rannacherturek2dlocalbasis.hh

// -*- tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 2 -*-
// vi: set et ts=4 sw=2 sts=2:
#ifndef DUNE_RANNACHER_TUREK_2D_LOCALBASIS_HH
#define DUNE_RANNACHER_TUREK_2D_LOCALBASIS_HH
 
#include <numeric>
#include <vector>
 
#include <dune/common/fvector.hh>
#include <dune/common/fmatrix.hh>
 
#include <dune/localfunctions/common/localbasis.hh>
 
namespace Dune
{
 
  template< class D, class R >
  struct RannacherTurek2DLocalBasis
  {
    typedef LocalBasisTraits< D, 2, FieldVector< D, 2 >,
        R, 1, FieldVector< R, 1 >,
        FieldMatrix< R, 1, 2 > > Traits;
 
    unsigned int size () const
    {
      return 4;
    }
 
    inline void evaluateFunction ( const typename Traits::DomainType &in,
                                   std::vector< typename Traits::RangeType > &out ) const
    {
      out.resize(4);
      typename Traits::DomainFieldType qbase = in[0]*in[0]-in[1]*in[1];
      out[0] =  .75 - 2*in[0] +   in[1] + qbase;
      out[1] = -.25           +   in[1] + qbase;
      out[2] =  .75 +   in[0] - 2*in[1] - qbase;
      out[3] = -.25 +   in[0]           - qbase;
    }
 
    inline void evaluateJacobian ( const typename Traits::DomainType &in,
                                   std::vector< typename Traits::JacobianType > &out ) const
    {
      out.resize(4);
 
      // see http://www.dune-project.org/doc/doxygen/html/classDune_1_1C1LocalBasisInterface.html#d6f8368f8aa43439cc7ef10419f6e2ea
      // out[i][j][k] = d_k \phi^i_j , where \phi^i_j is the j'th component of the i'th shape function.
 
      out[0][0][0] = -2 + 2*in[0]; out[0][0][1] =  1 - 2*in[1];
      out[1][0][0] =      2*in[0]; out[1][0][1] =  1 - 2*in[1];
      out[2][0][0] =  1 - 2*in[0]; out[2][0][1] = -2 + 2*in[1];
      out[3][0][0] =  1 - 2*in[0]; out[3][0][1] =      2*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 if (totalOrder == 1) {
        auto const direction = std::distance(order.begin(), std::find(order.begin(), order.end(), 1));
        out.resize(size());
 
        switch (direction) {
        case 0:
          out[0] = -2 + 2*in[0];
          out[1] =      2*in[0];
          out[2] =  1 - 2*in[0];
          out[3] =  1 - 2*in[0];
          break;
        case 1:
          out[0] =  1 - 2*in[1];
          out[1] =  1 - 2*in[1];
          out[2] = -2 + 2*in[1];
          out[3] =      2*in[1];
          break;
        default:
          DUNE_THROW(RangeError, "Component out of range.");
        }
      } else if (totalOrder == 2) {
        auto const direction = std::distance(order.begin(), std::find(order.begin(), order.end(), 2));
        out.resize(size());
 
        switch (direction) {
        case 0:
          out[0] = out[1] = 2;
          out[2] = out[3] =-2;
          break;
        case 1:
          out[0] = out[1] =-2;
          out[2] = out[3] = 2;
          break;
        default:
          out[0] = out[1] = out[2] = out[3] = 0;
          break;
        }
      } else {
        out[0] = out[1] = out[2] = out[3] = 0;
      }
    }
 
    unsigned int order () const
    {
      // must be 2 here since it contains x^2 and x^2
      return 2;
    }
  };
 
} //namespace Dune
 
#endif // #ifndef DUNE_RANNACHER_TUREK_2D_LOCALBASIS_HH