cell_hex8.c

一个用来实现偏微分方程中网格的计算库

// $Id: cell_hex8.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_hex8.h"
#include "edge_edge2.h"
#include "face_quad4.h"




// ------------------------------------------------------------
// Hex8 class static member initializations
const unsigned int Hex8::side_nodes_map[6][4] =
{
  {0, 3, 2, 1}, // Side 0
  {0, 1, 5, 4}, // Side 1
  {1, 2, 6, 5}, // Side 2
  {2, 3, 7, 6}, // Side 3
  {3, 0, 4, 7}, // Side 4
  {4, 5, 6, 7}  // Side 5
};

const unsigned int Hex8::edge_nodes_map[12][2] =
{
  {0, 1}, // Side 0
  {1, 2}, // Side 1
  {2, 3}, // Side 2
  {0, 3}, // Side 3
  {0, 4}, // Side 4
  {1, 5}, // Side 5
  {2, 6}, // Side 6
  {3, 7}, // Side 7
  {4, 5}, // Side 8
  {5, 6}, // Side 9
  {6, 7}, // Side 10
  {4, 7}  // Side 11
};


// ------------------------------------------------------------
// Hex8 class member functions

bool Hex8::is_vertex(const unsigned int) const
{
  return true;
}

bool Hex8::is_edge(const unsigned int) const
{
  return false;
}

bool Hex8::is_face(const unsigned int) const
{
  return false;
}

bool Hex8::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 Hex8::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 Hex8::has_affine_map() const
{
  // Make sure x-edge endpoints are affine
  Point v = this->point(1) - this->point(0);
  if (!v.relative_fuzzy_equals(this->point(2) - this->point(3)) ||
      !v.relative_fuzzy_equals(this->point(5) - this->point(4)) ||
      !v.relative_fuzzy_equals(this->point(6) - this->point(7)))
    return false;
  // Make sure xz-faces are identical parallelograms
  v = this->point(4) - this->point(0);
  if (!v.relative_fuzzy_equals(this->point(7) - this->point(3)))
    return false;
  // If all the above checks out, the map is affine
  return true;
}



AutoPtr<Elem> Hex8::build_side (const unsigned int i,
				bool proxy) const
{
  libmesh_assert (i < this->n_sides());

  if (proxy)
    {
      AutoPtr<Elem> ap(new Side<Quad4,Hex8>(this,i));
      return ap;
    }
  
  else
    {
      AutoPtr<Elem> face(new Quad4);

      // Think of a unit cube: (-1,1) x (-1,1)x (-1,1)
      switch (i)
	{
	case 0:  // the face at z = -1
	  {
	    face->set_node(0) = this->get_node(0);
	    face->set_node(1) = this->get_node(3);
	    face->set_node(2) = this->get_node(2);
	    face->set_node(3) = this->get_node(1);

	    return face;
	  }
	case 1:  // the face at y = -1
	  {
	    face->set_node(0) = this->get_node(0);
	    face->set_node(1) = this->get_node(1);
	    face->set_node(2) = this->get_node(5);
	    face->set_node(3) = this->get_node(4);
	
	    return face;
	  }
	case 2:  // the face at x = 1
	  {
	    face->set_node(0) = this->get_node(1);
	    face->set_node(1) = this->get_node(2);
	    face->set_node(2) = this->get_node(6);
	    face->set_node(3) = this->get_node(5);

	    return face;
	  }
	case 3: // the face at y = 1
	  {
	    face->set_node(0) = this->get_node(2);
	    face->set_node(1) = this->get_node(3);
	    face->set_node(2) = this->get_node(7);
	    face->set_node(3) = this->get_node(6);
	
	    return face;
	  }
	case 4: // the face at x = -1
	  {
	    face->set_node(0) = this->get_node(3);
	    face->set_node(1) = this->get_node(0);
	    face->set_node(2) = this->get_node(4);
	    face->set_node(3) = this->get_node(7);

	    return face;
	  }
	case 5: // the face at z = 1
	  {
	    face->set_node(0) = this->get_node(4);
	    face->set_node(1) = this->get_node(5);
	    face->set_node(2) = this->get_node(6);
	    face->set_node(3) = this->get_node(7);
	
	    return face;
	  }
	default:
	  {
	    libmesh_error();
	    return face;
	  }
	}
    }
  
  // We'll never get here.
  libmesh_error();
  AutoPtr<Elem> ap(NULL);  return ap;
}



AutoPtr<Elem> Hex8::build_edge (const unsigned int i) const
{
  libmesh_assert (i < this->n_edges());

  AutoPtr<Elem> ap(new SideEdge<Edge2,Hex8>(this,i));
  return ap;
}
  


void Hex8::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);

  conn.resize(8);

  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;
	conn[4] = this->node(4)+1;
	conn[5] = this->node(5)+1;
	conn[6] = this->node(6)+1;
	conn[7] = this->node(7)+1;
	return;
      }

    case VTK:
      {
	conn[0] = this->node(0);
	conn[1] = this->node(1);
	conn[2] = this->node(2);
	conn[3] = this->node(3);
	conn[4] = this->node(4);
	conn[5] = this->node(5);
	conn[6] = this->node(6);
	conn[7] = this->node(7);
        return;
      }

    default:
      libmesh_error();
    }

  libmesh_error();
}



#ifdef ENABLE_AMR

const float Hex8::_embedding_matrix[8][8][8] =
{
  // embedding matrix for child 0
  {
    //  0     1     2     3     4     5     6     7
    { 1.0,  0.0,  0.0,  0.0,  0.0,  0.0,  0.0,  0.0}, // 0
    { 0.5,  0.5,  0.0,  0.0,  0.0,  0.0,  0.0,  0.0}, // 1
    { .25,  .25,  .25,  .25,  0.0,  0.0,  0.0,  0.0}, // 2
    { 0.5,  0.0,  0.0,  0.5,  0.0,  0.0,  0.0,  0.0}, // 3
    { 0.5,  0.0,  0.0,  0.0,  0.5,  0.0,  0.0,  0.0}, // 4
    { .25,  .25,  0.0,  0.0,  .25,  .25,  0.0,  0.0}, // 5
    {.125, .125, .125, .125, .125, .125, .125, .125}, // 6
    { .25,  0.0,  0.0,  .25,  .25,  0.0,  0.0,  .25}  // 7
  },

  // embedding matrix for child 1
  {
    //  0     1     2     3     4     5     6     7
    { 0.5,  0.5,  0.0,  0.0,  0.0,  0.0,  0.0,  0.0}, // 0
    { 0.0,  1.0,  0.0,  0.0,  0.0,  0.0,  0.0,  0.0}, // 1
    { 0.0,  0.5,  0.5,  0.0,  0.0,  0.0,  0.0,  0.0}, // 2
    { .25,  .25,  .25,  .25,  0.0,  0.0,  0.0,  0.0}, // 3
    { .25,  .25,  0.0,  0.0,  .25,  .25,  0.0,  0.0}, // 4
    { 0.0,  0.5,  0.0,  0.0,  0.0,  0.5,  0.0,  0.0}, // 5
    { 0.0,  .25,  .25,  0.0,  0.0,  .25,  .25,  0.0}, // 6
    {.125, .125, .125, .125, .125, .125, .125, .125}  // 7
  },

  // embedding matrix for child 2
  {
    //  0      1    2     3     4     5     6     7
    { 0.5,  0.0,  0.0,  0.5,  0.0,  0.0,  0.0,  0.0}, // 0
    { .25,  .25,  .25,  .25,  0.0,  0.0,  0.0,  0.0}, // 1
    { 0.0,  0.0,  0.5,  0.5,  0.0,  0.0,  0.0,  0.0}, // 2
    { 0.0,  0.0,  0.0,  1.0,  0.0,  0.0,  0.0,  0.0}, // 3
    { .25,  0.0,  0.0,  .25,  .25,  0.0,  0.0,  .25}, // 4
    {.125, .125, .125, .125, .125, .125, .125, .125}, // 5
    { 0.0,  0.0,  .25,  .25,  0.0,  0.0,  .25,  .25}, // 6
    { 0.0,  0.0,  0.0,  0.5,  0.0,  0.0,  0.0,  0.5}  // 7
  },

  // embedding matrix for child 3
  {
    //  0      1    2     3     4     5     6     7
    { .25,  .25,  .25,  .25,  0.0,  0.0,  0.0,  0.0}, // 0
    { 0.0,  0.5,  0.5,  0.0,  0.0,  0.0,  0.0,  0.0}, // 1
    { 0.0,  0.0,  1.0,  0.0,  0.0,  0.0,  0.0,  0.0}, // 2
    { 0.0,  0.0,  0.5,  0.5,  0.0,  0.0,  0.0,  0.0}, // 3
    {.125, .125, .125, .125, .125, .125, .125, .125}, // 4
    { 0.0,  .25,  .25,  0.0,  0.0,  .25,  .25,  0.0}, // 5
    { 0.0,  0.0,  0.5,  0.0,  0.0,  0.0,  0.5,  0.0}, // 6
    { 0.0,  0.0,  .25,  .25,  0.0,  0.0,  .25,  .25}  // 7
  },

  // embedding matrix for child 4
  {
    //  0      1    2     3     4     5     6     7
    { 0.5,  0.0,  0.0,  0.0,  0.5,  0.0,  0.0,  0.0}, // 0
    { .25,  .25,  0.0,  0.0,  .25,  .25,  0.0,  0.0}, // 1
    {.125, .125, .125, .125, .125, .125, .125, .125}, // 2
    { .25,  0.0,  0.0,  .25,  .25,  0.0,  0.0,  .25}, // 3
    { 0.0,  0.0,  0.0,  0.0,  1.0,  0.0,  0.0,  0.0}, // 4
    { 0.0,  0.0,  0.0,  0.0,  0.5,  0.5,  0.0,  0.0}, // 5
    { 0.0,  0.0,  0.0,  0.0,  .25,  .25,  .25,  .25}, // 6
    { 0.0,  0.0,  0.0,  0.0,  0.5,  0.0,  0.0,  0.5}  // 7
  },

  // embedding matrix for child 5
  {
    //  0      1    2     3     4     5     6     7
    { .25,  .25,  0.0,  0.0,  .25,  .25,  0.0,  0.0}, // 0
    { 0.0,  0.5,  0.0,  0.0,  0.0,  0.5,  0.0,  0.0}, // 1
    { 0.0,  .25,  .25,  0.0,  0.0,  .25,  .25,  0.0}, // 2
    {.125, .125, .125, .125, .125, .125, .125, .125}, // 3
    { 0.0,  0.0,  0.0,  0.0,  0.5,  0.5,  0.0,  0.0}, // 4
    { 0.0,  0.0,  0.0,  0.0,  0.0,  1.0,  0.0,  0.0}, // 5
    { 0.0,  0.0,  0.0,  0.0,  0.0,  0.5,  0.5,  0.0}, // 6
    { 0.0,  0.0,  0.0,  0.0,  .25,  .25,  .25,  .25}  // 7
  },

  // embedding matrix for child 6
  {
    //  0      1    2     3     4     5     6     7
    { .25,  0.0,  0.0,  .25,  .25,  0.0,  0.0,  .25}, // 0
    {.125, .125, .125, .125, .125, .125, .125, .125}, // 1
    { 0.0,  0.0,  .25,  .25,  0.0,  0.0,  .25,  .25}, // 2
    { 0.0,  0.0,  0.0,  0.5,  0.0,  0.0,  0.0,  0.5}, // 3
    { 0.0,  0.0,  0.0,  0.0,  0.5,  0.0,  0.0,  0.5}, // 4
    { 0.0,  0.0,  0.0,  0.0,  .25,  .25,  .25,  .25}, // 5
    { 0.0,  0.0,  0.0,  0.0,  0.0,  0.0,  0.5,  0.5}, // 6
    { 0.0,  0.0,  0.0,  0.0,  0.0,  0.0,  0.0,  1.0}  // 7
  },

  // embedding matrix for child 7
  {
    //  0      1    2     3     4     5     6     7
    {.125, .125, .125, .125, .125, .125, .125, .125}, // 0
    { 0.0,  .25,  .25,  0.0,  0.0,  .25,  .25,  0.0}, // 1
    { 0.0,  0.0,  0.5,  0.0,  0.0,  0.0,  0.5,  0.0}, // 2
    { 0.0,  0.0,  .25,  .25,  0.0,  0.0,  .25,  .25}, // 3
    { 0.0,  0.0,  0.0,  0.0,  .25,  .25,  .25,  .25}, // 4
    { 0.0,  0.0,  0.0,  0.0,  0.0,  0.5,  0.5,  0.0}, // 5
    { 0.0,  0.0,  0.0,  0.0,  0.0,  0.0,  1.0,  0.0}, // 6
    { 0.0,  0.0,  0.0,  0.0,  0.0,  0.0,  0.5,  0.5}  // 7
  }
};

#endif



Real Hex8::volume () const
{
  // Compute the volume of the tri-linear hex by splitting it
  // into 6 sub-pyramids and applying the formula in:
  // "Calculation of the Volume of a General Hexahedron
  // for Flow Predictions", AIAA Journal v.23, no.6, 1984, p.954-
  
  static const unsigned char sub_pyr[6][4] =
    {
      {0, 3, 2, 1},
      {6, 7, 4, 5},
      {0, 1, 5, 4},
      {3, 7, 6, 2},
      {0, 4, 7, 3},
      {1, 2, 6, 5}
    };

  // The centroid is a convenient point to use
  // for the apex of all the pyramids.
  const Point R = this->centroid();
  Node* pyr_base[4];
  
  Real vol=0.;

  // Compute the volume using 6 sub-pyramids
  for (unsigned int n=0; n<6; ++n)
    {
      // Set the nodes of the pyramid base
      for (unsigned int i=0; i<4; ++i)
	pyr_base[i] = this->_nodes[sub_pyr[n][i]];
      
      // Compute diff vectors
      Point a ( *pyr_base[0] - R );
      Point b ( *pyr_base[1] - *pyr_base[3] );
      Point c ( *pyr_base[2] - *pyr_base[0] );
      Point d ( *pyr_base[3] - *pyr_base[0] );
      Point e ( *pyr_base[1] - *pyr_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;
    }
  
  return vol;
}