H2Lib
3.0

Main container object for computation of BEM related matrices and vectors. More...
#include <bem2d.h>
Data Fields  
pccurve2d  gr 
Polygonal two dimensional mesh. More...  
psingquad1d  sq 
Quadrature rules used within BEM computation. More...  
uint  N_neumann 
Number of degrees of freedom for neumann data.  
basisfunctionbem2d  basis_neumann 
Type of basis function for neumanndata.  
uint  N_dirichlet 
Number of degrees of freedom for dirichlet data.  
basisfunctionbem2d  basis_dirichlet 
Type of basis function for dirichletdata.  
real *  mass 
Massmatrix of reference basis functions. More...  
field  alpha 
Boundary integral operator + mass matrix.  
uint *  v2t 
vertex to triangle map. More...  
uint *  v2ts 
Vertex to triangle map stating indices. More...  
void(*  nearfield )(const uint *ridx, const uint *cidx, pcbem2d bem, bool ntrans, pamatrix N) 
Computes nearfield entries of Galerkin matrices. More...  
void(*  farfield_rk )(pccluster rc, uint rname, pccluster cc, uint cname, pcbem2d bem, prkmatrix R) 
Computes rankkapproximations of a given block. More...  
void(*  farfield_u )(uint rname, uint cname, pcbem2d bem, puniform U) 
Computes coupling matrix for uniform matrices. More...  
void(*  leaf_row )(pcbem2d bem, pclusterbasis rb, uint rname) 
Computes the the matrix for a leaf cluster . More...  
void(*  leaf_col )(pcbem2d bem, pclusterbasis cb, uint cname) 
Computes the the matrix for a leaf cluster . More...  
void(*  transfer_row )(pcbem2d bem, pclusterbasis rb, uint rname) 
Computes the transfermatrices for a cluster . More...  
void(*  transfer_col )(pcbem2d bem, pclusterbasis cb, uint cname) 
Computes the transfermatrices for a cluster . More...  
paprxbem2d  aprx 
A collection of necessary data structures for approximating matrices with various techniques. More...  
pparbem2d  par 
Some helpers to make parallel computations possible. More...  
pkernelbem2d  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 bem2d object is not intended, though possible. Therefore call a problem specific constructor such as new_slp_laplace_bem2d or new_dlp_laplace_bem2d . 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 bem2d object. Afterwards you can build up your desired matrix approximation with a few simple functions calls, delivered by the bem2d object, using your favored approximation technique. Calling another of these " set " functions will reinitialize the bem2d object and you can build another approximation with a different technique.
paprxbem2d 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 . 
bem  BEMobject containing additional information for computation of the matrix entries. 
U  An Object of type uniform containing the coupling matrix , the row clusterbasis U>rb and the column clusterbasis U>cb . 
pccurve2d gr 
pkernelbem2d 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_bem2d and new_dlp_laplace_bem2d should serve.
void(* leaf_col) (pcbem2d bem, pclusterbasis cb, uint cname) 
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. 
cb  current column clusterbasis. The Matrix will be saved into cb>V . 
cname  Enumerated number of current column clusterbasis cb . 
void(* leaf_row) (pcbem2d bem, pclusterbasis rb, uint rname) 
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. 
rb  current row clusterbasis. The Matrix will be saved into rb>V . 
rname  Enumerated number of current row clusterbasis 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  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

pparbem2d 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.
psingquad1d sq 
Quadrature rules used within BEM computation.
Singular quadrature formulas used within boundaryintegralOperator computation.
void(* transfer_col) (pcbem2d bem, pclusterbasis cb, uint cname) 
Computes the transfermatrices 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. 
cb  Current column clusterbasis. The Matrices will be saved into cb>son[s'1]>E . 
cname  Enumerated number of current column clusterbasis cb . 
void(* transfer_row) (pcbem2d bem, pclusterbasis rb, uint rname) 
Computes the transfermatrices 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. 
rb  Current row clusterbasis. The Matrices will be saved into rb>son[t'1]>E . 
rname  Enumerated number of current row clusterbasis rb . 
uint* v2t 
vertex to triangle map.
A list of triangle indices corresponding to each vertex index. A vertex is part of all triangles ranging from
uint* v2ts 