dbc_mod Module Reference

"(D)irichlet (B)oundary (C)onditions" A module for evaluating Dirichlet boundary conditions for the Fourier decomposed Ampere and Poisson equations. More...

Functions/Subroutines
subroutine, public	dbc_weights (weights, R, Z, n, grid)
	Returns weights \( w_i(R,Z) \) for approximating the integral \( \Phi(R,Z)=\int_{\Omega'}\frac{R' f(R',Z')}{\sqrt{R'^2+R^2+(Z-Z')^2}}g(k,n)dR'dZ' \) as \( \Phi(R,Z)\approx\sum_{i=1}^{n_{\textrm{nodes}}} w_i f_i \). Here \( g(k,n)=\int_0^{2\pi}\frac{\cos(nx)}{\sqrt{1-k\cos(x)}}dx \) and \( k(R,Z,R',Z')=\frac{2RR'}{R^2+R'^2+(R-R')^2} \). The data \( f(R',Z') \) is assumed piecewise linear over the triangulation of the domain \( \Omega \) and Gauss quadrature is used for the \( dR'dZ' \) integral. More...
real(kind=8) function, public	dbc_triangle (R, Z, RS, ZS, FS, n)
	Evaluates the integral \( Phi(R',Z')=\int_{\Delta}\frac{R' f(R',Z')}{\sqrt{R'^2+R^2+(Z-Z')^2}}g(k,n)dR'dZ' \) where \( g(k,n)=\int_0^{2\pi}\frac{\cos(nx)}{\sqrt{1-k\cos(x)}}dx \) and \( k(R,Z,R',Z')=\frac{2RR'}{R^2+R'^2+(R-R')^2} \) using linear interpolation for the data \( f(R',Z') \) over the triangle \( \Delta \) and Gauss quadrature for the \( dR'dZ' \) integral. More...
real(kind=8) function, dimension(3)	dbc_triangle2dbarycoords (xs, ys, x, y)

Variables
integer, parameter	ngauss =6
	number of points for the Gauss-quadrature over a unit triangle More...
real(kind=8), parameter	pi = 4*atan(1.0D0)
	value for pi used inside the module. More...
real(kind=8), dimension(6), parameter	xi =(/ 0.816847572980459D0, 0.091576213509771D0, 0.091576213509771D0, 0.108103018168070D0, 0.445948490915965D0, 0.445948490915965D0 /)
	x coordinates for the Gauss-quadrature over a unit triangle More...
real(kind=8), dimension(6), parameter	yi =(/ 0.091576213509771D0, 0.816847572980459D0, 0.091576213509771D0, 0.445948490915965D0, 0.108103018168070D0, 0.445948490915965D0 /)
	y coordinates for the Gauss-quadrature over a unit triangle More...
real(kind=8), dimension(6), parameter	wi =(/ 0.109951743655322D0, 0.109951743655322D0, 0.109951743655322D0, 0.223381589678011D0, 0.223381589678011D0, 0.223381589678011D0 /)
	weight for the Gauss point in Gauss-quadrature over a unit triangle More...

Detailed Description

"(D)irichlet (B)oundary (C)onditions" A module for evaluating Dirichlet boundary conditions for the Fourier decomposed Ampere and Poisson equations.

Author

Eero Hirvijoki

Function/Subroutine Documentation

dbc_triangle()

real(kind=8) function, public dbc_mod::dbc_triangle	(	real(kind=8), intent(in)	R,
		real(kind=8), intent(in)	Z,
		real(kind=8), dimension(3), intent(in)	RS,
		real(kind=8), dimension(3), intent(in)	ZS,
		real(kind=8), dimension(3), intent(in)	FS,
		integer, intent(in)	n
	)

Evaluates the integral \( Phi(R',Z')=\int_{\Delta}\frac{R' f(R',Z')}{\sqrt{R'^2+R^2+(Z-Z')^2}}g(k,n)dR'dZ' \) where \( g(k,n)=\int_0^{2\pi}\frac{\cos(nx)}{\sqrt{1-k\cos(x)}}dx \) and \( k(R,Z,R',Z')=\frac{2RR'}{R^2+R'^2+(R-R')^2} \) using linear interpolation for the data \( f(R',Z') \) over the triangle \( \Delta \) and Gauss quadrature for the \( dR'dZ' \) integral.

Author

Eero Hirvijoki

Parameters

[in]	R	cylindrical R for the position where to evaluate the integral
[in]	Z	cylindrical Z for the position where to evaluate the integral
[in]	RS	cylindrical R for the triangle vertices
[in]	ZS	cylindrical Z for the triangle vertices
[in]	FS	the function \( f(R,Z) \) values at the triangle vertices
[in]	n	the mode number for the toroidal angular integrals.

Todo:

Right now I'm not aware of anything that should be improved.

Here is the call graph for this function:

Here is the caller graph for this function:

dbc_triangle2dbarycoords()

real(kind=8) function, dimension(3) dbc_mod::dbc_triangle2dbarycoords ( real(kind=8), dimension(3), intent(in)  xs, real(kind=8), dimension(3), intent(in)  ys, real(kind=8), intent(in)  x, real(kind=8), intent(in)  y  )

private

Here is the caller graph for this function:

dbc_weights()

subroutine, public dbc_mod::dbc_weights	(	real(kind=8), dimension(grid%nnode), intent(out)	weights,
		real(kind=8), intent(in)	R,
		real(kind=8), intent(in)	Z,
		integer, intent(in)	n,
		type(grid_type), intent(in)	grid
	)

Returns weights \( w_i(R,Z) \) for approximating the integral \( \Phi(R,Z)=\int_{\Omega'}\frac{R' f(R',Z')}{\sqrt{R'^2+R^2+(Z-Z')^2}}g(k,n)dR'dZ' \) as \( \Phi(R,Z)\approx\sum_{i=1}^{n_{\textrm{nodes}}} w_i f_i \). Here \( g(k,n)=\int_0^{2\pi}\frac{\cos(nx)}{\sqrt{1-k\cos(x)}}dx \) and \( k(R,Z,R',Z')=\frac{2RR'}{R^2+R'^2+(R-R')^2} \). The data \( f(R',Z') \) is assumed piecewise linear over the triangulation of the domain \( \Omega \) and Gauss quadrature is used for the \( dR'dZ' \) integral.

Author

Eero Hirvijoki

Parameters

[out]	weights	the precomputed weights for evaluating the integral
[in]	R	cylindrical R of the position for which the weights are precomputed
[in]	Z	cylindrical Z of the position for which the weights are precomputed
[in]	n	the mode number for the angular integrals.
[in]	grid	the structure containing the mesh and connectivity

Todo:

Right now I'm not aware of anything that should be improved.

Here is the call graph for this function:

Here is the caller graph for this function:

Variable Documentation

ngauss

integer, parameter dbc_mod::ngauss =6

private

number of points for the Gauss-quadrature over a unit triangle

pi

real(kind=8), parameter dbc_mod::pi = 4*atan(1.0D0)

private

value for pi used inside the module.

wi

real(kind=8), dimension(6), parameter dbc_mod::wi =(/ 0.109951743655322D0, 0.109951743655322D0, 0.109951743655322D0, 0.223381589678011D0, 0.223381589678011D0, 0.223381589678011D0 /)

private

weight for the Gauss point in Gauss-quadrature over a unit triangle

xi

real(kind=8), dimension(6), parameter dbc_mod::xi =(/ 0.816847572980459D0, 0.091576213509771D0, 0.091576213509771D0, 0.108103018168070D0, 0.445948490915965D0, 0.445948490915965D0 /)

private

x coordinates for the Gauss-quadrature over a unit triangle

yi

real(kind=8), dimension(6), parameter dbc_mod::yi =(/ 0.091576213509771D0, 0.816847572980459D0, 0.091576213509771D0, 0.445948490915965D0, 0.108103018168070D0, 0.445948490915965D0 /)

private

y coordinates for the Gauss-quadrature over a unit triangle