interpolate.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_PDELAB_GRIDFUNCTIONSPACE_INTERPOLATE_HH
#define DUNE_PDELAB_GRIDFUNCTIONSPACE_INTERPOLATE_HH
 
#include <vector>
#include <utility>
 
#include <dune/common/exceptions.hh>
 
#include <dune/localfunctions/common/interfaceswitch.hh>
#include <dune/localfunctions/common/virtualinterface.hh>
 
#include <dune/typetree/typetree.hh>
#include <dune/typetree/pairtraversal.hh>
 
#include <dune/pdelab/function/localfunction.hh>
#include <dune/pdelab/gridfunctionspace/gridfunctionspace.hh>
#include <dune/pdelab/gridfunctionspace/lfsindexcache.hh>
 
namespace Dune {
  namespace PDELab {
 
    namespace {
 
      template<typename LF, typename XG>
      struct InterpolateLeafFromScalarVisitor
        : public TypeTree::TreeVisitor
        , public TypeTree::DynamicTraversal
      {
 
        template<typename LFS, typename TreePath>
        void leaf(const LFS& lfs, TreePath treePath) const
        {
          std::vector<typename XG::ElementType> xl(lfs.size());
 
          // call interpolate for the basis
          FiniteElementInterfaceSwitch<typename LFS::Traits::FiniteElement>::interpolation(lfs.finiteElement()).
            interpolate(lf, xl);
 
          // write coefficients into local vector
          xg.write_sub_container(lfs,xl);
        }
 
        InterpolateLeafFromScalarVisitor(const LF& lf_, XG& xg_)
          : lf(lf_)
          , xg(xg_)
        {}
 
        const LF& lf;
        XG& xg;
      };
 
 
      template<typename LF, typename XG>
      struct InterpolateLeafFromVectorVisitor
        : public TypeTree::TreeVisitor
        , public TypeTree::DynamicTraversal
      {
        using Domain = typename Functions::SignatureTraits<LF>::Domain;
        using Range = typename Functions::SignatureTraits<LF>::Range;
        using RangeField = typename FieldTraits<Range>::field_type;
 
        template<typename LFS, typename TreePath>
        void leaf(const LFS& lfs, TreePath treePath) const
        {
          std::vector<typename XG::ElementType> xl(lfs.size());
 
          using LFSRange = typename LFS::Traits::FiniteElement::Traits::LocalBasisType::Traits::RangeType;
          static_assert(std::is_convertible<LFSRange, typename FieldTraits< LFSRange >::field_type>::value,
            "only interpolation into scalar leaf function spaces is implemented");
 
          // call interpolate for the basis
          auto f = [&](const Domain& x) -> RangeField { return lf(x)[index]; };
 
          FiniteElementInterfaceSwitch<typename LFS::Traits::FiniteElement>::interpolation(lfs.finiteElement()).
            interpolate(f, xl);
 
          // write coefficients into local vector
          xg.write_sub_container(lfs,xl);
 
          // increment index
          index++;
        }
 
        InterpolateLeafFromVectorVisitor(const LF& lf_, XG& xg_)
          : lf(lf_)
          , index(0)
          , xg(xg_)
        {}
 
        const LF& lf;
        mutable std::size_t index;
        XG& xg;
      };
 
 
      template<typename E, typename XG>
      struct InterpolateVisitor
        : public TypeTree::TreePairVisitor
        , public TypeTree::DynamicTraversal
      {
 
        template<typename F, typename LFS, typename TreePath>
        typename std::enable_if<F::isLeaf && LFS::isLeaf>::type
        leaf(const F& f, const LFS& lfs, TreePath treePath) const
        {
          if (lfs.size() == 0)
            return;
 
          std::vector<typename XG::ElementType> xl(lfs.size());
          FiniteElementInterfaceSwitch<typename LFS::Traits::FiniteElement>::
              interpolation(lfs.finiteElement())
                  .interpolate(f, xl);
 
          // write coefficients into local vector
          xg.write_sub_container(lfs, xl);
        }
 
        // interpolate PowerLFS from scalar-valued function
        template<typename F, typename LFS, typename TreePath,
                 typename Range = typename Functions::SignatureTraits<F>::Range>
        typename std::enable_if<F::isLeaf &&
                           std::is_convertible<Range, typename FieldTraits< Range >::field_type>::value &&
                           (!LFS::isLeaf)>::type
        leaf(const F& f, const LFS& lfs, TreePath treePath) const
        {
          // call interpolate for the basis
          TypeTree::applyToTree(lfs,InterpolateLeafFromScalarVisitor<F,XG>(f, xg));
        }
 
        // interpolate PowerLFS from vector-valued function
        template<typename F, typename LFS, typename TreePath,
                 typename Range = typename Functions::SignatureTraits<F>::Range>
        typename std::enable_if<F::isLeaf &&
                          (!std::is_convertible<Range, typename FieldTraits< Range >::field_type>::value) &&
                          (!LFS::isLeaf)>::type
        leaf(const F& f, const LFS& lfs, TreePath treePath) const
        {
          static_assert(TypeTree::TreeInfo<LFS>::leafCount == Range::dimension,
                        "Number of leaves and dimension of range type " \
                        "must match for automatic interpolation of "    \
                        "vector-valued function");
 
          TypeTree::applyToTree(lfs,InterpolateLeafFromVectorVisitor<F,XG>(f,xg));
        }
 
        InterpolateVisitor(const E& e_, XG& xg_)
          : e(e_)
          , xg(xg_)
        {}
 
      private:
        const E& e;
        XG& xg;
      };
 
    } // anonymous namespace
 
 
    template<typename F, typename GFS, typename XG>
    void interpolate (const F& f, const GFS& gfs, XG& xg)
    {
      // this is the leaf version now
 
      // get some types
      using EntitySet = typename GFS::Traits::EntitySet;
      using Element = typename EntitySet::Element;
 
      auto entity_set = gfs.entitySet();
 
      // make local function
      auto lf = makeLocalFunctionTree(f, gfs.gridView());
 
      // make local function space
      typedef LocalFunctionSpace<GFS> LFS;
      LFS lfs(gfs);
      typedef LFSIndexCache<LFS> LFSCache;
      LFSCache lfs_cache(lfs);
      typedef typename XG::template LocalView<LFSCache> XView;
 
      XView x_view(xg);
 
      // loop once over the grid
      for (const auto& element : elements(entity_set))
        {
          // bind local function space to element
          lf.bind(element);
          lfs.bind(element);
          lfs_cache.update();
          x_view.bind(lfs_cache);
 
          // call interpolate
          TypeTree::applyToTreePair(lf,lfs,InterpolateVisitor<Element,XView>(element,x_view));
 
          x_view.unbind();
          lf.unbind();
        }
 
      x_view.detach();
    }
 
  } // namespace PDELab
} // namespace Dune
 
#endif // DUNE_PDELAB_GRIDFUNCTIONSPACE_INTERPOLATE_HH