/usr/include/dune/localfunctions/raviartthomas/raviartthomas1cube2d/raviartthomas1cube2dlocalbasis.hh is in libdune-localfunctions-dev 2.5.0-2.
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#ifndef DUNE_LOCALFUNCTIONS_RAVIARTTHOMAS1_CUBE2D_LOCALBASIS_HH
#define DUNE_LOCALFUNCTIONS_RAVIARTTHOMAS1_CUBE2D_LOCALBASIS_HH
#include <numeric>
#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 quadrilateral.
*
* \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 RT1Cube2DLocalBasis
{
public:
typedef LocalBasisTraits<D,2,Dune::FieldVector<D,2>,R,2,Dune::FieldVector<R,2>,
Dune::FieldMatrix<R,2,2> > Traits;
//! \brief Standard constructor
RT1Cube2DLocalBasis ()
{
sign0 = sign1 = sign2 = sign3 = 1.0;
}
/**
* \brief Make set number s, where 0 <= s < 16
*
* \param s Edge orientation indicator
*/
RT1Cube2DLocalBasis (unsigned int s)
{
sign0 = sign1 = sign2 = sign3 = 1.0;
if (s & 1)
{
sign0 = -1.0;
}
if (s & 2)
{
sign1 = -1.0;
}
if (s & 4)
{
sign2 = -1.0;
}
if (s & 8)
{
sign3 = -1.0;
}
}
//! \brief number of shape functions
unsigned int size () const
{
return 12;
}
/**
* \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(12);
out[0][0] = sign0*(-1.0 + 4.0*in[0]-3*in[0]*in[0]);
out[0][1] = 0.0;
out[1][0] = 3.0 - 12.0*in[0] - 6.0*in[1] + 24.0*in[0]*in[1]+9*in[0]*in[0] - 18.0*in[0]*in[0]*in[1];
out[1][1] = 0.0;
out[2][0] = sign1*(-2.0*in[0] + 3.0*in[0]*in[0]);
out[2][1] = 0.0;
out[3][0] = -6.0*in[0] + 12.0*in[0]*in[1] + 9.0*in[0]*in[0] - 18.0*in[0]*in[0]*in[1];
out[3][1] = 0.0;
out[4][0] = 0.0;
out[4][1] = sign2*(-1.0 + 4.0*in[1] - 3.0*in[1]*in[1]);
out[5][0] = 0.0;
out[5][1] = -3.0 + 6.0*in[0] + 12.0*in[1] - 24.0*in[0]*in[1] - 9.0*in[1]*in[1] + 18.0*in[0]*in[1]*in[1];
out[6][0] = 0.0;
out[6][1] = sign3*(-2.0*in[1] + 3.0*in[1]*in[1]);
out[7][0] = 0.0;
out[7][1] = 6.0*in[1] - 12.0*in[0]*in[1] - 9.0*in[1]*in[1] + 18.0*in[0]*in[1]*in[1];
out[8][0] = 24.0*in[0] - 36.0*in[0]*in[1] - 24.0*in[0]*in[0] + 36.0*in[0]*in[0]*in[1];
out[8][1] = 0.0;
out[9][0] = 0.0;
out[9][1] = 24.0*in[1] - 36.0*in[0]*in[1] - 24.0*in[1]*in[1] + 36.0*in[0]*in[1]*in[1];
out[10][0] = -36.0*in[0] + 72.0*in[0]*in[1] + 36.0*in[0]*in[0] - 72.0*in[0]*in[0]*in[1];
out[10][1] = 0.0;
out[11][0] = 0.0;
out[11][1] = -36.0*in[1] + 72.0*in[0]*in[1] + 36*in[1]*in[1] - 72.0*in[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(12);
out[0][0][0] = sign0*(4.0 - 6.0*in[0]);
out[0][0][1] = 0.0;
out[0][1][0] = 0.0;
out[0][1][1] = 0.0;
out[1][0][0] = -12.0 + 24.0*in[1] + 18.0*in[0] - 36.0*in[0]*in[1];
out[1][0][1] = -6 + 24.0*in[0] - 18.0*in[0]*in[0];
out[1][1][0] = 0.0;
out[1][1][1] = 0.0;
out[2][0][0] = sign1*(-2.0 + 6.0*in[0]);
out[2][0][1] = 0.0;
out[2][1][0] = 0.0;
out[2][1][1] = 0.0;
out[3][0][0] = -6.0 + 12.0*in[1] + 18.0*in[0] - 36.0*in[0]*in[1];
out[3][0][1] = 12.0*in[0] - 18.0*in[0]*in[0];
out[3][1][0] = 0.0;
out[3][1][1] = 0.0;
out[4][0][0] = 0.0;
out[4][0][1] = 0.0;
out[4][1][0] = 0.0;
out[4][1][1] = sign2*(4.0 - 6.0*in[1]);
out[5][0][0] = 0.0;
out[5][0][1] = 0.0;
out[5][1][0] = 6.0 - 24.0*in[1] + 18.0*in[1]*in[1];
out[5][1][1] = 12.0 - 24.0*in[0] - 18.0*in[1] + 36.0*in[0]*in[1];
out[6][0][0] = 0.0;
out[6][0][1] = 0.0;
out[6][1][0] = 0.0;
out[6][1][1] = sign3*(-2.0 + 6.0*in[1]);
out[7][0][0] = 0.0;
out[7][0][1] = 0.0;
out[7][1][0] = -12.0*in[1] + 18.0*in[1]*in[1];
out[7][1][1] = 6.0 - 12.0*in[0] - 18.0*in[1] + 36.0*in[1]*in[0];
out[8][0][0] = 24.0 - 36.0*in[1] - 48.0*in[0] + 72.0*in[0]*in[1];
out[8][0][1] = -36.0*in[0] + 36.0*in[0]*in[0];
out[8][1][0] = 0.0;
out[8][1][1] = 0.0;
out[9][0][0] = 0.0;
out[9][0][1] = 0.0;
out[9][1][0] = -36.0*in[1] + 36.0*in[1]*in[1];
out[9][1][1] = 24.0 - 36.0*in[0] - 48.0*in[1] + 72.0*in[0]*in[1];
out[10][0][0] = -36.0 + 72.0*in[1] + 72.0*in[0] - 144.0*in[0]*in[1];
out[10][0][1] = 72.0*in[0] - 72.0*in[0]*in[0];
out[10][1][0] = 0.0;
out[10][1][1] = 0.0;
out[11][0][0] = 0.0;
out[11][0][1] = 0.0;
out[11][1][0] = 72.0*in[1] - 72.0*in[1]*in[1];
out[11][1][1] = -36.0 + 72.0*in[0] + 72.0*in[1] - 144.0*in[0]*in[1];
}
//! \brief Evaluate partial derivatives of all shape functions
void partial (const std::array<unsigned int, 2>& order,
const typename Traits::DomainType& in, // position
std::vector<typename Traits::RangeType>& out) const // return value
{
auto totalOrder = std::accumulate(order.begin(), order.end(), 0);
if (totalOrder == 0) {
evaluateFunction(in, out);
} else {
DUNE_THROW(NotImplemented, "Desired derivative order is not implemented");
}
}
//! \brief Polynomial order of the shape functions
unsigned int order () const
{
return 3;
}
private:
R sign0, sign1, sign2, sign3;
};
}
#endif // DUNE_LOCALFUNCTIONS_RAVIARTTHOMAS1_CUBE2D_LOCALBASIS_HH
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