taylorhoodbasis.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_TAYLORHOODBASIS_HH
#define DUNE_FUNCTIONS_FUNCTIONSPACEBASES_TAYLORHOODBASIS_HH
 
#include <dune/common/exceptions.hh>
#include <dune/common/reservedvector.hh>
 
#include <dune/typetree/powernode.hh>
#include <dune/typetree/compositenode.hh>
 
#include <dune/functions/functionspacebases/nodes.hh>
 
#include <dune/functions/functionspacebases/lagrangebasis.hh>
#include <dune/functions/functionspacebases/defaultglobalbasis.hh>
 
namespace Dune {
namespace Functions {
 
 
// *****************************************************************************
// This is the reusable part of the basis. It contains
//
//   TaylorHoodPreBasis
//   TaylorHoodNodeIndexSet
//   TaylorHoodBasisTree
//   TaylorHoodVelocityTree
//
// 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>
class TaylorHoodVelocityTree;
 
template<typename GV>
class TaylorHoodBasisTree;
 
template<typename GV, class MI, bool HI>
class TaylorHoodNodeIndexSet;
 
 
 
template<typename GV, class MI, bool HI=false>
class TaylorHoodPreBasis
{
  static const bool useHybridIndices = HI;
 
  static const int dim = GV::dimension;
 
  template<class, class, bool>
  friend class TaylorHoodNodeIndexSet;
 
public:
 
  using GridView = GV;
 
  using size_type = std::size_t;
 
  using Node = TaylorHoodBasisTree<GV>;
 
  using IndexSet = TaylorHoodNodeIndexSet<GV, MI, HI>;
 
  using MultiIndex = MI;
 
  using SizePrefix = Dune::ReservedVector<size_type, 2>;
 
private:
 
  using PQMultiIndex = std::array<size_type, 1>;
  using PQ1PreBasis = LagrangePreBasis<GV,1,PQMultiIndex>;
  using PQ2PreBasis = LagrangePreBasis<GV,2,PQMultiIndex>;
 
public:
 
  TaylorHoodPreBasis(const GridView& gv) :
    gridView_(gv),
    pq1PreBasis_(gv),
    pq2PreBasis_(gv)
  {}
 
  void initializeIndices()
  {
    pq1PreBasis_.initializeIndices();
    pq2PreBasis_.initializeIndices();
  }
 
  const GridView& gridView() const
  {
    return gridView_;
  }
 
  void update (const GridView& gv)
  {
    pq1PreBasis_.update(gv);
    pq2PreBasis_.update(gv);
  }
 
  Node makeNode() const
  {
    return Node{};
  }
 
  IndexSet makeIndexSet() const
  {
    return IndexSet{*this};
  }
 
  size_type size() const
  {
    return 2;
  }
 
  size_type size(const SizePrefix prefix) const
  {
    return sizeImp<useHybridIndices>(prefix);
  }
 
private:
 
  template<bool hi,
    typename std::enable_if<not hi,int>::type = 0>
  size_type sizeImp(const SizePrefix prefix) const
  {
    if (prefix.size() == 0)
      return 2;
    if (prefix.size() == 1)
    {
      if (prefix[0] == 0)
        return dim * pq2PreBasis_.size();
      if (prefix[0] == 1)
        return pq1PreBasis_.size();
    }
    assert(prefix.size() == 2);
    return 0;
  }
 
  template<bool hi,
    typename std::enable_if<hi,int>::type = 0>
  size_type sizeImp(const SizePrefix prefix) const
  {
    if (prefix.size() == 0)
      return 2;
    if (prefix.size() == 1)
    {
      if (prefix[0] == 0)
        return pq2PreBasis_.size();
      if (prefix[0] == 1)
        return pq1PreBasis_.size();
    }
    if (prefix.size() == 2)
    {
      if (prefix[0] == 0)
        return dim;
      if (prefix[0] == 1)
        return 0;
    }
    assert(prefix.size() == 3);
    return 0;
  }
 
public:
 
  size_type dimension() const
  {
    return dim * pq2PreBasis_.size() + pq1PreBasis_.size();
  }
 
  size_type maxNodeSize() const
  {
    return dim * pq2PreBasis_.maxNodeSize() + pq1PreBasis_.maxNodeSize();
  }
 
protected:
  GridView gridView_;
 
  PQ1PreBasis pq1PreBasis_;
  PQ2PreBasis pq2PreBasis_;
};
 
 
 
template<typename GV>
class TaylorHoodVelocityTree :
    public PowerBasisNode<LagrangeNode<GV,2>, GV::dimension>
{
  using PQ2Node = LagrangeNode<GV,2>;
  using Base = PowerBasisNode<PQ2Node, GV::dimension>;
 
public:
  TaylorHoodVelocityTree()
  {
    for(int i=0; i<GV::dimension; ++i)
      this->setChild(i, std::make_shared<PQ2Node>());
  }
};
 
template<typename GV>
class TaylorHoodBasisTree :
    public CompositeBasisNode<
      TaylorHoodVelocityTree<GV>,
      LagrangeNode<GV,1>
    >
{
  using VelocityNode=TaylorHoodVelocityTree<GV>;
  using PressureNode=LagrangeNode<GV,1>;
 
  using Base=CompositeBasisNode<VelocityNode, PressureNode>;
 
public:
  TaylorHoodBasisTree()
  {
    this->template setChild<0>(std::make_shared<VelocityNode>());
    this->template setChild<1>(std::make_shared<PressureNode>());
  }
};
 
 
 
template<typename GV, class MI, bool HI>
class TaylorHoodNodeIndexSet
{
  static const bool useHybridIndices = HI;
 
  static const int dim = GV::dimension;
 
public:
 
  using size_type = std::size_t;
 
  using MultiIndex = MI;
 
  using PreBasis = TaylorHoodPreBasis<GV, MI, HI>;
 
  using Node = TaylorHoodBasisTree<GV>;
 
  using PQ1NodeIndexSet = typename PreBasis::PQ1PreBasis::IndexSet;
  using PQ2NodeIndexSet = typename PreBasis::PQ2PreBasis::IndexSet;
 
  TaylorHoodNodeIndexSet(const PreBasis & preBasis) :
    preBasis_(&preBasis),
    pq1NodeIndexSet_(preBasis_->pq1PreBasis_.makeIndexSet()),
    pq2NodeIndexSet_(preBasis_->pq2PreBasis_.makeIndexSet())
  {}
 
  void bind(const Node& node)
  {
    using namespace TypeTree::Indices;
    node_ = &node;
    pq1NodeIndexSet_.bind(node.child(_1));
    pq2NodeIndexSet_.bind(node.child(_0, 0));
  }
 
  void unbind()
  {
    node_ = nullptr;
    pq1NodeIndexSet_.unbind();
    pq2NodeIndexSet_.unbind();
  }
 
  size_type size() const
  {
    return node_->size();
  }
 
  template<typename It>
  It indices(It multiIndices) const
  {
    return indicesImp<useHybridIndices>(multiIndices);
  }
 
  static const void multiIndexPushFront(MultiIndex& M, size_type M0)
  {
    M.resize(M.size()+1);
    for(std::size_t i=M.size()-1; i>0; --i)
      M[i] = M[i-1];
    M[0] = M0;
  }
 
  template<bool hi, class It,
    typename std::enable_if<not hi,int>::type = 0>
  It indicesImp(It multiIndices) const
  {
    for(std::size_t child=0; child<dim; ++child)
    {
      size_type subTreeSize = pq2NodeIndexSet_.size();
      pq2NodeIndexSet_.indices(multiIndices);
      for (std::size_t i = 0; i<subTreeSize; ++i)
      {
        multiIndexPushFront(multiIndices[i], 0);
        multiIndices[i][1] = multiIndices[i][1]*dim + child;
      }
      multiIndices += subTreeSize;
    }
    pq1NodeIndexSet_.indices(multiIndices);
    size_type subTreeSize = pq1NodeIndexSet_.size();
    for (std::size_t i = 0; i<subTreeSize; ++i)
      multiIndexPushFront(multiIndices[i], 1);
    multiIndices += subTreeSize;
    return multiIndices;
  }
 
  template<bool hi, class It,
    typename std::enable_if<hi,int>::type = 0>
  It indicesImp(It multiIndices) const
  {
    for(std::size_t child=0; child<dim; ++child)
    {
      size_type subTreeSize = pq2NodeIndexSet_.size();
      pq2NodeIndexSet_.indices(multiIndices);
      for (std::size_t i = 0; i<subTreeSize; ++i)
      {
        multiIndexPushFront(multiIndices[i], 0);
        multiIndices[i].push_back(i);
      }
      multiIndices += subTreeSize;
    }
    pq1NodeIndexSet_.indices(multiIndices);
    size_type subTreeSize = pq1NodeIndexSet_.size();
    for (std::size_t i = 0; i<subTreeSize; ++i)
      multiIndexPushFront(multiIndices[i], 1);
    multiIndices += subTreeSize;
    return multiIndices;
  }
 
private:
  const PreBasis* preBasis_;
  PQ1NodeIndexSet pq1NodeIndexSet_;
  PQ2NodeIndexSet pq2NodeIndexSet_;
 
  const Node* node_;
};
 
 
 
namespace BasisFactory {
 
namespace Imp {
 
class TaylorHoodPreBasisFactory
{
public:
  static const std::size_t requiredMultiIndexSize=2;
 
  template<class MultiIndex, class GridView>
  auto makePreBasis(const GridView& gridView) const
  {
    return TaylorHoodPreBasis<GridView, MultiIndex>(gridView);
  }
 
};
 
} // end namespace BasisFactory::Imp
 
auto taylorHood()
{
  return Imp::TaylorHoodPreBasisFactory();
}
 
} // end namespace BasisFactory
 
// *****************************************************************************
// This is the actual global basis implementation based on the reusable parts.
// *****************************************************************************
 
template<typename GV>
using TaylorHoodBasis = DefaultGlobalBasis<TaylorHoodPreBasis<GV, Dune::ReservedVector<std::size_t, 2>> >;
 
 
 
} // end namespace Functions
} // end namespace Dune
 
 
#endif // DUNE_FUNCTIONS_FUNCTIONSPACEBASES_TAYLORHOODBASIS_HH