xref: /phasta/phSolver/common/GaussLegendreSimplex.c (revision 595995161822a203c8467e0e4a253d7bd7d6df32)

/*$Id$*/
#include <math.h>

#ifdef __cplusplus
extern "C" {
#endif

void brickToTet(double xi,double eta, double zeta,
                double *r, double *s, double *t, double *J);

void quadToTri(double xi,double eta,
               double *r, double *s,double *J);
double quadToTriJac(double xi,double eta);
int GaussLegendre1D(int, double **,double **);

int GaussLegendreTet(int n1,int n2,int n3,double GLrstw[][4],double *GLwt) {
  /* get degenerate n1Xn2Xn3 Gauss-Legendre scheme to integrate over a tet */
  int i,j,k,index=0;
  double *pt1,*pt2,*pt3,*wt1,*wt2,*wt3,dJ;
  const double six=6.000000000000000;

  GaussLegendre1D(n1,&pt1,&wt1);
  GaussLegendre1D(n2,&pt2,&wt2);
  GaussLegendre1D(n3,&pt3,&wt3);
  for(i=0; i < n1; i++) {
    for(j=0; j < n2; j++) {
      for(k=0; k < n3; k++) {
        brickToTet(pt1[i],pt2[j],pt3[k],&GLrstw[index][0],
                   &GLrstw[index][1],&GLrstw[index][2],&dJ);
        GLrstw[index][3] = 1.0e0-GLrstw[index][0]-GLrstw[index][1]
                                -GLrstw[index][2];
        GLwt[index++] = dJ*wt1[i]*wt2[j]*wt3[k]*six;
      }
    }
  }
  return index;
}
int GaussLegendreTri(int n1,int n2,double GLr[][3],double *GLwt) {
  /* get degenerate n1Xn2 Gauss-Legendre scheme to integrate over a tet */
  int i,j,index=0;
  double *pt1,*pt2,*wt1,*wt2,dJ;
  const double two = 2.0000000000000000;

  GaussLegendre1D(n1,&pt1,&wt1);
  GaussLegendre1D(n2,&pt2,&wt2);
  for(i=0; i < n1; i++) {
    for(j=0; j < n2; j++) {
      quadToTri(pt1[i],pt2[j],&GLr[index][0],&GLr[index][1],&dJ);
      GLr[index][2] = 1.0e0-GLr[index][0]-GLr[index][1];
      GLwt[index++] = dJ*wt1[i]*wt2[j]*two;
    }
  }
  return index;
}

void brickToTet(double xi,double eta, double zeta,
                      double *r, double *s, double *t, double *J) {
  double r1,rs1;
  *r = 0.5e0*(1.0e0+xi);
  r1 = 1.0e0-(*r);
  *s = 0.5e0*(1.0e0+eta)*r1;
  rs1 = 1.0e0-(*r)-(*s);
  *t = 0.5e0*(1.0e0+zeta)*rs1;
  *J = 0.125e0*r1*rs1;
}

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;
}

double quadToTriJac(double xi,double eta) {
  return 0.125e0*(1.0e0-eta);
}

#ifdef __cplusplus
}
#endif