/usr/include/dune/localfunctions/dualmortarbasis/dualq1.hh is in libdune-localfunctions-dev 2.3.1-1.
This file is owned by root:root, with mode 0o644.
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// vi: set et ts=4 sw=2 sts=2:
#ifndef DUNE_DUAL_Q1_LOCALFINITEELEMENT_HH
#define DUNE_DUAL_Q1_LOCALFINITEELEMENT_HH
#include <dune/common/fvector.hh>
#include <dune/common/fmatrix.hh>
#include <dune/geometry/type.hh>
#include <dune/geometry/quadraturerules.hh>
#include <dune/localfunctions/common/localfiniteelementtraits.hh>
#include "dualq1/dualq1localbasis.hh"
#include "dualq1/dualq1localcoefficients.hh"
#include "dualq1/dualq1localinterpolation.hh"
namespace Dune
{
/** \brief The local dual Q1 finite element on cubes
\tparam D Domain data type
\tparam R Range data type
\tparam dim Dimension of the hypercube
*/
template<class D, class R, int dim>
class DualQ1LocalFiniteElement
{
public:
/** \todo Please doc me !
*/
typedef LocalFiniteElementTraits<DualQ1LocalBasis<D,R,dim>,DualQ1LocalCoefficients<dim>,
DualQ1LocalInterpolation<dim,DualQ1LocalBasis<D,R,dim> > > Traits;
/** \todo Please doc me !
*/
DualQ1LocalFiniteElement ()
{
gt.makeCube(dim);
// dual basis functions are linear combinations of Lagrange elements
// compute these coefficients here because the basis and the local interpolation needs them
const Dune::QuadratureRule<D,dim>& quad = Dune::QuadratureRules<D,dim>::rule(gt, 2*dim);
const int size = 1 <<dim;
// assemble mass matrix on the reference element
Dune::FieldMatrix<R, size, size> massMat;
massMat = 0;
// and the integrals of the lagrange shape functions
std::vector<Dune::FieldVector<R,1> > integral(size);
for (int i=0; i<size; i++)
integral[i] = 0;
for(size_t pt=0; pt<quad.size(); pt++) {
const Dune::FieldVector<D ,dim>& pos = quad[pt].position();
std::vector<typename Traits::LocalBasisType::Traits::RangeType> q1Values(size);
// evaluate q1 basis functions
for (int i=0; i<size; i++) {
q1Values[i] = 1;
for (int j=0; j<dim; j++)
// if j-th bit of i is set multiply with in[j], else with 1-in[j]
q1Values[i] *= (i & (1<<j)) ? pos[j] : 1-pos[j];
}
double weight = quad[pt].weight();
for (int k=0; k<size; k++) {
integral[k] += q1Values[k]*weight;
for (int l=0; l<=k; l++)
massMat[k][l] += weight*(q1Values[k]*q1Values[l]);
}
}
// make matrix symmetric
for (int i=0; i<size-1; i++)
for (int j=i+1; j<size; j++)
massMat[i][j] = massMat[j][i];
//solve for the coefficients
Dune::array<Dune::FieldVector<R, size>, size> coefficients;
for (int i=0; i<size; i++) {
Dune::FieldVector<R, size> rhs(0);
rhs[i] = integral[i];
coefficients[i] = 0;
massMat.solve(coefficients[i] ,rhs);
}
basis.setCoefficients(coefficients);
interpolation.setCoefficients(coefficients);
}
/** \todo Please doc me !
*/
const typename Traits::LocalBasisType& localBasis () const
{
return basis;
}
/** \todo Please doc me !
*/
const typename Traits::LocalCoefficientsType& localCoefficients () const
{
return coefficients;
}
/** \todo Please doc me !
*/
const typename Traits::LocalInterpolationType& localInterpolation () const
{
return interpolation;
}
/** \todo Please doc me !
*/
GeometryType type () const
{
return gt;
}
DualQ1LocalFiniteElement* clone () const
{
return new DualQ1LocalFiniteElement(*this);
}
private:
DualQ1LocalBasis<D,R,dim> basis;
DualQ1LocalCoefficients<dim> coefficients;
DualQ1LocalInterpolation<dim,DualQ1LocalBasis<D,R,dim> > interpolation;
GeometryType gt;
};
}
#endif
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