gauss_triangle.c

cfd求解器使用与gmsh网格的求解

#define RCSID "$Id: Gauss_Triangle.c,v 1.14 2006/02/26 00:42:54 geuzaine Exp $"
/*
 * Copyright (C) 1997-2006 P. Dular, C. Geuzaine
 *
 * This program is free software; you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation; either version 2 of the License, or
 * (at your option) any later version.
 *
 * This program is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU General Public License for more details.
 *
 * You should have received a copy of the GNU General Public License
 * along with this program; if not, write to the Free Software
 * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307
 * USA.
 *
 * Please report all bugs and problems to <[e-mail]>.
 */

#include "GetDP.h"
#include "Quadrature.h"
#include "Gauss_Triangle.h"

/* Gauss Integration over a triangle */

void  Gauss_Triangle (int Nbr_Points, int Num,
		      double *u, double *v, double *w, double *wght) {

  GetDP_Begin("Gauss_Triangle");

  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 : 
    Msg(DIRECT, ERROR_STR "Wrong number of Gauss points for Triangle");
    Msg(GERROR, "Valid choices: 1, 3, 4, 6, 7, 12, 13, 16");
    break;
  }

  GetDP_End ;
}


/* Degenerate n1Xn2 Gauss-Legendre scheme to integrate over a tri */

int glt[MAX_LINE_POINTS] = {-1};
double *glxt[MAX_LINE_POINTS], *glyt[MAX_LINE_POINTS], *glpt[MAX_LINE_POINTS];

void quadToTri(double xi,double eta,double *r, double *s, double *J) {
  double r1;

  GetDP_Begin("quadToTri");

  *r = 0.5e0*(1.0e0+xi);
  r1 = 1.0e0-(*r);
  *s = 0.5e0*(1.0e0+eta)*r1;
  *J = 0.25e0*r1;  

  GetDP_End ;
}

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;

  GetDP_Begin("GaussLegendre_Line");

  nb = (int)sqrt((double)Nbr_Points);

  if(nb*nb != Nbr_Points || nb > MAX_LINE_POINTS)
    Msg(GERROR, "Number of points should be n^2 with n in [1,%d]", MAX_LINE_POINTS) ;

  if(glt[0] < 0) for(i=0 ; i < MAX_LINE_POINTS ; i++) glt[i] = 0 ;

  if(!glt[nb-1]){
    Msg(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] ;

  GetDP_End ;
}


/* 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) {

  GetDP_Begin("GaussSingularR_Triangle");

  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 : 
    Msg(DIRECT, ERROR_STR "Wrong number of (modified) Gauss points for Triangle");
    Msg(GERROR, "Valid choices: 1, 3, 4");
    break;
  }

  GetDP_End ;
}