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 neumann-data.

basisfunctionbem3d	col_basis
	Type of basis function for dirichlet-data.

real *	mass
	Mass-matrix of reference basis functions. More...

field	alpha
	Boundary integral operator + $\alpha$ 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 rank-k-approximations 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 $t \in \mathcal L_{\mathcal I}$ . More...

void(*	leaf_wave_row )(uint rname, pcbem3d bem)
	Computes the the matrix $V_{t,c_\iota}$ for a leaf cluster $t \in \mathcal L_{\mathcal I}$ and a direction $c_\iota$ . More...

void(*	leaf_col )(uint cname, pcbem3d bem)
	Computes the the matrix for a leaf cluster $s \in \mathcal L_{\mathcal J}$ . More...

void(*	leaf_wave_col )(uint cname, pcbem3d bem)
	Computes the the matrix $W_{s, c_\iota}$ for a leaf cluster $s \in \mathcal L_{\mathcal J}$ and a direction $c_\iota$ . More...

void(*	transfer_row )(uint rname, pcbem3d bem)
	Computes the transfer matrices $E_{t'}$ for a cluster $t \in \mathcal T_{\mathcal I} \, , t' \in \operatorname{sons}(t)$ . More...

void(*	transfer_wave_row )(uint rname, pcbem3d bem)
	Computes the transfer matrices $E_{t', c_\iota}$ for a cluster $t \in \mathcal T_{\mathcal I} \, , t' \in \operatorname{sons}(t)$ and directions $c_\iota$ . The father cluster is using the wave-Lagrange basis while the sons $t' \in \operatorname{sons}(t)$ use the standard Lagrange basis. More...

void(*	transfer_wave_wave_row )(uint rname, pcbem3d bem)
	Computes the transfer matrices $E_{t', c_\iota}$ for a cluster $t \in \mathcal T_{\mathcal I} \, , t' \in \operatorname{sons}(t)$ and directions $c_\iota$ . Both, the father cluster and sons $t' \in \operatorname{sons}(t)$ are using the wave-Lagrange basis. More...

void(*	transfer_col )(uint cname, pcbem3d bem)
	Computes the transfer matrices $F_{s'}$ for a cluster $s \in \mathcal T_{\mathcal J} \, , s' \in \operatorname{sons}(s)$ . More...

void(*	transfer_wave_col )(uint cname, pcbem3d bem)
	Computes the transfer matrices $F_{s', c_\iota}$ for a cluster $s \in \mathcal T_{\mathcal J} \, , s' \in \operatorname{sons}(s)$ and directions $c_\iota$ . The father cluster is using the wave-Lagrange basis while the sons $s' \in \operatorname{sons}(s)$ use the standard Lagrange basis. More...

void(*	transfer_wave_wave_col )(uint cname, pcbem3d bem)
	Computes the transfer matrices $F_{s', c_\iota}$ for a cluster $s \in \mathcal T_{\mathcal J} \, , s' \in \operatorname{sons}(s)$ and directions $c_\iota$ . Both, the father cluster and sons $s' \in \operatorname{sons}(s)$ are using the wave-Lagrange 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...

Detailed Description

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.

Field Documentation

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.

void(* farfield_rk) (pccluster rc, uint rname, pccluster cc, uint cname, pcbem3d bem, prkmatrix R)

Computes rank-k-approximations of a given block.

This callback function computes a rank-k-approximation of a matrix block given by row cluster rc and column cluster cc. The Matrices A and B are stored in a rank-k-matrix R.

Parameters

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	BEM-object containing additional information for computation of the matrix entries.
R	Rank-k-matrix, which takes up the resulting matrices `A` and `B` . The rank k is defined by the underlying approximation technique.

void(* farfield_u) (uint rname, uint cname, uint bname, pcbem3d bem)

Computes coupling matrix $ S_b $ for uniform matrices.

While using h2-matrices the coupling matrices $ S_b $ are computed by this callback function. Coupling matrices are stored in the struct uniform defining a certain block of the whole h2-matrix.

Parameters

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	BEM-object containing additional information for computation of the matrix entries.

void(* farfield_wave_u) (uint rname, uint cname, uint bname, pcbem3d bem)

Computes coupling matrix $ S_b^c $ for duniform matrices for some direction $c$ .

While using Dh2-matrices the coupling matrices $ S_b^c $ are computed by this callback function. Coupling matrices are stored in the struct duniform defining a certain block of the whole Dh2-matrix.

Parameters

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	BEM-object containing additional information for computation of the matrix entries.

pcsurface3d gr

Polyedric 3 dimensional surface mesh.

Polyedric boundary mesh used for the BEM-problem.

See also: _surface3d.

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 dirichlet-data. As an example the constructors new_slp_laplace_bem3d and new_dlp_laplace_bem3d should serve.

See also: kernelbem2d

void(* leaf_col) (uint cname, pcbem3d bem)

Computes the the matrix $ W_s $ for a leaf cluster $s \in \mathcal L_{\mathcal J}$ .

leaf_col is used for building up a clusterbasis for the set $\mathcal L_{\mathcal J}$ for h2matrices. For each $s \in \mathcal L_{\mathcal J}$ leaf_col will construct the matrix $ W_s $ . In case of nested clusterbasis transfer_col has also to be set to a valid function constructing suitable transfer matrices $ F_s $ .

Parameters

bem	BEM-object containing additional information for computation of the matrix entries.
cname	Enumerated number of current column clusterbasis `cb`.

void(* leaf_row) (uint rname, pcbem3d bem)

Computes the the matrix $ V_t $ for a leaf cluster $t \in \mathcal L_{\mathcal I}$ .

leaf_row is used for building up a clusterbasis for the set $\mathcal L_{\mathcal I}$ for h2matrices. For each $t \in \mathcal L_{\mathcal I}$ leaf_row will construct the matrix $ V_t $ . In case of nested clusterbasis transfer_row has also to be set to a valid function constructing suitable transfer matrices $ E_t $ .

Parameters

bem	BEM-object containing additional information for computation of the matrix entries.
rname	Enumerated number of current row clusterbasis `rb`.

void(* leaf_wave_col) (uint cname, pcbem3d bem)

Computes the the matrix $W_{s, c_\iota}$ for a leaf cluster $s \in \mathcal L_{\mathcal J}$ and a direction $c_\iota$ .

leaf_wave_col is used for building up a dclusterbasis for the set $\mathcal L_{\mathcal J}$ for Dh2matrices. For each $s \in \mathcal L_{\mathcal J}$ and for all directions $c_\iota$ leaf_wave_col will construct the matrix $W_{s, c_\iota}$ . 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 $F_{s, c_\iota}$ .

Parameters

bem	BEM-object containing additional information for computation of the matrix entries.
cname	Enumerated number of current column dclusterbasis `cb`.

void(* leaf_wave_row) (uint rname, pcbem3d bem)

Computes the the matrix $V_{t,c_\iota}$ for a leaf cluster $t \in \mathcal L_{\mathcal I}$ and a direction $c_\iota$ .

leaf_wave_row is used for building up a dclusterbasis for the set $\mathcal L_{\mathcal I}$ for Dh2matrices. For each $t \in \mathcal L_{\mathcal I}$ and all directions $c_\iota$ . leaf_wave_row will construct the matrix $V_{t,c_\iota}$ . 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 $E_{t,c_\iota}$ .

Parameters

bem	BEM-object containing additional information for computation of the matrix entries.
rname	Enumerated number of current row dclusterbasis `rb`.

real* mass

Mass-matrix of reference basis functions.

Mass-matrix for all combinations of reference basis functions $\widehat\varphi_i$ and $\widehat\psi_j$ . Entries are computed as:

$M_{ij} = \int_\Gamma \widehat\varphi_i(x) \cdot \widehat\psi_j(x) \, \mathrm d x$

void(* nearfield) (const uint *ridx, const uint *cidx, pcbem3d bem, bool ntrans, pamatrix N)

Computes nearfield entries of Galerkin matrices.

This callback function computes 'nearfield' entries of the underlying problem and integral-operator.

Parameters

ridx	Defines the indices of row boundary elements used. If `ridx` equals NULL, then Elements `0, ..., N->rows-1` are used.
cidx	Defines the indices of column boundary elements used. If `cidx` equals NULL, then Elements `0, ..., N->cols-1` 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: $N_{ij} = \int_\Gamma \int_\Gamma \varphi_i(x) \, g(x,y) \, \psi_j(y) \, \mathrm d y \, \mathrm d x \, ,$ otherwise they are stored as $N_{ji} = \int_\Gamma \int_\Gamma \varphi_i(x) \, g(x,y) \, \psi_j(y) \, \mathrm d y \, \mathrm d x \, .$

void(* nearfield_far) (const uint *ridx, const uint *cidx, pcbem3d bem, bool ntrans, pamatrix N)

Computes nearfield entries of Galkerin matrices for disjoint clusters.

This callback function computes 'nearfield' entries of the underlying problem and integral-operator.

Parameters

ridx	Defines the indices of row boundary elements used. If `ridx` equals NULL, then Elements `0, ..., N->rows-1` are used.
cidx	Defines the indices of column boundary elements used. If `cidx` equals NULL, then Elements `0, ..., N->cols-1` 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: $N_{ij} = \int_\Gamma \int_\Gamma \varphi_i(x) \, g(x,y) \, \psi_j(y) \, \mathrm d y \, \mathrm d x \, ,$ otherwise they are stored as $N_{ji} = \int_\Gamma \int_\Gamma \varphi_i(x) \, g(x,y) \, \psi_j(y) \, \mathrm d y \, \mathrm d x \, .$

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 boundary-integral-Operator computation.

See also: _singquad2d.

void(* transfer_col) (uint cname, pcbem3d bem)

Computes the transfer matrices $F_{s'}$ for a cluster $s \in \mathcal T_{\mathcal J} \, , s' \in \operatorname{sons}(s)$ .

transfer_col will build up the transfer matrices $F_{s'}$ , for all $s \in \mathcal T_{\mathcal J}$ and $s' \in \operatorname{sons}(s)$ . For a cluster $s \in \mathcal T_{\mathcal J}$ transfer_col will compute the matrices $F_{s_1}, \ldots, F_{s_\sigma}$ , $\# \operatorname{sons}(s) = \sigma$ . The matrix $F_{s_1}$ is stored in cb->son[0]->E, $F_{s_2}$ is stored in cb->son[1]->E, $\ldots F_{t_\sigma}$ is stored in cb->son[ ]->E .

Parameters

bem	BEM-object containing additional information for computation of the matrix entries.
cname	Enumerated number of current column clusterbasis `cb`.

void(* transfer_row) (uint rname, pcbem3d bem)

Computes the transfer matrices $E_{t'}$ for a cluster $t \in \mathcal T_{\mathcal I} \, , t' \in \operatorname{sons}(t)$ .

transfer_row will build up the transfer matrices $E_{t'}$ , for all $t \in \mathcal T_{\mathcal I}$ and $t' \in \operatorname{sons}(t)$ . For a cluster $t \in \mathcal T_{\mathcal I}$ transfer_row will compute the matrices $E_{t_1}, \ldots, E_{t_\tau}$ , $\# \operatorname{sons}(t) = \tau$ . The matrix $E_{t_1}$ is stored in rb->son[0]->E, $E_{t_2}$ is stored in rb->son[1]->E, $\ldots E_{t_\tau}$ is stored in rb->son[ ]->E .

Parameters

bem	BEM-object containing additional information for computation of the matrix entries.
rname	Enumerated number of current row clusterbasis `rb`.

void(* transfer_wave_col) (uint cname, pcbem3d bem)

Computes the transfer matrices $F_{s', c_\iota}$ for a cluster $s \in \mathcal T_{\mathcal J} \, , s' \in \operatorname{sons}(s)$ and directions $c_\iota$ . The father cluster $s$ is using the wave-Lagrange basis while the sons $s' \in \operatorname{sons}(s)$ use the standard Lagrange basis.

transfer_wave_col will build up the transfer matrices $F_{s', c_\iota}$ , for all $s \in \mathcal T_{\mathcal J}$ and $s' \in \operatorname{sons}(s)$ and directions $c_\iota$ . For a cluster $s \in \mathcal T_{\mathcal J}$ transfer_wave_col will compute the matrices $F_{s_1, c_1}, \ldots, F_{s_1, c_d}, \ldots F_{s_\sigma, c_1}, \ldots F_{s_\sigma, c_d}$ , $\# \operatorname{sons}(s) = \sigma$ and $\iota \in \{ 1, \ldots, d \}$ . The matrix $F_{s_1, c_1}$ is stored in cb->son[0]->E + 0, $F_{s_1, c_2}$ is stored in cb->son[0]->E + 1, $\ldots F_{s_\tau, c_d}$ is stored in cb->son[ ]->E + (d - 1) .

Parameters

bem	BEM-object containing additional information for computation of the matrix entries.
cname	Enumerated number of current column dclusterbasis `cb`.

void(* transfer_wave_row) (uint rname, pcbem3d bem)

Computes the transfer matrices $E_{t', c_\iota}$ for a cluster $t \in \mathcal T_{\mathcal I} \, , t' \in \operatorname{sons}(t)$ and directions $c_\iota$ . The father cluster $t$ is using the wave-Lagrange basis while the sons $t' \in \operatorname{sons}(t)$ use the standard Lagrange basis.

transfer_wave_row will build up the transfer matrices $E_{t', c_\iota}$ , for all $t \in \mathcal T_{\mathcal I}$ and $t' \in \operatorname{sons}(t)$ and directions $c_\iota$ . For a cluster $t \in \mathcal T_{\mathcal I}$ transfer_wave_row will compute the matrices $E_{t_1, c_1}, \ldots, E_{t_1, c_d}, \ldots E_{t_\tau, c_1}, \ldots E_{t_\tau, c_d}$ , $\# \operatorname{sons}(t) = \tau$ and $\iota \in \{ 1, \ldots, d \}$ . The matrix $E_{t_1, c_1}$ is stored in rb->son[0]->E + 0, $E_{t_1, c_2}$ is stored in rb->son[0]->E + 1, $\ldots E_{t_\tau, c_d}$ is stored in rb->son[ ]->E + (d - 1) .

Parameters

bem	BEM-object containing additional information for computation of the matrix entries.
rname	Enumerated number of current row dclusterbasis `rb`.

void(* transfer_wave_wave_col) (uint cname, pcbem3d bem)

Computes the transfer matrices $F_{s', c_\iota}$ for a cluster $s \in \mathcal T_{\mathcal J} \, , s' \in \operatorname{sons}(s)$ and directions $c_\iota$ . Both, the father cluster $s$ and sons $s' \in \operatorname{sons}(s)$ are using the wave-Lagrange basis.

transfer_wave_wave_col will build up the transfer matrices $F_{s', c_\iota}$ , for all $s \in \mathcal T_{\mathcal J}$ and $s' \in \operatorname{sons}(s)$ and directions $c_\iota$ . For a cluster $s \in \mathcal T_{\mathcal J}$ transfer_wave_wave_col will compute the matrices $F_{s_1, c_1}, \ldots, F_{s_1, c_d}, \ldots F_{s_\sigma, c_1}, \ldots F_{s_\sigma, c_d}$ , $\# \operatorname{sons}(s) = \sigma$ and $\iota \in \{ 1, \ldots, d \}$ . The matrix $F_{s_1, c_1}$ is stored in cb->son[0]->E + 0, $F_{s_1, c_2}$ is stored in cb->son[0]->E + 1, $\ldots F_{t_\sigma, c_d}$ is stored in cb->son[ ]->E + (d - 1) . The used directions $c_\iota$ correspond to some difference between directions $c^f_\iota$ used for the father $t$ and directions $c^s_\iota$ . Therefore it holds

$c_\iota = c^f_\iota - c^s_\iota = c^f_\iota - \operatorname{sondir}(c^f_\iota)$

Parameters

bem	BEM-object containing additional information for computation of the matrix entries.
cname	Enumerated number of current column dclusterbasis `cb`.

void(* transfer_wave_wave_row) (uint rname, pcbem3d bem)

Computes the transfer matrices $E_{t', c_\iota}$ for a cluster $t \in \mathcal T_{\mathcal I} \, , t' \in \operatorname{sons}(t)$ and directions $c_\iota$ . Both, the father cluster $t$ and sons $t' \in \operatorname{sons}(t)$ are using the wave-Lagrange basis.

transfer_wave_wave_row will build up the transfer matrices $E_{t', c_\iota}$ , for all $t \in \mathcal T_{\mathcal I}$ and $t' \in \operatorname{sons}(t)$ and directions $c_\iota$ . For a cluster $t \in \mathcal T_{\mathcal I}$ transfer_wave_wave_row will compute the matrices $E_{t_1, c_1}, \ldots, E_{t_1, c_d}, \ldots E_{t_\tau, c_1}, \ldots E_{t_\tau, c_d}$ , $\# \operatorname{sons}(t) = \tau$ and $\iota \in \{ 1, \ldots, d \}$ . The matrix $E_{t_1, c_1}$ is stored in rb->son[0]->E + 0, $E_{t_1, c_2}$ is stored in rb->son[0]->E + 1, $\ldots E_{t_\tau, c_d}$ is stored in rb->son[ ]->E + (d - 1) . The used directions $c_\iota$ correspond to some difference between directions $c^f_\iota$ used for the father $t$ and directions $c^s_\iota$ . Therefore it holds

$c_\iota = c^f_\iota - c^s_\iota = c^f_\iota - \operatorname{sondir}(c^f_\iota)$

Parameters

bem	BEM-object 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 $ i $ the list v2t[i] enumerates all triangles that share this vertex $ i $ .
This can be usefull within computation of matrix entries when linear basis functions are involved.

The documentation for this struct was generated from the following file:

Library/bem3d.h

Data Fields

Detailed Description

Field Documentation