raviartthomas3cube2dlocalinterpolation.hh

// -*- tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 2 -*-
// vi: set et ts=4 sw=2 sts=2:
#ifndef DUNE_LOCALFUNCTIONS_RAVIARTTHOMAS3_CUBE2D_LOCALINTERPOLATION_HH
#define DUNE_LOCALFUNCTIONS_RAVIARTTHOMAS3_CUBE2D_LOCALINTERPOLATION_HH
 
#include <vector>
 
#include <dune/geometry/quadraturerules.hh>
#include <dune/localfunctions/common/localinterpolation.hh>
 
namespace Dune
{
 
  template<class LB>
  class RT3Cube2DLocalInterpolation
  {
 
  public:
 
    RT3Cube2DLocalInterpolation (std::bitset<4> s = 0)
    {
      for (size_t i=0; i<4; i++)
        sign_[i] = (s[i]) ? -1.0 : 1.0;
 
      n_[0] = {-1.0,  0.0};
      n_[1] = { 1.0,  0.0};
      n_[2] = { 0.0, -1.0};
      n_[3] = { 0.0,  1.0};
    }
 
    template<typename F, typename C>
    void interpolate (const F& ff, std::vector<C>& out) const
    {
      // f gives v*outer normal at a point on the edge!
      typedef typename LB::Traits::RangeFieldType Scalar;
      typedef typename LB::Traits::DomainFieldType Vector;
 
      auto&& f = Impl::makeFunctionWithCallOperator<typename LB::Traits::DomainType>(ff);
 
      out.resize(40);
      fill(out.begin(), out.end(), 0.0);
 
      const int qOrder = 9;
      const auto& rule1 = QuadratureRules<Scalar,1>::rule(GeometryTypes::cube(1), qOrder);
 
      for (auto&& qp : rule1)
      {
        Scalar qPos = qp.position();
        typename LB::Traits::DomainType localPos;
 
        localPos = {0.0, qPos};
        auto y = f(localPos);
        out[0] += (y[0]*n_[0][0] + y[1]*n_[0][1])*qp.weight()*sign_[0];
        out[1] += (y[0]*n_[0][0] + y[1]*n_[0][1])*(2.0*qPos - 1.0)*qp.weight();
        out[2] += (y[0]*n_[0][0] + y[1]*n_[0][1])*(6.0*qPos*qPos - 6.0*qPos + 1.0)*qp.weight()*sign_[0];
        out[3] += (y[0]*n_[0][0] + y[1]*n_[0][1])*(20.0*qPos*qPos*qPos - 30.0*qPos*qPos + 12.0*qPos - 1.0)*qp.weight();
 
        localPos = {1.0, qPos};
        y = f(localPos);
        out[4] += (y[0]*n_[1][0] + y[1]*n_[1][1])*qp.weight()*sign_[1];
        out[5] += (y[0]*n_[1][0] + y[1]*n_[1][1])*(1.0 - 2.0*qPos)*qp.weight();
        out[6] += (y[0]*n_[1][0] + y[1]*n_[1][1])*(6.0*qPos*qPos - 6.0*qPos + 1.0)*qp.weight()*sign_[1];
        out[7] += (y[0]*n_[1][0] + y[1]*n_[1][1])*(-20.0*qPos*qPos*qPos + 30.0*qPos*qPos - 12.0*qPos + 1.0)*qp.weight();
 
        localPos = {qPos, 0.0};
        y = f(localPos);
        out[8] += (y[0]*n_[2][0] + y[1]*n_[2][1])*qp.weight()*sign_[2];
        out[9] += (y[0]*n_[2][0] + y[1]*n_[2][1])*(1.0 - 2.0*qPos)*qp.weight();
        out[10] += (y[0]*n_[2][0] + y[1]*n_[2][1])*(6.0*qPos*qPos - 6.0*qPos + 1.0)*qp.weight()*sign_[2];
        out[11] += (y[0]*n_[2][0] + y[1]*n_[2][1])*(-20.0*qPos*qPos*qPos + 30.0*qPos*qPos - 12.0*qPos + 1.0)*qp.weight();
 
        localPos = {qPos, 1.0};
        y = f(localPos);
        out[12]  += (y[0]*n_[3][0] + y[1]*n_[3][1])*qp.weight()*sign_[3];
        out[13] += (y[0]*n_[3][0] + y[1]*n_[3][1])*(2.0*qPos - 1.0)*qp.weight();
        out[14] += (y[0]*n_[3][0] + y[1]*n_[3][1])*(6.0*qPos*qPos - 6.0*qPos + 1.0)*qp.weight()*sign_[3];
        out[15] += (y[0]*n_[3][0] + y[1]*n_[3][1])*(20.0*qPos*qPos*qPos - 30.0*qPos*qPos + 12.0*qPos - 1.0)*qp.weight();
      }
 
      const auto& rule2 = QuadratureRules<Vector,2>::rule(GeometryTypes::cube(2), qOrder);
 
      for (auto&& qp : rule2)
      {
        auto qPos = qp.position();
 
        auto y = f(qPos);
        double l0_x=1.0;
        double l1_x=2.0*qPos[0]-1.0;
        double l2_x=6.0*qPos[0]*qPos[0]-6.0*qPos[0]+1.0;
        double l3_x=20.0*qPos[0]*qPos[0]*qPos[0] - 30.0*qPos[0]*qPos[0] + 12.0*qPos[0] - 1.0;
        double l0_y=1.0;
        double l1_y=2.0*qPos[1]-1.0;
        double l2_y=6.0*qPos[1]*qPos[1]-6.0*qPos[1]+1.0;
        double l3_y=20.0*qPos[1]*qPos[1]*qPos[1] - 30.0*qPos[1]*qPos[1] + 12.0*qPos[1] - 1.0;
 
        out[16] += y[0]*l0_x*l0_y*qp.weight();
        out[17] += y[0]*l0_x*l1_y*qp.weight();
        out[18] += y[0]*l0_x*l2_y*qp.weight();
        out[19] += y[0]*l0_x*l3_y*qp.weight();
        out[20] += y[0]*l1_x*l0_y*qp.weight();
        out[21] += y[0]*l1_x*l1_y*qp.weight();
        out[22] += y[0]*l1_x*l2_y*qp.weight();
        out[23] += y[0]*l1_x*l3_y*qp.weight();
        out[24] += y[0]*l2_x*l0_y*qp.weight();
        out[25] += y[0]*l2_x*l1_y*qp.weight();
        out[26] += y[0]*l2_x*l2_y*qp.weight();
        out[27] += y[0]*l2_x*l3_y*qp.weight();
 
        out[28] += y[1]*l0_x*l0_y*qp.weight();
        out[29] += y[1]*l0_x*l1_y*qp.weight();
        out[30] += y[1]*l0_x*l2_y*qp.weight();
        out[31] += y[1]*l1_x*l0_y*qp.weight();
        out[32] += y[1]*l1_x*l1_y*qp.weight();
        out[33] += y[1]*l1_x*l2_y*qp.weight();
        out[34] += y[1]*l2_x*l0_y*qp.weight();
        out[35] += y[1]*l2_x*l1_y*qp.weight();
        out[36] += y[1]*l2_x*l2_y*qp.weight();
        out[37] += y[1]*l3_x*l0_y*qp.weight();
        out[38] += y[1]*l3_x*l1_y*qp.weight();
        out[39] += y[1]*l3_x*l2_y*qp.weight();
      }
    }
 
  private:
    // Edge orientations
    std::array<typename LB::Traits::RangeFieldType, 4> sign_;
 
    // Edge normals
    std::array<typename LB::Traits::DomainType, 4>     n_;
  };
}
 
#endif // DUNE_LOCALFUNCTIONS_RAVIARTTHOMAS3_CUBE2D_LOCALINTERPOLATION_HH