face_quad.h

一个用来实现偏微分方程中网格的计算库

// $Id: face_quad.h 2780 2008-04-11 23:31:32Z 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



#ifndef __quad_h__
#define __quad_h__


// C++ includes


// Local includes
#include "libmesh_common.h"
#include "face.h"


// Forward declarations


/**
 * The \p QUAD is an element in 2D composed of 4 sides.
 * It looks like this:
 * \verbatim
 *                   
 *         ----------- 
 *        |           |
 *        |           |
 *        |           | 
 *        |           |
 *        |           |
 *         ----------- 
 *                   
 * \endverbatim
 */

// ------------------------------------------------------------
// Quad class definition
class Quad : public Face
{
public:

  /**
   * Default quadrilateral element, takes number of nodes and 
   * parent. Derived classes implement 'true' elements.
   */
  Quad (const unsigned int nn, Elem* p) :
    Face(nn, Quad::n_sides(), p) {}
 
  /**
   * Constructor.  Explicitly specifies the number of
   * nodes and neighbors for which storage will be allocated.
   */
  Quad (const unsigned int nn,
	const unsigned int ns,
	Elem* p) :
    Face(nn, ns, p) {}

  /**
   * @returns 4.  All quad-derivatives are guaranteed to have at
   * least 4 nodes.
   */
  unsigned int n_nodes() const { return 4; }

  /**
   * @returns 4
   */
  unsigned int n_sides() const { return 4; }  

  /**
   * @returns 4.  All quadrilaterals have 4 vertices.
   */
  unsigned int n_vertices() const { return 4; }

  /**
   * @returns 4.  All quadrilaterals have 4 edges.
   */
  unsigned int n_edges() const { return 4; }

  /**
   * @returns 4
   */
  unsigned int n_children() const { return 4; }
  
  /*
   * @returns true iff the specified child is on the
   * specified side
   */
  virtual bool is_child_on_side(const unsigned int c,
			        const unsigned int s) const;
  
  /**
   * @returns an id associated with the \p s side of this element.
   * The id is not necessariy unique, but should be close.  This is
   * particularly useful in the \p MeshBase::find_neighbors() routine.
   */
  unsigned int key (const unsigned int s) const;

  /**
   * @returns a primitive (2-noded) edge for 
   * edge i.
   */
  AutoPtr<DofObject> side (const unsigned int i) const;
  
  /**
   * Based on the quality metric q specified by the user,
   * returns a quantitative assessment of element quality.
   */
  Real quality (const ElemQuality q) const;

  /**
   * Returns the suggested quality bounds for
   * the hex based on quality measure q.  These are
   * the values suggested by the CUBIT User's Manual.
   */
  std::pair<Real, Real> qual_bounds (const ElemQuality q) const;
  
  /**
   * Matrix that tells which vertices define the location
   * of mid-side (or second-order) nodes.  Since most 
   * second-order nodes are identical for \p Quad8 and \p Quad9,
   * we keep this matrix here in \p Quad
   */
  static const unsigned short int _second_order_adjacent_vertices[4][2];

  /**
   * Vector that names a child sharing each second order node. 
   */
  static const unsigned short int _second_order_vertex_child_number[9];

  /**
   * Vector that names the child vertex index for each second order node.
   */
  static const unsigned short int _second_order_vertex_child_index[9];
};


// ------------------------------------------------------------
// Quad class member functions


#endif