/usr/include/dune/localfunctions/raviartthomas/raviartthomas12d/raviartthomas12dlocalbasis.hh is in libdune-localfunctions-dev 2.3.1-1.
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#ifndef DUNE_LOCALFUNCTIONS_RAVIARTTHOMAS12DLOCALBASIS_HH
#define DUNE_LOCALFUNCTIONS_RAVIARTTHOMAS12DLOCALBASIS_HH
#include <vector>
#include <dune/common/fmatrix.hh>
#include "../../common/localbasis.hh"
namespace Dune
{
/**
* @ingroup LocalBasisImplementation
* \brief First order Raviart-Thomas 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 RT12DLocalBasis
{
public:
typedef LocalBasisTraits<D,2,Dune::FieldVector<D,2>,R,2,Dune::FieldVector<R,2>,
Dune::FieldMatrix<R,2,2> > Traits;
//! \brief Standard constructor
RT12DLocalBasis ()
{
sign0 = sign1 = sign2 = 1.0;
}
/**
* \brief Make set number s, where 0 <= s < 8
*
* \param s Edge orientation indicator
*/
RT12DLocalBasis (unsigned int s)
{
sign0 = sign1 = sign2 = 1.0;
if (s & 1)
{
sign0 = -1.0;
}
if (s & 2)
{
sign1 = -1.0;
}
if (s & 4)
{
sign2 = -1.0;
}
}
//! \brief number of shape functions
unsigned int size () const
{
return 8;
}
/**
* \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(8);
out[0][0] = sign0*(in[0] - 4.0*in[0]*in[1]);
out[0][1] = sign0*(-1.0 + 5.0*in[1] - 4.0*in[1]*in[1]);
out[1][0] = sign1*(-1.0 + 5.0*in[0] - 4.0*in[0]*in[0]);
out[1][1] = sign1*(in[1] - 4.0*in[0]*in[1]);
out[2][0] = sign2*(-3.0*in[0] + 4.0*in[0]*in[0] + 4.0*in[1]*in[0]);
out[2][1] = sign2*(-3.0*in[1] + 4.0*in[0]*in[1] + 4.0*in[1]*in[1]);
out[3][0] = -5.0*in[0] + 8.0*in[0]*in[0] + 4.0*in[1]*in[0];
out[3][1] = 3.0 - 6.0*in[0] - 7.0*in[1] + 8.0*in[0]*in[1] + 4.0*in[1]*in[1];
out[4][0] = -3.0 + 7.0*in[0] + 6.0*in[1] - 4.0*in[0]*in[0] - 8.0*in[1]*in[0];
out[4][1] = 5.0*in[1] - 4.0*in[0]*in[1] - 8.0*in[1]*in[1];
out[5][0] = in[0] - 4.0*in[0]*in[0] + 4.0*in[1]*in[0];
out[5][1] = -1.0*in[1] - 4.0*in[0]*in[1] + 4.0*in[1]*in[1];
out[6][0] = 16.0*in[0] - 16.0*in[0]*in[0] - 8.0*in[1]*in[0];
out[6][1] = 8.0*in[1] - 16.0*in[0]*in[1] - 8.0*in[1]*in[1];
out[7][0] = 8.0*in[0] - 8.0*in[0]*in[0] - 16.0*in[1]*in[0];
out[7][1] = 16.0*in[1] - 8.0*in[0]*in[1] - 16.0*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(8);
out[0][0][0] = sign0*(1.0 - 4.0*in[1]);
out[0][0][1] = sign0*(-4.0*in[0]);
out[0][1][0] = 0.0;
out[0][1][1] = sign0*(5.0 - 8.0*in[1]);
out[1][0][0] = sign1*(5.0 - 8.0*in[0]);
out[1][0][1] = 0.0;
out[1][1][0] = sign1*(-4.0*in[1]);
out[1][1][1] = sign1*(1.0 - 4.0*in[0]);
out[2][0][0] = sign2*(-3.0 + 8.0*in[0] + 4.0*in[1]);
out[2][0][1] = sign2*(4.0*in[0]);
out[2][1][0] = sign2*(4.0*in[1]);
out[2][1][1] = sign2*(-3.0 + 4.0*in[0] + 8.0*in[1]);
out[3][0][0] = -5.0 + 16.0*in[0] + 4.0*in[1];
out[3][0][1] = 4.0*in[0];
out[3][1][0] = -6.0 + 8.0*in[1];
out[3][1][1] = -7.0 + 8.0*in[0] + 8.0*in[1];
out[4][0][0] = 7.0 - 8.0*in[0] - 8.0*in[1];
out[4][0][1] = 6.0 - 8.0*in[0];
out[4][1][0] = -4.0*in[1];
out[4][1][1] = 5.0 - 4.0*in[0] - 16.0*in[1];
out[5][0][0] = 1.0 - 8.0*in[0] + 4*in[1];
out[5][0][1] = 4.0*in[0];
out[5][1][0] = -4.0*in[1];
out[5][1][1] = -1.0 - 4.0*in[0] + 8.0*in[1];
out[6][0][0] = 16.0 - 32.0*in[0] - 8.0*in[1];
out[6][0][1] = -8.0*in[0];
out[6][1][0] = -16.0*in[1];
out[6][1][1] = 8.0 - 16.0*in[0] - 16.0*in[1];
out[7][0][0] = 8.0 - 16.0*in[0] - 16.0*in[1];
out[7][0][1] = -16.0*in[0];
out[7][1][0] = -8.0*in[1];
out[7][1][1] = 16.0 - 8.0*in[0] - 32.0*in[1];
}
//! \brief Polynomial order of the shape functions
unsigned int order () const
{
return 2;
}
private:
R sign0, sign1, sign2;
};
}
#endif // DUNE_LOCALFUNCTIONS_RAVIARTTHOMAS12DLOCALBASIS_HH
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