quadrature_simpson_3d.c

一个用来实现偏微分方程中网格的计算库

// $Id: quadrature_simpson_3D.C 2788 2008-04-13 02:05:22Z roystgnr $

// The libMesh Finite Element Library.
// Copyright (C) 2002-2007  Benjamin S. Kirk, John W. Peterson
  
// This library is free software; you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public
// License as published by the Free Software Foundation; either
// version 2.1 of the License, or (at your option) any later version.
  
// This library 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
// Lesser General Public License for more details.
  
// You should have received a copy of the GNU Lesser General Public
// License along with this library; if not, write to the Free Software
// Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA



// Local includes
#include "quadrature_simpson.h"





void QSimpson::init_3D(const ElemType _type,
                       unsigned int)
{
#if DIM == 3
  
  //-----------------------------------------------------------------------
  // 3D quadrature rules
  switch (_type)
    {
      //---------------------------------------------
      // Hex quadrature rules
    case HEX8:
    case HEX20:
    case HEX27:
      {
	// We compute the 3D quadrature rule as a tensor
	// product of the 1D quadrature rule.
	QSimpson q1D(1);
	q1D.init(EDGE2);

	tensor_product_hex( q1D );
	
	return;
      }


      
      //---------------------------------------------
      // Tetrahedral quadrature rules
    case TET4:
    case TET10:
      {
	// This rule is created by combining 8 subtets
	// which use the trapezoidal rule.  The weights
	// may seem a bit odd, but they are correct,
	// and should add up to 1/6, the volume of the
	// reference tet.  The points of this rule are
	// at the nodal points of the TET10, allowing
	// you to generate diagonal element stiffness
	// matrices when using quadratic elements.
	// It should be able to integrate something
	// better than linears, but I'm not sure how
	// high.
	
	_points.resize(10);
	_weights.resize(10);
	
	_points[0](0) = 0.;   _points[5](0) = .5;  
	_points[0](1) = 0.;   _points[5](1) = .5;
	_points[0](2) = 0.;   _points[5](2) = 0.;
			      		   
	_points[1](0) = 1.;   _points[6](0) = 0.;
	_points[1](1) = 0.;   _points[6](1) = .5;
	_points[1](2) = 0.;   _points[6](2) = 0.;
			      		   
	_points[2](0) = 0.;   _points[7](0) = 0.;
	_points[2](1) = 1.;   _points[7](1) = 0.;
	_points[2](2) = 0.;   _points[7](2) = .5;
			      		   
	_points[3](0) = 0.;   _points[8](0) = .5;
	_points[3](1) = 0.;   _points[8](1) = 0.;
	_points[3](2) = 1.;   _points[8](2) = .5;
			      		   
	_points[4](0) = .5;   _points[9](0) = 0.;
	_points[4](1) = 0.;   _points[9](1) = .5;
	_points[4](2) = 0.;   _points[9](2) = .5;
	
	
	_weights[0] = .0052083333333333333333333333333333333333333333; // 1./192.
	_weights[1] = _weights[0];
	_weights[2] = _weights[0];
	_weights[3] = _weights[0];

	_weights[4] = .0243055555555555555555555555555555555555555555; // 14./576.
	_weights[5] = _weights[4];
	_weights[6] = _weights[4];
	_weights[7] = _weights[4];
	_weights[8] = _weights[4];
	_weights[9] = _weights[4];
	
	return;
      }
      
      
      
      //---------------------------------------------
      // Prism quadrature rules
    case PRISM6:
    case PRISM15:
    case PRISM18:
      {
	// We compute the 3D quadrature rule as a tensor
	// product of the 1D quadrature rule and a 2D
	// triangle quadrature rule

 	QSimpson q1D(1);
 	QSimpson q2D(2);

 	// Initialize 
 	q1D.init(EDGE2);
 	q2D.init(TRI3);

	tensor_product_prism(q1D, q2D);

	return;
      }

      
      //---------------------------------------------
      // Unsupported type
    default:
      {
	std::cerr << "ERROR: Unsupported type: " << _type << std::endl;
	libmesh_error();
      }
    }

  libmesh_error();

  return;
  
#endif
}