brezzidouglasmarini2cube2dlocalbasis.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:
// SPDX-FileCopyrightInfo: Copyright © DUNE Project contributors, see file LICENSE.md in module root
// SPDX-License-Identifier: LicenseRef-GPL-2.0-only-with-DUNE-exception
#ifndef DUNE_LOCALFUNCTIONS_BREZZIDOUGLASMARINI2_CUBE2D_LOCALBASIS_HH
#define DUNE_LOCALFUNCTIONS_BREZZIDOUGLASMARINI2_CUBE2D_LOCALBASIS_HH
 
#include <array>
#include <bitset>
#include <numeric>
#include <vector>
 
#include <dune/common/fmatrix.hh>
 
#include "../../common/localbasis.hh"
 
namespace Dune
{
  template<class D, class R>
  class BDM2Cube2DLocalBasis
  {
 
  public:
    typedef LocalBasisTraits<D,2,Dune::FieldVector<D,2>,
        R,2,Dune::FieldVector<R,2>,
        Dune::FieldMatrix<R,2,2> > Traits;
 
    BDM2Cube2DLocalBasis()
    {
      for (size_t i=0; i<4; i++)
        sign_[i] = 1.0;
    }
 
    BDM2Cube2DLocalBasis(std::bitset<4> s)
    {
      for (size_t i=0; i<4; i++)
        sign_[i] = s[i] ? -1.0 : 1.0;
    }
 
    unsigned int size() const
    {
      return 14;
    }
 
    inline void evaluateFunction(const typename Traits::DomainType& in,
                                 std::vector<typename Traits::RangeType>& out) const
    {
      out.resize(size());
 
      out[0][0] = sign_[0]*(-2.25 + 5.25*in[0] + 7.5*in[1] - 7.5*in[0]*in[1] - 3.0*in[0]*in[0] - 7.5*in[1]*in[1] + 7.5*in[0]*in[1]*in[1]);
      out[0][1] = sign_[0]*(-1.25*in[1] + 3.75*in[1]*in[1] - 2.5*in[1]*in[1]*in[1]);
      out[1][0] = 3.0 - 3.0*in[0]-6.0*in[1] + 6.0*in[0]*in[1];
      out[1][1] = 0.0;
      out[2][0] = sign_[0]*(-3.75 + 3.75*in[0] + 22.5*in[1] - 22.5*in[0]*in[1] - 22.5*in[1]*in[1] + 22.5*in[0]*in[1]*in[1]);
      out[2][1] = sign_[0]*(-3.75*in[1] + 11.25*in[1]*in[1] - 7.5*in[1]*in[1]*in[1]);
      out[3][0] = sign_[1]*(-0.75*in[0] - 7.5*in[0]*in[1] + 3.0*in[0]*in[0] + 7.5*in[0]*in[1]*in[1]);
      out[3][1] = sign_[1]*(-1.25*in[1] + 3.75*in[1]*in[1] - 2.5*in[1]*in[1]*in[1]);
      out[4][0] = 3.0*in[0] - 6.0*in[0]*in[1];
      out[4][1] = 0.0;
      out[5][0] = sign_[1]*(+3.75*in[0] - 22.5*in[0]*in[1] + 22.5*in[0]*in[1]*in[1]);
      out[5][1] = sign_[1]*(-3.75*in[1] + 11.25*in[1]*in[1] - 7.5*in[1]*in[1]*in[1]);
      out[6][0] = sign_[2]*(-1.25*in[0] + 3.75*in[0]*in[0] - 2.5*in[0]*in[0]*in[0]);
      out[6][1] = sign_[2]*(-2.25 + 7.5*in[0] + 5.25*in[1] - 7.5*in[0]*in[1] - 7.5*in[0]*in[0] - 3.0*in[1]*in[1] + 7.5*in[0]*in[0]*in[1]);
      out[7][0] = 0.0;
      out[7][1] = -3.0 + 6.0*in[0] + 3.0*in[1] - 6.0*in[0]*in[1];
      out[8][0] = sign_[2]*(-3.75*in[0] + 11.25*in[0]*in[0] - 7.5*in[0]*in[0]*in[0]);
      out[8][1] = sign_[2]*(-3.75 + 22.5*in[0] + 3.75*in[1] - 22.5*in[0]*in[1] - 22.5*in[0]*in[0] + 22.5*in[0]*in[0]*in[1]);
      out[9][0] = sign_[3]*(-1.25*in[0] + 3.75*in[0]*in[0] - 2.5*in[0]*in[0]*in[0]);
      out[9][1] = sign_[3]*(-0.75*in[1] - 7.5*in[0]*in[1] + 3.0*in[1]*in[1] + 7.5*in[0]*in[0]*in[1]);
      out[10][0] = 0.0;
      out[10][1] = -3.0*in[1] + 6.0*in[0]*in[1];
      out[11][0] = sign_[3]*(-3.75*in[0] + 11.25*in[0]*in[0] - 7.5*in[0]*in[0]*in[0]);
      out[11][1] = sign_[3]*(3.75*in[1] - 22.5*in[0]*in[1] + 22.5*in[0]*in[0]*in[1]);
      out[12][0] = 6.0*in[0] - 6.0*in[0]*in[0];
      out[12][1] = 0.0;
      out[13][0] = 0.0;
      out[13][1] = 6.0*in[1] - 6.0*in[1]*in[1];
    }
 
    inline void evaluateJacobian(const typename Traits::DomainType& in,
                                 std::vector<typename Traits::JacobianType>& out) const
    {
      out.resize(size());
 
      out[0][0][0] = sign_[0]*(5.25 - 7.5*in[1] - 6.0*in[0] + 7.5*in[1]*in[1]);
      out[0][0][1] = sign_[0]*(7.5 - 7.5*in[0] - 15.0*in[1] + 15.0*in[0]*in[1]);
      out[0][1][0] = 0.0;
      out[0][1][1] = sign_[0]*(-1.25 + 7.5*in[1] - 7.5*in[1]*in[1]);
 
      out[1][0][0] = -3.0 + 6.0*in[1];
      out[1][0][1] = -6.0 + 6.0*in[0];
      out[1][1][0] = 0.0;
      out[1][1][1] = 0.0;
 
      out[2][0][0] = sign_[0]*(3.75 - 22.5*in[1] + 22.5*in[1]*in[1]);
      out[2][0][1] = sign_[0]*(22.5 - 22.5*in[0] - 45.0*in[1] + 45.0*in[0]*in[1]);
      out[2][1][0] = 0.0;
      out[2][1][1] = sign_[0]*(-3.75 + 22.5*in[1] - 22.5*in[1]*in[1]);
 
      out[3][0][0] = sign_[1]*(-0.75 - 7.5*in[1] + 6.0*in[0] + 7.5*in[1]*in[1]);
      out[3][0][1] = sign_[1]*(-7.5*in[0] + 15.0*in[0]*in[1]);
      out[3][1][0] = 0.0;
      out[3][1][1] = sign_[1]*(-1.25 + 7.5*in[1] - 7.5*in[1]*in[1]);
 
      out[4][0][0] = 3.0 - 6.0*in[1];
      out[4][0][1] = -6.0*in[0];
      out[4][1][0] = 0.0;
      out[4][1][1] = 0.0;
 
      out[5][0][0] = sign_[1]*(3.75 - 22.5*in[1] + 22.5*in[1]*in[1]);
      out[5][0][1] = sign_[1]*(-22.5*in[0] + 45.0*in[0]*in[1]);
      out[5][1][0] = 0.0;
      out[5][1][1] = sign_[1]*(-3.75 + 22.5*in[1] - 22.5*in[1]*in[1]);
 
      out[6][0][0] = sign_[2]*(-1.25 + 7.5*in[0] - 7.5*in[0]*in[0]);
      out[6][0][1] = 0.0;
      out[6][1][0] = sign_[2]*(7.5 - 7.5*in[1] - 15.0*in[0] + 15.0*in[0]*in[1]);
      out[6][1][1] = sign_[2]*(5.25 - 7.5*in[0]- 6.0*in[1] + 7.5*in[0]*in[0]);
 
      out[7][0][0] = 0.0;
      out[7][0][1] = 0.0;
      out[7][1][0] = 6.0 - 6.0*in[1];
      out[7][1][1] = 3.0 - 6.0*in[0];
 
      out[8][0][0] = sign_[2]*(-3.75 + 22.5*in[0] - 22.5*in[0]*in[0]);
      out[8][0][1] = 0.0;
      out[8][1][0] = sign_[2]*(22.5 - 22.5*in[1] - 45.0*in[0] + 45.0*in[0]*in[1]);
      out[8][1][1] = sign_[2]*(3.75 - 22.5*in[0] + 22.5*in[0]*in[0]);
 
      out[9][0][0] = sign_[3]*(-1.25 + 7.5*in[0] - 7.5*in[0]*in[0]);
      out[9][0][1] = 0.0;
      out[9][1][0] = sign_[3]*(-7.5*in[1] + 15.0*in[0]*in[1]);
      out[9][1][1] = sign_[3]*(-0.75 - 7.5*in[0] + 6.0*in[1] + 7.5*in[0]*in[0]);
 
      out[10][0][0] = 0.0;
      out[10][0][1] = 0.0;
      out[10][1][0] = 6.0*in[1];
      out[10][1][1] = -3.0 + 6.0*in[0];
 
      out[11][0][0] = sign_[3]*(-3.75 + 22.5*in[0] - 22.5*in[0]*in[0]);
      out[11][0][1] = 0.0;
      out[11][1][0] = sign_[3]*(-22.5*in[1] + 45*in[0]*in[1]);
      out[11][1][1] = sign_[3]*(3.75 - 22.5*in[0] + 22.5*in[0]*in[0]);
 
      out[12][0][0] = 6.0 - 12.0*in[0];
      out[12][0][1] = 0.0;
      out[12][1][0] = 0.0;
      out[12][1][1] = 0.0;
 
      out[13][0][0] = 0.0;
      out[13][0][1] = 0.0;
      out[13][1][0] = 0.0;
      out[13][1][1] = 6.0 - 12.0*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 if (totalOrder == 1) {
        out.resize(size());
        auto const direction = std::distance(order.begin(), std::find(order.begin(), order.end(), 1));
 
        switch (direction) {
        case 0:
          out[0][0] = sign_[0]*(5.25 - 7.5*in[1] - 6.0*in[0] + 7.5*in[1]*in[1]);
          out[0][1] = 0.0;
 
          out[1][0] = -3.0 + 6.0*in[1];
          out[1][1] = 0.0;
 
          out[2][0] = sign_[0]*(3.75 - 22.5*in[1] + 22.5*in[1]*in[1]);
          out[2][1] = 0.0;
 
          out[3][0] = sign_[1]*(-0.75 - 7.5*in[1] + 6.0*in[0] + 7.5*in[1]*in[1]);
          out[3][1] = 0.0;
 
          out[4][0] = 3.0 - 6.0*in[1];
          out[4][1] = 0.0;
 
          out[5][0] = sign_[1]*(3.75 - 22.5*in[1] + 22.5*in[1]*in[1]);
          out[5][1] = 0.0;
 
          out[6][0] = sign_[2]*(-1.25 + 7.5*in[0] - 7.5*in[0]*in[0]);
          out[6][1] = sign_[2]*(7.5 - 7.5*in[1] - 15.0*in[0] + 15.0*in[0]*in[1]);
 
          out[7][0] = 0.0;
          out[7][1] = 6.0 - 6.0*in[1];
 
          out[8][0] = sign_[2]*(-3.75 + 22.5*in[0] - 22.5*in[0]*in[0]);
          out[8][1] = sign_[2]*(22.5 - 22.5*in[1] - 45.0*in[0] + 45.0*in[0]*in[1]);
 
          out[9][0] = sign_[3]*(-1.25 + 7.5*in[0] - 7.5*in[0]*in[0]);
          out[9][1] = sign_[3]*(-7.5*in[1] + 15.0*in[0]*in[1]);
 
          out[10][0] = 0.0;
          out[10][1] = 6.0*in[1];
 
          out[11][0] = sign_[3]*(-3.75 + 22.5*in[0] - 22.5*in[0]*in[0]);
          out[11][1] = sign_[3]*(-22.5*in[1] + 45*in[0]*in[1]);
 
          out[12][0] = 6.0 - 12.0*in[0];
          out[12][1] = 0.0;
 
          out[13][0] = 0.0;
          out[13][1] = 0.0;
          break;
        case 1:
          out[0][0] = sign_[0]*(7.5 - 7.5*in[0] - 15.0*in[1] + 15.0*in[0]*in[1]);
          out[0][1] = sign_[0]*(-1.25 + 7.5*in[1] - 7.5*in[1]*in[1]);
 
          out[1][0] = -6.0 + 6.0*in[0];
          out[1][1] = 0.0;
 
          out[2][0] = sign_[0]*(22.5 - 22.5*in[0] - 45.0*in[1] + 45.0*in[0]*in[1]);
          out[2][1] = sign_[0]*(-3.75 + 22.5*in[1] - 22.5*in[1]*in[1]);
 
          out[3][0] = sign_[1]*(-7.5*in[0] + 15.0*in[0]*in[1]);
          out[3][1] = sign_[1]*(-1.25 + 7.5*in[1] - 7.5*in[1]*in[1]);
 
          out[4][0] = -6.0*in[0];
          out[4][1] = 0.0;
 
          out[5][0] = sign_[1]*(-22.5*in[0] + 45.0*in[0]*in[1]);
          out[5][1] = sign_[1]*(-3.75 + 22.5*in[1] - 22.5*in[1]*in[1]);
 
          out[6][0] = 0.0;
          out[6][1] = sign_[2]*(5.25 - 7.5*in[0]- 6.0*in[1] + 7.5*in[0]*in[0]);
 
          out[7][0] = 0.0;
          out[7][1] = 3.0 - 6.0*in[0];
 
          out[8][0] = 0.0;
          out[8][1] = sign_[2]*(3.75 - 22.5*in[0] + 22.5*in[0]*in[0]);
 
          out[9][0] = 0.0;
          out[9][1] = sign_[3]*(-0.75 - 7.5*in[0] + 6.0*in[1] + 7.5*in[0]*in[0]);
 
          out[10][0] = 0.0;
          out[10][1] = -3.0 + 6.0*in[0];
 
          out[11][0] = 0.0;
          out[11][1] = sign_[3]*(3.75 - 22.5*in[0] + 22.5*in[0]*in[0]);
 
          out[12][0] = 0.0;
          out[12][1] = 0.0;
 
          out[13][0] = 0.0;
          out[13][1] = 6.0 - 12.0*in[1];
          break;
        default:
          DUNE_THROW(RangeError, "Component out of range.");
        }
      } else {
        DUNE_THROW(NotImplemented, "Desired derivative order is not implemented");
      }
    }
 
    unsigned int order() const
    {
      return 3;
    }
 
  private:
    std::array<R,4> sign_;
  };
} // end namespace Dune
#endif // DUNE_LOCALFUNCTIONS_BREZZIDOUGLASMARINI2_CUBE2D_LOCALBASIS_HH