ParallelDomainBase.cc 65.7 KB
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#include <algorithm>
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#include <iostream>
#include <fstream>
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#include <boost/lexical_cast.hpp>
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#include "parallel/ParallelDomainBase.h"
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#include "parallel/ParallelDomainDbg.h"
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#include "parallel/StdMpi.h"
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#include "ParMetisPartitioner.h"
#include "Mesh.h"
#include "Traverse.h"
#include "ElInfo.h"
#include "Element.h"
#include "MacroElement.h"
#include "PartitionElementData.h"
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#include "DOFMatrix.h"
#include "DOFVector.h"
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#include "SystemVector.h"
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#include "VtkWriter.h"
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#include "ElementDofIterator.h"
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#include "ProblemStatBase.h"
#include "StandardProblemIteration.h"
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#include "ElementFileWriter.h"
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#include "VertexVector.h"
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#include "MeshStructure.h"
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#include "ProblemVec.h"
#include "ProblemInstat.h"
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#include "Debug.h"
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namespace AMDiS {

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  using boost::lexical_cast;

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  inline bool cmpDofsByValue(const DegreeOfFreedom* dof1, const DegreeOfFreedom* dof2)
  {
    return (*dof1 < *dof2);
  }

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  ParallelDomainBase::ParallelDomainBase(ProblemVec *problemStat,
					 ProblemInstatVec *problemInstat)
    : iterationIF(problemStat),
      timeIF(problemInstat),
      probStat(problemStat),
      name(problemStat->getName()),
      feSpace(problemStat->getFESpace(0)),
      mesh(feSpace->getMesh()),
      refineManager(problemStat->getRefinementManager(0)),
      info(problemStat->getInfo()),
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      initialPartitionMesh(true),
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      nRankDofs(0),
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      rstart(0),
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      nComponents(problemStat->getNumComponents()),
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      deserialized(false),
      lastMeshChangeIndex(0)
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  {
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    FUNCNAME("ParallelDomainBase::ParalleDomainBase()");

    TEST_EXIT(mesh->getNumberOfDOFAdmin() == 1)
      ("Only meshes with one DOFAdmin are supported!\n");
    TEST_EXIT(mesh->getDOFAdmin(0).getNumberOfPreDOFs(0) == 0)
      ("Wrong pre dof number for DOFAdmin!\n");

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    mpiRank = MPI::COMM_WORLD.Get_rank();
    mpiSize = MPI::COMM_WORLD.Get_size();
    mpiComm = MPI::COMM_WORLD;
    partitioner = new ParMetisPartitioner(mesh, &mpiComm);
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    // Test if all fe spaces are equal. Yet, different fe spaces are not supported for
    // domain parallelization.
    const FiniteElemSpace *fe = probStat->getFESpace(0);
    for (int i = 0; i < nComponents; i++)
      TEST_EXIT(fe == probStat->getFESpace(i))
	("Parallelization does not supported different FE spaces!\n");

    // Create parallel serialization file writer, if needed.
    int writeSerialization = 0;
    GET_PARAMETER(0, name + "->output->write serialization", "%d", &writeSerialization);
    if (writeSerialization)
      probStat->getFileWriterList().push_back(new Serializer<ParallelDomainBase>(this));

    int readSerialization = 0;
    GET_PARAMETER(0, name + "->input->read serialization", "%d", &readSerialization);
    if (readSerialization) {
      std::string filename = "";
      GET_PARAMETER(0, name + "->input->serialization filename", &filename);
      filename += ".p" + lexical_cast<std::string>(mpiRank);
      MSG("Start serialization with %s\n", filename.c_str());
      std::ifstream in(filename.c_str());
      deserialize(in);
      in.close();
    }
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  }

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  void ParallelDomainBase::initParallelization(AdaptInfo *adaptInfo)
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  {
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    FUNCNAME("ParallelDomainBase::initParallelization()");

    TEST_EXIT(mpiSize > 1)
      ("Parallelization does not work with only one process!\n");

    // If the problem has been already read from a file, we do not need to do anything.
    if (deserialized)
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      return;

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    // Test, if the mesh is the macro mesh only! Paritioning of the mesh is supported
    // only for macro meshes, so it will not work yet if the mesh is already refined
    // in some way.
    testForMacroMesh();

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    // create an initial partitioning of the mesh
    partitioner->createPartitionData();
    // set the element weights, which are 1 at the very first begin
    setElemWeights(adaptInfo);
    // and now partition the mesh
    partitionMesh(adaptInfo);   

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#if (DEBUG != 0)
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    debug::ElementIdxToDofs elMap;
    debug::createSortedDofs(mesh, elMap);
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    if (mpiRank == 0) {
      int writePartMesh = 1;
      GET_PARAMETER(0, "dbg->write part mesh", "%d", &writePartMesh);
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      if (writePartMesh > 0)
	writePartitioningMesh("part.vtu");
      else 
	MSG("Skip write part mesh!\n");
    }
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#endif
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    // === Create interior boundary information. ===
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    createInteriorBoundaryInfo();
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    // === Create new global and local DOF numbering. ===

    createLocalGlobalNumbering();

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    // === Remove all macro elements that are not part of the rank partition. ===

    removeMacroElements();

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    // === Reset all DOFAdmins of the mesh. ===

    updateDofAdmins();

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    // === If in debug mode, make some tests. ===

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#if (DEBUG != 0)
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    MSG("AMDiS runs in debug mode, so make some test ...\n");
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    debug::testSortedDofs(mesh, elMap);
    ParallelDomainDbg::testInteriorBoundary(*this);
    ParallelDomainDbg::testCommonDofs(*this, true);
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    MSG("Debug mode tests finished!\n");
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    debug::writeMesh(feSpace, -1, "macromesh");   
#endif
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    // === Create periodic dof mapping, if there are periodic boundaries. ===

    createPeriodicMap();
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    // === Global refinements. ===
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    int globalRefinement = 0;
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    GET_PARAMETER(0, mesh->getName() + "->global refinements", "%d", &globalRefinement);
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    if (globalRefinement > 0) {
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      refineManager->globalRefine(mesh, globalRefinement);
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#if (DEBUG != 0)
    debug::writeMesh(feSpace, -1, "grmesh");
#endif

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      updateLocalGlobalNumbering();
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      // === Update periodic mapping, if there are periodic boundaries. ===
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      createPeriodicMap();
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    }
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    /// === Set DOF rank information to all matrices and vectors. ===

    for (int i = 0; i < nComponents; i++) {
      for (int j = 0; j < nComponents; j++)
 	if (probStat->getSystemMatrix(i, j))
 	  probStat->getSystemMatrix(i, j)->setRankDofs(isRankDof);      

      TEST_EXIT_DBG(probStat->getRHS()->getDOFVector(i))("No rhs vector!\n");
      TEST_EXIT_DBG(probStat->getSolution()->getDOFVector(i))("No solution vector!\n");

      probStat->getRHS()->getDOFVector(i)->setRankDofs(isRankDof);
      probStat->getSolution()->getDOFVector(i)->setRankDofs(isRankDof);
    }

    // === Remove periodic boundary conditions in sequential problem definition. ===

    // Remove periodic boundaries in boundary manager on matrices and vectors.
    for (int i = 0; i < nComponents; i++) {
      for (int j = 0; j < nComponents; j++) {
	DOFMatrix* mat = probStat->getSystemMatrix(i, j);
 	if (mat && mat->getBoundaryManager())
	  removeBoundaryCondition(const_cast<BoundaryIndexMap&>(mat->getBoundaryManager()->getBoundaryConditionMap()));
      }

      if (probStat->getSolution()->getDOFVector(i)->getBoundaryManager())
	removeBoundaryCondition(const_cast<BoundaryIndexMap&>(probStat->getSolution()->getDOFVector(i)->getBoundaryManager()->getBoundaryConditionMap()));

      if (probStat->getRHS()->getDOFVector(i)->getBoundaryManager())
	removeBoundaryCondition(const_cast<BoundaryIndexMap&>(probStat->getRHS()->getDOFVector(i)->getBoundaryManager()->getBoundaryConditionMap()));
    }

    // Remove periodic boundaries on elements in mesh.
    TraverseStack stack;
    ElInfo *elInfo = stack.traverseFirst(mesh,  -1, Mesh::CALL_EVERY_EL_PREORDER);
    while (elInfo) {
      elInfo->getElement()->deleteElementData(PERIODIC);
      elInfo = stack.traverseNext(elInfo);
    }    
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  }

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  void ParallelDomainBase::exitParallelization(AdaptInfo *adaptInfo)
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  {}
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  void ParallelDomainBase::updateDofAdmins()
  {
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    FUNCNAME("ParallelDomainBase::updateDofAdmins()");

    for (int i = 0; i < mesh->getNumberOfDOFAdmin(); i++) {
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      DOFAdmin& admin = const_cast<DOFAdmin&>(mesh->getDOFAdmin(i));
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      // There must be always more allocated DOFs than used DOFs in DOFAdmin. Otherwise,
      // it is not possible to define a first DOF hole.
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      if (static_cast<unsigned int>(admin.getSize()) == mapLocalGlobalDofs.size())
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	admin.enlargeDOFLists();
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      for (int j = 0; j < admin.getSize(); j++)
	admin.setDOFFree(j, true);
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      for (unsigned int j = 0; j < mapLocalGlobalDofs.size(); j++)
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 	admin.setDOFFree(j, false);

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      admin.setUsedSize(mapLocalGlobalDofs.size());
      admin.setUsedCount(mapLocalGlobalDofs.size());
      admin.setFirstHole(mapLocalGlobalDofs.size());
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    }
  }

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  void ParallelDomainBase::testForMacroMesh()
  {
    FUNCNAME("ParallelDomainBase::testForMacroMesh()");

    int nMacroElements = 0;

    TraverseStack stack;
    ElInfo *elInfo = stack.traverseFirst(mesh, -1, Mesh::CALL_LEAF_EL);
    while (elInfo) {
      TEST_EXIT(elInfo->getLevel() == 0)
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	("Mesh is already refined! This does not work with parallelization!\n");
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      nMacroElements++;

      elInfo = stack.traverseNext(elInfo);
    }

    TEST_EXIT(nMacroElements >= mpiSize)
      ("The mesh has less macro elements than number of mpi processes!\n");
  }

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  void ParallelDomainBase::synchVector(DOFVector<double> &vec)
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  {
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    StdMpi<std::vector<double> > stdMpi(mpiComm);
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    for (RankToDofContainer::iterator sendIt = sendDofs.begin();
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	 sendIt != sendDofs.end(); ++sendIt) {
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      std::vector<double> dofs;
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      int nSendDofs = sendIt->second.size();
      dofs.reserve(nSendDofs);
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      for (int i = 0; i < nSendDofs; i++)
	dofs.push_back(vec[*((sendIt->second)[i])]);
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      stdMpi.send(sendIt->first, dofs);
    }

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    for (RankToDofContainer::iterator recvIt = recvDofs.begin();
	 recvIt != recvDofs.end(); ++recvIt)
      stdMpi.recv(recvIt->first, recvIt->second.size());
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    stdMpi.startCommunication<double>(MPI_DOUBLE);
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    for (RankToDofContainer::iterator recvIt = recvDofs.begin();
	 recvIt != recvDofs.end(); ++recvIt)
      for (unsigned int i = 0; i < recvIt->second.size(); i++)
	vec[*(recvIt->second)[i]] = stdMpi.getRecvData(recvIt->first)[i];
  }
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  void ParallelDomainBase::synchVector(SystemVector &vec)
  {
    StdMpi<std::vector<double> > stdMpi(mpiComm);

    for (RankToDofContainer::iterator sendIt = sendDofs.begin();
	 sendIt != sendDofs.end(); ++sendIt) {
      std::vector<double> dofs;
      int nSendDofs = sendIt->second.size();
      dofs.reserve(nComponents * nSendDofs);
      
      for (int i = 0; i < nComponents; i++) {
	DOFVector<double> *dofvec = vec.getDOFVector(i);
	for (int j = 0; j < nSendDofs; j++)
	  dofs.push_back((*dofvec)[*((sendIt->second)[j])]);
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      }

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      stdMpi.send(sendIt->first, dofs);
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    }

    for (RankToDofContainer::iterator recvIt = recvDofs.begin();
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	 recvIt != recvDofs.end(); ++recvIt)
      stdMpi.recv(recvIt->first, recvIt->second.size() * nComponents);
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    stdMpi.startCommunication<double>(MPI_DOUBLE);
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    for (RankToDofContainer::iterator recvIt = recvDofs.begin();
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	 recvIt != recvDofs.end(); ++recvIt) {
      int nRecvDofs = recvIt->second.size();
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      int counter = 0;
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      for (int i = 0; i < nComponents; i++) {
	DOFVector<double> *dofvec = vec.getDOFVector(i);
 	for (int j = 0; j < nRecvDofs; j++)
	  (*dofvec)[*(recvIt->second)[j]] = 
	    stdMpi.getRecvData(recvIt->first)[counter++];
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      }
    }
  }

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  void ParallelDomainBase::removeBoundaryCondition(BoundaryIndexMap& boundaryMap)
  {
    BoundaryIndexMap::iterator it = boundaryMap.begin();
    while (it != boundaryMap.end()) {
      if (it->second->isPeriodic())
	boundaryMap.erase(it++);
      else
	++it;      
    }    
  }


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  void ParallelDomainBase::checkMeshChange()
  {
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    FUNCNAME("ParallelDomainBase::checkMeshChange()");

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    int dim = mesh->getDim();

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    // === If mesh has not been changed on all ranks, return. ===

    int recvAllValues = 0;
    int sendValue = static_cast<int>(mesh->getChangeIndex() != lastMeshChangeIndex);
    mpiComm.Allreduce(&sendValue, &recvAllValues, 1, MPI_INT, MPI_SUM);
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    if (recvAllValues == 0)
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      return;

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    // === At least one rank mesh has been changed, so the boundaries must be ===
    // === adapted to the new mesh structure.                                 ===
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    clock_t first = clock();
    
    do {
      // To check the interior boundaries, the ownership of the boundaries is not 
      // important. Therefore, we add all boundaries to one boundary container.
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      RankToBoundMap allBound;
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      for (InteriorBoundary::iterator it(myIntBoundary); !it.end(); ++it)
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	if (it->rankObj.subObj == INDEX_OF_DIM(dim - 1, dim))
	  allBound[it.getRank()].push_back(*it);
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      for (InteriorBoundary::iterator it(otherIntBoundary); !it.end(); ++it)
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	if (it->rankObj.subObj == INDEX_OF_DIM(dim - 1, dim))
	  allBound[it.getRank()].push_back(*it);
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      // === Check the boundaries and adapt mesh if necessary. ===
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      bool meshChanged = checkAndAdaptBoundary(allBound);

      // === Check on all ranks if at least one rank's mesh has changed. ===

      int sendValue = static_cast<int>(!meshChanged);
      recvAllValues = 0;
      mpiComm.Allreduce(&sendValue, &recvAllValues, 1, MPI_INT, MPI_SUM);
    } while (recvAllValues != 0);
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#if (DEBUG != 0)
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    debug::writeMesh(feSpace, -1, "mesh");
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#endif

    INFO(info, 8)("Parallel mesh adaption needed %.5f seconds\n", 
		  TIME_USED(first, clock()));

    // === Because the mesh has been changed, update the DOF numbering and mappings. ===
   
    updateLocalGlobalNumbering();
  }

  
  bool ParallelDomainBase::checkAndAdaptBoundary(RankToBoundMap &allBound)
  {
    FUNCNAME("ParallelDomainBase::checkAndAdaptBoundary()");

    // === Create mesh structure codes for all ranks boundary elements. ===
       
    std::map<int, MeshCodeVec> sendCodes;
   
    for (RankToBoundMap::iterator it = allBound.begin(); it != allBound.end(); ++it) {
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      for (std::vector<AtomicBoundary>::iterator boundIt = it->second.begin();
	   boundIt != it->second.end(); ++boundIt) {
	MeshStructure elCode;
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	elCode.init(boundIt->rankObj);
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	sendCodes[it->first].push_back(elCode);
      }
    }

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    StdMpi<MeshCodeVec> stdMpi(mpiComm, true);
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    stdMpi.send(sendCodes);
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    stdMpi.recv(allBound);
    stdMpi.startCommunication<unsigned long int>(MPI_UNSIGNED_LONG);
 
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    // === Compare received mesh structure codes. ===
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    bool meshFitTogether = true;

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    for (RankToBoundMap::iterator it = allBound.begin(); it != allBound.end(); ++it) {
      
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      MeshCodeVec &recvCodes = stdMpi.getRecvData()[it->first];
      int i = 0;
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      for (std::vector<AtomicBoundary>::iterator boundIt = it->second.begin();
	   boundIt != it->second.end(); ++boundIt) {
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	MeshStructure elCode;	
	elCode.init(boundIt->rankObj);
	
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	if (elCode.getCode() != recvCodes[i].getCode()) {
	  TEST_EXIT_DBG(refineManager)("Refinement manager is not set correctly!\n");
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	  bool b = fitElementToMeshCode(recvCodes[i], 
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					boundIt->rankObj.el,
					boundIt->rankObj.ithObj, 
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					boundIt->rankObj.elType);  
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	  if (b)
	    meshFitTogether = false;
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	}
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	i++;
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      }
    }

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    return meshFitTogether;
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  }
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  bool ParallelDomainBase::fitElementToMeshCode(MeshStructure &code, 
						Element *el, 
						int ithSide, 
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						int elType)
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  {
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    FUNCNAME("ParallelDomainBase::fitElementToMeshCode()");
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    if (code.empty())
      return false;
    
    int s1 = el->getSideOfChild(0, ithSide, elType);
    int s2 = el->getSideOfChild(1, ithSide, elType);

    TEST_EXIT_DBG(s1 != -1 || s2 != -1)("This should not happen!\n");

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    bool meshChanged = false;
    ElInfo *elInfo = el->getMesh()->createNewElInfo();    
    el->getMesh()->fillElInfo(elInfo, el, Mesh::FILL_NEIGH | Mesh::FILL_BOUND);

    if (s1 != -1 && s2 != -1) {
      meshChanged = fitElementToMeshCode2(code, el, elInfo, ithSide, elType);
      delete elInfo;
      return meshChanged;
    }
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    if (el->isLeaf()) {
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      if (code.getNumElements() == 1 && code.isLeafElement()) {
	delete elInfo;
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	return false;
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      }
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      el->setMark(1);
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      refineManager->refineFunction(elInfo);
      meshChanged = true;
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    }
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    ElInfo *childElInfo = el->getMesh()->createNewElInfo();

    if (s1 != -1) {
      childElInfo->fillElInfo(0, elInfo);
      meshChanged |= fitElementToMeshCode2(code, el->getFirstChild(), childElInfo, 
					   s1, el->getChildType(elType));
    } else {
      childElInfo->fillElInfo(1, elInfo);
      meshChanged |= fitElementToMeshCode2(code, el->getSecondChild(), childElInfo, 
					   s2, el->getChildType(elType));
    }

    delete childElInfo;
    delete elInfo;

    return meshChanged;
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  }

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  bool ParallelDomainBase::fitElementToMeshCode2(MeshStructure &code, 
						 Element *el, 
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						 ElInfo *elInfo,
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						 int ithSide, 
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						 int elType)
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  {
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    FUNCNAME("ParallelDomainBase::fitElementToMeshCode2()");

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    if (code.isLeafElement())
      return false;

    bool value = false;

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    TEST_EXIT_DBG(el != NULL)("This should not happen!\n");
    TEST_EXIT_DBG(elInfo != NULL)("This should not happen!\n");

    if (el->isLeaf()) {     
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      el->setMark(1);
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      refineManager->refineFunction(elInfo);
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      value = true;
    }

    int s1 = el->getSideOfChild(0, ithSide, elType);
    int s2 = el->getSideOfChild(1, ithSide, elType);
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    ElInfo *childElInfo = el->getMesh()->createNewElInfo();
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    if (s1 != -1) {
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      childElInfo->fillElInfo(0, elInfo);
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      code.nextElement();
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      value |= fitElementToMeshCode2(code, el->getFirstChild(), childElInfo, 
				     s1, el->getChildType(elType));
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    }  

    if (s2 != -1) {
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      childElInfo->fillElInfo(1, elInfo);
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      code.nextElement();	
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      value |= fitElementToMeshCode2(code, el->getSecondChild(), childElInfo,
				     s2, el->getChildType(elType));
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    }

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    delete childElInfo;

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    return value;
  }

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  void ParallelDomainBase::serialize(std::ostream &out, DofContainer &data)
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  {    
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    int vecSize = data.size();
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    SerUtil::serialize(out, vecSize);
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    for (int i = 0; i < vecSize; i++) {
      int dofIndex = (*data[i]);
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      SerUtil::serialize(out, dofIndex);
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    }
  }


  void ParallelDomainBase::deserialize(std::istream &in, DofContainer &data,
				       std::map<int, const DegreeOfFreedom*> &dofMap)
  {
    FUNCNAME("ParallelDomainBase::deserialize()");

    int vecSize = 0;
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    SerUtil::deserialize(in, vecSize);
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    data.resize(vecSize);
    for (int i = 0; i < vecSize; i++) {
      int dofIndex = 0;
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      SerUtil::deserialize(in, dofIndex);
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      TEST_EXIT_DBG(dofMap.count(dofIndex) != 0)
	("Dof index could not be deserialized correctly!\n");

      data[i] = dofMap[dofIndex];
    }
  }


  void ParallelDomainBase::serialize(std::ostream &out, RankToDofContainer &data)
  {
    int mapSize = data.size();
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    SerUtil::serialize(out, mapSize);
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    for (RankToDofContainer::iterator it = data.begin(); it != data.end(); ++it) {
      int rank = it->first;
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      SerUtil::serialize(out, rank);
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      serialize(out, it->second);
    }
  }

  
  void ParallelDomainBase::deserialize(std::istream &in, RankToDofContainer &data,
				       std::map<int, const DegreeOfFreedom*> &dofMap)
  {
    int mapSize = 0;
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    SerUtil::deserialize(in, mapSize);
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    for (int i = 0; i < mapSize; i++) {
      int rank = 0;
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      SerUtil::deserialize(in, rank);
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      deserialize(in, data[rank], dofMap);      
    }
  }

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  double ParallelDomainBase::setElemWeights(AdaptInfo *adaptInfo) 
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  {
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    FUNCNAME("ParallelDomainBase::setElemWeights()");
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    double localWeightSum = 0.0;
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    elemWeights.clear();
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    std::string filename = "";
    GET_PARAMETER(0, mesh->getName() + "->macro weights", &filename);
    if (filename != "") {
      MSG("Read macro weights from %s\n", filename.c_str());

      std::ifstream infile;
      infile.open(filename.c_str(), std::ifstream::in);
      while (!infile.eof()) {
	int elNum, elWeight;
	infile >> elNum;
	if (infile.eof())
	  break;
	infile >> elWeight;
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	elemWeights[elNum] = elWeight;
	localWeightSum += elWeight;
      }
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      infile.close();
    } else {
           
      TraverseStack stack;
      ElInfo *elInfo = stack.traverseFirst(mesh, -1, Mesh::CALL_EVERY_EL_PREORDER);
      while (elInfo) {
	Element *element = elInfo->getElement();
	
	// get partition data
	PartitionElementData *partitionData = dynamic_cast<PartitionElementData*>
	  (element->getElementData(PARTITION_ED));
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	if (partitionData && partitionData->getPartitionStatus() == IN) {
	  int elNum = -1;
	  if (partitionData->getLevel() == 0)
	    elNum = element->getIndex();
	  
	  TEST_EXIT_DBG(elNum != -1)("invalid element number\n");
	  if (element->isLeaf()) {
	    elemWeights[elNum] += 1.0;
	    localWeightSum += 1.0;
	  }
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	}
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	elInfo = stack.traverseNext(elInfo);
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      }
    }

    return localWeightSum;
  }

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  void ParallelDomainBase::partitionMesh(AdaptInfo *adaptInfo)
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  {
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    FUNCNAME("ParallelDomainBase::partitionMesh()");

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    if (initialPartitionMesh) {
      initialPartitionMesh = false;
      partitioner->fillCoarsePartitionVec(&oldPartitionVec);
      partitioner->partition(&elemWeights, INITIAL);
    } else {
      oldPartitionVec = partitionVec;
      partitioner->partition(&elemWeights, ADAPTIVE_REPART, 100.0 /*0.000001*/);
    }    

    partitioner->fillCoarsePartitionVec(&partitionVec);
  }

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  void ParallelDomainBase::solveInitialProblem(AdaptInfo *adaptInfo)
  {     
    if (timeIF)
      timeIF->solveInitialProblem(adaptInfo);
    
    synchVector(*(probStat->getSolution()));
  }


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  void ParallelDomainBase::createInteriorBoundaryInfo()
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  {
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    FUNCNAME("ParallelDomainBase::createInteriorBoundaryInfo()");
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    // === First, create the interior boundaries based on macro element's  ===
    // === neighbour informations.                                         ===

    createMacroElementInteriorBoundaryInfo();

    // === Second, search the whole mesh for interior boundaries that consists of ===
    // === substructures of the macro elements.                                   ===

    createSubstructureInteriorBoundaryInfo();


    // === Once we have this information, we must care about the order of the atomic ===
    // === bounds in the three boundary handling object. Eventually all the bound-   ===
    // === aries have to be in the same order on both ranks that share the bounday.  ===

    StdMpi<std::vector<AtomicBoundary> > stdMpi(mpiComm);
    stdMpi.send(myIntBoundary.boundary);
    stdMpi.recv(otherIntBoundary.boundary);
    stdMpi.startCommunication<int>(MPI_INT);
   
    // === The information about all neighbouring boundaries has been received. So ===
    // === the rank tests if its own atomic boundaries are in the same order. If   ===
    // === not, the atomic boundaries are swaped to the correct order.             ===

    for (RankToBoundMap::iterator rankIt = otherIntBoundary.boundary.begin();
	 rankIt != otherIntBoundary.boundary.end(); ++rankIt) {

      // === We have received from rank "rankIt->first" the ordered list of element ===
      // === indices. We now have to sort the corresponding list in this rank to    ===
      // === get the same order.                                                    ===
      
      for (int j = 0; j < static_cast<int>(rankIt->second.size()); j++) {
	// If the expected object is not at place, search for it.

	BoundaryObject &recvedBound = stdMpi.getRecvData()[rankIt->first][j].rankObj;

	if ((rankIt->second)[j].neighObj != recvedBound) {
	  int k = j + 1;
	  for (; k < static_cast<int>(rankIt->second.size()); k++)
 	    if ((rankIt->second)[k].neighObj == recvedBound)
	      break;

	  // The element must always be found, because the list is just in another order.
	  TEST_EXIT_DBG(k < static_cast<int>(rankIt->second.size()))
	    ("Should never happen!\n");

	  // Swap the current with the found element.
	  AtomicBoundary tmpBound = (rankIt->second)[k];
	  (rankIt->second)[k] = (rankIt->second)[j];
	  (rankIt->second)[j] = tmpBound;	
	}
      }
    }

    // === Do the same for the periodic boundaries. ===

    if (periodicBoundary.boundary.size() > 0) {
      stdMpi.clear();

      InteriorBoundary sendBounds, recvBounds;     
      for (RankToBoundMap::iterator rankIt = periodicBoundary.boundary.begin();
	   rankIt != periodicBoundary.boundary.end(); ++rankIt) {

	TEST_EXIT_DBG(rankIt->first != mpiRank)
	  ("It is no possible to have an interior boundary within a rank partition!\n");

	if (rankIt->first < mpiRank)
	  sendBounds.boundary[rankIt->first] = rankIt->second;
	else
	  recvBounds.boundary[rankIt->first] = rankIt->second;
      }

      stdMpi.send(sendBounds.boundary);
      stdMpi.recv(recvBounds.boundary);
      stdMpi.startCommunication<int>(MPI_INT);

      for (RankToBoundMap::iterator rankIt = periodicBoundary.boundary.begin();
	   rankIt != periodicBoundary.boundary.end(); ++rankIt) {
	if (rankIt->first <= mpiRank)
	  continue;
	  
	for (int j = 0; j < static_cast<int>(rankIt->second.size()); j++) {
	  
	  BoundaryObject &recvedBound = stdMpi.getRecvData()[rankIt->first][j].rankObj;
	  
	  if (periodicBoundary.boundary[rankIt->first][j].neighObj != recvedBound) {    
	    int k = j + 1;	    
	    for (; k < static_cast<int>(rankIt->second.size()); k++)
	      if (periodicBoundary.boundary[rankIt->first][k].neighObj == recvedBound)
		break;
	    
	    // The element must always be found, because the list is just in 
	    // another order.
	    TEST_EXIT_DBG(k < static_cast<int>(rankIt->second.size()))
	      ("Should never happen!\n");
	    
	    // Swap the current with the found element.
	    AtomicBoundary tmpBound = (rankIt->second)[k];
	    (rankIt->second)[k] = (rankIt->second)[j];
	    (rankIt->second)[j] = tmpBound;	
	  }  	  
	}
      }     
    } // periodicBoundary.boundary.size() > 0
  }


  void ParallelDomainBase::createMacroElementInteriorBoundaryInfo()
  {
    FUNCNAME("ParallelDomainBase::createMacroElementInteriorBoundaryInfo()");

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    int nNeighbours = mesh->getGeo(NEIGH);
    int dim = mesh->getDim();
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    GeoIndex subObj = INDEX_OF_DIM(dim - 1, dim);
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    // === First, traverse the mesh and search for all elements that have an  ===
    // === boundary with an element within another partition.                 ===
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    TraverseStack stack;
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    ElInfo *elInfo = 
      stack.traverseFirst(mesh, -1, 
			  Mesh::CALL_LEAF_EL | Mesh::FILL_NEIGH | Mesh::FILL_BOUND);
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    while (elInfo) {
      Element *element = elInfo->getElement();
      PartitionElementData *partitionData = 
	dynamic_cast<PartitionElementData*>(element->getElementData(PARTITION_ED));   
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      // Check, if the element is within rank's partition.
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      if (partitionData->getPartitionStatus() == IN) {
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	for (int i = 0; i < nNeighbours; i++) {
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	  if (!elInfo->getNeighbour(i))
	    continue;

	  PartitionElementData *neighbourPartitionData =
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	    dynamic_cast<PartitionElementData*>(elInfo->getNeighbour(i)->
						getElementData(PARTITION_ED));
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 	  if (neighbourPartitionData->getPartitionStatus() == OUT) {
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	    // We have found an element that is in rank's partition, but has a 
	    // neighbour outside of the rank's partition.

	    // === Create information about the boundary between the two elements. ===

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	    AtomicBoundary bound;	    	    
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	    bound.rankObj.el = element;
	    bound.rankObj.elIndex = element->getIndex();
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	    bound.rankObj.elType = elInfo->getType();
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	    bound.rankObj.subObj = subObj;
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	    bound.rankObj.ithObj = i;
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	    bound.neighObj.el = elInfo->getNeighbour(i);
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	    bound.neighObj.elIndex = elInfo->getNeighbour(i)->getIndex();
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	    bound.neighObj.elType = -1;
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	    bound.neighObj.subObj = subObj;
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	    bound.neighObj.ithObj = elInfo->getSideOfNeighbour(i);
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	    // Get rank number of the neighbouring element.
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	    int otherElementRank = partitionVec[elInfo->getNeighbour(i)->getIndex()];

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	    // === Add the boundary information object to the corresponding overall ===
	    // === boundary. There are three possibilities: if the boundary is a    ===
	    // === periodic boundary, just add it to \ref periodicBounadry. Here it ===
	    // === does not matter which rank is responsible for this boundary.     ===
	    // === Otherwise, the boundary is added either to \ref myIntBoundary or ===
	    // === to \ref otherIntBoundary. It dependes on which rank is respon-   ===
	    // === sible for this boundary.                                         ===

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	    if (BoundaryManager::isBoundaryPeriodic(elInfo->getBoundary(subObj, i))) {	      
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	      // We have found an element that is at an interior, periodic boundary.
	      AtomicBoundary& b = periodicBoundary.getNewAtomic(otherElementRank);
	      b = bound;
	    } else {
	      // We have found an element that is at an interior, non-periodic boundary.
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	      if (mpiRank > otherElementRank) {
		AtomicBoundary& b = myIntBoundary.getNewAtomic(otherElementRank);
		b = bound;
		b.rankObj.setReverseMode(b.neighObj, feSpace);
	      } else {
		AtomicBoundary& b = otherIntBoundary.getNewAtomic(otherElementRank);
		b = bound;	 
		b.neighObj.setReverseMode(b.rankObj, feSpace);
	      }	      
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	    }
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 	  }
	}
      }

      elInfo = stack.traverseNext(elInfo);
    }
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  }
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  void ParallelDomainBase::createSubstructureInteriorBoundaryInfo()
  {
    FUNCNAME("ParallelDomainBase::createSubstructureInteriorBoundaryInfo()");
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    // === Seach for all vertices/edges, which are part of an interior boundary,  ===
    // === but are not part of the interior boundaries that are created based on  ===
    // === the information of macro elements.                                     ===
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    int dim = mesh->getDim();
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    const BasisFunction *basFcts = feSpace->getBasisFcts();
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    std::vector<DegreeOfFreedom> localIndices(basFcts->getNumber());
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    // Maps each DOF in the whole domain to the rank that ownes this DOF.
    std::map<DegreeOfFreedom, int> dofOwner;
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    // Maps each DOF in ranks partition to the element object that contains this DOF.
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    std::map<DegreeOfFreedom, BoundaryObject> rankDofs;
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    // Maps each edge in the whole domain to the rank that ownes this edge.
    std::map<GlobalEdge, int> edgeOwner;
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    // Maps each edge in ranks partition to the element object that contains this edge.
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    std::map<GlobalEdge, BoundaryObject> rankEdges;
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    // === Traverse whole mesh and fill the maps defined above.                    ===
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    TraverseStack stack;
    ElInfo *elInfo = stack.traverseFirst(mesh, -1, Mesh::CALL_LEAF_EL);
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    while (elInfo) {
      Element *el = elInfo->getElement();
      basFcts->getLocalIndices(el, feSpace->getAdmin(), localIndices);

      PartitionElementData *partitionData = dynamic_cast<PartitionElementData*>
	(el->getElementData(PARTITION_ED));
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      // In 2d and 3d, traverse all vertices of current element.
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      for (int i = 0; i < mesh->getGeo(VERTEX); i++) {
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	DegreeOfFreedom dof0 = localIndices[i];
	// Update the owner of the current vertex DOF.
	dofOwner[dof0] = max(dofOwner[dof0], partitionVec[el->getIndex()]);

	// If the DOF is part of an element that is within ranks partition, add it
	// to the set of all ranks vertex DOFs.
	if (partitionData && partitionData->getPartitionStatus() == IN)
	  rankDofs[dof0] = BoundaryObject(el, elInfo->getType(), VERTEX, i);
      }      

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      // In 3d, traverse all edges of current element.
      if (dim == 3) {
	for (int i = 0; i < 6; i++) {
	  DegreeOfFreedom dof0 = localIndices[el->getVertexOfEdge(i, 0)];
	  DegreeOfFreedom dof1 = localIndices[el->getVertexOfEdge(i, 1)];
	  GlobalEdge edge = std::make_pair(min(dof0, dof1), max(dof0, dof1));

	  // Update the owner of the current edge.
	  edgeOwner[edge] = max(edgeOwner[edge], partitionVec[el->getIndex()]);
	  
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	  // If the edge is part of an element that is within ranks partition, add it
	  // to the set of all ranks edges.
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	  if (partitionData && partitionData->getPartitionStatus() == IN)
	    rankEdges[edge] = BoundaryObject(el, elInfo->getType(), EDGE, i);
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	}
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      }

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      elInfo = stack.traverseNext(elInfo);
    }

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    // === Create a set of all edges and vertices at ranks interior boundaries. ===
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    // Stores all edges at rank's interior boundaries.
    std::set<GlobalEdge> rankBoundaryEdges;
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    // Stores all vertices at rank's interior boundaries.
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    std::set<DegreeOfFreedom> rankBoundaryDofs;

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    // First, traverse the rank owned elements at the interior boundaries.
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    for (InteriorBoundary::iterator it(myIntBoundary); !it.end(); ++it) {
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      Element *el = it->rankObj.el;
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      basFcts->getLocalIndices(el, feSpace->getAdmin(), localIndices);
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      for (int i = 0; i < mesh->getGeo(VERTEX); i++) {
	int dofNo = el->getVertexOfPosition(it->rankObj.subObj, it->rankObj.ithObj, i);
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	DegreeOfFreedom dof = localIndices[dofNo];
	
	if (dofOwner[dof] > mpiRank)
	  it->rankObj.excludedSubstructures.push_back(std::make_pair(VERTEX, dofNo));
	else
	  rankBoundaryDofs.insert(dof);
      }    

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      if (dim == 3) {
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	for (int i = 0; i < 3; i++) {
	  int edgeNo = el->getEdgeOfFace(it->rankObj.ithObj, i);
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	  DegreeOfFreedom dof0 = localIndices[el->getVertexOfEdge(edgeNo, 0)];
	  DegreeOfFreedom dof1 = localIndices[el->getVertexOfEdge(edgeNo, 1)];
	  GlobalEdge edge = std::make_pair(min(dof0, dof1), max(dof0, dof1));	
	  
	  // If the edge at rank's interior boundarie has a higher owner rank, than
	  // we have to remove this edge from the corresponding boundary element.
	  // Otherwise, it is part of the interior boundary and we add it to the set
	  // rankBoundaryEdges.
	  if (edgeOwner[edge] > mpiRank)
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	    it->rankObj.excludedSubstructures.push_back(std::make_pair(EDGE, edgeNo));
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	  else
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	    rankBoundaryEdges.insert(edge);
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	}
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      }     
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    }

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    // Now, do the same with all other elements at the interior boundaries.
    for (InteriorBoundary::iterator it(otherIntBoundary); !it.end(); ++it) {
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      Element *el = it->rankObj.el;
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      basFcts->getLocalIndices(el, feSpace->getAdmin(), localIndices);
      
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      for (int i = 0; i < mesh->getGeo(VERTEX); i++) {
	int dofNo = el->getVertexOfPosition(it->rankObj.subObj, it->rankObj.ithObj, i);
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	DegreeOfFreedom dof = localIndices[dofNo];
	
	if (dofOwner[dof] > it.getRank())
	  it->rankObj.excludedSubstructures.push_back(std::make_pair(VERTEX, dofNo));
	else
	  rankBoundaryDofs.insert(dof);
      }	      

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      if (dim == 3) {
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	for (int i = 0; i < 3; i++) {
	  int edgeNo = el->getEdgeOfFace(it->rankObj.ithObj, i);
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	  DegreeOfFreedom dof0 = localIndices[el->getVertexOfEdge(edgeNo, 0)];
	  DegreeOfFreedom dof1 = localIndices[el->getVertexOfEdge(edgeNo, 1)];
	  GlobalEdge edge = std::make_pair(min(dof0, dof1), max(dof0, dof1));	
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	  if (edgeOwner[edge] > it.getRank())
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	    it->rankObj.excludedSubstructures.push_back(std::make_pair(EDGE, edgeNo));
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	  else
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	    rankBoundaryEdges.insert(edge);	    
	}
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      }     
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    }
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