bempp.api.fmm.helpers

FMM helper functions.

Module Contents

Functions

laplace_kernel(target_points, source_points, ...)	Evaluate the Laplace kernel.
modified_helmholtz_kernel(target_points, ...)	Evaluate the modified Helmholtz kernel.
helmholtz_kernel(target_points, source_points, ...)	Evaluate the Laplace kernel.
get_local_interaction_operator(grid, local_points, ...)	Get the local interaction operator.
get_local_interaction_evaluator_numba(grid_data, ...)	Return an evaluator for the local interactions.
numba_evaluate_local_interactions(grid_data, coeffs, ...)	Get the local interaction matrix on the grid.
get_local_interaction_matrix_impl(grid_data, ...)	Get the local interaction matrix on the grid.
map_space_to_points(space, local_points, weights[, ...])	Return mapper from grid coeffs to point evaluations.
map_space_to_points_impl(grid_data, local2global, ...)	Numba accelerated computational parts for point map.
grid_to_points(grid_data, local_points)	Map a grid to an array of points.
get_local_interaction_evaluator_opencl(grid, ...)	Return an evaluator for the local interactions.
debug_fmm(targets, sources, charges, mode, ...)	Compare the result of an FMM result with the corresponding dense computation.
dense_interaction_evaluator(targets, sources, charges, ...)	Dense evaluation of interaction between sources and targets.
dense_interaction_evaluator_impl(targets, sources, ...)	Dense evaluation of interaction between sources and targets.

Attributes

M_INV_4PI

bempp.api.fmm.helpers.M_INV_4PI

bempp.api.fmm.helpers.laplace_kernel(target_points, source_points, kernel_parameters, dtype, result_type)

Evaluate the Laplace kernel.

bempp.api.fmm.helpers.modified_helmholtz_kernel(target_points, source_points, kernel_parameters, dtype, result_type)

Evaluate the modified Helmholtz kernel.

bempp.api.fmm.helpers.helmholtz_kernel(target_points, source_points, kernel_parameters, dtype, result_type)

Evaluate the Laplace kernel.

bempp.api.fmm.helpers.get_local_interaction_operator(grid, local_points, kernel_function, kernel_parameters, precision, is_complex, device_interface=None)

Get the local interaction operator.

bempp.api.fmm.helpers.get_local_interaction_evaluator_numba(grid_data, local_points, kernel_function, kernel_parameters, dtype, result_type)

Return an evaluator for the local interactions.

bempp.api.fmm.helpers.numba_evaluate_local_interactions(grid_data, coeffs, local_points, kernel_function, kernel_parameters, dtype, result_type)

Get the local interaction matrix on the grid.

bempp.api.fmm.helpers.get_local_interaction_matrix_impl(grid_data, local_points, kernel_function, kernel_parameters, dtype, result_type)

Get the local interaction matrix on the grid.

bempp.api.fmm.helpers.map_space_to_points(space, local_points, weights, return_transpose=False)

Return mapper from grid coeffs to point evaluations.

bempp.api.fmm.helpers.map_space_to_points_impl(grid_data, local2global, local_multipliers, normal_multipliers, support_elements, numba_evaluate, shape_fun, local_points, weights, number_of_shape_functions)

Numba accelerated computational parts for point map.

bempp.api.fmm.helpers.grid_to_points(grid_data, local_points)

Map a grid to an array of points.

Returns a (N, 3) point array that stores the global vertices associated with the local points in each triangle. Points are stored in consecutive order for each element in the support_elements list. Hence, the returned array is of the form [ v_1^1, v_2^1, …, v_M^1, v_1^2, v_2^2, …], where v_i^j is the ith point in the jth element in the support_elements list.

Parameters

grid_dataGridData

A Bempp GridData object.

local_pointsnp.ndarray

(2, M) array of local coordinates.

bempp.api.fmm.helpers.get_local_interaction_evaluator_opencl(grid, local_points, kernel_function, kernel_parameters, dtype, result_type)

Return an evaluator for the local interactions.

bempp.api.fmm.helpers.debug_fmm(targets, sources, charges, mode, kernel_parameters, fmm_result)

Compare the result of an FMM result with the corresponding dense computation.

bempp.api.fmm.helpers.dense_interaction_evaluator(targets, sources, charges, mode, kernel_parameters)

Dense evaluation of interaction between sources and targets.

Parameters

targetsndarray

M x 3 array of target points.

sourcesndarray

N x 3 array of source points.

chargesndarray

N array of charges.

modestring

Either ‘laplace’, ‘helmholtz’, ‘modified_helmholtz’

kernel_parametersndarray

Array with kernel parameters

kernel_typedtype

Type of the kernel (numpy.float64 or numpy.complex128)

Returns the dense evaluation of the interaction between sources and targets with the given charges.

bempp.api.fmm.helpers.dense_interaction_evaluator_impl(targets, sources, charges, kernel, kernel_parameters, kernel_type)

Dense evaluation of interaction between sources and targets.

Parameters

targetsndarray

M x 3 array of target points.

sourcesndarray

N x 3 array of source points.

chargesndarray

N array of charges.

kernelNumba function object

The kernel object (either helpers.laplace, helpers.helmholtz or helpers.modified_helmholtz)

kernel_parametersndarray

Array with kernel parameters

kernel_typedtype

Type of the kernel (numpy.float64 or numpy.complex128)

Returns the dense evaluation of the interaction between sources and targets with the given charges.