grid/mmesh.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_MMESH_GRID_MMESH_HH
#define DUNE_MMESH_GRID_MMESH_HH
 
#include <memory>
#include <string>
#include <unordered_map>
#include <unordered_set>
 
// dune-common includes
#include <dune/common/deprecated.hh>
#include <dune/common/parallel/communication.hh>
#include <dune/common/parallel/mpihelper.hh>
#include <dune/common/version.hh>
#include <dune/grid/common/adaptcallback.hh>
#include <dune/grid/common/capabilities.hh>
#include <dune/grid/common/grid.hh>
#include <dune/grid/io/file/vtk/vtkwriter.hh>
 
// The components of the MMesh interface
#include "../interface/traits.hh"
#include "../misc/boundaryidprovider.hh"
#include "../misc/twistutility.hh"
#include "../remeshing/distance.hh"
#include "../remeshing/longestedgerefinement.hh"
#include "../remeshing/ratioindicator.hh"
#include "common.hh"
#include "connectedcomponent.hh"
#include "cutsettriangulation.hh"
#include "entity.hh"
#include "entityseed.hh"
#include "geometry.hh"
#include "hierarchiciterator.hh"
#include "incidentiterator.hh"
#include "indexsets.hh"
#include "interfaceiterator.hh"
#include "intersectioniterator.hh"
#include "leafiterator.hh"
#include "pointfieldvector.hh"
#include "rangegenerators.hh"
// Further includes below!
 
#if HAVE_MPI
#include <dune/common/parallel/mpicommunication.hh>
 
#include "../misc/communication.hh"
#include "../misc/partitionhelper.hh"
using Comm = MPI_Comm;
#else
using Comm = Dune::No_Comm;
#endif
 
namespace Dune {
 
// MMesh family
template <int dim, class HostGrid>
struct MMeshFamily {
 public:
  using Traits = GridTraits<
      dim, dim, MMesh<HostGrid, dim>, MMeshGeometry, MMeshEntity,
      MMeshLeafIterator,  // LevelIterator
      MMeshLeafIntersection,
      MMeshLeafIntersection,  // LevelIntersection
      MMeshLeafIntersectionIterator,
      MMeshLeafIntersectionIterator,  // LevelIntersectionIterator
      MMeshHierarchicIterator, MMeshLeafIterator,
      MMeshLeafIndexSet<const MMesh<HostGrid, dim>>,  // LevelIndexSet
      MMeshLeafIndexSet<const MMesh<HostGrid, dim>>,
      MMeshGlobalIdSet<const MMesh<HostGrid, dim>>, MMeshImpl::MultiId,
      MMeshGlobalIdSet<const MMesh<HostGrid, dim>>,  // LocalIdSet
      MMeshImpl::MultiId, Communication<Comm>, DefaultLevelGridViewTraits,
      DefaultLeafGridViewTraits, MMeshEntitySeed>;
};
 
 
template <class HostGrid, int dim, int codim>
class HostGridEntityChooser_ {
  struct type {};
};
 
template <class HG>
class HostGridEntityChooser_<HG, 2, 0> {
 public:
  using type = typename HG::Face_handle;
};
template <class HG>
class HostGridEntityChooser_<HG, 2, 1> {
 public:
  using type = std::pair<typename HG::Face_handle, int>;
};
template <class HG>
class HostGridEntityChooser_<HG, 2, 2> {
 public:
  using type = typename HG::Vertex_handle;
};
 
template <class HG>
class HostGridEntityChooser_<HG, 3, 0> {
 public:
  using type = typename HG::Cell_handle;
};
template <class HG>
class HostGridEntityChooser_<HG, 3, 1> {
 public:
  using type = std::pair<typename HG::Cell_handle, int>;
};
template <class HG>
class HostGridEntityChooser_<HG, 3, 2> {
 public:
  using type = CGAL::Triple<typename HG::Cell_handle, int, int>;
};
template <class HG>
class HostGridEntityChooser_<HG, 3, 3> {
 public:
  using type = typename HG::Vertex_handle;
};
 
template <class Point, class Edge, class IdType, class VertexHandle,
          class InterfaceGridConnectedComponent>
struct RefinementInsertionPointStruct {
  Point point;
  std::size_t insertionLevel = 0;
  Edge edge;
  IdType edgeId;
  VertexHandle v0, v1;
  bool isInterface = false;
  InterfaceGridConnectedComponent connectedcomponent;
};
 
//**********************************************************************
//
// --MMesh class
//
//************************************************************************
template <class HostGrid, int dim>
class MMesh
#ifndef DOXYGEN_SHOULD_SKIP_THIS
    : public GridDefaultImplementation<dim, dim,
                                       double,  
                                       MMeshFamily<dim, HostGrid>>
#endif /* DOXYGEN_SHOULD_SKIP_THIS */
{
 public:
  static constexpr int dimension = dim;
 
  using HostGridType = HostGrid;
 
  using GridFamily = MMeshFamily<dim, HostGrid>;
 
  using Point = typename HostGrid::Point;
 
  using FieldType = typename Point::R::RT;
 
  using IdType = MMeshImpl::MultiId;
 
  using BoundarySegments = std::unordered_map<IdType, std::size_t>;
 
  using BoundaryIds = std::unordered_map<std::size_t, std::size_t>;
 
  using InterfaceSegments = std::unordered_map<IdType, std::size_t>;
 
  //**********************************************************
  // The Interface Methods
  //**********************************************************
 
  using Traits = typename GridFamily::Traits;
 
  using GridImp = typename GridFamily::Traits::Grid;
 
  using GridPtrType = std::unique_ptr<GridImp>;
 
  using LeafIterator = typename Traits::template Codim<0>::LeafIterator;
 
  using GlobalCoordinate = Dune::FieldVector<FieldType, dimension>;
 
  template <int cd>
  using HostGridEntity =
      typename HostGridEntityChooser_<HostGridType, dimension, cd>::type;
 
  using ElementHandle = HostGridEntity<0>;
 
  using FacetHandle = HostGridEntity<1>;
 
  using EdgeHandle = HostGridEntity<dimension - 1>;
 
  using VertexHandle = HostGridEntity<dimension>;
 
  using ElementOutput = std::list<HostGridEntity<0>>;
 
  using BoundaryEdgesOutput = std::list<FacetHandle>;
 
  using Entity = typename Traits::template Codim<0>::Entity;
 
  using Facet = typename Traits::template Codim<1>::Entity;
 
  using Edge = typename Traits::template Codim<dimension - 1>::Entity;
 
  using Vertex = typename Traits::template Codim<dimension>::Entity;
 
  using CachingEntity = MMeshCachingEntity<0, dimension, const GridImp>;
 
  using ConnectedComponent = MMeshConnectedComponent<const GridImp>;
 
  using InterfaceElement = typename Traits::template Codim<1>::Entity;
 
  using Intersection = typename Traits::LeafIntersection;
 
  using InterfaceGrid = MMeshInterfaceGrid<GridImp>;
 
  using InterfaceEntity =
      typename InterfaceGrid::Traits::template Codim<0>::Entity;
 
  using InterfaceGridConnectedComponent =
      MMeshInterfaceConnectedComponent<const InterfaceGrid>;
 
  using RefinementInsertionPoint =
      RefinementInsertionPointStruct<Point, Edge, IdType, VertexHandle,
                                     InterfaceGridConnectedComponent>;
 
  using RemeshingIndicator = RatioIndicator<GridImp>;
 
  using RefinementStrategy = LongestEdgeRefinement<GridImp>;
 
  using InterfaceRefinementStrategy = LongestEdgeRefinement<InterfaceGrid>;
 
  explicit MMesh(HostGrid hostgrid) : MMesh(hostgrid, {}, {}, {}, {}) {}
 
  explicit MMesh(HostGrid hostgrid, BoundarySegments boundarySegments,
                 BoundarySegments interfaceBoundarySegments,
                 BoundaryIds boundaryIds, InterfaceSegments interfaceSegments)
      : hostgrid_(hostgrid),
        boundarySegments_(boundarySegments),
        boundaryIds_(boundaryIds),
        interfaceSegments_(interfaceSegments),
#ifdef HAVE_MPI
        comm_(MPIHelper::getCommunicator()),
#endif
        partitionHelper_(*this) {
    leafIndexSet_ = std::make_unique<MMeshLeafIndexSet<const GridImp>>(This());
    globalIdSet_ = std::make_unique<MMeshGlobalIdSet<const GridImp>>(This());
    globalIdSet_->update(This());
 
    interfaceGrid_ =
        std::make_shared<InterfaceGrid>(This(), interfaceBoundarySegments);
    loadBalance();
    indicator_.init(*this);
  }
 
  const GridImp* This() const { return static_cast<const GridImp*>(this); }
  GridImp* This() { return static_cast<GridImp*>(this); }
 
 public:
  void update() {
    setIds();
    setIndices();
    interfaceGrid_->setIds();
    interfaceGrid_->setIndices();
  }
 
 private:
  void setIds() { globalIdSet_->update(This()); }
 
  void setIndices() {
    leafIndexSet_->update(This());
 
    if (comm().size() == 1)
      localBoundarySegments_ = boundarySegments_;
    else {
      localBoundarySegments_.clear();
      std::size_t count = 0;
      for (const auto& e : elements(this->leafGridView()))
        for (const auto& is : intersections(this->leafGridView(), e))
          if (is.boundary()) {
            IdType iid = globalIdSet_->template id<1>(
                entity(is.impl().getHostIntersection()));
            localBoundarySegments_.insert(std::make_pair(iid, count++));
          }
    }
  }
 
 public:
  int maxLevel() const { return 0; }
 
  int size(int level, int codim) const {
    // we only have one level
    assert(level == 0);
    return size(codim);
  }
 
  size_t numBoundarySegments() const { return localBoundarySegments_.size(); }
 
  const BoundarySegments& boundarySegments() const {
    return localBoundarySegments_;
  }
 
  const BoundaryIds& boundaryIds() const { return boundaryIds_; }
 
  const InterfaceSegments& interfaceSegments() const {
    return interfaceSegments_;
  }
 
  InterfaceSegments& interfaceSegments() { return interfaceSegments_; }
 
  void addInterface(const Intersection& intersection,
                    const std::size_t marker = 1) {
    if (isInterface(intersection)) return;
 
    const auto& facet = entity(intersection.impl().getHostIntersection());
    std::vector<std::size_t> ids;
    for (std::size_t i = 0; i < facet.subEntities(dim); ++i) {
      const auto& vertex = facet.impl().template subEntity<dim>(i);
      vertex.impl().hostEntity()->info().isInterface = true;
      ids.push_back(globalIdSet().id(vertex).vt()[0]);
    }
    std::sort(ids.begin(), ids.end());
    interfaceSegments_.insert(std::make_pair(ids, marker));
 
    // Add interface element to connected component in order to mark element as
    // new
    const auto& ientity = asInterfaceEntity(intersection);
    InterfaceGridConnectedComponent connectedComponent(ientity);
    interfaceGrid_->markAsRefined({ids}, connectedComponent);
 
    interfaceGrid_->setIds();
    interfaceGrid_->setIndices();
 
    if (comm().size() > 0) partitionHelper_.computeInterfacePartitions();
  }
 
  template <class I>
  void addInterface(const I& intersection, const std::size_t marker = 1) {
    addInterface(intersection.impl().hostIntersection(), marker);
  }
 
  int size(int codim) const { return leafIndexSet().size(codim); }
 
  int size(int level, GeometryType type) const {
    // we only have one level
    assert(level == 0);
    return size(type);
  }
 
  int size(GeometryType type) const { return leafIndexSet().size(type); }
 
  const typename Traits::GlobalIdSet& globalIdSet() const {
    return *globalIdSet_;
  }
 
  const typename Traits::LocalIdSet& localIdSet() const {
    return *globalIdSet_;
  }
 
  const MMeshLeafIndexSet<const GridImp>& levelIndexSet(int level) const {
    if (level != 0)
      DUNE_THROW(GridError, "levelIndexSet of nonexisting level "
                                << level << " requested!");
    return *leafIndexSet_;
  }
 
  const MMeshLeafIndexSet<const GridImp>& leafIndexSet() const {
    return *leafIndexSet_;
  }
 
  template <class EntitySeed>
  typename Traits::template Codim<EntitySeed::codimension>::Entity entity(
      const EntitySeed& seed) const {
    using EntityImp = MMeshEntity<EntitySeed::codimension, dimension,
                                  const typename Traits::Grid>;
 
    auto hostEntity = seed.impl().hostEntity();
    assert(hostEntity != decltype(hostEntity)());
    return EntityImp(This(), hostEntity);
  }
 
  Vertex entity(const HostGridEntity<dimension>& vertexHandle) const {
    return entity(
        typename Traits::template Codim<dimension>::EntitySeed(vertexHandle));
  }
 
  Entity entity(const HostGridEntity<0>& elementHandle) const {
    return entity(
        typename Traits::template Codim<0>::EntitySeed(elementHandle));
  }
 
  InterfaceElement entity(const FacetHandle& facetHandle) const {
    return entity(typename Traits::template Codim<1>::EntitySeed(facetHandle));
  }
 
  template <int d = dim>
  std::enable_if_t<d == 3, Edge> entity(
      const HostGridEntity<2>& edgeHandle) const {
    return entity(typename Traits::template Codim<2>::EntitySeed(edgeHandle));
  }
 
  template <int codim>
  typename Traits::template Codim<codim>::LevelIterator lbegin(
      int level) const {
    return MMeshLeafIterator<codim, All_Partition, const GridImp>(This());
  }
 
  template <int codim>
  typename Traits::template Codim<codim>::LevelIterator lend(int level) const {
    return MMeshLeafIterator<codim, All_Partition, const GridImp>(This(), true);
  }
 
  template <int codim, PartitionIteratorType PiType>
  typename Traits::template Codim<codim>::template Partition<
      PiType>::LevelIterator
  lbegin(int level) const {
    return MMeshLeafIterator<codim, PiType, const GridImp>(This());
  }
 
  template <int codim, PartitionIteratorType PiType>
  typename Traits::template Codim<codim>::template Partition<
      PiType>::LevelIterator
  lend(int level) const {
    return MMeshLeafIterator<codim, PiType, const GridImp>(This(), true);
  }
 
  template <int codim>
  typename Traits::template Codim<codim>::LeafIterator leafbegin() const {
    return MMeshLeafIterator<codim, All_Partition, const GridImp>(This());
  }
 
  template <int codim>
  typename Traits::template Codim<codim>::LeafIterator leafend() const {
    return MMeshLeafIterator<codim, All_Partition, const GridImp>(This(), true);
  }
 
  template <int codim, PartitionIteratorType PiType>
  typename Traits::template Codim<codim>::template Partition<
      PiType>::LeafIterator
  leafbegin() const {
    return MMeshLeafIterator<codim, PiType, const GridImp>(This());
  }
 
  template <int codim, PartitionIteratorType PiType>
  typename Traits::template Codim<codim>::template Partition<
      PiType>::LeafIterator
  leafend() const {
    return MMeshLeafIterator<codim, PiType, const GridImp>(This(), true);
  }
 
  typename Traits::LevelIntersectionIterator ilevelbegin(
      const typename Traits::template Codim<0>::Entity& entity) const {
    return entity.impl().ilevelbegin();
  }
 
  typename Traits::LevelIntersectionIterator ilevelend(
      const typename Traits::template Codim<0>::Entity& entity) const {
    return entity.impl().ilevelend();
  }
 
  typename Traits::LeafIntersectionIterator ileafbegin(
      const typename Traits::template Codim<0>::Entity& entity) const {
    return entity.impl().ileafbegin();
  }
 
  typename Traits::LeafIntersectionIterator ileafend(
      const typename Traits::template Codim<0>::Entity& entity) const {
    return entity.impl().ileafend();
  }
 
  template <int codim>
  MMeshInterfaceIterator<codim, const GridImp> interfaceBegin(
      bool includeBoundary = false) const {
    using Impl =
        typename MMeshInterfaceIterator<codim, const GridImp>::Implementation;
    return MMeshInterfaceIterator<codim, const GridImp>(Impl(this, false));
  }
 
  template <int codim>
  MMeshInterfaceIterator<codim, const GridImp> interfaceEnd(
      bool includeBoundary = false) const {
    using Impl =
        typename MMeshInterfaceIterator<codim, const GridImp>::Implementation;
    return MMeshInterfaceIterator<codim, const GridImp>(
        Impl(this, true, includeBoundary));
  }
 
  MMeshInterfaceVertexIterator<const GridImp> interfaceVerticesBegin(
      bool includeBoundary = false) const {
    using Impl =
        typename MMeshInterfaceVertexIterator<const GridImp>::Implementation;
    return MMeshInterfaceVertexIterator<const GridImp>(
        Impl(this, includeBoundary));
  }
 
  MMeshInterfaceVertexIterator<const GridImp> interfaceVerticesEnd(
      bool includeBoundary = false) const {
    using Impl =
        typename MMeshInterfaceVertexIterator<const GridImp>::Implementation;
    return MMeshInterfaceVertexIterator<const GridImp>(
        Impl(this, true, includeBoundary));
  }
 
  bool isInterface(const Vertex& vertex) const {
    return vertex.impl().hostEntity()->info().isInterface;
  }
 
  bool isInterface(const Intersection& intersection) const {
    return isInterface(entity(intersection.impl().getHostIntersection()));
  }
 
  template <class OtherIntersection>
  bool isInterface(const OtherIntersection& intersection) const {
    return isInterface(intersection.impl().hostIntersection());
  }
 
  bool isInterface(const InterfaceElement& segment) const {
    static std::vector<std::size_t> ids(segment.subEntities(dimension));
    for (std::size_t i = 0; i < segment.subEntities(dimension); ++i) {
      const auto& vertex = segment.impl().template subEntity<dimension>(i);
      if (!vertex.impl().isInterface()) return false;
 
      ids[i] = this->globalIdSet().id(vertex).vt()[0];
    }
 
    std::sort(ids.begin(), ids.end());
 
    int count = interfaceSegments_.count(ids);
    assert(count <= 1);
    return (count > 0);
  }
 
  template <int d = dim>
  std::enable_if_t<d == 3, bool> isInterface(const Edge& edge) const {
    std::vector<std::size_t> ids;
    for (std::size_t i = 0; i < edge.subEntities(dimension); ++i) {
      const auto& vertex = edge.impl().template subEntity<dimension>(i);
 
      if (!isInterface(vertex)) return false;
 
      ids.push_back(this->globalIdSet().id(vertex).vt()[0]);
    }
 
    std::sort(ids.begin(), ids.end());
 
    for (const auto& iseg : interfaceSegments_) {
      const auto& seg = iseg.first.vt();
      if ((seg[0] == ids[0] && seg[1] == ids[1]) ||
          (seg[1] == ids[0] && seg[2] == ids[1]) ||
          (seg[0] == ids[0] && seg[2] == ids[1]))
        return true;
    }
 
    return false;
  }
 
  bool isOnInterface(const Entity& entity) const {
    for (std::size_t i = 0; i < entity.subEntities(1); ++i)
      if (isInterface(entity.template subEntity<1>(i))) return true;
 
    return false;
  }
 
  InterfaceEntity asInterfaceEntity(const InterfaceElement& segment) const {
    return InterfaceEntity{{interfaceGrid_.get(), segment.impl().hostEntity()}};
  }
 
  InterfaceEntity asInterfaceEntity(const Intersection& intersection) const {
    return InterfaceEntity{
        {interfaceGrid_.get(), intersection.impl().getHostIntersection()}};
  }
 
  template <class OtherIntersection>
  InterfaceEntity asInterfaceEntity(
      const OtherIntersection& intersection) const {
    return asInterfaceEntity(intersection.impl().hostIntersection());
  }
 
  Intersection asIntersection(const InterfaceEntity& interfaceEntity) const {
    const auto& host = interfaceEntity.impl().hostEntity();
    return asIntersection(host);
  }
 
  Intersection asIntersection(const Facet& facet) const {
    const auto& host = facet.impl().hostEntity();
    return asIntersection(host);
  }
 
  Intersection asIntersection(const FacetHandle& host) const {
    FacetHandle hostFacet = host;
 
    // make sure to get the intersection seen from inside at domain boundary
    if (hostgrid_.is_infinite(hostFacet.first))
      hostFacet = interfaceGrid().mirrorHostEntity(hostFacet);
 
    return MMeshLeafIntersection<const GridImp>(This(), hostFacet.first,
                                                hostFacet.second);
  }
 
  const Entity locate(const GlobalCoordinate& p,
                      const Entity& element = {}) const {
    return entity(
        hostgrid_.inexact_locate(makePoint(p), element.impl().hostEntity()));
  }
 
  void globalRefine(int steps = 1) {
    for (int i = 0; i < steps; ++i) {
      // mark all elements
      for (const auto& element : elements(this->leafGridView()))
        mark(1, element);
 
      preAdapt();
      adapt();
      postAdapt();
    }
  }
 
  bool mark(int refCount,
            const typename Traits::template Codim<0>::Entity& e) const {
    e.impl().mark(refCount);
    if (refCount > 0) ++refineMarked_;
    if (refCount < 0) ++coarsenMarked_;
    return true;
  }
 
  bool markElements() {
    bool change = false;
    indicator_.update();
 
    for (const auto& element : elements(this->leafGridView())) {
      mark(indicator_(element), element);
      change |= indicator_(element) != 0;
    }
 
    for (const auto& ielement : elements(interfaceGrid_->leafGridView())) {
      interfaceGrid_->mark(indicator_(ielement), ielement);
      change |= indicator_(ielement) != 0;
    }
 
    return change;
  }
 
  int getMark(const typename Traits::template Codim<0>::Entity& e) const {
    return e.impl().getMark();
  }
 
  bool preAdapt() {
    return (interfaceGrid_->preAdapt()) || (coarsenMarked_ > 0) ||
           (remove_.size() > 0);
  }
 
  void refineEdge(const Entity& entity, const std::size_t edgeIndex,
                  const double where = 0.5) {
    RefinementInsertionPoint ip;
    ip.edge = entity.template subEntity<dim - 1>(edgeIndex);
    ip.edgeId = globalIdSet().id(ip.edge);
    ip.point = makePoint(where * ip.edge.geometry().corner(0) +
                         (1 - where) * ip.edge.geometry().corner(1));
    ip.v0 = ip.edge.impl().template subEntity<dim>(0).impl().hostEntity();
    ip.v1 = ip.edge.impl().template subEntity<dim>(1).impl().hostEntity();
    ip.insertionLevel = ip.edge.impl().insertionLevel() + 1;
 
    if (isInterface(ip.edge)) {
      ip.isInterface = true;
      if constexpr (dim != 3) {
        InterfaceEntity component{
            {interfaceGrid_.get(), ip.edge.impl().hostEntity()}};
        ip.connectedcomponent = InterfaceGridConnectedComponent(component);
      }
    }
 
    if (inserted_.insert(ip.edgeId).second) {
      insert_.push_back(ip);
      if (verbose_)
        std::cout << "Insert vertex manually: " << ip.point << std::endl;
    }
  }
 
  void insertVertexInCell(const GlobalCoordinate& position) {
    RefinementInsertionPoint ip;
    ip.point = makePoint(position);
 
    insert_.push_back(ip);
    if (verbose_)
      std::cout << "Insert vertex in cell manually: " << ip.point << std::endl;
  }
 
  void removeVertex(
      const typename InterfaceGrid::Traits::template Codim<dim - 1>::Entity&
          interfaceVertex) {
    const Vertex& vertex = entity(interfaceVertex.impl().hostEntity());
    removeVertex(vertex);
  }
 
  void removeVertex(const Vertex& vertex) {
    if (removed_.insert(globalIdSet().id(vertex)).second) {
      remove_.push_back(vertex.impl().hostEntity());
      if (verbose_)
        std::cout << "Remove vertex manually: " << vertex.geometry().center()
                  << std::endl;
    }
  }
 
  bool adapt() {
    // Obtain the adaption points
    for (const auto& element : elements(this->leafGridView())) {
      int mark = element.impl().getMark();
 
      // refine
      if (mark == 1) {
        std::pair<Edge, GlobalCoordinate> pair =
            RefinementStrategy::refinement(element);
 
        RefinementInsertionPoint ip;
        ip.edge = pair.first;
        ip.edgeId = globalIdSet().id(ip.edge);
        ip.point = makePoint(pair.second);
        ip.v0 = ip.edge.impl().template subEntity<dim>(0).impl().hostEntity();
        ip.v1 = ip.edge.impl().template subEntity<dim>(1).impl().hostEntity();
        ip.insertionLevel = ip.edge.impl().insertionLevel() + 1;
 
        if (!isInterface(ip.edge))
          if (inserted_.insert(ip.edgeId).second) {
            insert_.push_back(ip);
            if (verbose_)
              std::cout << "Insert vertex because of marked cell: " << ip.point
                        << std::endl;
          }
      }
 
      // coarsen
      else if (mark == -1) {
        auto vertex = RefinementStrategy::coarsening(element);
 
        if (vertex != decltype(vertex)())
          if (removed_.insert(globalIdSet().id(vertex)).second) {
            remove_.push_back(vertex.impl().hostEntity());
            if (verbose_)
              std::cout << "Remove vertex because of marked cell: "
                        << vertex.geometry().center() << std::endl;
          }
      }
    }
 
    // Obtain the adaption points for the interface
    for (const auto& element : elements(this->interfaceGrid().leafGridView())) {
      int mark = this->interfaceGrid().getMark(element);
 
      // refine
      if (mark == 1) {
        auto pair = InterfaceRefinementStrategy::refinement(element);
 
        RefinementInsertionPoint ip;
        ip.edge = entity(pair.first.impl().hostEntity());
        ip.edgeId = globalIdSet().id(ip.edge);
        ip.point = makePoint(pair.second);
        ip.v0 = ip.edge.impl().template subEntity<dim>(0).impl().hostEntity();
        ip.v1 = ip.edge.impl().template subEntity<dim>(1).impl().hostEntity();
        ip.insertionLevel = ip.edge.impl().insertionLevel() + 1;
        ip.isInterface = true;
        ip.connectedcomponent = InterfaceGridConnectedComponent(element);
 
        if (inserted_.insert(ip.edgeId).second) {
          insert_.push_back(ip);
          if (verbose_)
            std::cout << "Insert interface vertex because of marked cell: "
                      << ip.point << std::endl;
        }
      }
 
      // coarsen
      else if (mark == -1) {
        auto ivertex = InterfaceRefinementStrategy::coarsening(element);
        if (ivertex != decltype(ivertex)()) {
          const Vertex& vertex = entity(ivertex.impl().hostEntity());
 
          if (removed_.insert(globalIdSet().id(vertex)).second) {
            remove_.push_back(vertex.impl().hostEntity());
            if (verbose_)
              std::cout << "Remove interface vertex because of marked cell: "
                        << vertex.geometry().center() << std::endl;
          }
        }
      }
    }
 
    if (verbose_)
      std::cout << "- insert " << insert_.size() << "\t remove "
                << remove_.size() << std::endl;
 
    return adapt_(true);
  }
 
  bool ensureInterfaceMovement(std::vector<GlobalCoordinate> shifts) {
    assert(shifts.size() ==
           this->interfaceGrid().leafIndexSet().size(dimension - 1));
    bool change = false;
 
    // check if grid is still valid
    for (const auto& element : elements(this->leafGridView()))
      if (signedVolume_(element) <= 0.0)
        DUNE_THROW(GridError,
                   "A cell has a negative volume! Maybe the interface has been "
                   "moved too far?");
 
    // temporarily move vertices
    moveInterface(shifts);
 
    for (const auto& element : elements(this->leafGridView()))
      if (signedVolume_(element) <= 0.0) {
        // disable removing of vertices in 3d
        if constexpr (dim == 3) {
          DUNE_THROW(GridError,
                     "Interface could not be moved, because the removal of "
                     "vertices is not supported in 3D!");
        } else {
          bool allInterface = true;
          for (std::size_t j = 0; j < element.subEntities(dimension); ++j) {
            const auto& v = element.template subEntity<dimension>(j);
 
            // if vertex is part of interface, we have to do more
            if (!v.impl().isInterface()) {
              if (RefinementStrategy::boundaryFlag(v) == 1) continue;
 
              bool inserted = removed_.insert(globalIdSet().id(v)).second;
              if (inserted) {
                remove_.push_back(v.impl().hostEntity());
                change = true;
                if (verbose_)
                  std::cout << "Remove vertex because of negative volume: "
                            << v.geometry().center() << std::endl;
              }
              allInterface = false;
            }
          }
 
          // if all vertices are part of the interface, we can try to compute an
          // intersection
          if (allInterface) {
            Edge interfaceEdge;
            for (std::size_t j = 0; j < element.subEntities(1); ++j) {
              const auto& edge = element.template subEntity<1>(j);
              if (isInterface(edge)) {
                if (interfaceEdge != Edge())  // with more than one interface
                                              // edge we don't know what to do
                  DUNE_THROW(GridError,
                             "Interface could not be moved because a "
                             "constrained cell with more than one interface "
                             "edge would have negative volume!");
 
                interfaceEdge = edge;
              }
            }
 
            // with no interface edge we can try to coarsen the interface
            if (interfaceEdge == Edge()) {
              bool allNonRemovable = true;
              for (std::size_t j = 0; j < element.subEntities(dimension); ++j) {
                const auto v = element.template subEntity<dimension>(j);
                const auto iv = interfaceGrid().entity(v.impl().hostEntity());
                if (RefinementStrategy::isRemoveable(iv)) {
                  allNonRemovable = false;
                  bool inserted = removed_.insert(globalIdSet().id(v)).second;
                  if (inserted) {
                    remove_.push_back(v.impl().hostEntity());
                    change = true;
                    if (verbose_)
                      std::cout << "Remove interface vertex because of "
                                   "negative volume: "
                                << v.geometry().center() << std::endl;
                  }
                }
              }
              if (allNonRemovable)
                DUNE_THROW(
                    GridError,
                    "Interface could not be moved because a constrained cell "
                    "without any interface edge would have negative volume!");
            } else {
              // compute intersection
              Vertex thirdVertex;
              for (std::size_t j = 0; j < element.subEntities(dimension); ++j) {
                const auto& v = element.template subEntity<dimension>(j);
                if (v !=
                        interfaceEdge.impl().template subEntity<dimension>(0) &&
                    v != interfaceEdge.impl().template subEntity<dimension>(1))
                  thirdVertex = v;
              }
 
              Vertex adjVertex;
              InterfaceEntity crossingEdge;
 
              const auto& iThirdVertex =
                  interfaceGrid().entity(thirdVertex.impl().hostEntity());
              for (const auto& e : incidentInterfaceElements(iThirdVertex)) {
                if (crossingEdge != InterfaceEntity())
                  DUNE_THROW(GridError,
                             "Interface could not be moved because two "
                             "interfaces cross!");
 
                crossingEdge = e;
 
                if (e.impl().template subEntity<1>(0) == iThirdVertex)
                  adjVertex = entity(
                      e.impl().template subEntity<1>(1).impl().hostEntity());
                else
                  adjVertex = entity(
                      e.impl().template subEntity<1>(0).impl().hostEntity());
              }
 
              // compute intersection
              const auto iegeo = interfaceEdge.geometry();
              const auto& c0 = iegeo.corner(0);
              const auto& c1 = iegeo.corner(1);
              const auto cegeo = crossingEdge.geometry();
              GlobalCoordinate x =
                  Dune::PolygonCutting<double, GlobalCoordinate>::
                      lineIntersectionPoint(c0, c1, cegeo.corner(0),
                                            cegeo.corner(1));
 
              // check if intersection point is in interfaceEdge
              if ((c0 - x) * (c1 - x) > 0.) continue;
 
              RefinementInsertionPoint ip;
              ip.edge = interfaceEdge;
              ip.edgeId = globalIdSet().id(interfaceEdge);
              ip.point = makePoint(x);
              ip.v0 = thirdVertex.impl().hostEntity();
              ip.insertionLevel = thirdVertex.impl().insertionLevel() + 1;
              ip.isInterface = true;
              ip.connectedcomponent = InterfaceGridConnectedComponent(
                  (interfaceEdge.geometry().volume() >
                   crossingEdge.geometry()
                       .volume())  // take the edge with the larger volume
                      ? interfaceGrid().entity(
                            interfaceEdge.impl().hostEntity())
                      : crossingEdge);
 
              if (verbose_)
                std::cout << "Insert interface intersection point: " << ip.point
                          << std::endl;
 
              insert_.push_back(ip);
              change = true;
 
              // move third vertex back to old position
              const auto& idx =
                  interfaceGrid().leafIndexSet().index(iThirdVertex);
              thirdVertex.impl().hostEntity()->point() =
                  makePoint(thirdVertex.geometry().center() - shifts[idx]);
              shifts[idx] = GlobalCoordinate(0.0);
            }
          }
        }
      }
 
    // move vertices back
    for (GlobalCoordinate& s : shifts) s *= -1.0;
    moveInterface(shifts);
 
    return change;
  }
 
  bool ensureVertexMovement(std::vector<GlobalCoordinate> shifts) {
    assert(shifts.size() == this->leafIndexSet().size(dimension));
    bool change = false;
 
    // temporarily move vertices
    moveVertices(shifts);
 
    for (const auto& element : elements(this->leafGridView()))
      if (signedVolume_(element) <= 0.0) {
        // disable removing of vertices in 3d
        if constexpr (dim == 3) {
          DUNE_THROW(GridError,
                     "Vertices could not be moved, because the removal of "
                     "vertices is not supported in 3D!");
        } else {
          for (std::size_t j = 0; j < element.subEntities(dimension); ++j) {
            const auto& v = element.template subEntity<dimension>(j);
 
            // if vertex is part of interface, we have to do more
            if (!v.impl().isInterface()) {
              if (RefinementStrategy::boundaryFlag(v) == 1) continue;
 
              bool inserted = removed_.insert(globalIdSet().id(v)).second;
              if (inserted) {
                remove_.push_back(v.impl().hostEntity());
                change = true;
                if (verbose_)
                  std::cout << "Remove vertex because of negative volume: "
                            << v.geometry().center() << std::endl;
              }
            }
          }
        }
      }
 
    // move vertices back
    for (GlobalCoordinate& s : shifts) s *= -1.0;
    moveVertices(shifts);
 
    return change;
  }
 
  template <class GridImp, class DataHandle>
  bool adapt(AdaptDataHandleInterface<GridImp, DataHandle>& handle) {
    preAdapt();
    adapt();
    sequence_ += 1;
 
    for (const auto& element : elements(this->leafGridView()))
      if (element.isNew()) {
        bool initialize = true;
 
        for (const auto& old : element.impl().connectedComponent().children()) {
          const Entity& father = old;
 
          MMeshImpl::CutSetTriangulation<Entity> cutSetTriangulation(old,
                                                                     element);
          for (auto& middle : cutSetTriangulation.triangles()) {
            middle.impl().bindFather(father);
            handle.prolongLocal(father, middle, true);
            middle.impl().bindFather(element);
            handle.restrictLocal(element, middle, initialize);
 
            initialize = false;
          }
        }
      }
 
    postAdapt();
    return true;
  }
 
 private:
  template <int d = dim>
  std::enable_if_t<d == 2, FieldType> signedVolume_(
      const Entity& element) const {
    return hostgrid_.triangle(element.impl().hostEntity()).area();
  }
 
  template <int d = dim>
  std::enable_if_t<d == 3, FieldType> signedVolume_(
      const Entity& element) const {
    return hostgrid_.tetrahedron(element.impl().hostEntity()).volume();
  }
 
  bool adapt_(bool buildComponents = true) {
    if (insert_.size() == 0 && remove_.size() == 0) return false;
 
    std::vector<std::size_t> insertComponentIds;
    std::vector<std::size_t> removeComponentIds;
    static constexpr bool writeComponents = verbose_;  // for debugging
 
    if (buildComponents) {
      // build the connected components
      componentCount_ =
          connectedComponents_.size() + 1;  // 0 is the default component
 
      // we have to mark the cells repeatedly for the case that conflict zones
      // overlap
      bool markAgain = true;
      std::size_t componentNumber;
      while (markAgain) {
        markAgain = false;
        insertComponentIds.clear();
        removeComponentIds.clear();
        insertComponentIds.reserve(insert_.size());
        removeComponentIds.reserve(remove_.size());
 
        // mark elements as mightVanish
        for (const auto& ip : insert_) {
          if (ip.edgeId != IdType())
            markAgain |= markElementsForInsertion_(ip.edge, componentNumber);
          else
            markAgain |= markElementForInsertion_(ip.point, componentNumber);
 
          insertComponentIds.push_back(componentNumber - 1);
        }
 
        // mark elements as mightVanish
        for (const auto& vh : remove_) {
          markAgain |= markElementsForRemoval_(vh, componentNumber);
          removeComponentIds.push_back(componentNumber - 1);
        }
      }
 
      buildConnectedComponents_();
 
      // plot connected components
      if (writeComponents) writeComponents_();
    }
 
    // actually insert the points
    std::vector<VertexHandle> newVertices;
    for (const auto& ip : insert_) {
      VertexHandle vh;
      bool connect = false;
      if (ip.edgeId != IdType()) {
        auto eh = ip.edge.impl().hostEntity();
 
        // if edge id has changed, we have to update the edge handle
        if (this->globalIdSet().id(ip.edge) != ip.edgeId) {
          // add empty entry to newVertices to match indices with
          // insertComponentIds
          newVertices.emplace_back();
 
          continue;
          // getEdge_( ip, eh ); // TODO this does not work correct yet
        }
 
        if (ip.v0 !=
                ip.edge.impl().template subEntity<dim>(0).impl().hostEntity() &&
            ip.v0 !=
                ip.edge.impl().template subEntity<dim>(1).impl().hostEntity())
          connect = true;
 
        if (ip.isInterface == true)
          vh = insertInInterface_(ip);
        else
          vh = insertInEdge_(ip.point, eh);
 
        vh->info().insertionLevel = ip.insertionLevel;
      } else {
        vh = insertInCell_(ip.point);
 
        // check if edge is really part of the triangulation
        if (ip.v0 != VertexHandle() &&
            !getHostGrid().tds().is_edge(ip.v0, vh))  // TODO 3D
        {
          // try again with half distance
          if constexpr (dimension == 2) hostgrid_.remove(vh);
 
          GlobalCoordinate x;
          x = makeFieldVector(ip.point);
          x -= makeFieldVector(ip.v0->point());
          x *= 0.5;
          x += makeFieldVector(ip.v0->point());
          vh = insertInCell_(makePoint(x));
 
          if (!getHostGrid().tds().is_edge(ip.v0, vh))  // TODO 3D
          {
            // DUNE_THROW( GridError, "Edge added to interface is not part of
            // the new triangulation: " << ip.v0->point() << " to " <<
            // vh->point() );
            std::cerr << "Error: Edge added to interface is not part of the "
                         "new triangulation: "
                      << ip.v0->point() << " to " << vh->point() << std::endl;
            continue;
          }
        }
 
        globalIdSet_->setNextId(vh);
        vh->info().insertionLevel = ip.insertionLevel;
 
        if (ip.isInterface) connect = true;
      }
 
      // connect vertex and ip.v0 with interface
      if (connect) {
        std::size_t id = vh->info().id;
        vh->info().isInterface = true;
        std::vector<std::size_t> ids;
        ids.push_back(id);
        ids.push_back(globalIdSet().id(entity(ip.v0)).vt()[0]);
        std::sort(ids.begin(), ids.end());
        interfaceSegments_.insert(std::make_pair(
            ids, 1));  // TODO: compute interface marker corresponding to ip.v0
 
        // pass this refinement information to the interface grid
        interfaceGrid_->markAsRefined(/*children*/ {ids},
                                      ip.connectedcomponent);
 
        // set boundary segment to the same as ip.v0 if possible, default to 0
        auto v0id = interfaceGrid_->globalIdSet()
                        .id(interfaceGrid_->entity(ip.v0))
                        .vt()[0];
        auto it = interfaceGrid_->boundarySegments().find({v0id});
        if (it != interfaceGrid_->boundarySegments().end())
          interfaceGrid_->addBoundarySegment({id}, it->second);
        else
          interfaceGrid_->addBoundarySegment({id}, 0);
      }
 
      // store vertex handles for later use
      newVertices.push_back(vh);
    }
 
    // actually remove the points
    int ci = 0;
    for (const auto& vh : remove_) {
      ElementOutput elements;
      if (vh->info().isInterface)
        elements = removeFromInterface_(vh);
      else
        hostgrid_.removeAndGiveNewElements(vh, elements);
 
      // flag all elements inside conflict area as new and map connected
      // component
      if (buildComponents)
        markElementsAfterRemoval_(elements, removeComponentIds[ci]);
      ci++;
    }
 
    // first update ids
    setIds();
    interfaceGrid_->setIds();
 
    // then, update partitions
    if (comm().size() > 1) partitionHelper_.updatePartitions();
 
    // afterwards, update index sets
    setIndices();
 
    if (buildComponents) {
      // flag incident elements as new and map connected component
      for (std::size_t i = 0; i < newVertices.size(); ++i)
        if (newVertices[i] != VertexHandle())
          markElementsAfterInsertion_(newVertices[i], insertComponentIds[i]);
    }
 
    // update interface grid
    interfaceGrid_->setIndices();
 
    if (buildComponents) {
      if (writeComponents) writeComponents_();
    }
 
    loadBalance();
    return newVertices.size() > 0;
  }
 
  template <int d = dim>
  std::enable_if_t<d == 2, void> getEdge_(const RefinementInsertionPoint& ip,
                                          EdgeHandle& eh) const {
    assert(hostgrid_.is_edge(ip.v0, ip.v1));
    hostgrid_.is_edge(ip.v0, ip.v1, eh.first, eh.second);
  }
 
  template <int d = dim>
  std::enable_if_t<d == 3, void> getEdge_(const RefinementInsertionPoint& ip,
                                          EdgeHandle& eh) const {
    assert(hostgrid_.is_edge(ip.v0, ip.v1, eh.first, eh.second, eh.third));
    hostgrid_.is_edge(ip.v0, ip.v1, eh.first, eh.second, eh.third);
  }
 
  template <int d = dim>
  std::enable_if_t<d == 2, VertexHandle> insertInEdge_(const Point& point,
                                                       const EdgeHandle& eh) {
    return hostgrid_.insert_in_edge(point, eh.first, eh.second);
  }
 
  template <int d = dim>
  std::enable_if_t<d == 3, VertexHandle> insertInEdge_(const Point& point,
                                                       const EdgeHandle& eh) {
    return hostgrid_.insert_in_edge(point, eh.first, eh.second, eh.third);
  }
 
  template <int d = dim>
  std::enable_if_t<d == 2, VertexHandle> insertInCell_(const Point& point) {
    auto face = hostgrid_.locate(point);
    return hostgrid_.insert_in_face(point, face);
  }
 
  template <int d = dim>
  std::enable_if_t<d == 3, VertexHandle> insertInCell_(const Point& point) {
    auto cell = hostgrid_.locate(point);
    return hostgrid_.insert_in_cell(point, cell);
  }
 
 public:
  void moveInterface(const std::vector<GlobalCoordinate>& shifts) {
    const auto& iindexSet = this->interfaceGrid().leafIndexSet();
    assert(shifts.size() == iindexSet.size(dimension - 1));
 
    for (const auto& vertex : vertices(this->interfaceGrid().leafGridView())) {
      const VertexHandle& vh = vertex.impl().hostEntity();
      vh->point() = makePoint(vertex.geometry().center() +
                              shifts[iindexSet.index(vertex)]);
    }
  }
 
  void moveVertices(const std::vector<GlobalCoordinate>& shifts) {
    const auto& indexSet = this->leafIndexSet();
    assert(shifts.size() == indexSet.size(dimension));
 
    for (const auto& vertex : vertices(this->leafGridView())) {
      const VertexHandle& vh = vertex.impl().hostEntity();
      vh->point() = makePoint(vertex.geometry().center() +
                              shifts[indexSet.index(vertex)]);
    }
  }
 
  template <typename Vertex>
  void addToInterface(const Vertex& vertex, const GlobalCoordinate& p) {
    RefinementInsertionPoint ip;
    ip.edgeId = IdType();
    ip.point = makePoint(p);
    ip.v0 = vertex.impl().hostEntity();
    ip.insertionLevel = vertex.impl().insertionLevel() + 1;
    ip.isInterface = true;
 
    // take some incident element as father
    for (const auto& elem : incidentInterfaceElements(vertex))
      if (!elem.isNew()) {
        ip.connectedcomponent = InterfaceGridConnectedComponent(elem);
        break;
      }
 
    insert_.push_back(ip);
    if (verbose_)
      std::cout << "Add vertex to interface: " << ip.point << std::endl;
  }
 
  void postAdapt() {
    for (const Entity& entity : elements(this->leafGridView())) {
      mark(0, entity);
      entity.impl().setIsNew(false);
      entity.impl().setWillVanish(false);
      entity.impl().hostEntity()->info().componentNumber = 0;
    }
 
    refineMarked_ = 0;
    coarsenMarked_ = 0;
    createdEntityConnectedComponentMap_.clear();
    vanishingEntityConnectedComponentMap_.clear();
    connectedComponents_.clear();
 
    insert_.clear();
    remove_.clear();
    inserted_.clear();
    removed_.clear();
  }
 
 private:
  void writeComponents_() const {
    static int performCount = 0;
    const auto& gridView = this->leafGridView();
    const auto& indexSet = this->leafIndexSet();
 
    std::vector<std::size_t> component(indexSet.size(0), 0);
    std::vector<std::size_t> findcomponent(indexSet.size(0), 0);
    std::vector<bool> isnew(indexSet.size(0), 0);
    std::vector<bool> mightvanish(indexSet.size(0), 0);
 
    for (const auto& e : elements(gridView)) {
      component[indexSet.index(e)] =
          e.impl().hostEntity()->info().componentNumber;
      isnew[indexSet.index(e)] = e.isNew();
      mightvanish[indexSet.index(e)] = e.mightVanish();
    }
 
    VTKWriter<typename Traits::LeafGridView> vtkWriter(gridView);
    vtkWriter.addCellData(component, "component");
    vtkWriter.addCellData(isnew, "isnew");
    vtkWriter.addCellData(mightvanish, "mightvanish");
    vtkWriter.write("mmesh-components-" + std::to_string(performCount));
 
    VTKWriter<typename InterfaceGrid::LeafGridView> ivtkWriter(
        interfaceGrid_->leafGridView());
    ivtkWriter.write("mmesh-components-interface-" +
                     std::to_string(performCount++));
  }
 
  void buildConnectedComponents_() {
    for (const Entity& entity : elements(this->leafGridView())) {
      if (entity.mightVanish()) {
        const auto& hostEntity = entity.impl().hostEntity();
        const IdType id = this->globalIdSet().id(entity);
 
        bool found = false;
        const std::size_t componentId = hostEntity->info().componentNumber - 1;
 
        // check if component for entity exists already and add entity if
        // necessary
        if (componentId < connectedComponents_.size()) {
          // sth. changed, we have to update the component to include this
          // entity
          if (!entity.isNew()) {
            ConnectedComponent& component = connectedComponents_[componentId];
            if (!component.hasEntity(entity)) component.update(entity);
          }
 
          vanishingEntityConnectedComponentMap_.insert(
              std::make_pair(id, componentId));
        }
        // else create new component
        else {
          connectedComponents_[componentId] =
              ConnectedComponent(This(), entity);
          vanishingEntityConnectedComponentMap_.insert(
              std::make_pair(id, componentId));
        }
      }
    }
  }
 
  VertexHandle insertInInterface_(const RefinementInsertionPoint& ip) {
    assert(isInterface(ip.edge));
 
    // get the vertex ids of the interface segment
    std::vector<std::size_t> ids;
    for (std::size_t i = 0; i < ip.edge.subEntities(dim); ++i)
      ids.push_back(
          globalIdSet().id(ip.edge.impl().template subEntity<dim>(i)).vt()[0]);
    std::sort(ids.begin(), ids.end());
 
    // erase old interface segment
    std::size_t marker = interfaceSegments_[ids];
    interfaceSegments_.erase(ids);
 
    // insert the point
    auto eh = ip.edge.impl().hostEntity();
    const auto& vh = insertInEdge_(ip.point, eh);
    vh->info().isInterface = true;
 
    // get the (next) id for vh
    std::size_t id = globalIdSet_->setNextId(vh);
 
    // insert the new interface segments
    std::vector<std::vector<std::size_t>> allNewIds;
    for (int i = 0; i < dimension; ++i) {
      std::vector<std::size_t> newIds;
      newIds.push_back(id);
      for (int j = 0; j < dimension - 1; ++j)
        newIds.push_back(ids[(i + j) % dimension]);
 
      std::sort(newIds.begin(), newIds.end());
      interfaceSegments_.insert(std::make_pair(newIds, marker));
      allNewIds.push_back(newIds);
    }
 
    // pass this refinement information to the interface grid
    interfaceGrid_->markAsRefined(/*children*/ allNewIds,
                                  ip.connectedcomponent);
 
    return vh;
  }
 
  template <int d = dimension>
  std::enable_if_t<d == 2, ElementOutput> removeFromInterface_(
      const VertexHandle& vh) {
    std::size_t id = vh->info().id;
    InterfaceGridConnectedComponent connectedComponent;
 
    // find and remove interface segments
    std::size_t marker = 1;
    std::vector<VertexHandle> otherVhs;
    for (const auto& e :
         incidentInterfaceElements(interfaceGrid_->entity(vh))) {
      // TODO: handle the case of overlapping components
      assert(!interfaceGrid_->hasConnectedComponent(e));
      connectedComponent.add(e);
 
      const auto v0 = e.template subEntity<1>(0).impl().hostEntity();
      const auto v1 = e.template subEntity<1>(1).impl().hostEntity();
 
      VertexHandle other = (v0 != vh) ? v0 : v1;
 
      std::vector<std::size_t> ids(2);
      ids[0] = id;
      ids[1] = other->info().id;
      std::sort(ids.begin(), ids.end());
 
      auto it = interfaceSegments_.find(ids);
      if (it != interfaceSegments_.end()) {
        marker = interfaceSegments_[ids];
        interfaceSegments_.erase(it);
        otherVhs.push_back(other);
      }
    }
 
    if (otherVhs.size() != 2)
      return {};  // otherwise, we remove a tip or a junction
 
    std::list<EdgeHandle> hole;
    hostgrid_.make_hole(vh, hole);
 
    ElementOutput elements;
    hostgrid_.remeshHoleConstrained(vh, hole, elements, otherVhs);
 
    // add the new interface segment
    std::vector<std::size_t> ids{
        {otherVhs[0]->info().id, otherVhs[1]->info().id}};
    std::sort(ids.begin(), ids.end());
    interfaceSegments_.insert(std::make_pair(ids, marker));
 
    // pass this refinement information to the interface grid
    interfaceGrid_->markAsRefined(/*children*/ {ids}, connectedComponent);
 
    return elements;
  }
 
  template <int d = dimension>
  std::enable_if_t<d == 3, ElementOutput> removeFromInterface_(
      const VertexHandle& vh) {
    DUNE_THROW(NotImplemented, "removeFromInterface() in 3d");
  }
 
 public:
  unsigned int overlapSize(int codim) const { return 0; }
 
  unsigned int ghostSize(int codim) const {
    std::size_t size = 0;
 
    if (codim == 0)
      for (const auto& e : elements(this->leafGridView(), Partitions::ghost))
        size++;
 
    if (codim == 1)
      for (const auto& f : facets(this->leafGridView()))
        if (f.partitionType() == GhostEntity) size++;
 
    if (codim == dimension)
      for (const auto& v : vertices(this->leafGridView()))
        if (v.partitionType() == GhostEntity) size++;
 
    return size;
  }
 
  unsigned int overlapSize(int level, int codim) const {
    return overlapSize(codim);
  }
 
  unsigned int ghostSize(int level, int codim) const {
    return ghostSize(codim);
  }
 
  void loadBalance() {
    partitionHelper_.distribute();
    update();
  };
 
  template <class T>
  bool loadBalance(const T& t) {
    DUNE_THROW(NotImplemented, "MMesh::loadBalance(t)");
  };
 
  void loadBalance(int strategy, int minlevel, int depth, int maxlevel,
                   int minelement) {
    DUNE_THROW(NotImplemented, "MMesh::loadBalance()");
  }
 
  const Communication<Comm>& comm() const { return comm_; }
 
  template <class Data, class InterfaceType, class CommunicationDirection>
  void communicate(Data& dataHandle, InterfaceType interface,
                   CommunicationDirection direction, int level = 0) const {
    if (comm().size() <= 1) return;
 
#if HAVE_MPI
    if ((interface == InteriorBorder_All_Interface) ||
        (interface == All_All_Interface)) {
      MMeshCommunication<GridImp, GridImp> communication(partitionHelper_);
      const auto& gv = this->leafGridView();
 
      switch (direction) {
        case ForwardCommunication:
          communication(gv.template begin<0, Interior_Partition>(),
                        gv.template end<0, Interior_Partition>(),
                        gv.template begin<0, Ghost_Partition>(),
                        gv.template end<0, Ghost_Partition>(), dataHandle,
                        InteriorEntity, GhostEntity,
                        (interface == All_All_Interface));
          break;
 
        case BackwardCommunication:
          communication(gv.template begin<0, Ghost_Partition>(),
                        gv.template end<0, Ghost_Partition>(),
                        gv.template begin<0, Interior_Partition>(),
                        gv.template end<0, Interior_Partition>(), dataHandle,
                        GhostEntity, InteriorEntity,
                        (interface == All_All_Interface));
          break;
      }
    } else
      DUNE_THROW(NotImplemented, "Communication on interface type "
                                     << interface << " not implemented.");
#else
    DUNE_THROW(NotImplemented, "MPI not found!");
#endif  // HAVE_MPI
  }
 
  // **********************************************************
  // End of Interface Methods
  // **********************************************************
 
  const HostGrid& getHostGrid() const { return hostgrid_; }
 
  HostGrid& getHostGrid() { return hostgrid_; }
 
  const InterfaceGrid& interfaceGrid() const { return *interfaceGrid_; }
 
  InterfaceGrid& interfaceGrid() { return *interfaceGrid_; }
 
  const auto& interfaceGridPtr() { return interfaceGrid_; }
 
  const ConnectedComponent& getConnectedComponent(const Entity& entity) const {
    const auto& it = createdEntityConnectedComponentMap_.find(
        this->globalIdSet().id(entity));
    assert(it->second < connectedComponents_.size());
    assert(it != createdEntityConnectedComponentMap_.end());
    assert(connectedComponents_.at(it->second).size() > 0);
    return connectedComponents_.at(it->second);
  }
 
  const RemeshingIndicator& indicator() const { return indicator_; }
 
  RemeshingIndicator& indicator() { return indicator_; }
 
  const auto& distance() const { return indicator_.distance(); }
 
  int sequence() const { return sequence_; }
 
  const PartitionHelper<GridImp>& partitionHelper() const {
    return partitionHelper_;
  }
 
 private:
  // count how much elements where marked
  mutable int coarsenMarked_;
  mutable int refineMarked_;
  mutable std::size_t componentCount_;
 
  std::unordered_map<IdType, ConnectedComponent> connectedComponents_;
 
  std::unordered_map<IdType, std::size_t> vanishingEntityConnectedComponentMap_;
  std::unordered_map<IdType, std::size_t> createdEntityConnectedComponentMap_;
 
  Communication<Comm> comm_;
  PartitionHelper<GridImp> partitionHelper_;
 
  std::unique_ptr<MMeshLeafIndexSet<const GridImp>> leafIndexSet_;
  std::unique_ptr<MMeshGlobalIdSet<const GridImp>> globalIdSet_;
  std::shared_ptr<InterfaceGrid> interfaceGrid_;
 
  std::vector<RefinementInsertionPoint> insert_;
  std::unordered_set<IdType> inserted_;
  std::vector<VertexHandle> remove_;
  std::unordered_set<IdType> removed_;
 
  HostGrid hostgrid_;
  BoundarySegments boundarySegments_, localBoundarySegments_;
  BoundaryIds boundaryIds_;
  InterfaceSegments interfaceSegments_;
  RemeshingIndicator indicator_;
 
  static const bool verbose_ = false;
  int sequence_ = 0;
 
 private:
  bool markElementsForInsertion_(const Edge& edge,
                                 std::size_t& componentNumber) {
    ElementOutput elements;
    getIncidentToEdge_(edge, elements);
 
    bool markAgain = getComponentNumber_(elements, componentNumber);
 
    // set componentNumber and mightVanish
    for (const auto& element : elements) {
      element->info().componentNumber = componentNumber;
      element->info().mightVanish = true;
    }
 
    return markAgain;
  }
 
  template <int d = dimension>
  std::enable_if_t<d == 2, void> getIncidentToEdge_(
      const Edge& edge, ElementOutput& elements) const {
    const auto& eh = edge.impl().hostEntity();
    elements.push_back(eh.first);
    elements.push_back(eh.first->neighbor(eh.second));
  }
 
  template <int d = dimension>
  std::enable_if_t<d == 3, void> getIncidentToEdge_(
      const Edge& edge, ElementOutput& elements) const {
    const auto& eh = edge.impl().hostEntity();
    auto cit = this->getHostGrid().incident_cells(eh);
    for (std::size_t i = 0; i < CGAL::circulator_size(cit); ++i, ++cit)
      elements.push_back(cit);
  }
 
  bool markElementForInsertion_(const Point& point,
                                std::size_t& componentNumber) {
    ElementOutput elements;
    elements.push_back(this->getHostGrid().locate(point));
 
    bool markAgain = getComponentNumber_(elements, componentNumber);
 
    // set componentNumber and mightVanish
    for (const auto& element : elements) {
      element->info().componentNumber = componentNumber;
      element->info().mightVanish = true;
    }
 
    return markAgain;
  }
 
  void markElementsAfterInsertion_(const HostGridEntity<dimension>& vh,
                                   const std::size_t componentId) {
    for (const auto& element : incidentElements(entity(vh))) {
      element.impl().hostEntity()->info().isNew = true;
      element.impl().hostEntity()->info().componentNumber = componentId + 1;
      const IdType id = this->globalIdSet().id(element);
      this->createdEntityConnectedComponentMap_.insert(
          std::make_pair(id, componentId));
    }
  }
 
  bool markElementsForRemoval_(const HostGridEntity<dimension>& vh,
                               std::size_t& componentNumber) {
    ElementOutput elements;
    for (const auto& element : incidentElements(entity(vh)))
      elements.push_back(element.impl().hostEntity());
 
    bool markAgain = getComponentNumber_(elements, componentNumber);
 
    // set componentNumber and mightVanish
    for (const auto& element : elements) {
      element->info().componentNumber = componentNumber;
      element->info().mightVanish = true;
    }
 
    return markAgain;
  }
 
  void markElementsAfterRemoval_(ElementOutput& elements,
                                 const std::size_t componentId) {
    // flag all elements in conflict as mightVanish
    for (const auto& element : elements) {
      element->info().isNew = true;
      element->info().componentNumber = componentId + 1;
 
      const auto id = this->globalIdSet().id(this->entity(element));
      this->createdEntityConnectedComponentMap_.insert(
          std::make_pair(id, componentId));
    }
  }
 
  bool getComponentNumber_(const ElementOutput& elements,
                           std::size_t& componentNumber) const {
    bool markAgain = false;
    componentNumber = 0;
 
    // search for a componentNumber
    for (const auto& element : elements)
      if (element->info().componentNumber > 0) {
        // check if we find different component numbers
        if (componentNumber != 0 &&
            element->info().componentNumber != componentNumber) {
          markAgain = true;
          componentNumber =
              std::min(element->info().componentNumber, componentNumber);
        } else
          componentNumber = element->info().componentNumber;
      }
 
    // if no componentNumber was found, create a new one
    if (componentNumber == 0) componentNumber = componentCount_++;
 
    return markAgain;
  }
 
};  // end Class MMesh
 
// Capabilites of MMesh
// --------------------
 
namespace Capabilities {
template <class HostGrid, int dim>
struct hasSingleGeometryType<MMesh<HostGrid, dim>> {
  static const bool v = true;
  static const unsigned int topologyId = Dune::GeometryType::simplex;
};
 
template <class HostGrid, int dim, int codim>
struct canCommunicate<MMesh<HostGrid, dim>, codim> {
  static const bool v = false;
};
 
template <class HostGrid, int dim>
struct canCommunicate<MMesh<HostGrid, dim>, 0> {
  static const bool v = true;
};
 
template <class HostGrid, int dim, int codim>
struct hasEntity<MMesh<HostGrid, dim>, codim> {
  static const bool v = (codim >= 0 && codim <= dim);
};
 
template <class HostGrid, int dim, int codim>
struct hasEntityIterator<MMesh<HostGrid, dim>, codim> {
  static const bool v = (codim >= 0 && codim <= dim);
};
 
template <class HostGrid, int dim>
struct isLevelwiseConforming<MMesh<HostGrid, dim>> {
  static const bool v = true;
};
 
template <class HostGrid, int dim>
struct isLeafwiseConforming<MMesh<HostGrid, dim>> {
  static const bool v = true;
};
 
template <class HostGrid, int dim>
struct hasBackupRestoreFacilities<MMesh<HostGrid, dim>> {
  static const bool v = false;
};
 
}  // end namespace Capabilities
 
}  // namespace Dune
 
template <int codim, int dim, class HostGrid>
std::ostream& operator<<(
    std::ostream& stream,
    const Dune::Entity<codim, dim, const Dune::MMesh<HostGrid, dim>,
                       Dune::MMeshEntity>& entity) {
  return stream << "MMeshEntity<codim=" << codim << ", dim=" << dim
                << ", center=(" << entity.geometry().center() << ")>";
}
 
#include "../interface/grid.hh"
#include "../misc/capabilities.hh"
#include "../misc/persistentcontainer.hh"
#include "dgfparser.hh"
#include "gmshgridfactory.hh"
#include "gmshreader.hh"
#include "gridfactory.hh"
#include "structuredgridfactory.hh"
 
#endif  // DUNE_MMESH_GRID_MMESH_HH