PetscSolver.cc 18.9 KB
Newer Older
1
2
3
4
5
6
7
8
9
10
11
12
//
// 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.


Thomas Witkowski's avatar
Thomas Witkowski committed
13
14
15
#include <vector>
#include <set>

Thomas Witkowski's avatar
Thomas Witkowski committed
16
#include "parallel/PetscSolver.h"
17
18
#include "parallel/StdMpi.h"
#include "parallel/ParallelDebug.h"
19
20
21
#include "DOFVector.h"
#include "Debug.h"
#include "SystemVector.h"
22

23
24
25
26
27
28
#include "petscksp.h"

namespace AMDiS {

  PetscErrorCode myKSPMonitor(KSP ksp, PetscInt iter, PetscReal rnorm, void *)
  {    
29
    if (iter % 100 == 0 && MPI::COMM_WORLD.Get_rank() == 0)
30
31
32
33
34
      std::cout << "[0]  Petsc-Iteration " << iter << ": " << rnorm << std::endl;

    return 0;
  }
 
35

Thomas Witkowski's avatar
Thomas Witkowski committed
36
  void PetscSolver::solve(AdaptInfo *adaptInfo, bool fixedMatrix)
37
  {
Thomas Witkowski's avatar
Thomas Witkowski committed
38
    FUNCNAME("PetscSolver::solve()");
39

40
41
    TEST_EXIT(meshDistributor)("Should not happen!\n");

42
    double wtime = MPI::Wtime();
43

44
    fillPetscMatrix(systemMatrix, rhs);
45
    solvePetscMatrix(*solution, adaptInfo);   
46

47
48
    INFO(info, 8)("solution of discrete system needed %.5f seconds\n", 
		  MPI::Wtime() - wtime);
49
50
51
  }


Thomas Witkowski's avatar
Thomas Witkowski committed
52
53
  void PetscSolver::setDofMatrix(DOFMatrix* mat, int dispMult, 
				 int dispAddRow, int dispAddCol)
54
  {
Thomas Witkowski's avatar
Thomas Witkowski committed
55
    FUNCNAME("PetscSolver::setDofMatrix()");
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72

    TEST_EXIT(mat)("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(mat->getBaseMatrix());
    traits::const_value<Matrix>::type value(mat->getBaseMatrix());

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

    std::vector<int> cols;
    std::vector<double> values;
    cols.reserve(300);
    values.reserve(300);
73
74
    
    std::vector<int> globalCols;
75
76
77
78
79
80
81
82

    // === Traverse all rows of the dof matrix and insert row wise the values ===
    // === to the petsc matrix.                                               ===

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

      // Global index of the current row dof.
83
      int globalRowDof = meshDistributor->mapLocalToGlobal(*cursor);
84
      // Test if the current row dof is a periodic dof.
85
86
      bool periodicRow = meshDistributor->isPeriodicDof(globalRowDof);

Thomas Witkowski's avatar
Thomas Witkowski committed
87
88
89
      if (!periodicRow) {
	// Calculate petsc row index.
	int rowIndex = globalRowDof * dispMult + dispAddRow;
90

91
92
93
	cols.clear();
	values.clear();

Thomas Witkowski's avatar
Thomas Witkowski committed
94
95
	for (icursor_type icursor = begin<nz>(cursor), icend = end<nz>(cursor); 
	     icursor != icend; ++icursor) {
96

Thomas Witkowski's avatar
Thomas Witkowski committed
97
98
99
100
	  // Global index of the current column index.
	  int globalColDof = meshDistributor->mapLocalToGlobal(col(*icursor));
	  // Test if the current col dof is a periodic dof.
	  bool periodicCol = meshDistributor->isPeriodicDof(globalColDof);
101

Thomas Witkowski's avatar
Thomas Witkowski committed
102
103
	  if (!periodicCol) {
	    // Calculate the exact position of the column index in the petsc matrix.
104
105
	    cols.push_back(globalColDof * dispMult + dispAddCol);
	    values.push_back(value(*icursor));
Thomas Witkowski's avatar
Thomas Witkowski committed
106
107
108
109
110
111
	  } else {
	    std::set<int>& perColAsc = meshDistributor->getPerDofAssociations(globalColDof);
	    std::set<int> perAsc;
	    for (std::set<int>::iterator it = perColAsc.begin(); it != perColAsc.end(); ++it)
	      if (*it >= -3)
		perAsc.insert(*it);
112
	    
Thomas Witkowski's avatar
Thomas Witkowski committed
113
114
115
116
117
118
119
	    double scaledValue = value(*icursor) * std::pow(0.5, static_cast<double>(perAsc.size()));
	    std::vector<int> newCols;
	    newCols.push_back(globalColDof);
	    
	    for (std::set<int>::iterator it = perAsc.begin(); it != perAsc.end(); ++it) {
	      int nCols = static_cast<int>(newCols.size());
	      for (int i = 0; i < nCols; i++) {
120
121
122
 		TEST_EXIT(meshDistributor->isPeriodicDof(*it, newCols[i]))
 		  ("Should not happen: %d %d\n", *it, newCols[i]);
		newCols.push_back(meshDistributor->getPeriodicMapping(*it, newCols[i]));
Thomas Witkowski's avatar
Thomas Witkowski committed
123
124
	      }
	    }
125

Thomas Witkowski's avatar
Thomas Witkowski committed
126
	    for (int i = 0; i < newCols.size(); i++) {
127
128
	      cols.push_back(newCols[i] * dispMult + dispAddCol);
	      values.push_back(scaledValue);	      
Thomas Witkowski's avatar
Thomas Witkowski committed
129
130
	    }
	  }
131
	}
132
133
134

	MatSetValues(petscMatrix, 1, &rowIndex, cols.size(), 
		     &(cols[0]), &(values[0]), ADD_VALUES);	
135
      } else {
Thomas Witkowski's avatar
Thomas Witkowski committed
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
	for (icursor_type icursor = begin<nz>(cursor), icend = end<nz>(cursor); 
	     icursor != icend; ++icursor) {	  

	  // Global index of the current column index.
	  int globalColDof = meshDistributor->mapLocalToGlobal(col(*icursor));

	  std::set<int>& perColAsc = meshDistributor->getPerDofAssociations(globalColDof);
	  std::set<int> perAsc;
	  for (std::set<int>::iterator it = perColAsc.begin(); it != perColAsc.end(); ++it)
	    if (*it >= -3)
	      perAsc.insert(*it);

	  std::set<int>& perRowAsc = meshDistributor->getPerDofAssociations(globalRowDof);
	  for (std::set<int>::iterator it = perRowAsc.begin(); it != perRowAsc.end(); ++it)
	    if (*it >= -3)
	      perAsc.insert(*it);

	  double scaledValue = value(*icursor) * std::pow(0.5, static_cast<double>(perAsc.size()));
	  std::vector<std::pair<int, int> > entry;
	  entry.push_back(std::make_pair(globalRowDof, globalColDof));

	  for (std::set<int>::iterator it = perAsc.begin(); it != perAsc.end(); ++it) {
	    int nEntry = static_cast<int>(entry.size());
	    for (int i = 0; i < nEntry; i++) {
160
	      int perRowDof = 0;
161
162
	      if (meshDistributor->getPeriodicMapping()[*it].count(entry[i].first))
		perRowDof = meshDistributor->getPeriodicMapping(*it, entry[i].first);
Thomas Witkowski's avatar
Thomas Witkowski committed
163
	      else
164
		perRowDof = entry[i].first;
Thomas Witkowski's avatar
Thomas Witkowski committed
165

166
	      int perColDof;
167
168
	      if (meshDistributor->getPeriodicMapping()[*it].count(entry[i].second))
		perColDof = meshDistributor->getPeriodicMapping(*it, entry[i].second);
Thomas Witkowski's avatar
Thomas Witkowski committed
169
	      else
170
		perColDof = entry[i].second;	      	      
171
	      
Thomas Witkowski's avatar
Thomas Witkowski committed
172

173
	      entry.push_back(std::make_pair(perRowDof, perColDof));
Thomas Witkowski's avatar
Thomas Witkowski committed
174
175
176
	    }
	  }

177
178
	  for (std::vector<std::pair<int, int> >::iterator eIt = entry.begin(); 
	       eIt != entry.end(); ++eIt) {
Thomas Witkowski's avatar
Thomas Witkowski committed
179
180
181
182
183
184
185
	    // Calculate petsc row index.
	    int rowIndex = eIt->first * dispMult + dispAddRow;
	    int colIndex = eIt->second * dispMult + dispAddCol;
	    MatSetValue(petscMatrix, rowIndex, colIndex, scaledValue, ADD_VALUES);
	  }
	}
      }
186
187
188
189
    }
  }


Thomas Witkowski's avatar
Thomas Witkowski committed
190
191
  void PetscSolver::setDofVector(Vec& petscVec, DOFVector<double>* vec, 
				 int dispMult, int dispAdd)
192
  {
Thomas Witkowski's avatar
Thomas Witkowski committed
193
    FUNCNAME("PetscSolver::setDofVector()");
194

195
196
197
198
    // Traverse all used dofs in the dof vector.
    DOFVector<double>::Iterator dofIt(vec, USED_DOFS);
    for (dofIt.reset(); !dofIt.end(); ++dofIt) {
      // Calculate global row index of the dof.
199
      DegreeOfFreedom globalRowDof = 
200
	meshDistributor->mapLocalToGlobal(dofIt.getDOFIndex());
201
      // Calculate petsc index of the row dof.
202
      int index = globalRowDof * dispMult + dispAdd;
203

204
205
206
      if (meshDistributor->isPeriodicDof(globalRowDof)) {
	std::set<int>& perAsc = meshDistributor->getPerDofAssociations(globalRowDof);
	double value = *dofIt / (perAsc.size() + 1.0);
207
208
	VecSetValues(petscVec, 1, &index, &value, ADD_VALUES);

209
210
211
212
	for (std::set<int>::iterator perIt = perAsc.begin(); perIt != perAsc.end(); ++perIt) {
	  int mappedDof = meshDistributor->getPeriodicMapping(*perIt, globalRowDof);
	  int mappedIndex = mappedDof * dispMult + dispAdd;
	  VecSetValues(petscVec, 1, &mappedIndex, &value, ADD_VALUES);
213
214
215
216
217
218
	}
      } else {
	// The dof index is not periodic.
	double value = *dofIt;
	VecSetValues(petscVec, 1, &index, &value, ADD_VALUES);
      }
219
    }
220
221
222
  }


Thomas Witkowski's avatar
Thomas Witkowski committed
223
  void PetscSolver::createPetscNnzStructure(Matrix<DOFMatrix*> *mat)
224
  {
Thomas Witkowski's avatar
Thomas Witkowski committed
225
    FUNCNAME("PetscSolver::createPetscNnzStructure()");
226
227
228
229

    TEST_EXIT_DBG(!d_nnz)("There is something wrong!\n");
    TEST_EXIT_DBG(!o_nnz)("There is something wrong!\n");

230
    int nRankRows = meshDistributor->getNumberRankDofs() * nComponents;
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
    d_nnz = new int[nRankRows];
    o_nnz = new int[nRankRows];
    for (int i = 0; i < nRankRows; i++) {
      d_nnz[i] = 0;
      o_nnz[i] = 0;
    }

    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 std::vector<std::pair<int, int> > MatrixNnzEntry;

    // Stores to each rank a list of nnz entries (i.e. pairs of row and column index)
    // that this rank will send to. This nnz entries will be assembled on this rank,
    // but because the row DOFs are not DOFs of this rank they will be send to the
    // owner of the row DOFs.
    std::map<int, MatrixNnzEntry> sendMatrixEntry;

249
250
251
252
253
254
255
256
257

    // First, create for all ranks we send data to MatrixNnzEntry object with 0 entries.
    typedef std::map<int, DofContainer> RankToDofContainer;
    RankToDofContainer& recvDofs = meshDistributor->getRecvDofs();
    for (RankToDofContainer::iterator it = recvDofs.begin();
	 it != recvDofs.end(); ++it)
      sendMatrixEntry[it->first].resize(0);


258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
    for (int i = 0; i < nComponents; i++) {
      for (int j = 0; j < nComponents; j++) {
 	if ((*mat)[i][j]) {
	  Matrix bmat = (*mat)[i][j]->getBaseMatrix();

	  traits::col<Matrix>::type col(bmat);
	  traits::const_value<Matrix>::type value(bmat);
	  
	  typedef traits::range_generator<row, Matrix>::type cursor_type;
	  typedef traits::range_generator<nz, cursor_type>::type icursor_type;
	  
	  for (cursor_type cursor = begin<row>(bmat), 
		 cend = end<row>(bmat); cursor != cend; ++cursor) {

	    // Map the local row number to the global DOF index and create from it
	    // the global PETSc row index of this DOF.
274
275
	    int petscRowIdx = 
	      meshDistributor->mapLocalToGlobal(*cursor) * nComponents + i;
276

277
	    if (meshDistributor->getIsRankDof(*cursor)) {
278
279
280
281
282

	      // === The current row DOF is a rank dof, so create the corresponding ===
	      // === nnz values directly on rank's nnz data.                        ===

	      // This is the local row index of the local PETSc matrix.
283
284
	      int localPetscRowIdx = 
		petscRowIdx - meshDistributor->getRstart() * nComponents;
285

286
	      TEST_EXIT_DBG(localPetscRowIdx >= 0 && localPetscRowIdx < nRankRows)
287
288
		("Should not happen! \n Debug info: localRowIdx = %d   globalRowIndx = %d   petscRowIdx = %d   localPetscRowIdx = %d   rStart = %d   nCompontens = %d   nRankRows = %d\n",
		 *cursor, meshDistributor->mapLocalToGlobal(*cursor), petscRowIdx, localPetscRowIdx, meshDistributor->getRstart(), nComponents, nRankRows);
289
290
291
292
	      
	      // Traverse all non zero entries in this row.
	      for (icursor_type icursor = begin<nz>(cursor), 
		     icend = end<nz>(cursor); icursor != icend; ++icursor) {
293
294
		int petscColIdx = 
		  meshDistributor->mapLocalToGlobal(col(*icursor)) * nComponents + j;
295

296
		if (value(*icursor) != 0.0 || petscRowIdx == petscColIdx) {
297
298
		  // The row DOF is a rank DOF, if also the column is a rank DOF, 
		  // increment the d_nnz values for this row, otherwise the o_nnz value.
299
300
		  if (petscColIdx >= meshDistributor->getRstart() * nComponents && 
		      petscColIdx < meshDistributor->getRstart() * nComponents + nRankRows)
301
302
303
304
305
306
		    d_nnz[localPetscRowIdx]++;
		  else
		    o_nnz[localPetscRowIdx]++;
		}    
	      }
	    } else {
307
308
	      typedef std::map<int, DofContainer> RankToDofContainer;

309
310
311
312
313
314
315
	      // === The current row DOF is not a rank dof, i.e., it will be created ===
	      // === on this rank, but after this it will be send to another rank    ===
	      // === matrix. So we need to send also the corresponding nnz structure ===
	      // === of this row to the corresponding rank.                          ===

	      // Find out who is the member of this DOF.
	      int sendToRank = -1;
316
317
	      for (RankToDofContainer::iterator it = meshDistributor->getRecvDofs().begin();
		   it != meshDistributor->getRecvDofs().end(); ++it) {
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
		for (DofContainer::iterator dofIt = it->second.begin();
		     dofIt != it->second.end(); ++dofIt) {
		  if (**dofIt == *cursor) {
		    sendToRank = it->first;
		    break;
		  }
		}

		if (sendToRank != -1)
		  break;
	      }

	      TEST_EXIT_DBG(sendToRank != -1)("Should not happen!\n");

	      // Send all non zero entries to the member of the row DOF.
	      for (icursor_type icursor = begin<nz>(cursor), 
		     icend = end<nz>(cursor); icursor != icend; ++icursor) {
		if (value(*icursor) != 0.0) {
336
337
		  int petscColIdx = 
		    meshDistributor->mapLocalToGlobal(col(*icursor)) * nComponents + j;
338
339
340
341
342
343
344
345
346
347
348
349
350
351
		  
		  sendMatrixEntry[sendToRank].
		    push_back(std::make_pair(petscRowIdx, petscColIdx));
		}
	      }

	    } // if (isRankDof[*cursor]) ... else ...
	  } // for each row in mat[i][j]
	} // if mat[i][j]
      } 
    }

    // === Send and recv the nnz row structure to/from other ranks. ===

352
    StdMpi<MatrixNnzEntry> stdMpi(meshDistributor->getMpiComm(), true);
353
    stdMpi.send(sendMatrixEntry);
354
    stdMpi.recv(meshDistributor->getSendDofs());
355
356
    stdMpi.startCommunication<int>(MPI_INT);

357

358
359
360
361
362
363
364
365
366
367
    // === Evaluate the nnz structure this rank got from other ranks and add it to ===
    // === the PETSc nnz data structure.                                           ===

    for (std::map<int, MatrixNnzEntry>::iterator it = stdMpi.getRecvData().begin();
	 it != stdMpi.getRecvData().end(); ++it) {
      if (it->second.size() > 0) {
	for (unsigned int i = 0; i < it->second.size(); i++) {
	  int r = it->second[i].first;
	  int c = it->second[i].second;

368
	  int localRowIdx = r - meshDistributor->getRstart() * nComponents;
369
370
371
372
373

	  TEST_EXIT_DBG(localRowIdx >= 0 && localRowIdx < nRankRows)
	    ("Got row index %d/%d (nRankRows = %d) from rank %d. Should not happen!\n",
	     r, localRowIdx, nRankRows, it->first);
	  
374
375
	  if (c < meshDistributor->getRstart() * nComponents || 
	      c >= meshDistributor->getRstart() * nComponents + nRankRows)
376
377
378
379
380
	    o_nnz[localRowIdx]++;
	  else
	    d_nnz[localRowIdx]++;
	}
      }
381
    }
382
383
384
385
386
387
388
389
390
391

    // The above algorithm for calculating the number of nnz per row over-
    // approximates the value, i.e., the number is always equal or larger to 
    // the real number of nnz values in the global parallel matrix. For small
    // matrices, the problem may arise, that the result is larger than the
    // number of elements in a row. This is fixed in the following.

    if (nRankRows < 100) 
      for (int i = 0; i < nRankRows; i++)
	d_nnz[i] = std::min(d_nnz[i], nRankRows);
392
393
394
  }


Thomas Witkowski's avatar
Thomas Witkowski committed
395
  void PetscSolver::fillPetscMatrix(Matrix<DOFMatrix*> *mat, SystemVector *vec)
396
  {
Thomas Witkowski's avatar
Thomas Witkowski committed
397
    FUNCNAME("PetscSolver::fillPetscMatrix()");
398

399
    double wtime = MPI::Wtime();
400
401
    int nRankRows = meshDistributor->getNumberRankDofs() * nComponents;
    int nOverallRows = meshDistributor->getNumberOverallDofs() * nComponents;
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416

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

    VecCreate(PETSC_COMM_WORLD, &petscRhsVec);
    VecSetSizes(petscRhsVec, nRankRows, nOverallRows);
    VecSetType(petscRhsVec, VECMPI);

    VecCreate(PETSC_COMM_WORLD, &petscSolVec);
    VecSetSizes(petscSolVec, nRankRows, nOverallRows);
    VecSetType(petscSolVec, VECMPI);

    VecCreate(PETSC_COMM_WORLD, &petscTmpVec);
    VecSetSizes(petscTmpVec, nRankRows, nOverallRows);
    VecSetType(petscTmpVec, VECMPI);

417
418
419
420
421
    int recvAllValues = 0;
    int sendValue = static_cast<int>(meshDistributor->getLastMeshChangeIndex() != lastMeshNnz);
    meshDistributor->getMpiComm().Allreduce(&sendValue, &recvAllValues, 1, MPI_INT, MPI_SUM);

    if (!d_nnz || recvAllValues != 0) {
422
423
      if (d_nnz) {
	delete [] d_nnz;
424
	d_nnz = NULL;
425
	delete [] o_nnz;
426
	o_nnz = NULL;
427
428
      }

429
      createPetscNnzStructure(mat);
430
      lastMeshNnz = meshDistributor->getLastMeshChangeIndex();
431
    }
432

433

434
435
436
    // === Create PETSc matrix with the computed nnz data structure. ===

    MatCreateMPIAIJ(PETSC_COMM_WORLD, nRankRows, nRankRows, nOverallRows, nOverallRows,
437
		    0, d_nnz, 0, o_nnz, &petscMatrix);
438
    
439
#if (DEBUG != 0)
440
    INFO(info, 8)("Fill petsc matrix 1 needed %.5f seconds\n", MPI::Wtime() - wtime);
441
#endif
442
443
444
445

#if (DEBUG != 0)
    int a, b;
    MatGetOwnershipRange(petscMatrix, &a, &b);
446
447
448
449
    TEST_EXIT(a == meshDistributor->getRstart() * nComponents)
      ("Wrong matrix ownership range!\n");
    TEST_EXIT(b == meshDistributor->getRstart() * nComponents + nRankRows)
      ("Wrong matrix ownership range!\n");
450
451
#endif

452

453
454
455
456
457
    // === Transfer values from DOF matrices to the PETSc matrix. === 

    for (int i = 0; i < nComponents; i++)
      for (int j = 0; j < nComponents; j++)
	if ((*mat)[i][j])
458
459
	  setDofMatrix((*mat)[i][j], nComponents, i, j);	
	
460
#if (DEBUG != 0)
461
    INFO(info, 8)("Fill petsc matrix 2 needed %.5f seconds\n", MPI::Wtime() - wtime);
462
#endif
463
464
465
466

    MatAssemblyBegin(petscMatrix, MAT_FINAL_ASSEMBLY);
    MatAssemblyEnd(petscMatrix, MAT_FINAL_ASSEMBLY);

467
#if (DEBUG != 0)
468
469
    INFO(info, 8)("Fill petsc matrix 3 needed %.5f seconds\n", 
		  TIME_USED(MPI::Wtime(), wtime));
470
#endif
471

472
473
474
475
476
477
478
479
    // === Transfer values from DOF vector to the PETSc vector. === 

    for (int i = 0; i < nComponents; i++)
      setDofVector(petscRhsVec, vec->getDOFVector(i), nComponents, i);

    VecAssemblyBegin(petscRhsVec);
    VecAssemblyEnd(petscRhsVec);

480
    INFO(info, 8)("Fill petsc matrix needed %.5f seconds\n", MPI::Wtime() - wtime);
481
482
483
  }


Thomas Witkowski's avatar
Thomas Witkowski committed
484
  void PetscSolver::solvePetscMatrix(SystemVector &vec, AdaptInfo *adaptInfo)
485
  {
Thomas Witkowski's avatar
Thomas Witkowski committed
486
    FUNCNAME("PetscSolver::solvePetscMatrix()");
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513

#if 0
    // Set old solution to be initiual guess for petsc solver.
    for (int i = 0; i < nComponents; i++)
      setDofVector(petscSolVec, vec->getDOFVector(i), nComponents, i);

    VecAssemblyBegin(petscSolVec);
    VecAssemblyEnd(petscSolVec);
#endif

    // === Init Petsc solver. ===

    KSP solver;
    KSPCreate(PETSC_COMM_WORLD, &solver);
    KSPSetOperators(solver, petscMatrix, petscMatrix, SAME_NONZERO_PATTERN); 
    KSPSetTolerances(solver, 0.0, 1e-8, PETSC_DEFAULT, PETSC_DEFAULT);
    KSPSetType(solver, KSPBCGS);
    KSPMonitorSet(solver, myKSPMonitor, PETSC_NULL, 0);
    KSPSetFromOptions(solver);
    // Do not delete the solution vector, use it for the initial guess.
    //    KSPSetInitialGuessNonzero(solver, PETSC_TRUE);


    // === Run Petsc. ===

    KSPSolve(solver, petscRhsVec, petscSolVec);

514

515
    // === Transfere values from Petsc's solution vectors to the dof vectors.
516

517
518
519
    PetscScalar *vecPointer;
    VecGetArray(petscSolVec, &vecPointer);

520
    int nRankDofs = meshDistributor->getNumberRankDofs();
521
    for (int i = 0; i < nComponents; i++) {
522
      DOFVector<double> &dofvec = *(vec.getDOFVector(i));
523
      for (int j = 0; j < nRankDofs; j++)
524
	dofvec[meshDistributor->mapLocalToDofIndex(j)] = 
525
	  vecPointer[j * nComponents + i]; 
526
527
528
529
530
531
532
    }

    VecRestoreArray(petscSolVec, &vecPointer);


    // === Synchronize dofs at common dofs, i.e., dofs that correspond to more ===
    // === than one partition.                                                 ===
533
    meshDistributor->synchVector(vec);
534
535
536
537
538
539
540


    // === Print information about solution process. ===

    int iterations = 0;
    KSPGetIterationNumber(solver, &iterations);
    MSG("  Number of iterations: %d\n", iterations);
541
542
    adaptInfo->setSolverIterations(iterations);

543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
    double norm = 0.0;
    MatMult(petscMatrix, petscSolVec, petscTmpVec);
    VecAXPY(petscTmpVec, -1.0, petscRhsVec);
    VecNorm(petscTmpVec, NORM_2, &norm);
    MSG("  Residual norm: %e\n", norm);


    // === Destroy Petsc's variables. ===

    MatDestroy(petscMatrix);
    VecDestroy(petscRhsVec);
    VecDestroy(petscSolVec);
    VecDestroy(petscTmpVec);
    KSPDestroy(solver);
  }

}