/usr/include/dune/localfunctions/brezzidouglasmarini/brezzidouglasmarini2cube2d/brezzidouglasmarini2cube2dlocalbasis.hh is in libdune-localfunctions-dev 2.3.1-1.
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#ifndef DUNE_LOCALFUNCTIONS_BREZZIDOUGLASMARINI2_CUBE2D_LOCALBASIS_HH
#define DUNE_LOCALFUNCTIONS_BREZZIDOUGLASMARINI2_CUBE2D_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 quadrilaterals.
*
* \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 BDM2Cube2DLocalBasis
{
public:
typedef LocalBasisTraits<D,2,Dune::FieldVector<D,2>,
R,2,Dune::FieldVector<R,2>,
Dune::FieldMatrix<R,2,2> > Traits;
//! \brief Standard constructor
BDM2Cube2DLocalBasis()
{
for (size_t i=0; i<4; i++)
sign_[i] = 1.0;
}
/**
* \brief Make set number s, where 0 <= s < 16
*
* \param s Edge orientation indicator
*/
BDM2Cube2DLocalBasis(std::bitset<4> s)
{
for (size_t i=0; i<4; i++)
sign_[i] = s[i] ? -1.0 : 1.0;
}
//! \brief number of shape functions
unsigned int size() const
{
return 14;
}
/**
* \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(size());
out[0][0] = sign_[0]*(-2.25 + 5.25*in[0] + 7.5*in[1] - 7.5*in[0]*in[1] - 3.0*in[0]*in[0] - 7.5*in[1]*in[1] + 7.5*in[0]*in[1]*in[1]);
out[0][1] = sign_[0]*(-1.25*in[1] + 3.75*in[1]*in[1] - 2.5*in[1]*in[1]*in[1]);
out[1][0] = 3.0 - 3.0*in[0]-6.0*in[1] + 6.0*in[0]*in[1];
out[1][1] = 0.0;
out[2][0] = sign_[0]*(-3.75 + 3.75*in[0] + 22.5*in[1] - 22.5*in[0]*in[1] - 22.5*in[1]*in[1] + 22.5*in[0]*in[1]*in[1]);
out[2][1] = sign_[0]*(-3.75*in[1] + 11.25*in[1]*in[1] - 7.5*in[1]*in[1]*in[1]);
out[3][0] = sign_[1]*(-0.75*in[0] - 7.5*in[0]*in[1] + 3.0*in[0]*in[0] + 7.5*in[0]*in[1]*in[1]);
out[3][1] = sign_[1]*(-1.25*in[1] + 3.75*in[1]*in[1] - 2.5*in[1]*in[1]*in[1]);
out[4][0] = 3.0*in[0] - 6.0*in[0]*in[1];
out[4][1] = 0.0;
out[5][0] = sign_[1]*(+3.75*in[0] - 22.5*in[0]*in[1] + 22.5*in[0]*in[1]*in[1]);
out[5][1] = sign_[1]*(-3.75*in[1] + 11.25*in[1]*in[1] - 7.5*in[1]*in[1]*in[1]);
out[6][0] = sign_[2]*(-1.25*in[0] + 3.75*in[0]*in[0] - 2.5*in[0]*in[0]*in[0]);
out[6][1] = sign_[2]*(-2.25 + 7.5*in[0] + 5.25*in[1] - 7.5*in[0]*in[1] - 7.5*in[0]*in[0] - 3.0*in[1]*in[1] + 7.5*in[0]*in[0]*in[1]);
out[7][0] = 0.0;
out[7][1] = -3.0 + 6.0*in[0] + 3.0*in[1] - 6.0*in[0]*in[1];
out[8][0] = sign_[2]*(-3.75*in[0] + 11.25*in[0]*in[0] - 7.5*in[0]*in[0]*in[0]);
out[8][1] = sign_[2]*(-3.75 + 22.5*in[0] + 3.75*in[1] - 22.5*in[0]*in[1] - 22.5*in[0]*in[0] + 22.5*in[0]*in[0]*in[1]);
out[9][0] = sign_[3]*(-1.25*in[0] + 3.75*in[0]*in[0] - 2.5*in[0]*in[0]*in[0]);
out[9][1] = sign_[3]*(-0.75*in[1] - 7.5*in[0]*in[1] + 3.0*in[1]*in[1] + 7.5*in[0]*in[0]*in[1]);
out[10][0] = 0.0;
out[10][1] = -3.0*in[1] + 6.0*in[0]*in[1];
out[11][0] = sign_[3]*(-3.75*in[0] + 11.25*in[0]*in[0] - 7.5*in[0]*in[0]*in[0]);
out[11][1] = sign_[3]*(3.75*in[1] - 22.5*in[0]*in[1] + 22.5*in[0]*in[0]*in[1]);
out[12][0] = 6.0*in[0] - 6.0*in[0]*in[0];
out[12][1] = 0.0;
out[13][0] = 0.0;
out[13][1] = 6.0*in[1] - 6.0*in[1]*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(size());
out[0][0][0] = sign_[0]*(5.25 - 7.5*in[1] - 6.0*in[0] + 7.5*in[1]*in[1]);
out[0][0][1] = sign_[0]*(7.5 - 7.5*in[0] - 15.0*in[1] + 15.0*in[0]*in[1]);
out[0][1][0] = 0.0;
out[0][1][1] = sign_[0]*(-1.25 + 7.5*in[1] - 7.5*in[1]*in[1]);
out[1][0][0] = -3.0 + 6.0*in[1];
out[1][0][1] = -6.0 + 6.0*in[0];
out[1][1][0] = 0.0;
out[1][1][1] = 0.0;
out[2][0][0] = sign_[0]*(3.75 - 22.5*in[1] + 22.5*in[1]*in[1]);
out[2][0][1] = sign_[0]*(22.5 - 22.5*in[0] - 45.0*in[1] + 45.0*in[0]*in[1]);
out[2][1][0] = 0.0;
out[2][1][1] = sign_[0]*(-3.75 + 22.5*in[1] - 22.5*in[1]*in[1]);
out[3][0][0] = sign_[1]*(-0.75 - 7.5*in[1] + 6.0*in[0] + 7.5*in[1]*in[1]);
out[3][0][1] = sign_[1]*(-7.5*in[0] + 15.0*in[0]*in[1]);
out[3][1][0] = 0.0;
out[3][1][1] = sign_[1]*(-1.25 + 7.5*in[1] - 7.5*in[1]*in[1]);
out[4][0][0] = 3.0 - 6.0*in[1];
out[4][0][1] = -6.0*in[0];
out[4][1][0] = 0.0;
out[4][1][1] = 0.0;
out[5][0][0] = sign_[1]*(3.75 - 22.5*in[1] + 22.5*in[1]*in[1]);
out[5][0][1] = sign_[1]*(-22.5*in[0] + 45.0*in[0]*in[1]);
out[5][1][0] = 0.0;
out[5][1][1] = sign_[1]*(-3.75 + 22.5*in[1] - 22.5*in[1]*in[1]);
out[6][0][0] = sign_[2]*(-1.25 + 7.5*in[0] - 7.5*in[0]*in[0]);
out[6][0][1] = 0.0;
out[6][1][0] = sign_[2]*(7.5 - 7.5*in[1] - 15.0*in[0] + 15.0*in[0]*in[1]);
out[6][1][1] = sign_[2]*(5.25 - 7.5*in[0]- 6.0*in[1] + 7.5*in[0]*in[0]);
out[7][0][0] = 0.0;
out[7][0][1] = 0.0;
out[7][1][0] = 6.0 - 6.0*in[1];
out[7][1][1] = 3.0 - 6.0*in[0];
out[8][0][0] = sign_[2]*(-3.75 + 22.5*in[0] - 22.5*in[0]*in[0]);
out[8][0][1] = 0.0;
out[8][1][0] = sign_[2]*(22.5 - 22.5*in[1] - 45.0*in[0] + 45.0*in[0]*in[1]);
out[8][1][1] = sign_[2]*(3.75 - 22.5*in[0] + 22.5*in[0]*in[0]);
out[9][0][0] = sign_[3]*(-1.25 + 7.5*in[0] - 7.5*in[0]*in[0]);
out[9][0][1] = 0.0;
out[9][1][0] = sign_[3]*(-7.5*in[1] + 15.0*in[0]*in[1]);
out[9][1][1] = sign_[3]*(-0.75 - 7.5*in[0] + 6.0*in[1] + 7.5*in[0]*in[0]);
out[10][0][0] = 0.0;
out[10][0][1] = 0.0;
out[10][1][0] = 6.0*in[1];
out[10][1][1] = -3.0 + 6.0*in[0];
out[11][0][0] = sign_[3]*(-3.75 + 22.5*in[0] - 22.5*in[0]*in[0]);
out[11][0][1] = 0.0;
out[11][1][0] = sign_[3]*(-22.5*in[1] + 45*in[0]*in[1]);
out[11][1][1] = sign_[3]*(3.75 - 22.5*in[0] + 22.5*in[0]*in[0]);
out[12][0][0] = 6.0 - 12.0*in[0];
out[12][0][1] = 0.0;
out[12][1][0] = 0.0;
out[12][1][1] = 0.0;
out[13][0][0] = 0.0;
out[13][0][1] = 0.0;
out[13][1][0] = 0.0;
out[13][1][1] = 6.0 - 12.0*in[1];
}
//! \brief Polynomial order of the shape functions
unsigned int order() const
{
return 3;
}
private:
array<R,4> sign_;
};
} // end namespace Dune
#endif // DUNE_LOCALFUNCTIONS_BREZZIDOUGLASMARINI2_CUBE2D_LOCALBASIS_HH
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