qklocalinterpolation.hh

// -*- tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 2 -*-
// vi: set et ts=4 sw=2 sts=2:
 
#ifndef DUNE_LOCALFUNCTIONS_QKLOCALINTERPOLATION_HH
#define DUNE_LOCALFUNCTIONS_QKLOCALINTERPOLATION_HH
 
#include <dune/common/fvector.hh>
#include <dune/common/power.hh>
 
#include <dune/geometry/type.hh>
 
#include <dune/localfunctions/common/localbasis.hh>
#include <dune/localfunctions/common/localfiniteelementtraits.hh>
 
 
namespace Dune
{
  template<int k, int d, class LB>
  class QkLocalInterpolation
  {
 
    // Return i as a d-digit number in the (k+1)-nary system
    static Dune::FieldVector<int,d> multiindex (int i)
    {
      Dune::FieldVector<int,d> alpha;
      for (int j=0; j<d; j++)
      {
        alpha[j] = i % (k+1);
        i = i/(k+1);
      }
      return alpha;
    }
 
  public:
 
    template<typename F, typename C>
    void interpolate (const F& f, std::vector<C>& out) const
    {
      typename LB::Traits::DomainType x;
      typename LB::Traits::RangeType y;
 
      out.resize(StaticPower<k+1,d>::power);
 
      for (int i=0; i<StaticPower<k+1,d>::power; i++)
      {
        // convert index i to multiindex
        Dune::FieldVector<int,d> alpha(multiindex(i));
 
        // Generate coordinate of the i-th Lagrange point
        for (int j=0; j<d; j++)
          x[j] = (1.0*alpha[j])/k;
 
        f.evaluate(x,y); out[i] = y;
      }
    }
  };
 
  template<int d, class LB>
  class QkLocalInterpolation<0,d,LB>
  {
  public:
    template<typename F, typename C>
    void interpolate (const F& f, std::vector<C>& out) const
    {
      typename LB::Traits::DomainType x(0);
      typename LB::Traits::RangeType y;
      f.evaluate(x,y);
      out.resize(1);
      out[0] = y;
    }
  };
 
}
 
 
#endif