ProblemVec.cc

#include <sstream>
#include <boost/lexical_cast.hpp>
#include "ProblemVec.h"
#include "RecoveryEstimator.h"
#include "Serializer.h"
#include "AbstractFunction.h"
#include "Operator.h"
#include "SystemVector.h"
#include "DOFMatrix.h"
#include "FiniteElemSpace.h"
#include "Estimator.h"
#include "Marker.h"
#include "AdaptInfo.h"
#include "FileWriter.h"
#include "CoarseningManager.h"
#include "RefinementManager.h"
#include "DualTraverse.h"
#include "Mesh.h"
#include "OEMSolver.h"
#include "DirichletBC.h"
#include "RobinBC.h"
#include "PeriodicBC.h"
#include "Lagrange.h"
#include "Flag.h"
#include "TraverseParallel.h"
#include "VtkWriter.h"
#include "ValueReader.h"
#include "ProblemVecDbg.h"
#include "Debug.h"

namespace AMDiS {

  using boost::lexical_cast;

  void ProblemVec::initialize(Flag initFlag,
			      ProblemVec *adoptProblem,
			      Flag adoptFlag)
  {
    FUNCNAME("ProblemVec::initialize()");

    // === create meshes ===
    if (meshes.size() != 0) { 
      WARNING("meshes already created\n");
    } else {
      if (initFlag.isSet(CREATE_MESH) || 
	  (!adoptFlag.isSet(INIT_MESH) &&
	   (initFlag.isSet(INIT_SYSTEM) || initFlag.isSet(INIT_FE_SPACE))))
	createMesh();

      if (adoptProblem && 
	  (adoptFlag.isSet(INIT_MESH) ||
	   adoptFlag.isSet(INIT_SYSTEM) ||
	   adoptFlag.isSet(INIT_FE_SPACE))) {
	meshes = adoptProblem->getMeshes();
	componentMeshes = adoptProblem->componentMeshes;
	refinementManager = adoptProblem->refinementManager;
	coarseningManager = adoptProblem->coarseningManager;

	// If the adopt problem has fewer components than this problem, but only one
	// mesh for all component, than scal up the componentMeshes array.
	if (adoptProblem->getNumComponents() < nComponents) {
	  TEST_EXIT(meshes.size() == 1)("Daran muss ich noch arbeiten!\n");
	  
	  componentMeshes.resize(nComponents);
	  for (int i = adoptProblem->getNumComponents(); i < nComponents; i++)
	    componentMeshes[i] = componentMeshes[0];
	}

      }
    }

    if (meshes.size() == 0) 
      WARNING("no mesh created\n");

    // === create fespace ===
    if (feSpaces.size() != 0) {
      WARNING("feSpaces already created\n");
    } else {
      if (initFlag.isSet(INIT_FE_SPACE) || 
	  (initFlag.isSet(INIT_SYSTEM) && !adoptFlag.isSet(INIT_FE_SPACE)))
	createFeSpace(NULL);

      if (adoptProblem &&
	  (adoptFlag.isSet(INIT_FE_SPACE) || adoptFlag.isSet(INIT_SYSTEM))) {
	feSpaces = adoptProblem->getFeSpaces();
	componentSpaces = adoptProblem->componentSpaces;
	traverseInfo = adoptProblem->traverseInfo;

	// If the adopt problem has fewer components than this problem, but only one
	// fe space for all component, than scal up the componentSpaces array.
	if (adoptProblem->getNumComponents() < nComponents) {
	  TEST_EXIT(feSpaces.size() == 1)("Daran muss ich noch arbeiten!\n");
	  
	  componentSpaces.resize(nComponents);
	  for (int i = adoptProblem->getNumComponents(); i < nComponents; i++)
	    componentSpaces[i] = componentSpaces[0];
	}

      }
    }

    if (feSpaces.size() == 0) 
      WARNING("no feSpace created\n");

    // === create system ===
    if (initFlag.isSet(INIT_SYSTEM)) 
      createMatricesAndVectors();
    
    if (adoptProblem && adoptFlag.isSet(INIT_SYSTEM)) {
      solution = adoptProblem->getSolution();
      rhs = adoptProblem->getRhs();
      systemMatrix = adoptProblem->getSystemMatrix();
    }

    // === create solver ===
    if (solver) {
      WARNING("solver already created\n");
    } else {
      if (initFlag.isSet(INIT_SOLVER)) {
	createSolver();
      } 
      if (adoptProblem && adoptFlag.isSet(INIT_SOLVER)) {
	TEST_EXIT(!solver)("solver already created\n");
	solver = adoptProblem->getSolver();
      }
    }

    if (!solver) 
      WARNING("no solver created\n");

    // === create estimator ===
    if (initFlag.isSet(INIT_ESTIMATOR))
      createEstimator();

    if (adoptProblem && adoptFlag.isSet(INIT_ESTIMATOR))
      estimator = adoptProblem->getEstimators();

    // === create marker ===
    if (initFlag.isSet(INIT_MARKER))
      createMarker();
    if (adoptProblem && adoptFlag.isSet(INIT_MARKER))
      marker = adoptProblem->getMarkers();

    // === create file writer ===
    if (initFlag.isSet(INIT_FILEWRITER))
      createFileWriter();
    
    // === read serialization and init mesh ===
    
    // There are two possiblities where the user can define a serialization
    // to be read from disk. Either by providing the parameter -rs when executing
    // the program or in the init file. The -rs parameter is always checked first,
    // because it can be added automatically when  rescheduling the program
    // before timeout of the runqueue.

    int readSerialization = 0;
    std::string serializationFilename = "";
    GET_PARAMETER(0, "argv->rs", &serializationFilename);

    // If the parameter -rs is set, we do nothing here, because the problem will be
    // deserialized in the constructor of a following AdaptInstationary initialization.
    if (!serializationFilename.compare("")) {
      int readSerializationWithAdaptInfo = 0;

      GET_PARAMETER(0, name + "->input->read serialization", "%d", &readSerialization);
      GET_PARAMETER(0, name + "->input->serialization with adaptinfo", "%d",
		    &readSerializationWithAdaptInfo);

      // The serialization file is only read, if the adaptInfo part should not be used.
      // If the adaptInfo part should be also read, the serialization file will be read
      // in the constructor of the AdaptInstationary problem, because we do not have here
      // the adaptInfo object.
      if (readSerialization && !readSerializationWithAdaptInfo) {
	GET_PARAMETER(0, name + "->input->serialization filename", 
		      &serializationFilename);
	TEST_EXIT(serializationFilename != "")("no serialization file\n");

	// If AMDiS is compiled for parallel computations, the deserialization is
	// controlled by the parallel problem object.
#ifndef HAVE_PARALLEL_DOMAIN_AMDIS
	std::ifstream in(serializationFilename.c_str());
	deserialize(in);
	in.close();

	MSG("Deserialization from file: %s\n", serializationFilename.c_str());
#endif

	deserialized = true;
      } else {
	int globalRefinements = 0;

	// If AMDiS is compiled for parallel computations, the global refinements are
	// ignored here. Later, each rank will add the global refinements to its 
	// private mesh.
#ifndef HAVE_PARALLEL_DOMAIN_AMDIS
	GET_PARAMETER(0, meshes[0]->getName() + "->global refinements", "%d", 
		      &globalRefinements);
#endif

	// Initialize the meshes if there is no serialization file.
	for (int i = 0; i < static_cast<int>(meshes.size()); i++) {
	  bool initMesh = initFlag.isSet(INIT_MESH);

	  if (initMesh && meshes[i] && !(meshes[i]->isInitialized()))
	    meshes[i]->initialize();	    
	}

	// === read value file and use it for the mesh values ===
	std::string valueFilename("");
	GET_PARAMETER(0, meshes[0]->getName() + "->value file name", &valueFilename); 
	if (valueFilename.length()) {
	  ValueReader::readValue(valueFilename,
				 meshes[0],
				 solution->getDOFVector(0),
				 meshes[0]->getMacroFileInfo());
	  meshes[0]->clearMacroFileInfo();
	}

	// === do global refinements ===

	for (unsigned int i = 0; i < meshes.size(); i++) {
	  bool initMesh = initFlag.isSet(INIT_MESH);

	  if (initMesh && meshes[i])
	    refinementManager->globalRefine(meshes[i], globalRefinements);
	}
      }
    }

    doOtherStuff();
  }


  void ProblemVec::createMesh() 
  {
    FUNCNAME("ProblemVec::createMesh()");

    componentMeshes.resize(nComponents);
    std::map<int, Mesh*> meshForRefinementSet;

    std::string meshName("");
    GET_PARAMETER(0, name + "->mesh", &meshName);
    TEST_EXIT(meshName != "")("no mesh name specified\n");
    int dim = 0;
    GET_PARAMETER(0, name + "->dim", "%d", &dim);
    TEST_EXIT(dim)("no problem dimension specified!\n");

    for (int i = 0; i < nComponents; i++) {
      int refSet = -1;
      GET_PARAMETER(0, name + "->refinement set[" + 
		       lexical_cast<std::string>(i) + "]", "%d", &refSet);
      if (refSet < 0)
	refSet = 0;
      
      if (meshForRefinementSet[refSet] == NULL) {
	Mesh *newMesh = new Mesh(meshName, dim);
	meshForRefinementSet[refSet] = newMesh;
	meshes.push_back(newMesh);
	nMeshes++;
      }
      componentMeshes[i] = meshForRefinementSet[refSet];
    }
    switch(dim) {
    case 1:
      coarseningManager = new CoarseningManager1d();
      refinementManager = new RefinementManager1d();
      break;
    case 2:
      coarseningManager = new CoarseningManager2d();
      refinementManager = new RefinementManager2d();
      break;
    case 3:
      coarseningManager = new CoarseningManager3d();
      refinementManager = new RefinementManager3d();
      break;
    default:
      ERROR_EXIT("invalid dim!\n");
    }
  }


  void ProblemVec::createFeSpace(DOFAdmin *admin)
  {
    FUNCNAME("ProblemVec::createFeSpace()");

    std::map<std::pair<Mesh*, int>, FiniteElemSpace*> feSpaceMap;
    int dim = -1;
    GET_PARAMETER(0, name + "->dim", "%d", &dim);
    TEST_EXIT(dim != -1)("no problem dimension specified!\n");

    componentSpaces.resize(nComponents, NULL);
    traverseInfo.resize(nComponents);

    for (int i = 0; i < nComponents; i++) {
      int degree = 1;
      GET_PARAMETER(0, name + "->polynomial degree[" + 
		    boost::lexical_cast<std::string>(i) + "]","%d", &degree);

      TEST_EXIT(componentSpaces[i] == NULL)("feSpace already created\n");

      if (feSpaceMap[std::pair<Mesh*, int>(componentMeshes[i], degree)] == NULL) {
	stringstream s;
	s << name << "->feSpace[" << i << "]";

	FiniteElemSpace *newFeSpace = 
	  FiniteElemSpace::provideFeSpace(admin, Lagrange::getLagrange(dim, degree),
					  componentMeshes[i], s.str());
	feSpaceMap[std::pair<Mesh*, int>(componentMeshes[i], degree)] = newFeSpace;
	feSpaces.push_back(newFeSpace);
      }
      componentSpaces[i] = feSpaceMap[std::pair<Mesh*, int>(componentMeshes[i], degree)];
    }

    for (int i = 0; i < nComponents; i++) {
      for (int j = 0; j < nComponents; j++)
	traverseInfo.getMatrix(i, j).setFeSpace(componentSpaces[i], componentSpaces[j]);
      
      traverseInfo.getVector(i).setFeSpace(componentSpaces[i]);
    }

    // create dof admin for vertex dofs if neccessary
    for (int i = 0; i < static_cast<int>(meshes.size()); i++) {
      if (meshes[i]->getNumberOfDOFs(VERTEX) == 0) {
	DimVec<int> ln_dof(meshes[i]->getDim(), DEFAULT_VALUE, 0);
	ln_dof[VERTEX] = 1;
	meshes[i]->createDOFAdmin("vertex dofs", ln_dof);      
      }
    }
  }


  void ProblemVec::createMatricesAndVectors()
  {
    FUNCNAME("ProblemVec::createMatricesAndVectors()");

    // === create vectors and system matrix ===

    systemMatrix = new Matrix<DOFMatrix*>(nComponents, nComponents);
    systemMatrix->set(NULL);
    rhs = new SystemVector("rhs", componentSpaces, nComponents);
    solution = new SystemVector("solution", componentSpaces, nComponents);

    for (int i = 0; i < nComponents; i++) {
      (*systemMatrix)[i][i] = new DOFMatrix(componentSpaces[i], 
					    componentSpaces[i], "A_ii");
      (*systemMatrix)[i][i]->setCoupleMatrix(false);

      std::string numberedName = "rhs[" + boost::lexical_cast<std::string>(i) + "]";
      rhs->setDOFVector(i, new DOFVector<double>(componentSpaces[i], numberedName));

      numberedName = "solution[" + boost::lexical_cast<std::string>(i) + "]";
      solution->setDOFVector(i, new DOFVector<double>(componentSpaces[i],
      						      numberedName));
      solution->getDOFVector(i)->setCoarsenOperation(COARSE_INTERPOL);
      solution->getDOFVector(i)->set(0.0);
    }
  }


  void ProblemVec::createSolver()
  {
    FUNCNAME("ProblemVec::createSolver()");

    // === create solver ===
    std::string solverType("0");
    GET_PARAMETER(0, name + "->solver", &solverType);
    OEMSolverCreator *solverCreator = 
      dynamic_cast<OEMSolverCreator*>(CreatorMap<OEMSolver>::getCreator(solverType));
    TEST_EXIT(solverCreator)("no solver type\n");
    solverCreator->setName(name + "->solver");
    solver = solverCreator->create();
    solver->initParameters();
  }


  void ProblemVec::createEstimator()
  {
    FUNCNAME("ProblemVec::createEstimator()");

    // create and set leaf data prototype
    for (unsigned int i = 0; i < meshes.size(); i++)
      meshes[i]->setElementDataPrototype
	(new LeafDataEstimatableVec(new LeafDataCoarsenableVec));

    for (int i = 0; i < nComponents; i++) {
      TEST_EXIT(estimator[i] == NULL)("estimator already created\n");
      std::string estName = 
	name + "->estimator[" + boost::lexical_cast<std::string>(i) + "]";

      // === create estimator ===
      std::string estimatorType("0");
      GET_PARAMETER(0, estName, &estimatorType);
      EstimatorCreator *estimatorCreator = 
	dynamic_cast<EstimatorCreator*>(CreatorMap<Estimator>::getCreator(estimatorType));
      if (estimatorCreator) {
	estimatorCreator->setName(estName);
	estimatorCreator->setRow(i);
	if (estimatorType == "recovery")
	  dynamic_cast<RecoveryEstimator::Creator*>(estimatorCreator)->
	    setSolution(solution->getDOFVector(i));       
	estimator[i] = estimatorCreator->create();
      }


      if (estimator[i])
	for (int j = 0; j < nComponents; j++)
	  estimator[i]->addSystem((*systemMatrix)[i][j], 
				  solution->getDOFVector(j), 
				  rhs->getDOFVector(j));      
    }
  }


  void ProblemVec::createMarker()
  {
    FUNCNAME("ProblemVec::createMarker()");

    int nMarkersCreated = 0;

    for (int i = 0; i < nComponents; i++) {
      marker[i] = Marker::createMarker
	(name + "->marker[" + boost::lexical_cast<std::string>(i) + "]", i);

      if (marker[i]) {
	nMarkersCreated++;

	// If there is more than one marker, and all components are defined
	// on the same mesh, the maximum marking has to be enabled.
 	if (nMarkersCreated > 1 && nMeshes == 1)
 	  marker[i]->setMaximumMarking(true);
      }
    }
  }


  void ProblemVec::createFileWriter()
  {
    FUNCNAME("ProblemVec::createFileWriter()");
  
    // Create one filewriter for all components of the problem
    std::string numberedName  = name + "->output";
    std::string filename = "";
    GET_PARAMETER(0, numberedName + "->filename", &filename);

    if (filename != "") {
      std::vector< DOFVector<double>* > solutionList(nComponents);

      for (int i = 0; i < nComponents; i++) {
	TEST_EXIT(componentMeshes[0] == componentMeshes[i])
	  ("All Meshes have to be equal to write a vector file.\n");

	solutionList[i] = solution->getDOFVector(i);
      }

      fileWriters.push_back(new FileWriter(numberedName,
					   componentMeshes[0],
					   solutionList));
    }

    // Create own filewriters for each components of the problem
    for (int i = 0; i < nComponents; i++) {
      numberedName = name + "->output[" + boost::lexical_cast<std::string>(i) + "]";
      filename = "";
      GET_PARAMETER(0, numberedName + "->filename", &filename);

      if (filename != "")
	fileWriters.push_back(new FileWriter(numberedName, 
					     componentMeshes[i], 
					     solution->getDOFVector(i)));      
    }

    // Check for serializer
    int writeSerialization = 0;
    GET_PARAMETER(0, name + "->write serialization", "%d", &writeSerialization);
    if (writeSerialization) {
      MSG("Use are using the obsolete parameter: %s->write serialization\n", name.c_str());
      MSG("Please use instead the following parameter: %s->output->write serialization\n", name.c_str());
      ERROR_EXIT("Usage of an obsolete parameter (see message above)!\n");
    }

    GET_PARAMETER(0, name + "->output->write serialization", "%d", &writeSerialization);

    if (writeSerialization)
      fileWriters.push_back(new Serializer<ProblemVec>(this));
  }


  void ProblemVec::doOtherStuff()
  {
  }


  void ProblemVec::solve(AdaptInfo *adaptInfo, bool fixedMatrix)
  {
    FUNCNAME("Problem::solve()");

    if (!solver) {
      WARNING("no solver\n");
      return;
    }

#ifdef _OPENMP
    double wtime = omp_get_wtime();
#endif

    clock_t first = clock();
    
    solver->solveSystem(solverMatrix, *solution, *rhs);

#ifdef _OPENMP
    INFO(info, 8)("solution of discrete system needed %.5f seconds system time / %.5f seconds wallclock time\n",
		  TIME_USED(first, clock()), omp_get_wtime() - wtime);
#else
    INFO(info, 8)("solution of discrete system needed %.5f seconds\n", 
		  TIME_USED(first, clock()));
#endif

    adaptInfo->setSolverIterations(solver->getIterations());
    adaptInfo->setMaxSolverIterations(solver->getMaxIterations());
    adaptInfo->setSolverTolerance(solver->getTolerance());
    adaptInfo->setSolverResidual(solver->getResidual());
  }


  void ProblemVec::estimate(AdaptInfo *adaptInfo) 
  {
    FUNCNAME("ProblemVec::estimate()");

    clock_t first = clock();

#ifdef _OPENMP
    double wtime = omp_get_wtime();
#endif

    if (computeExactError) {
      computeError(adaptInfo);
    } else {
      for (int i = 0; i < nComponents; i++) {
	Estimator *scalEstimator = estimator[i];
	
	if (scalEstimator) {
	  traverseInfo.updateStatus();
	  scalEstimator->setTraverseInfo(traverseInfo);
	  scalEstimator->estimate(adaptInfo->getTimestep());

	  adaptInfo->setEstSum(scalEstimator->getErrorSum(), i);
	  adaptInfo->setEstMax(scalEstimator->getErrorMax(), i);

	  if (adaptInfo->getRosenbrockMode() == false) {
	    adaptInfo->setTimeEstSum(scalEstimator->getTimeEst(), i);
	    adaptInfo->setTimeEstMax(scalEstimator->getTimeEstMax(), i);
	  }
	}
      }
    }

#ifdef _OPENMP
    INFO(info, 8)("estimation of the error needed %.5f seconds system time / %.5f seconds wallclock time\n",
		  TIME_USED(first, clock()), omp_get_wtime() - wtime);
#else
    INFO(info, 8)("estimation of the error needed %.5f seconds\n",
		  TIME_USED(first, clock()));
#endif
  }


  Flag ProblemVec::markElements(AdaptInfo *adaptInfo) 
  {
    FUNCNAME("ProblemVec::markElements()");

    TEST_EXIT_DBG(static_cast<unsigned int>(nComponents) == marker.size())
      ("Wrong number of markers!\n");

    Flag markFlag = 0;
    for (int i = 0; i < nComponents; i++) {
      if (marker[i])
	markFlag |= marker[i]->markMesh(adaptInfo, componentMeshes[i]);
      else
	WARNING("No marker for component %d\n", i);              
    }
    
    return markFlag;
  }


  Flag ProblemVec::refineMesh(AdaptInfo *adaptInfo) 
  {
    FUNCNAME("ProblemVec::refineMesh()");

    int nMeshes = static_cast<int>(meshes.size());
    Flag refineFlag = 0;
    for (int i = 0; i < nMeshes; i++)
      if (adaptInfo->isRefinementAllowed(i))
	refineFlag |= refinementManager->refineMesh(meshes[i]);

    return refineFlag;
  }


  Flag ProblemVec::coarsenMesh(AdaptInfo *adaptInfo) 
  {
    FUNCNAME("ProblemVec::coarsenMesh()");

    int nMeshes = static_cast<int>(meshes.size());
    Flag coarsenFlag = 0;
    for (int i = 0; i < nMeshes; i++)
      if (adaptInfo->isCoarseningAllowed(i))
	coarsenFlag |= coarseningManager->coarsenMesh(meshes[i]);

    return coarsenFlag;
  }


  Flag ProblemVec::oneIteration(AdaptInfo *adaptInfo, Flag toDo)
  {
    FUNCNAME("ProblemVec::oneIteration()");

    for (int i = 0; i < nComponents; i++)
      if (adaptInfo->spaceToleranceReached(i))
	adaptInfo->allowRefinement(false, i);
      else
	adaptInfo->allowRefinement(true, i);	

    return StandardProblemIteration::oneIteration(adaptInfo, toDo);
  }


  void ProblemVec::buildAfterCoarsen(AdaptInfo *adaptInfo, Flag flag,
				     bool asmMatrix, bool asmVector)
  {
    FUNCNAME("ProblemVec::buildAfterCoarsen()");

    if (dualMeshTraverseRequired()) {
      dualAssemble(adaptInfo, flag, asmMatrix, asmVector);
      return;
    }

    //    printOpenmpTraverseInfo(this, true);
    //    std::cout << "ElInfo = " << ElInfo::subElemMatrices.size() << std::endl;

    for (unsigned int i = 0; i < meshes.size(); i++)
      meshes[i]->dofCompress();


    clock_t first = clock();
#ifdef _OPENMP
    double wtime = omp_get_wtime();
#endif


    Flag assembleFlag = 
      flag | 
      (*systemMatrix)[0][0]->getAssembleFlag() | 
      rhs->getDOFVector(0)->getAssembleFlag()  |
      Mesh::CALL_LEAF_EL                        | 
      Mesh::FILL_COORDS                         |
      Mesh::FILL_DET                            |
      Mesh::FILL_GRD_LAMBDA |
      Mesh::FILL_NEIGH;

    if (useGetBound)
      assembleFlag |= Mesh::FILL_BOUND;

  
    traverseInfo.updateStatus();
    // Used to calculate the overall number of non zero entries.
    int nnz = 0;

    for (int i = 0; i < nComponents; i++) {

      MSG("%d DOFs for %s\n", 
	  componentSpaces[i]->getAdmin()->getUsedSize(), 
	  componentSpaces[i]->getName().c_str());

      rhs->getDOFVector(i)->set(0.0);

      for (int j = 0; j < nComponents; j++) {

	if (writeAsmInfo)
	  MSG("--------- %d %d -------------\n", i, j);

	// Only if this variable is true, the current matrix will be assembled.	
	bool assembleMatrix = true;
	// The DOFMatrix which should be assembled (or not, if assembleMatrix
	// will be set to false).
	DOFMatrix *matrix = (asmMatrix ? (*systemMatrix)[i][j] : NULL);

	if (writeAsmInfo && matrix) {
	  for (std::vector<Operator*>::iterator it = matrix->getOperatorsBegin();
	       it != matrix->getOperatorsEnd(); ++it) {
	    Assembler *assembler = (*it)->getAssembler();
	    if (assembler->getZeroOrderAssembler()) 
	      std::cout << "ZOA: " << assembler->getZeroOrderAssembler()->getName() << std::endl;
	    if (assembler->getFirstOrderAssembler(GRD_PSI)) 
	      std::cout << "FOA GRD_PSI: " << assembler->getFirstOrderAssembler(GRD_PSI)->getName() << std::endl;
	    if (assembler->getFirstOrderAssembler(GRD_PHI)) 
	      std::cout << "FOA GRD_PHI: " << assembler->getFirstOrderAssembler(GRD_PHI)->getName() << std::endl;
	    if (assembler->getSecondOrderAssembler()) 
	      std::cout << "SOA: " << assembler->getSecondOrderAssembler()->getName() << std::endl;
	  }
	}

	if (matrix) 
	  matrix->calculateNnz();
	
	// If the matrix was assembled before and it is marked to be assembled
	// only once, it will not be assembled.
	if (assembleMatrixOnlyOnce[i][j] && assembledMatrix[i][j]) {
	  assembleMatrix = false;
	} else if (matrix) {
	  matrix->getBaseMatrix().
	    change_dim(componentSpaces[i]->getAdmin()->getUsedSize(), 
		       componentSpaces[j]->getAdmin()->getUsedSize());

	  set_to_zero(matrix->getBaseMatrix());
	}

	// If there is no DOFMatrix, e.g., if it is completly 0, do not assemble.
	if (!matrix || !assembleMatrix)
	  assembleMatrix = false;

	// If the matrix should not be assembled, the rhs vector has to be considered.
	// This will be only done, if i == j. So, if both is not true, we can jump
	// to the next matrix.
	if (!assembleMatrix && i != j) {
	  if (matrix)
	    nnz += matrix->getBaseMatrix().nnz();

	  continue;
	}

	if (assembleMatrix && matrix->getBoundaryManager())
	  matrix->getBoundaryManager()->initMatrix(matrix);

	// The simplest case: either the right hand side has no operaters, no aux
	// fe spaces, or all aux fe spaces are equal to the row and col fe space.
	assembleOnOneMesh(componentSpaces[i],
			  assembleFlag,
			  assembleMatrix ? matrix : NULL,
			  ((i == j) && asmVector) ? rhs->getDOFVector(i) : NULL);
      
	assembledMatrix[i][j] = true;

	
	if (assembleMatrix)
	  matrix->finishInsertion();

 	if (assembleMatrix && matrix->getBoundaryManager())
 	  matrix->getBoundaryManager()->exitMatrix(matrix);	
	
	if (matrix)
	  nnz += matrix->getBaseMatrix().nnz();
      }

      // And now assemble boundary conditions on the vectors
      assembleBoundaryConditions(rhs->getDOFVector(i),
 				 solution->getDOFVector(i),
 				 componentMeshes[i],
 				 assembleFlag);     
    }  

    if (asmMatrix) {
      solverMatrix.setMatrix(*systemMatrix);
      createPrecon();

      INFO(info, 8)("fillin of assembled matrix: %d\n", nnz);
    }

#ifdef _OPENMP
    INFO(info, 8)("buildAfterCoarsen needed %.5f seconds system time / %.5f seconds wallclock time\n",
		  TIME_USED(first, clock()), omp_get_wtime() - wtime);
#else
    INFO(info, 8)("buildAfterCoarsen needed %.5f seconds\n", 
		  TIME_USED(first, clock()));    
#endif    
  }


  bool ProblemVec::dualMeshTraverseRequired()
  {
    FUNCNAME("ProblemVec::dualMeshTraverseRequired()");

    TEST_EXIT(meshes.size() <= 2)("More than two meshes are not yet supported!\n");

    return (meshes.size() == 2);
  }
  

  void ProblemVec::dualAssemble(AdaptInfo *adaptInfo, Flag flag, 
				bool asmMatrix, bool asmVector)
  {
    FUNCNAME("ProblemVec::dualAssemble()");

    TEST_EXIT(asmVector)("Not yet implemented!\n");

    for (unsigned int i = 0; i < meshes.size(); i++)
      meshes[i]->dofCompress();


    clock_t first = clock();
#ifdef _OPENMP
    double wtime = omp_get_wtime();
#endif

    
    Flag assembleFlag = 
      flag | 
      (*systemMatrix)[0][0]->getAssembleFlag() | 
      rhs->getDOFVector(0)->getAssembleFlag()  |
      Mesh::CALL_LEAF_EL                        | 
      Mesh::FILL_COORDS                         |
      Mesh::FILL_DET                            |
      Mesh::FILL_GRD_LAMBDA |
      Mesh::FILL_NEIGH;

    if (useGetBound)
      assembleFlag |= Mesh::FILL_BOUND;

    traverseInfo.updateStatus();

    if (writeAsmInfo) {
      MSG("TraverseInfo:\n");
      for (int i = 0; i < nComponents; i++) {
	MSG("  component %d:   difAuxSpace = %d\n", i, traverseInfo.difAuxSpace(i));
	
	for (int j = 0; j < nComponents; j++) {
	  MSG("  component %d-%d:  difAuxSpace = %d\n", 
	      i, j, traverseInfo.difAuxSpace(i, j));
	}
      }
    }

    // Used to calculate the overall number of non zero entries.
    int nnz = 0;

    for (int i = 0; i < nComponents; i++) {
      MSG("%d DOFs for %s\n", 
	  componentSpaces[i]->getAdmin()->getUsedSize(), 
	  componentSpaces[i]->getName().c_str());

      rhs->getDOFVector(i)->set(0.0);

      for (int j = 0; j < nComponents; j++) {
	
	if (writeAsmInfo)
	  std::cout << "-------" << i << " " << j << "----------------" << std::endl;

	// Only if this variable is true, the current matrix will be assembled.	
	bool assembleMatrix = true;
	// The DOFMatrix which should be assembled (or not, if assembleMatrix
	// will be set to false).
	DOFMatrix *matrix = (asmMatrix ? (*systemMatrix)[i][j] : NULL);

	if (writeAsmInfo && matrix) {
	  for (std::vector<Operator*>::iterator it = matrix->getOperatorsBegin();
	       it != matrix->getOperatorsEnd(); ++it) {
	    Assembler *assembler = (*it)->getAssembler();
	    if (assembler->getZeroOrderAssembler()) 
	      std::cout << "ZOA: " << assembler->getZeroOrderAssembler()->getName() << std::endl;
	    if (assembler->getFirstOrderAssembler(GRD_PSI)) 
	      std::cout << "FOA GRD_PSI: " << assembler->getFirstOrderAssembler(GRD_PSI)->getName() << std::endl;
	    if (assembler->getFirstOrderAssembler(GRD_PHI)) 
	      std::cout << "FOA GRD_PHI: " << assembler->getFirstOrderAssembler(GRD_PHI)->getName() << std::endl;
	    if (assembler->getSecondOrderAssembler()) 
	      std::cout << "SOA: " << assembler->getSecondOrderAssembler()->getName() << std::endl;
	  }
	}

	if (matrix) 
	  matrix->calculateNnz();
	
	// If the matrix was assembled before and it is marked to be assembled
	// only once, it will not be assembled.
	if (assembleMatrixOnlyOnce[i][j] && assembledMatrix[i][j]) {
	  assembleMatrix = false;
	} else if (matrix) {
	  matrix->getBaseMatrix().
	    change_dim(componentSpaces[i]->getAdmin()->getUsedSize(), 
		       componentSpaces[j]->getAdmin()->getUsedSize());

	  set_to_zero(matrix->getBaseMatrix());
	  matrix->startInsertion(matrix->getNnz());

	  if (matrix->getBoundaryManager())
	    matrix->getBoundaryManager()->initMatrix(matrix);
	}

	// If there is no DOFMatrix, e.g., if it is completly 0, do not assemble.
	if (!matrix || !assembleMatrix)
	  assembleMatrix = false;

	// If the matrix should not be assembled, the rhs vector has to be considered.
	// This will be only done, if i == j. So, if both is not true, we can jump
	// to the next matrix.
	if (!assembleMatrix && i != j)
	  if (matrix)
	    nnz += matrix->getBaseMatrix().nnz();

	if (matrix && !assembleMatrix) {
	  ERROR_EXIT("Not yet implemented!\n");
	}
      }
    }

    TEST_EXIT(meshes.size() == 2)("There is something wrong!\n");

    const BasisFunction *basisFcts = componentSpaces[0]->getBasisFcts();
    BoundaryType *bound = 
      useGetBound ? new BoundaryType[basisFcts->getNumber()] : NULL;

    DualTraverse dualTraverse;
    DualElInfo dualElInfo;
    int oldElIndex0 = -1;
    int oldElIndex1 = -1;
    dualTraverse.setFillSubElemMat(true, basisFcts);
    bool cont = dualTraverse.traverseFirst(meshes[0], meshes[1], -1, -1, 
					   assembleFlag, assembleFlag, dualElInfo);

    while (cont) {     
      bool newEl0 = (dualElInfo.rowElInfo->getElement()->getIndex() != oldElIndex0);
      bool newEl1 = (dualElInfo.colElInfo->getElement()->getIndex() != oldElIndex1);
      oldElIndex0 = dualElInfo.rowElInfo->getElement()->getIndex();
      oldElIndex1 = dualElInfo.colElInfo->getElement()->getIndex();      

      for (int i = 0; i <