/usr/include/dune/localfunctions/dualmortarbasis/dualp1/dualp1localbasis.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_DUAL_P1_LOCALBASIS_HH
#define DUNE_DUAL_P1_LOCALBASIS_HH
#include <dune/common/fvector.hh>
#include <dune/common/fmatrix.hh>
#include <dune/localfunctions/common/localbasis.hh>
namespace Dune
{
/**@ingroup LocalBasisImplementation
\brief Dual Lagrange shape functions on the simplex.
Defines the linear dual shape functions on the simplex.
\tparam D Type to represent the field in the domain.
\tparam R Type to represent the field in the range.
\tparam dim The dimension of the simplex
\nosubgrouping
*/
template<class D, class R, int dim>
class DualP1LocalBasis
{
public:
//! \brief export type traits for function signature
typedef LocalBasisTraits<D,dim,Dune::FieldVector<D,dim>,R,1,Dune::FieldVector<R,1>,
Dune::FieldMatrix<R,1,dim> > Traits;
//! \brief number of shape functions
unsigned int size () const
{
return dim+1;
}
//! \brief Evaluate all shape functions
inline void evaluateFunction (const typename Traits::DomainType& in,
std::vector<typename Traits::RangeType>& out) const
{
// evaluate P1 basis functions
std::vector<typename Traits::RangeType> p1Values(size());
p1Values[0] = 1.0;
for (int i=0; i<dim; i++) {
p1Values[0] -= in[i];
p1Values[i+1] = in[i];
}
// compute dual basis function values as a linear combination of the Lagrange values
out.resize(size());
for (int i=0; i<=dim; i++) {
out[i] = (dim+1)*p1Values[i];
for (int j=0; j<i; j++)
out[i] -= p1Values[j];
for (int j=i+1; j<=dim; j++)
out[i] -= p1Values[j];
}
}
//! \brief Evaluate Jacobian of all shape functions
inline void
evaluateJacobian (const typename Traits::DomainType& in,
std::vector<typename Traits::JacobianType>& out) const
{
// evaluate P1 jacobians
std::vector<typename Traits::JacobianType> p1Jacs(size());
for (int i=0; i<dim; i++)
p1Jacs[0][0][i] = -1;
for (int i=0; i<dim; i++)
for (int j=0; j<dim; j++)
p1Jacs[i+1][0][j] = (i==j);
// compute dual basis jacobians as linear combination of the Lagrange jacobians
out.resize(size());
for (size_t i=0; i<=dim; i++) {
out[i][0] = 0;
out[i][0].axpy((dim+1),p1Jacs[i][0]);
for (size_t j=0; j<i; j++)
out[i][0] -= p1Jacs[j][0];
for (int j=i+1; j<=dim; j++)
out[i][0] -= p1Jacs[j][0];
}
}
//! \brief Polynomial order of the shape functions
unsigned int order () const
{
return 1;
}
};
}
#endif
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