gauss_line.c

cfd求解器使用与gmsh网格的求解

#define RCSID "$Id: Gauss_Line.c,v 1.13 2006/02/26 00:42:53 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_Line.h"

/* Gauss integration over a line */

int gll[MAX_LINE_POINTS] = {-1};
double *glxl[MAX_LINE_POINTS], *glpl[MAX_LINE_POINTS];

void Gauss_Line (int Nbr_Points, int Num,
		 double *u, double *v, double *w, double *wght) {
  int i ;

  GetDP_Begin("Gauss_Line");

  switch (Nbr_Points) {

  case  1 : *u = lx1 [Num] ; *v = 0. ; *w = 0. ; *wght = lp1 [Num] ; break ;
  case  2 : *u = lx2 [Num] ; *v = 0. ; *w = 0. ; *wght = lp2 [Num] ; break ;
  case  3 : *u = lx3 [Num] ; *v = 0. ; *w = 0. ; *wght = lp3 [Num] ; break ;
  case  4 : *u = lx4 [Num] ; *v = 0. ; *w = 0. ; *wght = lp4 [Num] ; break ;
  case  5 : *u = lx5 [Num] ; *v = 0. ; *w = 0. ; *wght = lp5 [Num] ; break ;
  case  6 : *u = lx6 [Num] ; *v = 0. ; *w = 0. ; *wght = lp6 [Num] ; break ;
  case  7 : *u = lx7 [Num] ; *v = 0. ; *w = 0. ; *wght = lp7 [Num] ; break ;
  case  8 : *u = lx8 [Num] ; *v = 0. ; *w = 0. ; *wght = lp8 [Num] ; break ;
  case  9 : *u = lx9 [Num] ; *v = 0. ; *w = 0. ; *wght = lp9 [Num] ; break ;
  case 10 : *u = lx10[Num] ; *v = 0. ; *w = 0. ; *wght = lp10[Num] ; break ;
  case 11 : *u = lx11[Num] ; *v = 0. ; *w = 0. ; *wght = lp11[Num] ; break ;
  case 12 : *u = lx12[Num] ; *v = 0. ; *w = 0. ; *wght = lp12[Num] ; break ;
  case 13 : *u = lx13[Num] ; *v = 0. ; *w = 0. ; *wght = lp13[Num] ; break ;
  case 14 : *u = lx14[Num] ; *v = 0. ; *w = 0. ; *wght = lp14[Num] ; break ;
  case 15 : *u = lx15[Num] ; *v = 0. ; *w = 0. ; *wght = lp15[Num] ; break ;
  case 16 : *u = lx16[Num] ; *v = 0. ; *w = 0. ; *wght = lp16[Num] ; break ;
  case 17 : *u = lx17[Num] ; *v = 0. ; *w = 0. ; *wght = lp17[Num] ; break ;
  case 18 : *u = lx18[Num] ; *v = 0. ; *w = 0. ; *wght = lp18[Num] ; break ;
  case 19 : *u = lx19[Num] ; *v = 0. ; *w = 0. ; *wght = lp19[Num] ; break ;
  case 20 : *u = lx20[Num] ; *v = 0. ; *w = 0. ; *wght = lp20[Num] ; break ;
  default : 
    if(Nbr_Points <= MAX_LINE_POINTS){
      if(gll[0] < 0) for(i=0 ; i < MAX_LINE_POINTS ; i++) gll[i] = 0 ;
      if(!gll[Nbr_Points-1]){
	Msg(INFO, "Computing GaussLegendre %d for Line", Nbr_Points);
	glxl[Nbr_Points-1] = (double*)Malloc(Nbr_Points*sizeof(double));
	glpl[Nbr_Points-1] = (double*)Malloc(Nbr_Points*sizeof(double));
	GaussLegendre(-1., 1., glxl[Nbr_Points-1], glpl[Nbr_Points-1], Nbr_Points);
	gll[Nbr_Points-1] = 1;
      }
      *u = glxl[Nbr_Points-1][Num] ; *v = *w = 0. ; *wght = glpl[Nbr_Points-1][Num] ;
    }
    else
      Msg(GERROR, "Maximum number of integration points exceeded (%d > %d)",
	  Nbr_Points, MAX_LINE_POINTS) ;
    break ;
  }

  GetDP_End ;
}


#define EPS 3.0e-11

void GaussLegendre(double x1, double x2, double x[], double w[], int n){
  int m,j,i;
  double z1,z,xm,xl,pp,p3,p2,p1;

  GetDP_Begin("GaussLegendre");

  m=(n+1)/2;
  xm=0.5*(x2+x1);
  xl=0.5*(x2-x1);
  for (i=1;i<=m;i++) {
    z=cos(3.141592654*(i-0.25)/(n+0.5));
    do {
      p1=1.0;
      p2=0.0;
      for (j=1;j<=n;j++) {
	p3=p2;
	p2=p1;
	p1=((2.0*j-1.0)*z*p2-(j-1.0)*p3)/j;
      }
      pp=n*(z*p1-p2)/(z*z-1.0);
      z1=z;
      z=z1-p1/pp;
    } while (fabs(z-z1) > EPS);
    x[i-1]=xm-xl*z;
    x[n-i]=xm+xl*z;
    w[i-1]=2.0*xl/((1.0-z*z)*pp*pp);
    w[n-i]=w[i-1];
  }

  GetDP_End ;
}

#undef EPS