quadrature_simpson_2D.C

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// The libMesh Finite Element Library.
// Copyright (C) 2002-2019 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"
#include "libmesh/enum_to_string.h"
 
namespace libMesh
{
 
void QSimpson::init_2D(const ElemType, unsigned int)
{
#if LIBMESH_DIM > 1
 
  //-----------------------------------------------------------------------
  // 2D quadrature rules
  switch (_type)
    {
 
 
      //---------------------------------------------
      // Quadrilateral quadrature rules
    case QUAD4:
    case QUADSHELL4:
    case QUAD8:
    case QUADSHELL8:
    case QUAD9:
      {
        // We compute the 2D quadrature rule as a tensor
        // product of the 1D quadrature rule.
        QSimpson q1D(1);
        q1D.init(EDGE2);
        tensor_product_quad( q1D );
        return;
      }
 
 
      //---------------------------------------------
      // Triangle quadrature rules
    case TRI3:
    case TRISHELL3:
    case TRI3SUBDIVISION:
    case TRI6:
      {
        // I'm not sure if you would call this Simpson's
        // rule for triangles.  What it *Really* is is
        // four trapezoidal rules combined to give a six
        // point rule.  The points lie at the nodal locations
        // of the TRI6, so you can get diagonal element
        // stiffness matrix entries for quadratic elements.
        // This rule should be able to integrate a little
        // better than linears exactly.
 
        _points.resize(6);
        _weights.resize(6);
 
        _points[0](0) = 0.;
        _points[0](1) = 0.;
 
        _points[1](0) = 1.;
        _points[1](1) = 0.;
 
        _points[2](0) = 0.;
        _points[2](1) = 1.;
 
        _points[3](0) = 0.5;
        _points[3](1) = 0.;
 
        _points[4](0) = 0.;
        _points[4](1) = 0.5;
 
        _points[5](0) = 0.5;
        _points[5](1) = 0.5;
 
        _weights[0] = Real(1)/24;
        _weights[1] = Real(1)/24;
        _weights[2] = Real(1)/24;
        _weights[3] = 0.125;                            // 1./8.
        _weights[4] = 0.125;                            // 1./8.
        _weights[5] = 0.125;                            // 1./8.
 
        return;
      }
 
 
      //---------------------------------------------
      // Unsupported type
    default:
      libmesh_error_msg("Element type not supported!:" << Utility::enum_to_string(_type));
    }
#endif
}
 
} // namespace libMesh