cell_hex.c

一个用来实现偏微分方程中网格的计算库

// $Id: cell_hex.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
#include <algorithm> // for std::min, std::max

// Local includes
#include "cell_hex.h"
#include "cell_hex8.h"
#include "face_quad4.h"




// ------------------------------------------------------------
// Hex class member functions
unsigned int Hex::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 = -1

      return
	this->compute_key (this->node(0),
			   this->node(3),
			   this->node(2),
			   this->node(1));
      
    case 1:  // the face at y = -1

      return
	this->compute_key (this->node(0),
			   this->node(1),
			   this->node(5),
			   this->node(4));
      
    case 2:  // the face at x = 1

      return
	this->compute_key (this->node(1),
			   this->node(2),
			   this->node(6),
			   this->node(5));

    case 3: // the face at y = 1

      return
	this->compute_key (this->node(2),
			   this->node(3),
			   this->node(7),
			   this->node(6));
      
    case 4: // the face at x = -1
      
      return
	this->compute_key (this->node(3),
			   this->node(0),
			   this->node(4),
			   this->node(7));

    case 5: // the face at z = 1

      return
	this->compute_key (this->node(4),
			   this->node(5),
			   this->node(6),
			   this->node(7));	
    }

  // We'll never get here.
  libmesh_error();
  return 0;
}



AutoPtr<DofObject> Hex::side (const unsigned int i) const
{
  libmesh_assert (i < this->n_sides());


  
  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);

	AutoPtr<DofObject> ap(face);
        return ap;
      }
    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);
	
	AutoPtr<DofObject> ap(face);
        return ap;
      }
    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);

	AutoPtr<DofObject> ap(face);
        return ap;
      }
    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);
	
	AutoPtr<DofObject> ap(face);
        return ap;
      }
    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);

	AutoPtr<DofObject> ap(face);
        return ap;
      }
    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);
	
	AutoPtr<DofObject> ap(face);
        return ap;
      }
    default:
      {
	libmesh_error();
	AutoPtr<DofObject> ap(face);
        return ap;
      }
    }

  // We'll never get here.
  libmesh_error();
  AutoPtr<DofObject> ap(face);
  return ap;
}



bool Hex::is_child_on_side(const unsigned int c,
                           const unsigned int s) const
{
  libmesh_assert (c < this->n_children());
  libmesh_assert (s < this->n_sides());

  for (unsigned int i = 0; i != 4; ++i)
    if (Hex8::side_nodes_map[s][i] == c)
      return true;
  return false;
}



Real Hex::quality (const ElemQuality q) const
{
  switch (q)
    {
      
      /**
       * Compue the min/max diagonal ratio.
       * Source: CUBIT User's Manual.
       */
    case DIAGONAL:
      {
	// Diagonal between node 0 and node 6
	const Real d06 = this->length(0,6);

	// Diagonal between node 3 and node 5
	const Real d35 = this->length(3,5);

	// Diagonal between node 1 and node 7
	const Real d17 = this->length(1,7);

	// Diagonal between node 2 and node 4 
	const Real d24 = this->length(2,4);

	// Find the biggest and smallest diagonals
	const Real min = std::min(d06, std::min(d35, std::min(d17, d24)));
	const Real max = std::max(d06, std::max(d35, std::max(d17, d24)));

	libmesh_assert (max != 0.0);
	
	return min / max;

	break;
      }

      /**
       * Minimum ratio of lengths derived from opposite edges.
       * Source: CUBIT User's Manual.
       */
    case TAPER:
      {

	/**
	 * Compute the side lengths.
	 */
	const Real d01 = this->length(0,1);
	const Real d12 = this->length(1,2);
	const Real d23 = this->length(2,3);
	const Real d03 = this->length(0,3);
	const Real d45 = this->length(4,5);
	const Real d56 = this->length(5,6);
	const Real d67 = this->length(6,7);
	const Real d47 = this->length(4,7);
	const Real d04 = this->length(0,4);
	const Real d15 = this->length(1,5);
	const Real d37 = this->length(3,7);
	const Real d26 = this->length(2,6);

	std::vector<Real> edge_ratios(12);
	// Front
	edge_ratios[0] = std::min(d01, d45) / std::max(d01, d45);
	edge_ratios[1] = std::min(d04, d15) / std::max(d04, d15);

	// Right
	edge_ratios[2] = std::min(d15, d26) / std::max(d15, d26);
	edge_ratios[3] = std::min(d12, d56) / std::max(d12, d56);

	// Back
	edge_ratios[4] = std::min(d67, d23) / std::max(d67, d23);
	edge_ratios[5] = std::min(d26, d37) / std::max(d26, d37);

	// Left
	edge_ratios[6] = std::min(d04, d37) / std::max(d04, d37);
	edge_ratios[7] = std::min(d03, d47) / std::max(d03, d47);

	// Bottom
	edge_ratios[8] = std::min(d01, d23) / std::max(d01, d23);
	edge_ratios[9] = std::min(d03, d12) / std::max(d03, d12);

	// Top
	edge_ratios[10] = std::min(d45, d67) / std::max(d45, d67);
	edge_ratios[11] = std::min(d56, d47) / std::max(d56, d47);
	
	return *(std::min_element(edge_ratios.begin(), edge_ratios.end())) ;

	break;
      }


      /**
       * Minimum edge length divided by max diagonal length.
       * Source: CUBIT User's Manual.
       */
    case STRETCH:
      {
	const Real sqrt3 = 1.73205080756888;

	/**
	 * Compute the maximum diagonal.
	 */
	const Real d06 = this->length(0,6);
	const Real d17 = this->length(1,7);
	const Real d35 = this->length(3,5);
	const Real d24 = this->length(2,4);
	const Real max_diag = std::max(d06, std::max(d17, std::max(d35, d24)));

	libmesh_assert ( max_diag != 0.0 );

	/**
	 * Compute the minimum edge length.
	 */
	std::vector<Real> edges(12);
	edges[0]  = this->length(0,1);
	edges[1]  = this->length(1,2);
	edges[2]  = this->length(2,3);
	edges[3]  = this->length(0,3);
	edges[4]  = this->length(4,5);
	edges[5]  = this->length(5,6);
	edges[6]  = this->length(6,7);
	edges[7]  = this->length(4,7);
	edges[8]  = this->length(0,4);
	edges[9]  = this->length(1,5);
	edges[10] = this->length(2,6);
	edges[11] = this->length(3,7);

	const Real min_edge = *(std::min_element(edges.begin(), edges.end()));
	return sqrt3 * min_edge / max_diag ;
	break;
      }

      
      /**
       * I don't know what to do for this metric. 
       * Maybe the base class knows...
       */
    default:
      {
	return Elem::quality(q);
      }
    }

    
    // Will never get here...
    libmesh_error();
    return 0.;
}



std::pair<Real, Real> Hex::qual_bounds (const ElemQuality q) const
{
  std::pair<Real, Real> bounds;
  
  switch (q)
    {

    case ASPECT_RATIO:
      bounds.first  = 1.;
      bounds.second = 4.;
      break;
      
    case SKEW:
      bounds.first  = 0.;
      bounds.second = 0.5;
      break;

    case SHEAR:
    case SHAPE:
      bounds.first  = 0.3;
      bounds.second = 1.;
      break;

    case CONDITION:
      bounds.first  = 1.;
      bounds.second = 8.;
      break;

    case JACOBIAN:
      bounds.first  = 0.5;
      bounds.second = 1.;
      break;  
      
    case DISTORTION:
      bounds.first  = 0.6;
      bounds.second = 1.;
      break;  

    case TAPER:
      bounds.first  = 0.;
      bounds.second = 0.4;
      break;
      
    case STRETCH:
      bounds.first  = 0.25;
      bounds.second = 1.;
      break;
      
    case DIAGONAL:
      bounds.first  = 0.65;
      bounds.second = 1.;
      break;

    case SIZE:
      bounds.first  = 0.5;
      bounds.second = 1.;
      break;
      
    default:
      std::cout << "Warning: Invalid quality measure chosen." << std::endl;
      bounds.first  = -1;
      bounds.second = -1;
    }

  return bounds;
}



const unsigned short int Hex::_second_order_vertex_child_number[27] =
{
  99,99,99,99,99,99,99,99, // Vertices
  0,1,2,0,0,1,2,3,4,5,6,5, // Edges
  0,0,1,2,0,4,             // Faces
  0                        // Interior
};



const unsigned short int Hex::_second_order_vertex_child_index[27] =
{
  99,99,99,99,99,99,99,99, // Vertices
  1,2,3,3,4,5,6,7,5,6,7,7, // Edges
  2,5,6,7,7,6,             // Faces
  6                        // Interior
};


const unsigned short int Hex::_second_order_adjacent_vertices[12][2] = 
{
  { 0,  1}, // vertices adjacent to node 8 
  { 1,  2}, // vertices adjacent to node 9 
  { 2,  3}, // vertices adjacent to node 10 
  { 0,  3}, // vertices adjacent to node 11

  { 0,  4}, // vertices adjacent to node 12
  { 1,  5}, // vertices adjacent to node 13
  { 2,  6}, // vertices adjacent to node 14
  { 3,  7}, // vertices adjacent to node 15

  { 4,  5}, // vertices adjacent to node 16
  { 5,  6}, // vertices adjacent to node 17
  { 6,  7}, // vertices adjacent to node 18
  { 4,  7}  // vertices adjacent to node 19
};