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// This file is part of ff3d - http://www.freefem.org/ff3d
// Copyright (C) 2001, 2002, 2003 Stphane Del Pino
// This program is free software; you can redistribute it and/or modify
// it under the terms of the GNU General Public License as published by
// the Free Software Foundation; either version 2, or (at your option)
// any later version.
// This program 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 General Public License for more details.
// You should have received a copy of the GNU General Public License
// along with this program; if not, write to the Free Software Foundation,
// Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
// $Id: Q2HexahedronFiniteElement.hpp,v 1.2 2006/05/20 15:22:46 delpinux Exp $
#ifndef Q2_HEXAHEDRON_FINITE_ELEMENT_HPP
#define Q2_HEXAHEDRON_FINITE_ELEMENT_HPP
#include <TinyVector.hpp>
#include <TinyMatrix.hpp>
#include <QuadratureFormula.hpp>
#include <ConformTransformation.hpp>
#include <LagrangianFiniteElement.hpp>
#include <ThreadStaticBase.hpp>
class Q2HexahedronFiniteElement
: public ThreadStaticBase<Q2HexahedronFiniteElement>,
public LagrangianFiniteElement<27, Q2HexahedronFiniteElement,
QuadratureFormulaQ2Hexahedron>
{
private:
static TinyVector<3, real_t> __massCenter; /**< mass center of the reference element */
inline real_t __w1(const real_t& x) const
{
return (x-1)*(2*x-1);
}
inline real_t __w2(const real_t& x) const
{
return 4*x*(1-x);
}
inline real_t __w3(const real_t& x) const
{
return x*(2*x-1);
}
inline real_t __dw1(const real_t& x) const
{
return 4*x-3;
}
inline real_t __dw2(const real_t& x) const
{
return 4-8*x;
}
inline real_t __dw3(const real_t& x) const
{
return 4*x-1;
}
public:
enum {
numberOfDegreesOfFreedom = 27, /**< DOF means Degrees of Freedom */
numberOfVertexDegreesOfFreedom = 1,
numberOfEdgeDegreesOfFreedom = 1,
numberOfFaceDegreesOfFreedom = 1,
numberOfVolumeDegreesOfFreedom = 1,
numberOfFaceLivingDegreesOfFreedom = 9 // degrees of freedom carried by a face
};
/**
* Degrees of freedom living on faces
*/
static const size_t facesDOF[Hexahedron::NumberOfFaces][numberOfFaceLivingDegreesOfFreedom];
/**
* returns the mass center of the reference element
*
* @return __massCenter
*/
static const TinyVector<3, real_t>& massCenter()
{
return __massCenter;
}
/**
* Computes a hat function at a given point
*
* @param i the hat function number
* @param x the evaluation point
*
* @return \f$ w_i(\mathbf{x}) \f$
*/
real_t W (const size_t& i, const TinyVector<3, real_t>& x) const;
/**
* Computes a hat function derivative at a given point
*
* @param i the hat function number
* @param x the evaluation point
*
* @return \f$ \partial_x w_i(\mathbf{x}) \f$
*/
real_t dxW(const size_t& i, const TinyVector<3, real_t>& x) const;
/**
* Computes a hat function derivative at a given point
*
* @param i the hat function number
* @param x the evaluation point
*
* @return \f$ \partial_y w_i(\mathbf{x}) \f$
*/
real_t dyW(const size_t& i, const TinyVector<3, real_t>& x) const;
/**
* Computes a hat function derivative at a given point
*
* @param i the hat function number
* @param x the evaluation point
*
* @return \f$ \partial_z w_i(\mathbf{x}) \f$
*/
real_t dzW(const size_t& i, const TinyVector<3, real_t>& x) const;
inline const
TinyVector<QuadratureType::numberOfQuadraturePoints,
TinyVector<3, real_t> >&
integrationVertices() const
{
return QuadratureType::instance().vertices();
}
Q2HexahedronFiniteElement()
{
;
}
~Q2HexahedronFiniteElement()
{
;
}
};
#endif // Q2_HEXAHEDRON_FINITE_ELEMENT_HPP
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