lagrangedgbasis.hh

// -*- tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 2 -*-
// vi: set et ts=4 sw=2 sts=2:
#ifndef DUNE_FUNCTIONS_FUNCTIONSPACEBASES_LAGRANGEDGBASIS_HH
#define DUNE_FUNCTIONS_FUNCTIONSPACEBASES_LAGRANGEDGBASIS_HH
 
#include <array>
#include <dune/common/exceptions.hh>
 
#include <dune/functions/functionspacebases/nodes.hh>
#include <dune/functions/functionspacebases/defaultglobalbasis.hh>
#include <dune/functions/functionspacebases/flatmultiindex.hh>
#include <dune/functions/functionspacebases/lagrangebasis.hh>
 
 
 
 
namespace Dune {
namespace Functions {
 
 
 
// *****************************************************************************
// This is the reusable part of the basis. It contains
//
//   LagrangeDGPreBasis
//   LagrangeDGNodeIndexSet
//   LagrangeDGNode
//
// The pre-basis allows to create the others and is the owner of possible shared
// state. These three components do _not_ depend on the global basis or index
// set and can be used without a global basis.
// *****************************************************************************
 
template<typename GV, int k>
using LagrangeDGNode = LagrangeNode<GV, k>;
 
template<typename GV, int k, class MI>
class LagrangeDGNodeIndexSet;
 
 
template<typename GV, int k, class MI>
class LagrangeDGPreBasis
{
  static const int dim = GV::dimension;
 
public:
 
  using GridView = GV;
  using size_type = std::size_t;
 
 
  // Precompute the number of dofs per entity type
  const static int dofsPerEdge        = k+1;
  const static int dofsPerTriangle    = (k+1)*(k+2)/2;
  const static int dofsPerQuad        = (k+1)*(k+1);
  const static int dofsPerTetrahedron = (k+1)*(k+2)*(k+3)/6;
  const static int dofsPerPrism       = (k+1)*(k+1)*(k+2)/2;
  const static int dofsPerHexahedron  = (k+1)*(k+1)*(k+1);
  const static int dofsPerPyramid     = (k+1)*(k+2)*(2*k+3)/6;
 
 
  using Node = LagrangeDGNode<GV, k>;
 
  using IndexSet = LagrangeDGNodeIndexSet<GV, k, MI>;
 
  using MultiIndex = MI;
 
  using SizePrefix = Dune::ReservedVector<size_type, 1>;
 
  LagrangeDGPreBasis(const GridView& gv) :
    gridView_(gv)
  {}
 
 
  void initializeIndices()
  {
    switch (dim)
    {
      case 1:
      {
        break;
      }
      case 2:
      {
        quadrilateralOffset_ = dofsPerTriangle * gridView_.size(Dune::GeometryTypes::triangle);
        break;
      }
      case 3:
      {
        prismOffset_         = dofsPerTetrahedron * gridView_.size(Dune::GeometryTypes::tetrahedron);
 
        hexahedronOffset_    = prismOffset_         +   dofsPerPrism * gridView_.size(Dune::GeometryTypes::prism);
 
        pyramidOffset_       = hexahedronOffset_    +   dofsPerHexahedron * gridView_.size(Dune::GeometryTypes::hexahedron);
        break;
      }
    }
  }
 
  const GridView& gridView() const
  {
    return gridView_;
  }
 
  void update(const GridView& gv)
  {
    gridView_ = gv;
  }
 
  Node makeNode() const
  {
    return Node{};
  }
 
  IndexSet makeIndexSet() const
  {
    return IndexSet{*this};
  }
 
  size_type size() const
  {
    switch (dim)
    {
      case 1:
        return dofsPerEdge*gridView_.size(0);
      case 2:
      {
        return dofsPerTriangle*gridView_.size(Dune::GeometryTypes::triangle) + dofsPerQuad*gridView_.size(Dune::GeometryTypes::quadrilateral);
      }
      case 3:
      {
        return dofsPerTetrahedron*gridView_.size(Dune::GeometryTypes::tetrahedron)
             + dofsPerPyramid*gridView_.size(Dune::GeometryTypes::pyramid)
             + dofsPerPrism*gridView_.size(Dune::GeometryTypes::prism)
             + dofsPerHexahedron*gridView_.size(Dune::GeometryTypes::hexahedron);
      }
    }
    DUNE_THROW(Dune::NotImplemented, "No size method for " << dim << "d grids available yet!");
  }
 
  size_type size(const SizePrefix prefix) const
  {
    assert(prefix.size() == 0 || prefix.size() == 1);
    return (prefix.size() == 0) ? size() : 0;
  }
 
  size_type dimension() const
  {
    return size();
  }
 
  size_type maxNodeSize() const
  {
    return StaticPower<(k+1),GV::dimension>::power;
  }
 
//protected:
  GridView gridView_;
 
  size_t quadrilateralOffset_;
  size_t pyramidOffset_;
  size_t prismOffset_;
  size_t hexahedronOffset_;
};
 
 
 
template<typename GV, int k, class MI>
class LagrangeDGNodeIndexSet
{
  // Cannot be an enum -- otherwise the switch statement below produces compiler warnings
  static const int dim = GV::dimension;
 
public:
 
  using size_type = std::size_t;
 
  using MultiIndex = MI;
 
  using PreBasis = LagrangeDGPreBasis<GV, k, MI>;
 
  using Node = LagrangeDGNode<GV, k>;
 
  LagrangeDGNodeIndexSet(const PreBasis& preBasis) :
    preBasis_(&preBasis)
  {}
 
  void bind(const Node& node)
  {
    node_ = &node;
  }
 
  void unbind()
  {
    node_ = nullptr;
  }
 
  size_type size() const
  {
    return node_->finiteElement().size();
  }
 
  template<typename It>
  It indices(It it) const
  {
    const auto& gridIndexSet = preBasis_->gridView().indexSet();
    const auto& element = node_->element();
 
    for (size_type i = 0, end = size() ; i < end ; ++i, ++it)
      {
        switch (dim)
          {
          case 1:
            {
              *it = {preBasis_->dofsPerEdge*gridIndexSet.subIndex(element,0,0) + i};
              continue;
            }
          case 2:
            {
              if (element.type().isTriangle())
                {
                  *it = {preBasis_->dofsPerTriangle*gridIndexSet.subIndex(element,0,0) + i};
                  continue;
                }
              else if (element.type().isQuadrilateral())
                {
                  *it = { preBasis_->quadrilateralOffset_ + preBasis_->dofsPerQuad*gridIndexSet.subIndex(element,0,0) + i};
                  continue;
                }
              else
                DUNE_THROW(Dune::NotImplemented, "2d elements have to be triangles or quadrilaterals");
            }
          case 3:
            {
              if (element.type().isTetrahedron())
                {
                  *it = {preBasis_->dofsPerTetrahedron*gridIndexSet.subIndex(element,0,0) + i};
                  continue;
                }
              else if (element.type().isPrism())
                {
                  *it = { preBasis_->prismOffset_ + preBasis_->dofsPerPrism*gridIndexSet.subIndex(element,0,0) + i};
                  continue;
                }
              else if (element.type().isHexahedron())
                {
                  *it = { preBasis_->hexahedronOffset_ + preBasis_->dofsPerHexahedron*gridIndexSet.subIndex(element,0,0) + i};
                  continue;
                }
              else if (element.type().isPyramid())
                {
                  *it = { preBasis_->pyramidOffset_ + preBasis_->dofsPerPyramid*gridIndexSet.subIndex(element,0,0) + i};
                  continue;
                }
              else
                DUNE_THROW(Dune::NotImplemented, "3d elements have to be tetrahedrons, prisms, hexahedrons or pyramids");
            }
          }
        DUNE_THROW(Dune::NotImplemented, "No index method for " << dim << "d grids available yet!");
      }
    return it;
  }
 
protected:
  const PreBasis* preBasis_;
 
  const Node* node_;
};
 
 
 
 
namespace BasisFactory {
 
namespace Imp {
 
template<std::size_t k>
class LagrangeDGPreBasisFactory
{
public:
  static const std::size_t requiredMultiIndexSize = 1;
 
  template<class MultiIndex, class GridView>
  auto makePreBasis(const GridView& gridView) const
  {
    return LagrangeDGPreBasis<GridView, k, MultiIndex>(gridView);
  }
 
};
 
} // end namespace BasisFactory::Imp
 
 
 
template<std::size_t k>
auto lagrangeDG()
{
  return Imp::LagrangeDGPreBasisFactory<k>();
}
 
} // end namespace BasisFactory
 
 
 
// *****************************************************************************
// This is the actual global basis implementation based on the reusable parts.
// *****************************************************************************
 
template<typename GV, int k>
using LagrangeDGBasis = DefaultGlobalBasis<LagrangeDGPreBasis<GV, k, FlatMultiIndex<std::size_t>> >;
 
 
 
} // end namespace Functions
} // end namespace Dune
 
 
#endif // DUNE_FUNCTIONS_FUNCTIONSPACEBASES_LAGRANGEDGBASIS_HH