Actual source code: nn.c
petsc-3.8.4 2018-03-24
2: #include <../src/ksp/pc/impls/is/nn/nn.h>
4: /* -------------------------------------------------------------------------- */
5: /*
6: PCSetUp_NN - Prepares for the use of the NN preconditioner
7: by setting data structures and options.
9: Input Parameter:
10: . pc - the preconditioner context
12: Application Interface Routine: PCSetUp()
14: Notes:
15: The interface routine PCSetUp() is not usually called directly by
16: the user, but instead is called by PCApply() if necessary.
17: */
18: static PetscErrorCode PCSetUp_NN(PC pc)
19: {
23: if (!pc->setupcalled) {
24: /* Set up all the "iterative substructuring" common block */
25: PCISSetUp(pc,PETSC_TRUE);
26: /* Create the coarse matrix. */
27: PCNNCreateCoarseMatrix(pc);
28: }
29: return(0);
30: }
32: /* -------------------------------------------------------------------------- */
33: /*
34: PCApply_NN - Applies the NN preconditioner to a vector.
36: Input Parameters:
37: . pc - the preconditioner context
38: . r - input vector (global)
40: Output Parameter:
41: . z - output vector (global)
43: Application Interface Routine: PCApply()
44: */
45: static PetscErrorCode PCApply_NN(PC pc,Vec r,Vec z)
46: {
47: PC_IS *pcis = (PC_IS*)(pc->data);
49: PetscScalar m_one = -1.0;
50: Vec w = pcis->vec1_global;
53: /*
54: Dirichlet solvers.
55: Solving $ B_I^{(i)}r_I^{(i)} $ at each processor.
56: Storing the local results at vec2_D
57: */
58: VecScatterBegin(pcis->global_to_D,r,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);
59: VecScatterEnd (pcis->global_to_D,r,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);
60: KSPSolve(pcis->ksp_D,pcis->vec1_D,pcis->vec2_D);
62: /*
63: Computing $ r_B - \sum_j \tilde R_j^T A_{BI}^{(j)} (B_I^{(j)}r_I^{(j)}) $ .
64: Storing the result in the interface portion of the global vector w.
65: */
66: MatMult(pcis->A_BI,pcis->vec2_D,pcis->vec1_B);
67: VecScale(pcis->vec1_B,m_one);
68: VecCopy(r,w);
69: VecScatterBegin(pcis->global_to_B,pcis->vec1_B,w,ADD_VALUES,SCATTER_REVERSE);
70: VecScatterEnd (pcis->global_to_B,pcis->vec1_B,w,ADD_VALUES,SCATTER_REVERSE);
72: /*
73: Apply the interface preconditioner
74: */
75: PCNNApplyInterfacePreconditioner(pc,w,z,pcis->work_N,pcis->vec1_B,pcis->vec2_B,pcis->vec3_B,pcis->vec1_D,
76: pcis->vec3_D,pcis->vec1_N,pcis->vec2_N);
78: /*
79: Computing $ t_I^{(i)} = A_{IB}^{(i)} \tilde R_i z_B $
80: The result is stored in vec1_D.
81: */
82: VecScatterBegin(pcis->global_to_B,z,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);
83: VecScatterEnd (pcis->global_to_B,z,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);
84: MatMult(pcis->A_IB,pcis->vec1_B,pcis->vec1_D);
86: /*
87: Dirichlet solvers.
88: Computing $ B_I^{(i)}t_I^{(i)} $ and sticking into the global vector the blocks
89: $ B_I^{(i)}r_I^{(i)} - B_I^{(i)}t_I^{(i)} $.
90: */
91: VecScatterBegin(pcis->global_to_D,pcis->vec2_D,z,INSERT_VALUES,SCATTER_REVERSE);
92: VecScatterEnd (pcis->global_to_D,pcis->vec2_D,z,INSERT_VALUES,SCATTER_REVERSE);
93: KSPSolve(pcis->ksp_D,pcis->vec1_D,pcis->vec2_D);
94: VecScale(pcis->vec2_D,m_one);
95: VecScatterBegin(pcis->global_to_D,pcis->vec2_D,z,ADD_VALUES,SCATTER_REVERSE);
96: VecScatterEnd (pcis->global_to_D,pcis->vec2_D,z,ADD_VALUES,SCATTER_REVERSE);
97: return(0);
98: }
100: /* -------------------------------------------------------------------------- */
101: /*
102: PCDestroy_NN - Destroys the private context for the NN preconditioner
103: that was created with PCCreate_NN().
105: Input Parameter:
106: . pc - the preconditioner context
108: Application Interface Routine: PCDestroy()
109: */
110: static PetscErrorCode PCDestroy_NN(PC pc)
111: {
112: PC_NN *pcnn = (PC_NN*)pc->data;
116: PCISDestroy(pc);
118: MatDestroy(&pcnn->coarse_mat);
119: VecDestroy(&pcnn->coarse_x);
120: VecDestroy(&pcnn->coarse_b);
121: KSPDestroy(&pcnn->ksp_coarse);
122: if (pcnn->DZ_IN) {
123: PetscFree(pcnn->DZ_IN[0]);
124: PetscFree(pcnn->DZ_IN);
125: }
127: /*
128: Free the private data structure that was hanging off the PC
129: */
130: PetscFree(pc->data);
131: return(0);
132: }
134: /* -------------------------------------------------------------------------- */
135: /*MC
136: PCNN - Balancing Neumann-Neumann for scalar elliptic PDEs.
138: Options Database Keys:
139: + -pc_nn_turn_off_first_balancing - do not balance the residual before solving the local Neumann problems
140: (this skips the first coarse grid solve in the preconditioner)
141: . -pc_nn_turn_off_second_balancing - do not balance the solution solving the local Neumann problems
142: (this skips the second coarse grid solve in the preconditioner)
143: . -pc_is_damp_fixed <fact> -
144: . -pc_is_remove_nullspace_fixed -
145: . -pc_is_set_damping_factor_floating <fact> -
146: . -pc_is_not_damp_floating -
147: + -pc_is_not_remove_nullspace_floating -
149: Level: intermediate
151: Notes: The matrix used with this preconditioner must be of type MATIS
153: Unlike more 'conventional' Neumann-Neumann preconditioners this iterates over ALL the
154: degrees of freedom, NOT just those on the interface (this allows the use of approximate solvers
155: on the subdomains; though in our experience using approximate solvers is slower.).
157: Options for the coarse grid preconditioner can be set with -nn_coarse_pc_xxx
158: Options for the Dirichlet subproblem preconditioner can be set with -is_localD_pc_xxx
159: Options for the Neumann subproblem preconditioner can be set with -is_localN_pc_xxx
161: Contributed by Paulo Goldfeld
163: .seealso: PCCreate(), PCSetType(), PCType (for list of available types), PC, MATIS
164: M*/
166: PETSC_EXTERN PetscErrorCode PCCreate_NN(PC pc)
167: {
169: PC_NN *pcnn;
172: /*
173: Creates the private data structure for this preconditioner and
174: attach it to the PC object.
175: */
176: PetscNewLog(pc,&pcnn);
177: pc->data = (void*)pcnn;
179: PCISCreate(pc);
180: pcnn->coarse_mat = 0;
181: pcnn->coarse_x = 0;
182: pcnn->coarse_b = 0;
183: pcnn->ksp_coarse = 0;
184: pcnn->DZ_IN = 0;
186: /*
187: Set the pointers for the functions that are provided above.
188: Now when the user-level routines (such as PCApply(), PCDestroy(), etc.)
189: are called, they will automatically call these functions. Note we
190: choose not to provide a couple of these functions since they are
191: not needed.
192: */
193: pc->ops->apply = PCApply_NN;
194: pc->ops->applytranspose = 0;
195: pc->ops->setup = PCSetUp_NN;
196: pc->ops->destroy = PCDestroy_NN;
197: pc->ops->view = 0;
198: pc->ops->applyrichardson = 0;
199: pc->ops->applysymmetricleft = 0;
200: pc->ops->applysymmetricright = 0;
201: return(0);
202: }
204: /* -------------------------------------------------------------------------- */
205: /*
206: PCNNCreateCoarseMatrix -
207: */
208: PetscErrorCode PCNNCreateCoarseMatrix(PC pc)
209: {
210: MPI_Request *send_request, *recv_request;
212: PetscInt i, j, k;
213: PetscScalar *mat; /* Sub-matrix with this subdomain's contribution to the coarse matrix */
214: PetscScalar **DZ_OUT; /* proc[k].DZ_OUT[i][] = bit of vector to be sent from processor k to processor i */
216: /* aliasing some names */
217: PC_IS *pcis = (PC_IS*)(pc->data);
218: PC_NN *pcnn = (PC_NN*)pc->data;
219: PetscInt n_neigh = pcis->n_neigh;
220: PetscInt *neigh = pcis->neigh;
221: PetscInt *n_shared = pcis->n_shared;
222: PetscInt **shared = pcis->shared;
223: PetscScalar **DZ_IN; /* Must be initialized after memory allocation. */
226: /* Allocate memory for mat (the +1 is to handle the case n_neigh equal to zero) */
227: PetscMalloc1(n_neigh*n_neigh+1,&mat);
229: /* Allocate memory for DZ */
230: /* Notice that DZ_OUT[0] is allocated some space that is never used. */
231: /* This is just in order to DZ_OUT and DZ_IN to have exactly the same form. */
232: {
233: PetscInt size_of_Z = 0;
234: PetscMalloc ((n_neigh+1)*sizeof(PetscScalar*),&pcnn->DZ_IN);
235: DZ_IN = pcnn->DZ_IN;
236: PetscMalloc ((n_neigh+1)*sizeof(PetscScalar*),&DZ_OUT);
237: for (i=0; i<n_neigh; i++) size_of_Z += n_shared[i];
238: PetscMalloc ((size_of_Z+1)*sizeof(PetscScalar),&DZ_IN[0]);
239: PetscMalloc ((size_of_Z+1)*sizeof(PetscScalar),&DZ_OUT[0]);
240: }
241: for (i=1; i<n_neigh; i++) {
242: DZ_IN[i] = DZ_IN [i-1] + n_shared[i-1];
243: DZ_OUT[i] = DZ_OUT[i-1] + n_shared[i-1];
244: }
246: /* Set the values of DZ_OUT, in order to send this info to the neighbours */
247: /* First, set the auxiliary array pcis->work_N. */
248: PCISScatterArrayNToVecB(pcis->work_N,pcis->D,INSERT_VALUES,SCATTER_REVERSE,pc);
249: for (i=1; i<n_neigh; i++) {
250: for (j=0; j<n_shared[i]; j++) {
251: DZ_OUT[i][j] = pcis->work_N[shared[i][j]];
252: }
253: }
255: /* Non-blocking send/receive the common-interface chunks of scaled nullspaces */
256: /* Notice that send_request[] and recv_request[] could have one less element. */
257: /* We make them longer to have request[i] corresponding to neigh[i]. */
258: {
259: PetscMPIInt tag;
260: PetscObjectGetNewTag((PetscObject)pc,&tag);
261: PetscMalloc2(n_neigh+1,&send_request,n_neigh+1,&recv_request);
262: for (i=1; i<n_neigh; i++) {
263: MPI_Isend((void*)(DZ_OUT[i]),n_shared[i],MPIU_SCALAR,neigh[i],tag,PetscObjectComm((PetscObject)pc),&(send_request[i]));
264: MPI_Irecv((void*)(DZ_IN [i]),n_shared[i],MPIU_SCALAR,neigh[i],tag,PetscObjectComm((PetscObject)pc),&(recv_request[i]));
265: }
266: }
268: /* Set DZ_IN[0][] (recall that neigh[0]==rank, always) */
269: for (j=0; j<n_shared[0]; j++) DZ_IN[0][j] = pcis->work_N[shared[0][j]];
271: /* Start computing with local D*Z while communication goes on. */
272: /* Apply Schur complement. The result is "stored" in vec (more */
273: /* precisely, vec points to the result, stored in pc_nn->vec1_B) */
274: /* and also scattered to pcnn->work_N. */
275: PCNNApplySchurToChunk(pc,n_shared[0],shared[0],DZ_IN[0],pcis->work_N,pcis->vec1_B,
276: pcis->vec2_B,pcis->vec1_D,pcis->vec2_D);
278: /* Compute the first column, while completing the receiving. */
279: for (i=0; i<n_neigh; i++) {
280: MPI_Status stat;
281: PetscMPIInt ind=0;
282: if (i>0) { MPI_Waitany(n_neigh-1,recv_request+1,&ind,&stat); ind++;}
283: mat[ind*n_neigh+0] = 0.0;
284: for (k=0; k<n_shared[ind]; k++) mat[ind*n_neigh+0] += DZ_IN[ind][k] * pcis->work_N[shared[ind][k]];
285: }
287: /* Compute the remaining of the columns */
288: for (j=1; j<n_neigh; j++) {
289: PCNNApplySchurToChunk(pc,n_shared[j],shared[j],DZ_IN[j],pcis->work_N,pcis->vec1_B,
290: pcis->vec2_B,pcis->vec1_D,pcis->vec2_D);
291: for (i=0; i<n_neigh; i++) {
292: mat[i*n_neigh+j] = 0.0;
293: for (k=0; k<n_shared[i]; k++) mat[i*n_neigh+j] += DZ_IN[i][k] * pcis->work_N[shared[i][k]];
294: }
295: }
297: /* Complete the sending. */
298: if (n_neigh>1) {
299: MPI_Status *stat;
300: PetscMalloc1(n_neigh-1,&stat);
301: if (n_neigh-1) {MPI_Waitall(n_neigh-1,&(send_request[1]),stat);}
302: PetscFree(stat);
303: }
305: /* Free the memory for the MPI requests */
306: PetscFree2(send_request,recv_request);
308: /* Free the memory for DZ_OUT */
309: if (DZ_OUT) {
310: PetscFree(DZ_OUT[0]);
311: PetscFree(DZ_OUT);
312: }
314: {
315: PetscMPIInt size;
316: MPI_Comm_size(PetscObjectComm((PetscObject)pc),&size);
317: /* Create the global coarse vectors (rhs and solution). */
318: VecCreateMPI(PetscObjectComm((PetscObject)pc),1,size,&(pcnn->coarse_b));
319: VecDuplicate(pcnn->coarse_b,&(pcnn->coarse_x));
320: /* Create and set the global coarse AIJ matrix. */
321: MatCreate(PetscObjectComm((PetscObject)pc),&(pcnn->coarse_mat));
322: MatSetSizes(pcnn->coarse_mat,1,1,size,size);
323: MatSetType(pcnn->coarse_mat,MATAIJ);
324: MatSeqAIJSetPreallocation(pcnn->coarse_mat,1,NULL);
325: MatMPIAIJSetPreallocation(pcnn->coarse_mat,1,NULL,n_neigh,NULL);
326: MatSetOption(pcnn->coarse_mat,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_FALSE);
327: MatSetOption(pcnn->coarse_mat,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_FALSE);
328: MatSetValues(pcnn->coarse_mat,n_neigh,neigh,n_neigh,neigh,mat,ADD_VALUES);
329: MatAssemblyBegin(pcnn->coarse_mat,MAT_FINAL_ASSEMBLY);
330: MatAssemblyEnd (pcnn->coarse_mat,MAT_FINAL_ASSEMBLY);
331: }
333: {
334: PetscMPIInt rank;
335: PetscScalar one = 1.0;
336: MPI_Comm_rank(PetscObjectComm((PetscObject)pc),&rank);
337: /* "Zero out" rows of not-purely-Neumann subdomains */
338: if (pcis->pure_neumann) { /* does NOT zero the row; create an empty index set. The reason is that MatZeroRows() is collective. */
339: MatZeroRows(pcnn->coarse_mat,0,NULL,one,0,0);
340: } else { /* here it DOES zero the row, since it's not a floating subdomain. */
341: PetscInt row = (PetscInt) rank;
342: MatZeroRows(pcnn->coarse_mat,1,&row,one,0,0);
343: }
344: }
346: /* Create the coarse linear solver context */
347: {
348: PC pc_ctx, inner_pc;
349: KSP inner_ksp;
351: KSPCreate(PetscObjectComm((PetscObject)pc),&pcnn->ksp_coarse);
352: PetscObjectIncrementTabLevel((PetscObject)pcnn->ksp_coarse,(PetscObject)pc,2);
353: KSPSetOperators(pcnn->ksp_coarse,pcnn->coarse_mat,pcnn->coarse_mat);
354: KSPGetPC(pcnn->ksp_coarse,&pc_ctx);
355: PCSetType(pc_ctx,PCREDUNDANT);
356: KSPSetType(pcnn->ksp_coarse,KSPPREONLY);
357: PCRedundantGetKSP(pc_ctx,&inner_ksp);
358: KSPGetPC(inner_ksp,&inner_pc);
359: PCSetType(inner_pc,PCLU);
360: KSPSetOptionsPrefix(pcnn->ksp_coarse,"nn_coarse_");
361: KSPSetFromOptions(pcnn->ksp_coarse);
362: /* the vectors in the following line are dummy arguments, just telling the KSP the vector size. Values are not used */
363: KSPSetUp(pcnn->ksp_coarse);
364: }
366: /* Free the memory for mat */
367: PetscFree(mat);
369: /* for DEBUGGING, save the coarse matrix to a file. */
370: {
371: PetscBool flg = PETSC_FALSE;
372: PetscOptionsGetBool(NULL,NULL,"-pc_nn_save_coarse_matrix",&flg,NULL);
373: if (flg) {
374: PetscViewer viewer;
375: PetscViewerASCIIOpen(PETSC_COMM_WORLD,"coarse.m",&viewer);
376: PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_MATLAB);
377: MatView(pcnn->coarse_mat,viewer);
378: PetscViewerPopFormat(viewer);
379: PetscViewerDestroy(&viewer);
380: }
381: }
383: /* Set the variable pcnn->factor_coarse_rhs. */
384: pcnn->factor_coarse_rhs = (pcis->pure_neumann) ? 1.0 : 0.0;
386: /* See historical note 02, at the bottom of this file. */
387: return(0);
388: }
390: /* -------------------------------------------------------------------------- */
391: /*
392: PCNNApplySchurToChunk -
394: Input parameters:
395: . pcnn
396: . n - size of chunk
397: . idx - indices of chunk
398: . chunk - values
400: Output parameters:
401: . array_N - result of Schur complement applied to chunk, scattered to big array
402: . vec1_B - result of Schur complement applied to chunk
403: . vec2_B - garbage (used as work space)
404: . vec1_D - garbage (used as work space)
405: . vec2_D - garbage (used as work space)
407: */
408: 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)
409: {
411: PetscInt i;
412: PC_IS *pcis = (PC_IS*)(pc->data);
415: PetscMemzero((void*)array_N, pcis->n*sizeof(PetscScalar));
416: for (i=0; i<n; i++) array_N[idx[i]] = chunk[i];
417: PCISScatterArrayNToVecB(array_N,vec2_B,INSERT_VALUES,SCATTER_FORWARD,pc);
418: PCISApplySchur(pc,vec2_B,vec1_B,(Vec)0,vec1_D,vec2_D);
419: PCISScatterArrayNToVecB(array_N,vec1_B,INSERT_VALUES,SCATTER_REVERSE,pc);
420: return(0);
421: }
423: /* -------------------------------------------------------------------------- */
424: /*
425: PCNNApplyInterfacePreconditioner - Apply the interface preconditioner, i.e.,
426: the preconditioner for the Schur complement.
428: Input parameter:
429: . r - global vector of interior and interface nodes. The values on the interior nodes are NOT used.
431: Output parameters:
432: . z - global vector of interior and interface nodes. The values on the interface are the result of
433: the application of the interface preconditioner to the interface part of r. The values on the
434: interior nodes are garbage.
435: . work_N - array of local nodes (interior and interface, including ghosts); returns garbage (used as work space)
436: . vec1_B - vector of local interface nodes (including ghosts); returns garbage (used as work space)
437: . vec2_B - vector of local interface nodes (including ghosts); returns garbage (used as work space)
438: . vec3_B - vector of local interface nodes (including ghosts); returns garbage (used as work space)
439: . vec1_D - vector of local interior nodes; returns garbage (used as work space)
440: . vec2_D - vector of local interior nodes; returns garbage (used as work space)
441: . vec1_N - vector of local nodes (interior and interface, including ghosts); returns garbage (used as work space)
442: . vec2_N - vector of local nodes (interior and interface, including ghosts); returns garbage (used as work space)
444: */
445: PetscErrorCode PCNNApplyInterfacePreconditioner(PC pc, Vec r, Vec z, PetscScalar *work_N, Vec vec1_B, Vec vec2_B, Vec vec3_B, Vec vec1_D,Vec vec2_D, Vec vec1_N, Vec vec2_N)
446: {
448: PC_IS *pcis = (PC_IS*)(pc->data);
451: /*
452: First balancing step.
453: */
454: {
455: PetscBool flg = PETSC_FALSE;
456: PetscOptionsGetBool(NULL,NULL,"-pc_nn_turn_off_first_balancing",&flg,NULL);
457: if (!flg) {
458: PCNNBalancing(pc,r,(Vec)0,z,vec1_B,vec2_B,(Vec)0,vec1_D,vec2_D,work_N);
459: } else {
460: VecCopy(r,z);
461: }
462: }
464: /*
465: Extract the local interface part of z and scale it by D
466: */
467: VecScatterBegin(pcis->global_to_B,z,vec1_B,INSERT_VALUES,SCATTER_FORWARD);
468: VecScatterEnd (pcis->global_to_B,z,vec1_B,INSERT_VALUES,SCATTER_FORWARD);
469: VecPointwiseMult(vec2_B,pcis->D,vec1_B);
471: /* Neumann Solver */
472: PCISApplyInvSchur(pc,vec2_B,vec1_B,vec1_N,vec2_N);
474: /*
475: Second balancing step.
476: */
477: {
478: PetscBool flg = PETSC_FALSE;
479: PetscOptionsGetBool(NULL,NULL,"-pc_turn_off_second_balancing",&flg,NULL);
480: if (!flg) {
481: PCNNBalancing(pc,r,vec1_B,z,vec2_B,vec3_B,(Vec)0,vec1_D,vec2_D,work_N);
482: } else {
483: VecPointwiseMult(vec2_B,pcis->D,vec1_B);
484: VecSet(z,0.0);
485: VecScatterBegin(pcis->global_to_B,vec2_B,z,ADD_VALUES,SCATTER_REVERSE);
486: VecScatterEnd (pcis->global_to_B,vec2_B,z,ADD_VALUES,SCATTER_REVERSE);
487: }
488: }
489: return(0);
490: }
492: /* -------------------------------------------------------------------------- */
493: /*
494: PCNNBalancing - Computes z, as given in equations (15) and (16) (if the
495: input argument u is provided), or s, as given in equations
496: (12) and (13), if the input argument u is a null vector.
497: Notice that the input argument u plays the role of u_i in
498: equation (14). The equation numbers refer to [Man93].
500: Input Parameters:
501: . pcnn - NN preconditioner context.
502: . r - MPI vector of all nodes (interior and interface). It's preserved.
503: . u - (Optional) sequential vector of local interface nodes. It's preserved UNLESS vec3_B is null.
505: Output Parameters:
506: . z - MPI vector of interior and interface nodes. Returns s or z (see description above).
507: . vec1_B - Sequential vector of local interface nodes. Workspace.
508: . vec2_B - Sequential vector of local interface nodes. Workspace.
509: . vec3_B - (Optional) sequential vector of local interface nodes. Workspace.
510: . vec1_D - Sequential vector of local interior nodes. Workspace.
511: . vec2_D - Sequential vector of local interior nodes. Workspace.
512: . work_N - Array of all local nodes (interior and interface). Workspace.
514: */
515: PetscErrorCode PCNNBalancing(PC pc, Vec r, Vec u, Vec z, Vec vec1_B, Vec vec2_B, Vec vec3_B,Vec vec1_D, Vec vec2_D, PetscScalar *work_N)
516: {
518: PetscInt k;
519: PetscScalar value;
520: PetscScalar *lambda;
521: PC_NN *pcnn = (PC_NN*)(pc->data);
522: PC_IS *pcis = (PC_IS*)(pc->data);
525: PetscLogEventBegin(PC_ApplyCoarse,0,0,0,0);
526: if (u) {
527: if (!vec3_B) vec3_B = u;
528: VecPointwiseMult(vec1_B,pcis->D,u);
529: VecSet(z,0.0);
530: VecScatterBegin(pcis->global_to_B,vec1_B,z,ADD_VALUES,SCATTER_REVERSE);
531: VecScatterEnd (pcis->global_to_B,vec1_B,z,ADD_VALUES,SCATTER_REVERSE);
532: VecScatterBegin(pcis->global_to_B,z,vec2_B,INSERT_VALUES,SCATTER_FORWARD);
533: VecScatterEnd (pcis->global_to_B,z,vec2_B,INSERT_VALUES,SCATTER_FORWARD);
534: PCISApplySchur(pc,vec2_B,vec3_B,(Vec)0,vec1_D,vec2_D);
535: VecScale(vec3_B,-1.0);
536: VecCopy(r,z);
537: VecScatterBegin(pcis->global_to_B,vec3_B,z,ADD_VALUES,SCATTER_REVERSE);
538: VecScatterEnd (pcis->global_to_B,vec3_B,z,ADD_VALUES,SCATTER_REVERSE);
539: } else {
540: VecCopy(r,z);
541: }
542: VecScatterBegin(pcis->global_to_B,z,vec2_B,INSERT_VALUES,SCATTER_FORWARD);
543: VecScatterEnd (pcis->global_to_B,z,vec2_B,INSERT_VALUES,SCATTER_FORWARD);
544: PCISScatterArrayNToVecB(work_N,vec2_B,INSERT_VALUES,SCATTER_REVERSE,pc);
545: for (k=0, value=0.0; k<pcis->n_shared[0]; k++) value += pcnn->DZ_IN[0][k] * work_N[pcis->shared[0][k]];
546: value *= pcnn->factor_coarse_rhs; /* This factor is set in CreateCoarseMatrix(). */
547: {
548: PetscMPIInt rank;
549: MPI_Comm_rank(PetscObjectComm((PetscObject)pc),&rank);
550: VecSetValue(pcnn->coarse_b,rank,value,INSERT_VALUES);
551: /*
552: Since we are only inserting local values (one value actually) we don't need to do the
553: reduction that tells us there is no data that needs to be moved. Hence we comment out these
554: VecAssemblyBegin(pcnn->coarse_b);
555: VecAssemblyEnd (pcnn->coarse_b);
556: */
557: }
558: KSPSolve(pcnn->ksp_coarse,pcnn->coarse_b,pcnn->coarse_x);
559: if (!u) { VecScale(pcnn->coarse_x,-1.0); }
560: VecGetArray(pcnn->coarse_x,&lambda);
561: for (k=0; k<pcis->n_shared[0]; k++) work_N[pcis->shared[0][k]] = *lambda * pcnn->DZ_IN[0][k];
562: VecRestoreArray(pcnn->coarse_x,&lambda);
563: PCISScatterArrayNToVecB(work_N,vec2_B,INSERT_VALUES,SCATTER_FORWARD,pc);
564: VecSet(z,0.0);
565: VecScatterBegin(pcis->global_to_B,vec2_B,z,ADD_VALUES,SCATTER_REVERSE);
566: VecScatterEnd (pcis->global_to_B,vec2_B,z,ADD_VALUES,SCATTER_REVERSE);
567: if (!u) {
568: VecScatterBegin(pcis->global_to_B,z,vec2_B,INSERT_VALUES,SCATTER_FORWARD);
569: VecScatterEnd (pcis->global_to_B,z,vec2_B,INSERT_VALUES,SCATTER_FORWARD);
570: PCISApplySchur(pc,vec2_B,vec1_B,(Vec)0,vec1_D,vec2_D);
571: VecCopy(r,z);
572: }
573: VecScatterBegin(pcis->global_to_B,vec1_B,z,ADD_VALUES,SCATTER_REVERSE);
574: VecScatterEnd (pcis->global_to_B,vec1_B,z,ADD_VALUES,SCATTER_REVERSE);
575: PetscLogEventEnd(PC_ApplyCoarse,0,0,0,0);
576: return(0);
577: }
582: /* ------- E N D O F T H E C O D E ------- */
583: /* */
584: /* From now on, "footnotes" (or "historical notes"). */
585: /* */
586: /* ------------------------------------------------- */
590: /* --------------------------------------------------------------------------
591: Historical note 01
592: -------------------------------------------------------------------------- */
593: /*
594: We considered the possibility of an alternative D_i that would still
595: provide a partition of unity (i.e., $ \sum_i N_i D_i N_i^T = I $).
596: The basic principle was still the pseudo-inverse of the counting
597: function; the difference was that we would not count subdomains
598: that do not contribute to the coarse space (i.e., not pure-Neumann
599: subdomains).
601: This turned out to be a bad idea: we would solve trivial Neumann
602: problems in the not pure-Neumann subdomains, since we would be scaling
603: the balanced residual by zero.
604: */
609: /* --------------------------------------------------------------------------
610: Historical note 02
611: -------------------------------------------------------------------------- */
612: /*
613: We tried an alternative coarse problem, that would eliminate exactly a
614: constant error. Turned out not to improve the overall convergence.
615: */