taylorhoodbasis.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:
 
// SPDX-FileCopyrightText: Copyright © DUNE Project contributors, see file AUTHORS.md
// SPDX-License-Identifier: LicenseRef-GPL-2.0-only-with-DUNE-exception OR LGPL-3.0-or-later
 
#ifndef DUNE_FUNCTIONS_FUNCTIONSPACEBASES_TAYLORHOODBASIS_HH
#define DUNE_FUNCTIONS_FUNCTIONSPACEBASES_TAYLORHOODBASIS_HH
 
#include <dune/common/exceptions.hh>
#include <dune/common/reservedvector.hh>
#include <dune/common/indices.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
//   TaylorHoodBasisTree
//   TaylorHoodVelocityTree
//
// 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>
class TaylorHoodVelocityTree;
 
template<typename GV>
class TaylorHoodBasisTree;

template<typename GV, bool HI=false>
class TaylorHoodPreBasis
{
  static const bool useHybridIndices = HI;
 
  static const int dim = GV::dimension;
 
public:

  using GridView = GV;

  using size_type = std::size_t;

  using Node = TaylorHoodBasisTree<GV>;
 
  static constexpr size_type maxMultiIndexSize = useHybridIndices ? 3 : 2;
  static constexpr size_type minMultiIndexSize = 2;
  static constexpr size_type multiIndexBufferSize = maxMultiIndexSize;
 
private:
 
  using PQ1PreBasis = LagrangePreBasis<GV,1>;
  using PQ2PreBasis = LagrangePreBasis<GV,2>;
 
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{};
  }

  size_type size() const
  {
    return 2;
  }

  template<class SizePrefix>
  size_type size(const SizePrefix& prefix) const
  {
    return sizeImp<useHybridIndices>(prefix);
  }
 
private:
 
  template<bool hi, class SizePrefix,
    std::enable_if_t<not hi,int> = 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, class SizePrefix,
    std::enable_if_t<hi,int> = 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();
  }
 
  template<typename It>
  It indices(const Node& node, It it) const
  {
    return indicesImp<useHybridIndices>(node, it);
  }

  auto containerDescriptor() const
  {
    namespace CD = Dune::Functions::ContainerDescriptors;
    if constexpr(HI)
      return CD::makeDescriptor(
        CD::makeUniformDescriptor(pq2PreBasis_.size(),
          CD::FlatArray<GV::dimension>{}),
        CD::FlatVector{pq1PreBasis_.size()});
    else
      return CD::Array<CD::FlatVector,2>{
        CD::FlatVector{GV::dimension * pq2PreBasis_.size()},
        CD::FlatVector{pq1PreBasis_.size()} };
  }
 
protected:
 
  template<class MultiIndex>
  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,
    std::enable_if_t<not hi,int> = 0>
  It indicesImp(const Node& node, It multiIndices) const
  {
    using namespace Dune::Indices;
    for(std::size_t child=0; child<dim; ++child)
    {
      size_type subTreeSize = node.child(_0, 0).size();
      pq2PreBasis_.indices(node.child(_0, 0), multiIndices);
      for (std::size_t i = 0; i<subTreeSize; ++i)
      {
        multiIndexPushFront(multiIndices[i], 0);
        multiIndices[i][1] = multiIndices[i][1]*dim + child;
      }
      multiIndices += subTreeSize;
    }
    size_type subTreeSize = node.child(_1).size();
    pq1PreBasis_.indices(node.child(_1), multiIndices);
    for (std::size_t i = 0; i<subTreeSize; ++i)
      multiIndexPushFront(multiIndices[i], 1);
    multiIndices += subTreeSize;
    return multiIndices;
  }
 
  template<bool hi, class It,
    std::enable_if_t<hi,int> = 0>
  It indicesImp(const Node& node, It multiIndices) const
  {
    using namespace Dune::Indices;
    for(std::size_t child=0; child<dim; ++child)
    {
      size_type subTreeSize = node.child(_0, 0).size();
      pq2PreBasis_.indices(node.child(_0, 0), multiIndices);
      for (std::size_t i = 0; i<subTreeSize; ++i)
      {
        multiIndexPushFront(multiIndices[i], 0);
        multiIndices[i].push_back(i);
      }
      multiIndices += subTreeSize;
    }
    size_type subTreeSize = node.child(_1).size();
    pq1PreBasis_.indices(node.child(_1), multiIndices);
    for (std::size_t i = 0; i<subTreeSize; ++i)
      multiIndexPushFront(multiIndices[i], 1);
    multiIndices += subTreeSize;
    return multiIndices;
  }
 
  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, 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>(VelocityNode());
    this->template setChild<1>(PressureNode());
  }
};
 
 
 
namespace BasisFactory {

inline auto taylorHood()
{
  return [](const auto& gridView) {
    return TaylorHoodPreBasis<std::decay_t<decltype(gridView)>>(gridView);
  };
}
 
} // end namespace BasisFactory
 
// *****************************************************************************
// This is the actual global basis implementation based on the reusable parts.
// *****************************************************************************

template<typename GV>
using TaylorHoodBasis = DefaultGlobalBasis<TaylorHoodPreBasis<GV> >;
 
 
 
} // end namespace Functions
} // end namespace Dune
 
 
#endif // DUNE_FUNCTIONS_FUNCTIONSPACEBASES_TAYLORHOODBASIS_HH