Actual source code: fetidp.c

  1: #include <petsc/private/kspimpl.h>
  2: #include <petsc/private/pcbddcimpl.h>
  3: #include <petsc/private/pcbddcprivateimpl.h>
  4: #include <petscdm.h>

  6: static PetscBool  cited       = PETSC_FALSE;
  7: static PetscBool  cited2      = PETSC_FALSE;
  8: static const char citation[]  = "@article{ZampiniPCBDDC,\n"
  9:                                 "author = {Stefano Zampini},\n"
 10:                                 "title = {{PCBDDC}: A Class of Robust Dual-Primal Methods in {PETS}c},\n"
 11:                                 "journal = {SIAM Journal on Scientific Computing},\n"
 12:                                 "volume = {38},\n"
 13:                                 "number = {5},\n"
 14:                                 "pages = {S282-S306},\n"
 15:                                 "year = {2016},\n"
 16:                                 "doi = {10.1137/15M1025785},\n"
 17:                                 "URL = {http://dx.doi.org/10.1137/15M1025785},\n"
 18:                                 "eprint = {http://dx.doi.org/10.1137/15M1025785}\n"
 19:                                 "}\n"
 20:                                 "@article{ZampiniDualPrimal,\n"
 21:                                 "author = {Stefano Zampini},\n"
 22:                                 "title = {{D}ual-{P}rimal methods for the cardiac {B}idomain model},\n"
 23:                                 "volume = {24},\n"
 24:                                 "number = {04},\n"
 25:                                 "pages = {667-696},\n"
 26:                                 "year = {2014},\n"
 27:                                 "doi = {10.1142/S0218202513500632},\n"
 28:                                 "URL = {https://www.worldscientific.com/doi/abs/10.1142/S0218202513500632},\n"
 29:                                 "eprint = {https://www.worldscientific.com/doi/pdf/10.1142/S0218202513500632}\n"
 30:                                 "}\n";
 31: static const char citation2[] = "@article{li2013nonoverlapping,\n"
 32:                                 "title={A nonoverlapping domain decomposition method for incompressible Stokes equations with continuous pressures},\n"
 33:                                 "author={Li, Jing and Tu, Xuemin},\n"
 34:                                 "journal={SIAM Journal on Numerical Analysis},\n"
 35:                                 "volume={51},\n"
 36:                                 "number={2},\n"
 37:                                 "pages={1235--1253},\n"
 38:                                 "year={2013},\n"
 39:                                 "publisher={Society for Industrial and Applied Mathematics}\n"
 40:                                 "}\n";

 42: /*
 43:     This file implements the FETI-DP method in PETSc as part of KSP.
 44: */
 45: typedef struct {
 46:   KSP parentksp;
 47: } KSP_FETIDPMon;

 49: typedef struct {
 50:   KSP              innerksp;        /* the KSP for the Lagrange multipliers */
 51:   PC               innerbddc;       /* the inner BDDC object */
 52:   PetscBool        fully_redundant; /* true for using a fully redundant set of multipliers */
 53:   PetscBool        userbddc;        /* true if the user provided the PCBDDC object */
 54:   PetscBool        saddlepoint;     /* support for saddle point problems */
 55:   IS               pP;              /* index set for pressure variables */
 56:   Vec              rhs_flip;        /* see KSPFETIDPSetUpOperators */
 57:   KSP_FETIDPMon   *monctx;          /* monitor context, used to pass user defined monitors
 58:                                         in the physical space */
 59:   PetscObjectState matstate;        /* these are needed just in the saddle point case */
 60:   PetscObjectState matnnzstate;     /* where we are going to use MatZeroRows on pmat */
 61:   PetscBool        statechanged;
 62:   PetscBool        check;
 63: } KSP_FETIDP;

 65: static PetscErrorCode KSPFETIDPSetPressureOperator_FETIDP(KSP ksp, Mat P)
 66: {
 67:   KSP_FETIDP *fetidp = (KSP_FETIDP *)ksp->data;

 69:   PetscFunctionBegin;
 70:   if (P) fetidp->saddlepoint = PETSC_TRUE;
 71:   PetscCall(PetscObjectCompose((PetscObject)fetidp->innerbddc, "__KSPFETIDP_PPmat", (PetscObject)P));
 72:   PetscFunctionReturn(PETSC_SUCCESS);
 73: }

 75: /*@
 76:   KSPFETIDPSetPressureOperator - Sets the operator used to set up the pressure preconditioner for the saddle point `KSPFETIDP` solver,

 78:   Collective

 80:   Input Parameters:
 81: + ksp - the `KSPFETIDP` solver
 82: - P   - the linear operator to be preconditioned, usually the mass matrix.

 84:   Level: advanced

 86:   Notes:
 87:   The operator can be either passed in
 88: .vb
 89:   a) monolithic global ordering,
 90:   b) pressure-only global ordering, or
 91:   c) interface pressure ordering (if `-ksp_fetidp_pressure_all false`).
 92: .ve
 93:   In cases b) and c), the pressure ordering of dofs needs to satisfy
 94:   pid_1 < pid_2  iff  gid_1 < gid_2
 95:   where pid_1 and pid_2 are two different pressure dof numbers and gid_1 and gid_2 the corresponding
 96:   id in the monolithic global ordering.

 98: .seealso: [](ch_ksp), `KSPFETIDP`, `MATIS`, `PCBDDC`, `KSPFETIDPGetInnerBDDC()`, `KSPFETIDPGetInnerKSP()`, `KSPSetOperators()`
 99: @*/
100: PetscErrorCode KSPFETIDPSetPressureOperator(KSP ksp, Mat P)
101: {
102:   PetscFunctionBegin;
105:   PetscTryMethod(ksp, "KSPFETIDPSetPressureOperator_C", (KSP, Mat), (ksp, P));
106:   PetscFunctionReturn(PETSC_SUCCESS);
107: }

109: static PetscErrorCode KSPFETIDPGetInnerKSP_FETIDP(KSP ksp, KSP *innerksp)
110: {
111:   KSP_FETIDP *fetidp = (KSP_FETIDP *)ksp->data;

113:   PetscFunctionBegin;
114:   *innerksp = fetidp->innerksp;
115:   PetscFunctionReturn(PETSC_SUCCESS);
116: }

118: /*@
119:   KSPFETIDPGetInnerKSP - Gets the `KSP` object for the Lagrange multipliers from inside a `KSPFETIDP`

121:   Input Parameter:
122: . ksp - the `KSPFETIDP`

124:   Output Parameter:
125: . innerksp - the `KSP` for the multipliers

127:   Level: advanced

129: .seealso: [](ch_ksp), `KSPFETIDP`, `MATIS`, `PCBDDC`, `KSPFETIDPSetInnerBDDC()`, `KSPFETIDPGetInnerBDDC()`
130: @*/
131: PetscErrorCode KSPFETIDPGetInnerKSP(KSP ksp, KSP *innerksp)
132: {
133:   PetscFunctionBegin;
135:   PetscAssertPointer(innerksp, 2);
136:   PetscUseMethod(ksp, "KSPFETIDPGetInnerKSP_C", (KSP, KSP *), (ksp, innerksp));
137:   PetscFunctionReturn(PETSC_SUCCESS);
138: }

140: static PetscErrorCode KSPFETIDPGetInnerBDDC_FETIDP(KSP ksp, PC *pc)
141: {
142:   KSP_FETIDP *fetidp = (KSP_FETIDP *)ksp->data;

144:   PetscFunctionBegin;
145:   *pc = fetidp->innerbddc;
146:   PetscFunctionReturn(PETSC_SUCCESS);
147: }

149: /*@
150:   KSPFETIDPGetInnerBDDC - Gets the `PCBDDC` preconditioner used to set up the `KSPFETIDP` matrix for the Lagrange multipliers

152:   Input Parameter:
153: . ksp - the `KSPFETIDP` Krylov solver

155:   Output Parameter:
156: . pc - the `PCBDDC` preconditioner

158:   Level: advanced

160: .seealso: [](ch_ksp), `MATIS`, `PCBDDC`, `KSPFETIDP`, `KSPFETIDPSetInnerBDDC()`, `KSPFETIDPGetInnerKSP()`
161: @*/
162: PetscErrorCode KSPFETIDPGetInnerBDDC(KSP ksp, PC *pc)
163: {
164:   PetscFunctionBegin;
166:   PetscAssertPointer(pc, 2);
167:   PetscUseMethod(ksp, "KSPFETIDPGetInnerBDDC_C", (KSP, PC *), (ksp, pc));
168:   PetscFunctionReturn(PETSC_SUCCESS);
169: }

171: static PetscErrorCode KSPFETIDPSetInnerBDDC_FETIDP(KSP ksp, PC pc)
172: {
173:   KSP_FETIDP *fetidp = (KSP_FETIDP *)ksp->data;

175:   PetscFunctionBegin;
176:   PetscCall(PetscObjectReference((PetscObject)pc));
177:   PetscCall(PCDestroy(&fetidp->innerbddc));
178:   fetidp->innerbddc = pc;
179:   fetidp->userbddc  = PETSC_TRUE;
180:   PetscFunctionReturn(PETSC_SUCCESS);
181: }

183: /*@
184:   KSPFETIDPSetInnerBDDC - Provides the `PCBDDC` preconditioner used to set up the `KSPFETIDP` matrix for the Lagrange multipliers

186:   Collective

188:   Input Parameters:
189: + ksp - the `KSPFETIDP` Krylov solver
190: - pc  - the `PCBDDC` preconditioner

192:   Level: advanced

194:   Note:
195:   A `PC` is automatically created for the `KSPFETIDP` and can be accessed to change options with `KSPFETIDPGetInnerBDDC()` hence this routine is rarely needed

197: .seealso: [](ch_ksp), `MATIS`, `PCBDDC`, `KSPFETIDPGetInnerBDDC()`, `KSPFETIDPGetInnerKSP()`
198: @*/
199: PetscErrorCode KSPFETIDPSetInnerBDDC(KSP ksp, PC pc)
200: {
201:   PetscBool isbddc;

203:   PetscFunctionBegin;
206:   PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCBDDC, &isbddc));
207:   PetscCheck(isbddc, PetscObjectComm((PetscObject)ksp), PETSC_ERR_ARG_WRONG, "KSPFETIDPSetInnerBDDC need a PCBDDC preconditioner");
208:   PetscTryMethod(ksp, "KSPFETIDPSetInnerBDDC_C", (KSP, PC), (ksp, pc));
209:   PetscFunctionReturn(PETSC_SUCCESS);
210: }

212: static PetscErrorCode KSPBuildSolution_FETIDP(KSP ksp, Vec v, Vec *V)
213: {
214:   KSP_FETIDP *fetidp = (KSP_FETIDP *)ksp->data;
215:   Mat         F;
216:   Vec         Xl;

218:   PetscFunctionBegin;
219:   PetscCall(KSPGetOperators(fetidp->innerksp, &F, NULL));
220:   PetscCall(KSPBuildSolution(fetidp->innerksp, NULL, &Xl));
221:   if (v) {
222:     PetscCall(PCBDDCMatFETIDPGetSolution(F, Xl, v));
223:     *V = v;
224:   } else {
225:     PetscCall(PCBDDCMatFETIDPGetSolution(F, Xl, *V));
226:   }
227:   PetscFunctionReturn(PETSC_SUCCESS);
228: }

230: static PetscErrorCode KSPMonitor_FETIDP(KSP ksp, PetscInt it, PetscReal rnorm, void *ctx)
231: {
232:   KSP_FETIDPMon *monctx = (KSP_FETIDPMon *)ctx;

234:   PetscFunctionBegin;
235:   PetscCall(KSPMonitor(monctx->parentksp, it, rnorm));
236:   PetscFunctionReturn(PETSC_SUCCESS);
237: }

239: static PetscErrorCode KSPComputeEigenvalues_FETIDP(KSP ksp, PetscInt nmax, PetscReal *r, PetscReal *c, PetscInt *neig)
240: {
241:   KSP_FETIDP *fetidp = (KSP_FETIDP *)ksp->data;

243:   PetscFunctionBegin;
244:   PetscCall(KSPComputeEigenvalues(fetidp->innerksp, nmax, r, c, neig));
245:   PetscFunctionReturn(PETSC_SUCCESS);
246: }

248: static PetscErrorCode KSPComputeExtremeSingularValues_FETIDP(KSP ksp, PetscReal *emax, PetscReal *emin)
249: {
250:   KSP_FETIDP *fetidp = (KSP_FETIDP *)ksp->data;

252:   PetscFunctionBegin;
253:   PetscCall(KSPComputeExtremeSingularValues(fetidp->innerksp, emax, emin));
254:   PetscFunctionReturn(PETSC_SUCCESS);
255: }

257: static PetscErrorCode KSPFETIDPCheckOperators(KSP ksp, PetscViewer viewer)
258: {
259:   KSP_FETIDP     *fetidp = (KSP_FETIDP *)ksp->data;
260:   PC_BDDC        *pcbddc = (PC_BDDC *)fetidp->innerbddc->data;
261:   PC_IS          *pcis   = (PC_IS *)fetidp->innerbddc->data;
262:   Mat_IS         *matis  = (Mat_IS *)fetidp->innerbddc->pmat->data;
263:   Mat             F;
264:   FETIDPMat_ctx   fetidpmat_ctx;
265:   Vec             test_vec, test_vec_p = NULL, fetidp_global;
266:   IS              dirdofs, isvert;
267:   MPI_Comm        comm = PetscObjectComm((PetscObject)ksp);
268:   PetscScalar     sval, *array;
269:   PetscReal       val, rval;
270:   const PetscInt *vertex_indices;
271:   PetscInt        i, n_vertices;
272:   PetscBool       isascii;

274:   PetscFunctionBegin;
275:   PetscCheckSameComm(ksp, 1, viewer, 2);
276:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &isascii));
277:   PetscCheck(isascii, comm, PETSC_ERR_SUP, "Unsupported viewer");
278:   PetscCall(PetscViewerASCIIPrintf(viewer, "----------FETI-DP MAT  --------------\n"));
279:   PetscCall(PetscViewerASCIIAddTab(viewer, 2));
280:   PetscCall(KSPGetOperators(fetidp->innerksp, &F, NULL));
281:   PetscCall(PetscViewerPushFormat(viewer, PETSC_VIEWER_ASCII_INFO));
282:   PetscCall(MatView(F, viewer));
283:   PetscCall(PetscViewerPopFormat(viewer));
284:   PetscCall(PetscViewerASCIISubtractTab(viewer, 2));
285:   PetscCall(MatShellGetContext(F, &fetidpmat_ctx));
286:   PetscCall(PetscViewerASCIIPrintf(viewer, "----------FETI-DP TESTS--------------\n"));
287:   PetscCall(PetscViewerASCIIPrintf(viewer, "All tests should return zero!\n"));
288:   PetscCall(PetscViewerASCIIPrintf(viewer, "FETIDP MAT context in the "));
289:   if (fetidp->fully_redundant) {
290:     PetscCall(PetscViewerASCIIPrintf(viewer, "fully redundant case for lagrange multipliers.\n"));
291:   } else {
292:     PetscCall(PetscViewerASCIIPrintf(viewer, "Non-fully redundant case for lagrange multiplier.\n"));
293:   }
294:   PetscCall(PetscViewerFlush(viewer));

296:   /* Get Vertices used to define the BDDC */
297:   PetscCall(PCBDDCGraphGetCandidatesIS(pcbddc->mat_graph, NULL, NULL, NULL, NULL, &isvert));
298:   PetscCall(ISGetLocalSize(isvert, &n_vertices));
299:   PetscCall(ISGetIndices(isvert, &vertex_indices));

301:   /******************************************************************/
302:   /* TEST A/B: Test numbering of global fetidp dofs                 */
303:   /******************************************************************/
304:   PetscCall(MatCreateVecs(F, &fetidp_global, NULL));
305:   PetscCall(VecDuplicate(fetidpmat_ctx->lambda_local, &test_vec));
306:   PetscCall(VecSet(fetidp_global, 1.0));
307:   PetscCall(VecSet(test_vec, 1.));
308:   PetscCall(VecScatterBegin(fetidpmat_ctx->l2g_lambda, fetidp_global, fetidpmat_ctx->lambda_local, INSERT_VALUES, SCATTER_REVERSE));
309:   PetscCall(VecScatterEnd(fetidpmat_ctx->l2g_lambda, fetidp_global, fetidpmat_ctx->lambda_local, INSERT_VALUES, SCATTER_REVERSE));
310:   if (fetidpmat_ctx->l2g_p) {
311:     PetscCall(VecDuplicate(fetidpmat_ctx->vP, &test_vec_p));
312:     PetscCall(VecSet(test_vec_p, 1.));
313:     PetscCall(VecScatterBegin(fetidpmat_ctx->l2g_p, fetidp_global, fetidpmat_ctx->vP, INSERT_VALUES, SCATTER_REVERSE));
314:     PetscCall(VecScatterEnd(fetidpmat_ctx->l2g_p, fetidp_global, fetidpmat_ctx->vP, INSERT_VALUES, SCATTER_REVERSE));
315:   }
316:   PetscCall(VecAXPY(test_vec, -1.0, fetidpmat_ctx->lambda_local));
317:   PetscCall(VecNorm(test_vec, NORM_INFINITY, &val));
318:   PetscCall(VecDestroy(&test_vec));
319:   PetscCallMPI(MPI_Reduce(&val, &rval, 1, MPIU_REAL, MPIU_MAX, 0, comm));
320:   PetscCall(PetscViewerASCIIPrintf(viewer, "A: CHECK glob to loc: % 1.14e\n", (double)rval));

322:   if (fetidpmat_ctx->l2g_p) {
323:     PetscCall(VecAXPY(test_vec_p, -1.0, fetidpmat_ctx->vP));
324:     PetscCall(VecNorm(test_vec_p, NORM_INFINITY, &val));
325:     PetscCallMPI(MPI_Reduce(&val, &rval, 1, MPIU_REAL, MPIU_MAX, 0, comm));
326:     PetscCall(PetscViewerASCIIPrintf(viewer, "A: CHECK glob to loc (p): % 1.14e\n", (double)rval));
327:   }

329:   if (fetidp->fully_redundant) {
330:     PetscCall(VecSet(fetidp_global, 0.0));
331:     PetscCall(VecSet(fetidpmat_ctx->lambda_local, 0.5));
332:     PetscCall(VecScatterBegin(fetidpmat_ctx->l2g_lambda, fetidpmat_ctx->lambda_local, fetidp_global, ADD_VALUES, SCATTER_FORWARD));
333:     PetscCall(VecScatterEnd(fetidpmat_ctx->l2g_lambda, fetidpmat_ctx->lambda_local, fetidp_global, ADD_VALUES, SCATTER_FORWARD));
334:     PetscCall(VecSum(fetidp_global, &sval));
335:     val = PetscRealPart(sval) - fetidpmat_ctx->n_lambda;
336:     PetscCallMPI(MPI_Reduce(&val, &rval, 1, MPIU_REAL, MPIU_MAX, 0, comm));
337:     PetscCall(PetscViewerASCIIPrintf(viewer, "B: CHECK loc to glob: % 1.14e\n", (double)rval));
338:   }

340:   if (fetidpmat_ctx->l2g_p) {
341:     PetscCall(VecSet(pcis->vec1_N, 1.0));
342:     PetscCall(VecSet(pcis->vec1_global, 0.0));
343:     PetscCall(VecScatterBegin(matis->rctx, pcis->vec1_N, pcis->vec1_global, ADD_VALUES, SCATTER_REVERSE));
344:     PetscCall(VecScatterEnd(matis->rctx, pcis->vec1_N, pcis->vec1_global, ADD_VALUES, SCATTER_REVERSE));

346:     PetscCall(VecSet(fetidp_global, 0.0));
347:     PetscCall(VecSet(fetidpmat_ctx->vP, -1.0));
348:     PetscCall(VecScatterBegin(fetidpmat_ctx->l2g_p, fetidpmat_ctx->vP, fetidp_global, ADD_VALUES, SCATTER_FORWARD));
349:     PetscCall(VecScatterEnd(fetidpmat_ctx->l2g_p, fetidpmat_ctx->vP, fetidp_global, ADD_VALUES, SCATTER_FORWARD));
350:     PetscCall(VecScatterBegin(fetidpmat_ctx->g2g_p, fetidp_global, pcis->vec1_global, ADD_VALUES, SCATTER_REVERSE));
351:     PetscCall(VecScatterEnd(fetidpmat_ctx->g2g_p, fetidp_global, pcis->vec1_global, ADD_VALUES, SCATTER_REVERSE));
352:     PetscCall(VecScatterBegin(fetidpmat_ctx->g2g_p, pcis->vec1_global, fetidp_global, INSERT_VALUES, SCATTER_FORWARD));
353:     PetscCall(VecScatterEnd(fetidpmat_ctx->g2g_p, pcis->vec1_global, fetidp_global, INSERT_VALUES, SCATTER_FORWARD));
354:     PetscCall(VecSum(fetidp_global, &sval));
355:     val = PetscRealPart(sval);
356:     PetscCallMPI(MPI_Reduce(&val, &rval, 1, MPIU_REAL, MPIU_MAX, 0, comm));
357:     PetscCall(PetscViewerASCIIPrintf(viewer, "B: CHECK loc to glob (p): % 1.14e\n", (double)rval));
358:   }

360:   /******************************************************************/
361:   /* TEST C: It should hold B_delta*w=0, w\in\widehat{W}            */
362:   /* This is the meaning of the B matrix                            */
363:   /******************************************************************/

365:   PetscCall(VecSetRandom(pcis->vec1_N, NULL));
366:   PetscCall(VecSet(pcis->vec1_global, 0.0));
367:   PetscCall(VecScatterBegin(matis->rctx, pcis->vec1_N, pcis->vec1_global, ADD_VALUES, SCATTER_REVERSE));
368:   PetscCall(VecScatterEnd(matis->rctx, pcis->vec1_N, pcis->vec1_global, ADD_VALUES, SCATTER_REVERSE));
369:   PetscCall(VecScatterBegin(matis->rctx, pcis->vec1_global, pcis->vec1_N, INSERT_VALUES, SCATTER_FORWARD));
370:   PetscCall(VecScatterEnd(matis->rctx, pcis->vec1_global, pcis->vec1_N, INSERT_VALUES, SCATTER_FORWARD));
371:   PetscCall(VecScatterBegin(pcis->N_to_B, pcis->vec1_N, pcis->vec1_B, INSERT_VALUES, SCATTER_FORWARD));
372:   PetscCall(VecScatterEnd(pcis->N_to_B, pcis->vec1_N, pcis->vec1_B, INSERT_VALUES, SCATTER_FORWARD));
373:   /* Action of B_delta */
374:   PetscCall(MatMult(fetidpmat_ctx->B_delta, pcis->vec1_B, fetidpmat_ctx->lambda_local));
375:   PetscCall(VecSet(fetidp_global, 0.0));
376:   PetscCall(VecScatterBegin(fetidpmat_ctx->l2g_lambda, fetidpmat_ctx->lambda_local, fetidp_global, ADD_VALUES, SCATTER_FORWARD));
377:   PetscCall(VecScatterEnd(fetidpmat_ctx->l2g_lambda, fetidpmat_ctx->lambda_local, fetidp_global, ADD_VALUES, SCATTER_FORWARD));
378:   PetscCall(VecNorm(fetidp_global, NORM_INFINITY, &val));
379:   PetscCall(PetscViewerASCIIPrintf(viewer, "C: CHECK infty norm of B_delta*w (w continuous): % 1.14e\n", (double)val));

381:   /******************************************************************/
382:   /* TEST D: It should hold E_Dw = w - P_Dw w\in\widetilde{W}       */
383:   /* E_D = R_D^TR                                                   */
384:   /* P_D = B_{D,delta}^T B_{delta}                                  */
385:   /* eq.44 Mandel Tezaur and Dohrmann 2005                          */
386:   /******************************************************************/

388:   /* compute a random vector in \widetilde{W} */
389:   PetscCall(VecSetRandom(pcis->vec1_N, NULL));
390:   /* set zero at vertices and essential dofs */
391:   PetscCall(VecGetArray(pcis->vec1_N, &array));
392:   for (i = 0; i < n_vertices; i++) array[vertex_indices[i]] = 0.0;
393:   PetscCall(PCBDDCGraphGetDirichletDofs(pcbddc->mat_graph, &dirdofs));
394:   if (dirdofs) {
395:     const PetscInt *idxs;
396:     PetscInt        ndir;

398:     PetscCall(ISGetLocalSize(dirdofs, &ndir));
399:     PetscCall(ISGetIndices(dirdofs, &idxs));
400:     for (i = 0; i < ndir; i++) array[idxs[i]] = 0.0;
401:     PetscCall(ISRestoreIndices(dirdofs, &idxs));
402:   }
403:   PetscCall(VecRestoreArray(pcis->vec1_N, &array));
404:   /* store w for final comparison */
405:   PetscCall(VecDuplicate(pcis->vec1_B, &test_vec));
406:   PetscCall(VecScatterBegin(pcis->N_to_B, pcis->vec1_N, test_vec, INSERT_VALUES, SCATTER_FORWARD));
407:   PetscCall(VecScatterEnd(pcis->N_to_B, pcis->vec1_N, test_vec, INSERT_VALUES, SCATTER_FORWARD));

409:   /* Jump operator P_D : results stored in pcis->vec1_B */
410:   /* Action of B_delta */
411:   PetscCall(MatMult(fetidpmat_ctx->B_delta, test_vec, fetidpmat_ctx->lambda_local));
412:   PetscCall(VecSet(fetidp_global, 0.0));
413:   PetscCall(VecScatterBegin(fetidpmat_ctx->l2g_lambda, fetidpmat_ctx->lambda_local, fetidp_global, ADD_VALUES, SCATTER_FORWARD));
414:   PetscCall(VecScatterEnd(fetidpmat_ctx->l2g_lambda, fetidpmat_ctx->lambda_local, fetidp_global, ADD_VALUES, SCATTER_FORWARD));
415:   /* Action of B_Ddelta^T */
416:   PetscCall(VecScatterBegin(fetidpmat_ctx->l2g_lambda, fetidp_global, fetidpmat_ctx->lambda_local, INSERT_VALUES, SCATTER_REVERSE));
417:   PetscCall(VecScatterEnd(fetidpmat_ctx->l2g_lambda, fetidp_global, fetidpmat_ctx->lambda_local, INSERT_VALUES, SCATTER_REVERSE));
418:   PetscCall(MatMultTranspose(fetidpmat_ctx->B_Ddelta, fetidpmat_ctx->lambda_local, pcis->vec1_B));

420:   /* Average operator E_D : results stored in pcis->vec2_B */
421:   PetscCall(PCBDDCScalingExtension(fetidpmat_ctx->pc, test_vec, pcis->vec1_global));
422:   PetscCall(VecScatterBegin(pcis->global_to_B, pcis->vec1_global, pcis->vec2_B, INSERT_VALUES, SCATTER_FORWARD));
423:   PetscCall(VecScatterEnd(pcis->global_to_B, pcis->vec1_global, pcis->vec2_B, INSERT_VALUES, SCATTER_FORWARD));

425:   /* test E_D=I-P_D */
426:   PetscCall(VecAXPY(pcis->vec1_B, 1.0, pcis->vec2_B));
427:   PetscCall(VecAXPY(pcis->vec1_B, -1.0, test_vec));
428:   PetscCall(VecNorm(pcis->vec1_B, NORM_INFINITY, &val));
429:   PetscCall(VecDestroy(&test_vec));
430:   PetscCallMPI(MPI_Reduce(&val, &rval, 1, MPIU_REAL, MPIU_MAX, 0, comm));
431:   PetscCall(PetscViewerASCIIPrintf(viewer, "%d: CHECK infty norm of E_D + P_D - I: %1.14e\n", PetscGlobalRank, (double)val));

433:   /******************************************************************/
434:   /* TEST E: It should hold R_D^TP_Dw=0 w\in\widetilde{W}           */
435:   /* eq.48 Mandel Tezaur and Dohrmann 2005                          */
436:   /******************************************************************/

438:   PetscCall(VecSetRandom(pcis->vec1_N, NULL));
439:   /* set zero at vertices and essential dofs */
440:   PetscCall(VecGetArray(pcis->vec1_N, &array));
441:   for (i = 0; i < n_vertices; i++) array[vertex_indices[i]] = 0.0;
442:   if (dirdofs) {
443:     const PetscInt *idxs;
444:     PetscInt        ndir;

446:     PetscCall(ISGetLocalSize(dirdofs, &ndir));
447:     PetscCall(ISGetIndices(dirdofs, &idxs));
448:     for (i = 0; i < ndir; i++) array[idxs[i]] = 0.0;
449:     PetscCall(ISRestoreIndices(dirdofs, &idxs));
450:   }
451:   PetscCall(VecRestoreArray(pcis->vec1_N, &array));

453:   /* Jump operator P_D : results stored in pcis->vec1_B */

455:   PetscCall(VecScatterBegin(pcis->N_to_B, pcis->vec1_N, pcis->vec1_B, INSERT_VALUES, SCATTER_FORWARD));
456:   PetscCall(VecScatterEnd(pcis->N_to_B, pcis->vec1_N, pcis->vec1_B, INSERT_VALUES, SCATTER_FORWARD));
457:   /* Action of B_delta */
458:   PetscCall(MatMult(fetidpmat_ctx->B_delta, pcis->vec1_B, fetidpmat_ctx->lambda_local));
459:   PetscCall(VecSet(fetidp_global, 0.0));
460:   PetscCall(VecScatterBegin(fetidpmat_ctx->l2g_lambda, fetidpmat_ctx->lambda_local, fetidp_global, ADD_VALUES, SCATTER_FORWARD));
461:   PetscCall(VecScatterEnd(fetidpmat_ctx->l2g_lambda, fetidpmat_ctx->lambda_local, fetidp_global, ADD_VALUES, SCATTER_FORWARD));
462:   /* Action of B_Ddelta^T */
463:   PetscCall(VecScatterBegin(fetidpmat_ctx->l2g_lambda, fetidp_global, fetidpmat_ctx->lambda_local, INSERT_VALUES, SCATTER_REVERSE));
464:   PetscCall(VecScatterEnd(fetidpmat_ctx->l2g_lambda, fetidp_global, fetidpmat_ctx->lambda_local, INSERT_VALUES, SCATTER_REVERSE));
465:   PetscCall(MatMultTranspose(fetidpmat_ctx->B_Ddelta, fetidpmat_ctx->lambda_local, pcis->vec1_B));
466:   /* scaling */
467:   PetscCall(PCBDDCScalingExtension(fetidpmat_ctx->pc, pcis->vec1_B, pcis->vec1_global));
468:   PetscCall(VecNorm(pcis->vec1_global, NORM_INFINITY, &val));
469:   PetscCall(PetscViewerASCIIPrintf(viewer, "E: CHECK infty norm of R^T_D P_D: % 1.14e\n", (double)val));

471:   if (!fetidp->fully_redundant) {
472:     /******************************************************************/
473:     /* TEST F: It should holds B_{delta}B^T_{D,delta}=I               */
474:     /* Corollary thm 14 Mandel Tezaur and Dohrmann 2005               */
475:     /******************************************************************/
476:     PetscCall(VecDuplicate(fetidp_global, &test_vec));
477:     PetscCall(VecSetRandom(fetidp_global, NULL));
478:     if (fetidpmat_ctx->l2g_p) {
479:       PetscCall(VecSet(fetidpmat_ctx->vP, 0.));
480:       PetscCall(VecScatterBegin(fetidpmat_ctx->l2g_p, fetidpmat_ctx->vP, fetidp_global, INSERT_VALUES, SCATTER_FORWARD));
481:       PetscCall(VecScatterEnd(fetidpmat_ctx->l2g_p, fetidpmat_ctx->vP, fetidp_global, INSERT_VALUES, SCATTER_FORWARD));
482:     }
483:     /* Action of B_Ddelta^T */
484:     PetscCall(VecScatterBegin(fetidpmat_ctx->l2g_lambda, fetidp_global, fetidpmat_ctx->lambda_local, INSERT_VALUES, SCATTER_REVERSE));
485:     PetscCall(VecScatterEnd(fetidpmat_ctx->l2g_lambda, fetidp_global, fetidpmat_ctx->lambda_local, INSERT_VALUES, SCATTER_REVERSE));
486:     PetscCall(MatMultTranspose(fetidpmat_ctx->B_Ddelta, fetidpmat_ctx->lambda_local, pcis->vec1_B));
487:     /* Action of B_delta */
488:     PetscCall(MatMult(fetidpmat_ctx->B_delta, pcis->vec1_B, fetidpmat_ctx->lambda_local));
489:     PetscCall(VecSet(test_vec, 0.0));
490:     PetscCall(VecScatterBegin(fetidpmat_ctx->l2g_lambda, fetidpmat_ctx->lambda_local, test_vec, ADD_VALUES, SCATTER_FORWARD));
491:     PetscCall(VecScatterEnd(fetidpmat_ctx->l2g_lambda, fetidpmat_ctx->lambda_local, test_vec, ADD_VALUES, SCATTER_FORWARD));
492:     PetscCall(VecAXPY(fetidp_global, -1., test_vec));
493:     PetscCall(VecNorm(fetidp_global, NORM_INFINITY, &val));
494:     PetscCall(PetscViewerASCIIPrintf(viewer, "E: CHECK infty norm of P^T_D - I: % 1.14e\n", (double)val));
495:     PetscCall(VecDestroy(&test_vec));
496:   }
497:   PetscCall(PetscViewerASCIIPrintf(viewer, "-------------------------------------\n"));
498:   PetscCall(PetscViewerFlush(viewer));
499:   PetscCall(VecDestroy(&test_vec_p));
500:   PetscCall(ISDestroy(&dirdofs));
501:   PetscCall(VecDestroy(&fetidp_global));
502:   PetscCall(ISRestoreIndices(isvert, &vertex_indices));
503:   PetscCall(PCBDDCGraphRestoreCandidatesIS(pcbddc->mat_graph, NULL, NULL, NULL, NULL, &isvert));
504:   PetscFunctionReturn(PETSC_SUCCESS);
505: }

507: static PetscErrorCode KSPFETIDPSetUpOperators(KSP ksp)
508: {
509:   KSP_FETIDP      *fetidp = (KSP_FETIDP *)ksp->data;
510:   PC_BDDC         *pcbddc = (PC_BDDC *)fetidp->innerbddc->data;
511:   Mat              A, Ap;
512:   PetscInt         fidp[8] = {-1}, nfp = 8;
513:   PetscMPIInt      size;
514:   PetscBool        ismatis, pisz = PETSC_FALSE, allp = PETSC_FALSE, schp = PETSC_FALSE;
515:   PetscBool        flip = PETSC_FALSE; /* Usually, Stokes is written (B = -\int_\Omega \nabla \cdot u q)
516:                            | A B'| | v | = | f |
517:                            | B 0 | | p | = | g |
518:                             If -ksp_fetidp_saddlepoint_flip is true, the code assumes it is written as
519:                            | A B'| | v | = | f |
520:                            |-B 0 | | p | = |-g |
521:                          */
522:   PetscObjectState matstate, matnnzstate;

524:   PetscFunctionBegin;
525:   PetscOptionsBegin(PetscObjectComm((PetscObject)ksp), ((PetscObject)ksp)->prefix, "FETI-DP options", "PC");
526:   PetscCall(PetscOptionsIntArray("-ksp_fetidp_pressure_field", "Field id for pressures for saddle-point problems", NULL, fidp, &nfp, NULL));
527:   PetscCall(PetscOptionsBool("-ksp_fetidp_pressure_all", "Use the whole pressure set instead of just that at the interface", NULL, allp, &allp, NULL));
528:   PetscCall(PetscOptionsBool("-ksp_fetidp_saddlepoint_flip", "Flip the sign of the pressure-velocity (lower-left) block", NULL, flip, &flip, NULL));
529:   PetscCall(PetscOptionsBool("-ksp_fetidp_pressure_schur", "Use a BDDC solver for pressure", NULL, schp, &schp, NULL));
530:   PetscOptionsEnd();

532:   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)ksp), &size));
533:   fetidp->saddlepoint = (nfp > 0 ? PETSC_TRUE : fetidp->saddlepoint);
534:   if (size == 1) fetidp->saddlepoint = PETSC_FALSE;

536:   PetscCall(KSPGetOperators(ksp, &A, &Ap));
537:   PetscCall(PetscObjectTypeCompare((PetscObject)A, MATIS, &ismatis));
538:   PetscCheck(ismatis, PetscObjectComm((PetscObject)ksp), PETSC_ERR_USER, "Amat should be of type MATIS");

540:   /* Quiet return if the matrix states are unchanged.
541:      Needed only for the saddle point case since it uses MatZeroRows
542:      on a matrix that may not have changed */
543:   PetscCall(PetscObjectStateGet((PetscObject)A, &matstate));
544:   PetscCall(MatGetNonzeroState(A, &matnnzstate));
545:   if (matstate == fetidp->matstate && matnnzstate == fetidp->matnnzstate) PetscFunctionReturn(PETSC_SUCCESS);
546:   fetidp->matstate     = matstate;
547:   fetidp->matnnzstate  = matnnzstate;
548:   fetidp->statechanged = fetidp->saddlepoint;

550:   /* see if we have some fields attached */
551:   if (!pcbddc->n_ISForDofsLocal && !pcbddc->n_ISForDofs) {
552:     DM             dm;
553:     PetscContainer c;

555:     PetscCall(KSPGetDM(ksp, &dm));
556:     PetscCall(PetscObjectQuery((PetscObject)A, "_convert_nest_lfields", (PetscObject *)&c));
557:     if (dm) {
558:       IS      *fields;
559:       PetscInt nf, i;

561:       PetscCall(DMCreateFieldDecomposition(dm, &nf, NULL, &fields, NULL));
562:       PetscCall(PCBDDCSetDofsSplitting(fetidp->innerbddc, nf, fields));
563:       for (i = 0; i < nf; i++) PetscCall(ISDestroy(&fields[i]));
564:       PetscCall(PetscFree(fields));
565:     } else if (c) {
566:       MatISLocalFields lf;

568:       PetscCall(PetscContainerGetPointer(c, (void **)&lf));
569:       PetscCall(PCBDDCSetDofsSplittingLocal(fetidp->innerbddc, lf->nr, lf->rf));
570:     }
571:   }

573:   if (!fetidp->saddlepoint) {
574:     PetscCall(PCSetOperators(fetidp->innerbddc, A, A));
575:   } else {
576:     Mat          nA, lA, PPmat;
577:     MatNullSpace nnsp;
578:     IS           pP;
579:     PetscInt     totP;

581:     PetscCall(MatISGetLocalMat(A, &lA));
582:     PetscCall(PetscObjectCompose((PetscObject)fetidp->innerbddc, "__KSPFETIDP_lA", (PetscObject)lA));

584:     pP = fetidp->pP;
585:     if (!pP) { /* first time, need to compute pressure dofs */
586:       PC_IS                 *pcis  = (PC_IS *)fetidp->innerbddc->data;
587:       Mat_IS                *matis = (Mat_IS *)A->data;
588:       ISLocalToGlobalMapping l2g;
589:       IS                     lP = NULL, II, pII, lPall, Pall, is1, is2;
590:       const PetscInt        *idxs;
591:       PetscInt               nl, ni, *widxs;
592:       PetscInt               i, j, n_neigh, *neigh, *n_shared, **shared, *count;
593:       PetscInt               rst, ren, n;
594:       PetscBool              ploc;

596:       PetscCall(MatGetLocalSize(A, &nl, NULL));
597:       PetscCall(MatGetOwnershipRange(A, &rst, &ren));
598:       PetscCall(MatGetLocalSize(lA, &n, NULL));
599:       PetscCall(MatISGetLocalToGlobalMapping(A, &l2g, NULL));

601:       if (!pcis->is_I_local) { /* need to compute interior dofs */
602:         PetscCall(PetscCalloc1(n, &count));
603:         PetscCall(ISLocalToGlobalMappingGetInfo(l2g, &n_neigh, &neigh, &n_shared, &shared));
604:         for (i = 1; i < n_neigh; i++)
605:           for (j = 0; j < n_shared[i]; j++) count[shared[i][j]] += 1;
606:         for (i = 0, j = 0; i < n; i++)
607:           if (!count[i]) count[j++] = i;
608:         PetscCall(ISLocalToGlobalMappingRestoreInfo(l2g, &n_neigh, &neigh, &n_shared, &shared));
609:         PetscCall(ISCreateGeneral(PETSC_COMM_SELF, j, count, PETSC_OWN_POINTER, &II));
610:       } else {
611:         PetscCall(PetscObjectReference((PetscObject)pcis->is_I_local));
612:         II = pcis->is_I_local;
613:       }

615:       /* interior dofs in layout */
616:       PetscCall(PetscArrayzero(matis->sf_leafdata, n));
617:       PetscCall(PetscArrayzero(matis->sf_rootdata, nl));
618:       PetscCall(ISGetLocalSize(II, &ni));
619:       PetscCall(ISGetIndices(II, &idxs));
620:       for (i = 0; i < ni; i++) matis->sf_leafdata[idxs[i]] = 1;
621:       PetscCall(ISRestoreIndices(II, &idxs));
622:       PetscCall(PetscSFReduceBegin(matis->sf, MPIU_INT, matis->sf_leafdata, matis->sf_rootdata, MPI_REPLACE));
623:       PetscCall(PetscSFReduceEnd(matis->sf, MPIU_INT, matis->sf_leafdata, matis->sf_rootdata, MPI_REPLACE));
624:       PetscCall(PetscMalloc1(PetscMax(nl, n), &widxs));
625:       for (i = 0, ni = 0; i < nl; i++)
626:         if (matis->sf_rootdata[i]) widxs[ni++] = i + rst;
627:       PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)ksp), ni, widxs, PETSC_COPY_VALUES, &pII));

629:       /* pressure dofs */
630:       Pall  = NULL;
631:       lPall = NULL;
632:       ploc  = PETSC_FALSE;
633:       if (nfp == 0) { /* zero pressure block */
634:         PetscInt np;

636:         PetscCall(MatFindZeroDiagonals(A, &Pall));
637:         PetscCall(ISGetSize(Pall, &np));
638:         if (!np) { /* zero-block not found, defaults to last field (if set) */
639:           nfp     = 1;
640:           fidp[0] = pcbddc->n_ISForDofsLocal ? pcbddc->n_ISForDofsLocal - 1 : pcbddc->n_ISForDofs - 1;
641:           PetscCall(ISDestroy(&Pall));
642:         } else if (!pcbddc->n_ISForDofsLocal && !pcbddc->n_ISForDofs) {
643:           PetscCall(PCBDDCSetDofsSplitting(fetidp->innerbddc, 1, &Pall));
644:         }
645:       }
646:       if (!Pall) { /* look for registered fields when no zero block has been found */
647:         IS *tis;

649:         PetscCall(PetscMalloc1(nfp, &tis));
650:         if (pcbddc->n_ISForDofsLocal) {
651:           for (PetscInt i = 0; i < nfp; i++) {
652:             PetscInt fid = fidp[i];

654:             PetscCheck(fid >= 0 && fid < pcbddc->n_ISForDofsLocal, PetscObjectComm((PetscObject)ksp), PETSC_ERR_USER, "Invalid field id for pressure %" PetscInt_FMT ", max %" PetscInt_FMT, fid, pcbddc->n_ISForDofsLocal);
655:             /* need a sequential IS */
656:             PetscCall(ISOnComm(pcbddc->ISForDofsLocal[fid], PETSC_COMM_SELF, PETSC_COPY_VALUES, &tis[i]));
657:           }
658:           PetscCall(ISConcatenate(PETSC_COMM_SELF, nfp, tis, &lPall));
659:           ploc = PETSC_TRUE;
660:         } else if (pcbddc->n_ISForDofs) {
661:           for (PetscInt i = 0; i < nfp; i++) {
662:             PetscInt fid = fidp[i];

664:             PetscCheck(fid >= 0 && fid < pcbddc->n_ISForDofs, PetscObjectComm((PetscObject)ksp), PETSC_ERR_USER, "Invalid field id for pressure %" PetscInt_FMT ", max %" PetscInt_FMT, fid, pcbddc->n_ISForDofs);
665:             PetscCall(PetscObjectReference((PetscObject)pcbddc->ISForDofs[fid]));
666:             tis[i] = pcbddc->ISForDofs[fid];
667:           }
668:           PetscCall(ISConcatenate(PetscObjectComm((PetscObject)ksp), nfp, tis, &Pall));
669:           PetscCall(ISSort(Pall));
670:         } else SETERRQ(PetscObjectComm((PetscObject)ksp), PETSC_ERR_USER, "Cannot detect pressure field! Use KSPFETIDPGetInnerBDDC() + PCBDDCSetDofsSplitting or PCBDDCSetDofsSplittingLocal");
671:         for (PetscInt i = 0; i < nfp; i++) PetscCall(ISDestroy(&tis[i]));
672:         PetscCall(PetscFree(tis));
673:       }

675:       /* if the user requested the entire pressure,
676:          remove the interior pressure dofs from II (or pII) */
677:       if (allp) {
678:         if (ploc) {
679:           IS nII;
680:           PetscCall(ISDifference(II, lPall, &nII));
681:           PetscCall(ISDestroy(&II));
682:           II = nII;
683:         } else {
684:           IS nII;
685:           PetscCall(ISDifference(pII, Pall, &nII));
686:           PetscCall(ISDestroy(&pII));
687:           pII = nII;
688:         }
689:       }
690:       if (ploc) {
691:         PetscCall(ISDifference(lPall, II, &lP));
692:         PetscCall(PetscObjectCompose((PetscObject)fetidp->innerbddc, "__KSPFETIDP_lP", (PetscObject)lP));
693:       } else {
694:         PetscCall(ISDifference(Pall, pII, &pP));
695:         PetscCall(PetscObjectCompose((PetscObject)fetidp->innerbddc, "__KSPFETIDP_pP", (PetscObject)pP));
696:         /* need all local pressure dofs */
697:         PetscCall(PetscArrayzero(matis->sf_leafdata, n));
698:         PetscCall(PetscArrayzero(matis->sf_rootdata, nl));
699:         PetscCall(ISGetLocalSize(Pall, &ni));
700:         PetscCall(ISGetIndices(Pall, &idxs));
701:         for (i = 0; i < ni; i++) matis->sf_rootdata[idxs[i] - rst] = 1;
702:         PetscCall(ISRestoreIndices(Pall, &idxs));
703:         PetscCall(PetscSFBcastBegin(matis->sf, MPIU_INT, matis->sf_rootdata, matis->sf_leafdata, MPI_REPLACE));
704:         PetscCall(PetscSFBcastEnd(matis->sf, MPIU_INT, matis->sf_rootdata, matis->sf_leafdata, MPI_REPLACE));
705:         for (i = 0, ni = 0; i < n; i++)
706:           if (matis->sf_leafdata[i]) widxs[ni++] = i;
707:         PetscCall(ISCreateGeneral(PETSC_COMM_SELF, ni, widxs, PETSC_COPY_VALUES, &lPall));
708:       }

710:       if (!Pall) {
711:         PetscCall(PetscArrayzero(matis->sf_leafdata, n));
712:         PetscCall(PetscArrayzero(matis->sf_rootdata, nl));
713:         PetscCall(ISGetLocalSize(lPall, &ni));
714:         PetscCall(ISGetIndices(lPall, &idxs));
715:         for (i = 0; i < ni; i++) matis->sf_leafdata[idxs[i]] = 1;
716:         PetscCall(ISRestoreIndices(lPall, &idxs));
717:         PetscCall(PetscSFReduceBegin(matis->sf, MPIU_INT, matis->sf_leafdata, matis->sf_rootdata, MPI_REPLACE));
718:         PetscCall(PetscSFReduceEnd(matis->sf, MPIU_INT, matis->sf_leafdata, matis->sf_rootdata, MPI_REPLACE));
719:         for (i = 0, ni = 0; i < nl; i++)
720:           if (matis->sf_rootdata[i]) widxs[ni++] = i + rst;
721:         PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)ksp), ni, widxs, PETSC_COPY_VALUES, &Pall));
722:       }
723:       PetscCall(PetscObjectCompose((PetscObject)fetidp->innerbddc, "__KSPFETIDP_aP", (PetscObject)Pall));

725:       if (flip) {
726:         PetscInt npl;
727:         PetscCall(ISGetLocalSize(Pall, &npl));
728:         PetscCall(ISGetIndices(Pall, &idxs));
729:         PetscCall(MatCreateVecs(A, NULL, &fetidp->rhs_flip));
730:         PetscCall(VecSet(fetidp->rhs_flip, 1.));
731:         PetscCall(VecSetOption(fetidp->rhs_flip, VEC_IGNORE_OFF_PROC_ENTRIES, PETSC_TRUE));
732:         for (i = 0; i < npl; i++) PetscCall(VecSetValue(fetidp->rhs_flip, idxs[i], -1., INSERT_VALUES));
733:         PetscCall(VecAssemblyBegin(fetidp->rhs_flip));
734:         PetscCall(VecAssemblyEnd(fetidp->rhs_flip));
735:         PetscCall(PetscObjectCompose((PetscObject)fetidp->innerbddc, "__KSPFETIDP_flip", (PetscObject)fetidp->rhs_flip));
736:         PetscCall(ISRestoreIndices(Pall, &idxs));
737:       }
738:       PetscCall(ISDestroy(&Pall));
739:       PetscCall(ISDestroy(&pII));

741:       /* local selected pressures in subdomain-wise and global ordering */
742:       PetscCall(PetscArrayzero(matis->sf_leafdata, n));
743:       PetscCall(PetscArrayzero(matis->sf_rootdata, nl));
744:       if (!ploc) {
745:         PetscInt *widxs2;

747:         PetscCheck(pP, PetscObjectComm((PetscObject)ksp), PETSC_ERR_PLIB, "Missing parallel pressure IS");
748:         PetscCall(ISGetLocalSize(pP, &ni));
749:         PetscCall(ISGetIndices(pP, &idxs));
750:         for (i = 0; i < ni; i++) matis->sf_rootdata[idxs[i] - rst] = 1;
751:         PetscCall(ISRestoreIndices(pP, &idxs));
752:         PetscCall(PetscSFBcastBegin(matis->sf, MPIU_INT, matis->sf_rootdata, matis->sf_leafdata, MPI_REPLACE));
753:         PetscCall(PetscSFBcastEnd(matis->sf, MPIU_INT, matis->sf_rootdata, matis->sf_leafdata, MPI_REPLACE));
754:         for (i = 0, ni = 0; i < n; i++)
755:           if (matis->sf_leafdata[i]) widxs[ni++] = i;
756:         PetscCall(PetscMalloc1(ni, &widxs2));
757:         PetscCall(ISLocalToGlobalMappingApply(l2g, ni, widxs, widxs2));
758:         PetscCall(ISCreateGeneral(PETSC_COMM_SELF, ni, widxs, PETSC_COPY_VALUES, &lP));
759:         PetscCall(PetscObjectCompose((PetscObject)fetidp->innerbddc, "__KSPFETIDP_lP", (PetscObject)lP));
760:         PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)ksp), ni, widxs2, PETSC_OWN_POINTER, &is1));
761:         PetscCall(PetscObjectCompose((PetscObject)fetidp->innerbddc, "__KSPFETIDP_gP", (PetscObject)is1));
762:         PetscCall(ISDestroy(&is1));
763:       } else {
764:         PetscCheck(lP, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Missing sequential pressure IS");
765:         PetscCall(ISGetLocalSize(lP, &ni));
766:         PetscCall(ISGetIndices(lP, &idxs));
767:         for (i = 0; i < ni; i++)
768:           if (idxs[i] >= 0 && idxs[i] < n) matis->sf_leafdata[idxs[i]] = 1;
769:         PetscCall(ISRestoreIndices(lP, &idxs));
770:         PetscCall(PetscSFReduceBegin(matis->sf, MPIU_INT, matis->sf_leafdata, matis->sf_rootdata, MPI_REPLACE));
771:         PetscCall(ISLocalToGlobalMappingApply(l2g, ni, idxs, widxs));
772:         PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)ksp), ni, widxs, PETSC_COPY_VALUES, &is1));
773:         PetscCall(PetscObjectCompose((PetscObject)fetidp->innerbddc, "__KSPFETIDP_gP", (PetscObject)is1));
774:         PetscCall(ISDestroy(&is1));
775:         PetscCall(PetscSFReduceEnd(matis->sf, MPIU_INT, matis->sf_leafdata, matis->sf_rootdata, MPI_REPLACE));
776:         for (i = 0, ni = 0; i < nl; i++)
777:           if (matis->sf_rootdata[i]) widxs[ni++] = i + rst;
778:         PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)ksp), ni, widxs, PETSC_COPY_VALUES, &pP));
779:         PetscCall(PetscObjectCompose((PetscObject)fetidp->innerbddc, "__KSPFETIDP_pP", (PetscObject)pP));
780:       }
781:       PetscCall(PetscFree(widxs));

783:       /* If there's any "interior pressure",
784:          we may want to use a discrete harmonic solver instead
785:          of a Stokes harmonic for the Dirichlet preconditioner
786:          Need to extract the interior velocity dofs in interior dofs ordering (iV)
787:          and interior pressure dofs in local ordering (iP) */
788:       if (!allp) {
789:         ISLocalToGlobalMapping l2g_t;

791:         PetscCall(ISDifference(lPall, lP, &is1));
792:         PetscCall(PetscObjectCompose((PetscObject)fetidp->innerbddc, "__KSPFETIDP_iP", (PetscObject)is1));
793:         PetscCall(ISDifference(II, is1, &is2));
794:         PetscCall(ISDestroy(&is1));
795:         PetscCall(ISLocalToGlobalMappingCreateIS(II, &l2g_t));
796:         PetscCall(ISGlobalToLocalMappingApplyIS(l2g_t, IS_GTOLM_DROP, is2, &is1));
797:         PetscCall(ISGetLocalSize(is1, &i));
798:         PetscCall(ISGetLocalSize(is2, &j));
799:         PetscCheck(i == j, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Inconsistent local sizes %" PetscInt_FMT " and %" PetscInt_FMT " for iV", i, j);
800:         PetscCall(PetscObjectCompose((PetscObject)fetidp->innerbddc, "__KSPFETIDP_iV", (PetscObject)is1));
801:         PetscCall(ISLocalToGlobalMappingDestroy(&l2g_t));
802:         PetscCall(ISDestroy(&is1));
803:         PetscCall(ISDestroy(&is2));
804:       }

806:       /* exclude selected pressures from the inner BDDC */
807:       if (pcbddc->DirichletBoundariesLocal) {
808:         IS list[2], plP, isout;

810:         /* need a parallel IS */
811:         PetscCall(ISOnComm(lP, PetscObjectComm((PetscObject)ksp), PETSC_COPY_VALUES, &plP));
812:         list[0] = plP;
813:         list[1] = pcbddc->DirichletBoundariesLocal;
814:         PetscCall(ISConcatenate(PetscObjectComm((PetscObject)ksp), 2, list, &isout));
815:         PetscCall(ISSortRemoveDups(isout));
816:         PetscCall(ISDestroy(&plP));
817:         PetscCall(PCBDDCSetDirichletBoundariesLocal(fetidp->innerbddc, isout));
818:         PetscCall(ISDestroy(&isout));
819:       } else if (pcbddc->DirichletBoundaries) {
820:         IS list[2], isout;

822:         list[0] = pP;
823:         list[1] = pcbddc->DirichletBoundaries;
824:         PetscCall(ISConcatenate(PetscObjectComm((PetscObject)ksp), 2, list, &isout));
825:         PetscCall(ISSortRemoveDups(isout));
826:         PetscCall(PCBDDCSetDirichletBoundaries(fetidp->innerbddc, isout));
827:         PetscCall(ISDestroy(&isout));
828:       } else {
829:         IS plP;

831:         /* need a parallel IS */
832:         PetscCall(ISOnComm(lP, PetscObjectComm((PetscObject)ksp), PETSC_COPY_VALUES, &plP));
833:         PetscCall(PCBDDCSetDirichletBoundariesLocal(fetidp->innerbddc, plP));
834:         PetscCall(ISDestroy(&plP));
835:       }

837:       /* Need to zero output of interface BDDC for lP */
838:       {
839:         IS BB, lP_I, lP_B;

841:         PetscCall(ISComplement(II, 0, n, &BB));
842:         PetscCall(ISEmbed(lP, II, PETSC_TRUE, &lP_I));
843:         PetscCall(ISEmbed(lP, BB, PETSC_TRUE, &lP_B));
844:         PetscCall(PetscObjectCompose((PetscObject)fetidp->innerbddc, "__KSPFETIDP_lP_I", (PetscObject)lP_I));
845:         PetscCall(PetscObjectCompose((PetscObject)fetidp->innerbddc, "__KSPFETIDP_lP_B", (PetscObject)lP_B));
846:         PetscCall(ISDestroy(&BB));
847:         PetscCall(ISDestroy(&lP_I));
848:         PetscCall(ISDestroy(&lP_B));
849:       }
850:       PetscCall(ISDestroy(&II));

852:       /* save CSR information for the pressure BDDC solver (if any) */
853:       if (schp) {
854:         PetscInt np, nt;

856:         PetscCall(MatGetSize(matis->A, &nt, NULL));
857:         PetscCall(ISGetLocalSize(lP, &np));
858:         if (np) {
859:           PetscInt *xadj = pcbddc->mat_graph->xadj;
860:           PetscInt *adjn = pcbddc->mat_graph->adjncy;
861:           PetscInt  nv   = pcbddc->mat_graph->nvtxs_csr;

863:           if (nv && nv == nt) {
864:             ISLocalToGlobalMapping pmap;
865:             PetscInt              *schp_csr, *schp_xadj, *schp_adjn, p;
866:             PetscContainer         c;

868:             PetscCall(ISLocalToGlobalMappingCreateIS(lPall, &pmap));
869:             PetscCall(ISGetIndices(lPall, &idxs));
870:             for (p = 0, nv = 0; p < np; p++) {
871:               PetscInt x, n = idxs[p];

873:               PetscCall(ISGlobalToLocalMappingApply(pmap, IS_GTOLM_DROP, xadj[n + 1] - xadj[n], adjn + xadj[n], &x, NULL));
874:               nv += x;
875:             }
876:             PetscCall(PetscMalloc1(np + 1 + nv, &schp_csr));
877:             schp_xadj = schp_csr;
878:             schp_adjn = schp_csr + np + 1;
879:             for (p = 0, schp_xadj[0] = 0; p < np; p++) {
880:               PetscInt x, n = idxs[p];

882:               PetscCall(ISGlobalToLocalMappingApply(pmap, IS_GTOLM_DROP, xadj[n + 1] - xadj[n], adjn + xadj[n], &x, schp_adjn + schp_xadj[p]));
883:               schp_xadj[p + 1] = schp_xadj[p] + x;
884:             }
885:             PetscCall(ISRestoreIndices(lPall, &idxs));
886:             PetscCall(ISLocalToGlobalMappingDestroy(&pmap));
887:             PetscCall(PetscContainerCreate(PETSC_COMM_SELF, &c));
888:             PetscCall(PetscContainerSetPointer(c, schp_csr));
889:             PetscCall(PetscContainerSetCtxDestroy(c, PetscCtxDestroyDefault));
890:             PetscCall(PetscObjectCompose((PetscObject)fetidp->innerbddc, "__KSPFETIDP_pCSR", (PetscObject)c));
891:             PetscCall(PetscContainerDestroy(&c));
892:           }
893:         }
894:       }
895:       PetscCall(ISDestroy(&lPall));
896:       PetscCall(ISDestroy(&lP));
897:       fetidp->pP = pP;
898:     }

900:     /* total number of selected pressure dofs */
901:     PetscCall(ISGetSize(fetidp->pP, &totP));

903:     /* Set operator for inner BDDC */
904:     if (totP || fetidp->rhs_flip) {
905:       PetscCall(MatDuplicate(A, MAT_COPY_VALUES, &nA));
906:     } else {
907:       PetscCall(PetscObjectReference((PetscObject)A));
908:       nA = A;
909:     }
910:     if (fetidp->rhs_flip) {
911:       PetscCall(MatDiagonalScale(nA, fetidp->rhs_flip, NULL));
912:       if (totP) {
913:         Mat lA2;

915:         PetscCall(MatISGetLocalMat(nA, &lA));
916:         PetscCall(MatDuplicate(lA, MAT_COPY_VALUES, &lA2));
917:         PetscCall(PetscObjectCompose((PetscObject)fetidp->innerbddc, "__KSPFETIDP_lA", (PetscObject)lA2));
918:         PetscCall(MatDestroy(&lA2));
919:       }
920:     }

922:     /* assign operator to compute inner bddc */
923:     if (totP) {
924:       /* in this case, we remove all the used pressure couplings */
925:       PetscCall(MatSetOption(nA, MAT_NEW_NONZERO_LOCATION_ERR, PETSC_FALSE));
926:       PetscCall(MatZeroRowsColumnsIS(nA, fetidp->pP, 1., NULL, NULL));
927:     } else {
928:       PetscCall(PetscObjectCompose((PetscObject)fetidp->innerbddc, "__KSPFETIDP_lA", NULL));
929:     }
930:     PetscCall(MatGetNearNullSpace(Ap, &nnsp));
931:     if (!nnsp) PetscCall(MatGetNullSpace(Ap, &nnsp));
932:     if (!nnsp) PetscCall(MatGetNearNullSpace(A, &nnsp));
933:     if (!nnsp) PetscCall(MatGetNullSpace(A, &nnsp));
934:     PetscCall(MatSetNearNullSpace(nA, nnsp));
935:     PetscCall(PCSetOperators(fetidp->innerbddc, nA, nA));
936:     PetscCall(MatDestroy(&nA));

938:     /* non-zero rhs on interior dofs when applying the preconditioner */
939:     if (totP) pcbddc->switch_static = PETSC_TRUE;

941:     /* if there are no interface pressures, set inner bddc flag for benign saddle point */
942:     if (!totP) {
943:       pcbddc->benign_saddle_point = PETSC_TRUE;
944:       pcbddc->compute_nonetflux   = PETSC_TRUE;
945:     }

947:     /* Operators for pressure preconditioner */
948:     if (totP) {
949:       /* Extract pressure block if needed */
950:       if (!pisz) {
951:         Mat C;
952:         IS  nzrows = NULL;

954:         PetscCall(MatCreateSubMatrix(A, fetidp->pP, fetidp->pP, MAT_INITIAL_MATRIX, &C));
955:         PetscCall(MatFindNonzeroRows(C, &nzrows));
956:         if (nzrows) {
957:           PetscInt i;

959:           PetscCall(ISGetSize(nzrows, &i));
960:           PetscCall(ISDestroy(&nzrows));
961:           if (!i) pisz = PETSC_TRUE;
962:         }
963:         if (!pisz) {
964:           PetscCall(MatScale(C, -1.)); /* i.e. Almost Incompressible Elasticity, Stokes discretized with Q1xQ1_stabilized, Biot... */
965:           PetscCall(PetscObjectCompose((PetscObject)fetidp->innerbddc, "__KSPFETIDP_C", (PetscObject)C));
966:         }
967:         PetscCall(MatDestroy(&C));
968:       }
969:       /* Divergence mat */
970:       if (!pcbddc->divudotp) {
971:         Mat       B;
972:         IS        P;
973:         IS        l2l = NULL;
974:         PetscBool save;

976:         PetscCall(PetscObjectQuery((PetscObject)fetidp->innerbddc, "__KSPFETIDP_aP", (PetscObject *)&P));
977:         if (!pisz) {
978:           IS       F, V, Ps;
979:           PetscInt m, M;

981:           PetscCall(MatGetOwnershipRange(A, &m, &M));
982:           PetscCall(ISCreateStride(PetscObjectComm((PetscObject)A), M - m, m, 1, &F));
983:           PetscCall(ISDuplicate(P, &Ps));
984:           PetscCall(ISSort(Ps));
985:           PetscCall(ISComplement(Ps, m, M, &V));
986:           PetscCall(ISDestroy(&Ps));
987:           PetscCall(MatCreateSubMatrix(A, P, V, MAT_INITIAL_MATRIX, &B));
988:           {
989:             Mat_IS *Bmatis = (Mat_IS *)B->data;
990:             PetscCall(PetscObjectReference((PetscObject)Bmatis->getsub_cis));
991:             l2l = Bmatis->getsub_cis;
992:           }
993:           PetscCall(ISDestroy(&V));
994:           PetscCall(ISDestroy(&F));
995:         } else {
996:           PetscCall(MatCreateSubMatrix(A, P, NULL, MAT_INITIAL_MATRIX, &B));
997:         }
998:         save = pcbddc->compute_nonetflux; /* SetDivergenceMat activates nonetflux computation */
999:         PetscCall(PCBDDCSetDivergenceMat(fetidp->innerbddc, B, PETSC_FALSE, l2l));
1000:         pcbddc->compute_nonetflux = save;
1001:         PetscCall(MatDestroy(&B));
1002:         PetscCall(ISDestroy(&l2l));
1003:       }
1004:       if (A != Ap) { /* user has provided a different Pmat, this always supersedes the setter (TODO: is it OK?) */
1005:         /* use monolithic operator, we restrict later */
1006:         PetscCall(KSPFETIDPSetPressureOperator(ksp, Ap));
1007:       }
1008:       PetscCall(PetscObjectQuery((PetscObject)fetidp->innerbddc, "__KSPFETIDP_PPmat", (PetscObject *)&PPmat));

1010:       /* PPmat not present, use some default choice */
1011:       if (!PPmat) {
1012:         Mat C;

1014:         PetscCall(PetscObjectQuery((PetscObject)fetidp->innerbddc, "__KSPFETIDP_C", (PetscObject *)&C));
1015:         if (!schp && C) { /* non-zero pressure block, most likely Almost Incompressible Elasticity */
1016:           PetscCall(KSPFETIDPSetPressureOperator(ksp, C));
1017:         } else if (!pisz && schp) { /* we need the whole pressure mass matrix to define the interface BDDC */
1018:           IS P;

1020:           PetscCall(PetscObjectQuery((PetscObject)fetidp->innerbddc, "__KSPFETIDP_aP", (PetscObject *)&P));
1021:           PetscCall(MatCreateSubMatrix(A, P, P, MAT_INITIAL_MATRIX, &C));
1022:           PetscCall(MatScale(C, -1.));
1023:           PetscCall(KSPFETIDPSetPressureOperator(ksp, C));
1024:           PetscCall(MatDestroy(&C));
1025:         } else { /* identity (need to be scaled properly by the user using e.g. a Richardson method */
1026:           PetscInt nl;

1028:           PetscCall(ISGetLocalSize(fetidp->pP, &nl));
1029:           PetscCall(MatCreate(PetscObjectComm((PetscObject)ksp), &C));
1030:           PetscCall(MatSetSizes(C, nl, nl, totP, totP));
1031:           PetscCall(MatSetType(C, MATAIJ));
1032:           PetscCall(MatMPIAIJSetPreallocation(C, 1, NULL, 0, NULL));
1033:           PetscCall(MatSeqAIJSetPreallocation(C, 1, NULL));
1034:           PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
1035:           PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));
1036:           PetscCall(MatShift(C, 1.));
1037:           PetscCall(KSPFETIDPSetPressureOperator(ksp, C));
1038:           PetscCall(MatDestroy(&C));
1039:         }
1040:       }

1042:       /* Preconditioned operator for the pressure block */
1043:       PetscCall(PetscObjectQuery((PetscObject)fetidp->innerbddc, "__KSPFETIDP_PPmat", (PetscObject *)&PPmat));
1044:       if (PPmat) {
1045:         Mat      C;
1046:         IS       Pall;
1047:         PetscInt AM, PAM, PAN, pam, pan, am, an, pl, pIl, pAg, pIg;

1049:         PetscCall(PetscObjectQuery((PetscObject)fetidp->innerbddc, "__KSPFETIDP_aP", (PetscObject *)&Pall));
1050:         PetscCall(MatGetSize(A, &AM, NULL));
1051:         PetscCall(MatGetSize(PPmat, &PAM, &PAN));
1052:         PetscCall(ISGetSize(Pall, &pAg));
1053:         PetscCall(ISGetSize(fetidp->pP, &pIg));
1054:         PetscCall(MatGetLocalSize(PPmat, &pam, &pan));
1055:         PetscCall(MatGetLocalSize(A, &am, &an));
1056:         PetscCall(ISGetLocalSize(Pall, &pIl));
1057:         PetscCall(ISGetLocalSize(fetidp->pP, &pl));
1058:         PetscCheck(PAM == PAN, PetscObjectComm((PetscObject)ksp), PETSC_ERR_USER, "Pressure matrix must be square, unsupported %" PetscInt_FMT " x %" PetscInt_FMT, PAM, PAN);
1059:         PetscCheck(pam == pan, PetscObjectComm((PetscObject)ksp), PETSC_ERR_USER, "Local sizes of pressure matrix must be equal, unsupported %" PetscInt_FMT " x %" PetscInt_FMT, pam, pan);
1060:         PetscCheck(pam == am || pam == pl || pam == pIl, PETSC_COMM_SELF, PETSC_ERR_USER, "Invalid number of local rows %" PetscInt_FMT " for pressure matrix! Supported are %" PetscInt_FMT ", %" PetscInt_FMT " or %" PetscInt_FMT, pam, am, pl, pIl);
1061:         PetscCheck(pan == an || pan == pl || pan == pIl, PETSC_COMM_SELF, PETSC_ERR_USER, "Invalid number of local columns %" PetscInt_FMT " for pressure matrix! Supported are %" PetscInt_FMT ", %" PetscInt_FMT " or %" PetscInt_FMT, pan, an, pl, pIl);
1062:         if (PAM == AM) { /* monolithic ordering, restrict to pressure */
1063:           if (schp) {
1064:             PetscCall(MatCreateSubMatrix(PPmat, Pall, Pall, MAT_INITIAL_MATRIX, &C));
1065:             PetscCall(MatNullSpacePropagateAny_Private(PPmat, Pall, C));
1066:           } else {
1067:             PetscCall(MatCreateSubMatrix(PPmat, fetidp->pP, fetidp->pP, MAT_INITIAL_MATRIX, &C));
1068:           }
1069:         } else if (pAg == PAM) { /* global ordering for pressure only */
1070:           if (!allp && !schp) {  /* solving for interface pressure only */
1071:             IS restr;

1073:             PetscCall(ISRenumber(fetidp->pP, NULL, NULL, &restr));
1074:             PetscCall(MatCreateSubMatrix(PPmat, restr, restr, MAT_INITIAL_MATRIX, &C));
1075:             PetscCall(ISDestroy(&restr));
1076:           } else {
1077:             PetscCall(PetscObjectReference((PetscObject)PPmat));
1078:             C = PPmat;
1079:           }
1080:         } else if (pIg == PAM) { /* global ordering for selected pressure only */
1081:           PetscCheck(!schp, PetscObjectComm((PetscObject)ksp), PETSC_ERR_PLIB, "Need the entire matrix");
1082:           PetscCall(PetscObjectReference((PetscObject)PPmat));
1083:           C = PPmat;
1084:         } else SETERRQ(PetscObjectComm((PetscObject)ksp), PETSC_ERR_USER, "Unable to use the pressure matrix");

1086:         PetscCall(KSPFETIDPSetPressureOperator(ksp, C));
1087:         PetscCall(MatDestroy(&C));
1088:       } else SETERRQ(PetscObjectComm((PetscObject)ksp), PETSC_ERR_PLIB, "Missing Pmat for pressure block");
1089:     } else { /* totP == 0 */
1090:       PetscCall(PetscObjectCompose((PetscObject)fetidp->innerbddc, "__KSPFETIDP_pP", NULL));
1091:     }
1092:   }
1093:   PetscFunctionReturn(PETSC_SUCCESS);
1094: }

1096: static PetscErrorCode KSPSetUp_FETIDP(KSP ksp)
1097: {
1098:   KSP_FETIDP *fetidp = (KSP_FETIDP *)ksp->data;
1099:   PC_BDDC    *pcbddc = (PC_BDDC *)fetidp->innerbddc->data;
1100:   PetscBool   flg;

1102:   PetscFunctionBegin;
1103:   PetscCall(KSPFETIDPSetUpOperators(ksp));
1104:   /* set up BDDC */
1105:   PetscCall(PCSetErrorIfFailure(fetidp->innerbddc, ksp->errorifnotconverged));
1106:   PetscCall(PCSetUp(fetidp->innerbddc));
1107:   /* FETI-DP as it is implemented needs an exact coarse solver */
1108:   if (pcbddc->coarse_ksp) {
1109:     PetscCall(KSPSetTolerances(pcbddc->coarse_ksp, PETSC_SMALL, PETSC_SMALL, PETSC_CURRENT, 1000));
1110:     PetscCall(KSPSetNormType(pcbddc->coarse_ksp, KSP_NORM_DEFAULT));
1111:   }
1112:   /* FETI-DP as it is implemented needs exact local Neumann solvers */
1113:   PetscCall(KSPSetTolerances(pcbddc->ksp_R, PETSC_SMALL, PETSC_SMALL, PETSC_CURRENT, 1000));
1114:   PetscCall(KSPSetNormType(pcbddc->ksp_R, KSP_NORM_DEFAULT));

1116:   /* setup FETI-DP operators
1117:      If fetidp->statechanged is true, we need to update the operators
1118:      needed in the saddle-point case. This should be replaced
1119:      by a better logic when the FETI-DP matrix and preconditioner will
1120:      have their own classes */
1121:   if (pcbddc->new_primal_space || fetidp->statechanged) {
1122:     Mat F; /* the FETI-DP matrix */
1123:     PC  D; /* the FETI-DP preconditioner */
1124:     PetscCall(KSPReset(fetidp->innerksp));
1125:     PetscCall(PCBDDCCreateFETIDPOperators(fetidp->innerbddc, fetidp->fully_redundant, ((PetscObject)ksp)->prefix, &F, &D));
1126:     PetscCall(KSPSetOperators(fetidp->innerksp, F, F));
1127:     PetscCall(KSPSetTolerances(fetidp->innerksp, ksp->rtol, ksp->abstol, ksp->divtol, ksp->max_it));
1128:     PetscCall(KSPSetPC(fetidp->innerksp, D));
1129:     PetscCall(PetscObjectIncrementTabLevel((PetscObject)D, (PetscObject)fetidp->innerksp, 0));
1130:     PetscCall(KSPSetFromOptions(fetidp->innerksp));
1131:     PetscCall(MatCreateVecs(F, &fetidp->innerksp->vec_rhs, &fetidp->innerksp->vec_sol));
1132:     PetscCall(MatDestroy(&F));
1133:     PetscCall(PCDestroy(&D));
1134:     if (fetidp->check) {
1135:       PetscViewer viewer;

1137:       if (!pcbddc->dbg_viewer) {
1138:         viewer = PETSC_VIEWER_STDOUT_(PetscObjectComm((PetscObject)ksp));
1139:       } else {
1140:         viewer = pcbddc->dbg_viewer;
1141:       }
1142:       PetscCall(KSPFETIDPCheckOperators(ksp, viewer));
1143:     }
1144:   }
1145:   fetidp->statechanged     = PETSC_FALSE;
1146:   pcbddc->new_primal_space = PETSC_FALSE;

1148:   /* propagate settings to the inner solve */
1149:   PetscCall(KSPGetComputeSingularValues(ksp, &flg));
1150:   PetscCall(KSPSetComputeSingularValues(fetidp->innerksp, flg));
1151:   if (ksp->res_hist) PetscCall(KSPSetResidualHistory(fetidp->innerksp, ksp->res_hist, ksp->res_hist_max, ksp->res_hist_reset));
1152:   PetscCall(KSPSetErrorIfNotConverged(fetidp->innerksp, ksp->errorifnotconverged));
1153:   PetscCall(KSPSetUp(fetidp->innerksp));
1154:   PetscFunctionReturn(PETSC_SUCCESS);
1155: }

1157: static PetscErrorCode KSPSolve_FETIDP(KSP ksp)
1158: {
1159:   Mat                F, A;
1160:   MatNullSpace       nsp;
1161:   Vec                X, B, Xl, Bl;
1162:   KSP_FETIDP        *fetidp = (KSP_FETIDP *)ksp->data;
1163:   PC_BDDC           *pcbddc = (PC_BDDC *)fetidp->innerbddc->data;
1164:   KSPConvergedReason reason;
1165:   PC                 pc;
1166:   PCFailedReason     pcreason;
1167:   PetscInt           hist_len;
1168:   int                flg;

1170:   PetscFunctionBegin;
1171:   PetscCall(PetscCitationsRegister(citation, &cited));
1172:   if (fetidp->saddlepoint) PetscCall(PetscCitationsRegister(citation2, &cited2));
1173:   PetscCall(KSPGetOperators(ksp, &A, NULL));
1174:   PetscCall(KSPGetRhs(ksp, &B));
1175:   PetscCall(KSPGetSolution(ksp, &X));
1176:   PetscCall(KSPGetOperators(fetidp->innerksp, &F, NULL));
1177:   PetscCall(KSPGetRhs(fetidp->innerksp, &Bl));
1178:   PetscCall(KSPGetSolution(fetidp->innerksp, &Xl));
1179:   PetscCall(PCBDDCMatFETIDPGetRHS(F, B, Bl));
1180:   if (ksp->transpose_solve) {
1181:     PetscCall(KSPSolveTranspose(fetidp->innerksp, Bl, Xl));
1182:   } else {
1183:     PetscCall(KSPSolve(fetidp->innerksp, Bl, Xl));
1184:   }
1185:   PetscCall(KSPGetConvergedReason(fetidp->innerksp, &reason));
1186:   PetscCall(KSPGetPC(fetidp->innerksp, &pc));
1187:   PetscCall(PCGetFailedReason(pc, &pcreason));
1188:   flg = (reason < 0 && reason != KSP_DIVERGED_ITS) || pcreason;
1189:   PetscCall(VecFlag(Xl, flg));
1190:   if (flg) {
1191:     PetscInt its;

1193:     PetscCall(KSPGetIterationNumber(fetidp->innerksp, &its));
1194:     ksp->reason = KSP_DIVERGED_PC_FAILED;
1195:     PetscCall(PetscInfo(ksp, "Inner KSP solve failed: %s %s at iteration %" PetscInt_FMT "\n", KSPConvergedReasons[reason], PCFailedReasons[pcreason], its));
1196:   }
1197:   PetscCall(PCBDDCMatFETIDPGetSolution(F, Xl, X));
1198:   PetscCall(MatGetNullSpace(A, &nsp));
1199:   if (nsp) PetscCall(MatNullSpaceRemove(nsp, X));
1200:   /* update ksp with stats from inner ksp */
1201:   PetscCall(KSPGetConvergedReason(fetidp->innerksp, &ksp->reason));
1202:   PetscCall(KSPGetIterationNumber(fetidp->innerksp, &ksp->its));
1203:   ksp->totalits += ksp->its;
1204:   PetscCall(KSPGetResidualHistory(fetidp->innerksp, NULL, &hist_len));
1205:   ksp->res_hist_len = (size_t)hist_len;
1206:   /* restore defaults for inner BDDC (Pre/PostSolve flags) */
1207:   pcbddc->temp_solution_used        = PETSC_FALSE;
1208:   pcbddc->rhs_change                = PETSC_FALSE;
1209:   pcbddc->exact_dirichlet_trick_app = PETSC_FALSE;
1210:   PetscFunctionReturn(PETSC_SUCCESS);
1211: }

1213: static PetscErrorCode KSPReset_FETIDP(KSP ksp)
1214: {
1215:   KSP_FETIDP *fetidp = (KSP_FETIDP *)ksp->data;
1216:   PC_BDDC    *pcbddc;

1218:   PetscFunctionBegin;
1219:   PetscCall(ISDestroy(&fetidp->pP));
1220:   PetscCall(VecDestroy(&fetidp->rhs_flip));
1221:   /* avoid PCReset that does not take into account ref counting */
1222:   PetscCall(PCDestroy(&fetidp->innerbddc));
1223:   PetscCall(PCCreate(PetscObjectComm((PetscObject)ksp), &fetidp->innerbddc));
1224:   PetscCall(PCSetType(fetidp->innerbddc, PCBDDC));
1225:   pcbddc                   = (PC_BDDC *)fetidp->innerbddc->data;
1226:   pcbddc->symmetric_primal = PETSC_FALSE;
1227:   PetscCall(KSPDestroy(&fetidp->innerksp));
1228:   fetidp->saddlepoint  = PETSC_FALSE;
1229:   fetidp->matstate     = -1;
1230:   fetidp->matnnzstate  = -1;
1231:   fetidp->statechanged = PETSC_TRUE;
1232:   PetscFunctionReturn(PETSC_SUCCESS);
1233: }

1235: static PetscErrorCode KSPDestroy_FETIDP(KSP ksp)
1236: {
1237:   KSP_FETIDP *fetidp = (KSP_FETIDP *)ksp->data;

1239:   PetscFunctionBegin;
1240:   PetscCall(KSPReset_FETIDP(ksp));
1241:   PetscCall(PCDestroy(&fetidp->innerbddc));
1242:   PetscCall(KSPDestroy(&fetidp->innerksp));
1243:   PetscCall(PetscFree(fetidp->monctx));
1244:   PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPFETIDPSetInnerBDDC_C", NULL));
1245:   PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPFETIDPGetInnerBDDC_C", NULL));
1246:   PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPFETIDPGetInnerKSP_C", NULL));
1247:   PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPFETIDPSetPressureOperator_C", NULL));
1248:   PetscCall(PetscFree(ksp->data));
1249:   PetscFunctionReturn(PETSC_SUCCESS);
1250: }

1252: static PetscErrorCode KSPView_FETIDP(KSP ksp, PetscViewer viewer)
1253: {
1254:   KSP_FETIDP *fetidp = (KSP_FETIDP *)ksp->data;
1255:   PetscBool   iascii;

1257:   PetscFunctionBegin;
1258:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &iascii));
1259:   if (iascii) {
1260:     PetscCall(PetscViewerASCIIPrintf(viewer, "  fully redundant: %d\n", fetidp->fully_redundant));
1261:     PetscCall(PetscViewerASCIIPrintf(viewer, "  saddle point:    %d\n", fetidp->saddlepoint));
1262:     PetscCall(PetscViewerASCIIPrintf(viewer, "Inner KSP solver details\n"));
1263:   }
1264:   PetscCall(PetscViewerASCIIPushTab(viewer));
1265:   PetscCall(KSPView(fetidp->innerksp, viewer));
1266:   PetscCall(PetscViewerASCIIPopTab(viewer));
1267:   if (iascii) PetscCall(PetscViewerASCIIPrintf(viewer, "Inner BDDC solver details\n"));
1268:   PetscCall(PetscViewerASCIIPushTab(viewer));
1269:   PetscCall(PCView(fetidp->innerbddc, viewer));
1270:   PetscCall(PetscViewerASCIIPopTab(viewer));
1271:   PetscFunctionReturn(PETSC_SUCCESS);
1272: }

1274: static PetscErrorCode KSPSetFromOptions_FETIDP(KSP ksp, PetscOptionItems PetscOptionsObject)
1275: {
1276:   KSP_FETIDP *fetidp = (KSP_FETIDP *)ksp->data;

1278:   PetscFunctionBegin;
1279:   /* set options prefixes for the inner objects, since the parent prefix will be valid at this point */
1280:   PetscCall(PetscObjectSetOptionsPrefix((PetscObject)fetidp->innerksp, ((PetscObject)ksp)->prefix));
1281:   PetscCall(PetscObjectAppendOptionsPrefix((PetscObject)fetidp->innerksp, "fetidp_"));
1282:   if (!fetidp->userbddc) {
1283:     PetscCall(PetscObjectSetOptionsPrefix((PetscObject)fetidp->innerbddc, ((PetscObject)ksp)->prefix));
1284:     PetscCall(PetscObjectAppendOptionsPrefix((PetscObject)fetidp->innerbddc, "fetidp_bddc_"));
1285:   }
1286:   PetscOptionsHeadBegin(PetscOptionsObject, "KSP FETIDP options");
1287:   PetscCall(PetscOptionsBool("-ksp_fetidp_fullyredundant", "Use fully redundant multipliers", "none", fetidp->fully_redundant, &fetidp->fully_redundant, NULL));
1288:   PetscCall(PetscOptionsBool("-ksp_fetidp_saddlepoint", "Activates support for saddle-point problems", NULL, fetidp->saddlepoint, &fetidp->saddlepoint, NULL));
1289:   PetscCall(PetscOptionsBool("-ksp_fetidp_check", "Activates verbose debugging output FETI-DP operators", NULL, fetidp->check, &fetidp->check, NULL));
1290:   PetscOptionsHeadEnd();
1291:   PetscCall(PCSetFromOptions(fetidp->innerbddc));
1292:   PetscFunctionReturn(PETSC_SUCCESS);
1293: }

1295: /*MC
1296:      KSPFETIDP - The FETI-DP method {cite}`farhat2001feti`

1298:    Options Database Keys:
1299: +   -ksp_fetidp_fullyredundant <false>   - use a fully redundant set of Lagrange multipliers
1300: .   -ksp_fetidp_saddlepoint <false>      - activates support for saddle point problems, see {cite}`tu2015feti`
1301: .   -ksp_fetidp_saddlepoint_flip <false> - see note below
1302: .   -ksp_fetidp_pressure_field <-1>      - activates support for saddle point problems, and identifies the pressure field id.
1303:                                            If this information is not provided, the pressure field is detected by using `MatFindZeroDiagonals()`.
1304: -   -ksp_fetidp_pressure_all <false>     - if false, uses the interface pressures, as described in [2]. If true, uses the entire pressure field.

1306:    Level: Advanced

1308:    Notes:
1309:    The matrix for the `KSP` must be of type `MATIS`.

1311:    Usually, an incompressible Stokes problem is written as
1312: .vb
1313:    | A B^T | | v | = | f |
1314:    | B 0   | | p | = | g |
1315: .ve
1316:    with B representing $ -\int_\Omega \nabla \cdot u q $. If -ksp_fetidp_saddlepoint_flip is true, the code assumes that the user provides it as
1317: .vb
1318:    | A B^T | | v | = | f |
1319:    |-B 0   | | p | = |-g |
1320: .ve

1322:    The FETI-DP linear system (automatically generated constructing an internal `PCBDDC` object) is solved using an internal `KSP` object.

1324:    Options for the inner `KSP` and for the customization of the `PCBDDC` object can be specified at command line by using the prefixes `-fetidp_` and `-fetidp_bddc_`. E.g.,
1325: .vb
1326:    -fetidp_ksp_type gmres -fetidp_bddc_pc_bddc_symmetric false
1327: .ve
1328:    will use `KSPGMRES` for the solution of the linear system on the Lagrange multipliers, generated using a non-symmetric `PCBDDC`.

1330:    For saddle point problems with continuous pressures, the preconditioned operator for the pressure solver can be specified with `KSPFETIDPSetPressureOperator()`.
1331:    Alternatively, the pressure operator is extracted from the precondioned matrix (if it is different from the linear solver matrix).
1332:    If none of the above, an identity matrix will be created; the user then needs to scale it through a Richardson solver.
1333:    Options for the pressure solver can be prefixed with `-fetidp_fielsplit_p_`, E.g.
1334: .vb
1335:    -fetidp_fielsplit_p_ksp_type preonly -fetidp_fielsplit_p_pc_type lu -fetidp_fielsplit_p_pc_factor_mat_solver_type mumps
1336: .ve
1337:    In order to use the deluxe version of FETI-DP, you must customize the inner `PCBDDC` operator with -fetidp_bddc_pc_bddc_use_deluxe_scaling -fetidp_bddc_pc_bddc_deluxe_singlemat and use
1338:    non-redundant multipliers, i.e. `-ksp_fetidp_fullyredundant false`. Options for the scaling solver are prefixed by `-fetidp_bddelta_`, E.g.
1339: .vb
1340:    -fetidp_bddelta_pc_factor_mat_solver_type mumps -fetidp_bddelta_pc_type lu
1341: .ve

1343:    Some of the basic options such as the maximum number of iterations and tolerances are automatically passed from this `KSP` to the inner `KSP` that actually performs the iterations.

1345:    The converged reason and number of iterations computed are passed from the inner `KSP` to this `KSP` at the end of the solution.

1347:    Developer Note:
1348:    Even though this method does not directly use any norms, the user is allowed to set the `KSPNormType` to any value.
1349:    This is so users do not have to change `KSPNormType` options when they switch from other `KSP` methods to this one.

1351: .seealso: [](ch_ksp), `MATIS`, `PCBDDC`, `KSPFETIDPSetInnerBDDC()`, `KSPFETIDPGetInnerBDDC()`, `KSPFETIDPGetInnerKSP()`
1352: M*/
1353: PETSC_EXTERN PetscErrorCode KSPCreate_FETIDP(KSP ksp)
1354: {
1355:   KSP_FETIDP    *fetidp;
1356:   KSP_FETIDPMon *monctx;
1357:   PC_BDDC       *pcbddc;
1358:   PC             pc;

1360:   PetscFunctionBegin;
1361:   PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_NONE, PC_LEFT, 3));
1362:   PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_NONE, PC_RIGHT, 2));
1363:   PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_PRECONDITIONED, PC_LEFT, 2));
1364:   PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_PRECONDITIONED, PC_RIGHT, 2));
1365:   PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_UNPRECONDITIONED, PC_LEFT, 2));
1366:   PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_UNPRECONDITIONED, PC_RIGHT, 2));
1367:   PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_NATURAL, PC_LEFT, 2));

1369:   PetscCall(PetscNew(&fetidp));
1370:   fetidp->matstate     = -1;
1371:   fetidp->matnnzstate  = -1;
1372:   fetidp->statechanged = PETSC_TRUE;

1374:   ksp->data                              = (void *)fetidp;
1375:   ksp->ops->setup                        = KSPSetUp_FETIDP;
1376:   ksp->ops->solve                        = KSPSolve_FETIDP;
1377:   ksp->ops->destroy                      = KSPDestroy_FETIDP;
1378:   ksp->ops->computeeigenvalues           = KSPComputeEigenvalues_FETIDP;
1379:   ksp->ops->computeextremesingularvalues = KSPComputeExtremeSingularValues_FETIDP;
1380:   ksp->ops->view                         = KSPView_FETIDP;
1381:   ksp->ops->setfromoptions               = KSPSetFromOptions_FETIDP;
1382:   ksp->ops->buildsolution                = KSPBuildSolution_FETIDP;
1383:   ksp->ops->buildresidual                = KSPBuildResidualDefault;
1384:   PetscCall(KSPGetPC(ksp, &pc));
1385:   PetscCall(PCSetType(pc, PCNONE));
1386:   /* create the inner KSP for the Lagrange multipliers */
1387:   PetscCall(KSPCreate(PetscObjectComm((PetscObject)ksp), &fetidp->innerksp));
1388:   PetscCall(KSPGetPC(fetidp->innerksp, &pc));
1389:   PetscCall(PCSetType(pc, PCNONE));
1390:   /* monitor */
1391:   PetscCall(PetscNew(&monctx));
1392:   monctx->parentksp = ksp;
1393:   fetidp->monctx    = monctx;
1394:   PetscCall(KSPMonitorSet(fetidp->innerksp, KSPMonitor_FETIDP, fetidp->monctx, NULL));
1395:   /* create the inner BDDC */
1396:   PetscCall(PCCreate(PetscObjectComm((PetscObject)ksp), &fetidp->innerbddc));
1397:   PetscCall(PCSetType(fetidp->innerbddc, PCBDDC));
1398:   /* make sure we always obtain a consistent FETI-DP matrix
1399:      for symmetric problems, the user can always customize it through the command line */
1400:   pcbddc                   = (PC_BDDC *)fetidp->innerbddc->data;
1401:   pcbddc->symmetric_primal = PETSC_FALSE;
1402:   /* composed functions */
1403:   PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPFETIDPSetInnerBDDC_C", KSPFETIDPSetInnerBDDC_FETIDP));
1404:   PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPFETIDPGetInnerBDDC_C", KSPFETIDPGetInnerBDDC_FETIDP));
1405:   PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPFETIDPGetInnerKSP_C", KSPFETIDPGetInnerKSP_FETIDP));
1406:   PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPFETIDPSetPressureOperator_C", KSPFETIDPSetPressureOperator_FETIDP));
1407:   /* need to call KSPSetUp_FETIDP even with KSP_SETUP_NEWMATRIX */
1408:   ksp->setupnewmatrix = PETSC_TRUE;
1409:   PetscFunctionReturn(PETSC_SUCCESS);
1410: }