Actual source code: nn.c
petsc-3.6.1 2015-08-06
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: */
20: static PetscErrorCode PCSetUp_NN(PC pc)
21: {
25: if (!pc->setupcalled) {
26: /* Set up all the "iterative substructuring" common block */
27: PCISSetUp(pc,PETSC_TRUE);
28: /* Create the coarse matrix. */
29: PCNNCreateCoarseMatrix(pc);
30: }
31: return(0);
32: }
34: /* -------------------------------------------------------------------------- */
35: /*
36: PCApply_NN - Applies the NN preconditioner to a vector.
38: Input Parameters:
39: . pc - the preconditioner context
40: . r - input vector (global)
42: Output Parameter:
43: . z - output vector (global)
45: Application Interface Routine: PCApply()
46: */
49: static PetscErrorCode PCApply_NN(PC pc,Vec r,Vec z)
50: {
51: PC_IS *pcis = (PC_IS*)(pc->data);
53: PetscScalar m_one = -1.0;
54: Vec w = pcis->vec1_global;
57: /*
58: Dirichlet solvers.
59: Solving $ B_I^{(i)}r_I^{(i)} $ at each processor.
60: Storing the local results at vec2_D
61: */
62: VecScatterBegin(pcis->global_to_D,r,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);
63: VecScatterEnd (pcis->global_to_D,r,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);
64: KSPSolve(pcis->ksp_D,pcis->vec1_D,pcis->vec2_D);
66: /*
67: Computing $ r_B - \sum_j \tilde R_j^T A_{BI}^{(j)} (B_I^{(j)}r_I^{(j)}) $ .
68: Storing the result in the interface portion of the global vector w.
69: */
70: MatMult(pcis->A_BI,pcis->vec2_D,pcis->vec1_B);
71: VecScale(pcis->vec1_B,m_one);
72: VecCopy(r,w);
73: VecScatterBegin(pcis->global_to_B,pcis->vec1_B,w,ADD_VALUES,SCATTER_REVERSE);
74: VecScatterEnd (pcis->global_to_B,pcis->vec1_B,w,ADD_VALUES,SCATTER_REVERSE);
76: /*
77: Apply the interface preconditioner
78: */
79: PCNNApplyInterfacePreconditioner(pc,w,z,pcis->work_N,pcis->vec1_B,pcis->vec2_B,pcis->vec3_B,pcis->vec1_D,
80: pcis->vec3_D,pcis->vec1_N,pcis->vec2_N);
82: /*
83: Computing $ t_I^{(i)} = A_{IB}^{(i)} \tilde R_i z_B $
84: The result is stored in vec1_D.
85: */
86: VecScatterBegin(pcis->global_to_B,z,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);
87: VecScatterEnd (pcis->global_to_B,z,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);
88: MatMult(pcis->A_IB,pcis->vec1_B,pcis->vec1_D);
90: /*
91: Dirichlet solvers.
92: Computing $ B_I^{(i)}t_I^{(i)} $ and sticking into the global vector the blocks
93: $ B_I^{(i)}r_I^{(i)} - B_I^{(i)}t_I^{(i)} $.
94: */
95: VecScatterBegin(pcis->global_to_D,pcis->vec2_D,z,INSERT_VALUES,SCATTER_REVERSE);
96: VecScatterEnd (pcis->global_to_D,pcis->vec2_D,z,INSERT_VALUES,SCATTER_REVERSE);
97: KSPSolve(pcis->ksp_D,pcis->vec1_D,pcis->vec2_D);
98: VecScale(pcis->vec2_D,m_one);
99: VecScatterBegin(pcis->global_to_D,pcis->vec2_D,z,ADD_VALUES,SCATTER_REVERSE);
100: VecScatterEnd (pcis->global_to_D,pcis->vec2_D,z,ADD_VALUES,SCATTER_REVERSE);
101: return(0);
102: }
104: /* -------------------------------------------------------------------------- */
105: /*
106: PCDestroy_NN - Destroys the private context for the NN preconditioner
107: that was created with PCCreate_NN().
109: Input Parameter:
110: . pc - the preconditioner context
112: Application Interface Routine: PCDestroy()
113: */
116: static PetscErrorCode PCDestroy_NN(PC pc)
117: {
118: PC_NN *pcnn = (PC_NN*)pc->data;
122: PCISDestroy(pc);
124: MatDestroy(&pcnn->coarse_mat);
125: VecDestroy(&pcnn->coarse_x);
126: VecDestroy(&pcnn->coarse_b);
127: KSPDestroy(&pcnn->ksp_coarse);
128: if (pcnn->DZ_IN) {
129: PetscFree(pcnn->DZ_IN[0]);
130: PetscFree(pcnn->DZ_IN);
131: }
133: /*
134: Free the private data structure that was hanging off the PC
135: */
136: PetscFree(pc->data);
137: return(0);
138: }
140: /* -------------------------------------------------------------------------- */
141: /*MC
142: PCNN - Balancing Neumann-Neumann for scalar elliptic PDEs.
144: Options Database Keys:
145: + -pc_nn_turn_off_first_balancing - do not balance the residual before solving the local Neumann problems
146: (this skips the first coarse grid solve in the preconditioner)
147: . -pc_nn_turn_off_second_balancing - do not balance the solution solving the local Neumann problems
148: (this skips the second coarse grid solve in the preconditioner)
149: . -pc_is_damp_fixed <fact> -
150: . -pc_is_remove_nullspace_fixed -
151: . -pc_is_set_damping_factor_floating <fact> -
152: . -pc_is_not_damp_floating -
153: + -pc_is_not_remove_nullspace_floating -
155: Level: intermediate
157: Notes: The matrix used with this preconditioner must be of type MATIS
159: Unlike more 'conventional' Neumann-Neumann preconditioners this iterates over ALL the
160: degrees of freedom, NOT just those on the interface (this allows the use of approximate solvers
161: on the subdomains; though in our experience using approximate solvers is slower.).
163: Options for the coarse grid preconditioner can be set with -nn_coarse_pc_xxx
164: Options for the Dirichlet subproblem preconditioner can be set with -is_localD_pc_xxx
165: Options for the Neumann subproblem preconditioner can be set with -is_localN_pc_xxx
167: Contributed by Paulo Goldfeld
169: .seealso: PCCreate(), PCSetType(), PCType (for list of available types), PC, MATIS
170: M*/
174: PETSC_EXTERN PetscErrorCode PCCreate_NN(PC pc)
175: {
177: PC_NN *pcnn;
180: /*
181: Creates the private data structure for this preconditioner and
182: attach it to the PC object.
183: */
184: PetscNewLog(pc,&pcnn);
185: pc->data = (void*)pcnn;
187: PCISCreate(pc);
188: pcnn->coarse_mat = 0;
189: pcnn->coarse_x = 0;
190: pcnn->coarse_b = 0;
191: pcnn->ksp_coarse = 0;
192: pcnn->DZ_IN = 0;
194: /*
195: Set the pointers for the functions that are provided above.
196: Now when the user-level routines (such as PCApply(), PCDestroy(), etc.)
197: are called, they will automatically call these functions. Note we
198: choose not to provide a couple of these functions since they are
199: not needed.
200: */
201: pc->ops->apply = PCApply_NN;
202: pc->ops->applytranspose = 0;
203: pc->ops->setup = PCSetUp_NN;
204: pc->ops->destroy = PCDestroy_NN;
205: pc->ops->view = 0;
206: pc->ops->applyrichardson = 0;
207: pc->ops->applysymmetricleft = 0;
208: pc->ops->applysymmetricright = 0;
209: return(0);
210: }
212: /* -------------------------------------------------------------------------- */
213: /*
214: PCNNCreateCoarseMatrix -
215: */
218: PetscErrorCode PCNNCreateCoarseMatrix(PC pc)
219: {
220: MPI_Request *send_request, *recv_request;
222: PetscInt i, j, k;
223: PetscScalar *mat; /* Sub-matrix with this subdomain's contribution to the coarse matrix */
224: PetscScalar **DZ_OUT; /* proc[k].DZ_OUT[i][] = bit of vector to be sent from processor k to processor i */
226: /* aliasing some names */
227: PC_IS *pcis = (PC_IS*)(pc->data);
228: PC_NN *pcnn = (PC_NN*)pc->data;
229: PetscInt n_neigh = pcis->n_neigh;
230: PetscInt *neigh = pcis->neigh;
231: PetscInt *n_shared = pcis->n_shared;
232: PetscInt **shared = pcis->shared;
233: PetscScalar **DZ_IN; /* Must be initialized after memory allocation. */
236: /* Allocate memory for mat (the +1 is to handle the case n_neigh equal to zero) */
237: PetscMalloc1(n_neigh*n_neigh+1,&mat);
239: /* Allocate memory for DZ */
240: /* Notice that DZ_OUT[0] is allocated some space that is never used. */
241: /* This is just in order to DZ_OUT and DZ_IN to have exactly the same form. */
242: {
243: PetscInt size_of_Z = 0;
244: PetscMalloc ((n_neigh+1)*sizeof(PetscScalar*),&pcnn->DZ_IN);
245: DZ_IN = pcnn->DZ_IN;
246: PetscMalloc ((n_neigh+1)*sizeof(PetscScalar*),&DZ_OUT);
247: for (i=0; i<n_neigh; i++) size_of_Z += n_shared[i];
248: PetscMalloc ((size_of_Z+1)*sizeof(PetscScalar),&DZ_IN[0]);
249: PetscMalloc ((size_of_Z+1)*sizeof(PetscScalar),&DZ_OUT[0]);
250: }
251: for (i=1; i<n_neigh; i++) {
252: DZ_IN[i] = DZ_IN [i-1] + n_shared[i-1];
253: DZ_OUT[i] = DZ_OUT[i-1] + n_shared[i-1];
254: }
256: /* Set the values of DZ_OUT, in order to send this info to the neighbours */
257: /* First, set the auxiliary array pcis->work_N. */
258: PCISScatterArrayNToVecB(pcis->work_N,pcis->D,INSERT_VALUES,SCATTER_REVERSE,pc);
259: for (i=1; i<n_neigh; i++) {
260: for (j=0; j<n_shared[i]; j++) {
261: DZ_OUT[i][j] = pcis->work_N[shared[i][j]];
262: }
263: }
265: /* Non-blocking send/receive the common-interface chunks of scaled nullspaces */
266: /* Notice that send_request[] and recv_request[] could have one less element. */
267: /* We make them longer to have request[i] corresponding to neigh[i]. */
268: {
269: PetscMPIInt tag;
270: PetscObjectGetNewTag((PetscObject)pc,&tag);
271: PetscMalloc2(n_neigh+1,&send_request,n_neigh+1,&recv_request);
272: for (i=1; i<n_neigh; i++) {
273: MPI_Isend((void*)(DZ_OUT[i]),n_shared[i],MPIU_SCALAR,neigh[i],tag,PetscObjectComm((PetscObject)pc),&(send_request[i]));
274: MPI_Irecv((void*)(DZ_IN [i]),n_shared[i],MPIU_SCALAR,neigh[i],tag,PetscObjectComm((PetscObject)pc),&(recv_request[i]));
275: }
276: }
278: /* Set DZ_IN[0][] (recall that neigh[0]==rank, always) */
279: for (j=0; j<n_shared[0]; j++) DZ_IN[0][j] = pcis->work_N[shared[0][j]];
281: /* Start computing with local D*Z while communication goes on. */
282: /* Apply Schur complement. The result is "stored" in vec (more */
283: /* precisely, vec points to the result, stored in pc_nn->vec1_B) */
284: /* and also scattered to pcnn->work_N. */
285: PCNNApplySchurToChunk(pc,n_shared[0],shared[0],DZ_IN[0],pcis->work_N,pcis->vec1_B,
286: pcis->vec2_B,pcis->vec1_D,pcis->vec2_D);
288: /* Compute the first column, while completing the receiving. */
289: for (i=0; i<n_neigh; i++) {
290: MPI_Status stat;
291: PetscMPIInt ind=0;
292: if (i>0) { MPI_Waitany(n_neigh-1,recv_request+1,&ind,&stat); ind++;}
293: mat[ind*n_neigh+0] = 0.0;
294: for (k=0; k<n_shared[ind]; k++) mat[ind*n_neigh+0] += DZ_IN[ind][k] * pcis->work_N[shared[ind][k]];
295: }
297: /* Compute the remaining of the columns */
298: for (j=1; j<n_neigh; j++) {
299: PCNNApplySchurToChunk(pc,n_shared[j],shared[j],DZ_IN[j],pcis->work_N,pcis->vec1_B,
300: pcis->vec2_B,pcis->vec1_D,pcis->vec2_D);
301: for (i=0; i<n_neigh; i++) {
302: mat[i*n_neigh+j] = 0.0;
303: for (k=0; k<n_shared[i]; k++) mat[i*n_neigh+j] += DZ_IN[i][k] * pcis->work_N[shared[i][k]];
304: }
305: }
307: /* Complete the sending. */
308: if (n_neigh>1) {
309: MPI_Status *stat;
310: PetscMalloc1(n_neigh-1,&stat);
311: if (n_neigh-1) {MPI_Waitall(n_neigh-1,&(send_request[1]),stat);}
312: PetscFree(stat);
313: }
315: /* Free the memory for the MPI requests */
316: PetscFree2(send_request,recv_request);
318: /* Free the memory for DZ_OUT */
319: if (DZ_OUT) {
320: PetscFree(DZ_OUT[0]);
321: PetscFree(DZ_OUT);
322: }
324: {
325: PetscMPIInt size;
326: MPI_Comm_size(PetscObjectComm((PetscObject)pc),&size);
327: /* Create the global coarse vectors (rhs and solution). */
328: VecCreateMPI(PetscObjectComm((PetscObject)pc),1,size,&(pcnn->coarse_b));
329: VecDuplicate(pcnn->coarse_b,&(pcnn->coarse_x));
330: /* Create and set the global coarse AIJ matrix. */
331: MatCreate(PetscObjectComm((PetscObject)pc),&(pcnn->coarse_mat));
332: MatSetSizes(pcnn->coarse_mat,1,1,size,size);
333: MatSetType(pcnn->coarse_mat,MATAIJ);
334: MatSeqAIJSetPreallocation(pcnn->coarse_mat,1,NULL);
335: MatMPIAIJSetPreallocation(pcnn->coarse_mat,1,NULL,n_neigh,NULL);
336: MatSetOption(pcnn->coarse_mat,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_FALSE);
337: MatSetOption(pcnn->coarse_mat,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_FALSE);
338: MatSetValues(pcnn->coarse_mat,n_neigh,neigh,n_neigh,neigh,mat,ADD_VALUES);
339: MatAssemblyBegin(pcnn->coarse_mat,MAT_FINAL_ASSEMBLY);
340: MatAssemblyEnd (pcnn->coarse_mat,MAT_FINAL_ASSEMBLY);
341: }
343: {
344: PetscMPIInt rank;
345: PetscScalar one = 1.0;
346: MPI_Comm_rank(PetscObjectComm((PetscObject)pc),&rank);
347: /* "Zero out" rows of not-purely-Neumann subdomains */
348: if (pcis->pure_neumann) { /* does NOT zero the row; create an empty index set. The reason is that MatZeroRows() is collective. */
349: MatZeroRows(pcnn->coarse_mat,0,NULL,one,0,0);
350: } else { /* here it DOES zero the row, since it's not a floating subdomain. */
351: PetscInt row = (PetscInt) rank;
352: MatZeroRows(pcnn->coarse_mat,1,&row,one,0,0);
353: }
354: }
356: /* Create the coarse linear solver context */
357: {
358: PC pc_ctx, inner_pc;
359: KSP inner_ksp;
361: KSPCreate(PetscObjectComm((PetscObject)pc),&pcnn->ksp_coarse);
362: PetscObjectIncrementTabLevel((PetscObject)pcnn->ksp_coarse,(PetscObject)pc,2);
363: KSPSetOperators(pcnn->ksp_coarse,pcnn->coarse_mat,pcnn->coarse_mat);
364: KSPGetPC(pcnn->ksp_coarse,&pc_ctx);
365: PCSetType(pc_ctx,PCREDUNDANT);
366: KSPSetType(pcnn->ksp_coarse,KSPPREONLY);
367: PCRedundantGetKSP(pc_ctx,&inner_ksp);
368: KSPGetPC(inner_ksp,&inner_pc);
369: PCSetType(inner_pc,PCLU);
370: KSPSetOptionsPrefix(pcnn->ksp_coarse,"nn_coarse_");
371: KSPSetFromOptions(pcnn->ksp_coarse);
372: /* the vectors in the following line are dummy arguments, just telling the KSP the vector size. Values are not used */
373: KSPSetUp(pcnn->ksp_coarse);
374: }
376: /* Free the memory for mat */
377: PetscFree(mat);
379: /* for DEBUGGING, save the coarse matrix to a file. */
380: {
381: PetscBool flg = PETSC_FALSE;
382: PetscOptionsGetBool(NULL,"-pc_nn_save_coarse_matrix",&flg,NULL);
383: if (flg) {
384: PetscViewer viewer;
385: PetscViewerASCIIOpen(PETSC_COMM_WORLD,"coarse.m",&viewer);
386: PetscViewerSetFormat(viewer,PETSC_VIEWER_ASCII_MATLAB);
387: MatView(pcnn->coarse_mat,viewer);
388: PetscViewerDestroy(&viewer);
389: }
390: }
392: /* Set the variable pcnn->factor_coarse_rhs. */
393: pcnn->factor_coarse_rhs = (pcis->pure_neumann) ? 1.0 : 0.0;
395: /* See historical note 02, at the bottom of this file. */
396: return(0);
397: }
399: /* -------------------------------------------------------------------------- */
400: /*
401: PCNNApplySchurToChunk -
403: Input parameters:
404: . pcnn
405: . n - size of chunk
406: . idx - indices of chunk
407: . chunk - values
409: Output parameters:
410: . array_N - result of Schur complement applied to chunk, scattered to big array
411: . vec1_B - result of Schur complement applied to chunk
412: . vec2_B - garbage (used as work space)
413: . vec1_D - garbage (used as work space)
414: . vec2_D - garbage (used as work space)
416: */
419: 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)
420: {
422: PetscInt i;
423: PC_IS *pcis = (PC_IS*)(pc->data);
426: PetscMemzero((void*)array_N, pcis->n*sizeof(PetscScalar));
427: for (i=0; i<n; i++) array_N[idx[i]] = chunk[i];
428: PCISScatterArrayNToVecB(array_N,vec2_B,INSERT_VALUES,SCATTER_FORWARD,pc);
429: PCISApplySchur(pc,vec2_B,vec1_B,(Vec)0,vec1_D,vec2_D);
430: PCISScatterArrayNToVecB(array_N,vec1_B,INSERT_VALUES,SCATTER_REVERSE,pc);
431: return(0);
432: }
434: /* -------------------------------------------------------------------------- */
435: /*
436: PCNNApplyInterfacePreconditioner - Apply the interface preconditioner, i.e.,
437: the preconditioner for the Schur complement.
439: Input parameter:
440: . r - global vector of interior and interface nodes. The values on the interior nodes are NOT used.
442: Output parameters:
443: . z - global vector of interior and interface nodes. The values on the interface are the result of
444: the application of the interface preconditioner to the interface part of r. The values on the
445: interior nodes are garbage.
446: . work_N - array of local nodes (interior and interface, including ghosts); returns garbage (used as work space)
447: . vec1_B - vector of local interface nodes (including ghosts); returns garbage (used as work space)
448: . vec2_B - vector of local interface nodes (including ghosts); returns garbage (used as work space)
449: . vec3_B - vector of local interface nodes (including ghosts); returns garbage (used as work space)
450: . vec1_D - vector of local interior nodes; returns garbage (used as work space)
451: . vec2_D - vector of local interior nodes; returns garbage (used as work space)
452: . vec1_N - vector of local nodes (interior and interface, including ghosts); returns garbage (used as work space)
453: . vec2_N - vector of local nodes (interior and interface, including ghosts); returns garbage (used as work space)
455: */
458: 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)
459: {
461: PC_IS *pcis = (PC_IS*)(pc->data);
464: /*
465: First balancing step.
466: */
467: {
468: PetscBool flg = PETSC_FALSE;
469: PetscOptionsGetBool(NULL,"-pc_nn_turn_off_first_balancing",&flg,NULL);
470: if (!flg) {
471: PCNNBalancing(pc,r,(Vec)0,z,vec1_B,vec2_B,(Vec)0,vec1_D,vec2_D,work_N);
472: } else {
473: VecCopy(r,z);
474: }
475: }
477: /*
478: Extract the local interface part of z and scale it by D
479: */
480: VecScatterBegin(pcis->global_to_B,z,vec1_B,INSERT_VALUES,SCATTER_FORWARD);
481: VecScatterEnd (pcis->global_to_B,z,vec1_B,INSERT_VALUES,SCATTER_FORWARD);
482: VecPointwiseMult(vec2_B,pcis->D,vec1_B);
484: /* Neumann Solver */
485: PCISApplyInvSchur(pc,vec2_B,vec1_B,vec1_N,vec2_N);
487: /*
488: Second balancing step.
489: */
490: {
491: PetscBool flg = PETSC_FALSE;
492: PetscOptionsGetBool(NULL,"-pc_turn_off_second_balancing",&flg,NULL);
493: if (!flg) {
494: PCNNBalancing(pc,r,vec1_B,z,vec2_B,vec3_B,(Vec)0,vec1_D,vec2_D,work_N);
495: } else {
496: VecPointwiseMult(vec2_B,pcis->D,vec1_B);
497: VecSet(z,0.0);
498: VecScatterBegin(pcis->global_to_B,vec2_B,z,ADD_VALUES,SCATTER_REVERSE);
499: VecScatterEnd (pcis->global_to_B,vec2_B,z,ADD_VALUES,SCATTER_REVERSE);
500: }
501: }
502: return(0);
503: }
505: /* -------------------------------------------------------------------------- */
506: /*
507: PCNNBalancing - Computes z, as given in equations (15) and (16) (if the
508: input argument u is provided), or s, as given in equations
509: (12) and (13), if the input argument u is a null vector.
510: Notice that the input argument u plays the role of u_i in
511: equation (14). The equation numbers refer to [Man93].
513: Input Parameters:
514: . pcnn - NN preconditioner context.
515: . r - MPI vector of all nodes (interior and interface). It's preserved.
516: . u - (Optional) sequential vector of local interface nodes. It's preserved UNLESS vec3_B is null.
518: Output Parameters:
519: . z - MPI vector of interior and interface nodes. Returns s or z (see description above).
520: . vec1_B - Sequential vector of local interface nodes. Workspace.
521: . vec2_B - Sequential vector of local interface nodes. Workspace.
522: . vec3_B - (Optional) sequential vector of local interface nodes. Workspace.
523: . vec1_D - Sequential vector of local interior nodes. Workspace.
524: . vec2_D - Sequential vector of local interior nodes. Workspace.
525: . work_N - Array of all local nodes (interior and interface). Workspace.
527: */
530: 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)
531: {
533: PetscInt k;
534: PetscScalar value;
535: PetscScalar *lambda;
536: PC_NN *pcnn = (PC_NN*)(pc->data);
537: PC_IS *pcis = (PC_IS*)(pc->data);
540: PetscLogEventBegin(PC_ApplyCoarse,0,0,0,0);
541: if (u) {
542: if (!vec3_B) vec3_B = u;
543: VecPointwiseMult(vec1_B,pcis->D,u);
544: VecSet(z,0.0);
545: VecScatterBegin(pcis->global_to_B,vec1_B,z,ADD_VALUES,SCATTER_REVERSE);
546: VecScatterEnd (pcis->global_to_B,vec1_B,z,ADD_VALUES,SCATTER_REVERSE);
547: VecScatterBegin(pcis->global_to_B,z,vec2_B,INSERT_VALUES,SCATTER_FORWARD);
548: VecScatterEnd (pcis->global_to_B,z,vec2_B,INSERT_VALUES,SCATTER_FORWARD);
549: PCISApplySchur(pc,vec2_B,vec3_B,(Vec)0,vec1_D,vec2_D);
550: VecScale(vec3_B,-1.0);
551: VecCopy(r,z);
552: VecScatterBegin(pcis->global_to_B,vec3_B,z,ADD_VALUES,SCATTER_REVERSE);
553: VecScatterEnd (pcis->global_to_B,vec3_B,z,ADD_VALUES,SCATTER_REVERSE);
554: } else {
555: VecCopy(r,z);
556: }
557: VecScatterBegin(pcis->global_to_B,z,vec2_B,INSERT_VALUES,SCATTER_FORWARD);
558: VecScatterEnd (pcis->global_to_B,z,vec2_B,INSERT_VALUES,SCATTER_FORWARD);
559: PCISScatterArrayNToVecB(work_N,vec2_B,INSERT_VALUES,SCATTER_REVERSE,pc);
560: for (k=0, value=0.0; k<pcis->n_shared[0]; k++) value += pcnn->DZ_IN[0][k] * work_N[pcis->shared[0][k]];
561: value *= pcnn->factor_coarse_rhs; /* This factor is set in CreateCoarseMatrix(). */
562: {
563: PetscMPIInt rank;
564: MPI_Comm_rank(PetscObjectComm((PetscObject)pc),&rank);
565: VecSetValue(pcnn->coarse_b,rank,value,INSERT_VALUES);
566: /*
567: Since we are only inserting local values (one value actually) we don't need to do the
568: reduction that tells us there is no data that needs to be moved. Hence we comment out these
569: VecAssemblyBegin(pcnn->coarse_b);
570: VecAssemblyEnd (pcnn->coarse_b);
571: */
572: }
573: KSPSolve(pcnn->ksp_coarse,pcnn->coarse_b,pcnn->coarse_x);
574: if (!u) { VecScale(pcnn->coarse_x,-1.0); }
575: VecGetArray(pcnn->coarse_x,&lambda);
576: for (k=0; k<pcis->n_shared[0]; k++) work_N[pcis->shared[0][k]] = *lambda * pcnn->DZ_IN[0][k];
577: VecRestoreArray(pcnn->coarse_x,&lambda);
578: PCISScatterArrayNToVecB(work_N,vec2_B,INSERT_VALUES,SCATTER_FORWARD,pc);
579: VecSet(z,0.0);
580: VecScatterBegin(pcis->global_to_B,vec2_B,z,ADD_VALUES,SCATTER_REVERSE);
581: VecScatterEnd (pcis->global_to_B,vec2_B,z,ADD_VALUES,SCATTER_REVERSE);
582: if (!u) {
583: VecScatterBegin(pcis->global_to_B,z,vec2_B,INSERT_VALUES,SCATTER_FORWARD);
584: VecScatterEnd (pcis->global_to_B,z,vec2_B,INSERT_VALUES,SCATTER_FORWARD);
585: PCISApplySchur(pc,vec2_B,vec1_B,(Vec)0,vec1_D,vec2_D);
586: VecCopy(r,z);
587: }
588: VecScatterBegin(pcis->global_to_B,vec1_B,z,ADD_VALUES,SCATTER_REVERSE);
589: VecScatterEnd (pcis->global_to_B,vec1_B,z,ADD_VALUES,SCATTER_REVERSE);
590: PetscLogEventEnd(PC_ApplyCoarse,0,0,0,0);
591: return(0);
592: }
598: /* ------- E N D O F T H E C O D E ------- */
599: /* */
600: /* From now on, "footnotes" (or "historical notes"). */
601: /* */
602: /* ------------------------------------------------- */
606: /* --------------------------------------------------------------------------
607: Historical note 01
608: -------------------------------------------------------------------------- */
609: /*
610: We considered the possibility of an alternative D_i that would still
611: provide a partition of unity (i.e., $ \sum_i N_i D_i N_i^T = I $).
612: The basic principle was still the pseudo-inverse of the counting
613: function; the difference was that we would not count subdomains
614: that do not contribute to the coarse space (i.e., not pure-Neumann
615: subdomains).
617: This turned out to be a bad idea: we would solve trivial Neumann
618: problems in the not pure-Neumann subdomains, since we would be scaling
619: the balanced residual by zero.
620: */
625: /* --------------------------------------------------------------------------
626: Historical note 02
627: -------------------------------------------------------------------------- */
628: /*
629: We tried an alternative coarse problem, that would eliminate exactly a
630: constant error. Turned out not to improve the overall convergence.
631: */