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/PetscHelper.h"
#include "parallel/StdMpi.h"
#include "parallel/MpiHelper.h"
#include "solver/PetscTypes.h"

using namespace std;

namespace AMDiS { namespace Parallel {

  PetscSolverGlobalMatrix::PetscSolverGlobalMatrix(string name, bool setOptions)
    : PetscSolver(name),
      zeroStartVector(false),
      printMatInfo(false)
  { FUNCNAME_DBG("PetscSolverGlobalMatrix()");

    bool matSolverPackage = false;
    if (setOptions) {
      PetscParameters params;

      // 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.find(kspSolver) != params.matSolverPackage.end()) {
	// direct solvers
	petsc::options_insert_string(("-" + kspPrefix + "ksp_type preonly").c_str());
	petsc::options_insert_string(("-" + kspPrefix + "pc_type lu").c_str());
	petsc::options_insert_string(("-" + kspPrefix + "pc_factor_mat_solver_package " + kspSolver).c_str());
	setMaxIterations(1);
	zeroStartVector = true;
	matSolverPackage = true;
      } else if (params.emptyParam.find(kspSolver) == params.emptyParam.end() && solverName != "petsc") {
	// other solvers
	petsc::options_insert_string(("-" + 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 (!precon.size())
	Parameters::get(name + "->right precon", precon);
      if (!matSolverPackage && params.emptyParam.find(precon) == params.emptyParam.end()) {
	precon = (params.preconMap.find(precon) != params.preconMap.end() ? params.preconMap[precon] : precon);
	petsc::options_insert_string(("-" + kspPrefix + "pc_type " + precon).c_str());
      }

      petsc::options_insert_string(("-" + kspPrefix + "ksp_max_it " + boost::lexical_cast<std::string>(getMaxIterations())).c_str());
      petsc::options_insert_string(("-" + kspPrefix + "ksp_rtol " + boost::lexical_cast<std::string>(getRelative())).c_str());
      petsc::options_insert_string(("-" + kspPrefix + "ksp_atol " + boost::lexical_cast<std::string>(getTolerance())).c_str());

      if (getInfo() >= 20)
	petsc::options_insert_string(("-" + kspPrefix + "ksp_monitor_true_residual").c_str());
      else if (getInfo() >= 10)
	petsc::options_insert_string(("-" + kspPrefix + "ksp_monitor").c_str());
    }
    if (!matSolverPackage) {
      Parameters::get(name + "->use zero start vector", zeroStartVector);
    }
    Parameters::get("parallel->print matrix info", printMatInfo);

#ifndef NDEBUG
    bool printOptionsInfo = false;
    Parameters::get("parallel->debug->print options info", printOptionsInfo);
    if (printOptionsInfo) {
    MSG("PetscOptionsView:\n");
    PetscViewer viewer;
    PetscViewerCreate(PETSC_COMM_WORLD, &viewer);
    PetscViewerSetType(viewer, PETSCVIEWERASCII);
    petsc::options_view(viewer);
    PetscViewerDestroy(&viewer);

    }
#endif
  }


  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");

#ifndef NDEBUG
    Timer t;
#endif

    createMatVec(*seqMat);

    if (coarseSpaceMap.size()) {
      fillPetscMatrixWithCoarseSpace(seqMat);
      return;
    }

    // === Create PETSc vector (solution and a temporary vector). ===

#ifndef NDEBUG
    MSG("Fill petsc matrix 1 needed %.5f seconds\n", t.elapsed());
    t.reset();
#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);

#ifndef NDEBUG
    MSG("Fill petsc matrix 2 needed %.5f seconds\n", t.elapsed());
    t.reset();
#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(*seqMat, mat[0][0]);


#ifndef NDEBUG
    MSG("Fill petsc matrix 3 needed %.5f seconds\n", t.elapsed());
#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_DBG("PetscSolverGlobalMatrix::fillPetscMatrixWithCoarseSpace()");

    TEST_EXIT_DBG(interiorMap)("No interiorMap! Should not happen!\n");
    TEST_EXIT_DBG(coarseSpaceMap.size() == (size_t)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);
    petsc::ksp_set_operators(kspInterior, getMatInterior(), getMatInterior());
    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_DBG("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);
    }
  }


  /// 1.) set startsolution
  /// 2.) create null-space
  /// 3.) solve Ax=b
  /// 4.) destroy null-space
  /// 5.) transfer solution back to DOFVector
  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;
    SystemVector *basisVec;
    if (nullspace.size() > 0 ||
	hasConstantNullspace ||
	constNullspaceComponent.size() > 0) {
      TEST_EXIT_DBG(nullspace.size() <= 1)("Not yet implemented!\n");

      if (constNullspaceComponent.size() > 0) {
	nullspace.clear();
        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");
	petsc::mat_nullspace_remove(matNullspace, getVecRhsInterior());
      }
    } else {
      TEST_EXIT(removeRhsNullspace == false)
	("No nullspace provided that should be removed from rhs!\n");
    }

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

    // delete PETSc stuff
    if (nullspace.size() > 0) {
      MatNullSpaceDestroy(&matNullspace);
      VecDestroy(&nullspaceBasis);
    }
    
    // delete allocated memory
    if ((nullspace.size() > 0 || hasConstantNullspace) && constNullspaceComponent.size() > 0) {
	delete basisVec;
    }

    // === 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)
  {
    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()
  {
    matDestroy();

    exitPreconditioner(pcInterior);
    exitSolver(kspInterior);
  }


  void 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 " + boost::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)
  {
    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)
  {
    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)
  {
    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)
  {
    KSPCreate(domainComm, &ksp);
    petsc::ksp_set_operators(ksp, getMatInterior(), getMatInterior());
    KSPSetTolerances(ksp, 0.0, 1e-8, PETSC_DEFAULT, PETSC_DEFAULT);
    KSPSetType(ksp, KSPBCGS);
    KSPSetOptionsPrefix(ksp, kspPrefix.c_str());
    MatSetOptionsPrefix(getMatInterior(), 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)
  {
    KSPDestroy(&ksp);
  }


  void PetscSolverGlobalMatrix::initPreconditioner(PC pc)
  {
    PCSetFromOptions(pc);
    createFieldSplit(pc);
  }


  void PetscSolverGlobalMatrix::exitPreconditioner(PC pc)
  { }


  /// called by \ref fillPetscMatrix
  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);

    // Get periodic mapping object
    PeriodicMap &perMap = meshDistributor->getPeriodicMap();
    std::map<int, int> associatedRows;
    std::set<DegreeOfFreedom> &dirichletRows = seqMat->getDirichletRows();

    const FiniteElemSpace *rowFe = seqMat->getRowFeSpace();
    const FiniteElemSpace *colFe = seqMat->getColFeSpace();

    for (cursor_type cursor = begin<row>(seqMat->getBaseMatrix()),
         cend = end<row>(seqMat->getBaseMatrix()); cursor != cend; ++cursor) {
      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;

      int rowIndex = interiorMap->getMatIndex(rowComp, globalRowDof);
      int assRowIndex = -1;

      if (periodicRow) {
        std::set<int> perAsc;
        perMap.fillAssociations(rowFe, globalRowDof,
                          meshDistributor->getElementObjectDb(), perAsc);

        vector<int> newRows;
        perMap.mapDof(rowFe, globalRowDof, perAsc, newRows);

        assRowIndex = interiorMap->getMatIndex(rowComp,
                                *std::max_element(newRows.begin(),newRows.end()));
      }

      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;
        // Get PETSc's mat col index.
        int colIndex = interiorMap->getMatIndex(colComp, globalColDof);

        cols.push_back(colIndex);
        values.push_back(value(*icursor));
          }

          if (!periodicRow || assRowIndex == rowIndex)
        MatSetValues(getMatInterior(), 1, &rowIndex, cols.size(),
                &(cols[0]), &(values[0]), ADD_VALUES);
          else {
        MatSetValues(getMatInterior(), 1, &assRowIndex, cols.size(),
                &(cols[0]), &(values[0]), ADD_VALUES);

        associatedRows.insert(std::make_pair(rowIndex, assRowIndex));
          }
        }

        int globalPeriodic = associatedRows.size();
        Parallel::mpi::globalAdd(globalPeriodic);

        if (globalPeriodic) {

          MatAssemblyBegin(getMatInterior(), MAT_FLUSH_ASSEMBLY);
          MatAssemblyEnd(getMatInterior(), MAT_FLUSH_ASSEMBLY);

          int c[2]; double v[2] = {1.0, -1.0};

          std::map<int, int>::iterator mapIt = associatedRows.begin();
          for (;mapIt != associatedRows.end(); mapIt++) {
        c[0] = mapIt->first;
        c[1] = mapIt->second;

        MatSetValues(getMatInterior(), 1, &c[0], 2, c, v, INSERT_VALUES);
      }

      MatAssemblyBegin(getMatInterior(), MAT_FLUSH_ASSEMBLY);
      MatAssemblyEnd(getMatInterior(), MAT_FLUSH_ASSEMBLY);
    }
  }


  /// called by \ref fillPetscRhs
  void PetscSolverGlobalMatrix::setDofVector(Vec vecInterior,
					     Vec vecCoarse,
					     DOFVector<double>* vec,
					     int rowComp,
					     bool rankOnly)
  {
    FUNCNAME_DBG("PetscSolverGlobalMatrix::setDofVector()");

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

    std::set<int> associatedRows;

    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);