face_quad9.c

一个用来实现偏微分方程中网格的计算库

// $Id: face_quad9.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_edge3.h"
#include "face_quad9.h"




// ------------------------------------------------------------
// Quad9 class static member initializations
const unsigned int Quad9::side_nodes_map[4][3] =
{
  {0, 1, 4}, // Side 0
  {1, 2, 5}, // Side 1
  {2, 3, 6}, // Side 2
  {3, 0, 7}  // Side 3
};


#ifdef ENABLE_AMR

const float Quad9::_embedding_matrix[4][9][9] =
{
  // embedding matrix for child 0
  {
    //         0           1           2           3           4           5           6           7           8
    {    1.00000,    0.00000,    0.00000,    0.00000,    0.00000,    0.00000,    0.00000,    0.00000,    0.00000 }, // 0
    {    0.00000,    0.00000,    0.00000,    0.00000,    1.00000,    0.00000,    0.00000,    0.00000,    0.00000 }, // 1
    {    0.00000,    0.00000,    0.00000,    0.00000,    0.00000,    0.00000,    0.00000,    0.00000,    1.00000 }, // 2
    {    0.00000,    0.00000,    0.00000,    0.00000,    0.00000,    0.00000,    0.00000,    1.00000,    0.00000 }, // 3
    {   0.375000,  -0.125000,    0.00000,    0.00000,   0.750000,    0.00000,    0.00000,    0.00000,    0.00000 }, // 4
    {    0.00000,    0.00000,    0.00000,    0.00000,   0.375000,    0.00000,  -0.125000,    0.00000,   0.750000 }, // 5
    {    0.00000,    0.00000,    0.00000,    0.00000,    0.00000,  -0.125000,    0.00000,   0.375000,   0.750000 }, // 6
    {   0.375000,    0.00000,    0.00000,  -0.125000,    0.00000,    0.00000,    0.00000,   0.750000,    0.00000 }, // 7
    {   0.140625, -0.0468750,  0.0156250, -0.0468750,   0.281250, -0.0937500, -0.0937500,   0.281250,   0.562500 }  // 8
  },

  // embedding matrix for child 1
  {
    //         0           1           2           3           4           5           6           7           8
    {    0.00000,    0.00000,    0.00000,    0.00000,    1.00000,    0.00000,    0.00000,    0.00000,    0.00000 }, // 0
    {    0.00000,    1.00000,    0.00000,    0.00000,    0.00000,    0.00000,    0.00000,    0.00000,    0.00000 }, // 1
    {    0.00000,    0.00000,    0.00000,    0.00000,    0.00000,    1.00000,    0.00000,    0.00000,    0.00000 }, // 2
    {    0.00000,    0.00000,    0.00000,    0.00000,    0.00000,    0.00000,    0.00000,    0.00000,    1.00000 }, // 3
    {  -0.125000,   0.375000,    0.00000,    0.00000,   0.750000,    0.00000,    0.00000,    0.00000,    0.00000 }, // 4
    {    0.00000,   0.375000,  -0.125000,    0.00000,    0.00000,   0.750000,    0.00000,    0.00000,    0.00000 }, // 5
    {    0.00000,    0.00000,    0.00000,    0.00000,    0.00000,   0.375000,    0.00000,  -0.125000,   0.750000 }, // 6
    {    0.00000,    0.00000,    0.00000,    0.00000,   0.375000,    0.00000,  -0.125000,    0.00000,   0.750000 }, // 7
    { -0.0468750,   0.140625, -0.0468750,  0.0156250,   0.281250,   0.281250, -0.0937500, -0.0937500,   0.562500 }  // 8
  },

  // embedding matrix for child 2
  {
    //         0           1           2           3           4           5           6           7           8
    {    0.00000,    0.00000,    0.00000,    0.00000,    0.00000,    0.00000,    0.00000,    1.00000,    0.00000 }, // 0
    {    0.00000,    0.00000,    0.00000,    0.00000,    0.00000,    0.00000,    0.00000,    0.00000,    1.00000 }, // 1
    {    0.00000,    0.00000,    0.00000,    0.00000,    0.00000,    0.00000,    1.00000,    0.00000,    0.00000 }, // 2
    {    0.00000,    0.00000,    0.00000,    1.00000,    0.00000,    0.00000,    0.00000,    0.00000,    0.00000 }, // 3
    {    0.00000,    0.00000,    0.00000,    0.00000,    0.00000,  -0.125000,    0.00000,   0.375000,   0.750000 }, // 4
    {    0.00000,    0.00000,    0.00000,    0.00000,  -0.125000,    0.00000,   0.375000,    0.00000,   0.750000 }, // 5
    {    0.00000,    0.00000,  -0.125000,   0.375000,    0.00000,    0.00000,   0.750000,    0.00000,    0.00000 }, // 6
    {  -0.125000,    0.00000,    0.00000,   0.375000,    0.00000,    0.00000,    0.00000,   0.750000,    0.00000 }, // 7
    { -0.0468750,  0.0156250, -0.0468750,   0.140625, -0.0937500, -0.0937500,   0.281250,   0.281250,   0.562500 }  // 8
  },

  // embedding matrix for child 3
  {
    //         0           1           2           3           4           5           6           7           8
    {    0.00000,    0.00000,    0.00000,    0.00000,    0.00000,    0.00000,    0.00000,    0.00000,    1.00000 }, // 0
    {    0.00000,    0.00000,    0.00000,    0.00000,    0.00000,    1.00000,    0.00000,    0.00000,    0.00000 }, // 1
    {    0.00000,    0.00000,    1.00000,    0.00000,    0.00000,    0.00000,    0.00000,    0.00000,    0.00000 }, // 2
    {    0.00000,    0.00000,    0.00000,    0.00000,    0.00000,    0.00000,    1.00000,    0.00000,    0.00000 }, // 3
    {    0.00000,    0.00000,    0.00000,    0.00000,    0.00000,   0.375000,    0.00000,  -0.125000,   0.750000 }, // 4
    {    0.00000,  -0.125000,   0.375000,    0.00000,    0.00000,   0.750000,    0.00000,    0.00000,    0.00000 }, // 5
    {    0.00000,    0.00000,   0.375000,  -0.125000,    0.00000,    0.00000,   0.750000,    0.00000,    0.00000 }, // 6
    {    0.00000,    0.00000,    0.00000,    0.00000,  -0.125000,    0.00000,   0.375000,    0.00000,   0.750000 }, // 7
    {  0.0156250, -0.0468750,   0.140625, -0.0468750, -0.0937500,   0.281250,   0.281250, -0.0937500,   0.562500 }  // 8
  }
};

#endif



// ------------------------------------------------------------
// Quad9 class member functions

bool Quad9::is_vertex(const unsigned int i) const
{
  if (i < 4)
    return true;
  return false;
}

bool Quad9::is_edge(const unsigned int i) const
{
  if (i < 4)
    return false;
  if (i > 7)
    return false;
  return true;
}

bool Quad9::is_face(const unsigned int i) const
{
  if (i > 7)
    return true;
  return false;
}

bool Quad9::is_node_on_side(const unsigned int n,
			    const unsigned int s) const
{
  libmesh_assert(s < n_sides());
  for (unsigned int i = 0; i != 3; ++i)
    if (side_nodes_map[s][i] == n)
      return true;
  return false;
}



bool Quad9::has_affine_map() const
{
  // make sure corners form a parallelogram
  Point v = this->point(1) - this->point(0);
  if (!v.relative_fuzzy_equals(this->point(2) - this->point(3)))
    return false;
  // make sure "horizontal" sides are straight
  v /= 2;
  if (!v.relative_fuzzy_equals(this->point(4) - this->point(0)) ||
      !v.relative_fuzzy_equals(this->point(6) - this->point(3)))
    return false;
  // make sure "vertical" sides are straight
  // and the center node is centered
  v = (this->point(3) - this->point(0))/2;
  if (!v.relative_fuzzy_equals(this->point(7) - this->point(0)) ||
      !v.relative_fuzzy_equals(this->point(5) - this->point(1)) ||
      !v.relative_fuzzy_equals(this->point(8) - this->point(4)))
    return false;
  return true;
}


 
unsigned int Quad9::key (const unsigned int s) const
{
  libmesh_assert (s < this->n_sides());
  
  switch (s)
    {
    case 0:

      return
	this->compute_key (this->node(4));
	      
    case 1:

      return
	this->compute_key (this->node(5));
	
    case 2:

      return
	this->compute_key (this->node(6));
	
    case 3:

      return
	this->compute_key (this->node(7));
    }


  // We will never get here...  Look at the code above.
  libmesh_error();
  return 0;
}



AutoPtr<Elem> Quad9::build_side (const unsigned int i,
				 bool proxy) const
{
  libmesh_assert (i < this->n_sides());

  if (proxy)
    {
      AutoPtr<Elem> ap(new Side<Edge3,Quad9>(this,i));
      return ap;
    }

  else
    {
      Edge3* edge = new Edge3;

      switch (i)
	{
	case 0:
	  {
	    edge->set_node(0) = this->get_node(0);
	    edge->set_node(1) = this->get_node(1);
	    edge->set_node(2) = this->get_node(4);
	
	    AutoPtr<Elem> ap(edge);  return ap;
	  }
	case 1:
	  {
	    edge->set_node(0) = this->get_node(1);
	    edge->set_node(1) = this->get_node(2);
	    edge->set_node(2) = this->get_node(5);
	
	    AutoPtr<Elem> ap(edge);  return ap;
	  }
	case 2:
	  {
	    edge->set_node(0) = this->get_node(2);
	    edge->set_node(1) = this->get_node(3);
	    edge->set_node(2) = this->get_node(6);
	
	    AutoPtr<Elem> ap(edge);  return ap;
	  }
	case 3:
	  {
	    edge->set_node(0) = this->get_node(3);
	    edge->set_node(1) = this->get_node(0);
	    edge->set_node(2) = this->get_node(7);
	
	    AutoPtr<Elem> ap(edge);  return ap;
	  }
	default:
	  {
	    libmesh_error();
	  }
	}
    }

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







void Quad9::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);

  conn.resize(4);

  switch (iop)
    {
    case TECPLOT:
      {
	switch(sf)
	  {
	  case 0:
	    // linear sub-quad 0
	    conn[0] = this->node(0)+1;
	    conn[1] = this->node(4)+1;
	    conn[2] = this->node(8)+1;
	    conn[3] = this->node(7)+1;
	    return;

	  case 1:
	    // linear sub-quad 1
	    conn[0] = this->node(4)+1;
	    conn[1] = this->node(1)+1;
	    conn[2] = this->node(5)+1;
	    conn[3] = this->node(8)+1;
	    return;

	  case 2:
	    // linear sub-quad 2
	    conn[0] = this->node(7)+1;
	    conn[1] = this->node(8)+1;
	    conn[2] = this->node(6)+1;
	    conn[3] = this->node(3)+1;
	    return;

	  case 3:
	    // linear sub-quad 3
	    conn[0] = this->node(8)+1;
	    conn[1] = this->node(5)+1;
	    conn[2] = this->node(2)+1;
	    conn[3] = this->node(6)+1;
	    return;

	  default:
	    libmesh_error();
	  }
      }

    case VTK:
      {
        conn.resize(9);
        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);
        conn[8] = this->node(8);
	return;

	  /*
	switch(sf)
	  {
	  case 0:
	    // linear sub-quad 0
	    conn[0] = this->node(0);
	    conn[1] = this->node(4);
	    conn[2] = this->node(8);
	    conn[3] = this->node(7);

	    return;

	  case 1:
	    // linear sub-quad 1
	    conn[0] = this->node(4);
	    conn[1] = this->node(1);
	    conn[2] = this->node(5);
	    conn[3] = this->node(8);

	    return;

	  case 2:
	    // linear sub-quad 2
	    conn[0] = this->node(7);
	    conn[1] = this->node(8);
	    conn[2] = this->node(6);
	    conn[3] = this->node(3);

	    return;

	  case 3:
	    // linear sub-quad 3
	    conn[0] = this->node(8);
	    conn[1] = this->node(5);
	    conn[2] = this->node(2);
	    conn[3] = this->node(6);

	    return;

	  default:
	    libmesh_error();
	  }*/
      }

    default:
      {
	libmesh_error();
      }
    }

  libmesh_error();
}




unsigned int Quad9::n_second_order_adjacent_vertices (const unsigned int n) const
{
  switch (n)
    {
      case 4:
      case 5:
      case 6:
      case 7:
	return 2;

      case 8:
	return 4;

      default:
	libmesh_error();
    }

  libmesh_error();
  return libMesh::invalid_uint;
}



unsigned short int Quad9::second_order_adjacent_vertex (const unsigned int n,
							const unsigned int v) const
{ 
  libmesh_assert (n >= this->n_vertices());
  libmesh_assert (n <  this->n_nodes());

  switch (n)
    {
      case 8:
      {
	libmesh_assert (v < 4);
	return static_cast<unsigned short int>(v);
      }

      default:
      {
	libmesh_assert (v < 2);
	// use the matrix that we inherited from \p Quad
	return _second_order_adjacent_vertices[n-this->n_vertices()][v]; 
      }
    }
}



std::pair<unsigned short int, unsigned short int>
Quad9::second_order_child_vertex (const unsigned int n) const
{
  libmesh_assert (n >= this->n_vertices());
  libmesh_assert (n < this->n_nodes());
  /*
   * the _second_order_vertex_child_* vectors are
   * stored in face_quad.C, since they are identical
   * for Quad8 and Quad9 (for the first 4 higher-order nodes)
   */
  return std::pair<unsigned short int, unsigned short int>
    (_second_order_vertex_child_number[n],
     _second_order_vertex_child_index[n]);
}