H2Lib
3.0

Main container object for computation of BEM related matrices and vectors. More...
#include <bem3d.h>
Data Fields  
pcsurface3d  gr 
Polyedric 3 dimensional surface mesh. More...  
psingquad2d  sq 
Quadrature rules used within BEM computation. More...  
basisfunctionbem3d  row_basis 
Type of basis function for neumanndata.  
basisfunctionbem3d  col_basis 
Type of basis function for dirichletdata.  
real *  mass 
Massmatrix of reference basis functions. More...  
field  alpha 
Boundary integral operator + mass matrix.  
field  k 
Wavenumber for Helmholtz type problems, possibly complex valued.  
field  kernel_const 
A constant factor extracted from the kernel function to speed up quadrature.  
plistnode *  v2t 
This field describes the mapping from the vertices of a geometry to the triangles they belong to. More...  
void(*  nearfield )(const uint *ridx, const uint *cidx, pcbem3d bem, bool ntrans, pamatrix N) 
Computes nearfield entries of Galerkin matrices. More...  
void(*  nearfield_far )(const uint *ridx, const uint *cidx, pcbem3d bem, bool ntrans, pamatrix N) 
Computes nearfield entries of Galkerin matrices for disjoint clusters. More...  
void(*  farfield_rk )(pccluster rc, uint rname, pccluster cc, uint cname, pcbem3d bem, prkmatrix R) 
Computes rankkapproximations of a given block. More...  
void(*  farfield_u )(uint rname, uint cname, uint bname, pcbem3d bem) 
Computes coupling matrix for uniform matrices. More...  
void(*  farfield_wave_u )(uint rname, uint cname, uint bname, pcbem3d bem) 
Computes coupling matrix for duniform matrices for some direction . More...  
void(*  leaf_row )(uint rname, pcbem3d bem) 
Computes the the matrix for a leaf cluster . More...  
void(*  leaf_wave_row )(uint rname, pcbem3d bem) 
Computes the the matrix for a leaf cluster and a direction . More...  
void(*  leaf_col )(uint cname, pcbem3d bem) 
Computes the the matrix for a leaf cluster . More...  
void(*  leaf_wave_col )(uint cname, pcbem3d bem) 
Computes the the matrix for a leaf cluster and a direction . More...  
void(*  transfer_row )(uint rname, pcbem3d bem) 
Computes the transfer matrices for a cluster . More...  
void(*  transfer_wave_row )(uint rname, pcbem3d bem) 
Computes the transfer matrices for a cluster and directions . The father cluster is using the waveLagrange basis while the sons use the standard Lagrange basis. More...  
void(*  transfer_wave_wave_row )(uint rname, pcbem3d bem) 
Computes the transfer matrices for a cluster and directions . Both, the father cluster and sons are using the waveLagrange basis. More...  
void(*  transfer_col )(uint cname, pcbem3d bem) 
Computes the transfer matrices for a cluster . More...  
void(*  transfer_wave_col )(uint cname, pcbem3d bem) 
Computes the transfer matrices for a cluster and directions . The father cluster is using the waveLagrange basis while the sons use the standard Lagrange basis. More...  
void(*  transfer_wave_wave_col )(uint cname, pcbem3d bem) 
Computes the transfer matrices for a cluster and directions . Both, the father cluster and sons are using the waveLagrange basis. More...  
paprxbem3d  aprx 
A collection of necessary data structures for approximating matrices with various techniques. More...  
pparbem3d  par 
Some helpers to make parallel computations possible. More...  
pkernelbem3d  kernels 
A collection of callback functions for different types of kernel evaluations. More...  
Main container object for computation of BEM related matrices and vectors.
This struct defines the essential part of all calculations concerning BEM. Just creating a simple bem3d object is not intended, though possible. Therefore call a problem specific constructor such as new_slp_laplace_bem3d or new_dlp_laplace_bem3d . This will initialize all needed callback functions to build up at least dense matrices. To be able to create h or h2matrix approximations one needs to call one of the set_hmatrix_aprx* or set_h2matrix_aprx* depending on the type of your matrix, to fully initialize the bem3d object. Afterwards you can build up your desired matrix approximation with a few simple functions calls, delivered by the bem3d object, using your favored approximation technique. Calling another of these " set " functions will reinitialize the bem3d object and you can build another approximation with a different technique.
paprxbem3d aprx 
A collection of necessary data structures for approximating matrices with various techniques.
Necessary Objects for approximation matrices with different approximation schemes are stored within aprx.
Computes rankkapproximations of a given block.
This callback function computes a rankkapproximation of a matrix block given by row cluster rc
and column cluster cc
. The Matrices A
and B
are stored in a rankkmatrix R
.
rc  Current row cluster . 
rname  Enumerated number of current row cluster rc . 
cc  Current column cluster 
cname  Enumerated number of current column cluster cc . 
bem  BEMobject containing additional information for computation of the matrix entries. 
R  Rankkmatrix, which takes up the resulting matrices A and B . The rank k is defined by the underlying approximation technique. 
Computes coupling matrix for uniform matrices.
While using h2matrices the coupling matrices are computed by this callback function. Coupling matrices are stored in the struct uniform defining a certain block of the whole h2matrix.
rname  Enumerated number of current row cluster clusterbasis U>rb . 
cname  Enumerated number of current column clusterbasis U>cb . 
bmame  Enumerated number of current block. From that number an object of type uniform containing the coupling matrix , the row clusterbasis U>rb and the column clusterbasis U>cb can be derived. 
bem  BEMobject containing additional information for computation of the matrix entries. 
Computes coupling matrix for duniform matrices for some direction .
While using Dh2matrices the coupling matrices are computed by this callback function. Coupling matrices are stored in the struct duniform defining a certain block of the whole Dh2matrix.
rname  Enumerated number of current row dcluster dclusterbasis U>rb . 
cname  Enumerated number of current column dclusterbasis U>cb . 
bmame  Enumerated number of current dblock. From that number an object of type duniform containing the coupling matrix , the row dclusterbasis U>rb and the column dclusterbasis U>cb can be derived. 
bem  BEMobject containing additional information for computation of the matrix entries. 
pcsurface3d gr 
Polyedric 3 dimensional surface mesh.
Polyedric boundary mesh used for the BEMproblem.
pkernelbem3d kernels 
A collection of callback functions for different types of kernel evaluations.
This struct defines a set of callback functions that are based on the fundamental solution of the underlying problem. They are used to build up approximations that will be used within farfield_rk , farfield_u , leaf_row , leaf_col , transfer_row and transfer_col. In Order to receive correct result, the callback functions defined in kernels have to be set correctly to the given problem by a constructor. These callback functions also depend on the utilized basis functions for either neumann and dirichletdata. As an example the constructors new_slp_laplace_bem3d and new_dlp_laplace_bem3d should serve.
Computes the the matrix for a leaf cluster .
leaf_col is used for building up a clusterbasis for the set for h2matrices. For each leaf_col will construct the matrix . In case of nested clusterbasis transfer_col has also to be set to a valid function constructing suitable transfer matrices .
bem  BEMobject containing additional information for computation of the matrix entries. 
cname  Enumerated number of current column clusterbasis cb . 
Computes the the matrix for a leaf cluster .
leaf_row is used for building up a clusterbasis for the set for h2matrices. For each leaf_row will construct the matrix . In case of nested clusterbasis transfer_row has also to be set to a valid function constructing suitable transfer matrices .
bem  BEMobject containing additional information for computation of the matrix entries. 
rname  Enumerated number of current row clusterbasis rb . 
Computes the the matrix for a leaf cluster and a direction .
leaf_wave_col is used for building up a dclusterbasis for the set for Dh2matrices. For each and for all directions leaf_wave_col will construct the matrix . In case of nested dclusterbasis transfer_wave_col and transfer_wave_wave_col also have to be set to valid functions constructing suitable transfer matrices .
bem  BEMobject containing additional information for computation of the matrix entries. 
cname  Enumerated number of current column dclusterbasis cb . 
Computes the the matrix for a leaf cluster and a direction .
leaf_wave_row is used for building up a dclusterbasis for the set for Dh2matrices. For each and all directions . leaf_wave_row will construct the matrix . In case of nested dclusterbasis transfer_wave_row and transfer_wave_wave_row also have to be set to valid functions constructing suitable transfer matrices .
bem  BEMobject containing additional information for computation of the matrix entries. 
rname  Enumerated number of current row dclusterbasis rb . 
real* mass 
Massmatrix of reference basis functions.
Massmatrix for all combinations of reference basis functions and . Entries are computed as:
Computes nearfield entries of Galerkin matrices.
This callback function computes 'nearfield' entries of the underlying problem and integraloperator.
ridx  Defines the indices of row boundary elements used. If ridx equals NULL, then Elements 0, ..., N>rows1 are used. 
cidx  Defines the indices of column boundary elements used. If cidx equals NULL, then Elements 0, ..., N>cols1 are used. 
bem  Bem3d object, that contains additional Information for the computation of the matrix entries. 
ntrans  Is a boolean flag to indicates the way of storing the entries in matrix N . If ntrans == true the matrix entries will be stored in a transposed way. 
N  For ntrans == false the matrix entries are computed as: otherwise they are stored as

Computes nearfield entries of Galkerin matrices for disjoint clusters.
This callback function computes 'nearfield' entries of the underlying problem and integraloperator.
ridx  Defines the indices of row boundary elements used. If ridx equals NULL, then Elements 0, ..., N>rows1 are used. 
cidx  Defines the indices of column boundary elements used. If cidx equals NULL, then Elements 0, ..., N>cols1 are used. 
bem  Bem3d object, that contains additional Information for the computation of the matrix entries. 
ntrans  Is a boolean flag to indicates the way of storing the entries in matrix N . If ntrans == true the matrix entries will be stored in a transposed way. 
N  For ntrans == false the matrix entries are computed as: otherwise they are stored as

pparbem3d par 
Some helpers to make parallel computations possible.
For the sake of parallelism we need some auxiliary data structure, which are all collected within the struct par. Most commonly used is this struct for enumerated non linear data structures such als cluster or blocktrees.
psingquad2d sq 
Quadrature rules used within BEM computation.
Singular quadrature formulas used within boundaryintegralOperator computation.
Computes the transfer matrices for a cluster .
transfer_col will build up the transfer matrices , for all and . For a cluster transfer_col will compute the matrices , . The matrix is stored in cb>son[0]>E
, is stored in cb>son[1]>E
, is stored in cb>son[ ]>E
.
bem  BEMobject containing additional information for computation of the matrix entries. 
cname  Enumerated number of current column clusterbasis cb . 
Computes the transfer matrices for a cluster .
transfer_row will build up the transfer matrices , for all and . For a cluster transfer_row will compute the matrices , . The matrix is stored in rb>son[0]>E
, is stored in rb>son[1]>E
, is stored in rb>son[ ]>E
.
bem  BEMobject containing additional information for computation of the matrix entries. 
rname  Enumerated number of current row clusterbasis rb . 
Computes the transfer matrices for a cluster and directions . The father cluster is using the waveLagrange basis while the sons use the standard Lagrange basis.
transfer_wave_col will build up the transfer matrices , for all and and directions . For a cluster transfer_wave_col will compute the matrices , and . The matrix is stored in cb>son[0]>E + 0
, is stored in cb>son[0]>E + 1
, is stored in cb>son[ ]>E + (d  1)
.
bem  BEMobject containing additional information for computation of the matrix entries. 
cname  Enumerated number of current column dclusterbasis cb . 
Computes the transfer matrices for a cluster and directions . The father cluster is using the waveLagrange basis while the sons use the standard Lagrange basis.
transfer_wave_row will build up the transfer matrices , for all and and directions . For a cluster transfer_wave_row will compute the matrices , and . The matrix is stored in rb>son[0]>E + 0
, is stored in rb>son[0]>E + 1
, is stored in rb>son[ ]>E + (d  1)
.
bem  BEMobject containing additional information for computation of the matrix entries. 
rname  Enumerated number of current row dclusterbasis rb . 
Computes the transfer matrices for a cluster and directions . Both, the father cluster and sons are using the waveLagrange basis.
transfer_wave_wave_col will build up the transfer matrices , for all and and directions . For a cluster transfer_wave_wave_col will compute the matrices , and . The matrix is stored in cb>son[0]>E + 0
, is stored in cb>son[0]>E + 1
, is stored in cb>son[ ]>E + (d  1)
. The used directions correspond to some difference between directions used for the father and directions . Therefore it holds
bem  BEMobject containing additional information for computation of the matrix entries. 
cname  Enumerated number of current column dclusterbasis cb . 
Computes the transfer matrices for a cluster and directions . Both, the father cluster and sons are using the waveLagrange basis.
transfer_wave_wave_row will build up the transfer matrices , for all and and directions . For a cluster transfer_wave_wave_row will compute the matrices , and . The matrix is stored in rb>son[0]>E + 0
, is stored in rb>son[0]>E + 1
, is stored in rb>son[ ]>E + (d  1)
. The used directions correspond to some difference between directions used for the father and directions . Therefore it holds
bem  BEMobject containing additional information for computation of the matrix entries. 
rname  Enumerated number of current row dclusterbasis rb . 
plistnode* v2t 
This field describes the mapping from the vertices of a geometry to the triangles they belong to.
The length of this array is equal to the number of vertices. For each vertex the list v2t[i]
enumerates all triangles that share this vertex .
This can be usefull within computation of matrix entries when linear basis functions are involved.