cell_hex20.h

一个用来实现偏微分方程中网格的计算库

// $Id: cell_hex20.h 2501 2007-11-20 02:33:29Z benkirk $

// 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



#ifndef __cell_hex20_h__
#define __cell_hex20_h__

// C++ includes

// Local includes
#include "cell_hex.h"




/**
 * The \p Hex20 is an element in 3D composed of 20 nodes.
 * It is numbered like this:
   \verbatim
   HEX20:      7              18             6     			      
               o--------------o--------------o     			      
              /:                            /|     			      
             / :                           / |     			      
            /  :                          /  |     			      
         19/   :                       17/   |     			      
          o    :                        o    |     			      
         /     :                       /     |     			      
        /    15o                      /    14o     
       /       :                     /       |     
     4/        :    16             5/        |     
     o--------------o--------------o         |     			      
     |         :                   |         |     
     |         :                   |         |     
     |         :              10   |         |                                
     |        3o..............o....|.........o     
     |        .                    |        / 2      
     |       .                   13|       /        
  12 o      .                      o      /         
     |     .                       |     /          
     |  11o                        |    o           
     |   .                         |   / 9          
     |  .                          |  /             
     | .                           | /              
     |.                            |/               
     o--------------o--------------o                
     0              8              1                
   \endverbatim
 */

// ------------------------------------------------------------
// Hex20 class definition
class Hex20 : public Hex
{
public:

  /**
   * Constructor.  By default this element has no parent.
   */
  Hex20  (Elem* p=NULL);
  
  /**
   * @returns \p HEX20
   */
  ElemType     type ()   const { return HEX20; }

  /**
   * @returns 20
   */
  unsigned int n_nodes() const { return 20; }
  
  /**
   * @returns 1
   */
  unsigned int n_sub_elem() const { return 1; }

  /**
   * @returns true iff the specified (local) node number is a vertex.
   */
  virtual bool is_vertex(const unsigned int i) const;

  /**
   * @returns true iff the specified (local) node number is an edge.
   */
  virtual bool is_edge(const unsigned int i) const;

  /**
   * @returns true iff the specified (local) node number is a face.
   */
  virtual bool is_face(const unsigned int i) const;
  
  /*
   * @returns true iff the specified (local) node number is on the
   * specified side
   */
  virtual bool is_node_on_side(const unsigned int n,
			       const unsigned int s) const;

  /*
   * @returns true iff the specified (local) node number is on the
   * specified edge
   */
  virtual bool is_node_on_edge(const unsigned int n,
			       const unsigned int e) const;

  /*
   * @returns true iff the element map is definitely affine within
   * numerical tolerances
   */
  virtual bool has_affine_map () const;

  /**
   * @returns SECOND
   */
  Order default_order() const { return SECOND; }
  
  /**
   * Builds a \p QUAD8 built coincident with face i.
   * The \p AutoPtr<Elem> handles the memory aspect.
   */
  AutoPtr<Elem> build_side (const unsigned int i,
			    bool proxy) const;

  /**
   * Builds a \p EDGE3 built coincident with edge i.
   * The \p AutoPtr<Elem> handles the memory aspect.
   */
  AutoPtr<Elem> build_edge (const unsigned int i) const;

  virtual void connectivity(const unsigned int sc,
			    const IOPackage iop,
			    std::vector<unsigned int>& conn) const;

  /**
   * @returns 2 for all \p n
   */
  unsigned int n_second_order_adjacent_vertices (const unsigned int) const
      { return 2; }

  /**
   * @returns the element-local number of the  \f$ v^{th} \f$ vertex
   * that defines the \f$ n^{th} \f$ second-order node.
   * Note that \p n is counted as depicted above, \f$ 8 \le n < 20 \f$.
   */
  unsigned short int second_order_adjacent_vertex (const unsigned int n,
						   const unsigned int v) const;

  /**
   * @returns the child number \p c and element-local index \p v of the
   * \f$ n^{th} \f$ second-order node on the parent element.  Note that
   * the return values are always less \p this->n_children() and 
   * \p this->child(c)->n_vertices(), while \p n has to be greater or equal
   * to \p * this->n_vertices().  For linear elements this returns 0,0.
   * On refined second order elements, the return value will satisfy
   * \p this->get_node(n)==this->child(c)->get_node(v)
   */
  virtual std::pair<unsigned short int, unsigned short int> 
	  second_order_child_vertex (const unsigned int n) const;

  /**
   * This maps the \f$ j^{th} \f$ node of the \f$ i^{th} \f$ side to
   * element node numbers.
   */
  static const unsigned int side_nodes_map[6][8];
  
  /**
   * This maps the \f$ j^{th} \f$ node of the \f$ i^{th} \f$ edge to
   * element node numbers.
   */
  static const unsigned int edge_nodes_map[12][3];
  

protected:
  
  
#ifdef ENABLE_AMR

  /**
   * Matrix used to create the elements children.
   */
  float embedding_matrix (const unsigned int i,
			  const unsigned int j,
			  const unsigned int k) const
  { return _embedding_matrix[i][j][k]; }

  /**
   * Matrix that computes new nodal locations/solution values
   * from current nodes/solution.
   */
  static const float _embedding_matrix[8][20][20];
  
#endif

};


   
// ------------------------------------------------------------
// Hex20 class member functions
inline
Hex20::Hex20(Elem* p) :
  Hex(Hex20::n_nodes(), p) 
{
}


#endif