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| subroutine, public | dbc_mod::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...
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| real(kind=8) function, public | dbc_mod::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...
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| real(kind=8) function, dimension(3) | dbc_mod::dbc_triangle2dbarycoords (xs, ys, x, y) |
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| integer, parameter | dbc_mod::ngauss =6 |
| | number of points for the Gauss-quadrature over a unit triangle More...
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| real(kind=8), parameter | dbc_mod::pi = 4*atan(1.0D0) |
| | value for pi used inside the module. More...
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| real(kind=8), dimension(6), parameter | dbc_mod::xi =(/ 0.816847572980459D0, 0.091576213509771D0, 0.091576213509771D0, 0.108103018168070D0, 0.445948490915965D0, 0.445948490915965D0 /) |
| | x coordinates for the Gauss-quadrature over a unit triangle More...
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| real(kind=8), dimension(6), parameter | dbc_mod::yi =(/ 0.091576213509771D0, 0.816847572980459D0, 0.091576213509771D0, 0.445948490915965D0, 0.108103018168070D0, 0.445948490915965D0 /) |
| | y coordinates for the Gauss-quadrature over a unit triangle More...
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| real(kind=8), dimension(6), parameter | dbc_mod::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...
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