MeshDistributor.h 34.2 KB
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/******************************************************************************
 *
 * AMDiS - Adaptive multidimensional simulations
 *
 * Copyright (C) 2013 Dresden University of Technology. All Rights Reserved.
 * Web: https://fusionforge.zih.tu-dresden.de/projects/amdis
 *
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 * Authors:
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 * Simon Vey, Thomas Witkowski, Andreas Naumann, Simon Praetorius, et al.
 *
 * This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
 * WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
 *
 *
 * This file is part of AMDiS
 *
 * See also license.opensource.txt in the distribution.
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 *
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 ******************************************************************************/
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/** \file MeshDistributor.h */
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#ifndef AMDIS_MESHDISTRIBUTOR_H
#define AMDIS_MESHDISTRIBUTOR_H
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#include <mpi.h>
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#include "parallel/DofComm.h"
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#include "parallel/ElementObjectDatabase.h"
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#include "parallel/ParallelTypes.h"
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#include "parallel/MeshLevelData.h"
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#include "parallel/MeshPartitioner.h"
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#include "parallel/InteriorBoundary.h"
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#include "parallel/ParallelDofMapping.h"
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#include "parallel/PeriodicMap.h"
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#include "parallel/StdMpi.h"
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#include "AMDiS_fwd.h"
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#include "Containers.h"
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#include "Global.h"
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#include "ProblemTimeInterface.h"
#include "ProblemIterationInterface.h"
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#include "FiniteElemSpace.h"
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#include "Serializer.h"
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#include "BoundaryManager.h"
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#include <string>

#include "operations/functors.hpp"
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namespace AMDiS { namespace Parallel {
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  struct BoundaryDofInfo
  {
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    std::map<GeoIndex, DofContainerSet> geoDofs;
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  };

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  class MeshDistributor
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  {
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  private:
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    MeshDistributor();
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  public:
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    ~MeshDistributor();

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    /// Initialization of mesh distributor.
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    void initParallelization();
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    /// Clean up procedure for the mesh distributor and attached objects.
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    void exitParallelization();
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    /** \brief
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     * Register a parallel DOF mapping. This DOF mapping object will than
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     * automatically updated by the mesh distributer after mesh changes.
     *
     * \param[in]  dofMap   Parallel DOF mapping object.
     */
    void registerDofMap(ParallelDofMapping &dofMap);

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    /** \brief
     * Removes a registered DOF mapping from the mesh distributor.
     *
     * \param[in] dofMap   Parallel DOF mapping object to be removed.
     */
    void removeDofMap(ParallelDofMapping &dofMap);

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    /// Adds a DOFVector to the set of \ref interchangeVecs. Thus, this vector
    /// will be automatically interchanged between ranks when mesh is
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    /// repartitioned.
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    template< typename T >
    void addInterchangeVector(DOFVector<T> *vec) {}
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    void addInterchangeVector(DOFVector<double> *vec)
    {
      interchangeVectors.push_back(vec);
    }

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    /// Removes the pointer to DOFVector @param vec from the
    /// set of interchange vectors.
    template< typename T >
    void removeInterchangeVector(DOFVector<T> *vec) {}
    void removeInterchangeVector(DOFVector< double >* vec)
    {
      std::vector< DOFVector< double >* >::iterator it;
      it = std::find(interchangeVectors.begin(), interchangeVectors.end(), vec);
      if ( it != interchangeVectors.end())
        interchangeVectors.erase(it);
    }

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    /// Adds all DOFVectors of a SystemVector to \ref interchangeVecs.
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    void addInterchangeVector(SystemVector *vec);
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    /// The same as for DOFVectors
    void removeInterchangeVector(SystemVector* vec);
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    /** \brief
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     * This function checks if the mesh has changed on at least one rank. In
     * this case, the interior boundaries are adapted on all ranks such that
     * they fit together on all ranks. Furthermore the function
     * \ref updateLocalGlobalNumbering() is called to update the DOF numberings
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     * and mappings on all rank due to the new mesh structure.
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     *
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     * \param[in]  tryRepartition   If this parameter is true, repartitioning
     *                              may be done. This depends on several other
     *                              parameters. If the parameter is false, the
     *                              mesh is only checked and adapted but never
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     *                              repartitioned.
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     */
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    void checkMeshChange(bool tryRepartition = true);
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    /// Checks if is required to repartition the mesh. If this is the case, a new
    /// partition will be created and the mesh will be redistributed between the
    /// ranks.
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    bool repartitionMesh();
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    void getImbalanceFactor(double &imbalance,
			    int &minDofs,
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			    int &maxDofs,
			    int &sumDofs);

    double getImbalanceFactor();

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    /// Calculates the imbalancing factor and prints it to screen.
    void printImbalanceFactor();

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    /// Test, if the mesh consists of macro elements only. The mesh partitioning
    /// of the parallelization works for macro meshes only and would fail, if the
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    /// mesh is already refined in some way. Therefore, this function will exit
    /// the program if it finds a non macro element in the mesh.
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    void testForMacroMesh();
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    inline std::string getName()
    {
      return name;
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    }
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    inline Mesh* getMacroMesh()
    {
      return macroMesh;
    }
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    inline Mesh* getMesh(int i = 0)
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    {
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      return meshes[i];
    }
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    inline int getNumberOfMeshes()
    {
      return meshes.size();
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    }

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    /// Returns the periodic mapping handler, \ref periodicMap.
    inline PeriodicMap& getPeriodicMap()
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    {
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      return periodicMap;
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    }
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//     DofComm& getDofComm(int level)
//     {
//       return dofComm[level];
//     }
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    DofComm& getDofComm(Mesh* mesh, int level)
    {
      return dofComms[mesh][level];
    }
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    std::map<Mesh*, MultiLevelDofComm>& getDofComms()
    {
      return dofComms;
    }
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    InteriorBoundary& getIntBoundary(int level)
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    {
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      return intBoundary[level];
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    }
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    std::map<int, int>& getPartitionMap()
    {
      return partitionMap;
    }
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    inline long getLastMeshChangeIndex()
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    {
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      int overallMeshChangeIndex = 0;
      for(size_t i = 0; i < meshes.size(); i++) {
	overallMeshChangeIndex += lastMeshChangeIndexs[meshes[i]];
      }
      return overallMeshChangeIndex;
    }
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    inline long getLastMeshChangeIndex(Mesh* m)
    {
      return lastMeshChangeIndexs[m];
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    }
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    inline int getMpiRank()
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    {
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      return mpiRank;
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    }
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    inline int getMpiSize(int level)
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    {
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      return levelData.getMpiComm(level).Get_size();
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    }

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    inline MPI::Intracomm& getMpiComm(int level)
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    {
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      return levelData.getMpiComm(level);
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    }

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    inline bool isInitialized()
    {
      return initialized;
    }

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    // Writes all data of this object to an output stream.
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    void serialize(std::ostream &out);
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    // Reads the object data from an input stream.
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    void deserialize(std::istream &in);
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    /// Works quite similar to the function \ref synchVector, but instead the
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    /// values of subdomain vectors are combined along the boundaries, by a
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    /// binary functor.
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    // minorRank => majorRank
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    template<typename T, typename Operator>
    void synchVector(DOFVector<T> &vec, Operator op)
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    {
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      const FiniteElemSpace *fe = vec.getFeSpace();
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      MultiLevelDofComm& dofComm = dofComms[fe->getMesh()];
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      int nLevels = levelData.getNumberOfLevels();
      for (int level = nLevels - 1; level >= 0; level--) {
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	StdMpi<std::vector<T> > stdMpi(levelData.getMpiComm(level));
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	for (DofComm::Iterator it(dofComm[level].getRecvDofs(), fe);
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	     !it.end(); it.nextRank()) {
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	  std::vector<T> dofs;
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	  dofs.reserve(it.getDofs().size());
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	  for (; !it.endDofIter(); it.nextDof())
	    dofs.push_back(vec[it.getDofIndex()]);
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	  stdMpi.send(it.getRank(), dofs);
	}
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	for (DofComm::Iterator it(dofComm[level].getSendDofs(), fe);
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	     !it.end(); it.nextRank())
	  stdMpi.recv(it.getRank());
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	stdMpi.startCommunication();
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	for (DofComm::Iterator it(dofComm[level].getSendDofs(), fe);
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	     !it.end(); it.nextRank())
	  for (; !it.endDofIter(); it.nextDof())
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	    op(vec[it.getDofIndex()],
	       stdMpi.getRecvData(it.getRank())[it.getDofCounter()]);
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      }
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      synchVector(vec);
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    }
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    /** \brief
    * Synchronize \p vec using indicator vector \p additionalVecs, e.g. let
    * additionalVecs[0] be 1 on all dofs the value should be taken from
    my rank
    * and 0 elsewhere.
    */
    // op(std::vector<T>& out, std::vector<T> const& in)
    template<typename T, typename Operator>
    void synchMultiVector(DOFVector<T> &vec, std::vector<DOFVector<T>*> additionalVecs, Operator op)
    {
    // get FE space and check equal FE space
    const FiniteElemSpace *fe = vec.getFeSpace();
    MultiLevelDofComm& dofComm = dofComms[fe->getMesh()];
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    typedef typename std::vector<DOFVector<T>*>::iterator Iterator;

    int nLevels = levelData.getNumberOfLevels();
    for (int level = nLevels - 1; level >= 0; level--)
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    {
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        StdMpi < std::vector<std::vector<T> > >
        stdMpi(levelData.getMpiComm(level));

        for (DofComm::Iterator it(dofComm[level].getRecvDofs(), fe);
        !it.end(); it.nextRank())
        {
        std::vector<std::vector<T> > dofs;
        dofs.reserve(it.getDofs().size());
        for (; !it.endDofIter(); it.nextDof())
        {
        std::vector<T> values;
        values.reserve(additionalVecs.size() + 1);
        values.push_back( vec[it.getDofIndex()] );
        for (Iterator vecIt = additionalVecs.begin(); vecIt !=
    additionalVecs.end(); ++vecIt )
        values.push_back( (**vecIt)[it.getDofIndex()] );
        dofs.push_back( values );
        }
        stdMpi.send(it.getRank(), dofs);
        }
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        for (DofComm::Iterator it(dofComm[level].getSendDofs(), fe);
        !it.end(); it.nextRank())
        stdMpi.recv(it.getRank());
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        stdMpi.startCommunication();
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        for (DofComm::Iterator it(dofComm[level].getSendDofs(), fe);
        !it.end(); it.nextRank()) {
        for (; !it.endDofIter(); it.nextDof()) {
    std::vector<T> values;
    values.reserve(additionalVecs.size() + 1);
    values.push_back( vec[it.getDofIndex()] );
    for (Iterator vecIt = additionalVecs.begin(); vecIt !=
        additionalVecs.end(); ++vecIt )
    values.push_back( (**vecIt)[it.getDofIndex()] );
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    op(values, stdMpi.getRecvData(it.getRank())[it.getDofCounter()]);
    }
        }
    }
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    synchVector(vec);
    }
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    /** \brief
    * This function must be used if the values of a set of DOFVectors must be
    * synchronized over all ranks. That means, that each rank sends the
    * values of the DOFs, which are owned by the rank and lie on an interior
    * boundary, to all other ranks also having these DOFs.
    *
    * The synchronization direction is from major to minor rank. This means
    * that the value of the rank with the higher number sends its value
    * to the rank with the lower number.
    */
    // majorRank => minorRank
    template<typename T>
    void synchVector(std::vector<DOFVector<T>*> &vecs)
    {
      if (vecs.size() > 0)
      {
        // get FE space
        const FiniteElemSpace *fe = vecs[0]->getFeSpace();
        // TODO: check equal FE space
        // The lines below do not work!
        // for ( typename std::vector<DOFVector<T>*>::iterator vecIt = vecs.begin(); vecIt != vecs.end(); ++vecIt)
        //   TEST_EXIT( (*vecIt)->getFeSpace()->getBasisFcts()->getDegree() == fe->getBasisFcts()->getDegree() )("FE space of vectors to synch not equal!\n");

        MultiLevelDofComm& dofComm = dofComms[fe->getMesh()];
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        int nLevels = levelData.getNumberOfLevels();
        for (int level = nLevels - 1; level >= 0; level--)
        {
          StdMpi<std::vector<std::vector<T> > > stdMpi(levelData.getMpiComm(level));
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          for (DofComm::Iterator it(dofComm[level].getSendDofs(), fe); !it.end(); it.nextRank())
          {
            std::vector<std::vector<T> > dofs;
            dofs.reserve(it.getDofs().size());
            for (; !it.endDofIter(); it.nextDof())
            {
              std::vector<T> values;
              values.reserve(vecs.size());
              for (typename std::vector<DOFVector<T>*>::iterator vecIt = vecs.begin(); vecIt != vecs.end(); ++vecIt )
                values.push_back((**vecIt)[it.getDofIndex()]);
              dofs.push_back(values);
            }
            stdMpi.send(it.getRank(), dofs);
          }

          for (DofComm::Iterator it(dofComm[level].getRecvDofs(), fe); !it.end(); it.nextRank())
            stdMpi.recv(it.getRank());

          stdMpi.startCommunication();

          for (DofComm::Iterator it(dofComm[level].getRecvDofs(), fe); !it.end(); it.nextRank())
          {
            for (; !it.endDofIter(); it.nextDof())
            {
              std::vector<T> values = stdMpi.getRecvData(it.getRank())[it.getDofCounter()];
              typename std::vector<DOFVector<T>*>::iterator vecIt = vecs.begin();
              typename std::vector<T>::iterator valuesIt = values.begin();
              for (; vecIt != vecs.end(), valuesIt != values.end(); ++vecIt , ++valuesIt)
                (**vecIt)[it.getDofIndex()] = *valuesIt;
            }
          }
        }
      }
    }
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    /** \brief
    * Works quite similar to the function \ref synchVector with an operator/
    * assigner for the values on the subdomain boundaries of the DOFVector vec.
    * Additionally, the values stored in additionalVecs are synchronized in
    * the same way (direction (minor to major or major to minor rank)) as the
    * DOFs of the variable vec.
    */
    template<typename T, typename Operator>
    void synchVectorSameWay(DOFVector<T> &vec, std::vector<DOFVector<T>*> additionalVecs, Operator op)
    {
      // get FE space and check equal FE space
      const FiniteElemSpace *fe = vec.getFeSpace();
      // TODO: check equal FE space
      // The lines below do not work!
      // for ( typename std::vector<DOFVector<T>*>::iterator vecIt = additionalVecs.begin(); vecIt != additionalVecs.end(); ++vecIt)
      //   TEST_EXIT( (*vecIt)->getFeSpace()->getBasisFcts()->getDegree() == fe->getBasisFcts()->getDegree() )("FE space of vectors to synch not equal!\n");

      MultiLevelDofComm& dofComm = dofComms[fe->getMesh()];

      int nLevels = levelData.getNumberOfLevels();
      for (int level = nLevels - 1; level >= 0; level--)
      {
        StdMpi < std::vector<std::vector<T> > > stdMpi(levelData.getMpiComm(level));

        for (DofComm::Iterator it(dofComm[level].getRecvDofs(), fe); !it.end(); it.nextRank())
        {
          std::vector<std::vector<T> > dofs;
          dofs.reserve(it.getDofs().size());
          for (; !it.endDofIter(); it.nextDof())
          {
            std::vector<T> values;
            values.reserve(additionalVecs.size() + 1);
            values.push_back( vec[it.getDofIndex()] );
            for (typename std::vector<DOFVector<T>*>::iterator vecIt = additionalVecs.begin(); vecIt != additionalVecs.end(); ++vecIt )
              values.push_back( (**vecIt)[it.getDofIndex()] );
            dofs.push_back( values );
          }
          stdMpi.send(it.getRank(), dofs);
        }

        for (DofComm::Iterator it(dofComm[level].getSendDofs(), fe); !it.end(); it.nextRank())
          stdMpi.recv(it.getRank());

        stdMpi.startCommunication();

        for (DofComm::Iterator it(dofComm[level].getSendDofs(), fe); !it.end(); it.nextRank())
        {
          for (; !it.endDofIter(); it.nextDof())
          {
            DegreeOfFreedom idx = it.getDofIndex();
            std::vector<T> values = stdMpi.getRecvData(it.getRank())[it.getDofCounter()];

            T minorRankValue = vec[idx];
            T majorRankValue = values[0];
            op(vec[idx], values[0]);
            T synchValue = vec[idx];

            TEST_EXIT(additionalVecs.size() == values.size()-1)("The number of additional vectors and the received values do not match!\n");

            typename std::vector<DOFVector<T>*>::iterator vecIt = additionalVecs.begin();
            typename std::vector<T>::iterator valuesIt = values.begin();
            ++valuesIt; // exclude the first one since it belongs to the variable vec
            for (; vecIt != additionalVecs.end(), valuesIt != values.end(); ++vecIt , ++valuesIt)
              if (synchValue == majorRankValue)
                (**vecIt)[idx] = *valuesIt;
          }
        }
      }
      // call simple sync method
      std::vector<DOFVector<T>*> allDOFVectors;
      allDOFVectors.push_back(&vec);
      for ( int i = 0; i < additionalVecs.size(); ++i )
        allDOFVectors.push_back(additionalVecs[i]);
      synchVector(allDOFVectors);
    }
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    /** \brief
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     * This function must be used if the values of a DOFVector must be
     * synchronised over all ranks. That means, that each rank sends the
     * values of the DOFs, which are owned by the rank and lie on an interior
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     * boundary, to all other ranks also having these DOFs.
     *
     * This function must be used, for example, after the linear system is
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     * solved, or after the DOFVector is set by some user defined functions,
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     * e.g., initial solution functions.
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     */
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     // majorRank => minorRank
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    template<typename T>
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    void synchVector(DOFVector<T> &vec)
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    {
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      const FiniteElemSpace *fe = vec.getFeSpace();
      MultiLevelDofComm& dofComm = dofComms[fe->getMesh()];

      int nLevels = levelData.getNumberOfLevels();
      for (int level = nLevels - 1; level >= 0; level--) {
	StdMpi<std::vector<T> > stdMpi(levelData.getMpiComm(level));

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	for (DofComm::Iterator it(dofComm[level].getSendDofs(), fe);
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	     !it.end(); it.nextRank()) {

	  std::vector<T> dofs;
	  dofs.reserve(it.getDofs().size());
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	  for (; !it.endDofIter(); it.nextDof())
	    dofs.push_back(vec[it.getDofIndex()]);
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	  stdMpi.send(it.getRank(), dofs);
	}
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	for (DofComm::Iterator it(dofComm[level].getRecvDofs(), fe);
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	     !it.end(); it.nextRank())
	  stdMpi.recv(it.getRank());
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	stdMpi.startCommunication();
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	for (DofComm::Iterator it(dofComm[level].getRecvDofs(), fe);
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	     !it.end(); it.nextRank())
	  for (; !it.endDofIter(); it.nextDof())
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	    vec[it.getDofIndex()] =
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	      stdMpi.getRecvData(it.getRank())[it.getDofCounter()];
      }
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    }
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    /// Works in the same way as the function above defined for DOFVectors. Due
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    /// to performance, this function does not call \ref synchVector for each
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    /// DOFVector, but instead sends all values of all DOFVectors all at once.
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    void synchVector(SystemVector &vec);
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    /// Works quite similar to the function \ref synchVector, but instead the
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    /// values of subdomain vectors are add along the boundaries.
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    // minorRank => majorRank
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    template<typename T>
    void synchAddVector(DOFVector<T> &vec)
    {
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      const FiniteElemSpace *fe = vec.getFeSpace();
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      MultiLevelDofComm& dofComm = dofComms[fe->getMesh()];
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      int nLevels = levelData.getNumberOfLevels();
      for (int level = nLevels - 1; level >= 0; level--) {
	StdMpi<std::vector<T> > stdMpi(levelData.getMpiComm(level));

	for (DofComm::Iterator it(dofComm[level].getRecvDofs(), fe);
	     !it.end(); it.nextRank()) {
	  std::vector<T> dofs;
	  dofs.reserve(it.getDofs().size());
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	  for (; !it.endDofIter(); it.nextDof())
	    dofs.push_back(vec[it.getDofIndex()]);
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	  stdMpi.send(it.getRank(), dofs);
	}
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	for (DofComm::Iterator it(dofComm[level].getSendDofs(), fe);
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	     !it.end(); it.nextRank())
	  stdMpi.recv(it.getRank());
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	stdMpi.startCommunication();
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	for (DofComm::Iterator it(dofComm[level].getSendDofs(), fe);
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	     !it.end(); it.nextRank())
	  for (; !it.endDofIter(); it.nextDof())
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	    vec[it.getDofIndex()] +=
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	      stdMpi.getRecvData(it.getRank())[it.getDofCounter()];
      }

      synchVector(vec);
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    }

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    /// In 3D, a subdomain may not be a valid AMDiS mesh if it contains two
    /// parts which are only connected by an edge. In this case, the standard
    /// refinement algorithm does not work correctly, as two elements connected
    /// only on one edge are not neighours by definition. This functions checks
    /// for this situation and fix the problem. For this, the mesh is search for
    /// all edges connecting two elements that are otherwise not connected.
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    void fix3dMeshRefinement();

    /** \brief Is used only within \ref fix3dMeshRefinement.
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     *
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     * \param[in]  elems            Set of macro element indices.
     * \param[out] disconnectedEls  On output, this vector contains sets of
     *                              element indices. The union is equal to elems.
     *                              Each set contains all element indices, which
     *                              are reachable among each other by neighbour
     *                              relations. Elements within two different sets
     *                              cannot be reached via neigbourhood relation.
     */
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    void helpToFix(std::set<int> &elems,
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		   std::vector<std::set<int> > &disconnectedEls);
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    void setBoundaryDofRequirement(Flag flag)
    {
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      createBoundaryDofFlag |= flag;
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    }

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    BoundaryDofInfo& getBoundaryDofInfo(const FiniteElemSpace *feSpace,
					int level)
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    {
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      FUNCNAME("MeshDistributor::getBoundaryDofInfo()");

      TEST_EXIT_DBG(level < static_cast<int>(boundaryDofInfo.size()))
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	("Wrong level number: %d, whereas array size is %d!\n",
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	 level, boundaryDofInfo.size());

      return boundaryDofInfo[level][feSpace];
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    }

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    void getAllBoundaryDofs(const FiniteElemSpace *feSpace,
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			    int level,
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			    DofContainer& dofs);
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    ElementObjectDatabase& getElementObjectDb()
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    {
      return elObjDb;
    }
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    /// Adds a stationary problem to the global mesh distributor objects.
    static void addProblemStatGlobal(ProblemStatSeq *probStat);
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    MeshLevelData& getMeshLevelData()
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    {
      return levelData;
    }
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    /// Update dof communicators, boundary dof info and the parallel dof mappings.
    /// If it is called for all meshes, \ref updateLocalGlobalNumbering is automatically
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    /// called inside. If it is used for each mesh seperately, please don't forget to
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    /// add \ref updateLocalGlobalNumbering to update the global matrix index.
    void updateDofRelatedStruct();
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    void updateDofRelatedStruct(Mesh* mesh);
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    void updateLocalGlobalNumbering();
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    /// set variable \ref repartitioningAllowed
    void setRepartitioningAllowed(bool allowed)
    {
      repartitioningAllowed = allowed;
    }
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    void setElementWeights(std::map<int, double>& elWgts)
    {
      elemWeights = elWgts;
    }
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  protected:
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    /// Rebuild only part of the mesh domain, which is necessary
    void quickRepartition(Mesh* mesh);
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    /// Rebuild whole mesh domain
    void fullRepartition(Mesh* mesh);
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    /// Updates all registered parallel DOF mappings, see \ref dofMaps.
    void updateDofsToDofMapping(Mesh* mesh = NULL);

    /// Updates the DOF after the mesh has been changed, see \ref dofMaps.
    void updateDofsToDofMapping(ParallelDofMapping &dmap,
				    const FiniteElemSpace *feSpace);
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    /// Checks if repartition is needed.
    bool isRepartitionNecessary();
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    /// Creates an initial partitioning of the mesh.
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    void createInitialPartitioning();

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    /// Set for each element on the partitioning level the number of
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    /// leaf elements.
    void setInitialElementWeights();
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    /// Calculates \ref elemWeights with the gloabl max weight and
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    /// global sum of weight.
    void calculateElemWeights();
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    ///
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    void addProblemStat(ProblemStatSeq *probStat);

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    /// Determines the interior boundaries, i.e. boundaries between ranks, and
    /// stores all information about them in \ref interiorBoundary.
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    void createInteriorBoundary(bool firstCall);
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    ///
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    void createBoundaryDofs(Mesh* mesh = NULL);
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    /// Removes all macro elements from the mesh that are not part of ranks
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    /// partition.
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    void removeMacroElements();

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    /// Calls \ref createPeriodicMap(feSpace) for all FE spaces that are
    /// handled by the mesh distributor.
    void createPeriodicMap();

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    /// Creates, for a specific FE space, to all DOFs in rank's partition that
    /// are on a periodic boundary the mapping from dof index to the other
    /// periodic dof indices. This information is stored in \ref periodicDofMap.
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    void createPeriodicMap(const FiniteElemSpace *feSpace);
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    /// This function is called only once during the initialization when the
    /// whole macro mesh is available on all cores. It copies the pointers of all
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    /// macro elements to \ref allMacroElements and stores all neighbour
    /// information based on macro element indices (and not pointer based) in
    /// \ref macroElementNeighbours. These information are then used to
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    /// reconstruct macro elements during mesh redistribution.
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    void createMacroElementInfo();

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    void updateMacroElementInfo();

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    /** \brief
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     * Checks for all given interior boundaries if the elements fit together on
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     * both sides of the boundaries. If this is not the case, the mesh is
     * adapted. Because refinement of a certain element may forces the
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     * refinement of other elements, it is not guaranteed that all rank's meshes
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     * fit together after this function terminates. Hence, it must be called
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     * until a stable mesh refinement is reached.
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     *
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     * \param[in] allBound   Defines a map from rank to interior boundaries
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     *                       which should be checked.
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     * \param[in] mesh       The mesh the interior boundaries belong to.
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     *
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     * \return    If the mesh has  been changed by this function, it returns
     *            true. Otherwise, it returns false, i.e., the given interior
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     *            boundaries fit together on both sides.
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     */
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    bool checkAndAdaptBoundary(RankToBoundMap &allBound, Mesh* mesh);
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    /// Removes all periodic boundary condition information from all matrices and
    /// vectors of all stationary problems and from the mesh itself.
    void removePeriodicBoundaryConditions();

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    /// Removes all periodic boundary condition information from all matrices and
    /// vector of a given stationary problem.
    void removePeriodicBoundaryConditions(ProblemStatSeq *probStat);

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    // Removes all periodic boundaries from a given boundary map.
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    void removePeriodicBoundaryConditions(BoundaryIndexMap& boundaryMap);
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    void createMeshLevelStructure();

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    /// Writes a vector of dof pointers to an output stream.
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    void serialize(std::ostream &out, DofContainer &data);
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    /// Writes a \ref RankToDofContainer to an output stream.
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    void serialize(std::ostream &out,
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		   std::map<int, std::map<const FiniteElemSpace*, DofContainer> > &data);
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    /// Reads a vector of dof pointers from an input stream.
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    void deserialize(std::istream &in, DofContainer &data,
		     std::map<int, const DegreeOfFreedom*> &dofIndexMap);
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    /// Reads a \ref RankToDofContainer from an input stream.
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    void deserialize(std::istream &in,
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		     std::map<int, std::map<const FiniteElemSpace*, DofContainer> > &data,
		     std::map<const FiniteElemSpace*, std::map<int, const DegreeOfFreedom*> > &dofIndexMap);
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    /// Writes a mapping from dof pointers to some values to an output stream.
    template<typename T>
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    void serialize(std::ostream &out, std::map<const DegreeOfFreedom*, T> &data)
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    {
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      FUNCNAME("ParallelDomainBase::serialize()");

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      int mapSize = data.size();
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      SerUtil::serialize(out, mapSize);
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      for (typename std::map<const DegreeOfFreedom*, T>::iterator it = data.begin();
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	   it != data.end(); ++it) {
	int v1 = (*(it->first));
	T v2 = it->second;
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	SerUtil::serialize(out, v1);
	SerUtil::serialize(out, v2);
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      }
    }

    /// Reads a mapping from dof pointer to some values from an input stream.
    template<typename T>
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    void deserialize(std::istream &in, std::map<const DegreeOfFreedom*, T> &data,
		     std::map<int, const DegreeOfFreedom*> &dofIndexMap)
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    {
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      FUNCNAME("ParallelDomainBase::deserialize()");

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      int mapSize = 0;
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      SerUtil::deserialize(in, mapSize);
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      for (int i = 0; i < mapSize; i++) {
	int v1 = 0;
	T v2;
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	SerUtil::deserialize(in, v1);
	SerUtil::deserialize(in, v2);
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	TEST_EXIT_DBG(dofIndexMap.count(v1) != 0)
	  ("Cannot find DOF %d in map!\n", v1);
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	data[dofIndexMap[v1]] = v2;
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      }
    }
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  protected:
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    /// List of all stationary problems that are managed by this mesh
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    /// distributor.
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    std::vector<ProblemStatSeq*> problemStat;
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    /// If true, the mesh distributor is already initialized;
    bool initialized;

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    /// The rank of the current process.
    int mpiRank;

    /// Name of the problem (as used in the init files)
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    std::string name;
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    /// Set of all different FE spaces.
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    std::vector<const FiniteElemSpace*> feSpaces;
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    /// Always equal to meshes[0] which is used as macro
    /// mesh. For example, passed to \ref meshPartitioner.
    Mesh *macroMesh;
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    /// Meshes to be managed for parallelization. Currently only two meshes
    /// are allowed since multi mesh method is limited to two meshes.
    std::vector<Mesh*> meshes;
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    /// Stores the map of meshes and the corresponding FE spaces defined on them
    MeshToFeSpaces meshToFeSpaces;
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    /// A refinement manager that should be used on the mesh. It is used to
    /// refine elements at interior boundaries in order to fit together with
    /// elements on the other side of the interior boundary.
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    RefinementManager *refineManager;

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    /// Pointer to a mesh partitioner that is used to partition the mesh to
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    /// the ranks.
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    MeshPartitioner *partitioner;
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    /// Pointer to a mesh partitioner that is used for the very first
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    /// partitioning of the mesh. In most cases, this pointer points to the
    /// same object as \ref partitioner, but this must not be the case in
    /// general.
    MeshPartitioner *initialPartitioner;

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    /// Weights for the elements, i.e., the number of leaf elements within
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    /// this element.
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    std::map<int, double> elemWeights;
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    /// Stores to every macro element index the number of the rank that owns this
    /// macro element.
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    std::map<int, int> partitionMap;
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    /// Database to store and query all sub-objects of all elements of the
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    /// macro mesh.
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    ElementObjectDatabase elObjDb;
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    /// Defines the interior boundaries of the domain that result from
    /// partitioning the whole mesh.
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    MultiLevelInteriorBoundary intBoundary;
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    /// Dof communicator objects for each mesh
    std::map<Mesh*, MultiLevelDofComm> dofComms;
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    PeriodicMap periodicMap;
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    /// This set of values must be interchanged between ranks when the mesh is
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    /// repartitioned.
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    std::vector<DOFVector<double>*> interchangeVectors;
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    /// If the problem definition has been read from a serialization file, this
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    /// variable is true, otherwise it is false. This variable is used to stop the
    /// initialization function, if the problem definition has already been read
    /// from a serialization file.