raviartthomas1cube2dlocalbasis.hh

// -*- tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 2 -*-
// vi: set et ts=4 sw=2 sts=2:
#ifndef DUNE_LOCALFUNCTIONS_RAVIARTTHOMAS1_CUBE2D_LOCALBASIS_HH
#define DUNE_LOCALFUNCTIONS_RAVIARTTHOMAS1_CUBE2D_LOCALBASIS_HH
 
#include <numeric>
#include <vector>
 
#include <dune/common/fmatrix.hh>
 
#include "../../common/localbasis.hh"
 
namespace Dune
{
  template<class D, class R>
  class RT1Cube2DLocalBasis
  {
 
  public:
    typedef LocalBasisTraits<D,2,Dune::FieldVector<D,2>,R,2,Dune::FieldVector<R,2>,
        Dune::FieldMatrix<R,2,2> > Traits;
 
    RT1Cube2DLocalBasis (std::bitset<4> s = 0)
    {
      for (size_t i=0; i<4; i++)
        sign_[i] = (s[i]) ? -1.0 : 1.0;
    }
 
    unsigned int size () const
    {
      return 12;
    }
 
    inline void evaluateFunction (const typename Traits::DomainType& in,
                                  std::vector<typename Traits::RangeType>& out) const
    {
      out.resize(12);
 
      out[0][0] = sign_[0]*(-1.0 + 4.0*in[0]-3*in[0]*in[0]);
      out[0][1] = 0.0;
      out[1][0] = 3.0 - 12.0*in[0] - 6.0*in[1] + 24.0*in[0]*in[1]+9*in[0]*in[0] - 18.0*in[0]*in[0]*in[1];
      out[1][1] = 0.0;
      out[2][0] = sign_[1]*(-2.0*in[0] + 3.0*in[0]*in[0]);
      out[2][1] = 0.0;
      out[3][0] = -6.0*in[0] + 12.0*in[0]*in[1] + 9.0*in[0]*in[0] - 18.0*in[0]*in[0]*in[1];
      out[3][1] = 0.0;
      out[4][0] = 0.0;
      out[4][1] = sign_[2]*(-1.0 + 4.0*in[1] - 3.0*in[1]*in[1]);
      out[5][0] = 0.0;
      out[5][1] = -3.0 + 6.0*in[0] + 12.0*in[1] - 24.0*in[0]*in[1] - 9.0*in[1]*in[1] + 18.0*in[0]*in[1]*in[1];
      out[6][0] = 0.0;
      out[6][1] = sign_[3]*(-2.0*in[1] + 3.0*in[1]*in[1]);
      out[7][0] = 0.0;
      out[7][1] = 6.0*in[1] - 12.0*in[0]*in[1] - 9.0*in[1]*in[1] + 18.0*in[0]*in[1]*in[1];
      out[8][0] = 24.0*in[0] - 36.0*in[0]*in[1] - 24.0*in[0]*in[0] + 36.0*in[0]*in[0]*in[1];
      out[8][1] = 0.0;
      out[9][0] = 0.0;
      out[9][1] = 24.0*in[1] - 36.0*in[0]*in[1] - 24.0*in[1]*in[1] + 36.0*in[0]*in[1]*in[1];
      out[10][0] = -36.0*in[0] + 72.0*in[0]*in[1] + 36.0*in[0]*in[0] - 72.0*in[0]*in[0]*in[1];
      out[10][1] = 0.0;
      out[11][0] = 0.0;
      out[11][1] = -36.0*in[1] + 72.0*in[0]*in[1] + 36*in[1]*in[1] - 72.0*in[0]*in[1]*in[1];
    }
 
    inline void evaluateJacobian (const typename Traits::DomainType& in,
                                  std::vector<typename Traits::JacobianType>& out) const
    {
      out.resize(12);
 
      out[0][0][0] = sign_[0]*(4.0 - 6.0*in[0]);
      out[0][0][1] = 0.0;
      out[0][1][0] = 0.0;
      out[0][1][1] = 0.0;
 
      out[1][0][0] = -12.0 + 24.0*in[1] + 18.0*in[0] - 36.0*in[0]*in[1];
      out[1][0][1] = -6 + 24.0*in[0] - 18.0*in[0]*in[0];
      out[1][1][0] = 0.0;
      out[1][1][1] = 0.0;
 
      out[2][0][0] = sign_[1]*(-2.0 + 6.0*in[0]);
      out[2][0][1] = 0.0;
      out[2][1][0] = 0.0;
      out[2][1][1] = 0.0;
 
      out[3][0][0] = -6.0 + 12.0*in[1] + 18.0*in[0] - 36.0*in[0]*in[1];
      out[3][0][1] = 12.0*in[0] - 18.0*in[0]*in[0];
      out[3][1][0] = 0.0;
      out[3][1][1] = 0.0;
 
      out[4][0][0] = 0.0;
      out[4][0][1] = 0.0;
      out[4][1][0] = 0.0;
      out[4][1][1] = sign_[2]*(4.0 - 6.0*in[1]);
 
      out[5][0][0] = 0.0;
      out[5][0][1] = 0.0;
      out[5][1][0] = 6.0 - 24.0*in[1] + 18.0*in[1]*in[1];
      out[5][1][1] = 12.0 - 24.0*in[0] - 18.0*in[1] + 36.0*in[0]*in[1];
 
      out[6][0][0] = 0.0;
      out[6][0][1] = 0.0;
      out[6][1][0] = 0.0;
      out[6][1][1] = sign_[3]*(-2.0 + 6.0*in[1]);
 
      out[7][0][0] = 0.0;
      out[7][0][1] = 0.0;
      out[7][1][0] = -12.0*in[1] + 18.0*in[1]*in[1];
      out[7][1][1] = 6.0 - 12.0*in[0] - 18.0*in[1] + 36.0*in[1]*in[0];
 
      out[8][0][0] = 24.0 - 36.0*in[1] - 48.0*in[0] + 72.0*in[0]*in[1];
      out[8][0][1] = -36.0*in[0] + 36.0*in[0]*in[0];
      out[8][1][0] = 0.0;
      out[8][1][1] = 0.0;
 
      out[9][0][0] = 0.0;
      out[9][0][1] = 0.0;
      out[9][1][0] = -36.0*in[1] + 36.0*in[1]*in[1];
      out[9][1][1] = 24.0 - 36.0*in[0] - 48.0*in[1] + 72.0*in[0]*in[1];
 
      out[10][0][0] = -36.0 + 72.0*in[1] + 72.0*in[0] - 144.0*in[0]*in[1];
      out[10][0][1] = 72.0*in[0] - 72.0*in[0]*in[0];
      out[10][1][0] = 0.0;
      out[10][1][1] = 0.0;
 
      out[11][0][0] = 0.0;
      out[11][0][1] = 0.0;
      out[11][1][0] = 72.0*in[1] - 72.0*in[1]*in[1];
      out[11][1][1] = -36.0 + 72.0*in[0] + 72.0*in[1] - 144.0*in[0]*in[1];
    }
 
    void partial (const std::array<unsigned int, 2>& 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 3;
    }
 
  private:
    std::array<R,4> sign_;
  };
}
#endif // DUNE_LOCALFUNCTIONS_RAVIARTTHOMAS1_CUBE2D_LOCALBASIS_HH