face_quad4.c

一个用来实现偏微分方程中网格的计算库

// $Id: face_quad4.C 2789 2008-04-13 02:24:40Z 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

// C++ includes

// Local includes
#include "side.h"
#include "edge_edge2.h"
#include "face_quad4.h"




// ------------------------------------------------------------
// Quad class static member initialization
const unsigned int Quad4::side_nodes_map[4][2] =
{
  {0, 1}, // Side 0
  {1, 2}, // Side 1
  {2, 3}, // Side 2
  {3, 0}  // Side 3
};


#ifdef ENABLE_AMR

const float Quad4::_embedding_matrix[4][4][4] =
{
  // embedding matrix for child 0
  {
    // 0    1    2    3
    {1.0, 0.0, 0.0, 0.0}, // 0
    {0.5, 0.5, 0.0, 0.0}, // 1
    {.25, .25, .25, .25}, // 2
    {0.5, 0.0, 0.0, 0.5}  // 3
  },

  // embedding matrix for child 1
  {
    // 0    1    2    3
    {0.5, 0.5, 0.0, 0.0}, // 0
    {0.0, 1.0, 0.0, 0.0}, // 1
    {0.0, 0.5, 0.5, 0.0}, // 2
    {.25, .25, .25, .25}  // 3
  },

  // embedding matrix for child 2
  {
    // 0    1    2    3
    {0.5, 0.0, 0.0, 0.5}, // 0
    {.25, .25, .25, .25}, // 1
    {0.0, 0.0, 0.5, 0.5}, // 2
    {0.0, 0.0, 0.0, 1.0}  // 3
  },

  // embedding matrix for child 3
  {
    // 0    1    2    3
    {.25, .25, .25, .25}, // 0
    {0.0, 0.5, 0.5, 0.0}, // 1
    {0.0, 0.0, 1.0, 0.0}, // 2
    {0.0, 0.0, 0.5, 0.5}  // 3
  }
};

#endif





// ------------------------------------------------------------
// Quad4 class member functions

bool Quad4::is_vertex(const unsigned int) const
{
  return true;
}

bool Quad4::is_edge(const unsigned int) const
{
  return false;
}

bool Quad4::is_face(const unsigned int) const
{
  return false;
}

bool Quad4::is_node_on_side(const unsigned int n,
			    const unsigned int s) const
{
  libmesh_assert(s < n_sides());
  for (unsigned int i = 0; i != 2; ++i)
    if (side_nodes_map[s][i] == n)
      return true;
  return false;
}



bool Quad4::has_affine_map() const
{
  Point v = this->point(3) - this->point(0);
  return (v.relative_fuzzy_equals(this->point(2) - this->point(1)));
}



AutoPtr<Elem> Quad4::build_side (const unsigned int i,
				 bool proxy) const
{
  libmesh_assert (i < this->n_sides());

  if (proxy)
    {
      AutoPtr<Elem> ap(new Side<Edge2,Quad4>(this,i));
      return ap;
    }

  else
    {

      switch (i)
	{
	case 0:
	  {
	    Edge2* edge = new Edge2;

	    edge->set_node(0) = this->get_node(0);
	    edge->set_node(1) = this->get_node(1);
	
	    AutoPtr<Elem> ap(edge);  return ap;
	  }
	case 1:
	  {
	    Edge2* edge = new Edge2;

	    edge->set_node(0) = this->get_node(1);
	    edge->set_node(1) = this->get_node(2);
	
	    AutoPtr<Elem> ap(edge);  return ap;
	  }
	case 2:
	  {
	    Edge2* edge = new Edge2;

	    edge->set_node(0) = this->get_node(2);
	    edge->set_node(1) = this->get_node(3);
	
	    AutoPtr<Elem> ap(edge);  return ap;
	  }
	case 3:
	  {
	    Edge2* edge = new Edge2;

	    edge->set_node(0) = this->get_node(3);
	    edge->set_node(1) = this->get_node(0);
	
	    AutoPtr<Elem> ap(edge);  return ap;
	  }
	default:
	  {
	    libmesh_error();
	  }
	}
    }

  // We will never get here...
  AutoPtr<Elem> ap(NULL);  return ap;
}





void Quad4::connectivity(const unsigned int sf,
			 const IOPackage iop,
			 std::vector<unsigned int>& conn) const
{
  libmesh_assert (sf < this->n_sub_elem());
  libmesh_assert (iop != INVALID_IO_PACKAGE);

  // Create storage.
  conn.resize(4);

  switch (iop)
    {
    case TECPLOT:
      {
	conn[0] = this->node(0)+1;
	conn[1] = this->node(1)+1;
	conn[2] = this->node(2)+1;
	conn[3] = this->node(3)+1;
	return;
      }

    case VTK:
      {
	conn[0] = this->node(0);
	conn[1] = this->node(1);
	conn[2] = this->node(2);
	conn[3] = this->node(3);
	return;
      }

    default:
      libmesh_error();
    }

  libmesh_error();
}



Real Quad4::volume () const
{
  // The A,B,C,D naming scheme here corresponds exactly to the
  // libmesh counter-clockwise numbering scheme.
  
  //        3           2        D           C
  // QUAD4: o-----------o	 o-----------o
  //        |           |	 |           |
  //        |           |	 |           |
  //        |           | 	 |           |
  //        |           |	 |           |
  //        |           |	 |           |
  //        o-----------o	 o-----------o
  //        0           1	 A           B
  
  // Vector pointing from A to C
  Point AC ( this->point(2) - this->point(0) );
  
  // Vector pointing from A to B
  Point AB ( this->point(1) - this->point(0) );

  // Vector pointing from A to D
  Point AD ( this->point(3) - this->point(0) );

  // The diagonal vector minus the side vectors
  Point AC_AB_AD (AC - AB - AD);
    
  // Check for quick return for planar QUAD4.  This will
  // be the most common case, occuring for all purely 2D meshes.
  if (AC_AB_AD == Point(0.,0.,0.))
    return AB.cross(AD).size();
  
  else
    {
      // Use 2x2 quadrature to approximate the surface area.  (The
      // true integral is too difficult to compute analytically.)  The
      // accuracy here is exactly the same as would be obtained via a
      // call to Elem::volume(), however it is a bit more optimized to
      // do it this way.  The technique used is to integrate the magnitude
      // of the normal vector over the whole area.  See for example,
      //
      // Y. Zhang, C. Bajaj, G. Xu. Surface Smoothing and Quality
      // Improvement of Quadrilateral/Hexahedral Meshes with Geometric
      // Flow. The special issue of the Journal Communications in
      // Numerical Methods in Engineering (CNME), submitted as an
      // invited paper, 2006.
      // http://www.ices.utexas.edu/~jessica/paper/quadhexgf/quadhex_geomflow_CNM.pdf
      
      // 4-point rule
      const Real q[2] = {0.5 - std::sqrt(3.) / 6.,
			 0.5 + std::sqrt(3.) / 6.};

      Real vol=0.;
      for (unsigned int i=0; i<2; ++i)
	for (unsigned int j=0; j<2; ++j)
	  vol += (AB + q[i]*AC_AB_AD).cross(AD + q[j]*AC_AB_AD).size();
      
      return 0.25*vol;
    }
}