cell_prism18.h

一个用来实现偏微分方程中网格的计算库

// $Id: cell_prism18.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_prism18_h__
#define __cell_prism18_h__

// C++ includes

// Local includes
#include "cell_prism.h"




/**
 * The \p Prism18 is an element in 3D composed of 18 nodes.
 * It is numbered like this:
   \verbatim
   PRISM18:
            5
            o
           /:\
          / : \
         /  :  \
        /   :   \
    14 o    :    o 13
      /     :     \ 
     /      :      \
    /       o 11    \
 3 /        :        \4
  o---------o---------o
  |         :12       |
  |         :         |
  |    o    :    o    |
  |   17    o   16    |
  |        .2.        |
  |       .   .       |
9 o      .  o  .      o 10
  |     .  15   .     |
  |  8 o         o 7  |
  |   .           .   |
  |  .             .  |
  | .               . |
  |.                 .|
  o---------o---------o
  0         6         1

  
   \endverbatim
 */

// ------------------------------------------------------------
// Prism class definition
class Prism18 : public Prism
{
public:

  /**
   * Constructor.  By default this element has no parent.
   */
  Prism18  (Elem* p=NULL);
  
  /**
   * @returns \p PRISM18
   */
  ElemType     type () const   { return PRISM18; }

  /**
   * @returns 18
   */
  unsigned int n_nodes() const { return 18; }

  /**
   * @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 QUAD9 or \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 or \p INFEDGE2 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 edge nodes and 4 for face nodes
   */
  unsigned int n_second_order_adjacent_vertices (const unsigned int) const;

  /**
   * @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$ 6 \le n < 18 \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[5][9];

  /**
   * 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[9][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][18][18];
  
#endif
  
  /**
   * Matrix that tells which vertices define the location
   * of mid-side (or second-order) nodes.  This matrix
   * handles only the second-order nodes that are unique
   * to \p Prism18.  All other second-order nodes are identical
   * with \p Prism15, and are therefore handled through a 
   * matrix contained in \p cell_prism.C
   */
  static const unsigned short int _remaining_second_order_adjacent_vertices[3][4];
  
};



// ------------------------------------------------------------
// Prism18 class member functions
inline
Prism18::Prism18(Elem* p) :
  Prism(Prism18::n_nodes(), p) 
{
}


#endif // #define __cell_prism18_h__