cell_prism6.c

一个用来实现偏微分方程中网格的计算库

// $Id: cell_prism6.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 "cell_prism6.h"
#include "edge_edge2.h"
#include "face_quad4.h"
#include "face_tri3.h"



// ------------------------------------------------------------
// Prism6 class static member initializations
const unsigned int Prism6::side_nodes_map[5][4] =
{
  {0, 2, 1, 99}, // Side 0
  {0, 1, 4,  3}, // Side 1
  {1, 2, 5,  4}, // Side 2
  {2, 0, 3,  5}, // Side 3
  {3, 4, 5, 99}  // Side 4
};

const unsigned int Prism6::edge_nodes_map[9][2] =
{
  {0, 1}, // Side 0
  {1, 2}, // Side 1
  {0, 2}, // Side 2
  {0, 3}, // Side 3
  {1, 4}, // Side 4
  {2, 5}, // Side 5
  {3, 4}, // Side 6
  {4, 5}, // Side 7
  {3, 5}  // Side 8
};


// ------------------------------------------------------------
// Prism6 class member functions

bool Prism6::is_vertex(const unsigned int) const
{
  return true;
}

bool Prism6::is_edge(const unsigned int) const
{
  return false;
}

bool Prism6::is_face(const unsigned int) const
{
  return false;
}

bool Prism6::is_node_on_side(const unsigned int n,
			     const unsigned int s) const
{
  libmesh_assert(s < n_sides());
  for (unsigned int i = 0; i != 4; ++i)
    if (side_nodes_map[s][i] == n)
      return true;
  return false;
}

bool Prism6::is_node_on_edge(const unsigned int n,
			     const unsigned int e) const
{
  libmesh_assert(e < n_edges());
  for (unsigned int i = 0; i != 2; ++i)
    if (edge_nodes_map[e][i] == n)
      return true;
  return false;
}



bool Prism6::has_affine_map() const
{
  // Make sure z edges are affine
  Point v = this->point(3) - this->point(0);
  if (!v.relative_fuzzy_equals(this->point(4) - this->point(1)) ||
      !v.relative_fuzzy_equals(this->point(5) - this->point(2)))
    return false;
  return true;
}



AutoPtr<Elem> Prism6::build_side (const unsigned int i,
				  bool proxy) const
{
  libmesh_assert (i < this->n_sides());

  if (proxy)
    {
      switch(i)
	{
	case 0:
	case 4:
	  {
	    AutoPtr<Elem> face(new Side<Tri3,Prism6>(this,i));
	    return face;
	  }

	case 1:
	case 2:
	case 3:
	  {
	    AutoPtr<Elem> face(new Side<Quad4,Prism6>(this,i));
	    return face;
	  }

	default:
	  {
	    libmesh_error();
	  }
	}
    }

  else
    {
      switch (i)
	{
	case 0:  // the triangular face at z=-1
	  {
	    AutoPtr<Elem> face(new Tri3);

	    face->set_node(0) = this->get_node(0);
	    face->set_node(1) = this->get_node(2);
	    face->set_node(2) = this->get_node(1);

	    return face;
	  }
	case 1:  // the quad face at y=0
	  {
	    AutoPtr<Elem> face(new Quad4);
	
	    face->set_node(0) = this->get_node(0);
	    face->set_node(1) = this->get_node(1);
	    face->set_node(2) = this->get_node(4);
	    face->set_node(3) = this->get_node(3);
	
	    return face;
	  }
	case 2:  // the other quad face
	  {
	    AutoPtr<Elem> face(new Quad4);

	    face->set_node(0) = this->get_node(1);
	    face->set_node(1) = this->get_node(2);
	    face->set_node(2) = this->get_node(5);
	    face->set_node(3) = this->get_node(4);

	    return face;
	  }
	case 3: // the quad face at x=0
	  {
	    AutoPtr<Elem> face(new Quad4);

	    face->set_node(0) = this->get_node(2);
	    face->set_node(1) = this->get_node(0);
	    face->set_node(2) = this->get_node(3);
	    face->set_node(3) = this->get_node(5);
	
	    return face;
	  }
	case 4: // the triangular face at z=1
	  {
	    AutoPtr<Elem> face(new Tri3);

	    face->set_node(0) = this->get_node(3);
	    face->set_node(1) = this->get_node(4);
	    face->set_node(2) = this->get_node(5);

	    return face;
	  }
	default:
	  {
	    libmesh_error();
	  }
	}
    }
  
  // We'll never get here.
  libmesh_error();
  AutoPtr<Elem> ap(NULL);  return ap;
}



AutoPtr<Elem> Prism6::build_edge (const unsigned int i) const
{
  libmesh_assert (i < this->n_edges());

  return AutoPtr<Elem>(new SideEdge<Edge2,Prism6>(this,i));
}



void Prism6::connectivity(const unsigned int sc,
			  const IOPackage iop,
			  std::vector<unsigned int>& conn) const
{
  libmesh_assert (_nodes != NULL);
  libmesh_assert (sc < this->n_sub_elem());
  libmesh_assert (iop != INVALID_IO_PACKAGE);

  switch (iop)
    {
    case TECPLOT:
      {
	conn.resize(8);
	conn[0] = this->node(0)+1;
	conn[1] = this->node(1)+1;
	conn[2] = this->node(2)+1;
	conn[3] = this->node(2)+1;
	conn[4] = this->node(3)+1;
	conn[5] = this->node(4)+1;
	conn[6] = this->node(5)+1;
	conn[7] = this->node(5)+1;
	return;
      }

    case VTK:
      {
	conn.resize(6);
	conn[0] = this->node(0);
	conn[1] = this->node(2);
	conn[2] = this->node(1);
	conn[3] = this->node(3);
	conn[4] = this->node(5);
	conn[5] = this->node(4);
	return;
      }

    default:
      libmesh_error();
    }

  libmesh_error();
}



#ifdef ENABLE_AMR

const float Prism6::_embedding_matrix[8][6][6] =
{
  // embedding matrix for child 0
  {
    //  0     1     2     3     4     5
    { 1.0,  0.0,  0.0,  0.0,  0.0,  0.0}, // 0
    { 0.5,  0.5,  0.0,  0.0,  0.0,  0.0}, // 1
    { 0.5,  0.0,  0.5,  0.0,  0.0,  0.0}, // 2
    { 0.5,  0.0,  0.0,  0.5,  0.0,  0.0}, // 3
    { .25,  .25,  0.0,  .25,  .25,  0.0}, // 4
    { .25,  0.0,  .25,  .25,  0.0,  .25}  // 5
  },

  // embedding matrix for child 1
  {
    //  0     1     2     3     4     5
    { 0.5,  0.5,  0.0,  0.0,  0.0,  0.0}, // 0
    { 0.0,  1.0,  0.0,  0.0,  0.0,  0.0}, // 1
    { 0.0,  0.5,  0.5,  0.0,  0.0,  0.0}, // 2
    { .25,  .25,  0.0,  .25,  .25,  0.0}, // 3
    { 0.0,  0.5,  0.0,  0.0,  0.5,  0.0}, // 4
    { 0.0,  .25,  .25,  0.0,  .25,  .25}  // 5
  },

  // embedding matrix for child 2
  {
    //  0     1     2     3     4     5
    { 0.5,  0.0,  0.5,  0.0,  0.0,  0.0}, // 0
    { 0.0,  0.5,  0.5,  0.0,  0.0,  0.0}, // 1
    { 0.0,  0.0,  1.0,  0.0,  0.0,  0.0}, // 2
    { .25,  0.0,  .25,  .25,  0.0,  .25}, // 3
    { 0.0,  .25,  .25,  0.0,  .25,  .25}, // 4
    { 0.0,  0.0,  0.5,  0.0,  0.0,  0.5}  // 5
  },

  // embedding matrix for child 3
  {
    //  0     1     2     3     4     5
    { 0.5,  0.5,  0.0,  0.0,  0.0,  0.0}, // 0
    { 0.0,  0.5,  0.5,  0.0,  0.0,  0.0}, // 1
    { 0.5,  0.0,  0.5,  0.0,  0.0,  0.0}, // 2
    { .25,  .25,  0.0,  .25,  .25,  0.0}, // 3
    { 0.0,  .25,  .25,  0.0,  .25,  .25}, // 4
    { .25,  0.0,  .25,  .25,  0.0,  .25}  // 5
  },

  // embedding matrix for child 4
  {
    //  0     1     2     3     4     5
    { 0.5,  0.0,  0.0,  0.5,  0.0,  0.0}, // 0
    { .25,  .25,  0.0,  .25,  .25,  0.0}, // 1
    { .25,  0.0,  .25,  .25,  0.0,  .25}, // 2
    { 0.0,  0.0,  0.0,  1.0,  0.0,  0.0}, // 3
    { 0.0,  0.0,  0.0,  0.5,  0.5,  0.0}, // 4
    { 0.0,  0.0,  0.0,  0.5,  0.0,  0.5}  // 5
  },

  // embedding matrix for child 5
  {
    //  0     1     2     3     4     5
    { .25,  .25,  0.0,  .25,  .25,  0.0}, // 0
    { 0.0,  0.5,  0.0,  0.0,  0.5,  0.0}, // 1
    { 0.0,  .25,  .25,  0.0,  .25,  .25}, // 2
    { 0.0,  0.0,  0.0,  0.5,  0.5,  0.0}, // 3
    { 0.0,  0.0,  0.0,  0.0,  1.0,  0.0}, // 4
    { 0.0,  0.0,  0.0,  0.0,  0.5,  0.5}  // 5
  },

  // embedding matrix for child 6
  {
    //  0     1     2     3     4     5
    { .25,  0.0,  .25,  .25,  0.0,  .25}, // 0
    { 0.0,  .25,  .25,  0.0,  .25,  .25}, // 1
    { 0.0,  0.0,  0.5,  0.0,  0.0,  0.5}, // 2
    { 0.0,  0.0,  0.0,  0.5,  0.0,  0.5}, // 3
    { 0.0,  0.0,  0.0,  0.0,  0.5,  0.5}, // 4
    { 0.0,  0.0,  0.0,  0.0,  0.0,  1.0}  // 5
  },

  // embedding matrix for child 7
  {
    //  0     1     2     3     4     5
    { .25,  .25,  0.0,  .25,  .25,  0.0}, // 0
    { 0.0,  .25,  .25,  0.0,  .25,  .25}, // 1
    { .25,  0.0,  .25,  .25,  0.0,  .25}, // 2
    { 0.0,  0.0,  0.0,  0.5,  0.5,  0.0}, // 3
    { 0.0,  0.0,  0.0,  0.0,  0.5,  0.5}, // 4
    { 0.0,  0.0,  0.0,  0.5,  0.0,  0.5}  // 5
  }
};

#endif



Real Prism6::volume () const
{
  // The volume of the prism is computed by splitting
  // it into 2 tetrahedra and 3 pyramids with bilinear bases.
  // Then the volume formulae for the tetrahedron and pyramid
  // are applied and summed to obtain the prism's volume.

  static const unsigned char sub_pyr[3][4] =
    {
      {0, 1, 4, 3},
      {1, 2, 5, 4},
      {0, 3, 5, 2}
    };

  static const unsigned char sub_tet[2][3] =
    {
      {0, 1, 2},
      {5, 4, 3}
    };

  // The centroid is a convenient point to use
  // for the apex of all the pyramids.
  const Point R = this->centroid();

  // temporary storage for Nodes which form the base of the
  // subelements
  Node* base[4];

  // volume accumulation variable
  Real vol=0.;

  // Add up the sub-pyramid volumes
  for (unsigned int n=0; n<3; ++n)
    {
      // Set the nodes of the pyramid base
      for (unsigned int i=0; i<4; ++i)
	base[i] = this->_nodes[sub_pyr[n][i]];
      
      // Compute diff vectors
      Point a ( *base[0] - R );
      Point b ( *base[1] - *base[3] );
      Point c ( *base[2] - *base[0] );
      Point d ( *base[3] - *base[0] );
      Point e ( *base[1] - *base[0] );

      // Compute pyramid volume
      Real sub_vol = (1./6.)*(a*(b.cross(c))) + (1./12.)*(c*(d.cross(e)));

      libmesh_assert (sub_vol>0.);

      vol += sub_vol;
    }


  // Add up the sub-tet volumes
  for (unsigned int n=0; n<2; ++n)
    {
      // Set the nodes of the pyramid base
      for (unsigned int i=0; i<3; ++i)
	base[i] = this->_nodes[sub_tet[n][i]];

      // The volume of a tetrahedron is 1/6 the box product formed
      // by its base and apex vectors
      Point a ( R - *base[0] );
      
      // b is the vector pointing from 0 to 1
      Point b ( *base[1] - *base[0] );
      
      // c is the vector pointing from 0 to 2
      Point c ( *base[2] - *base[0] );
      
      Real sub_vol =  (1.0 / 6.0) * (a * (b.cross(c)));

      libmesh_assert (sub_vol>0.);

      vol += sub_vol;
    }  


  // Done with all sub-volumes, so return
  return vol;
 }