File: Gauss_Quadrangle.cpp

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// GetDP - Copyright (C) 1997-2016 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_Quadrangle.h"
#include "Message.h"
#include "MallocUtils.h"

/* Classic Gauss Integration over a quadrangle */

void Gauss_Quadrangle (int Nbr_Points, int Num,
		       double *u, double *v, double *w, double *wght)
{
  switch (Nbr_Points) {
  case  1 : *u= xq1 [Num] ; *v= yq1 [Num] ; *w= 0. ; *wght= pq1 [Num] ; break ;
  case  3 : *u= xq3 [Num] ; *v= yq3 [Num] ; *w= 0. ; *wght= pq3 [Num] ; break ;
  case  4 : *u= xq4 [Num] ; *v= yq4 [Num] ; *w= 0. ; *wght= pq4 [Num] ; break ;
  case  7 : *u= xq7 [Num] ; *v= yq7 [Num] ; *w= 0. ; *wght= pq7 [Num] ; break ;
  default :
    Message::Error("Wrong number of Gauss points for Quadrangle: "
                   "valid choices: 1, 3, 4, 7");
    break;
  }
}

/* Gauss-Legendre scheme to integrate over a quadrangle */

static int glq[MAX_LINE_POINTS] = {-1};
static double *glxq[MAX_LINE_POINTS], *glyq[MAX_LINE_POINTS], *glpq[MAX_LINE_POINTS];

void GaussLegendre_Quadrangle(int Nbr_Points, int Num,
			      double *u, double *v, double *w, double *wght)
{
  int i, j, index = 0, nb;
  double pt1, pt2, wt1, wt2, 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(glq[0] < 0) for(i = 0; i < MAX_LINE_POINTS; i++) glq[i] = 0;

  if(!glq[nb - 1]){
    Message::Info("Computing GaussLegendre %dX%d for Quadrangle", nb, nb);
    glxq[nb - 1] = (double*)Malloc(Nbr_Points * sizeof(double));
    glyq[nb - 1] = (double*)Malloc(Nbr_Points * sizeof(double));
    glpq[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);
	glxq[nb - 1][index] = pt1;
	glyq[nb - 1][index] = pt2;
	glpq[nb - 1][index++] = wt1*wt2;
      }
    }
    glq[nb - 1] = 1;
  }

  *u = glxq[nb - 1][Num] ; *v = glyq[nb - 1][Num] ; *w = 0. ; *wght = glpq[nb - 1][Num] ;
}

/* Gauss Integration over a quadrangle with a 1/R singularity over node (-1,-1,0) */

void GaussSingularR_Quadrangle(int Nbr_Points, int Num,
			       double *u, double *v, double *w, double *wght)
{
  switch (Nbr_Points) {
  case  1 : *u= xqs1 [Num] ; *v= yqs1 [Num] ; *w= 0. ; *wght= pqs1 [Num] ; break ;
  case  3 : *u= xqs3 [Num] ; *v= yqs3 [Num] ; *w= 0. ; *wght= pqs3 [Num] ; break ;
  case  4 : *u= xqs4 [Num] ; *v= yqs4 [Num] ; *w= 0. ; *wght= pqs4 [Num] ; break ;
  default :
    Message::Error("Wrong number of (modified) Gauss Points for Quadrangle: "
                   "valid choices: 1, 3, 4");
    break;
  }
}