cell_hex27.c

一个用来实现偏微分方程中网格的计算库

// $Id: cell_hex27.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_hex27.h"
#include "edge_edge3.h"
#include "face_quad9.h"



// ------------------------------------------------------------
// Hex27 class static member initializations
const unsigned int Hex27::side_nodes_map[6][9] =
{
  {0, 3, 2, 1, 11, 10,  9,  8, 20}, // Side 0
  {0, 1, 5, 4,  8, 13, 16, 12, 21}, // Side 1
  {1, 2, 6, 5,  9, 14, 17, 13, 22}, // Side 2
  {2, 3, 7, 6, 10, 15, 18, 14, 23}, // Side 3
  {3, 0, 4, 7, 11, 12, 19, 15, 24}, // Side 4
  {4, 5, 6, 7, 16, 17, 18, 19, 25}  // Side 5
};

const unsigned int Hex27::edge_nodes_map[12][3] =
{
  {0, 1, 8},  // Side 0
  {1, 2, 9},  // Side 1
  {2, 3, 10}, // Side 2
  {0, 3, 11}, // Side 3
  {0, 4, 12}, // Side 4
  {1, 5, 13}, // Side 5
  {2, 6, 14}, // Side 6
  {3, 7, 15}, // Side 7
  {4, 5, 16}, // Side 8
  {5, 6, 17}, // Side 9
  {6, 7, 18}, // Side 10
  {4, 7, 19}  // Side 11
};



// ------------------------------------------------------------
// Hex27 class member functions

bool Hex27::is_vertex(const unsigned int i) const
{
  if (i < 8)
    return true;
  return false;
}

bool Hex27::is_edge(const unsigned int i) const
{
  if (i < 8)
    return false;
  if (i > 19)
    return false;
  return true;
}

bool Hex27::is_face(const unsigned int i) const
{
  if (i == 26)
    return false;
  if (i > 19)
    return true;
  return false;
}

bool Hex27::is_node_on_side(const unsigned int n,
			    const unsigned int s) const
{
  libmesh_assert(s < n_sides());
  for (unsigned int i = 0; i != 9; ++i)
    if (side_nodes_map[s][i] == n)
      return true;
  return false;
}

bool Hex27::is_node_on_edge(const unsigned int n,
			    const unsigned int e) const
{
  libmesh_assert(e < n_edges());
  for (unsigned int i = 0; i != 3; ++i)
    if (edge_nodes_map[e][i] == n)
      return true;
  return false;
}



bool Hex27::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 x-edges are straight
  // and x-face and center points are centered
  v /= 2;
  if (!v.relative_fuzzy_equals(this->point(8) - this->point(0)) ||
      !v.relative_fuzzy_equals(this->point(10) - this->point(3)) ||
      !v.relative_fuzzy_equals(this->point(16) - this->point(4)) ||
      !v.relative_fuzzy_equals(this->point(18) - this->point(7)) ||
      !v.relative_fuzzy_equals(this->point(20) - this->point(11)) ||
      !v.relative_fuzzy_equals(this->point(21) - this->point(12)) ||
      !v.relative_fuzzy_equals(this->point(23) - this->point(15)) ||
      !v.relative_fuzzy_equals(this->point(25) - this->point(19)) ||
      !v.relative_fuzzy_equals(this->point(26) - this->point(24)))
    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;
  v /= 2;
  if (!v.relative_fuzzy_equals(this->point(12) - this->point(0)) ||
      !v.relative_fuzzy_equals(this->point(13) - this->point(1)) ||
      !v.relative_fuzzy_equals(this->point(14) - this->point(2)) ||
      !v.relative_fuzzy_equals(this->point(15) - this->point(3)) ||
      !v.relative_fuzzy_equals(this->point(22) - this->point(9)) ||
      !v.relative_fuzzy_equals(this->point(24) - this->point(11)))
    return false;
  // Make sure y-edges are straight
  v = (this->point(3) - this->point(0))/2;
  if (!v.relative_fuzzy_equals(this->point(11) - this->point(0)) ||
      !v.relative_fuzzy_equals(this->point(9) - this->point(1)) ||
      !v.relative_fuzzy_equals(this->point(17) - this->point(5)) ||
      !v.relative_fuzzy_equals(this->point(19) - this->point(4)))
    return false;
  // If all the above checks out, the map is affine
  return true;
}



unsigned int Hex27::key (const unsigned int s) const
{
 libmesh_assert (s < this->n_sides());

  // Think of a unit cube: (-1,1) x (-1,1) x (1,1)
  switch (s)
    {
    case 0:  // the face at z=0

      return
	this->compute_key (this->node(20));

    case 1:  // the face at y = 0

      return
	this->compute_key (this->node(21));

    case 2:  // the face at x=1