partitionofunity.hh

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#ifndef DUNE_PDELAB_BACKEND_ISTL_GENEO_PARTITIONOFUNITY_HH
#define DUNE_PDELAB_BACKEND_ISTL_GENEO_PARTITIONOFUNITY_HH
 
template<class X, class GFS, class CC>
X standardPartitionOfUnity(const GFS& gfs, const CC& cc) {
 
  X part_unity(gfs, 1);
 
  Dune::PDELab::set_constrained_dofs(cc,0.0,part_unity); // Zero on subdomain boundary
 
  Dune::PDELab::AddDataHandle<GFS,X> parth(gfs,part_unity);
  gfs.gridView().communicate(parth,Dune::All_All_Interface,Dune::ForwardCommunication);
 
  Dune::PDELab::set_constrained_dofs(cc,0.0,part_unity); // Zero on subdomain boundary (Need that a 2nd time due to add comm before!)
 
  for (auto iter = part_unity.begin(); iter != part_unity.end(); iter++) {
    if (*iter > 0)
      *iter = 1.0 / *iter;
  }
  return part_unity;
}
 
template<class X, class GFS,  class LFS, class CC>
X sarkisPartitionOfUnity(const GFS& gfs, LFS& lfs, const CC& cc, int cells_x, int cells_y, int overlap, int partition_x, int partition_y) {
  using Dune::PDELab::Backend::native;
 
  int my_rank = gfs.gridView().comm().rank();
  const int dim = 2;
 
  // throw exception if the setup is currently not supported by the Sarkis partition of unity
  typedef typename GFS::Traits::GridView::Grid::ctype DF;
 
  if (gfs.gridView().grid().dimension != dim)
    DUNE_THROW(Dune::NotImplemented, "Currently, Sarkis partition of unity is only supported for 2 dimensional grids.");
 
  if (GFS::Traits::FiniteElement::Traits::LocalBasisType::order() != 1)
    DUNE_THROW(Dune::NotImplemented, "Currently, Sarkis partition of unity is only supported for polynomial bases of order 1");
 
  // we assume the grid is instantiated as a (0.0, 1.0) x (0.0, 1.0) grid, so we do an exact flaoting point comparison here
  if (gfs.gridView().grid().domainSize() != Dune::FieldVector<DF, 2>(1.0))
    DUNE_THROW(Dune::NotImplemented, "Currently, Sarkis partition of unity is only supported for the (0,1) x (0,1) unit square.");
 
  X part_unity(gfs, 1);
 
  for (auto it = gfs.gridView().template begin<0>(); it != gfs.gridView().template end<0>(); ++it) {
 
    lfs.bind(*it);
 
    auto geo  = it->geometry();
    const auto gt = geo.type();
    const auto& ref_el = Dune::ReferenceElements<double, dim>::general(gt);
 
    auto& coeffs = lfs.finiteElement().localCoefficients();
 
    for (std::size_t i = 0; i < coeffs.size(); ++i) {
 
      auto local_pos = ref_el.position (coeffs.localKey(i).subEntity(), coeffs.localKey(i).codim());
 
      auto global_pos = geo.global(local_pos);
 
      auto subindex = gfs.entitySet().indexSet().subIndex(*it, coeffs.localKey(i).subEntity(), coeffs.localKey(i).codim());
 
      double Hx = 1.0 / (double)partition_x;
      double Hy = 1.0 / (double)partition_y;
      double hx = (double)overlap / cells_x;
      double hy = (double)overlap / cells_y;
 
      int row = std::floor(my_rank / partition_x);
      int col = my_rank - partition_x * row;
 
      double dx1 = (col + 1) * Hx + hx - global_pos[0];
      double dx2 = global_pos[0] - (col * Hx - hx);
 
      double dy1 = (row + 1) * Hy + hy - global_pos[1];
      double dy2 = global_pos[1] - (row * Hy - hy);
 
      if (row == 0) dy2 = 2*Hy;
      if (row == partition_y - 1) dy1 = 2*Hy;
      if (col == 0) dx2 = 2*Hx;
      if (col == partition_x - 1) dx1 = 2*Hx;
 
      native(part_unity)[subindex] = std::min(std::min(std::min(dx1, dx2), dy1), dy2);
    }
  }
 
  X sum_dists(part_unity);
  Dune::PDELab::AddDataHandle<GFS,X> addh_dists(gfs,sum_dists);
  gfs.gridView().communicate(addh_dists,Dune::All_All_Interface,Dune::ForwardCommunication);
 
  auto iter_sum = sum_dists.begin();
  for (auto iter = part_unity.begin(); iter != part_unity.end(); iter++) {
    if (*iter > 0)
      *iter *= 1.0 / *iter_sum;
    iter_sum++;
  }
 
  Dune::PDELab::set_constrained_dofs(cc,0.0,part_unity); // Zero on Dirichlet domain boundary
 
  return part_unity;
}
 
 
#endif //DUNE_PDELAB_BACKEND_ISTL_GENEO_PARTITIONOFUNITY_HH