#include <stdio.h>
#include <omp.h>
#include "basic.h"
#include "amatrix.h"
#include "gaussquad.h"
#include "factorizations.h"
#include "krylov.h"
#include "sparsematrix.h"
#include "cluster.h"
#include "clustergeometry.h"
#include "block.h"
#include "hmatrix.h"
#include "clusterbasis.h"
#include "h2matrix.h"
#include "dcluster.h"
#include "dblock.h"
#include "dclusterbasis.h"
#include "dh2matrix.h"
#include "krylovsolvers.h"
#include "hcoarsen.h"
#include "h2update.h"
#include "aca.h"
#include "macrosurface3d.h"
#include "surface3d.h"
#include "singquad2d.h"

Data Structures
struct	_bem3d
	Main container object for computation of BEM related matrices and vectors. More...

struct	_kernelbem3d
	Substructure containing callback functions to different types of kernel evaluations. More...

struct	_listnode
	simple singly linked list to store unsigned inter values. More...

struct	_tri_list
	Simple singly connected list to efficiently store a list of triangles. More...

struct	_vert_list
	Simple singly connected list to efficiently store a list of vertices. More...

Typedefs
typedef struct _bem3d	bem3d

typedef bem3d *	pbem3d

typedef const bem3d *	pcbem3d

typedef struct _aprxbem3d	aprxbem3d

typedef aprxbem3d *	paprxbem3d

typedef const aprxbem3d *	pcaprxbem3d

typedef struct _parbem3d	parbem3d

typedef parbem3d *	pparbem3d

typedef const parbem3d *	pcparbem3d

typedef struct _kernelbem3d	kernelbem3d

typedef kernelbem3d *	pkernelbem3d

typedef const kernelbem3d *	pckernelbem3d

typedef void(*	quadpoints3d) (pcbem3d bem, const real bmin[3], const real bmax[3], const real delta, real(Z)[3], real(N)[3])
	Callback function type for parameterizations. More...

typedef enum _basisfunctionbem3d	basisfunctionbem3d

typedef field(*	boundary_func3d) (const real x, const real n, void *data)

typedef field(*	kernel_func3d) (const real x, const real y, const real nx, const real ny, void *data)
	Evaluate a fundamental solution or its normal derivatives at points `x` and `y`. More...

typedef field(*	kernel_wave_func3d) (const real x, const real y, const real nx, const real ny, pcreal dir, void *data)
	Evaluate a modified fundamental solution or its normal derivatives at points `x` and `y`. More...

typedef struct _listnode	listnode

typedef listnode *	plistnode

typedef struct _tri_list	tri_list

typedef tri_list *	ptri_list

typedef struct _vert_list	vert_list

typedef vert_list *	pvert_list

Enumerations
enum	_basisfunctionbem3d { BASIS_NONE_BEM3D = 0, BASIS_CONSTANT_BEM3D = 'c', BASIS_LINEAR_BEM3D = 'l' }
	Possible types of basis functions. More...

Functions
pvert_list	new_vert_list (pvert_list next)
	Create a new list to store a number of vertex indices. More...

void	del_vert_list (pvert_list vl)
	Recursively deletes a vert_list. More...

ptri_list	new_tri_list (ptri_list next)
	Create a new list to store a number of triangles indices. More...

void	del_tri_list (ptri_list tl)
	Recursively deletes a tri_list. More...

pbem3d	new_bem3d (pcsurface3d gr, basisfunctionbem3d row_basis, basisfunctionbem3d col_basis)
	Main constructor for bem3d objects. More...

void	del_bem3d (pbem3d bem)
	Destructor for bem3d objects. More...

pclustergeometry	build_bem3d_const_clustergeometry (pcbem3d bem, uint **idx)
	Creates a clustergeometry object for a BEM-Problem using piecewise constant basis functions. More...

pclustergeometry	build_bem3d_linear_clustergeometry (pcbem3d bem, uint **idx)
	Creates a clustergeometry object for a BEM-Problem using linear basis functions. More...

pclustergeometry	build_bem3d_clustergeometry (pcbem3d bem, uint **idx, basisfunctionbem3d basis)
	Creates a clustergeometry object for a BEM-Problem using the type of basis functions specified by basis. More...

pcluster	build_bem3d_cluster (pcbem3d bem, uint clf, basisfunctionbem3d basis)
	Creates a clustertree for specified basis functions. More...

void	assemble_cc_near_bem3d (const uint ridx, const uint cidx, pcbem3d bem, bool ntrans, pamatrix N, kernel_func3d kernel)
	Compute general entries of a boundary integral operator with piecewise constant basis functions for both Ansatz and test functions. More...

void	assemble_cc_far_bem3d (const uint ridx, const uint cidx, pcbem3d bem, bool ntrans, pamatrix N, kernel_func3d kernel)
	Compute general entries of a boundary integral operator with piecewise constant basis functions for both Ansatz and test functions. More...

void	assemble_cl_near_bem3d (const uint ridx, const uint cidx, pcbem3d bem, bool ntrans, pamatrix N, kernel_func3d kernel)
	Compute general entries of a boundary integral operator with piecewise constant basis functions for Test and piecewise linear basis functions for Ansatz functions. More...

void	assemble_cl_far_bem3d (const uint ridx, const uint cidx, pcbem3d bem, bool ntrans, pamatrix N, kernel_func3d kernel)
	Compute general entries of a boundary integral operator with piecewise constant basis functions for Test and piecewise linear basis functions for Ansatz functions. More...

void	assemble_lc_near_bem3d (const uint ridx, const uint cidx, pcbem3d bem, bool ntrans, pamatrix N, kernel_func3d kernel)
	Compute general entries of a boundary integral operator with piecewise linear basis functions for Test and piecewise contant basis functions for Ansatz functions. More...

void	assemble_lc_far_bem3d (const uint ridx, const uint cidx, pcbem3d bem, bool ntrans, pamatrix N, kernel_func3d kernel)
	Compute general entries of a boundary integral operator with piecewise linear basis functions for Test and piecewise contant basis functions for Ansatz functions. More...

void	assemble_ll_near_bem3d (const uint ridx, const uint cidx, pcbem3d bem, bool ntrans, pamatrix N, kernel_func3d kernel)
	Compute general entries of a boundary integral operator with piecewise linear basis functions for both Ansatz and test functions. More...

void	assemble_ll_far_bem3d (const uint ridx, const uint cidx, pcbem3d bem, bool ntrans, pamatrix N, kernel_func3d kernel)
	Compute general entries of a boundary integral operator with piecewise linear basis functions for both Ansatz and test functions. More...

void	fill_bem3d (pcbem3d bem, const real(X)[3], const real(Y)[3], const real(NX)[3], const real(NY)[3], pamatrix V, kernel_func3d kernel)
	Evaluate a kernel function at some points and . More...

void	fill_wave_bem3d (pcbem3d bem, const real(X)[3], const real(Y)[3], const real(NX)[3], const real(NY)[3], pamatrix V, pcreal dir, kernel_wave_func3d kernel)
	Evaluate a modified kernel function at some points and for some direction . More...

void	fill_row_c_bem3d (const uint idx, const real(Z)[3], pcbem3d bem, pamatrix V, kernel_func3d kernel)
	This function will integrate a kernel function on the boundary domain in the first argument using piecewise constant basis function. For the second argument some given points will be used. The results will be stored in a matrix `V`. More...

void	fill_col_c_bem3d (const uint idx, const real(Z)[3], pcbem3d bem, pamatrix V, kernel_func3d kernel)
	This function will integrate a kernel function on the boundary domain in the second argument using piecewise constant basis function. For the first argument some given points will be used. The results will be stored in a matrix `V`. More...

void	fill_row_l_bem3d (const uint idx, const real(Z)[3], pcbem3d bem, pamatrix V, kernel_func3d kernel)
	This function will integrate a kernel function on the boundary domain in the first argument using piecewise linear basis function. For the second argument some given points will be used. The results will be stored in a matrix `V`. More...

void	fill_col_l_bem3d (const uint idx, const real(Z)[3], pcbem3d bem, pamatrix V, kernel_func3d kernel)
	This function will integrate a kernel function on the boundary domain in the second argument using piecewise linear basis function. For the first argument some given points will be used. The results will be stored in a matrix `V`. More...

void	fill_dnz_row_c_bem3d (const uint idx, const real(Z)[3], const real(*N)[3], pcbem3d bem, pamatrix V, kernel_func3d kernel)
	This function will integrate a normal derivative of a kernel function with respect to on the boundary domain in the first argument using piecewise constant basis function. For the second argument some given points will be used. The results will be stored in a matrix `V`. More...

void	fill_dnz_col_c_bem3d (const uint idx, const real(Z)[3], const real(*N)[3], pcbem3d bem, pamatrix V, kernel_func3d kernel)
	This function will integrate a normal derivative of a kernel function with respect to on the boundary domain in the second argument using piecewise constant basis function. For the first argument some given points will be used. The results will be stored in a matrix `V`. More...

void	fill_dnz_row_l_bem3d (const uint idx, const real(Z)[3], const real(*N)[3], pcbem3d bem, pamatrix V, kernel_func3d kernel)
	This function will integrate a normal derivative of a kernel function with respect to on the boundary domain in the first argument using piecewise linear basis function. For the second argument some given points will be used. The results will be stored in a matrix `V`. More...

void	fill_dnz_col_l_bem3d (const uint idx, const real(Z)[3], const real(*N)[3], pcbem3d bem, pamatrix V, kernel_func3d kernel)
	This function will integrate a normal derivative of a kernel function with respect to on the boundary domain in the second argument using piecewise linear basis function. For the first argument some given points will be used. The results will be stored in a matrix `V`. More...

void	setup_hmatrix_recomp_bem3d (pbem3d bem, bool recomp, real accur_recomp, bool coarsen, real accur_coarsen)
	Initialize the bem object for on the fly recompression techniques. More...

void	setup_hmatrix_aprx_inter_row_bem3d (pbem3d bem, pccluster rc, pccluster cc, pcblock tree, uint m)
	This function initializes the bem3d object for approximating a matrix with tensorinterpolation within the row cluster. More...

void	setup_hmatrix_aprx_inter_col_bem3d (pbem3d bem, pccluster rc, pccluster cc, pcblock tree, uint m)
	This function initializes the bem3d object for approximating a matrix with tensorinterpolation within the column cluster. More...

void	setup_hmatrix_aprx_inter_mixed_bem3d (pbem3d bem, pccluster rc, pccluster cc, pcblock tree, uint m)
	This function initializes the bem3d object for approximating a matrix with tensorinterpolation within one of row or column cluster. More...

void	setup_hmatrix_aprx_green_row_bem3d (pbem3d bem, pccluster rc, pccluster cc, pcblock tree, uint m, uint l, real delta, quadpoints3d quadpoints)
	creating hmatrix approximation using green's method with row cluster . More...

void	setup_hmatrix_aprx_green_col_bem3d (pbem3d bem, pccluster rc, pccluster cc, pcblock tree, uint m, uint l, real delta, quadpoints3d quadpoints)
	creating hmatrix approximation using green's method with column cluster . More...

void	setup_hmatrix_aprx_green_mixed_bem3d (pbem3d bem, pccluster rc, pccluster cc, pcblock tree, uint m, uint l, real delta, quadpoints3d quadpoints)
	creating hmatrix approximation using green's method with one of row or column cluster . More...

void	setup_hmatrix_aprx_greenhybrid_row_bem3d (pbem3d bem, pccluster rc, pccluster cc, pcblock tree, uint m, uint l, real delta, real accur, quadpoints3d quadpoints)
	creating hmatrix approximation using green's method with row cluster connected with recompression technique using ACA. More...

void	setup_hmatrix_aprx_greenhybrid_col_bem3d (pbem3d bem, pccluster rc, pccluster cc, pcblock tree, uint m, uint l, real delta, real accur, quadpoints3d quadpoints)
	creating hmatrix approximation using green's method with column cluster connected with recompression technique using ACA. More...

void	setup_hmatrix_aprx_greenhybrid_mixed_bem3d (pbem3d bem, pccluster rc, pccluster cc, pcblock tree, uint m, uint l, real delta, real accur, quadpoints3d quadpoints)
	creating hmatrix approximation using green's method with row or column cluster connected with recompression technique using ACA. More...

void	setup_hmatrix_aprx_aca_bem3d (pbem3d bem, pccluster rc, pccluster cc, pcblock tree, real accur)
	Approximate matrix block with ACA using full pivoting. More...

void	setup_hmatrix_aprx_paca_bem3d (pbem3d bem, pccluster rc, pccluster cc, pcblock tree, real accur)
	Approximate matrix block with ACA using partial pivoting. More...

void	setup_hmatrix_aprx_hca_bem3d (pbem3d bem, pccluster rc, pccluster cc, pcblock tree, uint m, real accur)
	Approximate matrix block with hybrid cross approximation using Interpolation and ACA with full pivoting. More...

void	setup_h2matrix_recomp_bem3d (pbem3d bem, bool hiercomp, real accur_hiercomp)
	Enables hierarchical recompression for hmatrices. More...

void	setup_h2matrix_aprx_inter_bem3d (pbem3d bem, pcclusterbasis rb, pcclusterbasis cb, pcblock tree, uint m)
	Initialize the bem3d object for approximating a h2matrix with tensorinterpolation. More...

void	setup_h2matrix_aprx_greenhybrid_bem3d (pbem3d bem, pcclusterbasis rb, pcclusterbasis cb, pcblock tree, uint m, uint l, real delta, real accur, quadpoints3d quadpoints)
	Initialize the bem3d object for approximating a h2matrix with green's method and ACA based recompression. More...

void	setup_h2matrix_aprx_greenhybrid_ortho_bem3d (pbem3d bem, pcclusterbasis rb, pcclusterbasis cb, pcblock tree, uint m, uint l, real delta, real accur, quadpoints3d quadpoints)
	Initialize the bem3d object for approximating a h2matrix with green's method and ACA based recompression. The resulting clusterbasis will be orthogonal. More...

void	setup_dh2matrix_aprx_inter_bem3d (pbem3d bem, pcdclusterbasis rb, pcdclusterbasis cb, pcdblock tree, uint m)
	Initialize the bem3d object for an interpolation based $\mathcal{DH}^2$ -matrix approximation. More...

void	setup_dh2matrix_aprx_inter_ortho_bem3d (pbem3d bem, pcdclusterbasis rb, pcdclusterbasis cb, pcdblock tree, uint m)
	Initialize the bem3d object for an interpolation based $\mathcal{DH}^2$ -matrix approximation with orthogonal directional cluster basis. More...

void	setup_dh2matrix_aprx_inter_recomp_bem3d (pbem3d bem, pcdclusterbasis rb, pcdclusterbasis cb, pcdblock tree, uint m, ptruncmode tm, real eps)
	Initialize the bem3d object for an interpolation based $\mathcal{DH}^2$ -matrix approximation with orthogonal directional cluster basis. During the filling process the $\mathcal{DH}^2$ -matrix will be recompressed with respective to truncmode and the given accuracy `eps`. More...

void	assemble_bem3d_amatrix (pbem3d bem, pamatrix G)
	Assemble a dense matrix for some boundary integral operator given by `bem`. More...

void	assemble_bem3d_hmatrix (pbem3d bem, pblock b, phmatrix G)
	Fills a hmatrix with a predefined approximation technique. More...

void	assemblecoarsen_bem3d_hmatrix (pbem3d bem, pblock b, phmatrix G)
	Fills a hmatrix with a predefined approximation technique using coarsening strategy. More...

void	assemble_bem3d_nearfield_hmatrix (pbem3d bem, pblock b, phmatrix G)
	Fills the nearfield blocks of a hmatrix. More...

void	assemble_bem3d_farfield_hmatrix (pbem3d bem, pblock b, phmatrix G)
	Fills the farfield blocks of a hmatrix with a predefined approximation technique. More...

void	assemble_bem3d_h2matrix_row_clusterbasis (pcbem3d bem, pclusterbasis rb)
	This function computes the matrix entries for the nested clusterbasis $V_t \, , t \in \mathcal T_{\mathcal I}$ . More...

void	assemble_bem3d_h2matrix_col_clusterbasis (pcbem3d bem, pclusterbasis cb)
	This function computes the matrix entries for the nested clusterbasis $W_s \, , s \in \mathcal T_{\mathcal J}$ . More...

void	assemble_bem3d_h2matrix (pbem3d bem, ph2matrix G)
	Fills a h2matrix with a predefined approximation technique. More...

void	assemble_bem3d_nearfield_h2matrix (pbem3d bem, ph2matrix G)
	Fills the nearfield part of a h2matrix. More...

void	assemble_bem3d_farfield_h2matrix (pbem3d bem, ph2matrix G)
	Fills a h2matrix with a predefined approximation technique. More...

void	assemblehiercomp_bem3d_h2matrix (pbem3d bem, pblock b, ph2matrix G)
	Fills an h2matrix with a predefined approximation technique using hierarchical recompression. More...

void	assemble_bem3d_dh2matrix_row_dclusterbasis (pcbem3d bem, pdclusterbasis rb)
	This function computes the matrix entries for the nested dclusterbasis $V_t \, , t \in \mathcal T_{\mathcal I}$ . More...

void	assemble_bem3d_dh2matrix_col_dclusterbasis (pcbem3d bem, pdclusterbasis cb)
	This function computes the matrix entries for the nested dclusterbasis $W_s \, , s \in \mathcal T_{\mathcal J}$ . More...

void	assemble_bem3d_dh2matrix_ortho_row_dclusterbasis (pcbem3d bem, pdclusterbasis rb, pdclusteroperator ro)
	Function for filling a directional row cluster basis with orthogonal matrices. More...

void	assemble_bem3d_dh2matrix_ortho_col_dclusterbasis (pcbem3d bem, pdclusterbasis cb, pdclusteroperator co)
	Function for filling a directional column cluster basis with orthogonal matrices. More...

void	assemble_bem3d_dh2matrix_recomp_both_dclusterbasis (pcbem3d bem, pdclusterbasis rb, pdclusteroperator bro, pdclusterbasis cb, pdclusteroperator bco, pcdblock broot)
	Function for filling both directional cluster bases with orthogonal matrices. More...

void	assemble_bem3d_dh2matrix (pbem3d bem, pdh2matrix G)
	Fills a dh2matrix with a predefined approximation technique. More...

void	assemble_bem3d_nearfield_dh2matrix (pbem3d bem, pdh2matrix G)
	Fills the nearfield part of a dh2matrix. More...

void	assemble_bem3d_farfield_dh2matrix (pbem3d bem, pdh2matrix G)
	Fills a dh2matrix with a predefined approximation technique. More...

void	assemble_bem3d_lagrange_c_amatrix (const uint *idx, pcrealavector px, pcrealavector py, pcrealavector pz, pcbem3d bem, pamatrix V)
	This function will integrate Lagrange polynomials on the boundary domain using piecewise constant basis function and store the results in a matrix `V`. More...

void	assemble_bem3d_lagrange_wave_c_amatrix (const uint *idx, pcrealavector px, pcrealavector py, pcrealavector pz, pcreal dir, pcbem3d bem, pamatrix V)
	This function will integrate modified Lagrange polynomials on the boundary domain using piecewise constant basis function and store the results in a matrix `V`. More...

void	assemble_bem3d_lagrange_l_amatrix (const uint *idx, pcrealavector px, pcrealavector py, pcrealavector pz, pcbem3d bem, pamatrix V)
	This function will integrate Lagrange polynomials on the boundary domain using linear basis function and store the results in a matrix `V`. More...

void	assemble_bem3d_lagrange_wave_l_amatrix (const uint *idx, pcrealavector px, pcrealavector py, pcrealavector pz, pcreal dir, pcbem3d bem, pamatrix V)
	This function will integrate modified Lagrange polynomials on the boundary domain using linear basis function and store the results in a matrix `V`. More...

void	assemble_bem3d_dn_lagrange_c_amatrix (const uint *idx, pcrealavector px, pcrealavector py, pcrealavector pz, pcbem3d bem, pamatrix V)
	This function will integrate the normal derivatives of the Lagrange polynomials on the boundary domain using piecewise constant basis function and store the results in a matrix `V`. More...

void	assemble_bem3d_dn_lagrange_wave_c_amatrix (const uint *idx, pcrealavector px, pcrealavector py, pcrealavector pz, pcreal dir, pcbem3d bem, pamatrix V)
	This function will integrate the normal derivatives of the modified Lagrange polynomials on the boundary domain using piecewise constant basis function and store the results in a matrix `V`. More...

void	assemble_bem3d_dn_lagrange_l_amatrix (const uint *idx, pcrealavector px, pcrealavector py, pcrealavector pz, pcbem3d bem, pamatrix V)
	This function will integrate the normal derivatives of the Lagrange polynomials on the boundary domain using linear basis function and store the results in a matrix `V`. More...

void	assemble_bem3d_dn_lagrange_wave_l_amatrix (const uint *idx, pcrealavector px, pcrealavector py, pcrealavector pz, pcreal dir, pcbem3d bem, pamatrix V)
	This function will integrate the normal derivatives of the modified Lagrange polynomials on the boundary domain using linear basis function and store the results in a matrix `V`. More...

void	assemble_bem3d_lagrange_amatrix (const real(*X)[3], pcrealavector px, pcrealavector py, pcrealavector pz, pcbem3d bem, pamatrix V)
	This function will evaluate the Lagrange polynomials in a given point set `X` and store the results in a matrix `V`. More...

void	assemble_bem3d_lagrange_wave_amatrix (const real(*X)[3], pcrealavector px, pcrealavector py, pcrealavector pz, pcreal dir, pcbem3d bem, pamatrix V)
	This function will evaluate the modified Lagrange polynomials in a given point set `X` and store the results in a matrix `V`. More...

real	normL2_bem3d (pbem3d bem, boundary_func3d f, void *data)
	Compute the $L_2(\Gamma)$ -norm of some given function `f`. More...

real	normL2_c_bem3d (pbem3d bem, pavector x)
	Compute the $L_2(\Gamma)$ -norm of some given function in terms of a piecewise constant basis $\left( \varphi_i \right)_{i \in \mathcal I}$ . More...

real	normL2diff_c_bem3d (pbem3d bem, pavector x, boundary_func3d f, void *data)
	Compute the $L_2(\Gamma)$ difference norm of some given function in terms of a piecewise constant basis $\left( \varphi_i \right)_{i \in \mathcal I}$ and some other function . More...

real	normL2_l_bem3d (pbem3d bem, pavector x)
	Compute the $L_2(\Gamma)$ -norm of some given function in terms of a piecewise linear basis $\left( \varphi_i \right)_{i \in \mathcal I}$ . More...

real	normL2diff_l_bem3d (pbem3d bem, pavector x, boundary_func3d f, void *data)
	Compute the $L_2(\Gamma)$ difference norm of some given function in terms of a piecewise linear basis $\left( \varphi_i \right)_{i \in \mathcal I}$ and some other function . More...

void	integrate_bem3d_c_avector (pbem3d bem, boundary_func3d f, pavector w, void *data)
	Computes the integral of a given function using piecewise constant basis functions over the boundary of a domain. More...

void	integrate_bem3d_l_avector (pbem3d bem, boundary_func3d f, pavector w, void *data)
	Computes the integral of a given function using piecewise linear basis functions over the boundary of a domain. More...

void	projectL2_bem3d_c_avector (pbem3d bem, boundary_func3d f, pavector w, void *data)
	Computes the -projection of a given function using piecewise constant basis functions over the boundary of a domain. More...

void	projectL2_bem3d_l_avector (pbem3d bem, boundary_func3d f, pavector w, void *data)
	Computes the -projection of a given function using linear basis functions over the boundary of a domain. More...

void	setup_vertex_to_triangle_map_bem3d (pbem3d bem)
	initializes the field `bem->v2t` when using linear basis functions More...

void	build_bem3d_cube_quadpoints (pcbem3d bem, const real a[3], const real b[3], const real delta, real(Z)[3], real(N)[3])
	Generating quadrature points, weights and normal vectors on a cube parameterization. More...

prkmatrix	build_bem3d_rkmatrix (pccluster row, pccluster col, void *data)
	For a block defined by `row` and `col` this function will build a rank-k-approximation and return the rkmatrix. More...

pamatrix	build_bem3d_amatrix (pccluster row, pccluster col, void *data)
	For a block defined by `row` and `col` this function will compute the full submatrix and return an amatrix. More...

void	build_bem3d_curl_sparsematrix (pcbem3d bem, psparsematrix C0, psparsematrix C1, psparsematrix *C2)
	Set up the surface curl operator. More...

Detailed Description

Author: Sven Christophersen

Date: 2011

Data Structures

Typedefs

Enumerations

Functions

Detailed Description