gauss_quadrangle.h

cfd求解器使用与gmsh网格的求解

/*
 * 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]>.
 */

/* 3 integration points */

double xq3[3] = {0.816496580928,-0.408248290464,-0.408248290464};
double yq3[3] = {0.0,0.840896415255,-0.840896415255};
double pq3[3] = {1.33333333333,1.33333333333,1.33333333333,};

/* 4 integration points */

double xq4[4] = {0.577350269189,-0.577350269189,0.577350269189,-0.577350269189};
double yq4[4] = {0.577350269189,0.577350269189,-0.577350269189,-0.577350269189};
double pq4[4] = {1.,1.,1.,1.};

/* 7 integration points */

double xq7[7] = {0.0,-0.683130051064,0.683130051064,0.890654421782,
		 -0.890654421782,0.374256642286,-0.374256642286};
double yq7[7] = {0.0,-0.683130051064,0.683130051064,-0.374256642286,0.374256642286,
		   -0.890654421782,0.890654421782,};
double pq7[7] = {1.142857142857,0.595238095238,0.595238095238,
		 0.416666666666,0.416666666666,0.416666666666,0.416666666666};

/* 
   GAUSS QUADRANGLE WITH 1/R SINGULARITY OVER NODE (-1,-1,0)
   
   ref.: H. L. G. Pina, J. L. M. Fernandes, C. A. Brebbia, 
         Some numerical integration formulae over triangles and 
	 squares with a 1/R singularity, 
	 Appl. Math. Modelling, Vol 5, June 1981, pp 209--211 
*/ 

/* 1 integration point */

double xqs1[1] = {-0.26501817};
double yqs1[1] = {-0.26501817};
double pqs1[1] = {3.52549435};

/* 3 integration points */

double xqs3[3] = {-0.58105530,1.0,-0.21877566};
double yqs3[3] = {-0.58105530,-0.21877566,1.0};
double pqs3[3] = {2.37881900,0.57333767,0.57333767};

/* 4 integration points */

double xqs4[4] = {-0.37512304,0.69629093,-0.92928746,-0.15602536};
double yqs4[4] = {-0.92928746,-0.15602536,-0.37512304,0.69629093};
double pqs4[4] = {1.02276580,0.73998134,1.02276580,0.73998134};