quadrature_simpson_3D.C

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// The libMesh Finite Element Library.
// Copyright (C) 2002-2014 Benjamin S. Kirk, John W. Peterson, Roy H. Stogner

// 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 "libmesh/quadrature_simpson.h"

namespace libMesh
{





void QSimpson::init_3D(const ElemType type_in,
                       unsigned int)
{
#if LIBMESH_DIM == 3

  //-----------------------------------------------------------------------
  // 3D quadrature rules
  switch (type_in)
    {
      //---------------------------------------------
      // 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:
      libmesh_error_msg("ERROR: Unsupported type: " << type_in);
    }
#endif
}

} // namespace libMesh