousLagrangeSpace(grid, polorder)
lhs_op = LincombOperator([
make_marix_operator(
assemble_SWIPDG_matrix(dg_space, diff, diffusion_tensor),
'PRESSURE') for diff in diffusion_factor['functions']
], diffusion_factor['coefficients'])
rhs_func = VectorFunctional(
lhs_op.range.make_array((assemble_L2_vector(dg_space, f), )))
dg_product = make_marix_operator(
assemble_DG_product_matrix(dg_space, diffusion_factor_bar,
diffusion_tensor), 'PRESSURE')
fom = StationaryDiscretization(lhs_op,
rhs_func,
products={'energy_penalty': dg_product},
visualizer=DuneGDTVisualizer(dg_space))
fom = fom.with_(
parameter_space=CubicParameterSpace(fom.parameter_type, 0.1, 1.))
fom.enable_caching('disk')
return grid, dg_space, dg_product, fom
def discretize(num_refinements):
grid = GridProvider([-1, -1], [1, 1], [4, 4]) # The ESV2007 test is [-1, 1]^2, 4x4 elements, ...
grid.refine(num_refinements)
dg_space = DiscontinuousLagrangeSpace(grid, 1)
lhs_op = LincombOperator(
[make_marix_operator(assemble_SWIPDG_matrix(dg_space, diff), 'PRESSURE') for diff in diffusion['functions']],
diffusion['coefficients'])
rhs_func = VectorFunctional(lhs_op.range.make_array((assemble_L2_vector(dg_space, f),)))
dg_product = make_marix_operator(assemble_DG_product_matrix(dg_space), 'PRESSURE')
fom = StationaryDiscretization(
lhs_op, rhs_func, products={'energy_penalty': dg_product}, visualizer=DuneGDTVisualizer(dg_space))
fom = fom.with_(parameter_space=CubicParameterSpace(fom.parameter_type, 0.1, 1.))
fom.enable_caching('disk')
return grid, dg_space, dg_product, fom
def discretize(grid_and_problem_data, T, nt, polorder):
d, data = discretize_stationary(grid_and_problem_data, polorder)
assert isinstance(d.parameter_space, CubicParameterSpace)
parameter_range = grid_and_problem_data['parameter_range']
d = InstationaryDiscretization(T,
d.operator.source.zeros(1),
d.operator,
d.rhs,
mass=d.operators['l2'],
time_stepper=ImplicitEulerTimeStepper(nt=nt,
solver_options='operator'),
products=d.products,
operators={kk: vv for kk, vv in d.operators.items()
if kk not in ('operator', 'rhs') and vv not in (d.operators, d.rhs)},
visualizer=DuneGDTVisualizer(data['space']))
d = d.with_(parameter_space=CubicParameterSpace(d.parameter_type, parameter_range[0], parameter_range[1]))
return d, data
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 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(grid_and_problem_data):
logger = getLogger('discretize_elliptic.discretize_block_SWIPDG')
logger.info('discretizing ... ')
grid, boundary_info, inner_boundary_id = (grid_and_problem_data['grid'],
grid_and_problem_data['boundary_info'],
grid_and_problem_data['inner_boundary_id'])
local_all_dirichlet_boundary_info = make_subdomain_boundary_info(grid, {'type': 'xt.grid.boundaryinfo.alldirichlet'})
local_all_neumann_boundary_info = make_subdomain_boundary_info(grid, {'type': 'xt.grid.boundaryinfo.allneumann'})
neighborhood_boundary_info = make_subdomain_boundary_info(
grid,
{'type': 'xt.grid.boundaryinfo.boundarysegmentindexbased',
'default': 'dirichlet',
'neumann': '[{} {}]'.format(inner_boundary_id, inner_boundary_id+1)})
affine_lambda, kappa, f = (grid_and_problem_data['lambda'],
grid_and_problem_data['kappa'],
grid_and_problem_data['f'])
lambda_bar, lambda_hat = grid_and_problem_data['lambda_bar'], grid_and_problem_data['lambda_hat']
mu_bar, mu_hat, parameter_range = (grid_and_problem_data['mu_bar'],
grid_and_problem_data['mu_hat'],
grid_and_problem_data['parameter_range'])
block_space = make_block_space(grid)
local_patterns = [block_space.local_space(ii).compute_pattern('face_and_volume')
for ii in range(block_space.num_blocks)]
coupling_patterns_in_in = {}
coupling_patterns_out_out = {}
coupling_patterns_in_out = {}
coupling_patterns_out_in = {}
for ii in range(grid.num_subdomains):
for jj in grid.neighboring_subdomains(ii):
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')
boundary_patterns = {}
for ii in grid.boundary_subdomains():
boundary_patterns[ii] = block_space.local_space(ii).compute_pattern('face_and_volume')
def discretize_lhs_for_lambda(lambda_):
local_matrices = [None]*grid.num_subdomains
local_vectors = [None]*grid.num_subdomains
boundary_matrices = {}
coupling_matrices_in_in = {}
coupling_matrices_out_out = {}
coupling_matrices_in_out = {}
coupling_matrices_out_in = {}
for ii in range(grid.num_subdomains):
local_matrices[ii] = Matrix(block_space.local_space(ii).size(),
block_space.local_space(ii).size(),
local_patterns[ii])
local_vectors[ii] = Vector(block_space.local_space(ii).size())
if ii in grid.boundary_subdomains():
boundary_matrices[ii] = Matrix(block_space.local_space(ii).size(),
block_space.local_space(ii).size(),
boundary_patterns[ii])
for jj in grid.neighboring_subdomains(ii):
if ii < jj: # Assemble primally (visit each coupling only once).
coupling_matrices_in_in[(ii, jj)] = Matrix(block_space.local_space(ii).size(),
block_space.local_space(ii).size(),
coupling_patterns_in_in[(ii, jj)])
coupling_matrices_out_out[(ii, jj)] = Matrix(block_space.local_space(jj).size(),
block_space.local_space(jj).size(),
coupling_patterns_out_out[(ii, jj)])
coupling_matrices_in_out[(ii, jj)] = Matrix(block_space.local_space(ii).size(),
block_space.local_space(jj).size(),
coupling_patterns_in_out[(ii, jj)])
coupling_matrices_out_in[(ii, jj)] = Matrix(block_space.local_space(jj).size(),
block_space.local_space(ii).size(),
coupling_patterns_out_in[(ii, jj)])
def assemble_local_contributions(subdomain):
ipdg_operator = make_elliptic_swipdg_matrix_operator(lambda_, kappa, local_all_neumann_boundary_info,
local_matrices[subdomain],
block_space.local_space(subdomain))
l2_functional = make_l2_volume_vector_functional(f, local_vectors[subdomain],
block_space.local_space(subdomain))
local_assembler = make_system_assembler(block_space.local_space(subdomain))
local_assembler.append(ipdg_operator)
local_assembler.append(l2_functional)
local_assembler.assemble()
for ii in range(grid.num_subdomains):
assemble_local_contributions(ii)
local_ipdg_coupling_operator = make_local_elliptic_swipdg_coupling_operator(lambda_, kappa)
def assemble_coupling_contributions(subdomain, neighboring_subdomain):
coupling_assembler = block_space.coupling_assembler(subdomain, neighboring_subdomain)
coupling_assembler.append(local_ipdg_coupling_operator,
coupling_matrices_in_in[(subdomain, neighboring_subdomain)],
coupling_matrices_out_out[(subdomain, neighboring_subdomain)],
coupling_matrices_in_out[(subdomain, neighboring_subdomain)],
coupling_matrices_out_in[(subdomain, neighboring_subdomain)])
coupling_assembler.assemble()
for ii in range(grid.num_subdomains):
for jj in grid.neighboring_subdomains(ii):
if ii < jj: # Assemble primally (visit each coupling only once).
assemble_coupling_contributions(ii, jj)
local_ipdg_boundary_operator = make_local_elliptic_swipdg_boundary_operator(lambda_, kappa)
apply_on_dirichlet_intersections = make_apply_on_dirichlet_intersections(boundary_info)
def assemble_boundary_contributions(subdomain):
boundary_assembler = block_space.boundary_assembler(subdomain)
boundary_assembler.append(local_ipdg_boundary_operator,
boundary_matrices[subdomain],
apply_on_dirichlet_intersections)
boundary_assembler.assemble()
for ii in grid.boundary_subdomains():
assemble_boundary_contributions(ii)
global_pattern = SparsityPatternDefault(block_space.mapper.size)
for ii in range(grid.num_subdomains):
block_space.mapper.copy_local_to_global(local_patterns[ii], ii, global_pattern)
if ii in grid.boundary_subdomains():
block_space.mapper.copy_local_to_global(boundary_patterns[ii], ii, global_pattern)
for jj in grid.neighboring_subdomains(ii):
if ii < jj: # Assemble primally (visit each coupling only once).
block_space.mapper.copy_local_to_global(coupling_patterns_in_in[(ii, jj)], ii, ii, global_pattern)
block_space.mapper.copy_local_to_global(coupling_patterns_out_out[(ii, jj)], jj, jj, global_pattern)
block_space.mapper.copy_local_to_global(coupling_patterns_in_out[(ii, jj)], ii, jj, global_pattern)
block_space.mapper.copy_local_to_global(coupling_patterns_out_in[(ii, jj)], jj, ii, global_pattern)
system_matrix = Matrix(block_space.mapper.size, block_space.mapper.size, global_pattern)
rhs_vector = Vector(block_space.mapper.size, 0.)
for ii in range(grid.num_subdomains):
block_space.mapper.copy_local_to_global(local_matrices[ii], local_patterns[ii], ii, system_matrix)
block_space.mapper.copy_local_to_global(local_vectors[ii], ii, rhs_vector)
if ii in grid.boundary_subdomains():
block_space.mapper.copy_local_to_global(boundary_matrices[ii], boundary_patterns[ii], ii, ii, system_matrix)
for jj in grid.neighboring_subdomains(ii):
if ii < jj: # Assemble primally (visit each coupling only once).
block_space.mapper.copy_local_to_global(coupling_matrices_in_in[(ii, jj)],
coupling_patterns_in_in[(ii, jj)],
ii, ii, system_matrix)
block_space.mapper.copy_local_to_global(coupling_matrices_out_out[(ii, jj)],
coupling_patterns_out_out[(ii, jj)],
jj, jj, system_matrix)
block_space.mapper.copy_local_to_global(coupling_matrices_in_out[(ii, jj)],
coupling_patterns_in_out[(ii, jj)],
ii, jj, system_matrix)
block_space.mapper.copy_local_to_global(coupling_matrices_out_in[(ii, jj)],
coupling_patterns_out_in[(ii, jj)],
jj, ii, system_matrix)
op = DuneXTMatrixOperator(system_matrix)
mats = np.full((grid.num_subdomains, grid.num_subdomains), None)
for ii in range(grid.num_subdomains):
for jj in range(ii, grid.num_subdomains):
if ii == jj:
mats[ii, ii] = Matrix(block_space.local_space(ii).size(),
block_space.local_space(ii).size(),
local_patterns[ii])
elif (ii, jj) in coupling_matrices_in_out:
mats[ii, jj] = Matrix(block_space.local_space(ii).size(),
block_space.local_space(jj).size(),
coupling_patterns_in_out[(ii, jj)])
mats[jj, ii] = Matrix(block_space.local_space(jj).size(),
block_space.local_space(ii).size(),
coupling_patterns_out_in[(ii, jj)])
for ii in range(grid.num_subdomains):
for jj in range(ii, grid.num_subdomains):
if ii == jj:
mats[ii, ii].axpy(1., local_matrices[ii])
if ii in boundary_matrices:
mats[ii, ii].axpy(1., boundary_matrices[ii])
elif (ii, jj) in coupling_matrices_in_out:
mats[ii, ii].axpy(1., coupling_matrices_in_in[(ii, jj)])
mats[jj, jj].axpy(1., coupling_matrices_out_out[(ii, jj)])
mats[ii, jj].axpy(1., coupling_matrices_in_out[(ii, jj)])
mats[jj, ii].axpy(1., coupling_matrices_out_in[(ii, jj)])
ops = np.full((grid.num_subdomains, grid.num_subdomains), None)
for (ii, jj), mat in np.ndenumerate(mats):
ops[ii, jj] = DuneXTMatrixOperator(mat,
source_id='domain_{}'.format(jj),
range_id='domain_{}'.format(ii)) if mat else None
block_op = BlockOperator(ops)
rhs = VectorFunctional(op.range.make_array([rhs_vector]))
rhss = []
for ii in range(grid.num_subdomains):
rhss.append(ops[ii, ii].range.make_array([local_vectors[ii]]))
block_rhs = VectorFunctional(block_op.range.make_array(rhss))
return op, block_op, rhs, block_rhs
ops, block_ops, rhss, block_rhss = zip(*(discretize_lhs_for_lambda(l) for l in affine_lambda['functions']))
rhs = rhss[0]
block_rhs = block_rhss[0]
lambda_coeffs = affine_lambda['coefficients']
op = LincombOperator(ops, lambda_coeffs)
block_op = LincombOperator(block_ops, lambda_coeffs, name='lhs')
operators = {'global_op': op, 'global_rhs': rhs}
global_rt_space = make_rt_space(grid)
def assemble_oswald_interpolation_error():
oi_ops = [OswaldInterpolationErrorOperator(ii, ii, ii, block_op.source, grid, block_space,
global_rt_space, neighborhood_boundary_info,
None, None, None, None)
for ii in range(grid.num_subdomains)]
return BlockDiagonalOperator(oi_ops, name='oswald_interpolation_error')
oi_op = assemble_oswald_interpolation_error()
def assemble_flux_reconstruction(lambda_xi):
fr_ops = [FluxReconstructionOperator(ii, ii, ii, block_op.source, grid, block_space,
global_rt_space, neighborhood_boundary_info,
lambda_hat, lambda_xi, lambda_xi, kappa)
for ii in range(grid.num_subdomains)]
return BlockDiagonalOperator(fr_ops)
fr_op = LincombOperator([assemble_flux_reconstruction(lambda_xi) for lambda_xi in affine_lambda['functions']],
lambda_coeffs, name='flux_reconstruction')
spaces = block_op.source.subspaces
rt_spaces = fr_op.range.subspaces
# assemble local products
for ii in range(grid.num_subdomains):
local_space = block_space.local_space(ii)
# we want a larger pattern for the elliptic part, to allow for axpy with the penalty part
tmp_local_matrix = Matrix(local_space.size(),
local_space.size(),
local_space.compute_pattern('face_and_volume'))
local_product_ops = []
local_product_coeffs = []
for func, coeff in zip(affine_lambda['functions'], affine_lambda['coefficients']):
local_product_ops.append(make_elliptic_matrix_operator(
func, kappa, tmp_local_matrix.copy(), local_space, over_integrate=0))
local_product_coeffs.append(coeff)
local_product_ops.append(make_penalty_product_matrix_operator(
grid, ii, local_all_dirichlet_boundary_info,
local_space,
func, kappa, over_integrate=0))
local_product_coeffs.append(coeff)
del tmp_local_matrix
local_assembler = make_system_assembler(local_space)
for local_product_op in local_product_ops:
local_assembler.append(local_product_op)
local_assembler.assemble()
local_product_name = 'local_energy_dg_product_{}'.format(ii)
local_product = LincombOperator([DuneXTMatrixOperator(op.matrix(),
source_id='domain_{}'.format(ii),
range_id='domain_{}'.format(ii))
for op in local_product_ops],
local_product_coeffs,
name=local_product_name)
operators[local_product_name] = local_product.assemble(mu_bar).with_(name=local_product_name)
# assemble error estimator
for ii in range(grid.num_subdomains):
neighborhood = grid.neighborhood_of(ii)
def assemble_estimator_noconformity():
nc_ops = np.full((grid.num_subdomains,) * 2, None)
for jj in neighborhood:
for kk in neighborhood:
nc_ops[jj, kk] = NonconformityOperator(ii, jj, kk, block_op.source, grid, block_space,
global_rt_space, neighborhood_boundary_info,
lambda_bar, None, None, kappa)
return BlockOperator(nc_ops, range_spaces=oi_op.range.subspaces, source_spaces=oi_op.range.subspaces,
name='nonconformity_{}'.format(ii))
def assemble_estimator_diffusive_flux_aa(lambda_xi, lambda_xi_prime):
df_ops = np.full((grid.num_subdomains,) * 2, None)
df_ops[ii, ii] = DiffusiveFluxOperatorAA(ii, ii, ii, block_op.source, grid, block_space,
global_rt_space, neighborhood_boundary_info,
lambda_hat, lambda_xi, lambda_xi_prime, kappa)
return BlockOperator(df_ops, range_spaces=spaces, source_spaces=spaces)
def assemble_estimator_diffusive_flux_bb():
df_ops = np.full((grid.num_subdomains,) * 2, None)
for jj in neighborhood:
for kk in neighborhood:
df_ops[jj, kk] = DiffusiveFluxOperatorBB(ii, jj, kk, block_op.source, grid, block_space,
global_rt_space, neighborhood_boundary_info,
lambda_hat, None, None, kappa)
return BlockOperator(df_ops, range_spaces=rt_spaces, source_spaces=rt_spaces,
name='diffusive_flux_bb_{}'.format(ii))
def assemble_estimator_diffusive_flux_ab(lambda_xi):
df_ops = np.full((grid.num_subdomains,) * 2, None)
for kk in neighborhood:
df_ops[ii, kk] = DiffusiveFluxOperatorAB(ii, ii, kk, block_op.source, grid, block_space,
global_rt_space, neighborhood_boundary_info,
lambda_hat, lambda_xi, None, kappa)
return BlockOperator(df_ops, range_spaces=spaces, source_spaces=rt_spaces)
def assemble_estimator_residual():
r2_ops = np.full((grid.num_subdomains,) * 2, None)
for jj in neighborhood:
for kk in neighborhood:
r2_ops[jj, kk] = ResidualPartOperator(ii, jj, kk, block_op.source, grid, block_space,
global_rt_space, neighborhood_boundary_info,
lambda_hat, None, None, kappa)
return BlockOperator(r2_ops, range_spaces=rt_spaces, source_spaces=rt_spaces, name='residual_{}'.format(ii))
def assemble_estimator_residual_functional():
r1_ops = np.full((1, grid.num_subdomains,), None)
for jj in neighborhood:
r1_ops[0, jj] = ResidualPartFunctional(f, ii, jj, jj, block_op.source, grid, block_space,
global_rt_space, neighborhood_boundary_info,
lambda_hat, None, None, kappa)
return BlockOperator(r1_ops, source_spaces=rt_spaces, name='residual_functional_{}'.format(ii))
operators['nc_{}'.format(ii)] = assemble_estimator_noconformity()
operators['r1_{}'.format(ii)] = assemble_estimator_residual_functional()
operators['r2_{}'.format(ii)] = assemble_estimator_residual()
operators['df_aa_{}'.format(ii)] = LincombOperator(
[assemble_estimator_diffusive_flux_aa(lambda_xi, lambda_xi_prime)
for lambda_xi in affine_lambda['functions']
for lambda_xi_prime in affine_lambda['functions']],
[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()
operators['df_ab_{}'.format(ii)] = LincombOperator(
[assemble_estimator_diffusive_flux_ab(lambda_xi) for lambda_xi in affine_lambda['functions']],
lambda_coeffs,
name='diffusive_flux_ab_{}'.format(ii)
)
min_diffusion_evs = np.array([min_diffusion_eigenvalue(grid, ii, lambda_hat, kappa) for ii in
range(grid.num_subdomains)])
subdomain_diameters = np.array([subdomain_diameter(grid, ii) for ii in range(grid.num_subdomains)])
local_eta_rf_squared = np.array([apply_l2_product(grid, ii, f, f, over_integrate=2) for ii in
range(grid.num_subdomains)])
estimator = Estimator(min_diffusion_evs, subdomain_diameters, local_eta_rf_squared, lambda_coeffs, mu_bar, mu_hat,
fr_op, oi_op)
neighborhoods = [grid.neighborhood_of(ii) for ii in range(grid.num_subdomains)]
local_boundary_info = make_subdomain_boundary_info(grid_and_problem_data['grid'],
{'type': 'xt.grid.boundaryinfo.alldirichlet'})
d = DuneDiscretization(block_op, block_rhs,
neighborhoods,
(grid, local_boundary_info, affine_lambda, kappa, f, block_space),
visualizer=DuneGDTVisualizer(block_space),
operators=operators, estimator=estimator)
d = d.with_(parameter_space=CubicParameterSpace(d.parameter_type, parameter_range[0], parameter_range[1]))
return d, block_space
def discretize(grid_and_problem_data, T, nt):
d, d_data = discretize_ell(grid_and_problem_data)
assert isinstance(d.parameter_space, CubicParameterSpace)
parameter_range = grid_and_problem_data['parameter_range']
block_space = d_data['block_space']
# assemble global L2 product
l2_mat = d.global_operator.operators[0].matrix.copy(
) # to ensure matching pattern
l2_mat.scal(0.)
for ii in range(block_space.num_blocks):
local_l2_product = d.l2_product._blocks[ii, ii]
block_space.mapper.copy_local_to_global(
local_l2_product.matrix, local_l2_product.matrix.pattern(), ii,
l2_mat)
mass = d.l2_product
operators = {
k: v
for k, v in d.operators.items() if k not in d.special_operators
}
global_mass = DuneXTMatrixOperator(l2_mat)
local_div_ops, local_l2_products, local_projections, local_rt_projections = \
d_data['local_div_ops'], d_data['local_l2_products'], d_data['local_projections'], d_data['local_rt_projections']
for ii in range(d_data['grid'].num_subdomains):
local_div = Concatenation(
[local_div_ops[ii], local_rt_projections[ii]])
operators['r_ud_{}'.format(ii)] = \
Concatenation([local_projections[ii].T, local_l2_products[ii], local_div], name='r_ud_{}'.format(ii))
operators['r_l2_{}'.format(ii)] = \
Concatenation([local_projections[ii].T, local_l2_products[ii], local_projections[ii]],
name='r_l2_{}'.format(ii))
e = d.estimator
estimator = ParabolicEstimator(e.min_diffusion_evs, e.subdomain_diameters,
e.local_eta_rf_squared, e.lambda_coeffs,
e.mu_bar, e.mu_hat, e.flux_reconstruction,
e.oswald_interpolation_error)
d = InstationaryDuneDiscretization(
d.global_operator,
d.global_rhs,
global_mass,
T,
d.operator.source.zeros(1),
d.operator,
d.rhs,
mass=mass,
time_stepper=ImplicitEulerTimeStepper(nt=nt,
solver_options='operator'),
products=d.products,
operators=operators,
estimator=estimator,
visualizer=DuneGDTVisualizer(block_space))
d = d.with_(parameter_space=CubicParameterSpace(
d.parameter_type, parameter_range[0], parameter_range[1]))
return d, d_data