Actual source code: nn.c
1: #include <../src/ksp/pc/impls/is/nn/nn.h>
3: /*
4: PCSetUp_NN - Prepares for the use of the NN preconditioner
5: by setting data structures and options.
7: Input Parameter:
8: . pc - the preconditioner context
10: Application Interface Routine: PCSetUp()
12: Note:
13: The interface routine PCSetUp() is not usually called directly by
14: the user, but instead is called by PCApply() if necessary.
15: */
16: static PetscErrorCode PCSetUp_NN(PC pc)
17: {
18: PetscFunctionBegin;
19: if (!pc->setupcalled) {
20: /* Set up all the "iterative substructuring" common block */
21: PetscCall(PCISSetUp(pc, PETSC_TRUE, PETSC_TRUE));
22: /* Create the coarse matrix. */
23: PetscCall(PCNNCreateCoarseMatrix(pc));
24: }
25: PetscFunctionReturn(PETSC_SUCCESS);
26: }
28: /*
29: PCApply_NN - Applies the NN preconditioner to a vector.
31: Input Parameters:
32: + pc - the preconditioner context
33: - r - input vector (global)
35: Output Parameter:
36: . z - output vector (global)
38: Application Interface Routine: PCApply()
39: */
40: static PetscErrorCode PCApply_NN(PC pc, Vec r, Vec z)
41: {
42: PC_IS *pcis = (PC_IS *)(pc->data);
43: PetscScalar m_one = -1.0;
44: Vec w = pcis->vec1_global;
46: PetscFunctionBegin;
47: /*
48: Dirichlet solvers.
49: Solving $ B_I^{(i)}r_I^{(i)} $ at each processor.
50: Storing the local results at vec2_D
51: */
52: PetscCall(VecScatterBegin(pcis->global_to_D, r, pcis->vec1_D, INSERT_VALUES, SCATTER_FORWARD));
53: PetscCall(VecScatterEnd(pcis->global_to_D, r, pcis->vec1_D, INSERT_VALUES, SCATTER_FORWARD));
54: PetscCall(KSPSolve(pcis->ksp_D, pcis->vec1_D, pcis->vec2_D));
56: /*
57: Computing $ r_B - \sum_j \tilde R_j^T A_{BI}^{(j)} (B_I^{(j)}r_I^{(j)}) $ .
58: Storing the result in the interface portion of the global vector w.
59: */
60: PetscCall(MatMult(pcis->A_BI, pcis->vec2_D, pcis->vec1_B));
61: PetscCall(VecScale(pcis->vec1_B, m_one));
62: PetscCall(VecCopy(r, w));
63: PetscCall(VecScatterBegin(pcis->global_to_B, pcis->vec1_B, w, ADD_VALUES, SCATTER_REVERSE));
64: PetscCall(VecScatterEnd(pcis->global_to_B, pcis->vec1_B, w, ADD_VALUES, SCATTER_REVERSE));
66: /*
67: Apply the interface preconditioner
68: */
69: PetscCall(PCNNApplyInterfacePreconditioner(pc, w, z, pcis->work_N, pcis->vec1_B, pcis->vec2_B, pcis->vec3_B, pcis->vec1_D, pcis->vec3_D, pcis->vec1_N, pcis->vec2_N));
71: /*
72: Computing $ t_I^{(i)} = A_{IB}^{(i)} \tilde R_i z_B $
73: The result is stored in vec1_D.
74: */
75: PetscCall(VecScatterBegin(pcis->global_to_B, z, pcis->vec1_B, INSERT_VALUES, SCATTER_FORWARD));
76: PetscCall(VecScatterEnd(pcis->global_to_B, z, pcis->vec1_B, INSERT_VALUES, SCATTER_FORWARD));
77: PetscCall(MatMult(pcis->A_IB, pcis->vec1_B, pcis->vec1_D));
79: /*
80: Dirichlet solvers.
81: Computing $ B_I^{(i)}t_I^{(i)} $ and sticking into the global vector the blocks
82: $ B_I^{(i)}r_I^{(i)} - B_I^{(i)}t_I^{(i)} $.
83: */
84: PetscCall(VecScatterBegin(pcis->global_to_D, pcis->vec2_D, z, INSERT_VALUES, SCATTER_REVERSE));
85: PetscCall(VecScatterEnd(pcis->global_to_D, pcis->vec2_D, z, INSERT_VALUES, SCATTER_REVERSE));
86: PetscCall(KSPSolve(pcis->ksp_D, pcis->vec1_D, pcis->vec2_D));
87: PetscCall(VecScale(pcis->vec2_D, m_one));
88: PetscCall(VecScatterBegin(pcis->global_to_D, pcis->vec2_D, z, ADD_VALUES, SCATTER_REVERSE));
89: PetscCall(VecScatterEnd(pcis->global_to_D, pcis->vec2_D, z, ADD_VALUES, SCATTER_REVERSE));
90: PetscFunctionReturn(PETSC_SUCCESS);
91: }
93: /*
94: PCDestroy_NN - Destroys the private context for the NN preconditioner
95: that was created with PCCreate_NN().
97: Input Parameter:
98: . pc - the preconditioner context
100: Application Interface Routine: PCDestroy()
101: */
102: static PetscErrorCode PCDestroy_NN(PC pc)
103: {
104: PC_NN *pcnn = (PC_NN *)pc->data;
106: PetscFunctionBegin;
107: PetscCall(PCISReset(pc));
109: PetscCall(MatDestroy(&pcnn->coarse_mat));
110: PetscCall(VecDestroy(&pcnn->coarse_x));
111: PetscCall(VecDestroy(&pcnn->coarse_b));
112: PetscCall(KSPDestroy(&pcnn->ksp_coarse));
113: if (pcnn->DZ_IN) {
114: PetscCall(PetscFree(pcnn->DZ_IN[0]));
115: PetscCall(PetscFree(pcnn->DZ_IN));
116: }
118: /*
119: Free the private data structure that was hanging off the PC
120: */
121: PetscCall(PetscFree(pc->data));
122: PetscFunctionReturn(PETSC_SUCCESS);
123: }
125: /*MC
126: PCNN - Balancing Neumann-Neumann for scalar elliptic PDEs.
128: Options Database Keys:
129: + -pc_nn_turn_off_first_balancing - do not balance the residual before solving the local Neumann problems
130: (this skips the first coarse grid solve in the preconditioner)
131: . -pc_nn_turn_off_second_balancing - do not balance the solution solving the local Neumann problems
132: (this skips the second coarse grid solve in the preconditioner)
133: . -pc_is_damp_fixed <fact> -
134: . -pc_is_remove_nullspace_fixed -
135: . -pc_is_set_damping_factor_floating <fact> -
136: . -pc_is_not_damp_floating -
137: - -pc_is_not_remove_nullspace_floating -
139: Options Database prefixes for the subsolvers this preconditioner uses:
140: + -nn_coarse_pc_ - for the coarse grid preconditioner
141: . -is_localD_pc_ - for the Dirichlet subproblem preconditioner
142: - -is_localN_pc_ - for the Neumann subproblem preconditioner
144: Level: intermediate
146: Notes:
147: The matrix used with this preconditioner must be of type `MATIS`
149: Unlike more 'conventional' Neumann-Neumann preconditioners this iterates over ALL the
150: degrees of freedom, NOT just those on the interface (this allows the use of approximate solvers
151: on the subdomains; though in our experience using approximate solvers is slower.).
153: Contributed by Paulo Goldfeld
155: .seealso: [](ch_ksp), `PCCreate()`, `PCSetType()`, `PCType`, `PC`, `MATIS`, `PCBDDC`
156: M*/
158: PETSC_EXTERN PetscErrorCode PCCreate_NN(PC pc)
159: {
160: PC_NN *pcnn;
162: PetscFunctionBegin;
163: /*
164: Creates the private data structure for this preconditioner and
165: attach it to the PC object.
166: */
167: PetscCall(PetscNew(&pcnn));
168: pc->data = (void *)pcnn;
170: PetscCall(PCISInitialize(pc));
171: pcnn->coarse_mat = NULL;
172: pcnn->coarse_x = NULL;
173: pcnn->coarse_b = NULL;
174: pcnn->ksp_coarse = NULL;
175: pcnn->DZ_IN = NULL;
177: /*
178: Set the pointers for the functions that are provided above.
179: Now when the user-level routines (such as PCApply(), PCDestroy(), etc.)
180: are called, they will automatically call these functions. Note we
181: choose not to provide a couple of these functions since they are
182: not needed.
183: */
184: pc->ops->apply = PCApply_NN;
185: pc->ops->applytranspose = NULL;
186: pc->ops->setup = PCSetUp_NN;
187: pc->ops->destroy = PCDestroy_NN;
188: pc->ops->view = NULL;
189: pc->ops->applyrichardson = NULL;
190: pc->ops->applysymmetricleft = NULL;
191: pc->ops->applysymmetricright = NULL;
192: PetscFunctionReturn(PETSC_SUCCESS);
193: }
195: /*
196: PCNNCreateCoarseMatrix -
197: */
198: PetscErrorCode PCNNCreateCoarseMatrix(PC pc)
199: {
200: MPI_Request *send_request, *recv_request;
201: PetscInt i, j, k;
202: PetscScalar *mat; /* Sub-matrix with this subdomain's contribution to the coarse matrix */
203: PetscScalar **DZ_OUT; /* proc[k].DZ_OUT[i][] = bit of vector to be sent from processor k to processor i */
205: /* aliasing some names */
206: PC_IS *pcis = (PC_IS *)(pc->data);
207: PC_NN *pcnn = (PC_NN *)pc->data;
208: PetscInt n_neigh = pcis->n_neigh;
209: PetscInt *neigh = pcis->neigh;
210: PetscInt *n_shared = pcis->n_shared;
211: PetscInt **shared = pcis->shared;
212: PetscScalar **DZ_IN; /* Must be initialized after memory allocation. */
214: PetscFunctionBegin;
215: /* Allocate memory for mat (the +1 is to handle the case n_neigh equal to zero) */
216: PetscCall(PetscMalloc1(n_neigh * n_neigh + 1, &mat));
218: /* Allocate memory for DZ */
219: /* Notice that DZ_OUT[0] is allocated some space that is never used. */
220: /* This is just in order to DZ_OUT and DZ_IN to have exactly the same form. */
221: {
222: PetscInt size_of_Z = 0;
223: PetscCall(PetscMalloc((n_neigh + 1) * sizeof(PetscScalar *), &pcnn->DZ_IN));
224: DZ_IN = pcnn->DZ_IN;
225: PetscCall(PetscMalloc((n_neigh + 1) * sizeof(PetscScalar *), &DZ_OUT));
226: for (i = 0; i < n_neigh; i++) size_of_Z += n_shared[i];
227: PetscCall(PetscMalloc((size_of_Z + 1) * sizeof(PetscScalar), &DZ_IN[0]));
228: PetscCall(PetscMalloc((size_of_Z + 1) * sizeof(PetscScalar), &DZ_OUT[0]));
229: }
230: for (i = 1; i < n_neigh; i++) {
231: DZ_IN[i] = DZ_IN[i - 1] + n_shared[i - 1];
232: DZ_OUT[i] = DZ_OUT[i - 1] + n_shared[i - 1];
233: }
235: /* Set the values of DZ_OUT, in order to send this info to the neighbours */
236: /* First, set the auxiliary array pcis->work_N. */
237: PetscCall(PCISScatterArrayNToVecB(pc, pcis->work_N, pcis->D, INSERT_VALUES, SCATTER_REVERSE));
238: for (i = 1; i < n_neigh; i++) {
239: for (j = 0; j < n_shared[i]; j++) DZ_OUT[i][j] = pcis->work_N[shared[i][j]];
240: }
242: /* Non-blocking send/receive the common-interface chunks of scaled nullspaces */
243: /* Notice that send_request[] and recv_request[] could have one less element. */
244: /* We make them longer to have request[i] corresponding to neigh[i]. */
245: {
246: PetscMPIInt tag;
247: PetscCall(PetscObjectGetNewTag((PetscObject)pc, &tag));
248: PetscCall(PetscMalloc2(n_neigh + 1, &send_request, n_neigh + 1, &recv_request));
249: for (i = 1; i < n_neigh; i++) {
250: PetscCallMPI(MPI_Isend((void *)(DZ_OUT[i]), n_shared[i], MPIU_SCALAR, neigh[i], tag, PetscObjectComm((PetscObject)pc), &(send_request[i])));
251: PetscCallMPI(MPI_Irecv((void *)(DZ_IN[i]), n_shared[i], MPIU_SCALAR, neigh[i], tag, PetscObjectComm((PetscObject)pc), &(recv_request[i])));
252: }
253: }
255: /* Set DZ_IN[0][] (recall that neigh[0]==rank, always) */
256: for (j = 0; j < n_shared[0]; j++) DZ_IN[0][j] = pcis->work_N[shared[0][j]];
258: /* Start computing with local D*Z while communication goes on. */
259: /* Apply Schur complement. The result is "stored" in vec (more */
260: /* precisely, vec points to the result, stored in pc_nn->vec1_B) */
261: /* and also scattered to pcnn->work_N. */
262: PetscCall(PCNNApplySchurToChunk(pc, n_shared[0], shared[0], DZ_IN[0], pcis->work_N, pcis->vec1_B, pcis->vec2_B, pcis->vec1_D, pcis->vec2_D));
264: /* Compute the first column, while completing the receiving. */
265: for (i = 0; i < n_neigh; i++) {
266: MPI_Status stat;
267: PetscMPIInt ind = 0;
268: if (i > 0) {
269: PetscCallMPI(MPI_Waitany(n_neigh - 1, recv_request + 1, &ind, &stat));
270: ind++;
271: }
272: mat[ind * n_neigh + 0] = 0.0;
273: for (k = 0; k < n_shared[ind]; k++) mat[ind * n_neigh + 0] += DZ_IN[ind][k] * pcis->work_N[shared[ind][k]];
274: }
276: /* Compute the remaining of the columns */
277: for (j = 1; j < n_neigh; j++) {
278: PetscCall(PCNNApplySchurToChunk(pc, n_shared[j], shared[j], DZ_IN[j], pcis->work_N, pcis->vec1_B, pcis->vec2_B, pcis->vec1_D, pcis->vec2_D));
279: for (i = 0; i < n_neigh; i++) {
280: mat[i * n_neigh + j] = 0.0;
281: for (k = 0; k < n_shared[i]; k++) mat[i * n_neigh + j] += DZ_IN[i][k] * pcis->work_N[shared[i][k]];
282: }
283: }
285: /* Complete the sending. */
286: if (n_neigh > 1) {
287: MPI_Status *stat;
288: PetscCall(PetscMalloc1(n_neigh - 1, &stat));
289: if (n_neigh - 1) PetscCallMPI(MPI_Waitall(n_neigh - 1, &(send_request[1]), stat));
290: PetscCall(PetscFree(stat));
291: }
293: /* Free the memory for the MPI requests */
294: PetscCall(PetscFree2(send_request, recv_request));
296: /* Free the memory for DZ_OUT */
297: if (DZ_OUT) {
298: PetscCall(PetscFree(DZ_OUT[0]));
299: PetscCall(PetscFree(DZ_OUT));
300: }
302: {
303: PetscMPIInt size;
304: PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)pc), &size));
305: /* Create the global coarse vectors (rhs and solution). */
306: PetscCall(VecCreateMPI(PetscObjectComm((PetscObject)pc), 1, size, &(pcnn->coarse_b)));
307: PetscCall(VecDuplicate(pcnn->coarse_b, &(pcnn->coarse_x)));
308: /* Create and set the global coarse AIJ matrix. */
309: PetscCall(MatCreate(PetscObjectComm((PetscObject)pc), &(pcnn->coarse_mat)));
310: PetscCall(MatSetSizes(pcnn->coarse_mat, 1, 1, size, size));
311: PetscCall(MatSetType(pcnn->coarse_mat, MATAIJ));
312: PetscCall(MatSeqAIJSetPreallocation(pcnn->coarse_mat, 1, NULL));
313: PetscCall(MatMPIAIJSetPreallocation(pcnn->coarse_mat, 1, NULL, n_neigh, NULL));
314: PetscCall(MatSetOption(pcnn->coarse_mat, MAT_NEW_NONZERO_ALLOCATION_ERR, PETSC_FALSE));
315: PetscCall(MatSetOption(pcnn->coarse_mat, MAT_NEW_NONZERO_LOCATION_ERR, PETSC_FALSE));
316: PetscCall(MatSetValues(pcnn->coarse_mat, n_neigh, neigh, n_neigh, neigh, mat, ADD_VALUES));
317: PetscCall(MatAssemblyBegin(pcnn->coarse_mat, MAT_FINAL_ASSEMBLY));
318: PetscCall(MatAssemblyEnd(pcnn->coarse_mat, MAT_FINAL_ASSEMBLY));
319: }
321: {
322: PetscMPIInt rank;
323: PetscScalar one = 1.0;
324: PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)pc), &rank));
325: /* "Zero out" rows of not-purely-Neumann subdomains */
326: if (pcis->pure_neumann) { /* does NOT zero the row; create an empty index set. The reason is that MatZeroRows() is collective. */
327: PetscCall(MatZeroRows(pcnn->coarse_mat, 0, NULL, one, NULL, NULL));
328: } else { /* here it DOES zero the row, since it's not a floating subdomain. */
329: PetscInt row = (PetscInt)rank;
330: PetscCall(MatZeroRows(pcnn->coarse_mat, 1, &row, one, NULL, NULL));
331: }
332: }
334: /* Create the coarse linear solver context */
335: {
336: PC pc_ctx, inner_pc;
337: KSP inner_ksp;
339: PetscCall(KSPCreate(PetscObjectComm((PetscObject)pc), &pcnn->ksp_coarse));
340: PetscCall(KSPSetNestLevel(pcnn->ksp_coarse, pc->kspnestlevel));
341: PetscCall(PetscObjectIncrementTabLevel((PetscObject)pcnn->ksp_coarse, (PetscObject)pc, 2));
342: PetscCall(KSPSetOperators(pcnn->ksp_coarse, pcnn->coarse_mat, pcnn->coarse_mat));
343: PetscCall(KSPGetPC(pcnn->ksp_coarse, &pc_ctx));
344: PetscCall(PCSetType(pc_ctx, PCREDUNDANT));
345: PetscCall(KSPSetType(pcnn->ksp_coarse, KSPPREONLY));
346: PetscCall(PCRedundantGetKSP(pc_ctx, &inner_ksp));
347: PetscCall(KSPGetPC(inner_ksp, &inner_pc));
348: PetscCall(PCSetType(inner_pc, PCLU));
349: PetscCall(KSPSetOptionsPrefix(pcnn->ksp_coarse, "nn_coarse_"));
350: PetscCall(KSPSetFromOptions(pcnn->ksp_coarse));
351: /* the vectors in the following line are dummy arguments, just telling the KSP the vector size. Values are not used */
352: PetscCall(KSPSetUp(pcnn->ksp_coarse));
353: }
355: /* Free the memory for mat */
356: PetscCall(PetscFree(mat));
358: /* for DEBUGGING, save the coarse matrix to a file. */
359: {
360: PetscBool flg = PETSC_FALSE;
361: PetscCall(PetscOptionsGetBool(NULL, NULL, "-pc_nn_save_coarse_matrix", &flg, NULL));
362: if (flg) {
363: PetscViewer viewer;
364: PetscCall(PetscViewerASCIIOpen(PETSC_COMM_WORLD, "coarse.m", &viewer));
365: PetscCall(PetscViewerPushFormat(viewer, PETSC_VIEWER_ASCII_MATLAB));
366: PetscCall(MatView(pcnn->coarse_mat, viewer));
367: PetscCall(PetscViewerPopFormat(viewer));
368: PetscCall(PetscViewerDestroy(&viewer));
369: }
370: }
372: /* Set the variable pcnn->factor_coarse_rhs. */
373: pcnn->factor_coarse_rhs = (pcis->pure_neumann) ? 1.0 : 0.0;
375: /* See historical note 02, at the bottom of this file. */
376: PetscFunctionReturn(PETSC_SUCCESS);
377: }
379: /*
380: PCNNApplySchurToChunk -
382: Input parameters:
383: . pcnn
384: . n - size of chunk
385: . idx - indices of chunk
386: . chunk - values
388: Output parameters:
389: . array_N - result of Schur complement applied to chunk, scattered to big array
390: . vec1_B - result of Schur complement applied to chunk
391: . vec2_B - garbage (used as work space)
392: . vec1_D - garbage (used as work space)
393: . vec2_D - garbage (used as work space)
395: */
396: 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)
397: {
398: PetscInt i;
399: PC_IS *pcis = (PC_IS *)(pc->data);
401: PetscFunctionBegin;
402: PetscCall(PetscArrayzero(array_N, pcis->n));
403: for (i = 0; i < n; i++) array_N[idx[i]] = chunk[i];
404: PetscCall(PCISScatterArrayNToVecB(pc, array_N, vec2_B, INSERT_VALUES, SCATTER_FORWARD));
405: PetscCall(PCISApplySchur(pc, vec2_B, vec1_B, (Vec)0, vec1_D, vec2_D));
406: PetscCall(PCISScatterArrayNToVecB(pc, array_N, vec1_B, INSERT_VALUES, SCATTER_REVERSE));
407: PetscFunctionReturn(PETSC_SUCCESS);
408: }
410: /*
411: PCNNApplyInterfacePreconditioner - Apply the interface preconditioner, i.e.,
412: the preconditioner for the Schur complement.
414: Input parameter:
415: . r - global vector of interior and interface nodes. The values on the interior nodes are NOT used.
417: Output parameters:
418: . z - global vector of interior and interface nodes. The values on the interface are the result of
419: the application of the interface preconditioner to the interface part of r. The values on the
420: interior nodes are garbage.
421: . work_N - array of local nodes (interior and interface, including ghosts); returns garbage (used as work space)
422: . vec1_B - vector of local interface nodes (including ghosts); returns garbage (used as work space)
423: . vec2_B - vector of local interface nodes (including ghosts); returns garbage (used as work space)
424: . vec3_B - vector of local interface nodes (including ghosts); returns garbage (used as work space)
425: . vec1_D - vector of local interior nodes; returns garbage (used as work space)
426: . vec2_D - vector of local interior nodes; returns garbage (used as work space)
427: . vec1_N - vector of local nodes (interior and interface, including ghosts); returns garbage (used as work space)
428: . vec2_N - vector of local nodes (interior and interface, including ghosts); returns garbage (used as work space)
430: */
431: 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)
432: {
433: PC_IS *pcis = (PC_IS *)(pc->data);
435: PetscFunctionBegin;
436: /*
437: First balancing step.
438: */
439: {
440: PetscBool flg = PETSC_FALSE;
441: PetscCall(PetscOptionsGetBool(NULL, NULL, "-pc_nn_turn_off_first_balancing", &flg, NULL));
442: if (!flg) {
443: PetscCall(PCNNBalancing(pc, r, (Vec)0, z, vec1_B, vec2_B, (Vec)0, vec1_D, vec2_D, work_N));
444: } else {
445: PetscCall(VecCopy(r, z));
446: }
447: }
449: /*
450: Extract the local interface part of z and scale it by D
451: */
452: PetscCall(VecScatterBegin(pcis->global_to_B, z, vec1_B, INSERT_VALUES, SCATTER_FORWARD));
453: PetscCall(VecScatterEnd(pcis->global_to_B, z, vec1_B, INSERT_VALUES, SCATTER_FORWARD));
454: PetscCall(VecPointwiseMult(vec2_B, pcis->D, vec1_B));
456: /* Neumann Solver */
457: PetscCall(PCISApplyInvSchur(pc, vec2_B, vec1_B, vec1_N, vec2_N));
459: /*
460: Second balancing step.
461: */
462: {
463: PetscBool flg = PETSC_FALSE;
464: PetscCall(PetscOptionsGetBool(NULL, NULL, "-pc_turn_off_second_balancing", &flg, NULL));
465: if (!flg) {
466: PetscCall(PCNNBalancing(pc, r, vec1_B, z, vec2_B, vec3_B, (Vec)0, vec1_D, vec2_D, work_N));
467: } else {
468: PetscCall(VecPointwiseMult(vec2_B, pcis->D, vec1_B));
469: PetscCall(VecSet(z, 0.0));
470: PetscCall(VecScatterBegin(pcis->global_to_B, vec2_B, z, ADD_VALUES, SCATTER_REVERSE));
471: PetscCall(VecScatterEnd(pcis->global_to_B, vec2_B, z, ADD_VALUES, SCATTER_REVERSE));
472: }
473: }
474: PetscFunctionReturn(PETSC_SUCCESS);
475: }
477: /*
478: PCNNBalancing - Computes z, as given in equations (15) and (16) (if the
479: input argument u is provided), or s, as given in equations
480: (12) and (13), if the input argument u is a null vector.
481: Notice that the input argument u plays the role of u_i in
482: equation (14). The equation numbers refer to [Man93].
484: Input Parameters:
485: + pcnn - NN preconditioner context.
486: . r - MPI vector of all nodes (interior and interface). It's preserved.
487: - u - (Optional) sequential vector of local interface nodes. It's preserved UNLESS vec3_B is null.
489: Output Parameters:
490: + z - MPI vector of interior and interface nodes. Returns s or z (see description above).
491: . vec1_B - Sequential vector of local interface nodes. Workspace.
492: . vec2_B - Sequential vector of local interface nodes. Workspace.
493: . vec3_B - (Optional) sequential vector of local interface nodes. Workspace.
494: . vec1_D - Sequential vector of local interior nodes. Workspace.
495: . vec2_D - Sequential vector of local interior nodes. Workspace.
496: - work_N - Array of all local nodes (interior and interface). Workspace.
498: */
499: 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)
500: {
501: PetscInt k;
502: PetscScalar value;
503: PetscScalar *lambda;
504: PC_NN *pcnn = (PC_NN *)(pc->data);
505: PC_IS *pcis = (PC_IS *)(pc->data);
507: PetscFunctionBegin;
508: PetscCall(PetscLogEventBegin(PC_ApplyCoarse, pc, 0, 0, 0));
509: if (u) {
510: if (!vec3_B) vec3_B = u;
511: PetscCall(VecPointwiseMult(vec1_B, pcis->D, u));
512: PetscCall(VecSet(z, 0.0));
513: PetscCall(VecScatterBegin(pcis->global_to_B, vec1_B, z, ADD_VALUES, SCATTER_REVERSE));
514: PetscCall(VecScatterEnd(pcis->global_to_B, vec1_B, z, ADD_VALUES, SCATTER_REVERSE));
515: PetscCall(VecScatterBegin(pcis->global_to_B, z, vec2_B, INSERT_VALUES, SCATTER_FORWARD));
516: PetscCall(VecScatterEnd(pcis->global_to_B, z, vec2_B, INSERT_VALUES, SCATTER_FORWARD));
517: PetscCall(PCISApplySchur(pc, vec2_B, vec3_B, (Vec)0, vec1_D, vec2_D));
518: PetscCall(VecScale(vec3_B, -1.0));
519: PetscCall(VecCopy(r, z));
520: PetscCall(VecScatterBegin(pcis->global_to_B, vec3_B, z, ADD_VALUES, SCATTER_REVERSE));
521: PetscCall(VecScatterEnd(pcis->global_to_B, vec3_B, z, ADD_VALUES, SCATTER_REVERSE));
522: } else {
523: PetscCall(VecCopy(r, z));
524: }
525: PetscCall(VecScatterBegin(pcis->global_to_B, z, vec2_B, INSERT_VALUES, SCATTER_FORWARD));
526: PetscCall(VecScatterEnd(pcis->global_to_B, z, vec2_B, INSERT_VALUES, SCATTER_FORWARD));
527: PetscCall(PCISScatterArrayNToVecB(pc, work_N, vec2_B, INSERT_VALUES, SCATTER_REVERSE));
528: for (k = 0, value = 0.0; k < pcis->n_shared[0]; k++) value += pcnn->DZ_IN[0][k] * work_N[pcis->shared[0][k]];
529: value *= pcnn->factor_coarse_rhs; /* This factor is set in CreateCoarseMatrix(). */
530: {
531: PetscMPIInt rank;
532: PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)pc), &rank));
533: PetscCall(VecSetValue(pcnn->coarse_b, rank, value, INSERT_VALUES));
534: /*
535: Since we are only inserting local values (one value actually) we don't need to do the
536: reduction that tells us there is no data that needs to be moved. Hence we comment out these
537: PetscCall(VecAssemblyBegin(pcnn->coarse_b));
538: PetscCall(VecAssemblyEnd (pcnn->coarse_b));
539: */
540: }
541: PetscCall(KSPSolve(pcnn->ksp_coarse, pcnn->coarse_b, pcnn->coarse_x));
542: if (!u) PetscCall(VecScale(pcnn->coarse_x, -1.0));
543: PetscCall(VecGetArray(pcnn->coarse_x, &lambda));
544: for (k = 0; k < pcis->n_shared[0]; k++) work_N[pcis->shared[0][k]] = *lambda * pcnn->DZ_IN[0][k];
545: PetscCall(VecRestoreArray(pcnn->coarse_x, &lambda));
546: PetscCall(PCISScatterArrayNToVecB(pc, work_N, vec2_B, INSERT_VALUES, SCATTER_FORWARD));
547: PetscCall(VecSet(z, 0.0));
548: PetscCall(VecScatterBegin(pcis->global_to_B, vec2_B, z, ADD_VALUES, SCATTER_REVERSE));
549: PetscCall(VecScatterEnd(pcis->global_to_B, vec2_B, z, ADD_VALUES, SCATTER_REVERSE));
550: if (!u) {
551: PetscCall(VecScatterBegin(pcis->global_to_B, z, vec2_B, INSERT_VALUES, SCATTER_FORWARD));
552: PetscCall(VecScatterEnd(pcis->global_to_B, z, vec2_B, INSERT_VALUES, SCATTER_FORWARD));
553: PetscCall(PCISApplySchur(pc, vec2_B, vec1_B, (Vec)0, vec1_D, vec2_D));
554: PetscCall(VecCopy(r, z));
555: }
556: PetscCall(VecScatterBegin(pcis->global_to_B, vec1_B, z, ADD_VALUES, SCATTER_REVERSE));
557: PetscCall(VecScatterEnd(pcis->global_to_B, vec1_B, z, ADD_VALUES, SCATTER_REVERSE));
558: PetscCall(PetscLogEventEnd(PC_ApplyCoarse, pc, 0, 0, 0));
559: PetscFunctionReturn(PETSC_SUCCESS);
560: }
562: /* */
563: /* From now on, "footnotes" (or "historical notes"). */
564: /* */
565: /*
566: Historical note 01
568: We considered the possibility of an alternative D_i that would still
569: provide a partition of unity (i.e., $ \sum_i N_i D_i N_i^T = I $).
570: The basic principle was still the pseudo-inverse of the counting
571: function; the difference was that we would not count subdomains
572: that do not contribute to the coarse space (i.e., not pure-Neumann
573: subdomains).
575: This turned out to be a bad idea: we would solve trivial Neumann
576: problems in the not pure-Neumann subdomains, since we would be scaling
577: the balanced residual by zero.
578: */
580: /*
581: Historical note 02
583: We tried an alternative coarse problem, that would eliminate exactly a
584: constant error. Turned out not to improve the overall convergence.
585: */