cell_tet10.h

一个用来实现偏微分方程中网格的计算库

// $Id: cell_tet10.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_tet10_h__
#define __cell_tet10_h__

// C++ includes

// Local includes
#include "cell_tet.h"




/**
 * The \p Tet10 is an element in 3D composed of 10 nodes.
 * It is numbered like this:
  \verbatim
              3
  TET10:      o
             /|\
            / | \
        7  /  |  \9
          o   |   o
         /    |8   \
        /     o     \
       /    6 |      \
    0 o.....o.|.......o 2
       \      |      /
        \     |     /
         \    |    /
        4 o   |   o 5
           \  |  /
            \ | /
             \|/
              o
              1
   \endverbatim
 */

// ------------------------------------------------------------
// Tet10 class definition
class Tet10 : public Tet
{
public:

  /**
   * Constructor.  By default this element has no parent.
   */
  Tet10  (Elem* p=NULL);
  
  /**
   * @returns \p TET10
   */
  ElemType     type ()   const { return TET10; }

  /**
   * @returns 10
   */
  unsigned int n_nodes() const { return 10; }

  /**
   * @returns 8
   */
  unsigned int n_sub_elem() const { return 8; }
  
  /**
   * @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 TRI6 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$ 4 \le n < 10 \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[4][6];

  /**
   * 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[6][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][10][10];
  
  /**
   * This enumeration keeps track of which diagonal is selected during
   * refinement.  In general there are three possible diagonals to
   * choose when splitting the octahedron, and by choosing the shortest
   * one we obtain the best element shape.
   */
  enum Diagonal
    {DIAG_02_13=0,    // diagonal between edges (0,2) and (1,3)
     DIAG_03_12=1,    // diagonal between edges (0,3) and (1,2)
     DIAG_01_23=2,    // diagonal between edges (0,1) and (2,3)
     INVALID_DIAG=99  // diagonal not yet selected
    };

  mutable Diagonal _diagonal_selection;

#endif


private:
  
  /**
   * Matrix that tells which vertices define the location
   * of mid-side (or second-order) nodes
   */
  static const unsigned short int _second_order_adjacent_vertices[6][2];

  /**
   * Vector that names a child sharing each second order node. 
   */
  static const unsigned short int _second_order_vertex_child_number[10];

  /**
   * Vector that names the child vertex index for each second order node.
   */
  static const unsigned short int _second_order_vertex_child_index[10];
};



// ------------------------------------------------------------
// Tet10 class member functions
inline
Tet10::Tet10(Elem* p) :
  Tet(Tet10::n_nodes(), p)
#ifdef ENABLE_AMR
  , _diagonal_selection(INVALID_DIAG)
#endif
{
}


#endif