// GetDP - Copyright (C) 1997-2018 P. Dular and C. Geuzaine, University of Liege // // See the LICENSE.txt file for license information. Please report all // bugs and problems to the public mailing list <getdp@onelab.info>. #include <math.h> #include "Gauss.h" #include "Gauss_Triangle.h" #include "Message.h" #include "MallocUtils.h" /* Gauss Integration over a triangle */ void Gauss_Triangle(int Nbr_Points, int Num, double *u, double *v, double *w, double *wght) { switch (Nbr_Points) { case 1 : *u= xt1 [Num] ; *v= yt1 [Num] ; *w= 0. ; *wght= pt1 [Num] ; break ; case 3 : *u= xt3 [Num] ; *v= yt3 [Num] ; *w= 0. ; *wght= pt3 [Num] ; break ; case 4 : *u= xt4 [Num] ; *v= yt4 [Num] ; *w= 0. ; *wght= pt4 [Num] ; break ; case 6 : *u= xt6 [Num] ; *v= yt6 [Num] ; *w= 0. ; *wght= pt6 [Num] ; break ; case 7 : *u= xt7 [Num] ; *v= yt7 [Num] ; *w= 0. ; *wght= pt7 [Num] ; break ; case 12 : *u= xt12[Num] ; *v= yt12[Num] ; *w= 0. ; *wght= pt12[Num] ; break ; case 13 : *u= xt13[Num] ; *v= yt13[Num] ; *w= 0. ; *wght= pt13[Num] ; break ; case 16 : *u= xt16[Num] ; *v= yt16[Num] ; *w= 0. ; *wght= pt16[Num] ; break ; default : Message::Error("Wrong number of Gauss points for Triangle: " "valid choices: 1, 3, 4, 6, 7, 12, 13, 16"); break; } } /* Degenerate n1Xn2 Gauss-Legendre scheme to integrate over a tri */ static int glt[MAX_LINE_POINTS] = {-1}; static double *glxt[MAX_LINE_POINTS], *glyt[MAX_LINE_POINTS], *glpt[MAX_LINE_POINTS]; static void quadToTri(double xi,double eta,double *r, double *s, double *J) { double r1; *r = 0.5e0 * (1.0e0 + xi); r1 = 1.0e0 - (*r); *s = 0.5e0 * (1.0e0 + eta) * r1; *J = 0.25e0 * r1; } void GaussLegendre_Triangle(int Nbr_Points, int Num, double *u, double *v, double *w, double *wght) { int i,j,index=0,nb; double pt1,pt2,wt1,wt2,dJ,dum; nb = (int)sqrt((double)Nbr_Points); if(nb*nb != Nbr_Points || nb > MAX_LINE_POINTS){ Message::Error("Number of points should be n^2 with n in [1,%d]", MAX_LINE_POINTS) ; return; } if(glt[0] < 0) for(i=0 ; i < MAX_LINE_POINTS ; i++) glt[i] = 0 ; if(!glt[nb - 1]){ Message::Info("Computing degenerate GaussLegendre %dX%d for Triangle", nb, nb); glxt[nb - 1] = (double*)Malloc(Nbr_Points * sizeof(double)); glyt[nb - 1] = (double*)Malloc(Nbr_Points * sizeof(double)); glpt[nb - 1] = (double*)Malloc(Nbr_Points * sizeof(double)); for(i = 0; i < nb; i++) { Gauss_Line(nb, i, &pt1, &dum, &dum, &wt1); for(j = 0; j < nb; j++) { Gauss_Line(nb, j, &pt2, &dum, &dum, &wt2); quadToTri(pt1, pt2, &glxt[nb - 1][index], &glyt[nb - 1][index], &dJ); glpt[nb - 1][index++] = dJ * wt1 * wt2; } } glt[nb - 1] = 1; } *u = glxt[nb - 1][Num] ; *v = glyt[nb - 1][Num] ; *w = 0. ; *wght = glpt[nb - 1][Num] ; } /* Gauss Integration over a triangle with a 1/R singularity over node (0,0,0) */ void GaussSingularR_Triangle(int Nbr_Points, int Num, double *u, double *v, double *w, double *wght) { switch (Nbr_Points) { case 1 : *u= xts1 [Num] ; *v= yts1 [Num] ; *w= 0. ; *wght= pts1 [Num] ; break ; case 3 : *u= xts3 [Num] ; *v= yts3 [Num] ; *w= 0. ; *wght= pts3 [Num] ; break ; case 4 : *u= xts4 [Num] ; *v= yts4 [Num] ; *w= 0. ; *wght= pts4 [Num] ; break ; default : Message::Error("Wrong number of (modified) Gauss points for Triangle: " "valid choices: 1, 3, 4"); break; } }