PetscSolverGlobalMatrix.cc

/******************************************************************************
 *
 * AMDiS - Adaptive multidimensional simulations
 *
 * Copyright (C) 2013 Dresden University of Technology. All Rights Reserved.
 * Web: https://fusionforge.zih.tu-dresden.de/projects/amdis
 *
 * Authors: 
 * Simon Vey, Thomas Witkowski, Andreas Naumann, Simon Praetorius, et al.
 *
 * This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
 * WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
 *
 *
 * This file is part of AMDiS
 *
 * See also license.opensource.txt in the distribution.
 * 
 ******************************************************************************/

#include <mpi.h>
#include "DirichletBC.h"
#include "DOFVector.h"
#include "parallel/PetscSolverGlobalMatrix.h"
#include "parallel/StdMpi.h"
#include "parallel/MpiHelper.h"
#include "solver/PetscTypes.h"

namespace AMDiS { namespace Parallel {

  PetscSolverGlobalMatrix::PetscSolverGlobalMatrix(string name)
    : PetscSolver(name),
      zeroStartVector(false),
      printMatInfo(false)
  {
    PetscParameters params;
    bool matSolverPackage = false;
    
    // set the solver
    std::string solverName = "petsc";
    Parameters::get(name, solverName);
    if (solverName == "petsc") 
      Parameters::get(name + "->ksp_type", solverName);
    
    std::string kspSolver = params.solverMap[solverName];
    
    if (params.matSolverPackage[kspSolver]) {
      // direct solvers
      PetscOptionsInsertString(("-" + kspPrefix + "ksp_type preonly").c_str());
      PetscOptionsInsertString(("-" + kspPrefix + "pc_type lu").c_str());
      PetscOptionsInsertString(("-" + kspPrefix + "pc_factor_mat_solver_package " + (kspSolver != "direct" ? kspSolver : "mumps")).c_str());
      setMaxIterations(1);
      zeroStartVector = true;
      matSolverPackage = true;
    } else if (!params.emptyParam[kspSolver]) {    
      // other solvers
      PetscOptionsInsertString(("-" + kspPrefix + "ksp_type " + kspSolver).c_str());
    }
    
    
    // set the preconditioner
    string precon = "";
    Parameters::get(name + "->pc_type", precon);
    if (!precon.size())
      Parameters::get(name + "->left precon", precon);
    if (!matSolverPackage && !params.emptyParam[precon]) {
      precon = (params.preconMap.find(precon) != params.preconMap.end() ? params.preconMap[precon] : precon);
      PetscOptionsInsertString(("-" + kspPrefix + "pc_type " + precon).c_str());
    }
    
    PetscOptionsInsertString(("-" + kspPrefix + "ksp_max_it " + boost::lexical_cast<std::string>(getMaxIterations())).c_str());
    PetscOptionsInsertString(("-" + kspPrefix + "ksp_rtol " + boost::lexical_cast<std::string>(getRelative())).c_str());    
    PetscOptionsInsertString(("-" + kspPrefix + "ksp_atol " + boost::lexical_cast<std::string>(getTolerance())).c_str());   
    
    if (getInfo() >= 20)
      PetscOptionsInsertString(("-" + kspPrefix + "ksp_monitor_true_residual").c_str());
    else if (getInfo() >= 10)
      PetscOptionsInsertString(("-" + kspPrefix + "ksp_monitor").c_str());
    
    if (!matSolverPackage) {
      Parameters::get("parallel->use zero start vector", zeroStartVector);
    }
    Parameters::get("parallel->print matrix info", printMatInfo);
  }


  void PetscSolverGlobalMatrix::fillPetscMatrix(Matrix<DOFMatrix*> *seqMat)
  {
    FUNCNAME("PetscSolverGlobalMatrix::fillPetscMatrix()");

    TEST_EXIT_DBG(meshDistributor)("No mesh distributor object defined!\n");
    TEST_EXIT_DBG(interiorMap)("No parallel mapping object defined!\n");
    TEST_EXIT_DBG(seqMat)("No DOF matrix defined!\n");
    
#if (DEBUG != 0)
    double wtime = MPI::Wtime();
#endif

    createMatVec(*seqMat);

    if (coarseSpaceMap.size()) {
      fillPetscMatrixWithCoarseSpace(seqMat);
      return;
    }
    
    // === Create PETSc vector (solution and a temporary vector). ===

#if (DEBUG != 0)
    MSG("Fill petsc matrix 1 needed %.5f seconds\n", MPI::Wtime() - wtime);
#endif

    // === Transfer values from DOF matrices to the PETSc matrix. === 

    int nComponents = seqMat->getNumRows();
    for (int i = 0; i < nComponents; i++)
      for (int j = 0; j < nComponents; j++)
	if ((*seqMat)[i][j])
	  setDofMatrix((*seqMat)[i][j], i, j);

#if (DEBUG != 0)
    MSG("Fill petsc matrix 2 needed %.5f seconds\n", MPI::Wtime() - wtime);
#endif

    matAssembly();

    if (printMatInfo) {
      MatInfo matInfo;
      MatGetInfo(getMatInterior(), MAT_GLOBAL_SUM, &matInfo);
      MSG("Matrix info:\n");
      MSG("  memory usage: %e MB\n", matInfo.memory / (1024.0 * 1024.0));
      MSG("  mallocs: %d\n", static_cast<int>(matInfo.mallocs));
      MSG("  nz allocated: %d\n", static_cast<int>(matInfo.nz_allocated));
      MSG("  nz used: %d\n", static_cast<int>(matInfo.nz_used));
      MSG("  nz unneeded: %d\n", static_cast<int>(matInfo.nz_unneeded));
    }


    // === Init PETSc solver and preconditioner objects. ===

    initSolver(kspInterior);
    KSPGetPC(kspInterior, &pcInterior);
    initPreconditioner(pcInterior);


#if (DEBUG != 0)
    MSG("Fill petsc matrix 3 needed %.5f seconds\n", MPI::Wtime() - wtime);
#endif


    // === For debugging allow to write the matrix to a file. ===

    bool dbgWriteMatrix = false;
    Parameters::get("parallel->debug->write matrix", dbgWriteMatrix);
    if (dbgWriteMatrix) {
      PetscViewer matView;
      PetscViewerBinaryOpen(PETSC_COMM_WORLD, "mpi.mat",
			    FILE_MODE_WRITE, &matView);
      MatView(getMatInterior(), matView);
      PetscViewerDestroy(&matView);
    }
  }


  void PetscSolverGlobalMatrix::fillPetscMatrixWithCoarseSpace(Matrix<DOFMatrix*> *seqMat)
  {
    FUNCNAME("PetscSolverGlobalMatrix::fillPetscMatrixWithCoarseSpace()");

    TEST_EXIT_DBG(interiorMap)("Should not happen!\n");
    TEST_EXIT_DBG(coarseSpaceMap.size() == seqMat->getSize())
      ("Wrong sizes %d %d\n", coarseSpaceMap.size(), seqMat->getSize());

    // === Prepare traverse of sequentially created matrices. ===

    using mtl::tag::row; using mtl::tag::nz; using mtl::begin; using mtl::end;
    namespace traits = mtl::traits;
    typedef DOFMatrix::base_matrix_type Matrix;

    typedef traits::range_generator<row, Matrix>::type cursor_type;
    typedef traits::range_generator<nz, cursor_type>::type icursor_type;

    vector<int> cols, colsOther;
    vector<double> values, valuesOther;
    cols.reserve(300);
    colsOther.reserve(300);
    values.reserve(300);
    valuesOther.reserve(300);

    bool localMatrix = 
      (meshDistributor->getMeshLevelData().getMpiComm(meshLevel) == MPI::COMM_SELF);

    // === Traverse all sequentially created matrices and add the values to ===
    // === the global PETSc matrices.                                       ===

    int nComponents = seqMat->getSize();
    for (int rowComponent = 0; rowComponent < nComponents; rowComponent++) {
      for (int colComponent = 0; colComponent < nComponents; colComponent++) {
	DOFMatrix* dofMat = (*seqMat)[rowComponent][colComponent];

	if (!dofMat)
	  continue;

	ParallelDofMapping *rowCoarseSpace = coarseSpaceMap[rowComponent];
	ParallelDofMapping *colCoarseSpace = coarseSpaceMap[colComponent];

	std::set<DegreeOfFreedom> &dirichletRows = dofMat->getDirichletRows();

	traits::col<Matrix>::type col(dofMat->getBaseMatrix());
	traits::const_value<Matrix>::type value(dofMat->getBaseMatrix());
	
	// Traverse all rows.
	for (cursor_type cursor = begin<row>(dofMat->getBaseMatrix()), 
	       cend = end<row>(dofMat->getBaseMatrix()); cursor != cend; ++cursor) {

	  bool isRowCoarse = isCoarseSpace(rowComponent, cursor.value());

	  // For the case, this is a dirichlet row we have to check whether the 
	  // rank is also owner of this row DOF.
	  if (dirichletRows.count(cursor.value())) {
	    if ((!isRowCoarse && !(*interiorMap)[rowComponent].isRankDof(cursor.value())) ||
		(isRowCoarse && !(*rowCoarseSpace)[rowComponent].isRankDof(cursor.value())))
	      continue;    
	  }
  
	  cols.clear();
	  colsOther.clear();
	  values.clear();	  
	  valuesOther.clear();

	  // Traverse all columns.
	  for (icursor_type icursor = begin<nz>(cursor), icend = end<nz>(cursor); 
	       icursor != icend; ++icursor) {

	    bool isColCoarse = isCoarseSpace(colComponent, col(*icursor));

	    if (isColCoarse == false)
	      if ((*interiorMap)[colComponent].isSet(col(*icursor)) == false)
		continue;

	    if (isColCoarse == isRowCoarse) {
	      cols.push_back(col(*icursor));
	      values.push_back(value(*icursor));
	    } else {
	      colsOther.push_back(col(*icursor));
	      valuesOther.push_back(value(*icursor));
	    }
	  }  // for each nnz in row


	  // === Set matrix values. ===

	  if (isRowCoarse) {
	    for (unsigned int i = 0; i < cols.size(); i++)
	      cols[i] = colCoarseSpace->getMatIndex(colComponent, cols[i]);

	    int rowIndex = rowCoarseSpace->getMatIndex(rowComponent, cursor.value());
	    MatSetValues(getMatCoarseByComponent(rowComponent, colComponent),
	    		 1, &rowIndex, cols.size(),
	    		 &(cols[0]), &(values[0]), ADD_VALUES);

	    if (colsOther.size()) {
	      for (unsigned int i = 0; i < colsOther.size(); i++)
		colsOther[i] = 
		  interiorMap->getMatIndex(colComponent, colsOther[i]) + 
		  rStartInterior;	      

	      MatSetValues(getMatCoarseInteriorByComponent(rowComponent), 
	       		   1, &rowIndex, colsOther.size(),
 	       		   &(colsOther[0]), &(valuesOther[0]), ADD_VALUES);
	    }
	  } else {
	    if ((*interiorMap)[rowComponent].isSet(cursor.value()) == false)
	      continue;

	    int localRowIndex = 
	      (localMatrix ? 
	       interiorMap->getLocalMatIndex(rowComponent, cursor.value()) :
	       interiorMap->getMatIndex(rowComponent, cursor.value()));

	    for (unsigned int i = 0; i < cols.size(); i++) {
	      if (localMatrix)
		cols[i] = interiorMap->getLocalMatIndex(colComponent, cols[i]);
	      else
		cols[i] = interiorMap->getMatIndex(colComponent, cols[i]);
	    }
	    
	    MatSetValues(getMatInterior(), 1, &localRowIndex, cols.size(),
  	     		 &(cols[0]), &(values[0]), ADD_VALUES);
	    
	    if (colsOther.size()) {
	      int globalRowIndex = 
		interiorMap->getMatIndex(rowComponent, cursor.value()) + rStartInterior;
      
	      for (unsigned int i = 0; i < colsOther.size(); i++)
		colsOther[i] = 
		  colCoarseSpace->getMatIndex(colComponent, colsOther[i]);

	      MatSetValues(getMatInteriorCoarseByComponent(colComponent), 
			   1, &globalRowIndex, colsOther.size(),
			   &(colsOther[0]), &(valuesOther[0]), ADD_VALUES);
	    }
	  }
	} 
      }
    }

    matAssembly();

    // === Create solver for the non primal (thus local) variables. ===

    KSPCreate(domainComm, &kspInterior);
    KSPSetOperators(kspInterior, getMatInterior(), getMatInterior(),
		    SAME_NONZERO_PATTERN);
    KSPSetOptionsPrefix(kspInterior, "interior_");
    KSPSetType(kspInterior, KSPPREONLY);
    KSPGetPC(kspInterior, &pcInterior);
    if (isSymmetric) {
      PCSetType(pcInterior, PCCHOLESKY);
      PCFactorSetMatSolverPackage(pcInterior, MATSOLVERMUMPS);
    } else {
      PCSetType(pcInterior, PCLU);
      if (localMatrix)
	PCFactorSetMatSolverPackage(pcInterior, MATSOLVERUMFPACK);
      else
	PCFactorSetMatSolverPackage(pcInterior, MATSOLVERMUMPS);
    }
    KSPSetFromOptions(kspInterior);
  }


  void PetscSolverGlobalMatrix::fillPetscRhs(SystemVector *vec)
  {
    FUNCNAME("PetscSolverGlobalMatrix::fillPetscRhs()");

    TEST_EXIT_DBG(vec)("No DOF vector defined!\n");
    TEST_EXIT_DBG(interiorMap)("No parallel DOF map defined!\n");
    
    // === Transfer values from DOF vector to the PETSc vector. === 
    if (coarseSpaceMap.size()) {
      for (int i = 0; i < vec->getSize(); i++)
	setDofVector(getVecRhsInterior(), 
		     getVecRhsCoarseByComponent(i), vec->getDOFVector(i), i);
    } else {
      for (int i = 0; i < vec->getSize(); i++)
	setDofVector(getVecRhsInterior(), vec->getDOFVector(i), i);
    }

    vecRhsAssembly();

    // === For debugging allow to write the rhs vector to a file. ===

    bool dbgWriteRhs = false;
    Parameters::get("parallel->debug->write rhs", dbgWriteRhs);
    if (dbgWriteRhs) {
      PetscViewer vecView;
      PetscViewerBinaryOpen(PETSC_COMM_WORLD, "mpi.vec",
			    FILE_MODE_WRITE, &vecView);
      VecView(getVecRhsInterior(), vecView);
      PetscViewerDestroy(&vecView);
    }
  }


  void PetscSolverGlobalMatrix::solvePetscMatrix(SystemVector &vec, 
						 AdaptInfo *adaptInfo)
  {
    FUNCNAME("PetscSolverGlobalMatrix::solvePetscMatrix()");

    int nComponents = vec.getSize();

    // === Set old solution to be initiual guess for PETSc solver. ===
    if (!zeroStartVector) {
      TEST_EXIT(coarseSpaceMap.size() == 0)("Not yet supported!\n");

      VecSet(getVecSolInterior(), 0.0);
      
      for (int i = 0; i < nComponents; i++)
	setDofVector(getVecSolInterior(), vec.getDOFVector(i), i, true);

      vecSolAssembly();
    }


    MatNullSpace matNullspace;
    Vec nullspaceBasis;
    if (nullspace.size() > 0 || 
	hasConstantNullspace ||
	constNullspaceComponent.size() > 0) {
      TEST_EXIT_DBG(nullspace.size() <= 1)("Not yet implemented!\n");

      if (constNullspaceComponent.size() > 0) {
	nullspace.clear();
	SystemVector *basisVec = new SystemVector(vec);
	basisVec->set(0.0);
	for (unsigned int i = 0; i < constNullspaceComponent.size(); i++)
	  basisVec->getDOFVector(constNullspaceComponent[i])->set(1.0);

	nullspace.push_back(basisVec);
      } 

      if (nullspace.size() > 0) {
	VecDuplicate(getVecSolInterior(), &nullspaceBasis);
	setDofVector(nullspaceBasis, *(nullspace[0]), true);
	
	VecAssemblyBegin(nullspaceBasis);
	VecAssemblyEnd(nullspaceBasis);

	VecNormalize(nullspaceBasis, PETSC_NULL);
	
	MatNullSpaceCreate(domainComm, (hasConstantNullspace ? PETSC_TRUE : PETSC_FALSE), 
			   1, &nullspaceBasis, &matNullspace);

	MatMult(getMatInterior(), nullspaceBasis, getVecSolInterior());
	PetscReal n;
	VecNorm(getVecSolInterior(), NORM_2, &n);
	MSG("NORM IS: %e\n", n);
      } else {
	MatNullSpaceCreate(domainComm, PETSC_TRUE, 0, PETSC_NULL, &matNullspace);
      }

      MSG("NULLSPACE IS NOT REMOVED!\n");
      // MatSetNullSpace(getMatInterior(), matNullspace);
      // KSPSetNullSpace(kspInterior, matNullspace);

      // === Remove null space, if requested. ===

      if (removeRhsNullspace) {
	TEST_EXIT_DBG(coarseSpaceMap.empty())("Not supported!\n");

	MSG("Remove nullspace from rhs vector.\n");
	
	MatNullSpaceRemove(matNullspace, getVecRhsInterior(), PETSC_NULL);
      }
    } else {
      TEST_EXIT(removeRhsNullspace == false)
	("No nullspace provided that should be removed from rhs!\n");
    }

    // PETSc.
    solve(getVecRhsInterior(), getVecSolInterior());


    if (nullspace.size() > 0) {
      MatNullSpaceDestroy(&matNullspace);
      VecDestroy(&nullspaceBasis);
    }


    // === Transfere values from PETSc's solution vectors to the DOF vectors. ===
    PetscScalar *vecPointer;
    VecGetArray(getVecSolInterior(), &vecPointer);    

    int c = 0;
    for (int component = 0; component < nComponents; component++) {
      DOFVector<double> &dv = *(vec.getDOFVector(component));

      DofMap& d = (*interiorMap)[component].getMap();
      for (DofMap::iterator it = d.begin(); it != d.end(); ++it)
	if (it->second.local != -1)
	  dv[it->first] = vecPointer[c++];
    }

    VecRestoreArray(getVecSolInterior(), &vecPointer);

    // === Synchronize DOFs at common DOFs, i.e., DOFs that correspond to ===  
    // === more than one partition.                                       ===  
    meshDistributor->synchVector(vec);
  }


  void PetscSolverGlobalMatrix::solveGlobal(Vec &rhs, Vec &sol)
  {
    FUNCNAME("PetscSolverGlobalMatrix::solveGlobal()");

    Vec tmp;
    if (domainComm.Get_size() == 1)
      createLocalVec(*interiorMap, tmp);
    else
      createVec(*interiorMap, tmp);

    PetscScalar *tmpValues, *rhsValues;
    VecGetArray(tmp, &tmpValues);
    VecGetArray(rhs, &rhsValues);

    for (int i = 0; i < interiorMap->getRankDofs(); i++)
      tmpValues[i] = rhsValues[i];

    VecRestoreArray(rhs, &rhsValues);
    VecRestoreArray(tmp, &tmpValues);

    KSPSolve(kspInterior, tmp, tmp);

    VecGetArray(tmp, &tmpValues);
    VecGetArray(sol, &rhsValues);

    for (int i = 0; i < interiorMap->getRankDofs(); i++) 
      rhsValues[i] = tmpValues[i];

    VecRestoreArray(sol, &rhsValues);
    VecRestoreArray(tmp, &tmpValues);

    VecDestroy(&tmp);
  }


  void PetscSolverGlobalMatrix::destroyMatrixData()
  {
    FUNCNAME("PetscSolverGlobalMatrix::destroyMatrixData()");

    matDestroy();

    exitPreconditioner(pcInterior);

    exitSolver(kspInterior);
  }


  void PetscSolverGlobalMatrix::destroyVectorData()
  {
    FUNCNAME("PetscSolverGlobalMatrix::destroyVectorData()");

    vecDestroy();
  }


  void PetscSolverGlobalMatrix::createFieldSplit(PC pc)
  {
    FUNCNAME("PetscSolverGlobalMatrix::createFieldSplit()");

    vector<string> isNames;
    Parameters::get("parallel->solver->is blocks", isNames);

    int nBlocks = isNames.size();
    if (nBlocks == 0)
      return;

    for (int i = 0; i < nBlocks; i++) {
      MSG("Create for block %s\n", isNames[i].c_str());

      vector<int> blockComponents;
      Parameters::get("parallel->solver->is block " + lexical_cast<string>(i),
		      blockComponents);
      int nComponents = static_cast<int>(blockComponents.size());

      TEST_EXIT(nComponents > 0)("No IS block for block %d defined!\n", i);

      // Check if blocks are continous
      for (int j = 0; j < nComponents; j++) {
	TEST_EXIT(blockComponents[j] == blockComponents[0] + j)
	  ("Does not yet support not continous IS blocks! Block %s\n", 
	   isNames[i].c_str());
      }

      createFieldSplit(pc, isNames[i].c_str(), blockComponents);
    }
  }


  void PetscSolverGlobalMatrix::createFieldSplit(PC pc, 
						 const char* splitName, 
						 vector<int> &components)
  {
    FUNCNAME("PetscSolverGlobalMatrix::createFieldSplit()");

    IS is;
    interiorMap->createIndexSet(is, components[0], components.size());
    PCFieldSplitSetIS(pc, splitName, is);
    ISDestroy(&is);
  }
  
  
  void PetscSolverGlobalMatrix::extractVectorComponent(Vec input, int i, Vec *output, int numberOfComponents)
  {
    FUNCNAME("PetscSolverGlobalMatrix::extractVectorComponent()");
    IS is;
    interiorMap->createIndexSet(is, i, numberOfComponents);
    VecGetSubVector(input, is, output);
    ISDestroy(&is);
  }

  void PetscSolverGlobalMatrix::extractMatrixComponent(Mat input, int startRow, int numberOfRows, int startCol, int numberOfCols, Mat *output)
  {
    FUNCNAME("PetscSolverGlobalMatrix::extractMatrixComponent()");
    IS isrow, iscol;
    interiorMap->createIndexSet(isrow, startRow, numberOfRows);
    interiorMap->createIndexSet(iscol, startCol, numberOfCols);
    MatGetSubMatrix(input, isrow, iscol, MAT_INITIAL_MATRIX, output);
    ISDestroy(&iscol);
    ISDestroy(&isrow);
  }
  

  void PetscSolverGlobalMatrix::initSolver(KSP &ksp)
  {
    FUNCNAME("PetscSolverGlobalMatrix::initSolver()");

    KSPCreate(domainComm, &ksp);
    KSPSetOperators(ksp, getMatInterior(), getMatInterior(), 
		    SAME_NONZERO_PATTERN); 
    KSPSetTolerances(ksp, 0.0, 1e-8, PETSC_DEFAULT, PETSC_DEFAULT);
    KSPSetType(ksp, KSPBCGS);
    KSPSetOptionsPrefix(ksp, kspPrefix.c_str());
    KSPSetFromOptions(ksp);

    // Do not delete the solution vector, use it for the initial guess.
    if (!zeroStartVector)
      KSPSetInitialGuessNonzero(ksp, PETSC_TRUE);
  }  


  void PetscSolverGlobalMatrix::exitSolver(KSP &ksp)
  {
    FUNCNAME("PetscSolverGlobalMatrix::exitSolver()");

    KSPDestroy(&ksp);
  }  


  void PetscSolverGlobalMatrix::initPreconditioner(PC pc)
  {
    FUNCNAME("PetscSolverGlobalMatrix::initPreconditioner()");

    PCSetFromOptions(pc);
    createFieldSplit(pc);
  }

 
  void PetscSolverGlobalMatrix::exitPreconditioner(PC pc)
  {
    FUNCNAME("PetscSolverGlobalMatrix::exitPreconditioner()");
  }


  void PetscSolverGlobalMatrix::setDofMatrix(DOFMatrix* seqMat,
					     int rowComp, int colComp)
  {
    FUNCNAME("PetscSolverGlobalMatrix::setDofMatrix()");

    TEST_EXIT(seqMat)("No DOFMatrix!\n");

    using mtl::tag::row; using mtl::tag::nz; using mtl::begin; using mtl::end;
    namespace traits = mtl::traits;
    typedef DOFMatrix::base_matrix_type Matrix;

    traits::col<Matrix>::type col(seqMat->getBaseMatrix());
    traits::const_value<Matrix>::type value(seqMat->getBaseMatrix());

    typedef traits::range_generator<row, Matrix>::type cursor_type;
    typedef traits::range_generator<nz, cursor_type>::type icursor_type;

    vector<int> cols;
    vector<double> values;
    cols.reserve(300);
    values.reserve(300);
    
    vector<int> globalCols;

    // Get periodic mapping object
    PeriodicMap &perMap = meshDistributor->getPeriodicMap();
    std::set<DegreeOfFreedom> &dirichletRows = seqMat->getDirichletRows();
      
    const FiniteElemSpace *rowFe = seqMat->getRowFeSpace();
    const FiniteElemSpace *colFe = seqMat->getColFeSpace();

    // === Traverse all rows of the DOF matrix and insert row wise the values ===
    // === to the PETSc matrix.                                               ===

    for (cursor_type cursor = begin<row>(seqMat->getBaseMatrix()), 
	   cend = end<row>(seqMat->getBaseMatrix()); cursor != cend; ++cursor) {
      // Global index of the current row DOF.
      MultiIndex rowMultiIndex;
      if ((*interiorMap)[rowComp].find(cursor.value(), rowMultiIndex) == false)
	continue;

      int globalRowDof = rowMultiIndex.global;

      // Test if the current row DOF is a periodic DOF.
      bool periodicRow = perMap.isPeriodic(rowFe, globalRowDof);

      // Dirichlet rows can be set only be the owner ranks.
      if (dirichletRows.count(cursor.value()) && !((*interiorMap)[rowComp].isRankDof(cursor.value())))
	continue;

      if (!periodicRow) {
	// === Row DOF index is not periodic. ===

	// Get PETSc's mat row index.
	int rowIndex = interiorMap->getMatIndex(rowComp, globalRowDof);

	cols.clear();
	values.clear();

	for (icursor_type icursor = begin<nz>(cursor), icend = end<nz>(cursor); 
	     icursor != icend; ++icursor) {

	  // Global index of the current column index.
	  MultiIndex colMultiIndex;
	  if ((*interiorMap)[colComp].find(col(*icursor), colMultiIndex) == false)
	    continue;

	  int globalColDof = colMultiIndex.global;
	  // Test if the current col dof is a periodic dof.
	  bool periodicCol = perMap.isPeriodic(colFe, globalColDof);
	  // Get PETSc's mat col index.
	  int colIndex = interiorMap->getMatIndex(colComp, globalColDof);

	  // Ignore all zero entries, expect it is a diagonal entry.
 	  if (value(*icursor) == 0.0 && rowIndex != colIndex)
 	    continue;

	  if (!periodicCol) {
	    // Calculate the exact position of the column index in the PETSc matrix.
 	    cols.push_back(colIndex);
 	    values.push_back(value(*icursor));
	  } else {
	    // === Row index is not periodic, but column index is. ===

	    // Create set of all periodic associations of the column index.
	    std::set<int> perAsc;
	    perMap.fillAssociations(colFe, globalColDof, 
				    meshDistributor->getElementObjectDb(), perAsc);

	    // Scale value to the number of periodic associations of the column index.
	    double scaledValue = 
	      value(*icursor) * pow(0.5, static_cast<double>(perAsc.size()));

	    
	    // === Create set of all matrix column indices due to the periodic ===
	    // === associations of the column DOF index.                       ===

	    vector<int> newCols;
	    perMap.mapDof(colFe, globalColDof, perAsc, newCols);
	    for (unsigned int i = 0; i < newCols.size(); i++) {
	      cols.push_back(interiorMap->getMatIndex(colComp, newCols[i]));
	      values.push_back(scaledValue);	      
	    }
	  }
	}

  	MatSetValues(getMatInterior(), 1, &rowIndex, cols.size(), 
  		     &(cols[0]), &(values[0]), ADD_VALUES);	
      } else {
	// === Row DOF index is periodic. ===

	// Because this row is periodic, we will have to add the entries of this 
	// matrix row to multiple rows. The following maps store to each row an
	// array of column indices and values of the entries that must be added to
	// the PETSc matrix.
	map<int, vector<int> > colsMap;
	map<int, vector<double> > valsMap;

	// Traverse all column entries.
	for (icursor_type icursor = begin<nz>(cursor), icend = end<nz>(cursor); 
	     icursor != icend; ++icursor) {
	  // Global index of the current column index.
	  int globalColDof = (*interiorMap)[colComp][col(*icursor)].global;

	  // Ignore all zero entries, expect it is a diagonal entry.
 	  if (value(*icursor) == 0.0 && globalRowDof != globalColDof)
 	    continue;

	  // === Add all periodic associations of both, the row and the column ===
	  // === indices to the set perAsc.                                    ===

	  std::set<int> perAsc;
	  perMap.fillAssociations(colFe, globalColDof, 
				  meshDistributor->getElementObjectDb(), perAsc);
	  perMap.fillAssociations(rowFe, globalRowDof, 
				  meshDistributor->getElementObjectDb(), perAsc);

	  // Scale the value with respect to the number of periodic associations.
	  double scaledValue = 
	    value(*icursor) * pow(0.5, static_cast<double>(perAsc.size()));


	  // === Create all matrix entries with respect to the periodic  ===
	  // === associations of the row and column indices.             ===

	  vector<pair<int, int> > entry;
	  perMap.mapDof(rowFe, colFe, make_pair(globalRowDof, globalColDof),
			perAsc, entry);

	  // === Translate the matrix entries to PETSc's matrix.

	  for (unsigned int i = 0; i < entry.size(); i++) {
	    int rowIdx = interiorMap->getMatIndex(rowComp, entry[i].first);
	    int colIdx = interiorMap->getMatIndex(colComp, entry[i].second);

	    colsMap[rowIdx].push_back(colIdx);
	    valsMap[rowIdx].push_back(scaledValue);
	  }
	}


	// === Finally, add all periodic rows to the PETSc matrix. ===

	for (map<int, vector<int> >::iterator rowIt = colsMap.begin();
	     rowIt != colsMap.end(); ++rowIt) {
	  TEST_EXIT_DBG(rowIt->second.size() == valsMap[rowIt->first].size())
	    ("Should not happen!\n");

	  int rowIndex = rowIt->first;

	  MatSetValues(getMatInterior(), 1, &rowIndex, rowIt->second.size(),
		       &(rowIt->second[0]), &(valsMap[rowIt->first][0]), ADD_VALUES);
	}
      }
    }
  }


  void PetscSolverGlobalMatrix::setDofVector(Vec vecInterior, 
					     Vec vecCoarse,
					     DOFVector<double>* vec, 
					     int rowComp, 
					     bool rankOnly)
  {
    FUNCNAME("PetscSolverGlobalMatrix::setDofVector()");

    const FiniteElemSpace *feSpace = vec->getFeSpace();
    PeriodicMap &perMap = meshDistributor->getPeriodicMap();

    ParallelDofMapping *rowCoarseSpace = 
      (coarseSpaceMap.size() ? coarseSpaceMap[rowComp] : NULL);

    map<DegreeOfFreedom, double> &dirichletValues = vec->getDirichletValues();

    // Traverse all used DOFs in the dof vector.
    DOFVector<double>::Iterator dofIt(vec, USED_DOFS);
    for (dofIt.reset(); !dofIt.end(); ++dofIt) {
      
      DegreeOfFreedom dof = dofIt.getDOFIndex();

      if (rankOnly && !(*interiorMap)[rowComp].isRankDof(dof))
	continue;

      bool isCoarseDof = isCoarseSpace(rowComp, dof);

      // Dirichlet rows can be set only be the owner ranks.
      if (dirichletValues.count(dof)) {
	if ((!isCoarseDof && !((*interiorMap)[rowComp].isRankDof(dof))) ||
	    (isCoarseDof && !((*rowCoarseSpace)[rowComp].isRankDof(dof))))
	  continue;
      }

      if (isCoarseDof) {
	TEST_EXIT_DBG(vecCoarse != PETSC_NULL)("Should not happen!\n");

	int index = rowCoarseSpace->getMatIndex(rowComp, dof);
	VecSetValue(vecCoarse, index, *dofIt, ADD_VALUES);
      } else {
	if ((*interiorMap)[rowComp].isSet(dof) == false)
	  continue;

	// Calculate global row index of the DOF.
	DegreeOfFreedom globalRowDof = (*interiorMap)[rowComp][dof].global;
	
	// Get PETSc's mat index of the row DOF.
	int index = 0;
	if (interiorMap->isMatIndexFromGlobal())
	  index = 
	    interiorMap->getMatIndex(rowComp, globalRowDof) + rStartInterior;
	else
	  index =
	    interiorMap->getMatIndex(rowComp, dof) + rStartInterior;

	if (perMap.isPeriodic(feSpace, globalRowDof)) {
	  std::set<int>& perAsc = perMap.getAssociations(feSpace, globalRowDof);
	  double value = *dofIt / (perAsc.size() + 1.0);
	  VecSetValue(vecInterior, index, value, ADD_VALUES);

	  for (std::set<int>::iterator perIt = perAsc.begin(); 
	       perIt != perAsc.end(); ++perIt) {
	    int mappedDof = perMap.map(feSpace, *perIt, globalRowDof);
	    int mappedIndex = interiorMap->getMatIndex(rowComp, mappedDof);

	    VecSetValue(vecInterior, mappedIndex, value, ADD_VALUES);
	  }	  
	} else {	  
	  // The DOF index is not periodic.
	  VecSetValue(vecInterior, index, *dofIt, ADD_VALUES);
	}
      }
    }
  }


  PetscSolver* PetscSolverGlobalMatrix::createSubSolver(int component,
							string kspPrefix)
  {
    FUNCNAME("PetscSolverGlobalMatrix::createSubSolver()");

    vector<const FiniteElemSpace*> fe;
    fe.push_back(componentSpaces[component]);

    PetscSolver* subSolver = new PetscSolverGlobalMatrix("");
    subSolver->setKspPrefix(kspPrefix);
    subSolver->setMeshDistributor(meshDistributor, 0);
    subSolver->init(fe, fe);

    ParallelDofMapping &subDofMap = subSolver->getDofMap();
    subDofMap[0] = dofMap[component];
    subDofMap.update();

    return subSolver;
  }


  void PetscSolverGlobalMatrix::setConstantNullSpace(KSP ksp,
						     int constFeSpace,
						     bool test)
  {
    FUNCNAME("PetscSolverGlobalMatrix::setConstantNullSpace()");

    Vec nullSpaceBasis;
    VecDuplicate(getVecSolInterior(), &nullSpaceBasis);
    
    SystemVector basisVec("tmp", componentSpaces, componentSpaces.size(), true);
    basisVec.set(0.0);
    basisVec.getDOFVector(constFeSpace)->set(1.0);
    
    setDofVector(nullSpaceBasis, basisVec, true);
    VecAssemblyBegin(nullSpaceBasis);
    VecAssemblyEnd(nullSpaceBasis);
    VecNormalize(nullSpaceBasis, PETSC_NULL);
    
    if (test) {
      Vec tmp;
      MatGetVecs(getMatInterior(), &tmp, PETSC_NULL);
      MatMult(getMatInterior(), nullSpaceBasis,