def init_grid_and_problem(config):
logger = getLogger('senegal_proceedings_problem.senegal_proceedings_problem')
logger.info('initializing grid and problem ... ')
lower_left = [-1, -1]
upper_right = [1, 1]
inner_boundary_id = 18446744073709551573
grid = make_grid(lower_left=lower_left,
upper_right=upper_right,
num_elements=config['num_coarse_grid_elements'],
num_refinements=config['num_grid_refinements'],
num_partitions=config['num_grid_subdomains'],
num_oversampling_layers=config['num_grid_oversampling_layers'],
inner_boundary_segment_index=inner_boundary_id)
all_dirichlet_boundary_info = make_boundary_info(grid, {'type': 'xt.grid.boundaryinfo.alldirichlet'})
def make_values(background, foreground):
checkerboard_values = [[background]]*36
for ii in (7, 25):
checkerboard_values[ii] = [foreground]
return checkerboard_values
diffusion_functions = [make_checkerboard_function_1x1(grid, lower_left, upper_right,
[6, 6], make_values(1., 0.),
name='lambda_0'),
make_checkerboard_function_1x1(grid, lower_left, upper_right,
[6, 6], make_values(0., 1.),
name='lambda_1')]
parameter_type = {'diffusion': (2,)}
coefficients = [ExpressionParameterFunctional('1.1 + sin(diffusion[0])*diffusion[1]', parameter_type),
ExpressionParameterFunctional('1.1 + sin(diffusion[1])', parameter_type)]
kappa = make_constant_function_2x2(grid, [[1., 0.], [0., 1.]], name='kappa')
f = make_expression_function_1x1(grid, 'x', '0.5*pi*pi*cos(0.5*pi*x[0])*cos(0.5*pi*x[1])', order=2, name='f')
lambda_bar = make_checkerboard_function_1x1(grid, lower_left, upper_right, [6, 6], make_values(1.1, 1.1), name='lambda_bar')
lambda_hat = make_checkerboard_function_1x1(grid, lower_left, upper_right, [6, 6], make_values(1.1, 1.1), name='lambda_hat')
return {'grid': grid,
'boundary_info': all_dirichlet_boundary_info,
'inner_boundary_id': inner_boundary_id,
'lambda': {'functions': diffusion_functions,
'coefficients': coefficients},
'lambda_bar': lambda_bar,
'lambda_hat': lambda_hat,
'kappa': kappa,
'f': f,
'parameter_type': parameter_type,
'mu_bar': (0, 0),
'mu_hat': (0, 0),
'mu_min': (0, 0),
'mu_max': (np.pi, np.pi),
'parameter_range': (0, np.pi)}
def test_blockspace():
from dune.gdt.__spaces_block import make_block_dg_dd_subdomain_view_to_1x1_gdt_p1_space as make_block_space
grid = make_grid()
block_space = make_block_space(grid)
diffusion = make_expression_function_1x1(grid, 'x', '1', order=2, name='lambda_0')
kappa = make_constant_function_2x2(grid, [[1., 0.], [0., 1.]], name='kappa')
local_all_neumann_boundary_info = make_boundary_info_on_dd_subdomain_layer(grid, {'type': 'xt.grid.boundaryinfo.allneumann'})
local_matrices = [None] * grid.num_subdomains
local_patterns = [block_space.local_space(ii).compute_pattern('face_and_volume')
for ii in range(block_space.num_blocks)]
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])
ipdg_operator = make_elliptic_swipdg_matrix_operator(diffusion_factor=diffusion, diffusion_tensor=kappa,
boundary_info=local_all_neumann_boundary_info,
matrix=local_matrices[ii],
space=block_space.local_space(ii), over_integrate=2)
ipdg_operator.assemble()
def init_grid_and_problem(config, mu_bar=(1, 1, 1, 1), mu_hat=(1, 1, 1, 1)):
logger = getLogger('thermalblock_problem.thermalblock_problem')
logger.info('initializing grid and problem ... ')
lower_left = [-1, -1]
upper_right = [1, 1]
inner_boundary_id = 18446744073709551573
grid = make_grid((lower_left, upper_right), config['num_subdomains'],
config['half_num_fine_elements_per_subdomain_and_dim'],
inner_boundary_id)
all_dirichlet_boundary_info = make_boundary_info(
grid, {'type': 'xt.grid.boundaryinfo.alldirichlet'})
XBLOCKS = 2
YBLOCKS = 2
def diffusion_function_factory(ix, iy):
values = [[0.]] * (YBLOCKS * XBLOCKS)
values[ix + XBLOCKS * iy] = [1.]
return make_checkerboard_function_1x1(grid_provider=grid,
lower_left=lower_left,
upper_right=upper_right,
num_elements=[XBLOCKS, YBLOCKS],
values=values,
name='diffusion_{}_{}'.format(
ix, iy))
diffusion_functions = [
diffusion_function_factory(ix, iy)
for ix, iy in product(range(XBLOCKS), range(YBLOCKS))
]
parameter_type = {'diffusion': (YBLOCKS, XBLOCKS)}
coefficients = [
ProjectionParameterFunctional(component_name='diffusion',
component_shape=(YBLOCKS, XBLOCKS),
coordinates=(YBLOCKS - y - 1, x))
for x in range(XBLOCKS) for y in range(YBLOCKS)
]
kappa = make_constant_function_2x2(grid, [[1., 0.], [0., 1.]],
name='kappa')
f = make_expression_function_1x1(
grid,
'x',
'0.5*pi*pi*cos(0.5*pi*x[0])*cos(0.5*pi*x[1])',
order=2,
name='f')
lambda_bar_values = [[0.]] * (YBLOCKS * XBLOCKS)
lambda_hat_values = [[0.]] * (YBLOCKS * XBLOCKS)
counter = 0
for ix in range(YBLOCKS):
for iy in range(XBLOCKS):
lambda_bar_values[ix + XBLOCKS * iy] = [
coefficients[counter].evaluate(mu_bar)
]
lambda_hat_values[ix + XBLOCKS * iy] = [
coefficients[counter].evaluate(mu_hat)
]
counter += 1
lambda_bar = make_checkerboard_function_1x1(
grid_provider=grid,
lower_left=lower_left,
upper_right=upper_right,
num_elements=[XBLOCKS, YBLOCKS],
values=lambda_bar_values,
name='lambda_bar')
lambda_hat = make_checkerboard_function_1x1(
grid_provider=grid,
lower_left=lower_left,
upper_right=upper_right,
num_elements=[XBLOCKS, YBLOCKS],
values=lambda_hat_values,
name='lambda_hat')
return {
'grid':
grid,
'boundary_info':
all_dirichlet_boundary_info,
'inner_boundary_id':
inner_boundary_id,
'lambda': {
'functions': diffusion_functions,
'coefficients': coefficients
},
'lambda_bar':
lambda_bar,
'lambda_hat':
lambda_hat,
'kappa':
kappa,
'f':
f,
'parameter_type':
parameter_type,
'mu_bar':
mu_bar,
'mu_hat':
mu_hat,
'mu_min': (min(0.1, b, h) for b, h in zip(mu_bar, mu_hat)),
'mu_max': (max(1, b, h) for b, h in zip(mu_bar, mu_hat)),
'parameter_range':
(min((0.1, ) + mu_bar + mu_hat), max((1, ) + mu_bar + mu_hat))
}
def init_grid_and_problem(config, mu_bar=1, mu_hat=1, mpi_comm=MPI.COMM_WORLD):
# assert mpi_comm.Get_size() < MPI.COMM_WORLD.Get_size() or mpi_comm.Get_size() == 1
logger = getLogger('non_paramtric_problem')
logger.info('initializing grid and problem ... ')
lower_left = [-1, -1]
upper_right = [1, 1]
inner_boundary_id = 18446744073709551573
grid = make_grid((lower_left, upper_right),
config['num_subdomains'],
config['half_num_fine_elements_per_subdomain_and_dim'],
inner_boundary_id,
mpi_comm=mpi_comm)
all_dirichlet_boundary_info = make_boundary_info(
grid, {'type': 'xt.grid.boundaryinfo.alldirichlet'})
diffusion_functions = make_expression_function_1x1(
grid,
'x',
'1+(cos(0.5*pi*x[0])*cos(0.5*pi*x[1]))',
order=2,
name='lambda_0')
diffusion_functions = make_constant_function_1x1(grid, 1, name='lambda')
kappa = make_constant_function_2x2(grid, [[1., 0.], [0., 1.]],
name='kappa')
f = make_expression_function_1x1(
grid,
'x',
'0.5*pi*pi*cos(0.5*pi*x[0])*cos(0.5*pi*x[1])',
order=2,
name='f')
lambda_bar = make_expression_function_1x1(
grid,
'x',
'1+(1-{})*(cos(0.5*pi*x[0])*cos(0.5*pi*x[1]))'.format(mu_bar),
order=2,
name='lambda_bar')
lambda_hat = make_expression_function_1x1(
grid,
'x',
'1+(1-{})*(cos(0.5*pi*x[0])*cos(0.5*pi*x[1]))'.format(mu_hat),
order=2,
name='lambda_hat')
return {
'grid': grid,
'mpi_comm': mpi_comm,
'boundary_info': all_dirichlet_boundary_info,
'inner_boundary_id': inner_boundary_id,
'lambda': diffusion_functions,
'lambda_bar': lambda_bar,
'lambda_hat': lambda_hat,
'kappa': kappa,
'f': f,
'parameter_type': None,
'mu_bar': None,
'mu_hat': None,
'mu_min': None,
'mu_max': None,
'parameter_range': (min(0.1, mu_bar, mu_hat), max(1, mu_bar, mu_hat))
}
def init_grid_and_problem(config, mu_bar=1, mu_hat=1, mpi_comm=MPI.COMM_WORLD):
# assert mpi_comm.Get_size() < MPI.COMM_WORLD.Get_size() or mpi_comm.Get_size() == 1
logger = getLogger('OS2015_academic_problem.OS2015_academic_problem')
logger.info('initializing grid and problem ... ')
lower_left = [-1, -1]
upper_right = [1, 1]
inner_boundary_id = 18446744073709551573
grid = make_grid((lower_left, upper_right),
config['num_subdomains'],
config['half_num_fine_elements_per_subdomain_and_dim'],
inner_boundary_id,
mpi_comm=mpi_comm)
grid_info(logger.error, grid, mpi_comm)
all_dirichlet_boundary_info = make_boundary_info(
grid, {'type': 'xt.grid.boundaryinfo.alldirichlet'})
cos = '(cos(0.5*pi*x[0])*cos(0.5*pi*x[1]))'
diffusion_functions = [
make_expression_function_1x1(grid,
'x',
'1+{}'.format(cos),
order=2,
name='lambda_0'),
make_expression_function_1x1(grid,
'x',
'-1*{}'.format(cos),
order=2,
name='lambda_1')
]
# diffusion_functions = [make_expression_function_1x1(
# grid, 'x', '1', order=2, name='lambda_0'),
# make_expression_function_1x1(grid, 'x', 'x[0]', order=2, name='lambda_1')]
parameter_type = {'diffusion': (1, )}
coefficients = [
ExpressionParameterFunctional('1.', parameter_type),
ExpressionParameterFunctional('diffusion', parameter_type)
]
kappa = make_constant_function_2x2(grid, [[1., 0.], [0., 1.]],
name='kappa')
f = make_expression_function_1x1(grid,
'x',
'0.5*pi*pi*{}'.format(cos),
order=2,
name='f')
mbc = '1+(1-{})*{}'.format(mu_bar, cos)
lambda_bar = make_expression_function_1x1(grid,
'x',
mbc,
order=2,
name='lambda_bar')
lambda_hat = make_expression_function_1x1(grid,
'x',
mbc,
order=2,
name='lambda_hat')
return {
'grid': grid,
'mpi_comm': mpi_comm,
'boundary_info': all_dirichlet_boundary_info,
'inner_boundary_id': inner_boundary_id,
'lambda': {
'functions': diffusion_functions,
'coefficients': coefficients
},
'lambda_bar': lambda_bar,
'lambda_hat': lambda_hat,
'kappa': kappa,
'f': f,
'parameter_type': parameter_type,
'mu_bar': (mu_bar, ),
'mu_hat': (mu_hat, ),
'mu_min': (min(0.1, mu_bar, mu_hat), ),
'mu_max': (max(1, mu_bar, mu_hat), ),
'parameter_range': (min(0.1, mu_bar, mu_hat), max(1, mu_bar, mu_hat))
}
def init_grid_and_problem(config, mu_bar=(1, ), mu_hat=(1, )):
logger = getLogger(
'artificial_channels_problem.artificial_channels_problem')
logger.info('initializing grid and problem ... ')
lower_left = [0, 0]
upper_right = [1, 1]
mu_min = min((0.01, ) + mu_bar + mu_hat)
mu_max = max((1, ) + mu_bar + mu_hat)
inner_boundary_id = 18446744073709551573
grid = make_grid((lower_left, upper_right), config['num_subdomains'],
config['half_num_fine_elements_per_subdomain_and_dim'],
inner_boundary_id)
all_dirichlet_boundary_info = make_boundary_info(
grid, {'type': 'xt.grid.boundaryinfo.alldirichlet'})
def horizontal_channels(value):
return [[[[1 / 16, 1 / 8 - 1 / 32], [1 - 1 / 16, 1 / 8 + 1 / 32]],
value],
[[[1 / 16, 3 / 8 - 1 / 32], [1 - 1 / 16, 3 / 8 + 1 / 32]],
value],
[[[1 / 16, 5 / 8 - 1 / 32], [1 - 1 / 16, 5 / 8 + 1 / 32]],
value],
[[[1 / 16, 7 / 8 - 1 / 32], [1 - 1 / 16, 7 / 8 + 1 / 32]],
value]]
def fixed_vertical_connections(value):
return [[[[1 / 16, 1 / 8 + 1 / 32], [1 / 4 - 1 / 16, 3 / 8 - 1 / 32]],
value],
[[[1 / 16, 5 / 8 + 1 / 32], [1 / 4 - 1 / 16, 7 / 8 - 1 / 32]],
value],
[[[3 / 4 + 1 / 16, 1 / 8 + 1 / 32],
[1 - 1 / 16, 3 / 8 - 1 / 32]], value],
[[[3 / 4 + 1 / 16, 5 / 8 + 1 / 32],
[1 - 1 / 16, 7 / 8 - 1 / 32]], value]]
def switched_vertical_connections(value):
return [[[[1 / 16, 3 / 8 + 1 / 32], [1 / 4 - 1 / 16, 5 / 8 - 1 / 32]],
value],
[[[3 / 4 + 1 / 16, 3 / 8 + 1 / 32],
[1 - 1 / 16, 5 / 8 - 1 / 32]], value]]
diffusion_horizontal_channels = make_indicator_function_1x1(
grid, horizontal_channels(1), 'horizontal_channels')
diffusion_fixed_vertical_connections = make_indicator_function_1x1(
grid, fixed_vertical_connections(1), 'fixed_vertical_connections')
diffusion_switched_vertical_connections_right = make_indicator_function_1x1(
grid, switched_vertical_connections(1),
'switched_vertical_connections')
diffusion_background = (make_constant_function_1x1(grid, 1) -
diffusion_horizontal_channels -
diffusion_fixed_vertical_connections -
diffusion_switched_vertical_connections_right)
parameter_type = {'switch': (1, )}
lambda_functions = [
diffusion_background, diffusion_horizontal_channels,
diffusion_fixed_vertical_connections,
diffusion_switched_vertical_connections_right
]
lambda_coefficients = [
ExpressionParameterFunctional(str(mu_min), parameter_type),
ExpressionParameterFunctional(str(mu_max), parameter_type),
ExpressionParameterFunctional(str(mu_max), parameter_type),
ProjectionParameterFunctional(component_name='switch',
component_shape=(1, ),
coordinates=(0, ))
]
kappa = make_constant_function_2x2(grid, [[1., 0.], [0., 1.]],
name='kappa')
f_functions = [
make_indicator_function_1x1(grid, [
[[[1 / 16, 5 / 8 + 1 / 32], [1 / 4 - 1 / 16, 7 / 8 - 1 / 32]], 1],
], 'top_left'),
make_indicator_function_1x1(grid, [[
[[3 / 4 + 1 / 16, 1 / 8 + 1 / 32], [1 - 1 / 16, 3 / 8 - 1 / 32]], 1
], [[[3 / 4 + 1 / 16, 5 / 8 + 1 / 32], [1 - 1 / 16, 7 / 8 - 1 / 32]], 1
]], 'right')
]
f_coefficients = [
ExpressionParameterFunctional('sin(2 * 2 * pi * _t) > 0', {'_t': ()}),
ExpressionParameterFunctional('-1', None)
]
def create_lambda(mu):
return (
make_constant_function_1x1(grid, mu_min) -
make_indicator_function_1x1(grid, horizontal_channels(mu_min)) -
make_indicator_function_1x1(grid,
fixed_vertical_connections(mu_min)) -
make_indicator_function_1x1(
grid, switched_vertical_connections(mu_min)) +
make_indicator_function_1x1(grid, horizontal_channels(mu_max)) +
make_indicator_function_1x1(grid,
fixed_vertical_connections(mu_max)) +
make_indicator_function_1x1(grid,
switched_vertical_connections(mu[0])))
return {
'grid': grid,
'boundary_info': all_dirichlet_boundary_info,
'inner_boundary_id': inner_boundary_id,
'lambda': {
'functions': lambda_functions,
'coefficients': lambda_coefficients
},
'lambda_bar': create_lambda(mu_bar),
'lambda_hat': create_lambda(mu_hat),
'kappa': kappa,
'f': {
'functions': f_functions,
'coefficients': f_coefficients
},
'parameter_type': parameter_type,
'mu_bar': mu_bar,
'mu_hat': mu_hat,
'mu_min': (mu_min, ),
'mu_max': (mu_max, ),
'parameter_range': (mu_min, mu_max)
}