raviartthomasbasis.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:
#ifndef DUNE_FUNCTIONS_FUNCTIONSPACEBASES_RAVIARTTHOMASBASIS_HH
#define DUNE_FUNCTIONS_FUNCTIONSPACEBASES_RAVIARTTHOMASBASIS_HH
 
#include <array>
#include <dune/common/exceptions.hh>
 
#include <dune/grid/common/capabilities.hh>
#include <dune/grid/common/mcmgmapper.hh>
 
#include <dune/localfunctions/common/localfiniteelementvariant.hh>
#include <dune/localfunctions/raviartthomas.hh>
#include <dune/localfunctions/raviartthomas/raviartthomas0cube2d.hh>
#include <dune/localfunctions/raviartthomas/raviartthomas0cube3d.hh>
#include <dune/localfunctions/raviartthomas/raviartthomas02d.hh>
#include <dune/localfunctions/raviartthomas/raviartthomas03d.hh>
#include <dune/localfunctions/raviartthomas/raviartthomas1cube2d.hh>
#include <dune/localfunctions/raviartthomas/raviartthomas1cube3d.hh>
#include <dune/localfunctions/raviartthomas/raviartthomas12d.hh>
#include <dune/localfunctions/raviartthomas/raviartthomas2cube2d.hh>
 
#include <dune/functions/functionspacebases/globalvaluedlocalfiniteelement.hh>
#include <dune/functions/functionspacebases/nodes.hh>
#include <dune/functions/functionspacebases/defaultglobalbasis.hh>
 
namespace Dune {
namespace Functions {
 
namespace Impl {
 
  template<int dim, typename D, typename R, std::size_t k>
  struct RaviartThomasSimplexLocalInfo
  {
    // Dummy type, must be something that we can have a std::unique_ptr to
    using FiniteElement = void*;
  };
 
  template<typename D, typename R>
  struct RaviartThomasSimplexLocalInfo<2,D,R,0>
  {
    using FiniteElement = RT02DLocalFiniteElement<D,R>;
  };
 
  template<typename D, typename R>
  struct RaviartThomasSimplexLocalInfo<2,D,R,1>
  {
    using FiniteElement = RT12DLocalFiniteElement<D,R>;
  };
 
  template<typename D, typename R>
  struct RaviartThomasSimplexLocalInfo<3,D,R,0>
  {
    using FiniteElement = RT03DLocalFiniteElement<D,R>;
  };
 
  template<int dim, typename D, typename R, std::size_t k>
  struct RaviartThomasCubeLocalInfo
  {
    // Dummy type, must be something that we can have a std::unique_ptr to
    using FiniteElement = void*;
  };
 
  template<typename D, typename R>
  struct RaviartThomasCubeLocalInfo<2,D,R,0>
  {
    using FiniteElement = RT0Cube2DLocalFiniteElement<D,R>;
  };
 
  template<typename D, typename R>
  struct RaviartThomasCubeLocalInfo<2,D,R,1>
  {
    using FiniteElement = RT1Cube2DLocalFiniteElement<D,R>;
  };
 
  template<typename D, typename R>
  struct RaviartThomasCubeLocalInfo<2,D,R,2>
  {
    using FiniteElement = RT2Cube2DLocalFiniteElement<D,R>;
  };
 
  template<typename D, typename R>
  struct RaviartThomasCubeLocalInfo<3,D,R,0>
  {
    using FiniteElement = RT0Cube3DLocalFiniteElement<D,R>;
  };
 
  template<typename D, typename R>
  struct RaviartThomasCubeLocalInfo<3,D,R,1>
  {
    using FiniteElement = RT1Cube3DLocalFiniteElement<D,R>;
  };
 
  template<typename GV, int dim, typename R, std::size_t k>
  class RaviartThomasLocalFiniteElementMap
  {
    using D = typename GV::ctype;
    constexpr static bool hasFixedElementType = Capabilities::hasSingleGeometryType<typename GV::Grid>::v;
 
    using CubeFiniteElement    = typename RaviartThomasCubeLocalInfo<dim, D, R, k>::FiniteElement;
    using SimplexFiniteElement = typename RaviartThomasSimplexLocalInfo<dim, D, R, k>::FiniteElement;
 
  public:
 
    using T = LocalBasisTraits<D, dim, FieldVector<D,dim>, R, dim, FieldVector<R,dim>, FieldMatrix<D,dim,dim> >;
 
    constexpr static unsigned int  topologyId = Capabilities::hasSingleGeometryType<typename GV::Grid>::topologyId;  // meaningless if hasFixedElementType is false
    constexpr static GeometryType type = GeometryType(topologyId, GV::dimension);
 
    using FiniteElement = std::conditional_t<hasFixedElementType,
                                           std::conditional_t<type.isCube(),CubeFiniteElement,SimplexFiniteElement>,
                                           LocalFiniteElementVariant<CubeFiniteElement, SimplexFiniteElement> >;
 
    // Each element facet can have its orientation reversed, hence there are
    // 2^#facets different variants.
    static std::size_t numVariants(GeometryType type)
    {
      auto numFacets = referenceElement<D,dim>(type).size(1);
      return power(2,numFacets);
    }
 
    RaviartThomasLocalFiniteElementMap(const GV& gv)
      : elementMapper_(gv, mcmgElementLayout()),
        orient_(gv.size(0))
    {
      if constexpr (hasFixedElementType)
      {
        variants_.resize(numVariants(type));
        for (size_t i = 0; i < numVariants(type); i++)
          variants_[i] = FiniteElement(i);
      }
      else
      {
        // for mixed grids add offset for cubes
        variants_.resize(numVariants(GeometryTypes::simplex(dim)) + numVariants(GeometryTypes::cube(dim)));
        for (size_t i = 0; i < numVariants(GeometryTypes::simplex(dim)); i++)
          variants_[i] = SimplexFiniteElement(i);
        for (size_t i = 0; i < numVariants(GeometryTypes::cube(dim)); i++)
          variants_[i + numVariants(GeometryTypes::simplex(dim))] = CubeFiniteElement(i);
      }
 
      for(const auto& cell : elements(gv))
      {
        unsigned int myId = elementMapper_.index(cell);
        orient_[myId] = 0;
 
        for (const auto& intersection : intersections(gv,cell))
        {
          if (intersection.neighbor() && (elementMapper_.index(intersection.outside()) > myId))
            orient_[myId] |= (1 << intersection.indexInInside());
        }
 
        // for mixed grids add offset for cubes
        if constexpr (!hasFixedElementType)
          if (cell.type().isCube())
            orient_[myId] += numVariants(GeometryTypes::simplex(dim));
      }
    }
 
    template<class EntityType>
    const FiniteElement& find(const EntityType& e) const
    {
      return variants_[orient_[elementMapper_.index(e)]];
    }
 
    private:
      std::vector<FiniteElement> variants_;
      const Dune::MultipleCodimMultipleGeomTypeMapper<GV> elementMapper_;
      std::vector<unsigned char> orient_;
  };
 
 
} // namespace Impl
 
 
// *****************************************************************************
// This is the reusable part of the basis. It contains
//
//   RaviartThomasPreBasis
//   RaviartThomasNode
//
// The pre-basis allows to create the others and is the owner of possible shared
// state. These components do _not_ depend on the global basis and local view
// and can be used without a global basis.
// *****************************************************************************
 
template<typename GV, int k>
class RaviartThomasNode;
 
template<typename GV, int k>
class RaviartThomasPreBasis
{
  static const int dim = GV::dimension;
  using FiniteElementMap = typename Impl::RaviartThomasLocalFiniteElementMap<GV, dim, double, k>;
 
public:
 
  using GridView = GV;
  using size_type = std::size_t;
 
  using Node = RaviartThomasNode<GV, k>;
 
  static constexpr size_type maxMultiIndexSize = 1;
  static constexpr size_type minMultiIndexSize = 1;
  static constexpr size_type multiIndexBufferSize = 1;
 
  RaviartThomasPreBasis(const GridView& gv) :
    gridView_(gv),
    finiteElementMap_(gv)
  {
    // Currently there are some unresolved bugs with hybrid grids and higher order Raviart-Thomas elements
    if (gv.indexSet().types(0).size() > 1 and k>0)
      DUNE_THROW(Dune::NotImplemented, "Raviart-Thomas basis with index k>0 is only implemented for grids with a single element type");
 
    for(auto type : gv.indexSet().types(0))
      if (!type.isSimplex() && !type.isCube())
        DUNE_THROW(Dune::NotImplemented, "Raviart-Thomas elements are only implemented for grids with simplex or cube elements.");
 
    GeometryType type = gv.template begin<0>()->type();
    const static int dofsPerElement = type.isCube() ? ((dim == 2) ? k*(k+1)*dim : k*(k+1)*(k+1)*dim) : k*dim;
    const static int dofsPerFace    = type.isCube() ? (dim-2)*2*k+k+1 : (dim-1)*k+1 ;
 
    dofsPerCodim_ = {{dofsPerElement, dofsPerFace}};
  }
 
  void initializeIndices()
  {
    codimOffset_[0] = 0;
    codimOffset_[1] = codimOffset_[0] + dofsPerCodim_[0] * gridView_.size(0);
  }
 
  const GridView& gridView() const
  {
    return gridView_;
  }
 
  /* \brief Update the stored grid view, to be called if the grid has changed */
  void update (const GridView& gv)
  {
    gridView_ = gv;
  }
 
  Node makeNode() const
  {
    return Node{&finiteElementMap_};
  }
 
  size_type size() const
  {
    return dofsPerCodim_[0] * gridView_.size(0) + dofsPerCodim_[1] * gridView_.size(1);
  }
 
  template<class SizePrefix>
  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
  {
    size_type result = 0;
    for (auto&& type : gridView_.indexSet().types(0))
    {
      size_t numFaces = ReferenceElements<double,dim>::general(type).size(1);
      const static int dofsPerElement = type.isCube() ? ((dim == 2) ? k*(k+1)*dim : k*(k+1)*(k+1)*dim) : k*dim;
      const static int dofsPerFace    = type.isCube() ? (dim-2)*2*k+k+1 : (dim-1)*k+1 ;
      result = std::max(result, dofsPerElement + dofsPerFace * numFaces);
    }
 
    return result;
  }
 
  template<typename It>
  It indices(const Node& node, It it) const
  {
    const auto& gridIndexSet = gridView().indexSet();
    const auto& element = node.element();
 
    // throw if Element is not of predefined type
    if (not(element.type().isCube()) and not(element.type().isSimplex()))
      DUNE_THROW(Dune::NotImplemented, "RaviartThomasBasis only implemented for cube and simplex elements.");
 
    for(std::size_t i=0, end=node.size(); i<end; ++i, ++it)
    {
      Dune::LocalKey localKey = node.finiteElement().localCoefficients().localKey(i);
 
      // The dimension of the entity that the current dof is related to
      size_t subentity = localKey.subEntity();
      size_t codim = localKey.codim();
 
      if (not(codim==0 or codim==1))
        DUNE_THROW(Dune::NotImplemented, "Grid contains elements not supported for the RaviartThomasBasis");
 
      *it = { codimOffset_[codim] +
        dofsPerCodim_[codim] * gridIndexSet.subIndex(element, subentity, codim) + localKey.index() };
    }
 
    return it;
  }
 
protected:
  GridView gridView_;
  std::array<size_t,dim+1> codimOffset_;
  FiniteElementMap finiteElementMap_;
  // Number of dofs per entity type depending on the entity's codimension and type
  std::array<int,dim+1> dofsPerCodim_;
};
 
 
 
template<typename GV, int k>
class RaviartThomasNode :
  public LeafBasisNode
{
  static const int dim = GV::dimension;
 
public:
 
  using size_type = std::size_t;
  using Element = typename GV::template Codim<0>::Entity;
  using FiniteElementMap = typename Impl::RaviartThomasLocalFiniteElementMap<GV, dim, double, k>;
  using FiniteElement = Impl::GlobalValuedLocalFiniteElement<Impl::ContravariantPiolaTransformator,
                                                             typename FiniteElementMap::FiniteElement,
                                                             Element>;
 
  RaviartThomasNode(const FiniteElementMap* finiteElementMap) :
    element_(nullptr),
    finiteElementMap_(finiteElementMap)
  { }
 
  const Element& element() const
  {
    return *element_;
  }
 
  const FiniteElement& finiteElement() const
  {
    return finiteElement_;
  }
 
  void bind(const Element& e)
  {
    element_ = &e;
    finiteElement_.bind((finiteElementMap_->find(*element_)), e);
    this->setSize(finiteElement_.size());
  }
 
protected:
 
  FiniteElement finiteElement_;
  const Element* element_;
  const FiniteElementMap* finiteElementMap_;
};
 
namespace BasisFactory {
 
template<std::size_t k>
auto raviartThomas()
{
  return [](const auto& gridView) {
    return RaviartThomasPreBasis<std::decay_t<decltype(gridView)>, k>(gridView);
  };
}
 
} // end namespace BasisFactory
 
 
 
// *****************************************************************************
// This is the actual global basis implementation based on the reusable parts.
// *****************************************************************************
 
template<typename GV, int k>
using RaviartThomasBasis = DefaultGlobalBasis<RaviartThomasPreBasis<GV, k> >;
 
} // end namespace Functions
} // end namespace Dune
 
 
#endif // DUNE_FUNCTIONS_FUNCTIONSPACEBASES_RAVIARTTHOMASBASIS_HH