def bochner_norm(T, space_norm2, U, mu=None, order=2):
'''
L^2-in-time, X-in-space
'''
nt = len(U)
time_grid = OnedGrid(domain=(0., T), num_intervals=nt-1)
assert len(U) == time_grid.size(1)
qq = time_grid.quadrature_points(0, order=order)
integral = 0.
for entity in np.arange(time_grid.size(0)):
# get quadrature
qq_e = qq[entity] # points
ww = time_grid.reference_element.quadrature(order)[1] # weights
ie = time_grid.integration_elements(0)[entity] # integration element
# create shape function evaluations
a = time_grid.centers(1)[entity]
b = time_grid.centers(1)[entity + 1]
SF = np.array((1./(a - b)*qq_e[..., 0] - b/(a - b),
1./(b - a)*qq_e[..., 0] - a/(b - a)))
U_a = U._list[entity]
U_b = U._list[entity + 1]
values = np.zeros(len(qq_e))
for ii in np.arange(len(qq_e)):
# compute U(t)
U_t = U_a.copy()
U_t.scal(SF[0][ii])
U_t.axpy(SF[1][ii], U_b)
# compute the X-norm of U(t)
values[ii] = space_norm2(make_listvectorarray(U_t), mu)
integral += np.dot(values, ww)*ie
return np.sqrt(integral)
def __init__(self, d):
def wrap_op(op, name=None):
if not op.parametric() and op.num_components() == 0 and op.has_affine_part():
wrapped_op = self._wrapper[op.affine_part()]
else:
wrapped_op = self._wrapper[op]
return wrapped_op.with_(name=name) if name else wrapped_op
self._impl = d
operators = {'operator': wrap_op(d.get_operator())}
functionals = {'rhs': self._wrapper[d.get_rhs()]}
vector_operators = FrozenDict({k: VectorOperator(make_listvectorarray(self._wrapper[d.get_vector(k)]))
for k in list(d.available_vectors())})
self.operators = FrozenDict(operators)
self.functionals = FrozenDict(functionals)
self.vector_operators = FrozenDict(vector_operators)
self.operator = operators['operator']
self.rhs = functionals['rhs']
self.products = FrozenDict({k: wrap_op(d.get_product(k), k) for k in list(d.available_products())})
if self.products:
for k, v in self.products.iteritems():
setattr(self, '{}_product'.format(k), v)
setattr(self, '{}_norm'.format(k), induced_norm(v))
self.linear = all(op.linear for op in operators.itervalues())
self.solution_space = self.operator.source
self.build_parameter_type(inherits=operators.values() + functionals.values())
assert self.parameter_type == self._wrapper[d.parameter_type()]
self.solver_options = self._impl.solver_options()
def bochner_norm(T, space_norm2, U, mu=None, order=2):
'''
L^2-in-time, X-in-space
'''
nt = len(U)
time_grid = OnedGrid(domain=(0., T), num_intervals=nt - 1)
assert len(U) == time_grid.size(1)
qq = time_grid.quadrature_points(0, order=order)
integral = 0.
for entity in np.arange(time_grid.size(0)):
# get quadrature
qq_e = qq[entity] # points
ww = time_grid.reference_element.quadrature(order)[1] # weights
ie = time_grid.integration_elements(0)[entity] # integration element
# create shape function evaluations
a = time_grid.centers(1)[entity]
b = time_grid.centers(1)[entity + 1]
SF = np.array((1. / (a - b) * qq_e[..., 0] - b / (a - b),
1. / (b - a) * qq_e[..., 0] - a / (b - a)))
U_a = U._list[entity]
U_b = U._list[entity + 1]
values = np.zeros(len(qq_e))
for ii in np.arange(len(qq_e)):
# compute U(t)
U_t = U_a.copy()
U_t.scal(SF[0][ii])
U_t.axpy(SF[1][ii], U_b)
# compute the X-norm of U(t)
values[ii] = space_norm2(make_listvectorarray(U_t), mu)
integral += np.dot(values, ww) * ie
return np.sqrt(integral)
def solve(self, mu=None):
mu = self.parse_parameter(mu)
if not self.logging_disabled:
self.logger.info('Solving {} for {} ...'.format(self.name, mu))
mu = self._wrapper.dune_parameter(mu)
global_solution = self._impl.solve_and_return_ptr(mu)
assert global_solution.valid()
global_solution = make_listvectorarray(self._wrapper[global_solution])
return BlockVectorArray([self.localize_vector(global_solution, ss)
for ss in np.arange(self._impl.num_subdomains())])
def assemble_lincomb(self, operators, coefficients, solver_options=None, name=None):
assert not solver_options
assert len(operators) > 0
assert len(operators) == len(coefficients)
vec = operators[0]._impl.as_vector()
vec.scal(coefficients[0])
for op, c in izip(operators[1:], coefficients[1:]):
vec.axpy(c, op._impl.as_vector())
op = self._wrapper[vec]
return make_listvectorarray(op)
def prolong(coarse_disc, coarse_U):
time_grid_ref = OnedGrid(domain=(0., T), num_intervals=nt)
time_grid = OnedGrid(domain=(0., T), num_intervals=(len(coarse_U) - 1))
U_fine = [None for ii in time_grid_ref.centers(1)]
for n in np.arange(len(time_grid_ref.centers(1))):
t_n = time_grid_ref.centers(1)[n]
coarse_entity = min((time_grid.centers(1) <= t_n).nonzero()[0][-1],
time_grid.size(0) - 1)
a = time_grid.centers(1)[coarse_entity]
b = time_grid.centers(1)[coarse_entity + 1]
SF = np.array((1./(a - b)*t_n - b/(a - b),
1./(b - a)*t_n - a/(b - a)))
U_t = coarse_U.copy(ind=coarse_entity)
U_t.scal(SF[0][0])
U_t.axpy(SF[1][0], coarse_U, x_ind=(coarse_entity + 1))
U_fine[n] = wrapper[example.prolong(coarse_disc._impl, U_t._list[0]._impl)]
return make_listvectorarray(U_fine)
def prolong(coarse_disc, coarse_U):
time_grid_ref = OnedGrid(domain=(0., T), num_intervals=nt)
time_grid = OnedGrid(domain=(0., T), num_intervals=(len(coarse_U) - 1))
U_fine = [None for ii in time_grid_ref.centers(1)]
for n in np.arange(len(time_grid_ref.centers(1))):
t_n = time_grid_ref.centers(1)[n]
coarse_entity = min((time_grid.centers(1) <= t_n).nonzero()[0][-1],
time_grid.size(0) - 1)
a = time_grid.centers(1)[coarse_entity]
b = time_grid.centers(1)[coarse_entity + 1]
SF = np.array((1. / (a - b) * t_n - b / (a - b),
1. / (b - a) * t_n - a / (b - a)))
U_t = coarse_U.copy(ind=coarse_entity)
U_t.scal(SF[0][0])
U_t.axpy(SF[1][0], coarse_U, x_ind=(coarse_entity + 1))
U_fine[n] = wrapper[example.prolong(coarse_disc._impl,
U_t._list[0]._impl)]
return make_listvectorarray(U_fine)
def offline_phase(cfg, data):
logger = getLogger('.OS2015_SISC__6_2.offline_phase')
logger.setLevel('INFO')
discretization = data['discretization']
example = data['example']
local_products = data['local_products']
norm = data['norm']
mu_bar_dune = data['mu_bar_dune']
mu_hat_dune = data['mu_hat_dune']
wrapper = data['wrapper']
if cfg['training_sampling_strategy'] == 'random':
training_samples = list(
discretization.parameter_space.sample_randomly(
cfg['num_training_samples']))
elif cfg['training_sampling_strategy'] == 'uniform':
training_samples = list(
discretization.parameter_space.sample_uniformly(
cfg['num_training_samples']))
add_values(training_samples=training_samples)
if cfg['compute_some_solution_norms'] and len(training_samples) > 0:
logger.info('Computing solution norms:')
if norm is not None:
solution_norms = [
norm(discretization.solve(mu)) for mu in training_samples
]
else:
solution_norms = [
discretization.solve(mu).l2_norm()[0]
for mu in training_samples
]
logger.info(' range: [{}, {}]'.format(
np.amin(solution_norms), np.amax(solution_norms)))
logger.info(' mean: {}'.format(
np.mean(solution_norms)))
add_values(solution_norms=solution_norms)
extension_algorithm = partial(gram_schmidt_block_basis_extension,
product=local_products)
initial_basis = discretization.functionals['rhs'].source.empty()._blocks
if cfg['initialize_basis_with'] >= 0:
logger.info('Initializing local bases of up to order {} ...'.format(
cfg['initialize_basis_with']))
one = make_listvectorarray(wrapper[example.project('1')])
one = BlockVectorArray([
discretization.localize_vector(one, ss)
for ss in np.arange(discretization.num_subdomains)
])
initial_basis, _ = extension_algorithm(initial_basis, one)
if cfg['initialize_basis_with'] >= 1:
xx = make_listvectorarray(wrapper[example.project('x[0]')])
xx = BlockVectorArray([
discretization.localize_vector(xx, ss)
for ss in np.arange(discretization.num_subdomains)
])
initial_basis, _ = extension_algorithm(initial_basis, xx)
yy = make_listvectorarray(wrapper[example.project('x[1]')])
yy = BlockVectorArray([
discretization.localize_vector(yy, ss)
for ss in np.arange(discretization.num_subdomains)
])
initial_basis, _ = extension_algorithm(initial_basis, yy)
xy = make_listvectorarray(wrapper[example.project('x[0]*x[1]')])
xy = BlockVectorArray([
discretization.localize_vector(xy, ss)
for ss in np.arange(discretization.num_subdomains)
])
initial_basis, _ = extension_algorithm(initial_basis, xy)
if cfg['initialize_basis_with'] >= 2:
logger.warn('Ignoring initialize_basis_with higher than 1: {}'.format(
cfg['initialize_basis_with']))
logger.info('')
reduced_estimator = ReducedEstimator(discretization, example, wrapper,
mu_hat_dune, mu_bar_dune, norm,
cfg['estimator_compute'],
cfg['estimator_return'])
greedy_data = greedy(discretization,
partial(reduce_with_estimator,
reduced_estimator=reduced_estimator),
training_samples,
initial_basis=initial_basis,
use_estimator=cfg['greedy_use_estimator'],
error_norm=norm,
extension_algorithm=extension_algorithm,
max_extensions=cfg['greedy_max_extensions'],
target_error=cfg['greedy_target_error'])
add_values(time=greedy_data['time'],
max_err_mus=greedy_data['max_err_mus'],
extensions=greedy_data['extensions'],
max_errs=greedy_data['max_errs'],
offline_estimator_data=reduced_estimator.data)
rd, rc = greedy_data['reduced_discretization'], greedy_data[
'reconstructor']
basis, basis_mus = greedy_data['basis'], greedy_data['max_err_mus']
print('')
logger.info('Offline phase finished.')
logger.info('Basis sizes range from {} to {}.'.format(
np.min([len(bb) for bb in basis]), np.max([len(bb) for bb in basis])))
return {'basis': basis, 'basis_mus': basis_mus, 'rc': rc, 'rd': rd}
def online_phase(cfg, detailed_data, offline_data):
logger = getLogger('.OS2015_SISC__6_2.online_phase')
logger.setLevel('INFO')
def doerfler_marking(indicators, theta):
assert 0.0 < theta <= 1.0
indices = list(range(len(indicators)))
indicators = [ii**2 for ii in indicators]
indicators, indices = [list(x) for x in zip(*sorted(zip(indicators, indices),
key=lambda pair: pair[0],
reverse=True))]
total = np.sum(indicators)
sums = np.array([np.sum(indicators[:ii+1]) for ii in np.arange(len(indicators))])
where = sums > theta*total
if np.any(where):
return indices[:np.argmax(where)+1]
else:
return indices
discretization = detailed_data['discretization']
example = detailed_data['example']
local_products = detailed_data['local_products']
mu_bar_dune = detailed_data['mu_bar_dune']
mu_hat_dune = detailed_data['mu_hat_dune']
norm = detailed_data['norm']
wrapper = detailed_data['wrapper']
basis = offline_data['basis']
basis_mus = offline_data['basis_mus']
rd = offline_data['rd']
rc = offline_data['rc']
reduced_estimator = ReducedEstimator(discretization, example, wrapper, mu_hat_dune, mu_bar_dune,
norm, cfg['estimator_compute'], cfg['estimator_return'])
reduced_estimator.extension_step += 1
reduced_estimator.rc = rc
num_test_samples = cfg['num_test_samples']
target_error = cfg['online_target_error']
logger.info('Started online phase for {} samples'.format(num_test_samples))
test_samples = list(discretization.parameter_space.sample_randomly(num_test_samples))
if cfg['estimate_some_errors'] and len(test_samples) > 0:
logger.info('Estimating discretization errors:')
detailed_estimator = DetailedEstimator(example, wrapper, mu_hat_dune, mu_bar_dune)
estimates = [detailed_estimator.estimate(
discretization.globalize_vectors(discretization.solve(mu))._list[0]._impl,
wrapper.dune_parameter(mu)) for mu in test_samples]
max_error = np.amax(estimates)
logger.info(' range: [{}, {}]'.format(np.amin(estimates), max_error))
logger.info(' mean: {}'.format(np.mean(estimates)))
add_values(estimates=estimates)
if max_error > cfg['online_target_error']:
logger.warn('Given target error of {} is below the worst discretization error {}!'.format(
cfg['online_target_error'], max_error))
print('')
failures = 0
successes = 0
for mu in test_samples:
mu_dune = wrapper.dune_parameter(mu)
mu_in_basis = mu in basis_mus
age = np.ones(discretization.num_subdomains)
logger.info('Solving for {} ...'.format(mu))
U_red = rd.solve(mu)
logger.info('Estimating (mu is {}in the basis) ...'.format('already ' if mu_in_basis else 'not '))
error = reduced_estimator.estimate(U_red, mu, discretization)
if error > target_error:
if mu_in_basis:
logger.error(('The error ({}) is larger than the target_error ({}), '
+ 'but {} is already in the basis: aborting!').format(
error, target_error, mu))
logger.error('This usually means that the tolerances are poorly chosen!')
failures += 1
print('')
else:
try:
logger.info('The error ({}) is too large, starting local enrichment phase:'.format(error))
num_extensions = 0
intermediate_basis = [bb.copy() for bb in basis]
if cfg['local_indicators'] == 'model_reduction_error':
U_h = discretization.solve(mu)
assert len(U_h) == 1
while error > target_error and num_extensions < cfg['online_max_extensions']:
U_red_h = rc.reconstruct(U_red)
assert len(U_red_h) == 1
U_red_global = discretization.globalize_vectors(U_red_h)
U_red_dune = U_red_global._list[0]._impl
if (cfg['uniform_enrichment_factor'] > 0
and error/target_error > cfg['uniform_enrichment_factor']):
logger.info('- Enriching on all subdomains, since error/target_error = {}'.format(
error/target_error))
marked_subdomains = range(discretization.num_subdomains)
if 'age' in cfg['marking_strategy']:
age = np.ones(discretization.num_subdomains)
else:
logger.info('- Estimating local error contributions ...')
# compute local error indicators
if cfg['local_indicators'] == 'model_reduction_error':
difference = U_h - U_red_h
local_indicators = [induced_norm(local_products[ss])(difference._blocks[ss])
for ss in np.arange(discretization.num_subdomains)]
elif cfg['local_indicators'] == 'eta_red':
local_indicators = list(example.estimate_local(U_red_dune,
'eta_OS2014_*',
mu_hat_dune,
mu_bar_dune,
mu_dune))
else:
raise ConfigurationError('Unknown local_indicators given: {}'.format(
cfg['local_indicators']))
# mark subdomains
if 'doerfler' in cfg['marking_strategy']:
marked_subdomains = set(doerfler_marking(local_indicators,
cfg['doerfler_marking_theta']))
else:
raise ConfigurationError('Unknown marking_strategy given: {}'.format(
cfg['local_indicators']))
if 'neighbours' in cfg['marking_strategy']:
for ss in list(marked_subdomains):
neighbours = (list(discretization._impl.neighbouring_subdomains(ss)))
for nn in neighbours:
marked_subdomains.append(nn)
marked_subdomains = set(marked_subdomains)
if 'age' in cfg['marking_strategy']:
only_marked = len(marked_subdomains)
too_old = np.where(age > cfg['marking_max_age'])[0]
for ss in too_old:
marked_subdomains.add(ss)
logger.info((' {} subdomains marked ({} bc. of age), '
+ 'computing local solutions ...').format(
len(marked_subdomains), len(marked_subdomains) - only_marked))
else:
logger.info(' {} subdomains marked, computing local solutions ...'.format(
len(marked_subdomains)))
for ss in np.arange(discretization.num_subdomains):
if ss in marked_subdomains:
age[ss] = 1
else:
age[ss] += 1
# compute updated local solution
local_solutions = [None for ss in np.arange(discretization.num_subdomains)]
for subdomain in marked_subdomains:
local_boundary_values = cfg['local_boundary_values']
if not (local_boundary_values == 'dirichlet' or local_boundary_values == 'neumann'):
raise ConfigurationError('Unknown local_boundary_values given: {}'.format(
local_boundary_values))
oversampled_discretization = discretization.get_oversampled_discretization(
subdomain, local_boundary_values)
local_discretization = discretization.get_local_discretization(subdomain)
U_red_oversampled_dune = example.project_global_to_oversampled(U_red_dune, subdomain)
U_h_improved_oversampled_dune = example.solve_oversampled(
subdomain, local_boundary_values, U_red_oversampled_dune, mu_dune)
U_h_improved_local_dune = example.project_oversampled_to_local(
U_h_improved_oversampled_dune, subdomain)
U_h_improved_local = make_listvectorarray(wrapper[U_h_improved_local_dune])
local_solutions[subdomain] = U_h_improved_local
# extend local bases
logger.info(' Extending bases on {} subdomain{}...'.format(
len(marked_subdomains), '' if len(marked_subdomains) == 1 else 's'))
old_basis_size = sum([len(bb) for bb in intermediate_basis])
extended_bases, _ = gram_schmidt_block_basis_extension(
[intermediate_basis[ss] for ss in marked_subdomains],
[local_solutions[ss] for ss in marked_subdomains],
product=[local_products[ss] for ss in marked_subdomains])
assert len(extended_bases) == len(marked_subdomains)
for ii, subdomain in enumerate(marked_subdomains):
intermediate_basis[subdomain] = extended_bases[ii]
new_basis_size = sum([len(bb) for bb in intermediate_basis])
num_extensions += 1
logger.info(' Reducing ...')
rd, _, _ = reduce_generic_rb(discretization, intermediate_basis)
rc = GenericBlockRBReconstructor(intermediate_basis)
reduced_estimator.rc = rc
reduced_estimator.extension_step += 1
U_red = rd.solve(mu)
logger.info(' Estimating (total basis size: {})'.format(
sum(len(bb) for bb in intermediate_basis)))
new_error = reduced_estimator.estimate(U_red, mu, discretization)
order = np.log(new_error/error)/np.log(old_basis_size/new_basis_size)
logger.info(' {} (relative improvement: {})'.format(new_error, order))
if new_error > error:
logger.warn('The error has increased (from {} to {}) after enrichment!'.format(error,
new_error))
elif order < 1:
logger.warn(('The error has decreased only slightly '
+ '(from {} to {}) after enrichment!').format(error, new_error))
if num_extensions >= cfg['online_max_extensions'] and new_error > cfg['online_target_error']:
basis = intermediate_basis
raise EnrichmentError('Reached maximum number of {} extensions!'.format(
cfg['online_max_extensions']))
error = new_error
logger.info(' The error ({}) is below the target error, continuing ...'.format(error))
successes += 1
basis = intermediate_basis
logger.info('Basis sizes range from {} to {}.'.format(np.min([len(bb) for bb in basis]),
np.max([len(bb) for bb in basis])))
except EnrichmentError, ee:
logger.critical('Enrichment stopped because: {}'.format(ee))
logger.info('Basis sizes range from {} to {}.'.format(np.min([len(bb) for bb in basis]),
np.max([len(bb) for bb in basis])))
logger.info('Continuing with the next parameter ...')
failures += 1
print('')
else:
logger.info('The error ({}) is below the target error, continuing ...'.format(error))
successes += 1
print('')
for mu in (config['mu_min'], config['mu_max'])]
logger.info(' range: {} to {}'.format(np.min(estimates), np.max(estimates)))
if np.max(estimates) > config['target_error']:
logger.warn(('target error for greedy ({}) is below max estimated discretization error ({}), '
+ 'greedy will most likely fail!').format(config['target_error'], np.max(estimates)))
if config['initial_basis'] < 0:
config['initial_basis'] = 0
elif config['initial_basis'] > 1:
config['initial_basis'] = 1
logger.info('initializing local reduced bases of order up to {} ...'.format(config['initial_basis']))
local_products = [elliptic_disc.local_product(ss, config['extension_product'])
for ss in np.arange(elliptic_disc.num_subdomains)]
initial_basis = elliptic_disc.solution_space.empty()._blocks
for basis in (('1',) if config['initial_basis'] == 0 else ('1', 'x[0]', 'x[1]', 'x[0]*x[1]')):
vec = make_listvectorarray(wrapper[example.project(basis)])
vec = BlockVectorArray([elliptic_disc.localize_vector(vec, ss)
for ss in np.arange(elliptic_disc.num_subdomains)])
initial_basis, _ = gram_schmidt_block_basis_extension(initial_basis, vec, product=local_products)
f_h = elliptic_disc.rhs.as_vector(1.)
f_h = elliptic_disc.l2_product.apply_inverse(f_h)
initial_basis, _ = gram_schmidt_block_basis_extension(initial_basis, f_h, product=local_products)
detailed_data['initial_basis'] = initial_basis
greedy_data = reduce_pod_greedy(config, detailed_data, training_samples)
add_values(greedy_max_err_mus=greedy_data['max_err_mus'],
greedy_max_errs=greedy_data['max_errs'],
greedy_extensions=greedy_data['extensions'],
greedy_basis_sizes=[len(local_RB) for local_RB in greedy_data['basis']],
training_samples=training_samples)
np.max(estimates)))
if config['initial_basis'] < 0:
config['initial_basis'] = 0
elif config['initial_basis'] > 1:
config['initial_basis'] = 1
logger.info('initializing local reduced bases of order up to {} ...'.format(
config['initial_basis']))
local_products = [
elliptic_disc.local_product(ss, config['extension_product'])
for ss in np.arange(elliptic_disc.num_subdomains)
]
initial_basis = elliptic_disc.solution_space.empty()._blocks
for basis in (('1', ) if config['initial_basis'] == 0 else
('1', 'x[0]', 'x[1]', 'x[0]*x[1]')):
vec = make_listvectorarray(wrapper[example.project(basis)])
vec = BlockVectorArray([
elliptic_disc.localize_vector(vec, ss)
for ss in np.arange(elliptic_disc.num_subdomains)
])
initial_basis, _ = gram_schmidt_block_basis_extension(
initial_basis, vec, product=local_products)
f_h = elliptic_disc.rhs.as_vector(1.)
f_h = elliptic_disc.l2_product.apply_inverse(f_h)
initial_basis, _ = gram_schmidt_block_basis_extension(initial_basis,
f_h,
product=local_products)
detailed_data['initial_basis'] = initial_basis
greedy_data = reduce_pod_greedy(config, detailed_data, training_samples)
def localize_vector(self, global_vector, subdomain):
assert subdomain < self.num_subdomains
return make_listvectorarray([self._wrapper[self._impl.localize_vector(global_vector._list[ii]._impl,
subdomain)]
for ii in np.arange(len(global_vector))])
example = Example(logger_cfg, grid_cfg, boundary_cfg, problem_cfg)
stat_blocked_disc = wrapper[example.discretization()]
stat_nonblocked_disc = stat_blocked_disc.as_nonblocked()
logger.info(' grid has {} subdomains'.format(
stat_blocked_disc.num_subdomains))
logger.info(' discretization has {} DoFs'.format(
stat_nonblocked_disc.solution_space.dim))
logger.info(' parameter type is {}'.format(
stat_nonblocked_disc.parameter_type))
# logger.info('visualizing grid and data functions ...')
# example.visualize(problem_cfg.get_str('type'))
nonblocked_disc = InstationaryDiscretization(
T=config['end_time'],
initial_data=make_listvectorarray(
wrapper[stat_nonblocked_disc._impl.create_vector()]),
operator=stat_nonblocked_disc.operator,
rhs=stat_nonblocked_disc.rhs,
mass=stat_nonblocked_disc.products['l2'],
time_stepper=ImplicitEulerTimeStepper(
config['nt'], invert_options=solver_options.get_str('type')),
products=stat_nonblocked_disc.products,
operators=stat_nonblocked_disc.operators,
functionals=stat_nonblocked_disc.functionals,
vector_operators=stat_nonblocked_disc.vector_operators,
visualizer=InstationaryDuneVisualizer(
stat_nonblocked_disc,
problem_cfg.get_str('type') + '.solution'),
parameter_space=CubicParameterSpace(stat_nonblocked_disc.parameter_type,
0.1, 10),
cache_region='disk',
def discretize(num_elements, num_partitions, T, nt, initial_data, parameter_range, name='detailed discretization'):
Example = examples[2]['aluconformgrid']['fem']['istl']
logger_cfg = Example.logger_options()
logger_cfg.set('info', -1, True)
logger_cfg.set('info_color', 'blue', True)
grid_cfg = Example.grid_options('grid.multiscale.provider.cube')
grid_cfg.set('lower_left', '[0 0]', True)
grid_cfg.set('upper_right', '[5 1]', True)
grid_cfg.set('num_elements', num_elements, True)
grid_cfg.set('num_partitions', num_partitions, True)
boundary_cfg = Example.boundary_options('stuff.grid.boundaryinfo.alldirichlet')
problem_cfg = Example.problem_options('hdd.linearelliptic.problem.OS2015.spe10model1')
problem_cfg.set('parametric_channel', 'true', True)
problem_cfg.set('channel_boundary_layer', '0', True)
problem_cfg.set('filename', 'perm_case1.dat', True)
problem_cfg.set('lower_left', '[0 0]', True)
problem_cfg.set('upper_right', '[5 1]', True)
problem_cfg.set('num_elements', '[100 20]', True)
problem_cfg.set('forces.0.domain', '[0.95 1.10; 0.30 0.45]', True)
problem_cfg.set('forces.0.value', '2000', True)
problem_cfg.set('forces.1.domain', '[3.00 3.15; 0.75 0.90]', True)
problem_cfg.set('forces.1.value', '-1000', True)
problem_cfg.set('forces.2.domain', '[4.25 4.40; 0.25 0.40]', True)
problem_cfg.set('forces.2.value', '-1000', True)
problem_cfg.set('channel.0.value', '-1.07763239495', True)
problem_cfg.set('channel.1.value', '-1.07699512772', True)
problem_cfg.set('channel.2.value', '-1.07356156439', True)
problem_cfg.set('channel.3.value', '-1.06602281736', True)
problem_cfg.set('channel.4.value', '-1.06503683743', True)
problem_cfg.set('channel.5.value', '-1.07974870426', True)
problem_cfg.set('channel.6.value', '-1.05665895923', True)
problem_cfg.set('channel.7.value', '-1.08310334837', True)
problem_cfg.set('channel.8.value', '-1.05865484973', True)
problem_cfg.set('channel.9.value', '-1.05871039535', True)
problem_cfg.set('channel.10.value', '-1.08136695901', True)
problem_cfg.set('channel.11.value', '-1.08490172721', True)
problem_cfg.set('channel.12.value', '-1.06641120758', True)
problem_cfg.set('channel.13.value', '-1.06812773298', True)
problem_cfg.set('channel.14.value', '-1.07695652049', True)
problem_cfg.set('channel.15.value', '-1.08630079205', True)
problem_cfg.set('channel.16.value', '-1.08273722112', True)
problem_cfg.set('channel.17.value', '-1.07500402155', True)
problem_cfg.set('channel.18.value', '-1.08607142562', True)
problem_cfg.set('channel.19.value', '-1.07268761799', True)
problem_cfg.set('channel.20.value', '-1.08537037362', True)
problem_cfg.set('channel.21.value', '-1.08466927273', True)
problem_cfg.set('channel.22.value', '-1.08444661815', True)
problem_cfg.set('channel.23.value', '-1.08957037967', True)
problem_cfg.set('channel.24.value', '-1.08047394052', True)
problem_cfg.set('channel.25.value', '-1.08221229083', True)
problem_cfg.set('channel.26.value', '-1.08568599863', True)
problem_cfg.set('channel.27.value', '-1.08428347872', True)
problem_cfg.set('channel.28.value', '-1.09104098734', True)
problem_cfg.set('channel.29.value', '-1.09492700673', True)
problem_cfg.set('channel.30.value', '-1.09760440537', True)
problem_cfg.set('channel.31.value', '-1.09644989453', True)
problem_cfg.set('channel.32.value', '-1.09441681025', True)
problem_cfg.set('channel.33.value', '-1.09533290654', True)
problem_cfg.set('channel.34.value', '-1.1001430808', True)
problem_cfg.set('channel.35.value', '-1.10065627621', True)
problem_cfg.set('channel.36.value', '-1.10125877186', True)
problem_cfg.set('channel.37.value', '-1.10057485893', True)
problem_cfg.set('channel.38.value', '-1.10002261906', True)
problem_cfg.set('channel.39.value', '-1.10219154209', True)
problem_cfg.set('channel.40.value', '-1.09994463801', True)
problem_cfg.set('channel.41.value', '-1.10265630533', True)
problem_cfg.set('channel.42.value', '-1.10448566526', True)
problem_cfg.set('channel.43.value', '-1.10735820121', True)
problem_cfg.set('channel.44.value', '-1.1070022367', True)
problem_cfg.set('channel.45.value', '-1.10777650387', True)
problem_cfg.set('channel.46.value', '-1.10892785562', True)
problem_cfg.set('channel.0.domain', '[1.7 1.75; 0.5 0.55]', True)
problem_cfg.set('channel.1.domain', '[1.75 1.8; 0.5 0.55]', True)
problem_cfg.set('channel.2.domain', '[1.8 1.85; 0.5 0.55]', True)
problem_cfg.set('channel.3.domain', '[1.85 1.9; 0.5 0.55]', True)
problem_cfg.set('channel.4.domain', '[1.9 1.95; 0.5 0.55]', True)
problem_cfg.set('channel.5.domain', '[1.95 2.0; 0.5 0.55]', True)
problem_cfg.set('channel.6.domain', '[2.0 2.05; 0.5 0.55]', True)
problem_cfg.set('channel.7.domain', '[2.05 2.1; 0.5 0.55]', True)
problem_cfg.set('channel.8.domain', '[2.1 2.15; 0.5 0.55]', True)
problem_cfg.set('channel.9.domain', '[2.15 2.2; 0.5 0.55]', True)
problem_cfg.set('channel.10.domain', '[2.2 2.25; 0.5 0.55]', True)
problem_cfg.set('channel.11.domain', '[2.25 2.3; 0.5 0.55]', True)
problem_cfg.set('channel.12.domain', '[2.3 2.35; 0.5 0.55]', True)
problem_cfg.set('channel.13.domain', '[2.35 2.4; 0.5 0.55]', True)
problem_cfg.set('channel.14.domain', '[2.4 2.45; 0.5 0.55]', True)
problem_cfg.set('channel.15.domain', '[2.45 2.5; 0.5 0.55]', True)
problem_cfg.set('channel.16.domain', '[2.5 2.55; 0.5 0.55]', True)
problem_cfg.set('channel.17.domain', '[2.55 2.6; 0.5 0.55]', True)
problem_cfg.set('channel.18.domain', '[2.6 2.65; 0.5 0.55]', True)
problem_cfg.set('channel.19.domain', '[2.65 2.7; 0.5 0.55]', True)
problem_cfg.set('channel.20.domain', '[2.7 2.75; 0.5 0.55]', True)
problem_cfg.set('channel.21.domain', '[2.75 2.8; 0.5 0.55]', True)
problem_cfg.set('channel.22.domain', '[2.8 2.85; 0.5 0.55]', True)
problem_cfg.set('channel.23.domain', '[2.85 2.9; 0.5 0.55]', True)
problem_cfg.set('channel.24.domain', '[2.9 2.95; 0.5 0.55]', True)
problem_cfg.set('channel.25.domain', '[2.95 3.0; 0.5 0.55]', True)
problem_cfg.set('channel.26.domain', '[3.0 3.05; 0.5 0.55]', True)
problem_cfg.set('channel.27.domain', '[3.05 3.1; 0.5 0.55]', True)
problem_cfg.set('channel.28.domain', '[3.1 3.15; 0.5 0.55]', True)
problem_cfg.set('channel.29.domain', '[3.15 3.2; 0.5 0.55]', True)
problem_cfg.set('channel.30.domain', '[3.2 3.25; 0.5 0.55]', True)
problem_cfg.set('channel.31.domain', '[3.25 3.3; 0.5 0.55]', True)
problem_cfg.set('channel.32.domain', '[3.3 3.35; 0.5 0.55]', True)
problem_cfg.set('channel.33.domain', '[3.35 3.4; 0.5 0.55]', True)
problem_cfg.set('channel.34.domain', '[3.4 3.45; 0.5 0.55]', True)
problem_cfg.set('channel.35.domain', '[3.45 3.5; 0.5 0.55]', True)
problem_cfg.set('channel.36.domain', '[3.5 3.55; 0.5 0.55]', True)
problem_cfg.set('channel.37.domain', '[3.55 3.6; 0.5 0.55]', True)
problem_cfg.set('channel.38.domain', '[3.6 3.65; 0.5 0.55]', True)
problem_cfg.set('channel.39.domain', '[3.65 3.7; 0.5 0.55]', True)
problem_cfg.set('channel.40.domain', '[3.7 3.75; 0.5 0.55]', True)
problem_cfg.set('channel.41.domain', '[3.75 3.8; 0.5 0.55]', True)
problem_cfg.set('channel.42.domain', '[3.8 3.85; 0.5 0.55]', True)
problem_cfg.set('channel.43.domain', '[3.85 3.9; 0.5 0.55]', True)
problem_cfg.set('channel.44.domain', '[3.9 3.95; 0.5 0.55]', True)
problem_cfg.set('channel.45.domain', '[3.95 4.0; 0.5 0.55]', True)
problem_cfg.set('channel.46.domain', '[4.0 4.05; 0.5 0.55]', True)
problem_cfg.set('channel.47.value', '-1.10372589211', True)
problem_cfg.set('channel.48.value', '-1.1020889988', True)
problem_cfg.set('channel.49.value', '-1.09806955069', True)
problem_cfg.set('channel.50.value', '-1.10000902421', True)
problem_cfg.set('channel.51.value', '-1.08797468724', True)
problem_cfg.set('channel.52.value', '-1.08827472176', True)
problem_cfg.set('channel.53.value', '-1.08692237109', True)
problem_cfg.set('channel.54.value', '-1.07893190093', True)
problem_cfg.set('channel.55.value', '-1.08748373853', True)
problem_cfg.set('channel.56.value', '-1.07445197324', True)
problem_cfg.set('channel.57.value', '-1.08246613163', True)
problem_cfg.set('channel.58.value', '-1.06726790504', True)
problem_cfg.set('channel.59.value', '-1.07891217847', True)
problem_cfg.set('channel.60.value', '-1.07260827126', True)
problem_cfg.set('channel.61.value', '-1.07094062748', True)
problem_cfg.set('channel.62.value', '-1.0692399429', True)
problem_cfg.set('channel.63.value', '-1.00099885701', True)
problem_cfg.set('channel.64.value', '-1.00109544002', True)
problem_cfg.set('channel.65.value', '-0.966491003242', True)
problem_cfg.set('channel.66.value', '-0.802284684014', True)
problem_cfg.set('channel.67.value', '-0.980790923021', True)
problem_cfg.set('channel.68.value', '-0.614478271687', True)
problem_cfg.set('channel.69.value', '-0.288129858959', True)
problem_cfg.set('channel.70.value', '-0.929509396842', True)
problem_cfg.set('channel.71.value', '-0.992376505995', True)
problem_cfg.set('channel.72.value', '-0.968162494855', True)
problem_cfg.set('channel.73.value', '-0.397316938901', True)
problem_cfg.set('channel.74.value', '-0.970934956609', True)
problem_cfg.set('channel.75.value', '-0.784344730096', True)
problem_cfg.set('channel.76.value', '-0.539725422323', True)
problem_cfg.set('channel.77.value', '-0.915632282372', True)
problem_cfg.set('channel.78.value', '-0.275089177273', True)
problem_cfg.set('channel.79.value', '-0.949684959286', True)
problem_cfg.set('channel.80.value', '-0.936132529794', True)
problem_cfg.set('channel.47.domain', '[2.6 2.65; 0.45 0.50]', True)
problem_cfg.set('channel.48.domain', '[2.65 2.7; 0.45 0.50]', True)
problem_cfg.set('channel.49.domain', '[2.7 2.75; 0.45 0.50]', True)
problem_cfg.set('channel.50.domain', '[2.75 2.8; 0.45 0.50]', True)
problem_cfg.set('channel.51.domain', '[2.8 2.85; 0.45 0.50]', True)
problem_cfg.set('channel.52.domain', '[2.85 2.9; 0.45 0.50]', True)
problem_cfg.set('channel.53.domain', '[2.9 2.95; 0.45 0.50]', True)
problem_cfg.set('channel.54.domain', '[2.95 3.0; 0.45 0.50]', True)
problem_cfg.set('channel.55.domain', '[3.0 3.05; 0.45 0.50]', True)
problem_cfg.set('channel.56.domain', '[3.05 3.1; 0.45 0.50]', True)
problem_cfg.set('channel.57.domain', '[3.1 3.15; 0.45 0.50]', True)
problem_cfg.set('channel.58.domain', '[3.15 3.2; 0.45 0.50]', True)
problem_cfg.set('channel.59.domain', '[3.2 3.25; 0.45 0.50]', True)
problem_cfg.set('channel.60.domain', '[3.25 3.3; 0.45 0.50]', True)
problem_cfg.set('channel.61.domain', '[3.3 3.35; 0.45 0.50]', True)
problem_cfg.set('channel.62.domain', '[3.35 3.4; 0.45 0.50]', True)
problem_cfg.set('channel.63.domain', '[3.4 3.45; 0.45 0.50]', True)
problem_cfg.set('channel.64.domain', '[3.45 3.5; 0.45 0.50]', True)
problem_cfg.set('channel.65.domain', '[3.5 3.55; 0.45 0.50]', True)
problem_cfg.set('channel.66.domain', '[3.55 3.6; 0.45 0.50]', True)
problem_cfg.set('channel.67.domain', '[3.6 3.65; 0.45 0.50]', True)
problem_cfg.set('channel.68.domain', '[3.65 3.7; 0.45 0.50]', True)
problem_cfg.set('channel.69.domain', '[3.7 3.75; 0.45 0.50]', True)
problem_cfg.set('channel.70.domain', '[3.75 3.8; 0.45 0.50]', True)
problem_cfg.set('channel.71.domain', '[3.8 3.85; 0.45 0.50]', True)
problem_cfg.set('channel.72.domain', '[3.85 3.9; 0.45 0.50]', True)
problem_cfg.set('channel.73.domain', '[3.9 3.95; 0.45 0.50]', True)
problem_cfg.set('channel.74.domain', '[3.95 4.0; 0.45 0.50]', True)
problem_cfg.set('channel.75.domain', '[4.0 4.05; 0.45 0.50]', True)
problem_cfg.set('channel.76.domain', '[4.05 4.1; 0.45 0.50]', True)
problem_cfg.set('channel.77.domain', '[4.1 4.15; 0.45 0.50]', True)
problem_cfg.set('channel.78.domain', '[4.15 4.2; 0.45 0.50]', True)
problem_cfg.set('channel.79.domain', '[4.2 4.25; 0.45 0.50]', True)
problem_cfg.set('channel.80.domain', '[4.25 4.3; 0.45 0.50]', True)
problem_cfg.set('channel.81.value', '-1.10923642795', True)
problem_cfg.set('channel.82.value', '-1.10685618623', True)
problem_cfg.set('channel.83.value', '-1.1057800376', True)
problem_cfg.set('channel.84.value', '-1.10187723629', True)
problem_cfg.set('channel.85.value', '-1.10351710464', True)
problem_cfg.set('channel.86.value', '-1.10037551137', True)
problem_cfg.set('channel.87.value', '-1.09724407076', True)
problem_cfg.set('channel.88.value', '-1.09604600208', True)
problem_cfg.set('channel.89.value', '-1.09354469656', True)
problem_cfg.set('channel.90.value', '-1.08934455354', True)
problem_cfg.set('channel.91.value', '-1.08155476586', True)
problem_cfg.set('channel.92.value', '-1.07815397899', True)
problem_cfg.set('channel.93.value', '-1.09174062023', True)
problem_cfg.set('channel.94.value', '-1.07433616068', True)
problem_cfg.set('channel.95.value', '-1.08030587701', True)
problem_cfg.set('channel.81.domain', '[1.95 2.0; 0.40 0.45]', True)
problem_cfg.set('channel.82.domain', '[2.0 2.05; 0.40 0.45]', True)
problem_cfg.set('channel.83.domain', '[2.05 2.1; 0.40 0.45]', True)
problem_cfg.set('channel.84.domain', '[2.1 2.15; 0.40 0.45]', True)
problem_cfg.set('channel.85.domain', '[2.15 2.2; 0.40 0.45]', True)
problem_cfg.set('channel.86.domain', '[2.2 2.25; 0.40 0.45]', True)
problem_cfg.set('channel.87.domain', '[2.25 2.3; 0.40 0.45]', True)
problem_cfg.set('channel.88.domain', '[2.3 2.35; 0.40 0.45]', True)
problem_cfg.set('channel.89.domain', '[2.35 2.4; 0.40 0.45]', True)
problem_cfg.set('channel.90.domain', '[2.4 2.45; 0.40 0.45]', True)
problem_cfg.set('channel.91.domain', '[2.45 2.5; 0.40 0.45]', True)
problem_cfg.set('channel.92.domain', '[2.5 2.55; 0.40 0.45]', True)
problem_cfg.set('channel.93.domain', '[2.55 2.6; 0.40 0.45]', True)
problem_cfg.set('channel.94.domain', '[2.6 2.65; 0.40 0.45]', True)
problem_cfg.set('channel.95.domain', '[2.65 2.7; 0.40 0.45]', True)
problem_cfg.set('channel.96.value', '-1.00032869407', True)
problem_cfg.set('channel.97.value', '-1.01175908905', True)
problem_cfg.set('channel.98.value', '-1.04954395793', True)
problem_cfg.set('channel.99.value', '-1.017967697', True)
problem_cfg.set('channel.100.value', '-1.04647184091', True)
problem_cfg.set('channel.101.value', '-1.01911894831', True)
problem_cfg.set('channel.102.value', '-1.00699340158', True)
problem_cfg.set('channel.103.value', '-0.995492960025', True)
problem_cfg.set('channel.104.value', '-1.0373059007', True)
problem_cfg.set('channel.96.domain', '[2.25 2.3; 0.35 0.40]', True)
problem_cfg.set('channel.97.domain', '[2.3 2.35; 0.35 0.40]', True)
problem_cfg.set('channel.98.domain', '[2.35 2.4; 0.35 0.40]', True)
problem_cfg.set('channel.99.domain', '[2.4 2.45; 0.35 0.40]', True)
problem_cfg.set('channel.100.domain', '[2.45 2.5; 0.35 0.40]', True)
problem_cfg.set('channel.101.domain', '[2.5 2.55; 0.35 0.40]', True)
problem_cfg.set('channel.102.domain', '[2.55 2.6; 0.35 0.40]', True)
problem_cfg.set('channel.103.domain', '[2.6 2.65; 0.35 0.40]', True)
problem_cfg.set('channel.104.domain', '[2.65 2.7; 0.35 0.4]', True)
example = Example(logger_cfg, grid_cfg, boundary_cfg, problem_cfg, ['l2', 'h1', 'elliptic_penalty'])
elliptic_LRBMS_disc = wrapper[example.discretization()]
parameter_space = CubicParameterSpace(elliptic_LRBMS_disc.parameter_type, parameter_range[0], parameter_range[1])
elliptic_LRBMS_disc = elliptic_LRBMS_disc.with_(parameter_space=parameter_space)
elliptic_disc = elliptic_LRBMS_disc.as_nonblocked().with_(parameter_space=parameter_space)
def prolong(coarse_disc, coarse_U):
time_grid_ref = OnedGrid(domain=(0., T), num_intervals=nt)
time_grid = OnedGrid(domain=(0., T), num_intervals=(len(coarse_U) - 1))
U_fine = [None for ii in time_grid_ref.centers(1)]
for n in np.arange(len(time_grid_ref.centers(1))):
t_n = time_grid_ref.centers(1)[n]
coarse_entity = min((time_grid.centers(1) <= t_n).nonzero()[0][-1],
time_grid.size(0) - 1)
a = time_grid.centers(1)[coarse_entity]
b = time_grid.centers(1)[coarse_entity + 1]
SF = np.array((1./(a - b)*t_n - b/(a - b),
1./(b - a)*t_n - a/(b - a)))
U_t = coarse_U.copy(ind=coarse_entity)
U_t.scal(SF[0][0])
U_t.axpy(SF[1][0], coarse_U, x_ind=(coarse_entity + 1))
U_fine[n] = wrapper[example.prolong(coarse_disc._impl, U_t._list[0]._impl)]
return make_listvectorarray(U_fine)
if isinstance(initial_data, str):
initial_data = make_listvectorarray(wrapper[example.project(initial_data)])
# initial_data = elliptic_disc.operator.apply_inverse(initial_data, mu=(1, 1))
else:
coarse_disc = initial_data[0]
initial_data = initial_data[1]
assert len(initial_data) == 1
initial_data = example.prolong(coarse_disc._impl, initial_data._list[0]._impl)
initial_data = make_listvectorarray(wrapper[initial_data])
parabolic_disc = InstationaryDiscretization(T=T,
initial_data=initial_data,
operator=elliptic_disc.operator,
rhs=elliptic_disc.rhs,
mass=elliptic_disc.products['l2'],
time_stepper=ImplicitEulerTimeStepper(nt, solver_options='operator'),
products=elliptic_disc.products,
operators=elliptic_disc.operators,
functionals=elliptic_disc.functionals,
vector_operators=elliptic_disc.vector_operators,
visualizer=InstationaryDuneVisualizer(elliptic_disc, 'dune_discretization.solution'),
parameter_space=parameter_space,
cache_region='disk',
name='{} ({} DoFs)'.format(name, elliptic_disc.solution_space.dim))
return {'example': example,
'initial_data': initial_data,
'wrapper': wrapper,
'elliptic_LRBMS_disc': elliptic_LRBMS_disc,
'elliptic_disc': elliptic_disc,
'parabolic_disc': parabolic_disc,
'prolongator': prolong}
def discretize(num_elements,
num_partitions,
T,
nt,
initial_data,
parameter_range,
name='detailed discretization'):
Example = examples[2]['aluconformgrid']['fem']['istl']
logger_cfg = Example.logger_options()
logger_cfg.set('info', -1, True)
logger_cfg.set('info_color', 'blue', True)
grid_cfg = Example.grid_options('grid.multiscale.provider.cube')
grid_cfg.set('lower_left', '[0 0]', True)
grid_cfg.set('upper_right', '[5 1]', True)
grid_cfg.set('num_elements', num_elements, True)
grid_cfg.set('num_partitions', num_partitions, True)
boundary_cfg = Example.boundary_options(
'stuff.grid.boundaryinfo.alldirichlet')
problem_cfg = Example.problem_options(
'hdd.linearelliptic.problem.OS2015.spe10model1')
problem_cfg.set('parametric_channel', 'true', True)
problem_cfg.set('channel_boundary_layer', '0', True)
problem_cfg.set('filename', 'perm_case1.dat', True)
problem_cfg.set('lower_left', '[0 0]', True)
problem_cfg.set('upper_right', '[5 1]', True)
problem_cfg.set('num_elements', '[100 20]', True)
problem_cfg.set('forces.0.domain', '[0.95 1.10; 0.30 0.45]', True)
problem_cfg.set('forces.0.value', '2000', True)
problem_cfg.set('forces.1.domain', '[3.00 3.15; 0.75 0.90]', True)
problem_cfg.set('forces.1.value', '-1000', True)
problem_cfg.set('forces.2.domain', '[4.25 4.40; 0.25 0.40]', True)
problem_cfg.set('forces.2.value', '-1000', True)
problem_cfg.set('channel.0.value', '-1.07763239495', True)
problem_cfg.set('channel.1.value', '-1.07699512772', True)
problem_cfg.set('channel.2.value', '-1.07356156439', True)
problem_cfg.set('channel.3.value', '-1.06602281736', True)
problem_cfg.set('channel.4.value', '-1.06503683743', True)
problem_cfg.set('channel.5.value', '-1.07974870426', True)
problem_cfg.set('channel.6.value', '-1.05665895923', True)
problem_cfg.set('channel.7.value', '-1.08310334837', True)
problem_cfg.set('channel.8.value', '-1.05865484973', True)
problem_cfg.set('channel.9.value', '-1.05871039535', True)
problem_cfg.set('channel.10.value', '-1.08136695901', True)
problem_cfg.set('channel.11.value', '-1.08490172721', True)
problem_cfg.set('channel.12.value', '-1.06641120758', True)
problem_cfg.set('channel.13.value', '-1.06812773298', True)
problem_cfg.set('channel.14.value', '-1.07695652049', True)
problem_cfg.set('channel.15.value', '-1.08630079205', True)
problem_cfg.set('channel.16.value', '-1.08273722112', True)
problem_cfg.set('channel.17.value', '-1.07500402155', True)
problem_cfg.set('channel.18.value', '-1.08607142562', True)
problem_cfg.set('channel.19.value', '-1.07268761799', True)
problem_cfg.set('channel.20.value', '-1.08537037362', True)
problem_cfg.set('channel.21.value', '-1.08466927273', True)
problem_cfg.set('channel.22.value', '-1.08444661815', True)
problem_cfg.set('channel.23.value', '-1.08957037967', True)
problem_cfg.set('channel.24.value', '-1.08047394052', True)
problem_cfg.set('channel.25.value', '-1.08221229083', True)
problem_cfg.set('channel.26.value', '-1.08568599863', True)
problem_cfg.set('channel.27.value', '-1.08428347872', True)
problem_cfg.set('channel.28.value', '-1.09104098734', True)
problem_cfg.set('channel.29.value', '-1.09492700673', True)
problem_cfg.set('channel.30.value', '-1.09760440537', True)
problem_cfg.set('channel.31.value', '-1.09644989453', True)
problem_cfg.set('channel.32.value', '-1.09441681025', True)
problem_cfg.set('channel.33.value', '-1.09533290654', True)
problem_cfg.set('channel.34.value', '-1.1001430808', True)
problem_cfg.set('channel.35.value', '-1.10065627621', True)
problem_cfg.set('channel.36.value', '-1.10125877186', True)
problem_cfg.set('channel.37.value', '-1.10057485893', True)
problem_cfg.set('channel.38.value', '-1.10002261906', True)
problem_cfg.set('channel.39.value', '-1.10219154209', True)
problem_cfg.set('channel.40.value', '-1.09994463801', True)
problem_cfg.set('channel.41.value', '-1.10265630533', True)
problem_cfg.set('channel.42.value', '-1.10448566526', True)
problem_cfg.set('channel.43.value', '-1.10735820121', True)
problem_cfg.set('channel.44.value', '-1.1070022367', True)
problem_cfg.set('channel.45.value', '-1.10777650387', True)
problem_cfg.set('channel.46.value', '-1.10892785562', True)
problem_cfg.set('channel.0.domain', '[1.7 1.75; 0.5 0.55]', True)
problem_cfg.set('channel.1.domain', '[1.75 1.8; 0.5 0.55]', True)
problem_cfg.set('channel.2.domain', '[1.8 1.85; 0.5 0.55]', True)
problem_cfg.set('channel.3.domain', '[1.85 1.9; 0.5 0.55]', True)
problem_cfg.set('channel.4.domain', '[1.9 1.95; 0.5 0.55]', True)
problem_cfg.set('channel.5.domain', '[1.95 2.0; 0.5 0.55]', True)
problem_cfg.set('channel.6.domain', '[2.0 2.05; 0.5 0.55]', True)
problem_cfg.set('channel.7.domain', '[2.05 2.1; 0.5 0.55]', True)
problem_cfg.set('channel.8.domain', '[2.1 2.15; 0.5 0.55]', True)
problem_cfg.set('channel.9.domain', '[2.15 2.2; 0.5 0.55]', True)
problem_cfg.set('channel.10.domain', '[2.2 2.25; 0.5 0.55]', True)
problem_cfg.set('channel.11.domain', '[2.25 2.3; 0.5 0.55]', True)
problem_cfg.set('channel.12.domain', '[2.3 2.35; 0.5 0.55]', True)
problem_cfg.set('channel.13.domain', '[2.35 2.4; 0.5 0.55]', True)
problem_cfg.set('channel.14.domain', '[2.4 2.45; 0.5 0.55]', True)
problem_cfg.set('channel.15.domain', '[2.45 2.5; 0.5 0.55]', True)
problem_cfg.set('channel.16.domain', '[2.5 2.55; 0.5 0.55]', True)
problem_cfg.set('channel.17.domain', '[2.55 2.6; 0.5 0.55]', True)
problem_cfg.set('channel.18.domain', '[2.6 2.65; 0.5 0.55]', True)
problem_cfg.set('channel.19.domain', '[2.65 2.7; 0.5 0.55]', True)
problem_cfg.set('channel.20.domain', '[2.7 2.75; 0.5 0.55]', True)
problem_cfg.set('channel.21.domain', '[2.75 2.8; 0.5 0.55]', True)
problem_cfg.set('channel.22.domain', '[2.8 2.85; 0.5 0.55]', True)
problem_cfg.set('channel.23.domain', '[2.85 2.9; 0.5 0.55]', True)
problem_cfg.set('channel.24.domain', '[2.9 2.95; 0.5 0.55]', True)
problem_cfg.set('channel.25.domain', '[2.95 3.0; 0.5 0.55]', True)
problem_cfg.set('channel.26.domain', '[3.0 3.05; 0.5 0.55]', True)
problem_cfg.set('channel.27.domain', '[3.05 3.1; 0.5 0.55]', True)
problem_cfg.set('channel.28.domain', '[3.1 3.15; 0.5 0.55]', True)
problem_cfg.set('channel.29.domain', '[3.15 3.2; 0.5 0.55]', True)
problem_cfg.set('channel.30.domain', '[3.2 3.25; 0.5 0.55]', True)
problem_cfg.set('channel.31.domain', '[3.25 3.3; 0.5 0.55]', True)
problem_cfg.set('channel.32.domain', '[3.3 3.35; 0.5 0.55]', True)
problem_cfg.set('channel.33.domain', '[3.35 3.4; 0.5 0.55]', True)
problem_cfg.set('channel.34.domain', '[3.4 3.45; 0.5 0.55]', True)
problem_cfg.set('channel.35.domain', '[3.45 3.5; 0.5 0.55]', True)
problem_cfg.set('channel.36.domain', '[3.5 3.55; 0.5 0.55]', True)
problem_cfg.set('channel.37.domain', '[3.55 3.6; 0.5 0.55]', True)
problem_cfg.set('channel.38.domain', '[3.6 3.65; 0.5 0.55]', True)
problem_cfg.set('channel.39.domain', '[3.65 3.7; 0.5 0.55]', True)
problem_cfg.set('channel.40.domain', '[3.7 3.75; 0.5 0.55]', True)
problem_cfg.set('channel.41.domain', '[3.75 3.8; 0.5 0.55]', True)
problem_cfg.set('channel.42.domain', '[3.8 3.85; 0.5 0.55]', True)
problem_cfg.set('channel.43.domain', '[3.85 3.9; 0.5 0.55]', True)
problem_cfg.set('channel.44.domain', '[3.9 3.95; 0.5 0.55]', True)
problem_cfg.set('channel.45.domain', '[3.95 4.0; 0.5 0.55]', True)
problem_cfg.set('channel.46.domain', '[4.0 4.05; 0.5 0.55]', True)
problem_cfg.set('channel.47.value', '-1.10372589211', True)
problem_cfg.set('channel.48.value', '-1.1020889988', True)
problem_cfg.set('channel.49.value', '-1.09806955069', True)
problem_cfg.set('channel.50.value', '-1.10000902421', True)
problem_cfg.set('channel.51.value', '-1.08797468724', True)
problem_cfg.set('channel.52.value', '-1.08827472176', True)
problem_cfg.set('channel.53.value', '-1.08692237109', True)
problem_cfg.set('channel.54.value', '-1.07893190093', True)
problem_cfg.set('channel.55.value', '-1.08748373853', True)
problem_cfg.set('channel.56.value', '-1.07445197324', True)
problem_cfg.set('channel.57.value', '-1.08246613163', True)
problem_cfg.set('channel.58.value', '-1.06726790504', True)
problem_cfg.set('channel.59.value', '-1.07891217847', True)
problem_cfg.set('channel.60.value', '-1.07260827126', True)
problem_cfg.set('channel.61.value', '-1.07094062748', True)
problem_cfg.set('channel.62.value', '-1.0692399429', True)
problem_cfg.set('channel.63.value', '-1.00099885701', True)
problem_cfg.set('channel.64.value', '-1.00109544002', True)
problem_cfg.set('channel.65.value', '-0.966491003242', True)
problem_cfg.set('channel.66.value', '-0.802284684014', True)
problem_cfg.set('channel.67.value', '-0.980790923021', True)
problem_cfg.set('channel.68.value', '-0.614478271687', True)
problem_cfg.set('channel.69.value', '-0.288129858959', True)
problem_cfg.set('channel.70.value', '-0.929509396842', True)
problem_cfg.set('channel.71.value', '-0.992376505995', True)
problem_cfg.set('channel.72.value', '-0.968162494855', True)
problem_cfg.set('channel.73.value', '-0.397316938901', True)
problem_cfg.set('channel.74.value', '-0.970934956609', True)
problem_cfg.set('channel.75.value', '-0.784344730096', True)
problem_cfg.set('channel.76.value', '-0.539725422323', True)
problem_cfg.set('channel.77.value', '-0.915632282372', True)
problem_cfg.set('channel.78.value', '-0.275089177273', True)
problem_cfg.set('channel.79.value', '-0.949684959286', True)
problem_cfg.set('channel.80.value', '-0.936132529794', True)
problem_cfg.set('channel.47.domain', '[2.6 2.65; 0.45 0.50]', True)
problem_cfg.set('channel.48.domain', '[2.65 2.7; 0.45 0.50]', True)
problem_cfg.set('channel.49.domain', '[2.7 2.75; 0.45 0.50]', True)
problem_cfg.set('channel.50.domain', '[2.75 2.8; 0.45 0.50]', True)
problem_cfg.set('channel.51.domain', '[2.8 2.85; 0.45 0.50]', True)
problem_cfg.set('channel.52.domain', '[2.85 2.9; 0.45 0.50]', True)
problem_cfg.set('channel.53.domain', '[2.9 2.95; 0.45 0.50]', True)
problem_cfg.set('channel.54.domain', '[2.95 3.0; 0.45 0.50]', True)
problem_cfg.set('channel.55.domain', '[3.0 3.05; 0.45 0.50]', True)
problem_cfg.set('channel.56.domain', '[3.05 3.1; 0.45 0.50]', True)
problem_cfg.set('channel.57.domain', '[3.1 3.15; 0.45 0.50]', True)
problem_cfg.set('channel.58.domain', '[3.15 3.2; 0.45 0.50]', True)
problem_cfg.set('channel.59.domain', '[3.2 3.25; 0.45 0.50]', True)
problem_cfg.set('channel.60.domain', '[3.25 3.3; 0.45 0.50]', True)
problem_cfg.set('channel.61.domain', '[3.3 3.35; 0.45 0.50]', True)
problem_cfg.set('channel.62.domain', '[3.35 3.4; 0.45 0.50]', True)
problem_cfg.set('channel.63.domain', '[3.4 3.45; 0.45 0.50]', True)
problem_cfg.set('channel.64.domain', '[3.45 3.5; 0.45 0.50]', True)
problem_cfg.set('channel.65.domain', '[3.5 3.55; 0.45 0.50]', True)
problem_cfg.set('channel.66.domain', '[3.55 3.6; 0.45 0.50]', True)
problem_cfg.set('channel.67.domain', '[3.6 3.65; 0.45 0.50]', True)
problem_cfg.set('channel.68.domain', '[3.65 3.7; 0.45 0.50]', True)
problem_cfg.set('channel.69.domain', '[3.7 3.75; 0.45 0.50]', True)
problem_cfg.set('channel.70.domain', '[3.75 3.8; 0.45 0.50]', True)
problem_cfg.set('channel.71.domain', '[3.8 3.85; 0.45 0.50]', True)
problem_cfg.set('channel.72.domain', '[3.85 3.9; 0.45 0.50]', True)
problem_cfg.set('channel.73.domain', '[3.9 3.95; 0.45 0.50]', True)
problem_cfg.set('channel.74.domain', '[3.95 4.0; 0.45 0.50]', True)
problem_cfg.set('channel.75.domain', '[4.0 4.05; 0.45 0.50]', True)
problem_cfg.set('channel.76.domain', '[4.05 4.1; 0.45 0.50]', True)
problem_cfg.set('channel.77.domain', '[4.1 4.15; 0.45 0.50]', True)
problem_cfg.set('channel.78.domain', '[4.15 4.2; 0.45 0.50]', True)
problem_cfg.set('channel.79.domain', '[4.2 4.25; 0.45 0.50]', True)
problem_cfg.set('channel.80.domain', '[4.25 4.3; 0.45 0.50]', True)
problem_cfg.set('channel.81.value', '-1.10923642795', True)
problem_cfg.set('channel.82.value', '-1.10685618623', True)
problem_cfg.set('channel.83.value', '-1.1057800376', True)
problem_cfg.set('channel.84.value', '-1.10187723629', True)
problem_cfg.set('channel.85.value', '-1.10351710464', True)
problem_cfg.set('channel.86.value', '-1.10037551137', True)
problem_cfg.set('channel.87.value', '-1.09724407076', True)
problem_cfg.set('channel.88.value', '-1.09604600208', True)
problem_cfg.set('channel.89.value', '-1.09354469656', True)
problem_cfg.set('channel.90.value', '-1.08934455354', True)
problem_cfg.set('channel.91.value', '-1.08155476586', True)
problem_cfg.set('channel.92.value', '-1.07815397899', True)
problem_cfg.set('channel.93.value', '-1.09174062023', True)
problem_cfg.set('channel.94.value', '-1.07433616068', True)
problem_cfg.set('channel.95.value', '-1.08030587701', True)
problem_cfg.set('channel.81.domain', '[1.95 2.0; 0.40 0.45]', True)
problem_cfg.set('channel.82.domain', '[2.0 2.05; 0.40 0.45]', True)
problem_cfg.set('channel.83.domain', '[2.05 2.1; 0.40 0.45]', True)
problem_cfg.set('channel.84.domain', '[2.1 2.15; 0.40 0.45]', True)
problem_cfg.set('channel.85.domain', '[2.15 2.2; 0.40 0.45]', True)
problem_cfg.set('channel.86.domain', '[2.2 2.25; 0.40 0.45]', True)
problem_cfg.set('channel.87.domain', '[2.25 2.3; 0.40 0.45]', True)
problem_cfg.set('channel.88.domain', '[2.3 2.35; 0.40 0.45]', True)
problem_cfg.set('channel.89.domain', '[2.35 2.4; 0.40 0.45]', True)
problem_cfg.set('channel.90.domain', '[2.4 2.45; 0.40 0.45]', True)
problem_cfg.set('channel.91.domain', '[2.45 2.5; 0.40 0.45]', True)
problem_cfg.set('channel.92.domain', '[2.5 2.55; 0.40 0.45]', True)
problem_cfg.set('channel.93.domain', '[2.55 2.6; 0.40 0.45]', True)
problem_cfg.set('channel.94.domain', '[2.6 2.65; 0.40 0.45]', True)
problem_cfg.set('channel.95.domain', '[2.65 2.7; 0.40 0.45]', True)
problem_cfg.set('channel.96.value', '-1.00032869407', True)
problem_cfg.set('channel.97.value', '-1.01175908905', True)
problem_cfg.set('channel.98.value', '-1.04954395793', True)
problem_cfg.set('channel.99.value', '-1.017967697', True)
problem_cfg.set('channel.100.value', '-1.04647184091', True)
problem_cfg.set('channel.101.value', '-1.01911894831', True)
problem_cfg.set('channel.102.value', '-1.00699340158', True)
problem_cfg.set('channel.103.value', '-0.995492960025', True)
problem_cfg.set('channel.104.value', '-1.0373059007', True)
problem_cfg.set('channel.96.domain', '[2.25 2.3; 0.35 0.40]', True)
problem_cfg.set('channel.97.domain', '[2.3 2.35; 0.35 0.40]', True)
problem_cfg.set('channel.98.domain', '[2.35 2.4; 0.35 0.40]', True)
problem_cfg.set('channel.99.domain', '[2.4 2.45; 0.35 0.40]', True)
problem_cfg.set('channel.100.domain', '[2.45 2.5; 0.35 0.40]', True)
problem_cfg.set('channel.101.domain', '[2.5 2.55; 0.35 0.40]', True)
problem_cfg.set('channel.102.domain', '[2.55 2.6; 0.35 0.40]', True)
problem_cfg.set('channel.103.domain', '[2.6 2.65; 0.35 0.40]', True)
problem_cfg.set('channel.104.domain', '[2.65 2.7; 0.35 0.4]', True)
example = Example(logger_cfg, grid_cfg, boundary_cfg, problem_cfg,
['l2', 'h1', 'elliptic_penalty'])
elliptic_LRBMS_disc = wrapper[example.discretization()]
parameter_space = CubicParameterSpace(elliptic_LRBMS_disc.parameter_type,
parameter_range[0],
parameter_range[1])
elliptic_LRBMS_disc = elliptic_LRBMS_disc.with_(
parameter_space=parameter_space)
elliptic_disc = elliptic_LRBMS_disc.as_nonblocked().with_(
parameter_space=parameter_space)
def prolong(coarse_disc, coarse_U):
time_grid_ref = OnedGrid(domain=(0., T), num_intervals=nt)
time_grid = OnedGrid(domain=(0., T), num_intervals=(len(coarse_U) - 1))
U_fine = [None for ii in time_grid_ref.centers(1)]
for n in np.arange(len(time_grid_ref.centers(1))):
t_n = time_grid_ref.centers(1)[n]
coarse_entity = min((time_grid.centers(1) <= t_n).nonzero()[0][-1],
time_grid.size(0) - 1)
a = time_grid.centers(1)[coarse_entity]
b = time_grid.centers(1)[coarse_entity + 1]
SF = np.array((1. / (a - b) * t_n - b / (a - b),
1. / (b - a) * t_n - a / (b - a)))
U_t = coarse_U.copy(ind=coarse_entity)
U_t.scal(SF[0][0])
U_t.axpy(SF[1][0], coarse_U, x_ind=(coarse_entity + 1))
U_fine[n] = wrapper[example.prolong(coarse_disc._impl,
U_t._list[0]._impl)]
return make_listvectorarray(U_fine)
if isinstance(initial_data, str):
initial_data = make_listvectorarray(
wrapper[example.project(initial_data)])
# initial_data = elliptic_disc.operator.apply_inverse(initial_data, mu=(1, 1))
else:
coarse_disc = initial_data[0]
initial_data = initial_data[1]
assert len(initial_data) == 1
initial_data = example.prolong(coarse_disc._impl,
initial_data._list[0]._impl)
initial_data = make_listvectorarray(wrapper[initial_data])
parabolic_disc = InstationaryDiscretization(
T=T,
initial_data=initial_data,
operator=elliptic_disc.operator,
rhs=elliptic_disc.rhs,
mass=elliptic_disc.products['l2'],
time_stepper=ImplicitEulerTimeStepper(nt, solver_options='operator'),
products=elliptic_disc.products,
operators=elliptic_disc.operators,
functionals=elliptic_disc.functionals,
vector_operators=elliptic_disc.vector_operators,
visualizer=InstationaryDuneVisualizer(elliptic_disc,
'dune_discretization.solution'),
parameter_space=parameter_space,
cache_region='disk',
name='{} ({} DoFs)'.format(name, elliptic_disc.solution_space.dim))
return {
'example': example,
'initial_data': initial_data,
'wrapper': wrapper,
'elliptic_LRBMS_disc': elliptic_LRBMS_disc,
'elliptic_disc': elliptic_disc,
'parabolic_disc': parabolic_disc,
'prolongator': prolong
}
