PetscSolverGlobalMatrix.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 "AMDiS.h"
#include "parallel/PetscSolverGlobalMatrix.h"
#include "parallel/StdMpi.h"
#include "parallel/MpiHelper.h"

namespace AMDiS {

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

    petscData.init(interiorMap, coarseSpaceMap, 
		   subdomainLevel, mpiCommLocal, mpiCommGlobal,
		   meshDistributor);
    petscData.create();

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

    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");
    
    double wtime = MPI::Wtime();

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

    int nRankRows = interiorMap->getRankDofs();
    int nOverallRows = interiorMap->getOverallDofs();

    VecCreateMPI(mpiCommGlobal, nRankRows, nOverallRows, &petscSolVec);


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

#if (DEBUG != 0)
    int a, b;
    MatGetOwnershipRange(petscData.getInteriorMat(), &a, &b);
    TEST_EXIT(a == interiorMap->getStartDofs())("Wrong matrix ownership range!\n");
    TEST_EXIT(b == interiorMap->getStartDofs() + nRankRows)
      ("Wrong matrix ownership range!\n");
#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

    petscData.assembly();
    
    if (printMatInfo) {
      MatInfo matInfo;
      MatGetInfo(petscData.getInteriorMat(), 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));
    }

    // === Remove Dirichlet BC DOFs. ===

    //    removeDirichletBcDofs(mat);
    

    // === Init PETSc solver. ===

    KSPCreate(mpiCommGlobal, &kspInterior);
    KSPGetPC(kspInterior, &pcInterior);
    KSPSetOperators(kspInterior, 
		    petscData.getInteriorMat(), 
		    petscData.getInteriorMat(), 
		    SAME_NONZERO_PATTERN); 
    KSPSetTolerances(kspInterior, 0.0, 1e-8, PETSC_DEFAULT, PETSC_DEFAULT);
    KSPSetType(kspInterior, KSPBCGS);
    KSPSetOptionsPrefix(kspInterior, kspPrefix.c_str());
    KSPSetFromOptions(kspInterior);

    initPreconditioner(pcInterior);

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

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


  void PetscSolverGlobalMatrix::fillPetscMatrix(DOFMatrix *mat)
  {
    Matrix<DOFMatrix*> m(1, 1);
    m[0][0] = mat;
    fillPetscMatrix(&m);
  }


  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());

    vector<const FiniteElemSpace*> feSpaces = getFeSpaces(seqMat);

    int nRowsRankInterior = interiorMap->getRankDofs();
    int nRowsOverallInterior = interiorMap->getOverallDofs();


    // === 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);

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

    int nComponents = seqMat->getSize();
    for (int i = 0; i < nComponents; i++) {
      for (int j = 0; j < nComponents; j++) {
	if (!(*seqMat)[i][j])
	  continue;

	ParallelDofMapping *rowCoarseSpace = coarseSpaceMap[i];
	ParallelDofMapping *colCoarseSpace = coarseSpaceMap[j];

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

	  bool isRowCoarse = isCoarseSpace(i, feSpaces[i], *cursor);
  
	  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(j, feSpaces[j], col(*icursor));

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


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

	  if (isRowCoarse) {
	    int rowIndex = rowCoarseSpace->getMatIndex(i, *cursor);
	    for (unsigned int k = 0; k < cols.size(); k++)
	      cols[k] = colCoarseSpace->getMatIndex(j, cols[k]);

	    // matCoarseCoarse
	    MatSetValues(petscData.getCoarseMatComp(i),
			 1, &rowIndex, cols.size(),
			 &(cols[0]), &(values[0]), ADD_VALUES);

	    if (colsOther.size()) {
	      if (subdomainLevel == 0) {
		for (unsigned int k = 0; k < colsOther.size(); k++)
		  colsOther[k] = interiorMap->getMatIndex(j, colsOther[k]);
	      } else {
		for (unsigned int k = 0; k < colsOther.size(); k++)
		  colsOther[k] = 
		    interiorMap->getMatIndex(j, colsOther[k]) + rStartInterior;
	      }

	      // matCoarseInt
	      MatSetValues(petscData.getCoarseIntMatComp(i), 
			   1, &rowIndex, colsOther.size(),
 			   &(colsOther[0]), &(valuesOther[0]), ADD_VALUES);
	    }
	  } else {
	    int localRowIndex = 
	      (subdomainLevel == 0 ? interiorMap->getLocalMatIndex(i, *cursor) :
	       interiorMap->getMatIndex(i, *cursor));

	    for (unsigned int k = 0; k < cols.size(); k++) {
	      if (subdomainLevel == 0)
		cols[k] = interiorMap->getLocalMatIndex(j, cols[k]);
	      else
		cols[k] = interiorMap->getMatIndex(j, cols[k]);
	    }
	    
  	    MatSetValues(petscData.getInteriorMat(), 1, &localRowIndex, cols.size(),
  			 &(cols[0]), &(values[0]), ADD_VALUES);

	    if (colsOther.size()) {
	      int globalRowIndex = interiorMap->getMatIndex(i, *cursor);

	      if (subdomainLevel != 0)
		globalRowIndex += rStartInterior;

	      for (unsigned int k = 0; k < colsOther.size(); k++)
		colsOther[k] = colCoarseSpace->getMatIndex(j, colsOther[k]);

	      // matIntCoarse
  	      MatSetValues(petscData.getIntCoarseMatComp(i), 
			   1, &globalRowIndex, colsOther.size(),
  			   &(colsOther[0]), &(valuesOther[0]), ADD_VALUES);
	    }
	  }
	} 
      }
    }

    petscData.assembly();

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

    KSPCreate(mpiCommLocal, &kspInterior);
    KSPSetOperators(kspInterior, 
		    petscData.getInteriorMat(),
		    petscData.getInteriorMat(),
		    SAME_NONZERO_PATTERN);
    KSPSetOptionsPrefix(kspInterior, "interior_");
    KSPSetType(kspInterior, KSPPREONLY);
    KSPGetPC(kspInterior, &pcInterior);
    PCSetType(pcInterior, PCLU);
    if (subdomainLevel == 0)
      PCFactorSetMatSolverPackage(pcInterior, MATSOLVERUMFPACK);
    else
      PCFactorSetMatSolverPackage(pcInterior, MATSOLVERMUMPS);
    KSPSetFromOptions(kspInterior);  
  }


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

    VecCreateMPI(mpiCommGlobal, 
		 interiorMap->getRankDofs(), 
		 nGlobalOverallInterior,
		 &rhsInterior);

    if (coarseSpaceMap.size()) 
      VecCreateMPI(mpiCommGlobal, 
		   coarseSpaceMap[0]->getRankDofs(), 
		   coarseSpaceMap[0]->getOverallDofs(),
		   &rhsCoarseSpace);
    
    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(rhsInterior, rhsCoarseSpace, vec->getDOFVector(i), i);
    } else {
      for (int i = 0; i < vec->getSize(); i++)
	setDofVector(rhsInterior, vec->getDOFVector(i), i);
    }

    VecAssemblyBegin(rhsInterior);
    VecAssemblyEnd(rhsInterior);

    if (coarseSpaceMap.size()) {
      VecAssemblyBegin(rhsCoarseSpace);
      VecAssemblyEnd(rhsCoarseSpace);
    }


    // === Remove Dirichlet BC DOFs. ===
    //    removeDirichletBcDofs(vec);
 
  }


  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) {
      VecSet(petscSolVec, 0.0);
      
      for (int i = 0; i < nComponents; i++)
	setDofVector(petscSolVec, vec.getDOFVector(i), i, true);
      
      VecAssemblyBegin(petscSolVec);
      VecAssemblyEnd(petscSolVec);
    }


    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(petscSolVec, &nullspaceBasis);
	for (int i = 0; i < nComponents; i++)
	  setDofVector(nullspaceBasis, nullspace[0]->getDOFVector(i), i, true);
	
	VecAssemblyBegin(nullspaceBasis);
	VecAssemblyEnd(nullspaceBasis);

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

	MatMult(petscData.getInteriorMat(), nullspaceBasis, petscSolVec);
	PetscReal n;
	VecNorm(petscSolVec, NORM_2, &n);
	MSG("NORM IS: %e\n", n);
      } else {
	MatNullSpaceCreate(mpiCommGlobal, PETSC_TRUE, 0, PETSC_NULL, &matNullspace);
      }

      MatSetNullSpace(petscData.getInteriorMat(), 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, rhsInterior, PETSC_NULL);
      }
    } else {
      TEST_EXIT(removeRhsNullspace == false)
	("No nullspace provided that should be removed from rhs!\n");
    }

    // PETSc.
    solve(rhsInterior, petscSolVec);


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


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

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

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

    VecRestoreArray(petscSolVec, &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()");

    double wtime = MPI::Wtime();
    double t0 = 0.0, t1 = 0.0;

    Vec tmp;
    if (mpiCommLocal.Get_size() == 1)
      VecCreateSeq(mpiCommLocal, interiorMap->getRankDofs(), &tmp);
    else
      VecCreateMPI(mpiCommLocal,
		   interiorMap->getRankDofs(),
		   interiorMap->getOverallDofs(),
		   &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);

    t0 = MPI::Wtime() - wtime;

    wtime = MPI::Wtime();
    KSPSolve(kspInterior, tmp, tmp);
    t1 = MPI::Wtime() - wtime;

    wtime = MPI::Wtime();

    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);
    t0 += MPI::Wtime() - wtime;

    //    MSG("TIMEING: %.5f %.5f\n", t0, t1);
  }


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

    exitPreconditioner(pcInterior);

    petscData.destroy();

    KSPDestroy(&kspInterior);

    if (petscSolVec != PETSC_NULL) {
      VecDestroy(&petscSolVec);
      petscSolVec = PETSC_NULL;
    }
  }


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

    VecDestroy(&rhsInterior);

    if (coarseSpaceMap.size())
      VecDestroy(&rhsCoarseSpace);
  }


  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());
      }

      IS is;
      interiorMap->createIndexSet(is, blockComponents[0], nComponents);
      PCFieldSplitSetIS(pc, isNames[i].c_str(), is);
      ISDestroy(&is);
    }
  }


  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 nRowMat, int nColMat)
  {
    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();

    const FiniteElemSpace *rowFe = seqMat->getRowFeSpace();
    const FiniteElemSpace *colFe = seqMat->getColFeSpace();
    DofMap& rowMap = (*interiorMap)[rowFe].getMap();
    DofMap& colMap = (*interiorMap)[colFe].getMap();

    // === 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.
      int globalRowDof = rowMap[*cursor].global;

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

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

	// Get PETSc's mat row index.
	int rowIndex = interiorMap->getMatIndex(nRowMat, 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.
	  int globalColDof = colMap[col(*icursor)].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(nColMat, 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(nColMat, newCols[i]));
	      values.push_back(scaledValue);	      
	    }
	  }
	}

  	MatSetValues(petscData.getInteriorMat(), 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)[colFe][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(nRowMat, entry[i].first);
	    int colIdx = interiorMap->getMatIndex(nColMat, 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(petscData.getInteriorMat(), 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 nRowVec, 
					     bool rankOnly)
  {
    FUNCNAME("PetscSolverGlobalMatrix::setDofVector()");

    const FiniteElemSpace *feSpace = vec->getFeSpace();
    PeriodicMap &perMap = meshDistributor->getPeriodicMap();
    
    ParallelDofMapping *rowCoarseSpace = NULL;
    if (coarseSpaceMap.size())
      rowCoarseSpace = coarseSpaceMap[nRowVec];

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

      if (rankOnly && !(*interiorMap)[feSpace].isRankDof(dofIt.getDOFIndex()))
	continue;

      if (isCoarseSpace(nRowVec, feSpace, dofIt.getDOFIndex())) {
	TEST_EXIT_DBG(vecCoarse != PETSC_NULL)("Should not happen!\n");

	int index = rowCoarseSpace->getMatIndex(nRowVec, dofIt.getDOFIndex());
	VecSetValue(vecCoarse, index, *dofIt, ADD_VALUES);
      } else {
	// Calculate global row index of the DOF.
	DegreeOfFreedom globalRowDof = 
	  (*interiorMap)[feSpace][dofIt.getDOFIndex()].global;
	
	// Get PETSc's mat index of the row DOF.
	int index = 0;
	if (interiorMap->isMatIndexFromGlobal())
	  index = 
	    interiorMap->getMatIndex(nRowVec, globalRowDof) + rStartInterior;
	else
	  index =
	    interiorMap->getMatIndex(nRowVec, dofIt.getDOFIndex()) + 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(nRowVec, mappedDof);

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


  void PetscSolverGlobalMatrix::removeDirichletBcDofs(Matrix<DOFMatrix*> *mat)
  {
    FUNCNAME("PetscSolverGlobalMatrix::removeDirichletBcDofs()");    
  }


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

}