:py:mod:`bempp.api.fmm.helpers`
===============================

.. py:module:: bempp.api.fmm.helpers

.. autoapi-nested-parse::

   FMM helper functions.



Module Contents
---------------


Functions
~~~~~~~~~

.. autoapisummary::

   bempp.api.fmm.helpers.laplace_kernel
   bempp.api.fmm.helpers.modified_helmholtz_kernel
   bempp.api.fmm.helpers.helmholtz_kernel
   bempp.api.fmm.helpers.get_local_interaction_operator
   bempp.api.fmm.helpers.get_local_interaction_evaluator_numba
   bempp.api.fmm.helpers.numba_evaluate_local_interactions
   bempp.api.fmm.helpers.get_local_interaction_matrix_impl
   bempp.api.fmm.helpers.map_space_to_points
   bempp.api.fmm.helpers.map_space_to_points_impl
   bempp.api.fmm.helpers.grid_to_points
   bempp.api.fmm.helpers.get_local_interaction_evaluator_opencl
   bempp.api.fmm.helpers.debug_fmm
   bempp.api.fmm.helpers.dense_interaction_evaluator
   bempp.api.fmm.helpers.dense_interaction_evaluator_impl



Attributes
~~~~~~~~~~

.. autoapisummary::

   bempp.api.fmm.helpers.M_INV_4PI


.. py:data:: M_INV_4PI

   

.. py:function:: laplace_kernel(target_points, source_points, kernel_parameters, dtype, result_type)

   Evaluate the Laplace kernel.


.. py:function:: modified_helmholtz_kernel(target_points, source_points, kernel_parameters, dtype, result_type)

   Evaluate the modified Helmholtz kernel.


.. py:function:: helmholtz_kernel(target_points, source_points, kernel_parameters, dtype, result_type)

   Evaluate the Laplace kernel.


.. py:function:: get_local_interaction_operator(grid, local_points, kernel_function, kernel_parameters, precision, is_complex, device_interface=None)

   Get the local interaction operator.


.. py:function:: get_local_interaction_evaluator_numba(grid_data, local_points, kernel_function, kernel_parameters, dtype, result_type)

   Return an evaluator for the local interactions.


.. py:function:: numba_evaluate_local_interactions(grid_data, coeffs, local_points, kernel_function, kernel_parameters, dtype, result_type)

   Get the local interaction matrix on the grid.


.. py:function:: get_local_interaction_matrix_impl(grid_data, local_points, kernel_function, kernel_parameters, dtype, result_type)

   Get the local interaction matrix on the grid.


.. py:function:: map_space_to_points(space, local_points, weights, return_transpose=False)

   Return mapper from grid coeffs to point evaluations.


.. py:function:: 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.


.. py:function:: 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_data : GridData
       A Bempp GridData object.
   local_points : np.ndarray
       (2, M) array of local coordinates.


.. py:function:: get_local_interaction_evaluator_opencl(grid, local_points, kernel_function, kernel_parameters, dtype, result_type)

   Return an evaluator for the local interactions.


.. py:function:: debug_fmm(targets, sources, charges, mode, kernel_parameters, fmm_result)

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


.. py:function:: dense_interaction_evaluator(targets, sources, charges, mode, kernel_parameters)

   Dense evaluation of interaction between sources and targets.

   Parameters
   ----------
   targets : ndarray
       M x 3 array of target points.
   sources : ndarray
       N x 3 array of source points.
   charges : ndarray
       N array of charges.
   mode : string
       Either 'laplace', 'helmholtz', 'modified_helmholtz'
   kernel_parameters : ndarray
       Array with kernel parameters
   kernel_type : dtype
       Type of the kernel (numpy.float64 or numpy.complex128)

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


.. py:function:: dense_interaction_evaluator_impl(targets, sources, charges, kernel, kernel_parameters, kernel_type)

   Dense evaluation of interaction between sources and targets.

   Parameters
   ----------
   targets : ndarray
       M x 3 array of target points.
   sources : ndarray
       N x 3 array of source points.
   charges : ndarray
       N array of charges.
   kernel : Numba function object
       The kernel object (either helpers.laplace,
       helpers.helmholtz or helpers.modified_helmholtz)
   kernel_parameters : ndarray
       Array with kernel parameters
   kernel_type : dtype
       Type of the kernel (numpy.float64 or numpy.complex128)

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