refinedp1localbasis.hh

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// -*- tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 2 -*-
// vi: set et ts=4 sw=2 sts=2:
#ifndef DUNE_REFINED_P1_LOCALBASIS_HH
#define DUNE_REFINED_P1_LOCALBASIS_HH

#include <numeric>

#include <dune/common/fmatrix.hh>

#include <dune/localfunctions/refined/common/refinedsimplexlocalbasis.hh>

namespace Dune
{
  template<class D, class R, int dim>
  class RefinedP1LocalBasis
    : public RefinedSimplexLocalBasis<D,dim>
  {
  public:
    RefinedP1LocalBasis()
    {
      DUNE_THROW(Dune::NotImplemented,"RefinedP1LocalBasis not implemented for dim > 3.");
    }
  };

  template<class D, class R>
  class RefinedP1LocalBasis<D,R,1>
    : public RefinedSimplexLocalBasis<D,1>
  {
  public:
    typedef LocalBasisTraits<D,1,Dune::FieldVector<D,1>,R,1,Dune::FieldVector<R,1>,
        Dune::FieldMatrix<R,1,1> > Traits;

    unsigned int size () const
    {
      return 3;
    }

    inline void evaluateFunction (const typename Traits::DomainType& in,
                                  std::vector<typename Traits::RangeType>& out) const
    {
      out.resize(3);

      int subElement;
      typename Traits::DomainType local;
      this->getSubElement(in, subElement, local);

      switch (subElement) {
      case 0 :

        out[0] = 1 - local[0];
        out[1] = local[0];
        out[2] = 0;
        break;

      case 1 :

        out[0] = 0;
        out[1] = 1 - local[0];
        out[2] = local[0];
        break;

      }

    }

    inline void
    evaluateJacobian (const typename Traits::DomainType& in,         // position
                      std::vector<typename Traits::JacobianType>& out) const      // return value
    {
      out.resize(3);

      int subElement;
      typename Traits::DomainType local;
      this->getSubElement(in, subElement, local);

      switch (subElement) {
      case 0 :

        out[0][0][0] = -2;
        out[1][0][0] =  2;
        out[2][0][0] =  0;
        break;

      case 1 :

        out[0][0][0] =  0;
        out[1][0][0] = -2;
        out[2][0][0] =  2;
        break;

      }
    }

    void partial (const std::array<unsigned int, 1>& order,
                  const typename Traits::DomainType& in,         // position
                  std::vector<typename Traits::RangeType>& out) const      // return value
    {
      auto totalOrder = order[0];
      if (totalOrder == 0) {
        evaluateFunction(in, out);
      } else if (totalOrder == 1)
      {
        out.resize(3);

        int subElement;
        typename Traits::DomainType local;
        this->getSubElement(in, subElement, local);

        switch (subElement) {
          case 0:
            out[0] = -2;
            out[1] =  2;
            out[2] =  0;
            break;
          case 1:
            out[0] =  0;
            out[1] = -2;
            out[2] =  2;
            break;
        }
      } else {
        out.resize(3);
        out[0] = out[1] = out[2] = 0;
      }
    }

    unsigned int order () const
    {
      return 1;
    }

  };

  template<class D, class R>
  class RefinedP1LocalBasis<D,R,2>
    : public RefinedSimplexLocalBasis<D,2>
  {
  public:
    typedef LocalBasisTraits<D,2,Dune::FieldVector<D,2>,R,1,Dune::FieldVector<R,1>,
        Dune::FieldMatrix<R,1,2> > Traits;

    unsigned int size () const
    {
      return 6;
    }

    inline void evaluateFunction (const typename Traits::DomainType& in,
                                  std::vector<typename Traits::RangeType>& out) const
    {
      out.resize(6);

      int subElement;
      typename Traits::DomainType local;
      this->getSubElement(in, subElement, local);

      switch (subElement) {
      case 0 :

        out[0] = 1 - local[0] - local[1];
        out[1] = local[0];
        out[2] = 0;
        out[3] = local[1];
        out[4] = 0;
        out[5] = 0;
        break;

      case 1 :

        out[0] = 0;
        out[1] = 1 - local[0] - local[1];
        out[2] = local[0];
        out[3] = 0;
        out[4] = local[1];
        out[5] = 0;
        break;

      case 2 :

        out[0] = 0;
        out[1] =