Actual source code: nn.c
1: #define PETSCKSP_DLL
3: #include src/ksp/pc/impls/is/nn/nn.h
5: /* -------------------------------------------------------------------------- */
6: /*
7: PCSetUp_NN - Prepares for the use of the NN preconditioner
8: by setting data structures and options.
10: Input Parameter:
11: . pc - the preconditioner context
13: Application Interface Routine: PCSetUp()
15: Notes:
16: The interface routine PCSetUp() is not usually called directly by
17: the user, but instead is called by PCApply() if necessary.
18: */
21: static PetscErrorCode PCSetUp_NN(PC pc)
22: {
24:
26: if (!pc->setupcalled) {
27: /* Set up all the "iterative substructuring" common block */
28: PCISSetUp(pc);
29: /* Create the coarse matrix. */
30: PCNNCreateCoarseMatrix(pc);
31: }
32: return(0);
33: }
35: /* -------------------------------------------------------------------------- */
36: /*
37: PCApply_NN - Applies the NN preconditioner to a vector.
39: Input Parameters:
40: . pc - the preconditioner context
41: . r - input vector (global)
43: Output Parameter:
44: . z - output vector (global)
46: Application Interface Routine: PCApply()
47: */
50: static PetscErrorCode PCApply_NN(PC pc,Vec r,Vec z)
51: {
52: PC_IS *pcis = (PC_IS*)(pc->data);
54: PetscScalar m_one = -1.0;
55: Vec w = pcis->vec1_global;
58: /*
59: Dirichlet solvers.
60: Solving $ B_I^{(i)}r_I^{(i)} $ at each processor.
61: Storing the local results at vec2_D
62: */
63: VecScatterBegin(r,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD,pcis->global_to_D);
64: VecScatterEnd (r,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD,pcis->global_to_D);
65: KSPSolve(pcis->ksp_D,pcis->vec1_D,pcis->vec2_D);
66:
67: /*
68: Computing $ r_B - \sum_j \tilde R_j^T A_{BI}^{(j)} (B_I^{(j)}r_I^{(j)}) $ .
69: Storing the result in the interface portion of the global vector w.
70: */
71: MatMult(pcis->A_BI,pcis->vec2_D,pcis->vec1_B);
72: VecScale(pcis->vec1_B,m_one);
73: VecCopy(r,w);
74: VecScatterBegin(pcis->vec1_B,w,ADD_VALUES,SCATTER_REVERSE,pcis->global_to_B);
75: VecScatterEnd (pcis->vec1_B,w,ADD_VALUES,SCATTER_REVERSE,pcis->global_to_B);
77: /*
78: Apply the interface preconditioner
79: */
80: PCNNApplyInterfacePreconditioner(pc,w,z,pcis->work_N,pcis->vec1_B,pcis->vec2_B,pcis->vec3_B,pcis->vec1_D,
81: pcis->vec3_D,pcis->vec1_N,pcis->vec2_N);
83: /*
84: Computing $ t_I^{(i)} = A_{IB}^{(i)} \tilde R_i z_B $
85: The result is stored in vec1_D.
86: */
87: VecScatterBegin(z,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD,pcis->global_to_B);
88: VecScatterEnd (z,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD,pcis->global_to_B);
89: MatMult(pcis->A_IB,pcis->vec1_B,pcis->vec1_D);
91: /*
92: Dirichlet solvers.
93: Computing $ B_I^{(i)}t_I^{(i)} $ and sticking into the global vector the blocks
94: $ B_I^{(i)}r_I^{(i)} - B_I^{(i)}t_I^{(i)} $.
95: */
96: VecScatterBegin(pcis->vec2_D,z,INSERT_VALUES,SCATTER_REVERSE,pcis->global_to_D);
97: VecScatterEnd (pcis->vec2_D,z,INSERT_VALUES,SCATTER_REVERSE,pcis->global_to_D);
98: KSPSolve(pcis->ksp_D,pcis->vec1_D,pcis->vec2_D);
99: VecScale(pcis->vec2_D,m_one);
100: VecScatterBegin(pcis->vec2_D,z,ADD_VALUES,SCATTER_REVERSE,pcis->global_to_D);
101: VecScatterEnd (pcis->vec2_D,z,ADD_VALUES,SCATTER_REVERSE,pcis->global_to_D);
102: return(0);
103: }
105: /* -------------------------------------------------------------------------- */
106: /*
107: PCDestroy_NN - Destroys the private context for the NN preconditioner
108: that was created with PCCreate_NN().
110: Input Parameter:
111: . pc - the preconditioner context
113: Application Interface Routine: PCDestroy()
114: */
117: static PetscErrorCode PCDestroy_NN(PC pc)
118: {
119: PC_NN *pcnn = (PC_NN*)pc->data;
123: PCISDestroy(pc);
125: if (pcnn->coarse_mat) {MatDestroy(pcnn->coarse_mat);}
126: if (pcnn->coarse_x) {VecDestroy(pcnn->coarse_x);}
127: if (pcnn->coarse_b) {VecDestroy(pcnn->coarse_b);}
128: if (pcnn->ksp_coarse) {KSPDestroy(pcnn->ksp_coarse);}
129: if (pcnn->DZ_IN) {
130: PetscFree(pcnn->DZ_IN[0]);
131: PetscFree(pcnn->DZ_IN);
132: }
134: /*
135: Free the private data structure that was hanging off the PC
136: */
137: PetscFree(pcnn);
138: return(0);
139: }
141: /* -------------------------------------------------------------------------- */
142: /*MC
143: PCNN - Balancing Neumann-Neumann for scalar elliptic PDEs.
145: Options Database Keys:
146: + -pc_nn_turn_off_first_balancing - do not balance the residual before solving the local Neumann problems
147: (this skips the first coarse grid solve in the preconditioner)
148: . -pc_nn_turn_off_second_balancing - do not balance the solution solving the local Neumann problems
149: (this skips the second coarse grid solve in the preconditioner)
150: . -pc_is_damp_fixed <fact> -
151: . -pc_is_remove_nullspace_fixed -
152: . -pc_is_set_damping_factor_floating <fact> -
153: . -pc_is_not_damp_floating -
154: + -pc_is_not_remove_nullspace_floating -
156: Level: intermediate
158: Notes: The matrix used with this preconditioner must be of type MATIS
160: Unlike more 'conventional' Neumann-Neumann preconditioners this iterates over ALL the
161: degrees of freedom, NOT just those on the interface (this allows the use of approximate solvers
162: on the subdomains; though in our experience using approximate solvers is slower.).
164: Options for the coarse grid preconditioner can be set with -nn_coarse_pc_xxx
165: Options for the Dirichlet subproblem preconditioner can be set with -is_localD_pc_xxx
166: Options for the Neumann subproblem preconditioner can be set with -is_localN_pc_xxx
168: Contributed by Paulo Goldfeld
170: .seealso: PCCreate(), PCSetType(), PCType (for list of available types), PC, MatIS
171: M*/
175: PetscErrorCode PCCreate_NN(PC pc)
176: {
178: PC_NN *pcnn;
181: /*
182: Creates the private data structure for this preconditioner and
183: attach it to the PC object.
184: */
185: PetscNew(PC_NN,&pcnn);
186: pc->data = (void*)pcnn;
188: /*
189: Logs the memory usage; this is not needed but allows PETSc to
190: monitor how much memory is being used for various purposes.
191: */
192: PetscLogObjectMemory(pc,sizeof(PC_NN)+sizeof(PC_IS)); /* Is this the right thing to do? */
194: PCISCreate(pc);
195: pcnn->coarse_mat = 0;
196: pcnn->coarse_x = 0;
197: pcnn->coarse_b = 0;
198: pcnn->ksp_coarse = 0;
199: pcnn->DZ_IN = 0;
201: /*
202: Set the pointers for the functions that are provided above.
203: Now when the user-level routines (such as PCApply(), PCDestroy(), etc.)
204: are called, they will automatically call these functions. Note we
205: choose not to provide a couple of these functions since they are
206: not needed.
207: */
208: pc->ops->apply = PCApply_NN;
209: pc->ops->applytranspose = 0;
210: pc->ops->setup = PCSetUp_NN;
211: pc->ops->destroy = PCDestroy_NN;
212: pc->ops->view = 0;
213: pc->ops->applyrichardson = 0;
214: pc->ops->applysymmetricleft = 0;
215: pc->ops->applysymmetricright = 0;
216: return(0);
217: }
221: /* -------------------------------------------------------------------------- */
222: /*
223: PCNNCreateCoarseMatrix -
224: */
227: PetscErrorCode PCNNCreateCoarseMatrix (PC pc)
228: {
229: MPI_Request *send_request, *recv_request;
231: PetscInt i, j, k;
232: PetscScalar* mat; /* Sub-matrix with this subdomain's contribution to the coarse matrix */
233: PetscScalar** DZ_OUT; /* proc[k].DZ_OUT[i][] = bit of vector to be sent from processor k to processor i */
235: /* aliasing some names */
236: PC_IS* pcis = (PC_IS*)(pc->data);
237: PC_NN* pcnn = (PC_NN*)pc->data;
238: PetscInt n_neigh = pcis->n_neigh;
239: PetscInt* neigh = pcis->neigh;
240: PetscInt* n_shared = pcis->n_shared;
241: PetscInt** shared = pcis->shared;
242: PetscScalar** DZ_IN; /* Must be initialized after memory allocation. */
245: /* Allocate memory for mat (the +1 is to handle the case n_neigh equal to zero) */
246: PetscMalloc((n_neigh*n_neigh+1)*sizeof(PetscScalar),&mat);
248: /* Allocate memory for DZ */
249: /* Notice that DZ_OUT[0] is allocated some space that is never used. */
250: /* This is just in order to DZ_OUT and DZ_IN to have exactly the same form. */
251: {
252: PetscInt size_of_Z = 0;
253: PetscMalloc ((n_neigh+1)*sizeof(PetscScalar*),&pcnn->DZ_IN);
254: DZ_IN = pcnn->DZ_IN;
255: PetscMalloc ((n_neigh+1)*sizeof(PetscScalar*),&DZ_OUT);
256: for (i=0; i<n_neigh; i++) {
257: size_of_Z += n_shared[i];
258: }
259: PetscMalloc ((size_of_Z+1)*sizeof(PetscScalar),&DZ_IN[0]);
260: PetscMalloc ((size_of_Z+1)*sizeof(PetscScalar),&DZ_OUT[0]);
261: }
262: for (i=1; i<n_neigh; i++) {
263: DZ_IN[i] = DZ_IN [i-1] + n_shared[i-1];
264: DZ_OUT[i] = DZ_OUT[i-1] + n_shared[i-1];
265: }
267: /* Set the values of DZ_OUT, in order to send this info to the neighbours */
268: /* First, set the auxiliary array pcis->work_N. */
269: PCISScatterArrayNToVecB(pcis->work_N,pcis->D,INSERT_VALUES,SCATTER_REVERSE,pc);
270: for (i=1; i<n_neigh; i++){
271: for (j=0; j<n_shared[i]; j++) {
272: DZ_OUT[i][j] = pcis->work_N[shared[i][j]];
273: }
274: }
276: /* Non-blocking send/receive the common-interface chunks of scaled nullspaces */
277: /* Notice that send_request[] and recv_request[] could have one less element. */
278: /* We make them longer to have request[i] corresponding to neigh[i]. */
279: {
280: PetscMPIInt tag;
281: PetscObjectGetNewTag((PetscObject)pc,&tag);
282: PetscMalloc((2*(n_neigh)+1)*sizeof(MPI_Request),&send_request);
283: recv_request = send_request + (n_neigh);
284: for (i=1; i<n_neigh; i++) {
285: MPI_Isend((void*)(DZ_OUT[i]),n_shared[i],MPIU_SCALAR,neigh[i],tag,pc->comm,&(send_request[i]));
286: MPI_Irecv((void*)(DZ_IN [i]),n_shared[i],MPIU_SCALAR,neigh[i],tag,pc->comm,&(recv_request[i]));
287: }
288: }
290: /* Set DZ_IN[0][] (recall that neigh[0]==rank, always) */
291: for(j=0; j<n_shared[0]; j++) {
292: DZ_IN[0][j] = pcis->work_N[shared[0][j]];
293: }
295: /* Start computing with local D*Z while communication goes on. */
296: /* Apply Schur complement. The result is "stored" in vec (more */
297: /* precisely, vec points to the result, stored in pc_nn->vec1_B) */
298: /* and also scattered to pcnn->work_N. */
299: PCNNApplySchurToChunk(pc,n_shared[0],shared[0],DZ_IN[0],pcis->work_N,pcis->vec1_B,
300: pcis->vec2_B,pcis->vec1_D,pcis->vec2_D);
302: /* Compute the first column, while completing the receiving. */
303: for (i=0; i<n_neigh; i++) {
304: MPI_Status stat;
305: PetscMPIInt ind=0;
306: if (i>0) { MPI_Waitany(n_neigh-1,recv_request+1,&ind,&stat); ind++;}
307: mat[ind*n_neigh+0] = 0.0;
308: for (k=0; k<n_shared[ind]; k++) {
309: mat[ind*n_neigh+0] += DZ_IN[ind][k] * pcis->work_N[shared[ind][k]];
310: }
311: }
313: /* Compute the remaining of the columns */
314: for (j=1; j<n_neigh; j++) {
315: PCNNApplySchurToChunk(pc,n_shared[j],shared[j],DZ_IN[j],pcis->work_N,pcis->vec1_B,
316: pcis->vec2_B,pcis->vec1_D,pcis->vec2_D);
317: for (i=0; i<n_neigh; i++) {
318: mat[i*n_neigh+j] = 0.0;
319: for (k=0; k<n_shared[i]; k++) {
320: mat[i*n_neigh+j] += DZ_IN[i][k] * pcis->work_N[shared[i][k]];
321: }
322: }
323: }
325: /* Complete the sending. */
326: if (n_neigh>1) {
327: MPI_Status *stat;
328: PetscMalloc((n_neigh-1)*sizeof(MPI_Status),&stat);
329: if (n_neigh-1) {MPI_Waitall(n_neigh-1,&(send_request[1]),stat);}
330: PetscFree(stat);
331: }
333: /* Free the memory for the MPI requests */
334: PetscFree(send_request);
336: /* Free the memory for DZ_OUT */
337: if (DZ_OUT) {
338: PetscFree(DZ_OUT[0]);
339: PetscFree(DZ_OUT);
340: }
342: {
343: PetscMPIInt size;
344: MPI_Comm_size(pc->comm,&size);
345: /* Create the global coarse vectors (rhs and solution). */
346: VecCreateMPI(pc->comm,1,size,&(pcnn->coarse_b));
347: VecDuplicate(pcnn->coarse_b,&(pcnn->coarse_x));
348: /* Create and set the global coarse AIJ matrix. */
349: MatCreate(pc->comm,&(pcnn->coarse_mat));
350: MatSetSizes(pcnn->coarse_mat,1,1,size,size);
351: MatSetType(pcnn->coarse_mat,MATAIJ);
352: MatSeqAIJSetPreallocation(pcnn->coarse_mat,1,PETSC_NULL);
353: MatMPIAIJSetPreallocation(pcnn->coarse_mat,1,PETSC_NULL,1,PETSC_NULL);
354: MatSetValues(pcnn->coarse_mat,n_neigh,neigh,n_neigh,neigh,mat,ADD_VALUES);
355: MatAssemblyBegin(pcnn->coarse_mat,MAT_FINAL_ASSEMBLY);
356: MatAssemblyEnd (pcnn->coarse_mat,MAT_FINAL_ASSEMBLY);
357: }
359: {
360: PetscMPIInt rank;
361: PetscScalar one = 1.0;
362: MPI_Comm_rank(pc->comm,&rank);
363: /* "Zero out" rows of not-purely-Neumann subdomains */
364: if (pcis->pure_neumann) { /* does NOT zero the row; create an empty index set. The reason is that MatZeroRows() is collective. */
365: MatZeroRows(pcnn->coarse_mat,0,PETSC_NULL,one);
366: } else { /* here it DOES zero the row, since it's not a floating subdomain. */
367: PetscInt row = (PetscInt) rank;
368: MatZeroRows(pcnn->coarse_mat,1,&row,one);
369: }
370: }
372: /* Create the coarse linear solver context */
373: {
374: PC pc_ctx, inner_pc;
375: KSPCreate(pc->comm,&pcnn->ksp_coarse);
376: KSPSetOperators(pcnn->ksp_coarse,pcnn->coarse_mat,pcnn->coarse_mat,SAME_PRECONDITIONER);
377: KSPGetPC(pcnn->ksp_coarse,&pc_ctx);
378: PCSetType(pc_ctx,PCREDUNDANT);
379: KSPSetType(pcnn->ksp_coarse,KSPPREONLY);
380: PCRedundantGetPC(pc_ctx,&inner_pc);
381: PCSetType(inner_pc,PCLU);
382: KSPSetOptionsPrefix(pcnn->ksp_coarse,"nn_coarse_");
383: KSPSetFromOptions(pcnn->ksp_coarse);
384: /* the vectors in the following line are dummy arguments, just telling the KSP the vector size. Values are not used */
385: KSPSetUp(pcnn->ksp_coarse);
386: }
388: /* Free the memory for mat */
389: PetscFree(mat);
391: /* for DEBUGGING, save the coarse matrix to a file. */
392: {
393: PetscTruth flg;
394: PetscOptionsHasName(PETSC_NULL,"-pc_nn_save_coarse_matrix",&flg);
395: if (flg) {
396: PetscViewer viewer;
397: PetscViewerASCIIOpen(PETSC_COMM_WORLD,"coarse.m",&viewer);
398: PetscViewerSetFormat(viewer,PETSC_VIEWER_ASCII_MATLAB);
399: MatView(pcnn->coarse_mat,viewer);
400: PetscViewerDestroy(viewer);
401: }
402: }
404: /* Set the variable pcnn->factor_coarse_rhs. */
405: pcnn->factor_coarse_rhs = (pcis->pure_neumann) ? 1.0 : 0.0;
407: /* See historical note 02, at the bottom of this file. */
408: return(0);
409: }
411: /* -------------------------------------------------------------------------- */
412: /*
413: PCNNApplySchurToChunk -
415: Input parameters:
416: . pcnn
417: . n - size of chunk
418: . idx - indices of chunk
419: . chunk - values
421: Output parameters:
422: . array_N - result of Schur complement applied to chunk, scattered to big array
423: . vec1_B - result of Schur complement applied to chunk
424: . vec2_B - garbage (used as work space)
425: . vec1_D - garbage (used as work space)
426: . vec2_D - garbage (used as work space)
428: */
431: PetscErrorCode PCNNApplySchurToChunk(PC pc, PetscInt n, PetscInt* idx, PetscScalar *chunk, PetscScalar* array_N, Vec vec1_B, Vec vec2_B, Vec vec1_D, Vec vec2_D)
432: {
434: PetscInt i;
435: PC_IS *pcis = (PC_IS*)(pc->data);
438: PetscMemzero((void*)array_N, pcis->n*sizeof(PetscScalar));
439: for (i=0; i<n; i++) { array_N[idx[i]] = chunk[i]; }
440: PCISScatterArrayNToVecB(array_N,vec2_B,INSERT_VALUES,SCATTER_FORWARD,pc);
441: PCISApplySchur(pc,vec2_B,vec1_B,(Vec)0,vec1_D,vec2_D);
442: PCISScatterArrayNToVecB(array_N,vec1_B,INSERT_VALUES,SCATTER_REVERSE,pc);
443: return(0);
444: }
446: /* -------------------------------------------------------------------------- */
447: /*
448: PCNNApplyInterfacePreconditioner - Apply the interface preconditioner, i.e.,
449: the preconditioner for the Schur complement.
451: Input parameter:
452: . r - global vector of interior and interface nodes. The values on the interior nodes are NOT used.
454: Output parameters:
455: . z - global vector of interior and interface nodes. The values on the interface are the result of
456: the application of the interface preconditioner to the interface part of r. The values on the
457: interior nodes are garbage.
458: . work_N - array of local nodes (interior and interface, including ghosts); returns garbage (used as work space)
459: . vec1_B - vector of local interface nodes (including ghosts); returns garbage (used as work space)
460: . vec2_B - vector of local interface nodes (including ghosts); returns garbage (used as work space)
461: . vec3_B - vector of local interface nodes (including ghosts); returns garbage (used as work space)
462: . vec1_D - vector of local interior nodes; returns garbage (used as work space)
463: . vec2_D - vector of local interior nodes; returns garbage (used as work space)
464: . vec1_N - vector of local nodes (interior and interface, including ghosts); returns garbage (used as work space)
465: . vec2_N - vector of local nodes (interior and interface, including ghosts); returns garbage (used as work space)
467: */
470: PetscErrorCode PCNNApplyInterfacePreconditioner (PC pc, Vec r, Vec z, PetscScalar* work_N, Vec vec1_B, Vec vec2_B, Vec vec3_B, Vec vec1_D,
471: Vec vec2_D, Vec vec1_N, Vec vec2_N)
472: {
474: PC_IS* pcis = (PC_IS*)(pc->data);
477: /*
478: First balancing step.
479: */
480: {
481: PetscTruth flg;
482: PetscOptionsHasName(PETSC_NULL,"-pc_nn_turn_off_first_balancing",&flg);
483: if (!flg) {
484: PCNNBalancing(pc,r,(Vec)0,z,vec1_B,vec2_B,(Vec)0,vec1_D,vec2_D,work_N);
485: } else {
486: VecCopy(r,z);
487: }
488: }
490: /*
491: Extract the local interface part of z and scale it by D
492: */
493: VecScatterBegin(z,vec1_B,INSERT_VALUES,SCATTER_FORWARD,pcis->global_to_B);
494: VecScatterEnd (z,vec1_B,INSERT_VALUES,SCATTER_FORWARD,pcis->global_to_B);
495: VecPointwiseMult(vec2_B,pcis->D,vec1_B);
497: /* Neumann Solver */
498: PCISApplyInvSchur(pc,vec2_B,vec1_B,vec1_N,vec2_N);
500: /*
501: Second balancing step.
502: */
503: {
504: PetscTruth flg;
505: PetscOptionsHasName(PETSC_NULL,"-pc_turn_off_second_balancing",&flg);
506: if (!flg) {
507: PCNNBalancing(pc,r,vec1_B,z,vec2_B,vec3_B,(Vec)0,vec1_D,vec2_D,work_N);
508: } else {
509: VecPointwiseMult(vec2_B,pcis->D,vec1_B);
510: VecSet(z,0.0);
511: VecScatterBegin(vec2_B,z,ADD_VALUES,SCATTER_REVERSE,pcis->global_to_B);
512: VecScatterEnd (vec2_B,z,ADD_VALUES,SCATTER_REVERSE,pcis->global_to_B);
513: }
514: }
515: return(0);
516: }
518: /* -------------------------------------------------------------------------- */
519: /*
520: PCNNBalancing - Computes z, as given in equations (15) and (16) (if the
521: input argument u is provided), or s, as given in equations
522: (12) and (13), if the input argument u is a null vector.
523: Notice that the input argument u plays the role of u_i in
524: equation (14). The equation numbers refer to [Man93].
526: Input Parameters:
527: . pcnn - NN preconditioner context.
528: . r - MPI vector of all nodes (interior and interface). It's preserved.
529: . u - (Optional) sequential vector of local interface nodes. It's preserved UNLESS vec3_B is null.
531: Output Parameters:
532: . z - MPI vector of interior and interface nodes. Returns s or z (see description above).
533: . vec1_B - Sequential vector of local interface nodes. Workspace.
534: . vec2_B - Sequential vector of local interface nodes. Workspace.
535: . vec3_B - (Optional) sequential vector of local interface nodes. Workspace.
536: . vec1_D - Sequential vector of local interior nodes. Workspace.
537: . vec2_D - Sequential vector of local interior nodes. Workspace.
538: . work_N - Array of all local nodes (interior and interface). Workspace.
540: */
543: PetscErrorCode PCNNBalancing (PC pc, Vec r, Vec u, Vec z, Vec vec1_B, Vec vec2_B, Vec vec3_B,
544: Vec vec1_D, Vec vec2_D, PetscScalar *work_N)
545: {
547: PetscInt k;
548: PetscScalar value;
549: PetscScalar* lambda;
550: PC_NN* pcnn = (PC_NN*)(pc->data);
551: PC_IS* pcis = (PC_IS*)(pc->data);
555: if (u) {
556: if (!vec3_B) { vec3_B = u; }
557: VecPointwiseMult(vec1_B,pcis->D,u);
558: VecSet(z,0.0);
559: VecScatterBegin(vec1_B,z,ADD_VALUES,SCATTER_REVERSE,pcis->global_to_B);
560: VecScatterEnd (vec1_B,z,ADD_VALUES,SCATTER_REVERSE,pcis->global_to_B);
561: VecScatterBegin(z,vec2_B,INSERT_VALUES,SCATTER_FORWARD,pcis->global_to_B);
562: VecScatterEnd (z,vec2_B,INSERT_VALUES,SCATTER_FORWARD,pcis->global_to_B);
563: PCISApplySchur(pc,vec2_B,vec3_B,(Vec)0,vec1_D,vec2_D);
564: VecScale(vec3_B,-1.0);
565: VecCopy(r,z);
566: VecScatterBegin(vec3_B,z,ADD_VALUES,SCATTER_REVERSE,pcis->global_to_B);
567: VecScatterEnd (vec3_B,z,ADD_VALUES,SCATTER_REVERSE,pcis->global_to_B);
568: } else {
569: VecCopy(r,z);
570: }
571: VecScatterBegin(z,vec2_B,INSERT_VALUES,SCATTER_FORWARD,pcis->global_to_B);
572: VecScatterEnd (z,vec2_B,INSERT_VALUES,SCATTER_FORWARD,pcis->global_to_B);
573: PCISScatterArrayNToVecB(work_N,vec2_B,INSERT_VALUES,SCATTER_REVERSE,pc);
574: for (k=0, value=0.0; k<pcis->n_shared[0]; k++) { value += pcnn->DZ_IN[0][k] * work_N[pcis->shared[0][k]]; }
575: value *= pcnn->factor_coarse_rhs; /* This factor is set in CreateCoarseMatrix(). */
576: {
577: PetscMPIInt rank;
578: MPI_Comm_rank(pc->comm,&rank);
579: VecSetValue(pcnn->coarse_b,rank,value,INSERT_VALUES);
580: /*
581: Since we are only inserting local values (one value actually) we don't need to do the
582: reduction that tells us there is no data that needs to be moved. Hence we comment out these
583: VecAssemblyBegin(pcnn->coarse_b);
584: VecAssemblyEnd (pcnn->coarse_b);
585: */
586: }
587: KSPSolve(pcnn->ksp_coarse,pcnn->coarse_b,pcnn->coarse_x);
588: if (!u) { VecScale(pcnn->coarse_x,-1.0); }
589: VecGetArray(pcnn->coarse_x,&lambda);
590: for (k=0; k<pcis->n_shared[0]; k++) { work_N[pcis->shared[0][k]] = *lambda * pcnn->DZ_IN[0][k]; }
591: VecRestoreArray(pcnn->coarse_x,&lambda);
592: PCISScatterArrayNToVecB(work_N,vec2_B,INSERT_VALUES,SCATTER_FORWARD,pc);
593: VecSet(z,0.0);
594: VecScatterBegin(vec2_B,z,ADD_VALUES,SCATTER_REVERSE,pcis->global_to_B);
595: VecScatterEnd (vec2_B,z,ADD_VALUES,SCATTER_REVERSE,pcis->global_to_B);
596: if (!u) {
597: VecScatterBegin(z,vec2_B,INSERT_VALUES,SCATTER_FORWARD,pcis->global_to_B);
598: VecScatterEnd (z,vec2_B,INSERT_VALUES,SCATTER_FORWARD,pcis->global_to_B);
599: PCISApplySchur(pc,vec2_B,vec1_B,(Vec)0,vec1_D,vec2_D);
600: VecCopy(r,z);
601: }
602: VecScatterBegin(vec1_B,z,ADD_VALUES,SCATTER_REVERSE,pcis->global_to_B);
603: VecScatterEnd (vec1_B,z,ADD_VALUES,SCATTER_REVERSE,pcis->global_to_B);
605: return(0);
606: }
612: /* ------- E N D O F T H E C O D E ------- */
613: /* */
614: /* From now on, "footnotes" (or "historical notes"). */
615: /* */
616: /* ------------------------------------------------- */
620: /* --------------------------------------------------------------------------
621: Historical note 01
622: -------------------------------------------------------------------------- */
623: /*
624: We considered the possibility of an alternative D_i that would still
625: provide a partition of unity (i.e., $ \sum_i N_i D_i N_i^T = I $).
626: The basic principle was still the pseudo-inverse of the counting
627: function; the difference was that we would not count subdomains
628: that do not contribute to the coarse space (i.e., not pure-Neumann
629: subdomains).
631: This turned out to be a bad idea: we would solve trivial Neumann
632: problems in the not pure-Neumann subdomains, since we would be scaling
633: the balanced residual by zero.
634: */
639: /* --------------------------------------------------------------------------
640: Historical note 02
641: -------------------------------------------------------------------------- */
642: /*
643: We tried an alternative coarse problem, that would eliminate exactly a
644: constant error. Turned out not to improve the overall convergence.
645: */