H2Lib
3.0
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This module contains functions to setup and solve boundary integral equations for the Laplace operator in 2D. More...
Functions | |
pbem2d | new_slp_laplace_bem2d (pccurve2d gr, uint q, basisfunctionbem2d basis) |
Creates a new bem2d-object for computation of single layer potential matrix. More... | |
pbem2d | new_dlp_laplace_bem2d (pccurve2d gr, uint q, basisfunctionbem2d basis_neumann, basisfunctionbem2d basis_dirichlet, field alpha) |
Creates a new bem2d-object for computation of double layer potential matrix. More... | |
field | eval_dirichlet_linear_laplacebem2d (const real *x, const real *n) |
A simple linear harmonic function that will serve as dirichlet values. More... | |
field | eval_neumann_linear_laplacebem2d (const real *x, const real *n) |
A simple linear harmonic function that will serve as neumann values. More... | |
field | eval_dirichlet_quadratic_laplacebem2d (const real *x, const real *n) |
A simple quadratic harmonic function that will serve as dirichlet values. More... | |
field | eval_neumann_quadratic_laplacebem2d (const real *x, const real *n) |
A simple quadratic harmonic function that will serve as neumann values. More... | |
This module contains functions to setup and solve boundary integral equations for the Laplace operator in 2D.
A simple linear harmonic function that will serve as dirichlet values.
When computing the neumann data out of the dirichlet data one can use this function as test data which will generate dirichlet values of with the following values:
Corresponding neumann data can be generated by using eval_neumann_linear_laplacebem2d.
To build up an appropriate dirichlet data coefficient vector one needs the -projection. This can be done by passing this function to projectl2_bem2d_const_avector for piecewise constant basis functions.
x | Evaluation point. |
n | Normal vector to current evaluation point. |
A simple quadratic harmonic function that will serve as dirichlet values.
When computing the neumann data out of the dirichlet data one can use this function as test data which will generate dirichlet values of with the following values:
Corresponding neumann data can be generated by using eval_neumann_quadratic_laplacebem2d.
To build up an appropriate dirichlet data coefficient vector one needs the -projection. This can be done by passing this function to projectl2_bem2d_const_avector for piecewise constant basis functions.
x | Evaluation point. |
n | Normal vector to current evaluation point. |
A simple linear harmonic function that will serve as neumann values.
When computing the neumann data out of the dirichlet data one can use this function as test data which will generate neumann values of with the following values:
Corresponding dirichlet data can be generated by using eval_dirichlet_linear_laplacebem2d.
To build up an appropriate neumann data coefficient vector one needs the -projection. This can be done by passing this function to projectl2_bem2d_const_avector for piecewise constant basis functions.
x | Evaluation point. |
n | Normal vector to current evaluation point. |
A simple quadratic harmonic function that will serve as neumann values.
When computing the neumann data out of the dirichlet data one can use this function as test data which will generate neumann values of with the following values:
Corresponding dirichlet data can be generated by using eval_dirichlet_quadratic_laplacebem2d.
To build up an appropriate neumann data coefficient vector one needs the -projection. This can be done by passing this function to projectl2_bem2d_const_avector for piecewise constant basis functions.
x | Evaluation point. |
n | Normal vector to current evaluation point. |
pbem2d new_dlp_laplace_bem2d | ( | pccurve2d | gr, |
uint | q, | ||
basisfunctionbem2d | basis_neumann, | ||
basisfunctionbem2d | basis_dirichlet, | ||
field | alpha | ||
) |
Creates a new bem2d-object for computation of double layer potential matrix.
After calling this function the resulting bem-object will provide all functionality that is necessary to build up fully populated double layer potential matrix and also hmatrix or h2matrix approximation of this matrix.
gr | Polygonal, two dimensional geometry. |
q | Order of gaussian quadrature used within computation of matrix entries. |
basis_neumann | Type of basis functions used for neumann data. |
basis_dirichlet | Type of basis functions used for dirichlet data. |
alpha | Double layer operator + mass matrix. |
pbem2d new_slp_laplace_bem2d | ( | pccurve2d | gr, |
uint | q, | ||
basisfunctionbem2d | basis | ||
) |
Creates a new bem2d-object for computation of single layer potential matrix.
After calling this function the resulting bem-object will provide all functionality that is necessary to build up fully populated single layer potential matrix and also hmatrix or h2matrix approximation of this matrix.
gr | Polygonal, two dimensional geometry. |
q | Order of gaussian quadrature used within computation of matrix entries. |
basis | Type of basis functions used for neumann data. |