/usr/include/dune/localfunctions/brezzidouglasmarini/brezzidouglasmarini1simplex2d/brezzidouglasmarini1simplex2dlocalbasis.hh is in libdune-localfunctions-dev 2.3.1-1.
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// vi: set et ts=4 sw=2 sts=2:
#ifndef DUNE_LOCALFUNCTIONS_BREZZIDOUGLASMARINI1_SIMPLEX2D_LOCALBASIS_HH
#define DUNE_LOCALFUNCTIONS_BREZZIDOUGLASMARINI1_SIMPLEX2D_LOCALBASIS_HH
#include <vector>
#include <bitset>
#include <dune/common/fmatrix.hh>
#include "../../common/localbasis.hh"
namespace Dune
{
/**
* \ingroup LocalBasisImplementation
* \brief First order Brezzi-Douglas-Marini shape functions on the reference triangle.
*
* \tparam D Type to represent the field in the domain.
* \tparam R Type to represent the field in the range.
*
* \nosubgrouping
*/
template<class D, class R>
class BDM1Simplex2DLocalBasis
{
public:
typedef LocalBasisTraits<D,2,Dune::FieldVector<D,2>,R,2,Dune::FieldVector<R,2>,
Dune::FieldMatrix<R,2,2> > Traits;
//! \brief Standard constructor
BDM1Simplex2DLocalBasis ()
{
for (size_t i=0; i<3; i++)
sign_[i] = 1.0;
}
/**
* \brief Make set number s, where 0 <= s < 8
*
* \param s Edge orientation indicator
*/
BDM1Simplex2DLocalBasis (std::bitset<3> s)
{
for (size_t i=0; i<3; i++)
sign_[i] = s[i] ? -1.0 : 1.0;
}
//! \brief number of shape functions
unsigned int size () const
{
return 6;
}
/**
* \brief Evaluate all shape functions
*
* \param in Position
* \param out return value
*/
inline void evaluateFunction (const typename Traits::DomainType& in,
std::vector<typename Traits::RangeType>& out) const
{
out.resize(6);
out[0][0] = sign_[0]*in[0];
out[0][1] = sign_[0]*(in[1] - 1.0);
out[1][0] = sign_[1]*(in[0] - 1.0);
out[1][1] = sign_[1]*in[1];
out[2][0] = sign_[2]*in[0];
out[2][1] = sign_[2]*in[1];
out[3][0] = 3.0*in[0];
out[3][1] = 3.0 - 6.0*in[0] - 3.0*in[1];
out[4][0] = -3.0 + 3.0*in[0] + 6.0*in[1];
out[4][1] = -3.0*in[1];
out[5][0] = -3.0*in[0];
out[5][1] = 3.0*in[1];
}
/**
* \brief Evaluate Jacobian of all shape functions
*
* \param in Position
* \param out return value
*/
inline void evaluateJacobian (const typename Traits::DomainType& in,
std::vector<typename Traits::JacobianType>& out) const
{
out.resize(6);
out[0][0][0] = sign_[0];
out[0][0][1] = 0.0;
out[0][1][0] = 0.0;
out[0][1][1] = sign_[0];
out[1][0][0] = sign_[1];
out[1][0][1] = 0.0;
out[1][1][0] = 0.0;
out[1][1][1] = sign_[1];
out[2][0][0] = sign_[2];
out[2][0][1] = 0.0;
out[2][1][0] = 0.0;
out[2][1][1] = sign_[2];
out[3][0][0] = 3.0;
out[3][0][1] = 0.0;
out[3][1][0] = -6.0;
out[3][1][1] = -3.0;
out[4][0][0] = 3.0;
out[4][0][1] = 6.0;
out[4][1][0] = 0.0;
out[4][1][1] = -3.0;
out[5][0][0] = -3.0;
out[5][0][1] = 0.0;
out[5][1][0] = 0.0;
out[5][1][1] = 3.0;
}
//! \brief Polynomial order of the shape functions
unsigned int order () const
{
return 1;
}
private:
array<R,3> sign_;
};
}
#endif // DUNE_LOCALFUNCTIONS_BREZZIDOUGLASMARINI1_SIMPLEX2D_LOCALBASIS_HH
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