ProblemStat.cc

//
// Software License for AMDiS
//
// Copyright (c) 2010 Dresden University of Technology 
// All rights reserved.
// Authors: Simon Vey, Thomas Witkowski et al.
//
// This file is part of AMDiS
//
// See also license.opensource.txt in the distribution.


#include <sstream>
#include <boost/lexical_cast.hpp>

#include "ProblemStat.h"
#include "Serializer.h"
#include "AbstractFunction.h"
#include "Operator.h"
#include "SystemVector.h"
#include "DOFMatrix.h"
#include "FiniteElemSpace.h"
#include "Marker.h"
#include "AdaptInfo.h"
#include "io/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 "est/Estimator.h"
#include "io/VtkWriter.h"
#include "io/ValueReader.h"
#include "ProblemStatDbg.h"
#include "Debug.h"

namespace AMDiS {

  using namespace std;
  using boost::lexical_cast;

  ProblemStatSeq::ProblemStatSeq(string nameStr,
				 ProblemIterationInterface *problemIteration)
    : StandardProblemIteration(this),
      name(nameStr),
      nComponents(-1),
      nMeshes(0),
      traverseInfo(0),
      solver(NULL),
      solution(NULL),
      rhs(NULL),
      systemMatrix(NULL),
      useGetBound(true),
      refinementManager(NULL),
      coarseningManager(NULL),
      info(10),
      deserialized(false),
      computeExactError(false),
      boundaryConditionSet(false),
      writeAsmInfo(false)
  {
    Parameters::get(name + "->components", nComponents);
    TEST_EXIT(nComponents > 0)("components not set!\n");    
    estimator.resize(nComponents, NULL);
    marker.resize(nComponents, NULL);
    
    assembleMatrixOnlyOnce.resize(nComponents);
    assembledMatrix.resize(nComponents);
    for (int i = 0; i < nComponents; i++) {
      assembleMatrixOnlyOnce[i].resize(nComponents);
      assembledMatrix[i].resize(nComponents);
      for (int j = 0; j < nComponents; j++) {
	assembleMatrixOnlyOnce[i][j] = false;
	assembledMatrix[i][j] = false;
      }
    }
    
    exactSolutionFcts.resize(nComponents);


    // === Initialize name of components. ===

    componentNames.resize(nComponents, "");
    for (int i = 0; i < nComponents; i++)
      componentNames[i] = "solution[" + lexical_cast<string>(i) + "]";

    Parameters::get(name + "->name", componentNames);
    componentNames.resize(nComponents);

    for (int i = 0; i < nComponents; i++)
      Parameters::get(name + "->name[" + lexical_cast<string>(i) + "]",
		      componentNames[i]);
  }

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

	// 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 refinement/corasening-manager ===
    if (refinementManager != NULL && coarseningManager != NULL) { 
      WARNING("refinement-/coarseningmanager already created\n");
    } else {
      if (initFlag.isSet(CREATE_MESH) || 
          (!adoptFlag.isSet(INIT_MESH) &&
           (initFlag.isSet(INIT_SYSTEM) || initFlag.isSet(INIT_FE_SPACE))))
        createRefCoarseManager();

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

    if (refinementManager == NULL || coarseningManager == NULL) 
      WARNING("no refinement-/coarseningmanager 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;
    string serializationFilename = "";
    Parameters::get("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;

      Parameters::get(name + "->input->read serialization", readSerialization);
      Parameters::get(name + "->input->serialization with adaptinfo",
		      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) {
	Parameters::get(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
	MSG("Deserialization from file: %s\n", serializationFilename.c_str());
	ifstream in(serializationFilename.c_str());

	// Read the revision number of the AMDiS version which was used to create 
	// the serialization file.
	int revNumber = -1;
	SerUtil::deserialize(in, revNumber);

	deserialize(in);
	in.close();
#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
	Parameters::get(meshes[0]->getName() + "->global refinements", 
			globalRefinements);
#endif

	bool initMesh = initFlag.isSet(INIT_MESH);

	// Initialize the meshes if there is no serialization file.
	for (int i = 0; i < static_cast<int>(meshes.size()); i++)
	  if (initMesh && meshes[i] && !(meshes[i]->isInitialized()))
	    meshes[i]->initialize();	    	

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

	// === do global refinements ===

	for (unsigned int i = 0; i < meshes.size(); i++)
	  if (initMesh && meshes[i])
	    refinementManager->globalRefine(meshes[i], globalRefinements);	
      }
    }

    doOtherStuff();
  }


  void ProblemStatSeq::createMesh() 
  {
    FUNCNAME("ProblemStat::createMesh()");

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

    string meshName("");
    Parameters::get(name + "->mesh", meshName);
    TEST_EXIT(meshName != "")("No mesh name specified for \"%s->mesh\"!\n", 
			      name.c_str());

    int dim = 0;
    Parameters::get(name + "->dim", dim);
    TEST_EXIT(dim)("No problem dimension specified for \"%s->dim\"!\n",
		   name.c_str());

    for (int i = 0; i < nComponents; i++) {
      int refSet = -1;
      Parameters::get(name + "->refinement set[" + lexical_cast<string>(i) + "]", 
		      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];
    }
  }


  void ProblemStatSeq::createRefCoarseManager() 
  {
    FUNCNAME("ProblemStat::createRefCoarseManager()");

    int dim = 0;
    Parameters::get(name + "->dim", dim);
    TEST_EXIT(dim)("No problem dimension specified for \"%s->dim\"!\n",
                   name.c_str());

    switch (dim) {
    case 1:
      refinementManager = new RefinementManager1d();
      coarseningManager = new CoarseningManager1d();
      break;
    case 2:
      refinementManager = new RefinementManager2d();
      coarseningManager = new CoarseningManager2d();
      break;
    case 3:
      refinementManager = new RefinementManager3d();
      coarseningManager = new CoarseningManager3d();
      break;
    default:
      ERROR_EXIT("invalid dim!\n");
    }
  }


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

    map<pair<Mesh*, int>, FiniteElemSpace*> feSpaceMap;
    int dim = -1;
    Parameters::get(name + "->dim", 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;
      Parameters::get(name + "->polynomial degree[" + 
		      boost::lexical_cast<string>(i) + "]", degree);

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

      if (feSpaceMap[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[pair<Mesh*, int>(componentMeshes[i], degree)] = newFeSpace;
	feSpaces.push_back(newFeSpace);
      }

      componentSpaces[i] = feSpaceMap[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 ProblemStatSeq::createMatricesAndVectors()
  {
    FUNCNAME("ProblemStat::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);

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

      solution->setDOFVector(i, new DOFVector<double>(componentSpaces[i],
      						      componentNames[i]));
      solution->getDOFVector(i)->setCoarsenOperation(COARSE_INTERPOL);
      solution->getDOFVector(i)->set(0.0);
    }
  }


  void ProblemStatSeq::createSolver()
  {
    FUNCNAME("ProblemStat::createSolver()");

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


  void ProblemStatSeq::createEstimator()
  {
    FUNCNAME("ProblemStat::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");
      string estName = 
	name + "->estimator[" + boost::lexical_cast<string>(i) + "]";

      // === create estimator ===
      string estimatorType("0");
      Parameters::get(estName, estimatorType);
      EstimatorCreator *estimatorCreator = 
	dynamic_cast<EstimatorCreator*>(CreatorMap<Estimator>::getCreator(estimatorType, estName));
      if (estimatorCreator) {
	estimatorCreator->setName(estName);
	estimatorCreator->setRow(i);
	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 ProblemStatSeq::createMarker()
  {
    FUNCNAME("ProblemStat::createMarker()");

    int nMarkersCreated = 0;

    for (int i = 0; i < nComponents; i++) {
      marker[i] = Marker::createMarker
	(name + "->marker[" + boost::lexical_cast<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 ProblemStatSeq::createFileWriter()
  {
    FUNCNAME("ProblemStat::createFileWriter()");
  
    // Create one filewriter for all components of the problem
    string numberedName  = name + "->output";
    string filename = "";
    Parameters::get(numberedName + "->filename", filename);

    if (filename != "") {
      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<string>(i) + "]";
      filename = "";
      Parameters::get(numberedName + "->filename", filename);

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

    int writeSerialization = 0;
    Parameters::get(name + "->output->write serialization", writeSerialization);
    if (writeSerialization)
      fileWriters.push_back(new Serializer<ProblemStatSeq>(this));
  }


  void ProblemStatSeq::doOtherStuff()
  {
  }


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

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

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

    INFO(info, 8)("solution of discrete system needed %.5f seconds\n", 
		  TIME_USED(first, clock()));

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


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

#ifdef HAVE_PARALLEL_DOMAIN_AMDIS
    double first = MPI::Wtime();
#else
    clock_t first = clock();
#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 HAVE_PARALLEL_DOMAIN_AMDIS
    MPI::COMM_WORLD.Barrier();
    INFO(info, 8)("estimation of the error needed %.5f seconds\n", 
		  MPI::Wtime() - first);
#else
    INFO(info, 8)("estimation of the error needed %.5f seconds\n",
		  TIME_USED(first, clock()));
#endif
  }


  Flag ProblemStatSeq::markElements(AdaptInfo *adaptInfo) 
  {
    FUNCNAME("ProblemStat::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]);
    
    return markFlag;
  }


  Flag ProblemStatSeq::refineMesh(AdaptInfo *adaptInfo) 
  {
    FUNCNAME("ProblemStat::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 ProblemStatSeq::coarsenMesh(AdaptInfo *adaptInfo) 
  {
    FUNCNAME("ProblemStat::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 ProblemStatSeq::oneIteration(AdaptInfo *adaptInfo, Flag toDo)
  {
    FUNCNAME("ProblemStat::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 ProblemStatSeq::buildAfterCoarsen(AdaptInfo *adaptInfo, Flag flag,
					 bool asmMatrix, bool asmVector)
  {
    FUNCNAME("ProblemStat::buildAfterCoarsen()");

//     buildAfterCoarsen_sebastianMode(adaptInfo, flag);
//     return;

    if (dualMeshTraverseRequired()) {
#ifdef HAVE_PARALLEL_DOMAIN_AMDIS
      ERROR_EXIT("Dual mesh assemble does not work in parallel code!\n");
#endif

      dualAssemble(adaptInfo, flag, asmMatrix, asmVector);
      return;
    }

#ifdef HAVE_PARALLEL_DOMAIN_AMDIS
    double first = MPI::Wtime();
#endif


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


#ifdef HAVE_PARALLEL_DOMAIN_AMDIS
    MPI::COMM_WORLD.Barrier();
    INFO(info, 8)("dof compression needed %.5f seconds\n", 
		  MPI::Wtime() - first);

    first = MPI::Wtime();
#else
    clock_t first = clock();
#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()->getUsedDofs(), 
	  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 (vector<Operator*>::iterator it = matrix->getOperatorsBegin();
	       it != matrix->getOperatorsEnd(); ++it) {
	    Assembler *assembler = (*it)->getAssembler();
	    if (assembler->getZeroOrderAssembler()) 
	      cout << "ZOA: " << assembler->getZeroOrderAssembler()->getName() << endl;
	    if (assembler->getFirstOrderAssembler(GRD_PSI)) 
	      cout << "FOA GRD_PSI: " << assembler->getFirstOrderAssembler(GRD_PSI)->getName() << endl;
	    if (assembler->getFirstOrderAssembler(GRD_PHI)) 
	      cout << "FOA GRD_PHI: " << assembler->getFirstOrderAssembler(GRD_PHI)->getName() << endl;
	    if (assembler->getSecondOrderAssembler()) 
	      cout << "SOA: " << assembler->getSecondOrderAssembler()->getName() << 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) {
      solver->setMultipleRhs(false);