dualp1localbasis.hh

// -*- tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 2 -*-
// vi: set et ts=4 sw=2 sts=2:
#ifndef DUNE_DUAL_P1_LOCALBASIS_HH
#define DUNE_DUAL_P1_LOCALBASIS_HH
 
#include <numeric>
 
#include <dune/common/fvector.hh>
#include <dune/common/fmatrix.hh>
#include <dune/localfunctions/common/localbasis.hh>
 
namespace Dune
{
  template<class D, class R, int dim, bool faceDualT=false>
  class DualP1LocalBasis
  {
  public:
    static const bool faceDual = faceDualT;
    typedef LocalBasisTraits<D,dim,Dune::FieldVector<D,dim>,R,1,Dune::FieldVector<R,1>,
        Dune::FieldMatrix<R,1,dim> > Traits;
 
    unsigned int size () const
    {
      return dim+1;
    }
 
    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+!faceDual)*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];
      }
    }
 
    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+!faceDual,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];
      }
    }
 
    void partial (const std::array<unsigned int, dim>& 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");
      }
    }
 
    unsigned int order () const
    {
      return 1;
    }
  };
}
#endif