/usr/include/dune/localfunctions/raviartthomas/raviartthomas0cube2d/raviartthomas0cube2dall.hh is in libdune-localfunctions-dev 2.4.1-1.
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#ifndef DUNE_LOCALFUNCTIONS_RAVIARTTHOMAS0_CUBE2D_ALL_HH
#define DUNE_LOCALFUNCTIONS_RAVIARTTHOMAS0_CUBE2D_ALL_HH
#include <cstddef>
#include <vector>
#include <dune/common/fmatrix.hh>
#include <dune/localfunctions/common/localbasis.hh>
#include <dune/localfunctions/common/localkey.hh>
namespace Dune
{
/**@ingroup LocalBasisImplementation
\brief Lowest 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 RT0Cube2DLocalBasis
{
public:
typedef LocalBasisTraits<D,2,Dune::FieldVector<D,2>,R,2,Dune::FieldVector<R,2>,
Dune::FieldMatrix<R,2,2> > Traits;
//! \brief Standard constructor
RT0Cube2DLocalBasis ()
{
sign0 = sign1 = sign2 = sign3 = 1.0;
}
//! \brief Make set numer s, where 0<=s<16
RT0Cube2DLocalBasis (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 4;
}
//! \brief Evaluate all shape functions
inline void evaluateFunction (const typename Traits::DomainType& in,
std::vector<typename Traits::RangeType>& out) const
{
out.resize(4);
out[0][0] = sign0*(in[0]-1.0); out[0][1]=0.0;
out[1][0] = sign1*(in[0]); out[1][1]=0.0;
out[2][0] = 0.0; out[2][1]=sign2*(in[1]-1.0);
out[3][0] = 0.0; out[3][1]=sign3*(in[1]);
}
//! \brief Evaluate Jacobian of all shape functions
inline void
evaluateJacobian (const typename Traits::DomainType& in, // position
std::vector<typename Traits::JacobianType>& out) const // return value
{
out.resize(4);
out[0][0][0] = sign0; out[0][0][1] = 0;
out[0][1][0] = 0; out[0][1][1] = 0;
out[1][0][0] = sign1; out[1][0][1] = 0;
out[1][1][0] = 0; out[1][1][1] = 0;
out[2][0][0] = 0; out[2][0][1] = 0;
out[2][1][0] = 0; out[2][1][1] = sign2;
out[3][0][0] = 0; out[3][0][1] = 0;
out[3][1][0] = 0; out[3][1][1] = sign3;
}
//! \brief Polynomial order of the shape functions
unsigned int order () const
{
return 1;
}
private:
R sign0, sign1, sign2, sign3;
};
/**@ingroup LocalInterpolationImplementation
\brief Lowest order Raviart-Thomas shape functions on the reference quadrilateral.
\tparam LB corresponding LocalBasis giving traits
\nosubgrouping
*/
template<class LB>
class RT0Cube2DLocalInterpolation
{
public:
//! \brief Standard constructor
RT0Cube2DLocalInterpolation ()
{
sign0 = sign1 = sign2 = sign3 = 1.0;
}
//! \brief Make set numer s, where 0<=s<8
RT0Cube2DLocalInterpolation (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;
m0[0] = 0.0; m0[1] = 0.5;
m1[0] = 1.0; m1[1] = 0.5;
m2[0] = 0.5; m2[1] = 0.0;
m3[0] = 0.5; m3[1] = 1.0;
n0[0] = -1.0; n0[1] = 0.0;
n1[0] = 1.0; n1[1] = 0.0;
n2[0] = 0.0; n2[1] = -1.0;
n3[0] = 0.0; n3[1] = 1.0;
}
template<typename F, typename C>
void interpolate (const F& f, std::vector<C>& out) const
{
// f gives v*outer normal at a point on the edge!
typename F::Traits::RangeType y;
out.resize(4);
f.evaluate(m0,y); out[0] = (y[0]*n0[0]+y[1]*n0[1])*sign0;
f.evaluate(m1,y); out[1] = (y[0]*n1[0]+y[1]*n1[1])*sign1;
f.evaluate(m2,y); out[2] = (y[0]*n2[0]+y[1]*n2[1])*sign2;
f.evaluate(m3,y); out[3] = (y[0]*n3[0]+y[1]*n3[1])*sign3;
}
private:
typename LB::Traits::RangeFieldType sign0,sign1,sign2,sign3;
typename LB::Traits::DomainType m0,m1,m2,m3;
typename LB::Traits::DomainType n0,n1,n2,n3;
};
/**@ingroup LocalLayoutImplementation
\brief Layout map for RT0 elements on quadrilaterals
\nosubgrouping
\implements Dune::LocalCoefficientsVirtualImp
*/
class RT0Cube2DLocalCoefficients
{
public:
//! \brief Standard constructor
RT0Cube2DLocalCoefficients () : li(4)
{
for (std::size_t i=0; i<4; i++)
li[i] = LocalKey(i,1,0);
}
//! number of coefficients
std::size_t size () const
{
return 4;
}
//! get i'th index
const LocalKey& localKey (std::size_t i) const
{
return li[i];
}
private:
std::vector<LocalKey> li;
};
}
#endif // DUNE_LOCALFUNCTIONS_RAVIARTTHOMAS0_CUBE2D_ALL_HH
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