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GaussLegendre1D.h
GaussLegendre1D.h 11.31 KiB
// Gmsh - Copyright (C) 1997-2019 C. Geuzaine, J.-F. Remacle
//
// See the LICENSE.txt file for license information. Please report all
// issues on https://gitlab.onelab.info/gmsh/gmsh/issues.
/* 1 point rule points */
static double GL_pt1[1] = {0.000000000000000e+00};
/* 1 point rule weights */
static double GL_wt1[1] = {2.000000000000000e+00};
/* 2 point rule points */
static double GL_pt2[2] = {-5.773502691896257e-01, 5.773502691896257e-01};
/* 2 point rule weights */
static double GL_wt2[2] = {1.000000000000000e+00, 1.000000000000000e+00};
/* 3 point rule points */
static double GL_pt3[3] = {-7.745966692414834e-01, 0.000000000000000e+00,
7.745966692414834e-01};
/* 3 point rule weights */
static double GL_wt3[3] = {5.555555555555552e-01, 8.888888888888888e-01,
5.555555555555552e-01};
/* 4 point rule points */
static double GL_pt4[4] = {-8.611363115940526e-01, -3.399810435848563e-01,
3.399810435848563e-01, 8.611363115940526e-01};
/* 4 point rule weights */
static double GL_wt4[4] = {3.478548451374537e-01, 6.521451548625464e-01,
6.521451548625464e-01, 3.478548451374537e-01};
/* 5 point rule points */
static double GL_pt5[5] = {-9.061798459386640e-01, -5.384693101056831e-01,
0.000000000000000e+00, 5.384693101056831e-01,
9.061798459386640e-01};
/* 5 point rule weights */
static double GL_wt5[5] = {2.369268850561890e-01, 4.786286704993665e-01,
5.688888888888889e-01, 4.786286704993665e-01,
2.369268850561890e-01};
/* 6 point rule points */
static double GL_pt6[6] = {-9.324695142031521e-01, -6.612093864662646e-01,
-2.386191860831969e-01, 2.386191860831969e-01,
6.612093864662646e-01, 9.324695142031521e-01};
/* 6 point rule weights */
static double GL_wt6[6] = {1.713244923791705e-01, 3.607615730481386e-01,
4.679139345726913e-01, 4.679139345726913e-01,
3.607615730481386e-01, 1.713244923791705e-01};
/* 7 point rule points */
static double GL_pt7[7] = {-9.491079123427585e-01, -7.415311855993945e-01,
-4.058451513773972e-01, 0.000000000000000e+00,
4.058451513773972e-01, 7.415311855993945e-01,
9.491079123427585e-01};
/* 7 point rule weights */
static double GL_wt7[7] = {1.294849661688697e-01, 2.797053914892767e-01,
3.818300505051190e-01, 4.179591836734694e-01,
3.818300505051190e-01, 2.797053914892767e-01,
1.294849661688697e-01};
/* 8 point rule points */
static double GL_pt8[8] = {-9.602898564975363e-01, -7.966664774136268e-01,
-5.255324099163290e-01, -1.834346424956498e-01,
1.834346424956498e-01, 5.255324099163290e-01,
7.966664774136268e-01, 9.602898564975363e-01};
/* 8 point rule weights */
static double GL_wt8[8] = {1.012285362903768e-01, 2.223810344533745e-01,
3.137066458778874e-01, 3.626837833783620e-01,
3.626837833783620e-01, 3.137066458778874e-01,
2.223810344533745e-01, 1.012285362903768e-01};
/* 9 point rule points */
static double GL_pt9[9] = {
-9.681602395076261e-01, -8.360311073266359e-01, -6.133714327005905e-01,
-3.242534234038089e-01, 0.000000000000000e+00, 3.242534234038089e-01,
6.133714327005905e-01, 8.360311073266359e-01, 9.681602395076261e-01};
/* 9 point rule weights */
static double GL_wt9[9] = {
8.127438836157463e-02, 1.806481606948576e-01, 2.606106964029355e-01,
3.123470770400029e-01, 3.302393550012598e-01, 3.123470770400029e-01,
2.606106964029355e-01, 1.806481606948576e-01, 8.127438836157463e-02};
/* 10 point rule points */
static double GL_pt10[10] = {-9.739065285171716e-01, -8.650633666889845e-01,
-6.794095682990244e-01, -4.333953941292472e-01,
-1.488743389816312e-01, 1.488743389816312e-01,
4.333953941292472e-01, 6.794095682990244e-01,
8.650633666889845e-01, 9.739065285171716e-01};
/* 10 point rule weights */
static double GL_wt10[10] = {6.667134430868774e-02, 1.494513491505805e-01,
2.190863625159822e-01, 2.692667193099962e-01,
2.955242247147529e-01, 2.955242247147529e-01,
2.692667193099962e-01, 2.190863625159822e-01,
1.494513491505805e-01, 6.667134430868774e-02};
/* 11 point rule points */
static double GL_pt11[11] = {
-9.782286581460570e-01, -8.870625997680953e-01, -7.301520055740494e-01,
-5.190961292068118e-01, -2.695431559523450e-01, 0.000000000000000e+00,
2.695431559523450e-01, 5.190961292068118e-01, 7.301520055740494e-01,
8.870625997680953e-01, 9.782286581460570e-01};
/* 11 point rule weights */
static double GL_wt11[11] = {
5.566856711617354e-02, 1.255803694649047e-01, 1.862902109277343e-01,
2.331937645919903e-01, 2.628045445102466e-01, 2.729250867779006e-01,
2.628045445102466e-01, 2.331937645919903e-01, 1.862902109277343e-01,
1.255803694649047e-01, 5.566856711617354e-02};
/* 12 point rule points */
static double GL_pt12[12] = {
-9.815606342467192e-01, -9.041172563704748e-01, -7.699026741943047e-01,
-5.873179542866175e-01, -3.678314989981802e-01, -1.252334085114689e-01,
1.252334085114689e-01, 3.678314989981802e-01, 5.873179542866175e-01,
7.699026741943047e-01, 9.041172563704748e-01, 9.815606342467192e-01};
/* 12 point rule weights */
static double GL_wt12[12] = {
4.717533638651183e-02, 1.069393259953182e-01, 1.600783285433463e-01,
2.031674267230658e-01, 2.334925365383548e-01, 2.491470458134029e-01,
2.491470458134029e-01, 2.334925365383548e-01, 2.031674267230658e-01,
1.600783285433463e-01, 1.069393259953182e-01, 4.717533638651183e-02};
/* 13 point rule points */
static double GL_pt13[13] = {
-9.841830547185881e-01, -9.175983992229780e-01, -8.015780907333099e-01,
-6.423493394403402e-01, -4.484927510364468e-01, -2.304583159551348e-01,
1.232595164407831e-32, 2.304583159551348e-01, 4.484927510364468e-01,
6.423493394403402e-01, 8.015780907333099e-01, 9.175983992229780e-01,
9.841830547185881e-01};
/* 13 point rule weights */
static double GL_wt13[13] = { 4.048400476531581e-02, 9.212149983772838e-02, 1.388735102197872e-01,
1.781459807619457e-01, 2.078160475368884e-01, 2.262831802628971e-01,
2.325515532308739e-01, 2.262831802628971e-01, 2.078160475368884e-01,
1.781459807619457e-01, 1.388735102197872e-01, 9.212149983772838e-02,
4.048400476531581e-02};
/* 14 point rule points */
static double GL_pt14[14] = {
-9.862838086968123e-01, -9.284348836635736e-01, -8.272013150697650e-01,
-6.872929048116855e-01, -5.152486363581541e-01, -3.191123689278897e-01,
-1.080549487073437e-01, 1.080549487073437e-01, 3.191123689278897e-01,
5.152486363581541e-01, 6.872929048116855e-01, 8.272013150697650e-01,
9.284348836635736e-01, 9.862838086968123e-01};
/* 14 point rule weights */
static double GL_wt14[14] = {
3.511946033175199e-02, 8.015808715976037e-02, 1.215185706879031e-01,
1.572031671581936e-01, 1.855383974779378e-01, 2.051984637212955e-01,
2.152638534631578e-01, 2.152638534631578e-01, 2.051984637212955e-01,
1.855383974779378e-01, 1.572031671581936e-01, 1.215185706879031e-01,
8.015808715976037e-02, 3.511946033175199e-02};
/* 15 point rule points */
static double GL_pt15[15] = {
-9.879925180204854e-01, -9.372733924007060e-01, -8.482065834104272e-01,
-7.244177313601701e-01, -5.709721726085388e-01, -3.941513470775634e-01,
-2.011940939974345e-01, 1.232595164407831e-32, 2.011940939974345e-01,
3.941513470775634e-01, 5.709721726085388e-01, 7.244177313601701e-01,
8.482065834104272e-01, 9.372733924007060e-01, 9.879925180204854e-01};
/* 15 point rule weights */
static double GL_wt15[15] = {
3.075324199611663e-02, 7.036604748810814e-02, 1.071592204671720e-01,
1.395706779261543e-01, 1.662692058169940e-01, 1.861610000155622e-01,
1.984314853271116e-01, 2.025782419255613e-01, 1.984314853271116e-01,
1.861610000155622e-01, 1.662692058169940e-01, 1.395706779261543e-01,
1.071592204671720e-01, 7.036604748810814e-02, 3.075324199611663e-02};
/* 16 point rule points */
static double GL_pt16[16] = {
-9.894009349916499e-01, -9.445750230732326e-01, -8.656312023878318e-01,
-7.554044083550030e-01, -6.178762444026438e-01, -4.580167776572274e-01,
-2.816035507792589e-01, -9.501250983763744e-02, 9.501250983763744e-02,
2.816035507792589e-01, 4.580167776572274e-01, 6.178762444026438e-01,
7.554044083550030e-01, 8.656312023878318e-01, 9.445750230732326e-01,
9.894009349916499e-01};
/* 16 point rule weights */
static double GL_wt16[16] = {
2.715245941175406e-02, 6.225352393864778e-02, 9.515851168249290e-02,
1.246289712555339e-01, 1.495959888165768e-01, 1.691565193950026e-01,
1.826034150449236e-01, 1.894506104550685e-01, 1.894506104550685e-01,
1.826034150449236e-01, 1.691565193950026e-01, 1.495959888165768e-01,
1.246289712555339e-01, 9.515851168249290e-02, 6.225352393864778e-02,
2.715245941175406e-02};
/* 20 point rule points */
static double GL_pt20[20] = {
-9.931285991850949e-01, -9.639719272779138e-01, -9.122344282513259e-01,
-8.391169718222188e-01, -7.463319064601508e-01, -6.360536807265150e-01,
-5.108670019508271e-01, -3.737060887154196e-01, -2.277858511416451e-01,
-7.652652113349733e-02, 7.652652113349733e-02, 2.277858511416451e-01,
3.737060887154196e-01, 5.108670019508271e-01, 6.360536807265150e-01,
7.463319064601508e-01, 8.391169718222188e-01, 9.122344282513259e-01,
9.639719272779138e-01, 9.931285991850949e-01};
/* 20 point rule weights */
static double GL_wt20[20] = {
1.761400713915212e-02, 4.060142980038694e-02, 6.267204833410906e-02,
8.327674157670475e-02, 1.019301198172404e-01, 1.181945319615184e-01, 1.316886384491766e-01, 1.420961093183821e-01, 1.491729864726037e-01,
1.527533871307259e-01, 1.527533871307259e-01, 1.491729864726037e-01,
1.420961093183821e-01, 1.316886384491766e-01, 1.181945319615184e-01,
1.019301198172404e-01, 8.327674157670475e-02, 6.267204833410906e-02,
4.060142980038694e-02, 1.761400713915212e-02};
inline void gmshGaussLegendre1D(int nbQuadPoints, double **t, double **w)
{
switch(nbQuadPoints) {
case 1:
*t = GL_pt1;
*w = GL_wt1;
break;
case 2:
*t = GL_pt2;
*w = GL_wt2;
break;
case 3:
*t = GL_pt3;
*w = GL_wt3;
break;
case 4:
*t = GL_pt4;
*w = GL_wt4;
break;
case 5:
*t = GL_pt5;
*w = GL_wt5;
break;
case 6:
*t = GL_pt6;
*w = GL_wt6;
break;
case 7:
*t = GL_pt7;
*w = GL_wt7;
break;
case 8:
*t = GL_pt8;
*w = GL_wt8;
break;
case 9:
*t = GL_pt9;
*w = GL_wt9;
break;
case 10:
*t = GL_pt10;
*w = GL_wt10;
break;
case 11:
*t = GL_pt11;
*w = GL_wt11;
break;
case 12:
*t = GL_pt12;
*w = GL_wt12;
break;
case 13:
*t = GL_pt13;
*w = GL_wt13;
break;
case 14:
*t = GL_pt14;
*w = GL_wt14;
break;
case 15:
*t = GL_pt15;
*w = GL_wt15;
break;
case 16: *t = GL_pt16;
*w = GL_wt16;
break;
case 20:
*t = GL_pt20;
*w = GL_wt20;
break;
default:
*t = 0;
*w = 0;
break;
}
}