gauss_hexahedron.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]>.
 */

/* 6 integration points (DHATT ET TOUZOT, page 299) */

#define a1   0.40824826
#define a2   0.81649658
#define b1   0.70710678
#define c1   0.57735027
#define w1   1.3333333333

double xhex6[6] = { a1,  a1, -a1, -a1, -a2,  a2};
double yhex6[6] = { b1, -b1,  b1, -b1,  0.,  0.};
double zhex6[6] = {-c1, -c1,  c1,  c1, -c1,  c1};
double phex6[6] = { w1,  w1,  w1,  w1,  w1,  w1};

#undef a1
#undef a2
#undef b1
#undef c1
#undef w1

/* 34 integration points (DHATT ET TOUZOT, page 299) */

double xhex34[34] = {0.9317380000,-0.9317380000,0.,
		     0.,0.,0.,
		     0.9167441779,-0.9167441779,0.9167441779,
		     -0.9167441779,0.,0.,
		     0.,0.,0.9167441779,
		     -0.9167441779,0.9167441779,-0.9167441779,
		     0.4086003800,0.4086003800,
		     0.4086003800,0.4086003800,
		     -0.4086003800,-0.4086003800,
		     -0.4086003800,-0.4086003800,
		     0.7398529500,0.7398529500,
		     0.7398529500,0.7398529500,
		     -0.7398529500,-0.7398529500,
		     -0.7398529500,-0.7398529500};
double yhex34[34] = {0.,0.,0.9317380000,
		     -0.9317380000,0.,0.,
		     0.9167441779,0.9167441779,-0.9167441779,
		     -0.9167441779,0.9167441779,-0.9167441779,
		     0.9167441779,-0.9167441779,0.,
		     0.,0.,0.,
		     0.4086003800,0.4086003800,
		     -0.4086003800,-0.4086003800,
		     0.4086003800,0.4086003800,
		     -0.4086003800,-0.4086003800,
		     0.7398529500,0.7398529500,
		     -0.7398529500,-0.7398529500,
		     0.7398529500,0.7398529500,
		     -0.7398529500,-0.7398529500};
double zhex34[34] = {0.,0.,0.,
		     0.,0.9317380000,-0.9317380000,
		     0.,0.,0.,
		     0.,0.9167441779,0.9167441779,
		     -0.9167441779,-0.9167441779,0.9167441779,  
		     0.9167441779,-0.9167441779,-0.9167441779,
		     0.4086003800,-0.4086003800,
		     0.4086003800,-0.4086003800,
		     0.4086003800,-0.4086003800,
		     0.4086003800,-0.4086003800,
		     0.7398529500,-0.7398529500,
		     0.7398529500,-0.7398529500,
		     0.7398529500,-0.7398529500,
		     0.7398529500,-0.7398529500};
double phex34[34] = {0.28465447168,0.28465447168,
		     0.28465447168,0.28465447168, 
		     0.28465447168,0.28465447168,
		     0.09983142160,0.09983142160,
		     0.09983142160,0.09983142160,
		     0.09983142160,0.09983142160,
		     0.09983142160,0.09983142160,
		     0.09983142160,0.09983142160,
		     0.09983142160,0.09983142160,
		     0.42294183928,0.42294183928,
		     0.42294183928,0.42294183928,
		     0.42294183928,0.42294183928,
		     0.42294183928,0.42294183928,
		     0.21382017456,0.21382017456,  
		     0.21382017456,0.21382017456,  
		     0.21382017456,0.21382017456,  
		     0.21382017456,0.21382017456};

/* 77 integration points (STROUD, page 238) */

double xhex77[77] = {0.,
		     0.5384693101,-0.5384693101,0.,0.,0.,0.,
	             0.9061798459,-0.9061798459,0.,0.,0.,0.,
	             0.5384693101,0.5384693101,-0.5384693101,-0.5384693101,
	             0.5384693101,0.5384693101,-0.5384693101,-0.5384693101,
	             0.,0.,0.,0.,
	             0.9061798459,0.9061798459,-0.9061798459,-0.9061798459,
	             0.9061798459,0.9061798459,-0.9061798459,-0.9061798459,
	             0.,0.,0.,0.,
	             0.5384693101,0.5384693101,-0.5384693101,-0.5384693101,
	             0.9061798459,0.9061798459,-0.9061798459,-0.9061798459,
	             0.5384693101,0.5384693101,-0.5384693101,-0.5384693101,
	             0.9061798459,0.9061798459,-0.9061798459,-0.9061798459,
	             0.,0.,0.,0.,
	             0.,0.,0.,0.,
	             0.5384693101, 0.5384693101, 0.5384693101, 0.5384693101,
	             -0.5384693101,-0.5384693101,-0.5384693101,-0.5384693101,
	             0.9061798459, 0.9061798459, 0.9061798459, 0.9061798459,
	             -0.9061798459,-0.9061798459,-0.9061798459,-0.9061798459};
double yhex77[77] = {0.,
	             0.,0.,0.5384693101,-0.5384693101,0.,0.,
	             0.,0.,0.9061798459,-0.9061798459,0.,0.,
	             0.5384693101,-0.5384693101,0.5384693101,-0.5384693101,
	             0.,0.,0.,0.,
	             0.5384693101, 0.5384693101,-0.5384693101,-0.5384693101,
	             0.9061798459,-0.9061798459,0.9061798459,-0.9061798459,
	             0.,0.,0.,0.,
	             0.9061798459,0.9061798459,-0.9061798459,-0.9061798459,
	             0.9061798459,-0.9061798459,0.9061798459,-0.9061798459,
	             0.5384693101,-0.5384693101,0.5384693101,-0.5384693101,
	             0.,0.,0.,0.,
	             0.,0.,0.,0.,
	             0.5384693101,0.5384693101,-0.5384693101,-0.5384693101,
	             0.9061798459,0.9061798459,-0.9061798459,-0.9061798459,
	             0.5384693101,0.5384693101,-0.5384693101,-0.5384693101,
	             0.5384693101,0.5384693101,-0.5384693101,-0.5384693101,
	             0.9061798459,0.9061798459,-0.9061798459,-0.9061798459,
	             0.9061798459,0.9061798459,-0.9061798459,-0.9061798459};
double zhex77[77] = {0.,
	             0.,0.,0.,0.,0.5384693101,-0.5384693101,
	             0.,0.,0.,0.,0.9061798459,-0.9061798459,
	             0.,0.,0.,0.,
	             0.5384693101,-0.5384693101,0.5384693101,-0.5384693101,
	             0.5384693101,-0.5384693101,0.5384693101,-0.5384693101,
	             0.,0.,0.,0.,
	             0.9061798459,-0.9061798459,0.9061798459,-0.9061798459,
	             0.9061798459,-0.9061798459,0.9061798459,-0.9061798459,
	             0.,0.,0.,0.,
	             0.,0.,0.,0.,
	             0.9061798459,-0.9061798459,0.9061798459,-0.9061798459,
	             0.5384693101,-0.5384693101,0.5384693101,-0.5384693101,
	             0.9061798459,-0.9061798459,0.9061798459,-0.9061798459,
	             0.5384693101,-0.5384693101,0.5384693101,-0.5384693101,
	             0.5384693101,-0.5384693101,0.5384693101,-0.5384693101,
	             0.5384693101,-0.5384693101,0.5384693101,-0.5384693101,
	             0.9061798459,-0.9061798459,0.9061798459,-0.9061798459,
	             0.9061798459,-0.9061798459,0.9061798459,-0.9061798459};
double phex77[77] = {-2.2577865569E+00,
	             1.704933503,1.704933503,1.704933503,1.704933503,
	             1.704933503,1.704933503,
	             -0.2524056575,-0.2524056575,-0.2524056575,-0.2524056575,
	             -0.2524056575,-0.2524056575,
	             -0.8069802194,-0.8069802194,-0.8069802194,-0.8069802194,
	             -0.8069802194,-0.8069802194,-0.8069802194,-0.8069802194,
	             -0.8069802194,-0.8069802194,-0.8069802194,-0.8069802194,
	             3.4187901E-02,3.4187901E-02,3.4187901E-02,3.4187901E-02,
	             3.4187901E-02,3.4187901E-02,3.4187901E-02,3.4187901E-02,
	             3.4187901E-02,3.4187901E-02,3.4187901E-02,3.4187901E-02,
	             0.2268,0.2268,0.2268,0.2268,0.2268,0.2268,0.2268,0.2268,
	             0.2268,0.2268,0.2268,0.2268,0.2268,0.2268,0.2268,0.2268,
	             0.2268,0.2268,0.2268,0.2268,0.2268,0.2268,0.2268,0.2268,
	             0.6325755140,0.6325755140,0.6325755140,0.6325755140,
	             0.6325755140,0.6325755140,0.6325755140,0.6325755140,
	             3.9040398E-02,3.9040398E-02,3.9040398E-02,3.9040398E-02,
	             3.9040398E-02,3.9040398E-02,3.9040398E-02,3.9040398E-02};