Actual source code: fieldsplit.c

  1: #include <petsc/private/pcimpl.h>
  2: #include <petsc/private/kspimpl.h>
  3: #include <petscdm.h>
  4: #include <petscdevice.h>
  5: #if PetscDefined(HAVE_CUDA)
  6: #include <petscdevice_cuda.h>
  7: #endif
  8: #if PetscDefined(HAVE_HIP)
  9: #include <petscdevice_hip.h>
 10: #endif

 12: const char *const PCFieldSplitSchurPreTypes[]  = {"SELF", "SELFP", "A11", "USER", "FULL", "PCFieldSplitSchurPreType", "PC_FIELDSPLIT_SCHUR_PRE_", NULL};
 13: const char *const PCFieldSplitSchurFactTypes[] = {"DIAG", "LOWER", "UPPER", "FULL", "PCFieldSplitSchurFactType", "PC_FIELDSPLIT_SCHUR_FACT_", NULL};

 15: PetscLogEvent KSP_Solve_FS_0, KSP_Solve_FS_1, KSP_Solve_FS_S, KSP_Solve_FS_U, KSP_Solve_FS_L, KSP_Solve_FS_2, KSP_Solve_FS_3, KSP_Solve_FS_4;

 17: typedef struct _PC_FieldSplitLink *PC_FieldSplitLink;
 18: struct _PC_FieldSplitLink {
 19:   KSP               ksp;
 20:   Vec               x, y, z;
 21:   char             *splitname;
 22:   PetscInt          nfields;
 23:   PetscInt         *fields, *fields_col;
 24:   VecScatter        sctx;
 25:   IS                is, is_col;
 26:   PC_FieldSplitLink next, previous;
 27:   PetscLogEvent     event;

 29:   /* Used only when setting coordinates with PCSetCoordinates */
 30:   PetscInt   dim;
 31:   PetscInt   ndofs;
 32:   PetscReal *coords;
 33: };

 35: typedef struct {
 36:   PCCompositeType type;
 37:   PetscBool       defaultsplit; /* Flag for a system with a set of 'k' scalar fields with the same layout (and bs = k) */
 38:   PetscBool       splitdefined; /* Flag is set after the splits have been defined, to prevent more splits from being added */
 39:   PetscInt        bs;           /* Block size for IS and Mat structures */
 40:   PetscInt        nsplits;      /* Number of field divisions defined */
 41:   Vec            *x, *y, w1, w2;
 42:   Mat            *mat;    /* The diagonal block for each split */
 43:   Mat            *pmat;   /* The preconditioning diagonal block for each split */
 44:   Mat            *Afield; /* The rows of the matrix associated with each split */
 45:   PetscBool       issetup;

 47:   /* Only used when Schur complement preconditioning is used */
 48:   Mat                       B;          /* The (0,1) block */
 49:   Mat                       C;          /* The (1,0) block */
 50:   Mat                       schur;      /* The Schur complement S = A11 - A10 A00^{-1} A01, the KSP here, kspinner, is H_1 in [El08] */
 51:   Mat                       schurp;     /* Assembled approximation to S built by MatSchurComplement to be used as a matrix for constructing the preconditioner when solving with S */
 52:   Mat                       schur_user; /* User-provided matrix for constructing the preconditioner for the Schur complement */
 53:   PCFieldSplitSchurPreType  schurpre;   /* Determines which matrix is used for the Schur complement */
 54:   PCFieldSplitSchurFactType schurfactorization;
 55:   KSP                       kspschur;   /* The solver for S */
 56:   KSP                       kspupper;   /* The solver for A in the upper diagonal part of the factorization (H_2 in [El08]) */
 57:   PetscScalar               schurscale; /* Scaling factor for the Schur complement solution with DIAG factorization */

 59:   /* Only used when Golub-Kahan bidiagonalization preconditioning is used */
 60:   Mat          H;           /* The modified matrix H = A00 + nu*A01*A01'              */
 61:   PetscReal    gkbtol;      /* Stopping tolerance for lower bound estimate            */
 62:   PetscInt     gkbdelay;    /* The delay window for the stopping criterion            */
 63:   PetscReal    gkbnu;       /* Parameter for augmented Lagrangian H = A + nu*A01*A01' */
 64:   PetscInt     gkbmaxit;    /* Maximum number of iterations for outer loop            */
 65:   PetscBool    gkbmonitor;  /* Monitor for gkb iterations and the lower bound error   */
 66:   PetscViewer  gkbviewer;   /* Viewer context for gkbmonitor                          */
 67:   Vec          u, v, d, Hu; /* Work vectors for the GKB algorithm                     */
 68:   PetscScalar *vecz;        /* Contains intermediate values, eg for lower bound       */

 70:   PC_FieldSplitLink head;
 71:   PetscBool         isrestrict;       /* indicates PCFieldSplitRestrictIS() has been last called on this object, hack */
 72:   PetscBool         suboptionsset;    /* Indicates that the KSPSetFromOptions() has been called on the sub-KSPs */
 73:   PetscBool         dm_splits;        /* Whether to use DMCreateFieldDecomposition() whenever possible */
 74:   PetscBool         diag_use_amat;    /* Whether to extract diagonal matrix blocks from Amat, rather than Pmat (weaker than -pc_use_amat) */
 75:   PetscBool         offdiag_use_amat; /* Whether to extract off-diagonal matrix blocks from Amat, rather than Pmat (weaker than -pc_use_amat) */
 76:   PetscBool         detect;           /* Whether to form 2-way split by finding zero diagonal entries */
 77:   PetscBool         coordinates_set;  /* Whether PCSetCoordinates has been called */
 78: } PC_FieldSplit;

 80: /*
 81:     Note:
 82:     there is no particular reason that pmat, x, and y are stored as arrays in PC_FieldSplit instead of
 83:    inside PC_FieldSplitLink, just historical. If you want to be able to add new fields after already using the
 84:    PC you could change this.
 85: */

 87: /* This helper is so that setting a user-provided matrix is orthogonal to choosing to use it.  This way the
 88: * application-provided FormJacobian can provide this matrix without interfering with the user's (command-line) choices. */
 89: static Mat FieldSplitSchurPre(PC_FieldSplit *jac)
 90: {
 91:   switch (jac->schurpre) {
 92:   case PC_FIELDSPLIT_SCHUR_PRE_SELF:
 93:     return jac->schur;
 94:   case PC_FIELDSPLIT_SCHUR_PRE_SELFP:
 95:     return jac->schurp;
 96:   case PC_FIELDSPLIT_SCHUR_PRE_A11:
 97:     return jac->pmat[1];
 98:   case PC_FIELDSPLIT_SCHUR_PRE_FULL: /* We calculate this and store it in schur_user */
 99:   case PC_FIELDSPLIT_SCHUR_PRE_USER: /* Use a user-provided matrix if it is given, otherwise diagonal block */
100:   default:
101:     return jac->schur_user ? jac->schur_user : jac->pmat[1];
102:   }
103: }

105: #include <petscdraw.h>
106: static PetscErrorCode PCView_FieldSplit(PC pc, PetscViewer viewer)
107: {
108:   PC_FieldSplit    *jac = (PC_FieldSplit *)pc->data;
109:   PetscBool         isascii, isdraw;
110:   PetscInt          i, j;
111:   PC_FieldSplitLink ilink = jac->head;

113:   PetscFunctionBegin;
114:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &isascii));
115:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERDRAW, &isdraw));
116:   if (isascii) {
117:     if (jac->bs > 0) {
118:       PetscCall(PetscViewerASCIIPrintf(viewer, "  FieldSplit with %s composition: total splits = %" PetscInt_FMT ", blocksize = %" PetscInt_FMT "\n", PCCompositeTypes[jac->type], jac->nsplits, jac->bs));
119:     } else {
120:       PetscCall(PetscViewerASCIIPrintf(viewer, "  FieldSplit with %s composition: total splits = %" PetscInt_FMT "\n", PCCompositeTypes[jac->type], jac->nsplits));
121:     }
122:     if (pc->useAmat) PetscCall(PetscViewerASCIIPrintf(viewer, "  using Amat (not Pmat) as operator for blocks\n"));
123:     if (jac->diag_use_amat) PetscCall(PetscViewerASCIIPrintf(viewer, "  using Amat (not Pmat) as operator for diagonal blocks\n"));
124:     if (jac->offdiag_use_amat) PetscCall(PetscViewerASCIIPrintf(viewer, "  using Amat (not Pmat) as operator for off-diagonal blocks\n"));
125:     PetscCall(PetscViewerASCIIPrintf(viewer, "  Solver info for each split is in the following KSP objects:\n"));
126:     for (i = 0; i < jac->nsplits; i++) {
127:       if (ilink->fields) {
128:         PetscCall(PetscViewerASCIIPrintf(viewer, "Split number %" PetscInt_FMT " Fields ", i));
129:         PetscCall(PetscViewerASCIIUseTabs(viewer, PETSC_FALSE));
130:         for (j = 0; j < ilink->nfields; j++) {
131:           if (j > 0) PetscCall(PetscViewerASCIIPrintf(viewer, ","));
132:           PetscCall(PetscViewerASCIIPrintf(viewer, " %" PetscInt_FMT, ilink->fields[j]));
133:         }
134:         PetscCall(PetscViewerASCIIPrintf(viewer, "\n"));
135:         PetscCall(PetscViewerASCIIUseTabs(viewer, PETSC_TRUE));
136:       } else {
137:         PetscCall(PetscViewerASCIIPrintf(viewer, "Split number %" PetscInt_FMT " Defined by IS\n", i));
138:       }
139:       PetscCall(KSPView(ilink->ksp, viewer));
140:       ilink = ilink->next;
141:     }
142:   }

144:   if (isdraw) {
145:     PetscDraw draw;
146:     PetscReal x, y, w, wd;

148:     PetscCall(PetscViewerDrawGetDraw(viewer, 0, &draw));
149:     PetscCall(PetscDrawGetCurrentPoint(draw, &x, &y));
150:     w  = 2 * PetscMin(1.0 - x, x);
151:     wd = w / (jac->nsplits + 1);
152:     x  = x - wd * (jac->nsplits - 1) / 2.0;
153:     for (i = 0; i < jac->nsplits; i++) {
154:       PetscCall(PetscDrawPushCurrentPoint(draw, x, y));
155:       PetscCall(KSPView(ilink->ksp, viewer));
156:       PetscCall(PetscDrawPopCurrentPoint(draw));
157:       x += wd;
158:       ilink = ilink->next;
159:     }
160:   }
161:   PetscFunctionReturn(PETSC_SUCCESS);
162: }

164: static PetscErrorCode PCView_FieldSplit_Schur(PC pc, PetscViewer viewer)
165: {
166:   PC_FieldSplit             *jac = (PC_FieldSplit *)pc->data;
167:   PetscBool                  isascii, isdraw;
168:   PetscInt                   i, j;
169:   PC_FieldSplitLink          ilink = jac->head;
170:   MatSchurComplementAinvType atype;

172:   PetscFunctionBegin;
173:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &isascii));
174:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERDRAW, &isdraw));
175:   if (isascii) {
176:     if (jac->bs > 0) {
177:       PetscCall(PetscViewerASCIIPrintf(viewer, "  FieldSplit with Schur preconditioner, blocksize = %" PetscInt_FMT ", factorization %s\n", jac->bs, PCFieldSplitSchurFactTypes[jac->schurfactorization]));
178:     } else {
179:       PetscCall(PetscViewerASCIIPrintf(viewer, "  FieldSplit with Schur preconditioner, factorization %s\n", PCFieldSplitSchurFactTypes[jac->schurfactorization]));
180:     }
181:     if (pc->useAmat) PetscCall(PetscViewerASCIIPrintf(viewer, "  using Amat (not Pmat) as operator for blocks\n"));
182:     switch (jac->schurpre) {
183:     case PC_FIELDSPLIT_SCHUR_PRE_SELF:
184:       PetscCall(PetscViewerASCIIPrintf(viewer, "  Preconditioner for the Schur complement formed from S itself\n"));
185:       break;
186:     case PC_FIELDSPLIT_SCHUR_PRE_SELFP:
187:       if (jac->schur) {
188:         PetscCall(MatSchurComplementGetAinvType(jac->schur, &atype));
189:         PetscCall(PetscViewerASCIIPrintf(viewer, "  Preconditioner for the Schur complement formed from Sp, an assembled approximation to S, which uses A00's %sinverse\n", atype == MAT_SCHUR_COMPLEMENT_AINV_DIAG ? "diagonal's " : (atype == MAT_SCHUR_COMPLEMENT_AINV_BLOCK_DIAG ? "block diagonal's " : (atype == MAT_SCHUR_COMPLEMENT_AINV_FULL ? "full " : "lumped diagonal's "))));
190:       }
191:       break;
192:     case PC_FIELDSPLIT_SCHUR_PRE_A11:
193:       PetscCall(PetscViewerASCIIPrintf(viewer, "  Preconditioner for the Schur complement formed from A11\n"));
194:       break;
195:     case PC_FIELDSPLIT_SCHUR_PRE_FULL:
196:       PetscCall(PetscViewerASCIIPrintf(viewer, "  Preconditioner for the Schur complement formed from the exact Schur complement\n"));
197:       break;
198:     case PC_FIELDSPLIT_SCHUR_PRE_USER:
199:       if (jac->schur_user) {
200:         PetscCall(PetscViewerASCIIPrintf(viewer, "  Preconditioner for the Schur complement formed from user provided matrix\n"));
201:       } else {
202:         PetscCall(PetscViewerASCIIPrintf(viewer, "  Preconditioner for the Schur complement formed from A11\n"));
203:       }
204:       break;
205:     default:
206:       SETERRQ(PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_OUTOFRANGE, "Invalid Schur preconditioning type: %d", jac->schurpre);
207:     }
208:     PetscCall(PetscViewerASCIIPrintf(viewer, "  Split info:\n"));
209:     PetscCall(PetscViewerASCIIPushTab(viewer));
210:     for (i = 0; i < jac->nsplits; i++) {
211:       if (ilink->fields) {
212:         PetscCall(PetscViewerASCIIPrintf(viewer, "Split number %" PetscInt_FMT " Fields ", i));
213:         PetscCall(PetscViewerASCIIUseTabs(viewer, PETSC_FALSE));
214:         for (j = 0; j < ilink->nfields; j++) {
215:           if (j > 0) PetscCall(PetscViewerASCIIPrintf(viewer, ","));
216:           PetscCall(PetscViewerASCIIPrintf(viewer, " %" PetscInt_FMT, ilink->fields[j]));
217:         }
218:         PetscCall(PetscViewerASCIIPrintf(viewer, "\n"));
219:         PetscCall(PetscViewerASCIIUseTabs(viewer, PETSC_TRUE));
220:       } else {
221:         PetscCall(PetscViewerASCIIPrintf(viewer, "Split number %" PetscInt_FMT " Defined by IS\n", i));
222:       }
223:       ilink = ilink->next;
224:     }
225:     PetscCall(PetscViewerASCIIPrintf(viewer, "KSP solver for A00 block\n"));
226:     PetscCall(PetscViewerASCIIPushTab(viewer));
227:     if (jac->head) PetscCall(KSPView(jac->head->ksp, viewer));
228:     else PetscCall(PetscViewerASCIIPrintf(viewer, "  not yet available\n"));
229:     PetscCall(PetscViewerASCIIPopTab(viewer));
230:     if (jac->head && jac->kspupper != jac->head->ksp) {
231:       PetscCall(PetscViewerASCIIPrintf(viewer, "KSP solver for upper A00 in upper triangular factor\n"));
232:       PetscCall(PetscViewerASCIIPushTab(viewer));
233:       if (jac->kspupper) PetscCall(KSPView(jac->kspupper, viewer));
234:       else PetscCall(PetscViewerASCIIPrintf(viewer, "  not yet available\n"));
235:       PetscCall(PetscViewerASCIIPopTab(viewer));
236:     }
237:     PetscCall(PetscViewerASCIIPrintf(viewer, "KSP solver for S = A11 - A10 inv(A00) A01\n"));
238:     PetscCall(PetscViewerASCIIPushTab(viewer));
239:     if (jac->kspschur) {
240:       PetscCall(KSPView(jac->kspschur, viewer));
241:     } else {
242:       PetscCall(PetscViewerASCIIPrintf(viewer, "  not yet available\n"));
243:     }
244:     PetscCall(PetscViewerASCIIPopTab(viewer));
245:     PetscCall(PetscViewerASCIIPopTab(viewer));
246:   } else if (isdraw && jac->head) {
247:     PetscDraw draw;
248:     PetscReal x, y, w, wd, h;
249:     PetscInt  cnt = 2;
250:     char      str[32];

252:     PetscCall(PetscViewerDrawGetDraw(viewer, 0, &draw));
253:     PetscCall(PetscDrawGetCurrentPoint(draw, &x, &y));
254:     if (jac->kspupper != jac->head->ksp) cnt++;
255:     w  = 2 * PetscMin(1.0 - x, x);
256:     wd = w / (cnt + 1);

258:     PetscCall(PetscSNPrintf(str, 32, "Schur fact. %s", PCFieldSplitSchurFactTypes[jac->schurfactorization]));
259:     PetscCall(PetscDrawStringBoxed(draw, x, y, PETSC_DRAW_RED, PETSC_DRAW_BLACK, str, NULL, &h));
260:     y -= h;
261:     if (jac->schurpre == PC_FIELDSPLIT_SCHUR_PRE_USER && !jac->schur_user) {
262:       PetscCall(PetscSNPrintf(str, 32, "Prec. for Schur from %s", PCFieldSplitSchurPreTypes[PC_FIELDSPLIT_SCHUR_PRE_A11]));
263:     } else {
264:       PetscCall(PetscSNPrintf(str, 32, "Prec. for Schur from %s", PCFieldSplitSchurPreTypes[jac->schurpre]));
265:     }
266:     PetscCall(PetscDrawStringBoxed(draw, x + wd * (cnt - 1) / 2.0, y, PETSC_DRAW_RED, PETSC_DRAW_BLACK, str, NULL, &h));
267:     y -= h;
268:     x = x - wd * (cnt - 1) / 2.0;

270:     PetscCall(PetscDrawPushCurrentPoint(draw, x, y));
271:     PetscCall(KSPView(jac->head->ksp, viewer));
272:     PetscCall(PetscDrawPopCurrentPoint(draw));
273:     if (jac->kspupper != jac->head->ksp) {
274:       x += wd;
275:       PetscCall(PetscDrawPushCurrentPoint(draw, x, y));
276:       PetscCall(KSPView(jac->kspupper, viewer));
277:       PetscCall(PetscDrawPopCurrentPoint(draw));
278:     }
279:     x += wd;
280:     PetscCall(PetscDrawPushCurrentPoint(draw, x, y));
281:     PetscCall(KSPView(jac->kspschur, viewer));
282:     PetscCall(PetscDrawPopCurrentPoint(draw));
283:   }
284:   PetscFunctionReturn(PETSC_SUCCESS);
285: }

287: static PetscErrorCode PCView_FieldSplit_GKB(PC pc, PetscViewer viewer)
288: {
289:   PC_FieldSplit    *jac = (PC_FieldSplit *)pc->data;
290:   PetscBool         isascii, isdraw;
291:   PetscInt          i, j;
292:   PC_FieldSplitLink ilink = jac->head;

294:   PetscFunctionBegin;
295:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &isascii));
296:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERDRAW, &isdraw));
297:   if (isascii) {
298:     if (jac->bs > 0) {
299:       PetscCall(PetscViewerASCIIPrintf(viewer, "  FieldSplit with %s composition: total splits = %" PetscInt_FMT ", blocksize = %" PetscInt_FMT "\n", PCCompositeTypes[jac->type], jac->nsplits, jac->bs));
300:     } else {
301:       PetscCall(PetscViewerASCIIPrintf(viewer, "  FieldSplit with %s composition: total splits = %" PetscInt_FMT "\n", PCCompositeTypes[jac->type], jac->nsplits));
302:     }
303:     if (pc->useAmat) PetscCall(PetscViewerASCIIPrintf(viewer, "  using Amat (not Pmat) as operator for blocks\n"));
304:     if (jac->diag_use_amat) PetscCall(PetscViewerASCIIPrintf(viewer, "  using Amat (not Pmat) as operator for diagonal blocks\n"));
305:     if (jac->offdiag_use_amat) PetscCall(PetscViewerASCIIPrintf(viewer, "  using Amat (not Pmat) as operator for off-diagonal blocks\n"));

307:     PetscCall(PetscViewerASCIIPrintf(viewer, "  Stopping tolerance=%.1e, delay in error estimate=%" PetscInt_FMT ", maximum iterations=%" PetscInt_FMT "\n", (double)jac->gkbtol, jac->gkbdelay, jac->gkbmaxit));
308:     PetscCall(PetscViewerASCIIPrintf(viewer, "  Solver info for H = A00 + nu*A01*A01' matrix:\n"));
309:     PetscCall(PetscViewerASCIIPushTab(viewer));

311:     if (ilink->fields) {
312:       PetscCall(PetscViewerASCIIPrintf(viewer, "Split number 0 Fields "));
313:       PetscCall(PetscViewerASCIIUseTabs(viewer, PETSC_FALSE));
314:       for (j = 0; j < ilink->nfields; j++) {
315:         if (j > 0) PetscCall(PetscViewerASCIIPrintf(viewer, ","));
316:         PetscCall(PetscViewerASCIIPrintf(viewer, " %" PetscInt_FMT, ilink->fields[j]));
317:       }
318:       PetscCall(PetscViewerASCIIPrintf(viewer, "\n"));
319:       PetscCall(PetscViewerASCIIUseTabs(viewer, PETSC_TRUE));
320:     } else {
321:       PetscCall(PetscViewerASCIIPrintf(viewer, "Split number 0 Defined by IS\n"));
322:     }
323:     PetscCall(KSPView(ilink->ksp, viewer));

325:     PetscCall(PetscViewerASCIIPopTab(viewer));
326:   }

328:   if (isdraw) {
329:     PetscDraw draw;
330:     PetscReal x, y, w, wd;

332:     PetscCall(PetscViewerDrawGetDraw(viewer, 0, &draw));
333:     PetscCall(PetscDrawGetCurrentPoint(draw, &x, &y));
334:     w  = 2 * PetscMin(1.0 - x, x);
335:     wd = w / (jac->nsplits + 1);
336:     x  = x - wd * (jac->nsplits - 1) / 2.0;
337:     for (i = 0; i < jac->nsplits; i++) {
338:       PetscCall(PetscDrawPushCurrentPoint(draw, x, y));
339:       PetscCall(KSPView(ilink->ksp, viewer));
340:       PetscCall(PetscDrawPopCurrentPoint(draw));
341:       x += wd;
342:       ilink = ilink->next;
343:     }
344:   }
345:   PetscFunctionReturn(PETSC_SUCCESS);
346: }

348: /* Precondition: jac->bs is set to a meaningful value or MATNEST */
349: static PetscErrorCode PCFieldSplitSetRuntimeSplits_Private(PC pc)
350: {
351:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
352:   PetscInt       bs, i, nfields, *ifields, nfields_col, *ifields_col;
353:   PetscBool      flg, flg_col, mnest;
354:   char           optionname[128], splitname[8], optionname_col[128];

356:   PetscFunctionBegin;
357:   PetscCall(PetscObjectTypeCompare((PetscObject)pc->mat, MATNEST, &mnest));
358:   if (mnest) {
359:     PetscCall(MatNestGetSize(pc->pmat, &bs, NULL));
360:   } else {
361:     bs = jac->bs;
362:   }
363:   PetscCall(PetscMalloc2(bs, &ifields, bs, &ifields_col));
364:   for (i = 0, flg = PETSC_TRUE;; i++) {
365:     PetscCall(PetscSNPrintf(splitname, sizeof(splitname), "%" PetscInt_FMT, i));
366:     PetscCall(PetscSNPrintf(optionname, sizeof(optionname), "-pc_fieldsplit_%" PetscInt_FMT "_fields", i));
367:     PetscCall(PetscSNPrintf(optionname_col, sizeof(optionname_col), "-pc_fieldsplit_%" PetscInt_FMT "_fields_col", i));
368:     nfields     = bs;
369:     nfields_col = bs;
370:     PetscCall(PetscOptionsGetIntArray(((PetscObject)pc)->options, ((PetscObject)pc)->prefix, optionname, ifields, &nfields, &flg));
371:     PetscCall(PetscOptionsGetIntArray(((PetscObject)pc)->options, ((PetscObject)pc)->prefix, optionname_col, ifields_col, &nfields_col, &flg_col));
372:     if (!flg) break;
373:     else if (flg && !flg_col) {
374:       PetscCheck(nfields, PETSC_COMM_SELF, PETSC_ERR_USER, "Cannot list zero fields");
375:       PetscCall(PCFieldSplitSetFields(pc, splitname, nfields, ifields, ifields));
376:     } else {
377:       PetscCheck(nfields && nfields_col, PETSC_COMM_SELF, PETSC_ERR_USER, "Cannot list zero fields");
378:       PetscCheck(nfields == nfields_col, PETSC_COMM_SELF, PETSC_ERR_USER, "Number of row and column fields must match");
379:       PetscCall(PCFieldSplitSetFields(pc, splitname, nfields, ifields, ifields_col));
380:     }
381:   }
382:   if (i > 0) {
383:     /* Makes command-line setting of splits take precedence over setting them in code.
384:        Otherwise subsequent calls to PCFieldSplitSetIS() or PCFieldSplitSetFields() would
385:        create new splits, which would probably not be what the user wanted. */
386:     jac->splitdefined = PETSC_TRUE;
387:   }
388:   PetscCall(PetscFree2(ifields, ifields_col));
389:   PetscFunctionReturn(PETSC_SUCCESS);
390: }

392: static PetscErrorCode PCFieldSplitSetDefaults(PC pc)
393: {
394:   PC_FieldSplit    *jac                = (PC_FieldSplit *)pc->data;
395:   PC_FieldSplitLink ilink              = jac->head;
396:   PetscBool         fieldsplit_default = PETSC_FALSE, coupling = PETSC_FALSE;
397:   PetscInt          i;

399:   PetscFunctionBegin;
400:   /*
401:    Kinda messy, but at least this now uses DMCreateFieldDecomposition().
402:    Should probably be rewritten.
403:    */
404:   if (!ilink) {
405:     PetscCall(PetscOptionsGetBool(((PetscObject)pc)->options, ((PetscObject)pc)->prefix, "-pc_fieldsplit_detect_coupling", &coupling, NULL));
406:     if (pc->dm && jac->dm_splits && !jac->detect && !coupling) {
407:       PetscInt  numFields, f, i, j;
408:       char    **fieldNames;
409:       IS       *fields;
410:       DM       *dms;
411:       DM        subdm[128];
412:       PetscBool flg;

414:       PetscCall(DMCreateFieldDecomposition(pc->dm, &numFields, &fieldNames, &fields, &dms));
415:       /* Allow the user to prescribe the splits */
416:       for (i = 0, flg = PETSC_TRUE;; i++) {
417:         PetscInt ifields[128];
418:         IS       compField;
419:         char     optionname[128], splitname[8];
420:         PetscInt nfields = numFields;

422:         PetscCall(PetscSNPrintf(optionname, sizeof(optionname), "-pc_fieldsplit_%" PetscInt_FMT "_fields", i));
423:         PetscCall(PetscOptionsGetIntArray(((PetscObject)pc)->options, ((PetscObject)pc)->prefix, optionname, ifields, &nfields, &flg));
424:         if (!flg) break;
425:         PetscCheck(numFields <= 128, PetscObjectComm((PetscObject)pc), PETSC_ERR_SUP, "Cannot currently support %" PetscInt_FMT " > 128 fields", numFields);
426:         PetscCall(DMCreateSubDM(pc->dm, nfields, ifields, &compField, &subdm[i]));
427:         if (nfields == 1) {
428:           PetscCall(PCFieldSplitSetIS(pc, fieldNames[ifields[0]], compField));
429:         } else {
430:           PetscCall(PetscSNPrintf(splitname, sizeof(splitname), "%" PetscInt_FMT, i));
431:           PetscCall(PCFieldSplitSetIS(pc, splitname, compField));
432:         }
433:         PetscCall(ISDestroy(&compField));
434:         for (j = 0; j < nfields; ++j) {
435:           f = ifields[j];
436:           PetscCall(PetscFree(fieldNames[f]));
437:           PetscCall(ISDestroy(&fields[f]));
438:         }
439:       }
440:       if (i == 0) {
441:         for (f = 0; f < numFields; ++f) {
442:           PetscCall(PCFieldSplitSetIS(pc, fieldNames[f], fields[f]));
443:           PetscCall(PetscFree(fieldNames[f]));
444:           PetscCall(ISDestroy(&fields[f]));
445:         }
446:       } else {
447:         for (j = 0; j < numFields; j++) PetscCall(DMDestroy(dms + j));
448:         PetscCall(PetscFree(dms));
449:         PetscCall(PetscMalloc1(i, &dms));
450:         for (j = 0; j < i; ++j) dms[j] = subdm[j];
451:       }
452:       PetscCall(PetscFree(fieldNames));
453:       PetscCall(PetscFree(fields));
454:       if (dms) {
455:         PetscCall(PetscInfo(pc, "Setting up physics based fieldsplit preconditioner using the embedded DM\n"));
456:         for (ilink = jac->head, i = 0; ilink; ilink = ilink->next, ++i) {
457:           const char *prefix;
458:           PetscCall(PetscObjectGetOptionsPrefix((PetscObject)ilink->ksp, &prefix));
459:           PetscCall(PetscObjectSetOptionsPrefix((PetscObject)dms[i], prefix));
460:           PetscCall(KSPSetDM(ilink->ksp, dms[i]));
461:           PetscCall(KSPSetDMActive(ilink->ksp, PETSC_FALSE));
462:           PetscCall(PetscObjectIncrementTabLevel((PetscObject)dms[i], (PetscObject)ilink->ksp, 0));
463:           PetscCall(DMDestroy(&dms[i]));
464:         }
465:         PetscCall(PetscFree(dms));
466:       }
467:     } else {
468:       if (jac->bs <= 0) {
469:         if (pc->pmat) PetscCall(MatGetBlockSize(pc->pmat, &jac->bs));
470:         else jac->bs = 1;
471:       }

473:       if (jac->detect) {
474:         IS       zerodiags, rest;
475:         PetscInt nmin, nmax;

477:         PetscCall(MatGetOwnershipRange(pc->mat, &nmin, &nmax));
478:         if (jac->diag_use_amat) {
479:           PetscCall(MatFindZeroDiagonals(pc->mat, &zerodiags));
480:         } else {
481:           PetscCall(MatFindZeroDiagonals(pc->pmat, &zerodiags));
482:         }
483:         PetscCall(ISComplement(zerodiags, nmin, nmax, &rest));
484:         PetscCall(PCFieldSplitSetIS(pc, "0", rest));
485:         PetscCall(PCFieldSplitSetIS(pc, "1", zerodiags));
486:         PetscCall(ISDestroy(&zerodiags));
487:         PetscCall(ISDestroy(&rest));
488:       } else if (coupling) {
489:         IS       coupling, rest;
490:         PetscInt nmin, nmax;

492:         PetscCall(MatGetOwnershipRange(pc->mat, &nmin, &nmax));
493:         if (jac->offdiag_use_amat) {
494:           PetscCall(MatFindOffBlockDiagonalEntries(pc->mat, &coupling));
495:         } else {
496:           PetscCall(MatFindOffBlockDiagonalEntries(pc->pmat, &coupling));
497:         }
498:         PetscCall(ISCreateStride(PetscObjectComm((PetscObject)pc->mat), nmax - nmin, nmin, 1, &rest));
499:         PetscCall(ISSetIdentity(rest));
500:         PetscCall(PCFieldSplitSetIS(pc, "0", rest));
501:         PetscCall(PCFieldSplitSetIS(pc, "1", coupling));
502:         PetscCall(ISDestroy(&coupling));
503:         PetscCall(ISDestroy(&rest));
504:       } else {
505:         PetscCall(PetscOptionsGetBool(((PetscObject)pc)->options, ((PetscObject)pc)->prefix, "-pc_fieldsplit_default", &fieldsplit_default, NULL));
506:         if (!fieldsplit_default) {
507:           /* Allow user to set fields from command line,  if bs was known at the time of PCSetFromOptions_FieldSplit()
508:            then it is set there. This is not ideal because we should only have options set in XXSetFromOptions(). */
509:           PetscCall(PCFieldSplitSetRuntimeSplits_Private(pc));
510:           if (jac->splitdefined) PetscCall(PetscInfo(pc, "Splits defined using the options database\n"));
511:         }
512:         if ((fieldsplit_default || !jac->splitdefined) && !jac->isrestrict) {
513:           Mat       M = pc->pmat;
514:           PetscBool isnest;
515:           PetscInt  nf;

517:           PetscCall(PetscInfo(pc, "Using default splitting of fields\n"));
518:           PetscCall(PetscObjectTypeCompare((PetscObject)pc->pmat, MATNEST, &isnest));
519:           if (!isnest) {
520:             M = pc->mat;
521:             PetscCall(PetscObjectTypeCompare((PetscObject)pc->mat, MATNEST, &isnest));
522:           }
523:           if (!isnest) nf = jac->bs;
524:           else PetscCall(MatNestGetSize(M, &nf, NULL));
525:           for (i = 0; i < nf; i++) {
526:             char splitname[8];

528:             PetscCall(PetscSNPrintf(splitname, sizeof(splitname), "%" PetscInt_FMT, i));
529:             PetscCall(PCFieldSplitSetFields(pc, splitname, 1, &i, &i));
530:           }
531:           jac->defaultsplit = PETSC_TRUE;
532:         }
533:       }
534:     }
535:   } else if (jac->nsplits == 1) {
536:     IS       is2;
537:     PetscInt nmin, nmax;

539:     PetscCheck(ilink->is, PetscObjectComm((PetscObject)pc), PETSC_ERR_SUP, "Must provide at least two sets of fields to PCFieldSplit()");
540:     PetscCall(MatGetOwnershipRange(pc->mat, &nmin, &nmax));
541:     PetscCall(ISComplement(ilink->is, nmin, nmax, &is2));
542:     PetscCall(PCFieldSplitSetIS(pc, "1", is2));
543:     PetscCall(ISDestroy(&is2));
544:   }

546:   PetscCheck(jac->nsplits >= 2, PetscObjectComm((PetscObject)pc), PETSC_ERR_PLIB, "Unhandled case, must have at least two fields, not %" PetscInt_FMT, jac->nsplits);
547:   PetscFunctionReturn(PETSC_SUCCESS);
548: }

550: static PetscErrorCode MatGolubKahanComputeExplicitOperator(Mat A, Mat B, Mat C, Mat *H, PetscReal gkbnu)
551: {
552:   Mat       BT, T;
553:   PetscReal nrmT, nrmB;

555:   PetscFunctionBegin;
556:   PetscCall(MatHermitianTranspose(C, MAT_INITIAL_MATRIX, &T)); /* Test if augmented matrix is symmetric */
557:   PetscCall(MatAXPY(T, -1.0, B, DIFFERENT_NONZERO_PATTERN));
558:   PetscCall(MatNorm(T, NORM_1, &nrmT));
559:   PetscCall(MatNorm(B, NORM_1, &nrmB));
560:   PetscCheck(nrmB <= 0 || nrmT / nrmB < PETSC_SMALL, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Matrix is not symmetric/Hermitian, GKB is not applicable.");

562:   /* Compute augmented Lagrangian matrix H = A00 + nu*A01*A01'. This corresponds to */
563:   /* setting N := 1/nu*I in [Ar13].                                                 */
564:   PetscCall(MatHermitianTranspose(B, MAT_INITIAL_MATRIX, &BT));
565:   PetscCall(MatMatMult(B, BT, MAT_INITIAL_MATRIX, PETSC_CURRENT, H)); /* H = A01*A01'          */
566:   PetscCall(MatAYPX(*H, gkbnu, A, DIFFERENT_NONZERO_PATTERN));        /* H = A00 + nu*A01*A01' */

568:   PetscCall(MatDestroy(&BT));
569:   PetscCall(MatDestroy(&T));
570:   PetscFunctionReturn(PETSC_SUCCESS);
571: }

573: PETSC_EXTERN PetscErrorCode PetscOptionsFindPairPrefix_Private(PetscOptions, const char pre[], const char name[], const char *option[], const char *value[], PetscBool *flg);

575: static PetscErrorCode PCSetUp_FieldSplit(PC pc)
576: {
577:   PC_FieldSplit    *jac = (PC_FieldSplit *)pc->data;
578:   PC_FieldSplitLink ilink;
579:   PetscInt          i, nsplit;
580:   PetscBool         matnest = PETSC_FALSE;

582:   PetscFunctionBegin;
583:   pc->failedreason = PC_NOERROR;
584:   PetscCall(PCFieldSplitSetDefaults(pc));
585:   nsplit = jac->nsplits;
586:   ilink  = jac->head;
587:   if (pc->pmat) PetscCall(PetscObjectTypeCompare((PetscObject)pc->pmat, MATNEST, &matnest));

589:   /* get the matrices for each split */
590:   if (!jac->issetup) {
591:     PetscInt rstart, rend, nslots, bs;

593:     jac->issetup = PETSC_TRUE;

595:     /* This is done here instead of in PCFieldSplitSetFields() because may not have matrix at that point */
596:     if (jac->defaultsplit || !ilink->is) {
597:       if (jac->bs <= 0) jac->bs = nsplit;
598:     }

600:     /*  MatCreateSubMatrix() for [S]BAIJ matrices can only work if the indices include entire blocks of the matrix */
601:     PetscCall(MatGetBlockSize(pc->pmat, &bs));
602:     if (bs > 1 && (jac->bs <= bs || jac->bs % bs)) {
603:       PetscBool blk;

605:       PetscCall(PetscObjectTypeCompareAny((PetscObject)pc->pmat, &blk, MATBAIJ, MATSBAIJ, MATSEQBAIJ, MATSEQSBAIJ, MATMPIBAIJ, MATMPISBAIJ, NULL));
606:       PetscCheck(!blk, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONG, "Cannot use MATBAIJ with PCFIELDSPLIT and currently set matrix and PC blocksizes");
607:     }

609:     if (!matnest) { /* use the matrix blocksize and stride IS to determine the index sets that define the submatrices */
610:       bs = jac->bs;
611:       PetscCall(MatGetOwnershipRange(pc->pmat, &rstart, &rend));
612:       nslots = (rend - rstart) / bs;
613:       for (i = 0; i < nsplit; i++) {
614:         if (jac->defaultsplit) {
615:           PetscCall(ISCreateStride(PetscObjectComm((PetscObject)pc), nslots, rstart + i, nsplit, &ilink->is));
616:           PetscCall(PetscObjectReference((PetscObject)ilink->is));
617:           ilink->is_col = ilink->is;
618:         } else if (!ilink->is) {
619:           PetscBool same_fields = PETSC_TRUE;

621:           for (PetscInt k = 0; k < ilink->nfields; k++) {
622:             if (ilink->fields[k] != ilink->fields_col[k]) same_fields = PETSC_FALSE;
623:           }

625:           if (ilink->nfields > 1) {
626:             PetscInt *ii, *jj, j, k, nfields = ilink->nfields, *fields = ilink->fields, *fields_col = ilink->fields_col;

628:             PetscCall(PetscMalloc1(ilink->nfields * nslots, &ii));
629:             if (!same_fields) PetscCall(PetscMalloc1(ilink->nfields * nslots, &jj));
630:             for (j = 0; j < nslots; j++) {
631:               for (k = 0; k < nfields; k++) {
632:                 ii[nfields * j + k] = rstart + bs * j + fields[k];
633:                 if (!same_fields) jj[nfields * j + k] = rstart + bs * j + fields_col[k];
634:               }
635:             }
636:             PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)pc), nslots * nfields, ii, PETSC_OWN_POINTER, &ilink->is));
637:             if (!same_fields) PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)pc), nslots * nfields, jj, PETSC_OWN_POINTER, &ilink->is_col));
638:             else {
639:               PetscCall(PetscObjectReference((PetscObject)ilink->is));
640:               ilink->is_col = ilink->is;
641:             }
642:             PetscCall(ISSetBlockSize(ilink->is, nfields));
643:             PetscCall(ISSetBlockSize(ilink->is_col, nfields));
644:           } else {
645:             PetscCall(ISCreateStride(PetscObjectComm((PetscObject)pc), nslots, rstart + ilink->fields[0], bs, &ilink->is));
646:             if (!same_fields) PetscCall(ISCreateStride(PetscObjectComm((PetscObject)pc), nslots, rstart + ilink->fields_col[0], bs, &ilink->is_col));
647:             else {
648:               PetscCall(PetscObjectReference((PetscObject)ilink->is));
649:               ilink->is_col = ilink->is;
650:             }
651:           }
652:         }
653:         ilink = ilink->next;
654:       }
655:     } else { /* use the IS that define the MATNEST to determine the index sets that define the submatrices */
656:       IS      *rowis, *colis, *ises = NULL;
657:       PetscInt mis, nis;

659:       PetscCall(MatNestGetSize(pc->pmat, &mis, &nis));
660:       PetscCall(PetscMalloc2(mis, &rowis, nis, &colis));
661:       PetscCall(MatNestGetISs(pc->pmat, rowis, colis));
662:       if (!jac->defaultsplit) PetscCall(PetscMalloc1(mis, &ises));

664:       for (i = 0; i < nsplit; i++) {
665:         if (jac->defaultsplit) {
666:           PetscCall(ISDuplicate(rowis[i], &ilink->is));
667:           PetscCall(PetscObjectReference((PetscObject)ilink->is));
668:           ilink->is_col = ilink->is;
669:         } else if (!ilink->is) {
670:           if (ilink->nfields > 1) {
671:             for (PetscInt j = 0; j < ilink->nfields; j++) ises[j] = rowis[ilink->fields[j]];
672:             PetscCall(ISConcatenate(PetscObjectComm((PetscObject)pc), ilink->nfields, ises, &ilink->is));
673:           } else {
674:             PetscCall(ISDuplicate(rowis[ilink->fields[0]], &ilink->is));
675:           }
676:           PetscCall(PetscObjectReference((PetscObject)ilink->is));
677:           ilink->is_col = ilink->is;
678:         }
679:         ilink = ilink->next;
680:       }
681:       PetscCall(PetscFree2(rowis, colis));
682:       PetscCall(PetscFree(ises));
683:     }
684:   }

686:   ilink = jac->head;
687:   if (!jac->pmat) {
688:     Vec xtmp;

690:     PetscCall(MatCreateVecs(pc->pmat, &xtmp, NULL));
691:     PetscCall(PetscMalloc1(nsplit, &jac->pmat));
692:     PetscCall(PetscMalloc2(nsplit, &jac->x, nsplit, &jac->y));
693:     for (i = 0; i < nsplit; i++) {
694:       MatNullSpace sp;

696:       /* Check for matrix attached to IS */
697:       PetscCall(PetscObjectQuery((PetscObject)ilink->is, "pmat", (PetscObject *)&jac->pmat[i]));
698:       if (jac->pmat[i]) {
699:         PetscCall(PetscObjectReference((PetscObject)jac->pmat[i]));
700:         if (jac->type == PC_COMPOSITE_SCHUR) {
701:           jac->schur_user = jac->pmat[i];

703:           PetscCall(PetscObjectReference((PetscObject)jac->schur_user));
704:         }
705:       } else {
706:         const char *prefix;
707:         PetscCall(MatCreateSubMatrix(pc->pmat, ilink->is, ilink->is_col, MAT_INITIAL_MATRIX, &jac->pmat[i]));
708:         PetscCall(MatGetOptionsPrefix(jac->pmat[i], &prefix));
709:         if (!prefix) {
710:           PetscCall(KSPGetOptionsPrefix(ilink->ksp, &prefix));
711:           PetscCall(MatSetOptionsPrefix(jac->pmat[i], prefix));
712:         }
713:         PetscCall(MatSetFromOptions(jac->pmat[i]));
714:         PetscCall(MatViewFromOptions(jac->pmat[i], NULL, "-mat_view"));
715:       }
716:       /* create work vectors for each split */
717:       PetscCall(MatCreateVecs(jac->pmat[i], &jac->x[i], &jac->y[i]));
718:       ilink->x = jac->x[i];
719:       ilink->y = jac->y[i];
720:       ilink->z = NULL;
721:       /* compute scatter contexts needed by multiplicative versions and non-default splits */
722:       PetscCall(VecScatterCreate(xtmp, ilink->is, jac->x[i], NULL, &ilink->sctx));
723:       PetscCall(PetscObjectQuery((PetscObject)ilink->is, "nearnullspace", (PetscObject *)&sp));
724:       if (sp) PetscCall(MatSetNearNullSpace(jac->pmat[i], sp));
725:       ilink = ilink->next;
726:     }
727:     PetscCall(VecDestroy(&xtmp));
728:   } else {
729:     MatReuse      scall;
730:     MatNullSpace *nullsp = NULL;

732:     if (pc->flag == DIFFERENT_NONZERO_PATTERN) {
733:       PetscCall(MatGetNullSpaces(nsplit, jac->pmat, &nullsp));
734:       for (i = 0; i < nsplit; i++) PetscCall(MatDestroy(&jac->pmat[i]));
735:       scall = MAT_INITIAL_MATRIX;
736:     } else scall = MAT_REUSE_MATRIX;

738:     for (i = 0; i < nsplit; i++) {
739:       Mat pmat;

741:       /* Check for matrix attached to IS */
742:       PetscCall(PetscObjectQuery((PetscObject)ilink->is, "pmat", (PetscObject *)&pmat));
743:       if (!pmat) PetscCall(MatCreateSubMatrix(pc->pmat, ilink->is, ilink->is_col, scall, &jac->pmat[i]));
744:       ilink = ilink->next;
745:     }
746:     if (nullsp) PetscCall(MatRestoreNullSpaces(nsplit, jac->pmat, &nullsp));
747:   }
748:   if (jac->diag_use_amat) {
749:     ilink = jac->head;
750:     if (!jac->mat) {
751:       PetscCall(PetscMalloc1(nsplit, &jac->mat));
752:       for (i = 0; i < nsplit; i++) {
753:         PetscCall(MatCreateSubMatrix(pc->mat, ilink->is, ilink->is_col, MAT_INITIAL_MATRIX, &jac->mat[i]));
754:         ilink = ilink->next;
755:       }
756:     } else {
757:       MatReuse      scall;
758:       MatNullSpace *nullsp = NULL;

760:       if (pc->flag == DIFFERENT_NONZERO_PATTERN) {
761:         PetscCall(MatGetNullSpaces(nsplit, jac->mat, &nullsp));
762:         for (i = 0; i < nsplit; i++) PetscCall(MatDestroy(&jac->mat[i]));
763:         scall = MAT_INITIAL_MATRIX;
764:       } else scall = MAT_REUSE_MATRIX;

766:       for (i = 0; i < nsplit; i++) {
767:         PetscCall(MatCreateSubMatrix(pc->mat, ilink->is, ilink->is_col, scall, &jac->mat[i]));
768:         ilink = ilink->next;
769:       }
770:       if (nullsp) PetscCall(MatRestoreNullSpaces(nsplit, jac->mat, &nullsp));
771:     }
772:   } else {
773:     jac->mat = jac->pmat;
774:   }

776:   /* Check for null space attached to IS */
777:   ilink = jac->head;
778:   for (i = 0; i < nsplit; i++) {
779:     MatNullSpace sp;

781:     PetscCall(PetscObjectQuery((PetscObject)ilink->is, "nullspace", (PetscObject *)&sp));
782:     if (sp) PetscCall(MatSetNullSpace(jac->mat[i], sp));
783:     ilink = ilink->next;
784:   }

786:   if (jac->type != PC_COMPOSITE_ADDITIVE && jac->type != PC_COMPOSITE_SCHUR && jac->type != PC_COMPOSITE_GKB) {
787:     /* extract the rows of the matrix associated with each field: used for efficient computation of residual inside algorithm */
788:     /* FIXME: Can/should we reuse jac->mat whenever (jac->diag_use_amat) is true? */
789:     ilink = jac->head;
790:     if (nsplit == 2 && jac->type == PC_COMPOSITE_MULTIPLICATIVE) {
791:       /* special case need where Afield[0] is not needed and only certain columns of Afield[1] are needed since update is only on those rows of the solution */
792:       if (!jac->Afield) {
793:         PetscCall(PetscCalloc1(nsplit, &jac->Afield));
794:         if (jac->offdiag_use_amat) {
795:           PetscCall(MatCreateSubMatrix(pc->mat, ilink->next->is, ilink->is, MAT_INITIAL_MATRIX, &jac->Afield[1]));
796:         } else {
797:           PetscCall(MatCreateSubMatrix(pc->pmat, ilink->next->is, ilink->is, MAT_INITIAL_MATRIX, &jac->Afield[1]));
798:         }
799:       } else {
800:         MatReuse scall;

802:         if (pc->flag == DIFFERENT_NONZERO_PATTERN) {
803:           PetscCall(MatDestroy(&jac->Afield[1]));
804:           scall = MAT_INITIAL_MATRIX;
805:         } else scall = MAT_REUSE_MATRIX;

807:         if (jac->offdiag_use_amat) {
808:           PetscCall(MatCreateSubMatrix(pc->mat, ilink->next->is, ilink->is, scall, &jac->Afield[1]));
809:         } else {
810:           PetscCall(MatCreateSubMatrix(pc->pmat, ilink->next->is, ilink->is, scall, &jac->Afield[1]));
811:         }
812:       }
813:     } else {
814:       if (!jac->Afield) {
815:         PetscCall(PetscMalloc1(nsplit, &jac->Afield));
816:         for (i = 0; i < nsplit; i++) {
817:           if (jac->offdiag_use_amat) {
818:             PetscCall(MatCreateSubMatrix(pc->mat, ilink->is, NULL, MAT_INITIAL_MATRIX, &jac->Afield[i]));
819:           } else {
820:             PetscCall(MatCreateSubMatrix(pc->pmat, ilink->is, NULL, MAT_INITIAL_MATRIX, &jac->Afield[i]));
821:           }
822:           ilink = ilink->next;
823:         }
824:       } else {
825:         MatReuse scall;
826:         if (pc->flag == DIFFERENT_NONZERO_PATTERN) {
827:           for (i = 0; i < nsplit; i++) PetscCall(MatDestroy(&jac->Afield[i]));
828:           scall = MAT_INITIAL_MATRIX;
829:         } else scall = MAT_REUSE_MATRIX;

831:         for (i = 0; i < nsplit; i++) {
832:           if (jac->offdiag_use_amat) {
833:             PetscCall(MatCreateSubMatrix(pc->mat, ilink->is, NULL, scall, &jac->Afield[i]));
834:           } else {
835:             PetscCall(MatCreateSubMatrix(pc->pmat, ilink->is, NULL, scall, &jac->Afield[i]));
836:           }
837:           ilink = ilink->next;
838:         }
839:       }
840:     }
841:   }

843:   if (jac->type == PC_COMPOSITE_SCHUR) {
844:     PetscBool   isset, isspd = PETSC_FALSE, issym = PETSC_FALSE, flg;
845:     char        lscname[256];
846:     PetscObject LSC_L;

848:     PetscCheck(nsplit == 2, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_INCOMP, "To use Schur complement preconditioner you must have exactly 2 fields");

850:     /* If pc->mat is SPD, don't scale by -1 the Schur complement */
851:     PetscCall(MatIsSPDKnown(pc->pmat, &isset, &isspd));
852:     if (jac->schurscale == (PetscScalar)-1.0) jac->schurscale = (isset && isspd) ? 1.0 : -1.0;
853:     PetscCall(MatIsSymmetricKnown(pc->pmat, &isset, &issym));

855:     PetscCall(PetscObjectTypeCompareAny(jac->offdiag_use_amat ? (PetscObject)pc->mat : (PetscObject)pc->pmat, &flg, MATSEQSBAIJ, MATMPISBAIJ, ""));

857:     if (jac->schur) {
858:       KSP      kspA = jac->head->ksp, kspInner = NULL, kspUpper = jac->kspupper;
859:       MatReuse scall;

861:       if (pc->flag == DIFFERENT_NONZERO_PATTERN) {
862:         scall = MAT_INITIAL_MATRIX;
863:         PetscCall(MatDestroy(&jac->B));
864:         PetscCall(MatDestroy(&jac->C));
865:       } else scall = MAT_REUSE_MATRIX;

867:       PetscCall(MatSchurComplementGetKSP(jac->schur, &kspInner));
868:       ilink = jac->head;
869:       PetscCall(MatCreateSubMatrix(jac->offdiag_use_amat ? pc->mat : pc->pmat, ilink->is, ilink->next->is, scall, &jac->B));
870:       if (!flg) PetscCall(MatCreateSubMatrix(jac->offdiag_use_amat ? pc->mat : pc->pmat, ilink->next->is, ilink->is, scall, &jac->C));
871:       else {
872:         PetscCall(MatIsHermitianKnown(jac->offdiag_use_amat ? pc->mat : pc->pmat, &isset, &flg));
873:         if (isset && flg) PetscCall(MatCreateHermitianTranspose(jac->B, &jac->C));
874:         else PetscCall(MatCreateTranspose(jac->B, &jac->C));
875:       }
876:       ilink = ilink->next;
877:       PetscCall(MatSchurComplementUpdateSubMatrices(jac->schur, jac->mat[0], jac->pmat[0], jac->B, jac->C, jac->mat[1]));
878:       if (jac->schurpre == PC_FIELDSPLIT_SCHUR_PRE_SELFP) {
879:         PetscCall(MatDestroy(&jac->schurp));
880:         PetscCall(MatSchurComplementGetPmat(jac->schur, MAT_INITIAL_MATRIX, &jac->schurp));
881:       } else if (jac->schurpre == PC_FIELDSPLIT_SCHUR_PRE_FULL && jac->kspupper != jac->head->ksp) {
882:         PetscCall(MatDestroy(&jac->schur_user));
883:         PetscCall(MatSchurComplementComputeExplicitOperator(jac->schur, &jac->schur_user));
884:       }
885:       if (kspA != kspInner) PetscCall(KSPSetOperators(kspA, jac->mat[0], jac->pmat[0]));
886:       if (kspUpper != kspA) PetscCall(KSPSetOperators(kspUpper, jac->mat[0], jac->pmat[0]));
887:       PetscCall(KSPSetOperators(jac->kspschur, jac->schur, FieldSplitSchurPre(jac)));
888:     } else {
889:       const char  *Dprefix;
890:       char         schurprefix[256], schurmatprefix[256];
891:       char         schurtestoption[256];
892:       MatNullSpace sp;
893:       KSP          kspt;

895:       /* extract the A01 and A10 matrices */
896:       ilink = jac->head;
897:       PetscCall(MatCreateSubMatrix(jac->offdiag_use_amat ? pc->mat : pc->pmat, ilink->is, ilink->next->is, MAT_INITIAL_MATRIX, &jac->B));
898:       if (!flg) PetscCall(MatCreateSubMatrix(jac->offdiag_use_amat ? pc->mat : pc->pmat, ilink->next->is, ilink->is, MAT_INITIAL_MATRIX, &jac->C));
899:       else {
900:         PetscCall(MatIsHermitianKnown(jac->offdiag_use_amat ? pc->mat : pc->pmat, &isset, &flg));
901:         if (isset && flg) PetscCall(MatCreateHermitianTranspose(jac->B, &jac->C));
902:         else PetscCall(MatCreateTranspose(jac->B, &jac->C));
903:       }
904:       ilink = ilink->next;
905:       /* Use mat[0] (diagonal block of Amat) preconditioned by pmat[0] to define Schur complement */
906:       PetscCall(MatCreate(((PetscObject)jac->mat[0])->comm, &jac->schur));
907:       PetscCall(MatSetType(jac->schur, MATSCHURCOMPLEMENT));
908:       PetscCall(MatSchurComplementSetSubMatrices(jac->schur, jac->mat[0], jac->pmat[0], jac->B, jac->C, jac->mat[1]));
909:       PetscCall(PetscSNPrintf(schurmatprefix, sizeof(schurmatprefix), "%sfieldsplit_%s_", ((PetscObject)pc)->prefix ? ((PetscObject)pc)->prefix : "", ilink->splitname));
910:       PetscCall(MatSetOptionsPrefix(jac->schur, schurmatprefix));
911:       PetscCall(MatSchurComplementGetKSP(jac->schur, &kspt));
912:       PetscCall(KSPSetOptionsPrefix(kspt, schurmatprefix));

914:       /* Note: this is not true in general */
915:       PetscCall(MatGetNullSpace(jac->mat[1], &sp));
916:       if (sp) PetscCall(MatSetNullSpace(jac->schur, sp));

918:       PetscCall(PetscSNPrintf(schurtestoption, sizeof(schurtestoption), "-fieldsplit_%s_inner_", ilink->splitname));
919:       PetscCall(PetscOptionsFindPairPrefix_Private(((PetscObject)pc)->options, ((PetscObject)pc)->prefix, schurtestoption, NULL, NULL, &flg));
920:       if (flg) {
921:         DM  dmInner;
922:         KSP kspInner;
923:         PC  pcInner;

925:         PetscCall(MatSchurComplementGetKSP(jac->schur, &kspInner));
926:         PetscCall(KSPReset(kspInner));
927:         PetscCall(KSPSetOperators(kspInner, jac->mat[0], jac->pmat[0]));
928:         PetscCall(PetscSNPrintf(schurprefix, sizeof(schurprefix), "%sfieldsplit_%s_inner_", ((PetscObject)pc)->prefix ? ((PetscObject)pc)->prefix : "", ilink->splitname));
929:         /* Indent this deeper to emphasize the "inner" nature of this solver. */
930:         PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspInner, (PetscObject)pc, 2));
931:         PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspInner->pc, (PetscObject)pc, 2));
932:         PetscCall(KSPSetOptionsPrefix(kspInner, schurprefix));

934:         /* Set DM for new solver */
935:         PetscCall(KSPGetDM(jac->head->ksp, &dmInner));
936:         PetscCall(KSPSetDM(kspInner, dmInner));
937:         PetscCall(KSPSetDMActive(kspInner, PETSC_FALSE));

939:         /* Defaults to PCKSP as preconditioner */
940:         PetscCall(KSPGetPC(kspInner, &pcInner));
941:         PetscCall(PCSetType(pcInner, PCKSP));
942:         PetscCall(PCKSPSetKSP(pcInner, jac->head->ksp));
943:       } else {
944:         /* Use the outer solver for the inner solve, but revert the KSPPREONLY from PCFieldSplitSetFields_FieldSplit or
945:           * PCFieldSplitSetIS_FieldSplit. We don't want KSPPREONLY because it makes the Schur complement inexact,
946:           * preventing Schur complement reduction to be an accurate solve. Usually when an iterative solver is used for
947:           * S = D - C A_inner^{-1} B, we expect S to be defined using an accurate definition of A_inner^{-1}, so we make
948:           * GMRES the default. Note that it is also common to use PREONLY for S, in which case S may not be used
949:           * directly, and the user is responsible for setting an inexact method for fieldsplit's A^{-1}. */
950:         PetscCall(KSPSetType(jac->head->ksp, KSPGMRES));
951:         PetscCall(MatSchurComplementSetKSP(jac->schur, jac->head->ksp));
952:       }
953:       PetscCall(KSPSetOperators(jac->head->ksp, jac->mat[0], jac->pmat[0]));
954:       PetscCall(KSPSetFromOptions(jac->head->ksp));
955:       PetscCall(MatSetFromOptions(jac->schur));

957:       PetscCall(PetscObjectTypeCompare((PetscObject)jac->schur, MATSCHURCOMPLEMENT, &flg));
958:       if (flg) { /* Need to do this otherwise PCSetUp_KSP will overwrite the amat of jac->head->ksp */
959:         KSP kspInner;
960:         PC  pcInner;

962:         PetscCall(MatSchurComplementGetKSP(jac->schur, &kspInner));
963:         PetscCall(KSPGetPC(kspInner, &pcInner));
964:         PetscCall(PetscObjectTypeCompare((PetscObject)pcInner, PCKSP, &flg));
965:         if (flg) {
966:           KSP ksp;

968:           PetscCall(PCKSPGetKSP(pcInner, &ksp));
969:           if (ksp == jac->head->ksp) PetscCall(PCSetUseAmat(pcInner, PETSC_TRUE));
970:         }
971:       }
972:       PetscCall(PetscSNPrintf(schurtestoption, sizeof(schurtestoption), "-fieldsplit_%s_upper_", ilink->splitname));
973:       PetscCall(PetscOptionsFindPairPrefix_Private(((PetscObject)pc)->options, ((PetscObject)pc)->prefix, schurtestoption, NULL, NULL, &flg));
974:       if (flg) {
975:         DM dmInner;

977:         PetscCall(PetscSNPrintf(schurprefix, sizeof(schurprefix), "%sfieldsplit_%s_upper_", ((PetscObject)pc)->prefix ? ((PetscObject)pc)->prefix : "", ilink->splitname));
978:         PetscCall(KSPCreate(PetscObjectComm((PetscObject)pc), &jac->kspupper));
979:         PetscCall(KSPSetNestLevel(jac->kspupper, pc->kspnestlevel));
980:         PetscCall(KSPSetErrorIfNotConverged(jac->kspupper, pc->erroriffailure));
981:         PetscCall(KSPSetOptionsPrefix(jac->kspupper, schurprefix));
982:         PetscCall(PetscObjectIncrementTabLevel((PetscObject)jac->kspupper, (PetscObject)pc, 1));
983:         PetscCall(PetscObjectIncrementTabLevel((PetscObject)jac->kspupper->pc, (PetscObject)pc, 1));
984:         PetscCall(KSPGetDM(jac->head->ksp, &dmInner));
985:         PetscCall(KSPSetDM(jac->kspupper, dmInner));
986:         PetscCall(KSPSetDMActive(jac->kspupper, PETSC_FALSE));
987:         PetscCall(KSPSetFromOptions(jac->kspupper));
988:         PetscCall(KSPSetOperators(jac->kspupper, jac->mat[0], jac->pmat[0]));
989:         PetscCall(VecDuplicate(jac->head->x, &jac->head->z));
990:       } else {
991:         jac->kspupper = jac->head->ksp;
992:         PetscCall(PetscObjectReference((PetscObject)jac->head->ksp));
993:       }

995:       if (jac->schurpre == PC_FIELDSPLIT_SCHUR_PRE_SELFP) PetscCall(MatSchurComplementGetPmat(jac->schur, MAT_INITIAL_MATRIX, &jac->schurp));
996:       PetscCall(KSPCreate(PetscObjectComm((PetscObject)pc), &jac->kspschur));
997:       PetscCall(KSPSetNestLevel(jac->kspschur, pc->kspnestlevel));
998:       PetscCall(KSPSetErrorIfNotConverged(jac->kspschur, pc->erroriffailure));
999:       PetscCall(PetscObjectIncrementTabLevel((PetscObject)jac->kspschur, (PetscObject)pc, 1));
1000:       if (jac->schurpre == PC_FIELDSPLIT_SCHUR_PRE_SELF) {
1001:         PC pcschur;
1002:         PetscCall(KSPGetPC(jac->kspschur, &pcschur));
1003:         PetscCall(PCSetType(pcschur, PCNONE));
1004:         /* Note: This is bad if there exist preconditioners for MATSCHURCOMPLEMENT */
1005:       } else if (jac->schurpre == PC_FIELDSPLIT_SCHUR_PRE_FULL) {
1006:         if (jac->schurfactorization != PC_FIELDSPLIT_SCHUR_FACT_FULL || jac->kspupper != jac->head->ksp) PetscCall(MatSchurComplementComputeExplicitOperator(jac->schur, &jac->schur_user));
1007:       }
1008:       PetscCall(KSPSetOperators(jac->kspschur, jac->schur, FieldSplitSchurPre(jac)));
1009:       PetscCall(KSPGetOptionsPrefix(jac->head->next->ksp, &Dprefix));
1010:       PetscCall(KSPSetOptionsPrefix(jac->kspschur, Dprefix));
1011:       /* propagate DM */
1012:       {
1013:         DM sdm;
1014:         PetscCall(KSPGetDM(jac->head->next->ksp, &sdm));
1015:         if (sdm) {
1016:           PetscCall(KSPSetDM(jac->kspschur, sdm));
1017:           PetscCall(KSPSetDMActive(jac->kspschur, PETSC_FALSE));
1018:         }
1019:       }
1020:       /* really want setfromoptions called in PCSetFromOptions_FieldSplit(), but it is not ready yet */
1021:       /* need to call this every time, since the jac->kspschur is freshly created, otherwise its options never get set */
1022:       PetscCall(KSPSetFromOptions(jac->kspschur));
1023:     }
1024:     PetscCall(MatAssemblyBegin(jac->schur, MAT_FINAL_ASSEMBLY));
1025:     PetscCall(MatAssemblyEnd(jac->schur, MAT_FINAL_ASSEMBLY));
1026:     if (issym) PetscCall(MatSetOption(jac->schur, MAT_SYMMETRIC, PETSC_TRUE));
1027:     if (isspd) PetscCall(MatSetOption(jac->schur, MAT_SPD, PETSC_TRUE));

1029:     /* HACK: special support to forward L and Lp matrices that might be used by PCLSC */
1030:     PetscCall(PetscSNPrintf(lscname, sizeof(lscname), "%s_LSC_L", ilink->splitname));
1031:     PetscCall(PetscObjectQuery((PetscObject)pc->mat, lscname, &LSC_L));
1032:     if (!LSC_L) PetscCall(PetscObjectQuery((PetscObject)pc->pmat, lscname, &LSC_L));
1033:     if (LSC_L) PetscCall(PetscObjectCompose((PetscObject)jac->schur, "LSC_L", LSC_L));
1034:     PetscCall(PetscSNPrintf(lscname, sizeof(lscname), "%s_LSC_Lp", ilink->splitname));
1035:     PetscCall(PetscObjectQuery((PetscObject)pc->pmat, lscname, &LSC_L));
1036:     if (!LSC_L) PetscCall(PetscObjectQuery((PetscObject)pc->mat, lscname, &LSC_L));
1037:     if (LSC_L) PetscCall(PetscObjectCompose((PetscObject)jac->schur, "LSC_Lp", LSC_L));
1038:   } else if (jac->type == PC_COMPOSITE_GKB) {
1039:     PetscCheck(nsplit == 2, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_INCOMP, "To use GKB preconditioner you must have exactly 2 fields");
1040:     ilink = jac->head;
1041:     PetscCall(MatCreateSubMatrix(jac->offdiag_use_amat ? pc->mat : pc->pmat, ilink->is, ilink->next->is, MAT_INITIAL_MATRIX, &jac->B));
1042:     /* Create work vectors for GKB algorithm */
1043:     PetscCall(VecDuplicate(ilink->x, &jac->u));
1044:     PetscCall(VecDuplicate(ilink->x, &jac->Hu));
1045:     PetscCall(VecDuplicate(ilink->x, &jac->w2));
1046:     PetscCall(MatCreateSubMatrix(jac->offdiag_use_amat ? pc->mat : pc->pmat, ilink->next->is, ilink->is, MAT_INITIAL_MATRIX, &jac->C));
1047:     ilink = ilink->next;
1048:     /* Create work vectors for GKB algorithm */
1049:     PetscCall(VecDuplicate(ilink->x, &jac->v));
1050:     PetscCall(VecDuplicate(ilink->x, &jac->d));
1051:     PetscCall(VecDuplicate(ilink->x, &jac->w1));
1052:     PetscCall(MatGolubKahanComputeExplicitOperator(jac->mat[0], jac->B, jac->C, &jac->H, jac->gkbnu));
1053:     PetscCall(PetscCalloc1(jac->gkbdelay, &jac->vecz));

1055:     ilink = jac->head;
1056:     PetscCall(KSPSetOperators(ilink->ksp, jac->H, jac->H));
1057:     if (!jac->suboptionsset) PetscCall(KSPSetFromOptions(ilink->ksp));
1058:     /* Create gkb_monitor context */
1059:     if (jac->gkbmonitor) {
1060:       PetscInt tablevel;
1061:       PetscCall(PetscViewerCreate(PETSC_COMM_WORLD, &jac->gkbviewer));
1062:       PetscCall(PetscViewerSetType(jac->gkbviewer, PETSCVIEWERASCII));
1063:       PetscCall(PetscObjectGetTabLevel((PetscObject)ilink->ksp, &tablevel));
1064:       PetscCall(PetscViewerASCIISetTab(jac->gkbviewer, tablevel));
1065:       PetscCall(PetscObjectIncrementTabLevel((PetscObject)ilink->ksp, (PetscObject)ilink->ksp, 1));
1066:     }
1067:   } else {
1068:     /* set up the individual splits' PCs */
1069:     i     = 0;
1070:     ilink = jac->head;
1071:     while (ilink) {
1072:       PetscCall(KSPSetOperators(ilink->ksp, jac->mat[i], jac->pmat[i]));
1073:       /* really want setfromoptions called in PCSetFromOptions_FieldSplit(), but it is not ready yet */
1074:       if (!jac->suboptionsset) PetscCall(KSPSetFromOptions(ilink->ksp));
1075:       i++;
1076:       ilink = ilink->next;
1077:     }
1078:   }

1080:   /* Set coordinates to the sub PC objects whenever these are set */
1081:   if (jac->coordinates_set) {
1082:     PC pc_coords;
1083:     if (jac->type == PC_COMPOSITE_SCHUR) {
1084:       // Head is first block.
1085:       PetscCall(KSPGetPC(jac->head->ksp, &pc_coords));
1086:       PetscCall(PCSetCoordinates(pc_coords, jac->head->dim, jac->head->ndofs, jac->head->coords));
1087:       // Second one is Schur block, but its KSP object is in kspschur.
1088:       PetscCall(KSPGetPC(jac->kspschur, &pc_coords));
1089:       PetscCall(PCSetCoordinates(pc_coords, jac->head->next->dim, jac->head->next->ndofs, jac->head->next->coords));
1090:     } else if (jac->type == PC_COMPOSITE_GKB) {
1091:       PetscCall(PetscInfo(pc, "Warning: Setting coordinates does nothing for the GKB Fieldpslit preconditioner\n"));
1092:     } else {
1093:       ilink = jac->head;
1094:       while (ilink) {
1095:         PetscCall(KSPGetPC(ilink->ksp, &pc_coords));
1096:         PetscCall(PCSetCoordinates(pc_coords, ilink->dim, ilink->ndofs, ilink->coords));
1097:         ilink = ilink->next;
1098:       }
1099:     }
1100:   }

1102:   jac->suboptionsset = PETSC_TRUE;
1103:   PetscFunctionReturn(PETSC_SUCCESS);
1104: }

1106: static PetscErrorCode PCSetUpOnBlocks_FieldSplit_Schur(PC pc)
1107: {
1108:   PC_FieldSplit    *jac    = (PC_FieldSplit *)pc->data;
1109:   PC_FieldSplitLink ilinkA = jac->head;
1110:   KSP               kspA = ilinkA->ksp, kspUpper = jac->kspupper;

1112:   PetscFunctionBegin;
1113:   if (jac->schurfactorization == PC_FIELDSPLIT_SCHUR_FACT_FULL && kspUpper != kspA) {
1114:     PetscCall(KSPSetUp(kspUpper));
1115:     PetscCall(KSPSetUpOnBlocks(kspUpper));
1116:   }
1117:   PetscCall(KSPSetUp(kspA));
1118:   PetscCall(KSPSetUpOnBlocks(kspA));
1119:   if (jac->schurpre != PC_FIELDSPLIT_SCHUR_PRE_FULL) {
1120:     PetscCall(KSPSetUp(jac->kspschur));
1121:     PetscCall(KSPSetUpOnBlocks(jac->kspschur));
1122:   } else if (kspUpper == kspA) {
1123:     Mat          A;
1124:     PetscInt     m, M, N;
1125:     VecType      vtype;
1126:     PetscMemType mtype;
1127:     PetscScalar *array;

1129:     PetscCall(MatGetSize(jac->B, &M, &N));
1130:     PetscCall(MatGetLocalSize(jac->B, &m, NULL));
1131:     PetscCall(MatGetVecType(jac->B, &vtype));
1132:     PetscCall(VecGetArrayAndMemType(ilinkA->x, &array, &mtype));
1133:     PetscCall(VecRestoreArrayAndMemType(ilinkA->x, &array));
1134:     if (PetscMemTypeHost(mtype) || (!PetscDefined(HAVE_CUDA) && !PetscDefined(HAVE_HIP))) PetscCall(PetscMalloc1(m * (N + 1), &array));
1135: #if PetscDefined(HAVE_CUDA)
1136:     else if (PetscMemTypeCUDA(mtype)) PetscCallCUDA(cudaMalloc((void **)&array, sizeof(PetscScalar) * m * (N + 1)));
1137: #endif
1138: #if PetscDefined(HAVE_HIP)
1139:     else if (PetscMemTypeHIP(mtype)) PetscCallHIP(hipMalloc((void **)&array, sizeof(PetscScalar) * m * (N + 1)));
1140: #endif
1141:     PetscCall(MatCreateDenseFromVecType(PetscObjectComm((PetscObject)jac->schur), vtype, m, PETSC_DECIDE, M, N + 1, -1, array, &A)); // number of columns of the Schur complement plus one
1142:     PetscCall(PetscObjectCompose((PetscObject)jac->schur, "AinvB", (PetscObject)A));
1143:     PetscCall(MatDestroy(&A));
1144:   }
1145:   PetscFunctionReturn(PETSC_SUCCESS);
1146: }

1148: static PetscErrorCode PCSetUpOnBlocks_FieldSplit(PC pc)
1149: {
1150:   PC_FieldSplit    *jac   = (PC_FieldSplit *)pc->data;
1151:   PC_FieldSplitLink ilink = jac->head;

1153:   PetscFunctionBegin;
1154:   while (ilink) {
1155:     PetscCall(KSPSetUp(ilink->ksp));
1156:     PetscCall(KSPSetUpOnBlocks(ilink->ksp));
1157:     ilink = ilink->next;
1158:   }
1159:   PetscFunctionReturn(PETSC_SUCCESS);
1160: }

1162: static PetscErrorCode PCSetUpOnBlocks_FieldSplit_GKB(PC pc)
1163: {
1164:   PC_FieldSplit    *jac    = (PC_FieldSplit *)pc->data;
1165:   PC_FieldSplitLink ilinkA = jac->head;
1166:   KSP               ksp    = ilinkA->ksp;

1168:   PetscFunctionBegin;
1169:   PetscCall(KSPSetUp(ksp));
1170:   PetscCall(KSPSetUpOnBlocks(ksp));
1171:   PetscFunctionReturn(PETSC_SUCCESS);
1172: }

1174: static PetscErrorCode PCApply_FieldSplit_Schur(PC pc, Vec x, Vec y)
1175: {
1176:   PC_FieldSplit    *jac    = (PC_FieldSplit *)pc->data;
1177:   PC_FieldSplitLink ilinkA = jac->head, ilinkD = ilinkA->next;
1178:   KSP               kspA = ilinkA->ksp, kspLower = kspA, kspUpper = jac->kspupper;
1179:   Mat               AinvB = NULL;
1180:   PetscInt          N, P;

1182:   PetscFunctionBegin;
1183:   switch (jac->schurfactorization) {
1184:   case PC_FIELDSPLIT_SCHUR_FACT_DIAG:
1185:     /* [A00 0; 0 -S], positive definite, suitable for MINRES */
1186:     PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1187:     PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1188:     PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1189:     PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1190:     PetscCall(KSPSolve(kspA, ilinkA->x, ilinkA->y));
1191:     PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1192:     PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1193:     PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1194:     PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1195:     PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1196:     PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, 1));
1197:     PetscCall(KSPSolve(jac->kspschur, ilinkD->x, ilinkD->y));
1198:     PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y));
1199:     PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, -1));
1200:     PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1201:     PetscCall(VecScale(ilinkD->y, jac->schurscale));
1202:     PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1203:     PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1204:     PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1205:     break;
1206:   case PC_FIELDSPLIT_SCHUR_FACT_LOWER:
1207:     /* [A00 0; A10 S], suitable for left preconditioning */
1208:     PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1209:     PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1210:     PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1211:     PetscCall(KSPSolve(kspA, ilinkA->x, ilinkA->y));
1212:     PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1213:     PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1214:     PetscCall(MatMult(jac->C, ilinkA->y, ilinkD->x));
1215:     PetscCall(VecScale(ilinkD->x, -1.));
1216:     PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD));
1217:     PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1218:     PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD));
1219:     PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1220:     PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, 1));
1221:     PetscCall(KSPSolve(jac->kspschur, ilinkD->x, ilinkD->y));
1222:     PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, -1));
1223:     PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y));
1224:     PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1225:     PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1226:     PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1227:     PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1228:     break;
1229:   case PC_FIELDSPLIT_SCHUR_FACT_UPPER:
1230:     /* [A00 A01; 0 S], suitable for right preconditioning */
1231:     PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1232:     PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1233:     PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1234:     PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, 1));
1235:     PetscCall(KSPSolve(jac->kspschur, ilinkD->x, ilinkD->y));
1236:     PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, -1));
1237:     PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y));
1238:     PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1239:     PetscCall(MatMult(jac->B, ilinkD->y, ilinkA->x));
1240:     PetscCall(VecScale(ilinkA->x, -1.));
1241:     PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, ADD_VALUES, SCATTER_FORWARD));
1242:     PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1243:     PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, ADD_VALUES, SCATTER_FORWARD));
1244:     PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1245:     PetscCall(KSPSolve(kspA, ilinkA->x, ilinkA->y));
1246:     PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1247:     PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1248:     PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1249:     PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1250:     PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1251:     break;
1252:   case PC_FIELDSPLIT_SCHUR_FACT_FULL:
1253:     /* [1 0; A10 A00^{-1} 1] [A00 0; 0 S] [1 A00^{-1}A01; 0 1] */
1254:     PetscCall(MatGetSize(jac->B, NULL, &P));
1255:     N = P;
1256:     PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1257:     PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1258:     PetscCall(PetscLogEventBegin(KSP_Solve_FS_L, kspLower, ilinkA->x, ilinkA->y, NULL));
1259:     if (kspUpper == kspA) {
1260:       PetscCall(PetscObjectQuery((PetscObject)jac->schur, "AinvB", (PetscObject *)&AinvB));
1261:       if (AinvB) {
1262:         PetscCall(MatGetSize(AinvB, NULL, &N));
1263:         if (N > P) { // first time PCApply_FieldSplit_Schur() is called
1264:           PetscMemType mtype;
1265:           Vec          c = NULL;
1266:           PetscScalar *array;
1267:           PetscInt     m, M;

1269:           PetscCall(MatGetSize(jac->B, &M, NULL));
1270:           PetscCall(MatGetLocalSize(jac->B, &m, NULL));
1271:           PetscCall(MatDenseGetArrayAndMemType(AinvB, &array, &mtype));
1272:           if (PetscMemTypeHost(mtype) || (!PetscDefined(HAVE_CUDA) && !PetscDefined(HAVE_HIP))) PetscCall(VecCreateMPIWithArray(PetscObjectComm((PetscObject)jac->schur), 1, m, M, array + m * P, &c));
1273: #if PetscDefined(HAVE_CUDA)
1274:           else if (PetscMemTypeCUDA(mtype)) PetscCall(VecCreateMPICUDAWithArray(PetscObjectComm((PetscObject)jac->schur), 1, m, M, array + m * P, &c));
1275: #endif
1276: #if PetscDefined(HAVE_HIP)
1277:           else if (PetscMemTypeHIP(mtype)) PetscCall(VecCreateMPIHIPWithArray(PetscObjectComm((PetscObject)jac->schur), 1, m, M, array + m * P, &c));
1278: #endif
1279:           PetscCall(MatDenseRestoreArrayAndMemType(AinvB, &array));
1280:           PetscCall(VecCopy(ilinkA->x, c));
1281:           PetscCall(MatSchurComplementComputeExplicitOperator(jac->schur, &jac->schur_user));
1282:           PetscCall(KSPSetOperators(jac->kspschur, jac->schur, jac->schur_user));
1283:           PetscCall(VecCopy(c, ilinkA->y)); // retrieve the solution as the last column of the composed Mat
1284:           PetscCall(VecDestroy(&c));
1285:         }
1286:       }
1287:     }
1288:     if (N == P) PetscCall(KSPSolve(kspLower, ilinkA->x, ilinkA->y));
1289:     PetscCall(KSPCheckSolve(kspLower, pc, ilinkA->y));
1290:     PetscCall(PetscLogEventEnd(KSP_Solve_FS_L, kspLower, ilinkA->x, ilinkA->y, NULL));
1291:     PetscCall(MatMult(jac->C, ilinkA->y, ilinkD->x));
1292:     PetscCall(VecScale(ilinkD->x, -1.0));
1293:     PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD));
1294:     PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD));

1296:     PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1297:     PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, 1));
1298:     PetscCall(KSPSolve(jac->kspschur, ilinkD->x, ilinkD->y));
1299:     PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, -1));
1300:     PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y));
1301:     PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1302:     PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));

1304:     if (kspUpper == kspA) {
1305:       if (!AinvB) {
1306:         PetscCall(MatMult(jac->B, ilinkD->y, ilinkA->y));
1307:         PetscCall(VecAXPY(ilinkA->x, -1.0, ilinkA->y));
1308:         PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1309:         PetscCall(KSPSolve(kspA, ilinkA->x, ilinkA->y));
1310:         PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1311:         PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1312:       } else PetscCall(MatMultAdd(AinvB, ilinkD->y, ilinkA->y, ilinkA->y));
1313:     } else {
1314:       PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1315:       PetscCall(KSPSolve(kspA, ilinkA->x, ilinkA->y));
1316:       PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1317:       PetscCall(MatMult(jac->B, ilinkD->y, ilinkA->x));
1318:       PetscCall(PetscLogEventBegin(KSP_Solve_FS_U, kspUpper, ilinkA->x, ilinkA->z, NULL));
1319:       PetscCall(KSPSolve(kspUpper, ilinkA->x, ilinkA->z));
1320:       PetscCall(KSPCheckSolve(kspUpper, pc, ilinkA->z));
1321:       PetscCall(PetscLogEventEnd(KSP_Solve_FS_U, kspUpper, ilinkA->x, ilinkA->z, NULL));
1322:       PetscCall(VecAXPY(ilinkA->y, -1.0, ilinkA->z));
1323:     }
1324:     PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1325:     PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1326:     PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1327:   }
1328:   PetscFunctionReturn(PETSC_SUCCESS);
1329: }

1331: static PetscErrorCode PCApplyTranspose_FieldSplit_Schur(PC pc, Vec x, Vec y)
1332: {
1333:   PC_FieldSplit    *jac    = (PC_FieldSplit *)pc->data;
1334:   PC_FieldSplitLink ilinkA = jac->head, ilinkD = ilinkA->next;
1335:   KSP               kspA = ilinkA->ksp, kspLower = kspA, kspUpper = jac->kspupper;

1337:   PetscFunctionBegin;
1338:   switch (jac->schurfactorization) {
1339:   case PC_FIELDSPLIT_SCHUR_FACT_DIAG:
1340:     /* [A00 0; 0 -S], positive definite, suitable for MINRES */
1341:     PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1342:     PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1343:     PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1344:     PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1345:     PetscCall(KSPSolveTranspose(kspA, ilinkA->x, ilinkA->y));
1346:     PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1347:     PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1348:     PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1349:     PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1350:     PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1351:     PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, 1));
1352:     PetscCall(KSPSolveTranspose(jac->kspschur, ilinkD->x, ilinkD->y));
1353:     PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, -1));
1354:     PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y));
1355:     PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1356:     PetscCall(VecScale(ilinkD->y, jac->schurscale));
1357:     PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1358:     PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1359:     PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1360:     break;
1361:   case PC_FIELDSPLIT_SCHUR_FACT_UPPER:
1362:     PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1363:     PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1364:     PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1365:     PetscCall(KSPSolveTranspose(kspA, ilinkA->x, ilinkA->y));
1366:     PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1367:     PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1368:     PetscCall(MatMultTranspose(jac->B, ilinkA->y, ilinkD->x));
1369:     PetscCall(VecScale(ilinkD->x, -1.));
1370:     PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD));
1371:     PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1372:     PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD));
1373:     PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1374:     PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, 1));
1375:     PetscCall(KSPSolveTranspose(jac->kspschur, ilinkD->x, ilinkD->y));
1376:     PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, -1));
1377:     PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y));
1378:     PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1379:     PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1380:     PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1381:     PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1382:     break;
1383:   case PC_FIELDSPLIT_SCHUR_FACT_LOWER:
1384:     PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1385:     PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1386:     PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1387:     PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, 1));
1388:     PetscCall(KSPSolveTranspose(jac->kspschur, ilinkD->x, ilinkD->y));
1389:     PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, -1));
1390:     PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y));
1391:     PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1392:     PetscCall(MatMultTranspose(jac->C, ilinkD->y, ilinkA->x));
1393:     PetscCall(VecScale(ilinkA->x, -1.));
1394:     PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, ADD_VALUES, SCATTER_FORWARD));
1395:     PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1396:     PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, ADD_VALUES, SCATTER_FORWARD));
1397:     PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1398:     PetscCall(KSPSolveTranspose(kspA, ilinkA->x, ilinkA->y));
1399:     PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1400:     PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1401:     PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1402:     PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1403:     PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1404:     break;
1405:   case PC_FIELDSPLIT_SCHUR_FACT_FULL:
1406:     PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1407:     PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1408:     PetscCall(PetscLogEventBegin(KSP_Solve_FS_U, kspUpper, ilinkA->x, ilinkA->y, NULL));
1409:     PetscCall(KSPSolveTranspose(kspUpper, ilinkA->x, ilinkA->y));
1410:     PetscCall(KSPCheckSolve(kspUpper, pc, ilinkA->y));
1411:     PetscCall(PetscLogEventEnd(KSP_Solve_FS_U, kspUpper, ilinkA->x, ilinkA->y, NULL));
1412:     PetscCall(MatMultTranspose(jac->B, ilinkA->y, ilinkD->x));
1413:     PetscCall(VecScale(ilinkD->x, -1.0));
1414:     PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD));
1415:     PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD));

1417:     PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1418:     PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, 1));
1419:     PetscCall(KSPSolveTranspose(jac->kspschur, ilinkD->x, ilinkD->y));
1420:     PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, -1));
1421:     PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y));
1422:     PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1423:     PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));

1425:     if (kspLower == kspA) {
1426:       PetscCall(MatMultTranspose(jac->C, ilinkD->y, ilinkA->y));
1427:       PetscCall(VecAXPY(ilinkA->x, -1.0, ilinkA->y));
1428:       PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1429:       PetscCall(KSPSolveTranspose(kspA, ilinkA->x, ilinkA->y));
1430:       PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1431:       PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1432:     } else {
1433:       PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1434:       PetscCall(KSPSolveTranspose(kspA, ilinkA->x, ilinkA->y));
1435:       PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1436:       PetscCall(MatMultTranspose(jac->C, ilinkD->y, ilinkA->x));
1437:       PetscCall(PetscLogEventBegin(KSP_Solve_FS_L, kspLower, ilinkA->x, ilinkA->z, NULL));
1438:       PetscCall(KSPSolveTranspose(kspLower, ilinkA->x, ilinkA->z));
1439:       PetscCall(KSPCheckSolve(kspLower, pc, ilinkA->z));
1440:       PetscCall(PetscLogEventEnd(KSP_Solve_FS_L, kspLower, ilinkA->x, ilinkA->z, NULL));
1441:       PetscCall(VecAXPY(ilinkA->y, -1.0, ilinkA->z));
1442:     }
1443:     PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1444:     PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1445:     PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1446:   }
1447:   PetscFunctionReturn(PETSC_SUCCESS);
1448: }

1450: #define FieldSplitSplitSolveAdd(ilink, xx, yy) \
1451:   ((PetscErrorCode)(VecScatterBegin(ilink->sctx, xx, ilink->x, INSERT_VALUES, SCATTER_FORWARD) || VecScatterEnd(ilink->sctx, xx, ilink->x, INSERT_VALUES, SCATTER_FORWARD) || PetscLogEventBegin(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL) || \
1452:                     KSPSolve(ilink->ksp, ilink->x, ilink->y) || KSPCheckSolve(ilink->ksp, pc, ilink->y) || PetscLogEventEnd(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL) || VecScatterBegin(ilink->sctx, ilink->y, yy, ADD_VALUES, SCATTER_REVERSE) || \
1453:                     VecScatterEnd(ilink->sctx, ilink->y, yy, ADD_VALUES, SCATTER_REVERSE)))

1455: static PetscErrorCode PCApply_FieldSplit(PC pc, Vec x, Vec y)
1456: {
1457:   PC_FieldSplit    *jac   = (PC_FieldSplit *)pc->data;
1458:   PC_FieldSplitLink ilink = jac->head;
1459:   PetscInt          cnt, bs;

1461:   PetscFunctionBegin;
1462:   if (jac->type == PC_COMPOSITE_ADDITIVE) {
1463:     PetscBool matnest;

1465:     PetscCall(PetscObjectTypeCompare((PetscObject)pc->pmat, MATNEST, &matnest));
1466:     if (jac->defaultsplit && !matnest) {
1467:       PetscCall(VecGetBlockSize(x, &bs));
1468:       PetscCheck(jac->bs <= 0 || bs == jac->bs, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONGSTATE, "Blocksize of x vector %" PetscInt_FMT " does not match fieldsplit blocksize %" PetscInt_FMT, bs, jac->bs);
1469:       PetscCall(VecGetBlockSize(y, &bs));
1470:       PetscCheck(jac->bs <= 0 || bs == jac->bs, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONGSTATE, "Blocksize of y vector %" PetscInt_FMT " does not match fieldsplit blocksize %" PetscInt_FMT, bs, jac->bs);
1471:       PetscCall(VecStrideGatherAll(x, jac->x, INSERT_VALUES));
1472:       while (ilink) {
1473:         PetscCall(PetscLogEventBegin(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1474:         PetscCall(KSPSolve(ilink->ksp, ilink->x, ilink->y));
1475:         PetscCall(KSPCheckSolve(ilink->ksp, pc, ilink->y));
1476:         PetscCall(PetscLogEventEnd(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1477:         ilink = ilink->next;
1478:       }
1479:       PetscCall(VecStrideScatterAll(jac->y, y, INSERT_VALUES));
1480:     } else {
1481:       PetscCall(VecSet(y, 0.0));
1482:       while (ilink) {
1483:         PetscCall(FieldSplitSplitSolveAdd(ilink, x, y));
1484:         ilink = ilink->next;
1485:       }
1486:     }
1487:   } else if (jac->type == PC_COMPOSITE_MULTIPLICATIVE && jac->nsplits == 2) {
1488:     PetscCall(VecSet(y, 0.0));
1489:     /* solve on first block for first block variables */
1490:     PetscCall(VecScatterBegin(ilink->sctx, x, ilink->x, INSERT_VALUES, SCATTER_FORWARD));
1491:     PetscCall(VecScatterEnd(ilink->sctx, x, ilink->x, INSERT_VALUES, SCATTER_FORWARD));
1492:     PetscCall(PetscLogEventBegin(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1493:     PetscCall(KSPSolve(ilink->ksp, ilink->x, ilink->y));
1494:     PetscCall(KSPCheckSolve(ilink->ksp, pc, ilink->y));
1495:     PetscCall(PetscLogEventEnd(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1496:     PetscCall(VecScatterBegin(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE));
1497:     PetscCall(VecScatterEnd(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE));

1499:     /* compute the residual only onto second block variables using first block variables */
1500:     PetscCall(MatMult(jac->Afield[1], ilink->y, ilink->next->x));
1501:     ilink = ilink->next;
1502:     PetscCall(VecScale(ilink->x, -1.0));
1503:     PetscCall(VecScatterBegin(ilink->sctx, x, ilink->x, ADD_VALUES, SCATTER_FORWARD));
1504:     PetscCall(VecScatterEnd(ilink->sctx, x, ilink->x, ADD_VALUES, SCATTER_FORWARD));

1506:     /* solve on second block variables */
1507:     PetscCall(PetscLogEventBegin(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1508:     PetscCall(KSPSolve(ilink->ksp, ilink->x, ilink->y));
1509:     PetscCall(KSPCheckSolve(ilink->ksp, pc, ilink->y));
1510:     PetscCall(PetscLogEventEnd(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1511:     PetscCall(VecScatterBegin(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE));
1512:     PetscCall(VecScatterEnd(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE));
1513:   } else if (jac->type == PC_COMPOSITE_MULTIPLICATIVE || jac->type == PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE) {
1514:     if (!jac->w1) {
1515:       PetscCall(VecDuplicate(x, &jac->w1));
1516:       PetscCall(VecDuplicate(x, &jac->w2));
1517:     }
1518:     PetscCall(VecSet(y, 0.0));
1519:     PetscCall(FieldSplitSplitSolveAdd(ilink, x, y));
1520:     cnt = 1;
1521:     while (ilink->next) {
1522:       ilink = ilink->next;
1523:       /* compute the residual only over the part of the vector needed */
1524:       PetscCall(MatMult(jac->Afield[cnt++], y, ilink->x));
1525:       PetscCall(VecScale(ilink->x, -1.0));
1526:       PetscCall(VecScatterBegin(ilink->sctx, x, ilink->x, ADD_VALUES, SCATTER_FORWARD));
1527:       PetscCall(VecScatterEnd(ilink->sctx, x, ilink->x, ADD_VALUES, SCATTER_FORWARD));
1528:       PetscCall(PetscLogEventBegin(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1529:       PetscCall(KSPSolve(ilink->ksp, ilink->x, ilink->y));
1530:       PetscCall(KSPCheckSolve(ilink->ksp, pc, ilink->y));
1531:       PetscCall(PetscLogEventEnd(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1532:       PetscCall(VecScatterBegin(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE));
1533:       PetscCall(VecScatterEnd(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE));
1534:     }
1535:     if (jac->type == PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE) {
1536:       cnt -= 2;
1537:       while (ilink->previous) {
1538:         ilink = ilink->previous;
1539:         /* compute the residual only over the part of the vector needed */
1540:         PetscCall(MatMult(jac->Afield[cnt--], y, ilink->x));
1541:         PetscCall(VecScale(ilink->x, -1.0));
1542:         PetscCall(VecScatterBegin(ilink->sctx, x, ilink->x, ADD_VALUES, SCATTER_FORWARD));
1543:         PetscCall(VecScatterEnd(ilink->sctx, x, ilink->x, ADD_VALUES, SCATTER_FORWARD));
1544:         PetscCall(PetscLogEventBegin(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1545:         PetscCall(KSPSolve(ilink->ksp, ilink->x, ilink->y));
1546:         PetscCall(KSPCheckSolve(ilink->ksp, pc, ilink->y));
1547:         PetscCall(PetscLogEventEnd(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1548:         PetscCall(VecScatterBegin(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE));
1549:         PetscCall(VecScatterEnd(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE));
1550:       }
1551:     }
1552:   } else SETERRQ(PetscObjectComm((PetscObject)pc), PETSC_ERR_SUP, "Unsupported or unknown composition %d", (int)jac->type);
1553:   PetscFunctionReturn(PETSC_SUCCESS);
1554: }

1556: static PetscErrorCode PCApply_FieldSplit_GKB(PC pc, Vec x, Vec y)
1557: {
1558:   PC_FieldSplit    *jac    = (PC_FieldSplit *)pc->data;
1559:   PC_FieldSplitLink ilinkA = jac->head, ilinkD = ilinkA->next;
1560:   KSP               ksp = ilinkA->ksp;
1561:   Vec               u, v, Hu, d, work1, work2;
1562:   PetscScalar       alpha, z, nrmz2, *vecz;
1563:   PetscReal         lowbnd, nu, beta;
1564:   PetscInt          j, iterGKB;

1566:   PetscFunctionBegin;
1567:   PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1568:   PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1569:   PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1570:   PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));

1572:   u     = jac->u;
1573:   v     = jac->v;
1574:   Hu    = jac->Hu;
1575:   d     = jac->d;
1576:   work1 = jac->w1;
1577:   work2 = jac->w2;
1578:   vecz  = jac->vecz;

1580:   /* Change RHS to comply with matrix regularization H = A + nu*B*B' */
1581:   /* Add q = q + nu*B*b */
1582:   if (jac->gkbnu) {
1583:     nu = jac->gkbnu;
1584:     PetscCall(VecScale(ilinkD->x, jac->gkbnu));
1585:     PetscCall(MatMultAdd(jac->B, ilinkD->x, ilinkA->x, ilinkA->x)); /* q = q + nu*B*b */
1586:   } else {
1587:     /* Situation when no augmented Lagrangian is used. Then we set inner  */
1588:     /* matrix N = I in [Ar13], and thus nu = 1.                           */
1589:     nu = 1;
1590:   }

1592:   /* Transform rhs from [q,tilde{b}] to [0,b] */
1593:   PetscCall(PetscLogEventBegin(ilinkA->event, ksp, ilinkA->x, ilinkA->y, NULL));
1594:   PetscCall(KSPSolve(ksp, ilinkA->x, ilinkA->y));
1595:   PetscCall(KSPCheckSolve(ksp, pc, ilinkA->y));
1596:   PetscCall(PetscLogEventEnd(ilinkA->event, ksp, ilinkA->x, ilinkA->y, NULL));
1597:   PetscCall(MatMultHermitianTranspose(jac->B, ilinkA->y, work1));
1598:   PetscCall(VecAXPBY(work1, 1.0 / nu, -1.0, ilinkD->x)); /* c = b - B'*x        */

1600:   /* First step of algorithm */
1601:   PetscCall(VecNorm(work1, NORM_2, &beta)); /* beta = sqrt(nu*c'*c)*/
1602:   KSPCheckDot(ksp, beta);
1603:   beta = PetscSqrtReal(nu) * beta;
1604:   PetscCall(VecAXPBY(v, nu / beta, 0.0, work1)); /* v = nu/beta *c      */
1605:   PetscCall(MatMult(jac->B, v, work2));          /* u = H^{-1}*B*v      */
1606:   PetscCall(PetscLogEventBegin(ilinkA->event, ksp, work2, u, NULL));
1607:   PetscCall(KSPSolve(ksp, work2, u));
1608:   PetscCall(KSPCheckSolve(ksp, pc, u));
1609:   PetscCall(PetscLogEventEnd(ilinkA->event, ksp, work2, u, NULL));
1610:   PetscCall(MatMult(jac->H, u, Hu)); /* alpha = u'*H*u      */
1611:   PetscCall(VecDot(Hu, u, &alpha));
1612:   KSPCheckDot(ksp, alpha);
1613:   PetscCheck(PetscRealPart(alpha) > 0.0, PETSC_COMM_SELF, PETSC_ERR_NOT_CONVERGED, "GKB preconditioner diverged, H is not positive definite");
1614:   alpha = PetscSqrtReal(PetscAbsScalar(alpha));
1615:   PetscCall(VecScale(u, 1.0 / alpha));
1616:   PetscCall(VecAXPBY(d, 1.0 / alpha, 0.0, v)); /* v = nu/beta *c      */

1618:   z       = beta / alpha;
1619:   vecz[1] = z;

1621:   /* Computation of first iterate x(1) and p(1) */
1622:   PetscCall(VecAXPY(ilinkA->y, z, u));
1623:   PetscCall(VecCopy(d, ilinkD->y));
1624:   PetscCall(VecScale(ilinkD->y, -z));

1626:   iterGKB = 1;
1627:   lowbnd  = 2 * jac->gkbtol;
1628:   if (jac->gkbmonitor) PetscCall(PetscViewerASCIIPrintf(jac->gkbviewer, "%3" PetscInt_FMT " GKB Lower bound estimate %14.12e\n", iterGKB, (double)lowbnd));

1630:   while (iterGKB < jac->gkbmaxit && lowbnd > jac->gkbtol) {
1631:     iterGKB += 1;
1632:     PetscCall(MatMultHermitianTranspose(jac->B, u, work1)); /* v <- nu*(B'*u-alpha/nu*v) */
1633:     PetscCall(VecAXPBY(v, nu, -alpha, work1));
1634:     PetscCall(VecNorm(v, NORM_2, &beta)); /* beta = sqrt(nu)*v'*v      */
1635:     beta = beta / PetscSqrtReal(nu);
1636:     PetscCall(VecScale(v, 1.0 / beta));
1637:     PetscCall(MatMult(jac->B, v, work2)); /* u <- H^{-1}*(B*v-beta*H*u) */
1638:     PetscCall(MatMult(jac->H, u, Hu));
1639:     PetscCall(VecAXPY(work2, -beta, Hu));
1640:     PetscCall(PetscLogEventBegin(ilinkA->event, ksp, work2, u, NULL));
1641:     PetscCall(KSPSolve(ksp, work2, u));
1642:     PetscCall(KSPCheckSolve(ksp, pc, u));
1643:     PetscCall(PetscLogEventEnd(ilinkA->event, ksp, work2, u, NULL));
1644:     PetscCall(MatMult(jac->H, u, Hu)); /* alpha = u'*H*u            */
1645:     PetscCall(VecDot(Hu, u, &alpha));
1646:     KSPCheckDot(ksp, alpha);
1647:     PetscCheck(PetscRealPart(alpha) > 0.0, PETSC_COMM_SELF, PETSC_ERR_NOT_CONVERGED, "GKB preconditioner diverged, H is not positive definite");
1648:     alpha = PetscSqrtReal(PetscAbsScalar(alpha));
1649:     PetscCall(VecScale(u, 1.0 / alpha));

1651:     z       = -beta / alpha * z; /* z <- beta/alpha*z     */
1652:     vecz[0] = z;

1654:     /* Computation of new iterate x(i+1) and p(i+1) */
1655:     PetscCall(VecAXPBY(d, 1.0 / alpha, -beta / alpha, v)); /* d = (v-beta*d)/alpha */
1656:     PetscCall(VecAXPY(ilinkA->y, z, u));                   /* r = r + z*u          */
1657:     PetscCall(VecAXPY(ilinkD->y, -z, d));                  /* p = p - z*d          */
1658:     PetscCall(MatMult(jac->H, ilinkA->y, Hu));             /* ||u||_H = u'*H*u     */
1659:     PetscCall(VecDot(Hu, ilinkA->y, &nrmz2));

1661:     /* Compute Lower Bound estimate */
1662:     if (iterGKB > jac->gkbdelay) {
1663:       lowbnd = 0.0;
1664:       for (j = 0; j < jac->gkbdelay; j++) lowbnd += PetscAbsScalar(vecz[j] * vecz[j]);
1665:       lowbnd = PetscSqrtReal(lowbnd / PetscAbsScalar(nrmz2));
1666:     }

1668:     for (j = 0; j < jac->gkbdelay - 1; j++) vecz[jac->gkbdelay - j - 1] = vecz[jac->gkbdelay - j - 2];
1669:     if (jac->gkbmonitor) PetscCall(PetscViewerASCIIPrintf(jac->gkbviewer, "%3" PetscInt_FMT " GKB Lower bound estimate %14.12e\n", iterGKB, (double)lowbnd));
1670:   }

1672:   PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1673:   PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1674:   PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1675:   PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1676:   PetscFunctionReturn(PETSC_SUCCESS);
1677: }

1679: #define FieldSplitSplitSolveAddTranspose(ilink, xx, yy) \
1680:   ((PetscErrorCode)(VecScatterBegin(ilink->sctx, xx, ilink->y, INSERT_VALUES, SCATTER_FORWARD) || VecScatterEnd(ilink->sctx, xx, ilink->y, INSERT_VALUES, SCATTER_FORWARD) || PetscLogEventBegin(ilink->event, ilink->ksp, ilink->y, ilink->x, NULL) || \
1681:                     KSPSolveTranspose(ilink->ksp, ilink->y, ilink->x) || KSPCheckSolve(ilink->ksp, pc, ilink->x) || PetscLogEventEnd(ilink->event, ilink->ksp, ilink->y, ilink->x, NULL) || VecScatterBegin(ilink->sctx, ilink->x, yy, ADD_VALUES, SCATTER_REVERSE) || \
1682:                     VecScatterEnd(ilink->sctx, ilink->x, yy, ADD_VALUES, SCATTER_REVERSE)))

1684: static PetscErrorCode PCApplyTranspose_FieldSplit(PC pc, Vec x, Vec y)
1685: {
1686:   PC_FieldSplit    *jac   = (PC_FieldSplit *)pc->data;
1687:   PC_FieldSplitLink ilink = jac->head;
1688:   PetscInt          bs;

1690:   PetscFunctionBegin;
1691:   if (jac->type == PC_COMPOSITE_ADDITIVE) {
1692:     PetscBool matnest;

1694:     PetscCall(PetscObjectTypeCompare((PetscObject)pc->pmat, MATNEST, &matnest));
1695:     if (jac->defaultsplit && !matnest) {
1696:       PetscCall(VecGetBlockSize(x, &bs));
1697:       PetscCheck(jac->bs <= 0 || bs == jac->bs, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONGSTATE, "Blocksize of x vector %" PetscInt_FMT " does not match fieldsplit blocksize %" PetscInt_FMT, bs, jac->bs);
1698:       PetscCall(VecGetBlockSize(y, &bs));
1699:       PetscCheck(jac->bs <= 0 || bs == jac->bs, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONGSTATE, "Blocksize of y vector %" PetscInt_FMT " does not match fieldsplit blocksize %" PetscInt_FMT, bs, jac->bs);
1700:       PetscCall(VecStrideGatherAll(x, jac->x, INSERT_VALUES));
1701:       while (ilink) {
1702:         PetscCall(PetscLogEventBegin(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1703:         PetscCall(KSPSolveTranspose(ilink->ksp, ilink->x, ilink->y));
1704:         PetscCall(KSPCheckSolve(ilink->ksp, pc, ilink->y));
1705:         PetscCall(PetscLogEventEnd(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1706:         ilink = ilink->next;
1707:       }
1708:       PetscCall(VecStrideScatterAll(jac->y, y, INSERT_VALUES));
1709:     } else {
1710:       PetscCall(VecSet(y, 0.0));
1711:       while (ilink) {
1712:         PetscCall(FieldSplitSplitSolveAddTranspose(ilink, x, y));
1713:         ilink = ilink->next;
1714:       }
1715:     }
1716:   } else {
1717:     if (!jac->w1) {
1718:       PetscCall(VecDuplicate(x, &jac->w1));
1719:       PetscCall(VecDuplicate(x, &jac->w2));
1720:     }
1721:     PetscCall(VecSet(y, 0.0));
1722:     if (jac->type == PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE) {
1723:       PetscCall(FieldSplitSplitSolveAddTranspose(ilink, x, y));
1724:       while (ilink->next) {
1725:         ilink = ilink->next;
1726:         PetscCall(MatMultTranspose(pc->mat, y, jac->w1));
1727:         PetscCall(VecWAXPY(jac->w2, -1.0, jac->w1, x));
1728:         PetscCall(FieldSplitSplitSolveAddTranspose(ilink, jac->w2, y));
1729:       }
1730:       while (ilink->previous) {
1731:         ilink = ilink->previous;
1732:         PetscCall(MatMultTranspose(pc->mat, y, jac->w1));
1733:         PetscCall(VecWAXPY(jac->w2, -1.0, jac->w1, x));
1734:         PetscCall(FieldSplitSplitSolveAddTranspose(ilink, jac->w2, y));
1735:       }
1736:     } else {
1737:       while (ilink->next) { /* get to last entry in linked list */
1738:         ilink = ilink->next;
1739:       }
1740:       PetscCall(FieldSplitSplitSolveAddTranspose(ilink, x, y));
1741:       while (ilink->previous) {
1742:         ilink = ilink->previous;
1743:         PetscCall(MatMultTranspose(pc->mat, y, jac->w1));
1744:         PetscCall(VecWAXPY(jac->w2, -1.0, jac->w1, x));
1745:         PetscCall(FieldSplitSplitSolveAddTranspose(ilink, jac->w2, y));
1746:       }
1747:     }
1748:   }
1749:   PetscFunctionReturn(PETSC_SUCCESS);
1750: }

1752: static PetscErrorCode PCReset_FieldSplit(PC pc)
1753: {
1754:   PC_FieldSplit    *jac   = (PC_FieldSplit *)pc->data;
1755:   PC_FieldSplitLink ilink = jac->head, next;

1757:   PetscFunctionBegin;
1758:   while (ilink) {
1759:     PetscCall(KSPDestroy(&ilink->ksp));
1760:     PetscCall(VecDestroy(&ilink->x));
1761:     PetscCall(VecDestroy(&ilink->y));
1762:     PetscCall(VecDestroy(&ilink->z));
1763:     PetscCall(VecScatterDestroy(&ilink->sctx));
1764:     PetscCall(ISDestroy(&ilink->is));
1765:     PetscCall(ISDestroy(&ilink->is_col));
1766:     PetscCall(PetscFree(ilink->splitname));
1767:     PetscCall(PetscFree(ilink->fields));
1768:     PetscCall(PetscFree(ilink->fields_col));
1769:     next = ilink->next;
1770:     PetscCall(PetscFree(ilink));
1771:     ilink = next;
1772:   }
1773:   jac->head = NULL;
1774:   PetscCall(PetscFree2(jac->x, jac->y));
1775:   if (jac->mat && jac->mat != jac->pmat) {
1776:     PetscCall(MatDestroyMatrices(jac->nsplits, &jac->mat));
1777:   } else if (jac->mat) {
1778:     jac->mat = NULL;
1779:   }
1780:   if (jac->pmat) PetscCall(MatDestroyMatrices(jac->nsplits, &jac->pmat));
1781:   if (jac->Afield) PetscCall(MatDestroyMatrices(jac->nsplits, &jac->Afield));
1782:   jac->nsplits = 0;
1783:   PetscCall(VecDestroy(&jac->w1));
1784:   PetscCall(VecDestroy(&jac->w2));
1785:   if (jac->schur) PetscCall(PetscObjectCompose((PetscObject)jac->schur, "AinvB", NULL));
1786:   PetscCall(MatDestroy(&jac->schur));
1787:   PetscCall(MatDestroy(&jac->schurp));
1788:   PetscCall(MatDestroy(&jac->schur_user));
1789:   PetscCall(KSPDestroy(&jac->kspschur));
1790:   PetscCall(KSPDestroy(&jac->kspupper));
1791:   PetscCall(MatDestroy(&jac->B));
1792:   PetscCall(MatDestroy(&jac->C));
1793:   PetscCall(MatDestroy(&jac->H));
1794:   PetscCall(VecDestroy(&jac->u));
1795:   PetscCall(VecDestroy(&jac->v));
1796:   PetscCall(VecDestroy(&jac->Hu));
1797:   PetscCall(VecDestroy(&jac->d));
1798:   PetscCall(PetscFree(jac->vecz));
1799:   PetscCall(PetscViewerDestroy(&jac->gkbviewer));
1800:   jac->isrestrict = PETSC_FALSE;
1801:   PetscFunctionReturn(PETSC_SUCCESS);
1802: }

1804: static PetscErrorCode PCDestroy_FieldSplit(PC pc)
1805: {
1806:   PetscFunctionBegin;
1807:   PetscCall(PCReset_FieldSplit(pc));
1808:   PetscCall(PetscFree(pc->data));
1809:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCSetCoordinates_C", NULL));
1810:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetFields_C", NULL));
1811:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetIS_C", NULL));
1812:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetType_C", NULL));
1813:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetBlockSize_C", NULL));
1814:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitRestrictIS_C", NULL));
1815:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSchurGetSubKSP_C", NULL));
1816:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSubKSP_C", NULL));
1817:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBTol_C", NULL));
1818:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBMaxit_C", NULL));
1819:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBNu_C", NULL));
1820:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBDelay_C", NULL));
1821:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurPre_C", NULL));
1822:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSchurPre_C", NULL));
1823:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurFactType_C", NULL));
1824:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurScale_C", NULL));
1825:   PetscFunctionReturn(PETSC_SUCCESS);
1826: }

1828: static PetscErrorCode PCSetFromOptions_FieldSplit(PC pc, PetscOptionItems PetscOptionsObject)
1829: {
1830:   PetscInt        bs;
1831:   PetscBool       flg;
1832:   PC_FieldSplit  *jac = (PC_FieldSplit *)pc->data;
1833:   PCCompositeType ctype;

1835:   PetscFunctionBegin;
1836:   PetscOptionsHeadBegin(PetscOptionsObject, "FieldSplit options");
1837:   PetscCall(PetscOptionsBool("-pc_fieldsplit_dm_splits", "Whether to use DMCreateFieldDecomposition() for splits", "PCFieldSplitSetDMSplits", jac->dm_splits, &jac->dm_splits, NULL));
1838:   PetscCall(PetscOptionsInt("-pc_fieldsplit_block_size", "Blocksize that defines number of fields", "PCFieldSplitSetBlockSize", jac->bs, &bs, &flg));
1839:   if (flg) PetscCall(PCFieldSplitSetBlockSize(pc, bs));
1840:   jac->diag_use_amat = pc->useAmat;
1841:   PetscCall(PetscOptionsBool("-pc_fieldsplit_diag_use_amat", "Use Amat (not Pmat) to extract diagonal fieldsplit blocks", "PCFieldSplitSetDiagUseAmat", jac->diag_use_amat, &jac->diag_use_amat, NULL));
1842:   jac->offdiag_use_amat = pc->useAmat;
1843:   PetscCall(PetscOptionsBool("-pc_fieldsplit_off_diag_use_amat", "Use Amat (not Pmat) to extract off-diagonal fieldsplit blocks", "PCFieldSplitSetOffDiagUseAmat", jac->offdiag_use_amat, &jac->offdiag_use_amat, NULL));
1844:   PetscCall(PetscOptionsBool("-pc_fieldsplit_detect_saddle_point", "Form 2-way split by detecting zero diagonal entries", "PCFieldSplitSetDetectSaddlePoint", jac->detect, &jac->detect, NULL));
1845:   PetscCall(PCFieldSplitSetDetectSaddlePoint(pc, jac->detect)); /* Sets split type and Schur PC type */
1846:   PetscCall(PetscOptionsEnum("-pc_fieldsplit_type", "Type of composition", "PCFieldSplitSetType", PCCompositeTypes, (PetscEnum)jac->type, (PetscEnum *)&ctype, &flg));
1847:   if (flg) PetscCall(PCFieldSplitSetType(pc, ctype));
1848:   /* Only setup fields once */
1849:   if (jac->bs > 0 && jac->nsplits == 0) {
1850:     /* only allow user to set fields from command line.
1851:        otherwise user can set them in PCFieldSplitSetDefaults() */
1852:     PetscCall(PCFieldSplitSetRuntimeSplits_Private(pc));
1853:     if (jac->splitdefined) PetscCall(PetscInfo(pc, "Splits defined using the options database\n"));
1854:   }
1855:   if (jac->type == PC_COMPOSITE_SCHUR) {
1856:     PetscCall(PetscOptionsGetEnum(((PetscObject)pc)->options, ((PetscObject)pc)->prefix, "-pc_fieldsplit_schur_factorization_type", PCFieldSplitSchurFactTypes, (PetscEnum *)&jac->schurfactorization, &flg));
1857:     if (flg) PetscCall(PetscInfo(pc, "Deprecated use of -pc_fieldsplit_schur_factorization_type\n"));
1858:     PetscCall(PetscOptionsEnum("-pc_fieldsplit_schur_fact_type", "Which off-diagonal parts of the block factorization to use", "PCFieldSplitSetSchurFactType", PCFieldSplitSchurFactTypes, (PetscEnum)jac->schurfactorization, (PetscEnum *)&jac->schurfactorization, NULL));
1859:     PetscCall(PetscOptionsEnum("-pc_fieldsplit_schur_precondition", "How to build preconditioner for Schur complement", "PCFieldSplitSetSchurPre", PCFieldSplitSchurPreTypes, (PetscEnum)jac->schurpre, (PetscEnum *)&jac->schurpre, NULL));
1860:     PetscCall(PetscOptionsScalar("-pc_fieldsplit_schur_scale", "Scale Schur complement", "PCFieldSplitSetSchurScale", jac->schurscale, &jac->schurscale, NULL));
1861:   } else if (jac->type == PC_COMPOSITE_GKB) {
1862:     PetscCall(PetscOptionsReal("-pc_fieldsplit_gkb_tol", "The tolerance for the lower bound stopping criterion", "PCFieldSplitSetGKBTol", jac->gkbtol, &jac->gkbtol, NULL));
1863:     PetscCall(PetscOptionsInt("-pc_fieldsplit_gkb_delay", "The delay value for lower bound criterion", "PCFieldSplitSetGKBDelay", jac->gkbdelay, &jac->gkbdelay, NULL));
1864:     PetscCall(PetscOptionsBoundedReal("-pc_fieldsplit_gkb_nu", "Parameter in augmented Lagrangian approach", "PCFieldSplitSetGKBNu", jac->gkbnu, &jac->gkbnu, NULL, 0.0));
1865:     PetscCall(PetscOptionsInt("-pc_fieldsplit_gkb_maxit", "Maximum allowed number of iterations", "PCFieldSplitSetGKBMaxit", jac->gkbmaxit, &jac->gkbmaxit, NULL));
1866:     PetscCall(PetscOptionsBool("-pc_fieldsplit_gkb_monitor", "Prints number of GKB iterations and error", "PCFieldSplitGKB", jac->gkbmonitor, &jac->gkbmonitor, NULL));
1867:   }
1868:   /*
1869:     In the initial call to this routine the sub-solver data structures do not exist so we cannot call KSPSetFromOptions() on them yet.
1870:     But after the initial setup of ALL the layers of sub-solvers is completed we do want to call KSPSetFromOptions() on the sub-solvers every time it
1871:     is called on the outer solver in case changes were made in the options database

1873:     But even after PCSetUp_FieldSplit() is called all the options inside the inner levels of sub-solvers may still not have been set thus we only call the KSPSetFromOptions()
1874:     if we know that the entire stack of sub-solvers below this have been complete instantiated, we check this by seeing if any solver iterations are complete.
1875:     Without this extra check test p2p1fetidp_olof_full and others fail with incorrect matrix types.

1877:     There could be a negative side effect of calling the KSPSetFromOptions() below.

1879:     If one captured the PetscObjectState of the options database one could skip these calls if the database has not changed from the previous call
1880:   */
1881:   if (jac->issetup) {
1882:     PC_FieldSplitLink ilink = jac->head;
1883:     if (jac->type == PC_COMPOSITE_SCHUR) {
1884:       if (jac->kspupper && jac->kspupper->totalits > 0) PetscCall(KSPSetFromOptions(jac->kspupper));
1885:       if (jac->kspschur && jac->kspschur->totalits > 0) PetscCall(KSPSetFromOptions(jac->kspschur));
1886:     }
1887:     while (ilink) {
1888:       if (ilink->ksp->totalits > 0) PetscCall(KSPSetFromOptions(ilink->ksp));
1889:       ilink = ilink->next;
1890:     }
1891:   }
1892:   PetscOptionsHeadEnd();
1893:   PetscFunctionReturn(PETSC_SUCCESS);
1894: }

1896: static PetscErrorCode PCFieldSplitSetFields_FieldSplit(PC pc, const char splitname[], PetscInt n, const PetscInt *fields, const PetscInt *fields_col)
1897: {
1898:   PC_FieldSplit    *jac = (PC_FieldSplit *)pc->data;
1899:   PC_FieldSplitLink ilink, next = jac->head;
1900:   char              prefix[128];
1901:   PetscInt          i;
1902:   PetscLogEvent     nse;

1904:   PetscFunctionBegin;
1905:   if (jac->splitdefined) {
1906:     PetscCall(PetscInfo(pc, "Ignoring new split \"%s\" because the splits have already been defined\n", splitname));
1907:     PetscFunctionReturn(PETSC_SUCCESS);
1908:   }
1909:   for (i = 0; i < n; i++) PetscCheck(fields[i] >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Negative field %" PetscInt_FMT " requested", fields[i]);
1910:   PetscCall(PetscNew(&ilink));
1911:   if (splitname) {
1912:     PetscCall(PetscStrallocpy(splitname, &ilink->splitname));
1913:   } else {
1914:     PetscCall(PetscMalloc1(3, &ilink->splitname));
1915:     PetscCall(PetscSNPrintf(ilink->splitname, 2, "%" PetscInt_FMT, jac->nsplits));
1916:   }
1917:   PetscCall(PetscMPIIntCast(jac->nsplits, &nse));
1918:   ilink->event = jac->nsplits < 5 ? KSP_Solve_FS_0 + nse : KSP_Solve_FS_0 + 4; /* Splits greater than 4 logged in 4th split */
1919:   PetscCall(PetscMalloc1(n, &ilink->fields));
1920:   PetscCall(PetscArraycpy(ilink->fields, fields, n));
1921:   PetscCall(PetscMalloc1(n, &ilink->fields_col));
1922:   PetscCall(PetscArraycpy(ilink->fields_col, fields_col, n));

1924:   ilink->nfields = n;
1925:   ilink->next    = NULL;
1926:   PetscCall(KSPCreate(PetscObjectComm((PetscObject)pc), &ilink->ksp));
1927:   PetscCall(KSPSetNestLevel(ilink->ksp, pc->kspnestlevel));
1928:   PetscCall(KSPSetErrorIfNotConverged(ilink->ksp, pc->erroriffailure));
1929:   PetscCall(PetscObjectIncrementTabLevel((PetscObject)ilink->ksp, (PetscObject)pc, 1));
1930:   PetscCall(KSPSetType(ilink->ksp, KSPPREONLY));

1932:   PetscCall(PetscSNPrintf(prefix, sizeof(prefix), "%sfieldsplit_%s_", ((PetscObject)pc)->prefix ? ((PetscObject)pc)->prefix : "", ilink->splitname));
1933:   PetscCall(KSPSetOptionsPrefix(ilink->ksp, prefix));

1935:   if (!next) {
1936:     jac->head       = ilink;
1937:     ilink->previous = NULL;
1938:   } else {
1939:     while (next->next) next = next->next;
1940:     next->next      = ilink;
1941:     ilink->previous = next;
1942:   }
1943:   jac->nsplits++;
1944:   PetscFunctionReturn(PETSC_SUCCESS);
1945: }

1947: static PetscErrorCode PCFieldSplitSchurGetSubKSP_FieldSplit(PC pc, PetscInt *n, KSP **subksp)
1948: {
1949:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

1951:   PetscFunctionBegin;
1952:   *subksp = NULL;
1953:   if (n) *n = 0;
1954:   if (jac->type == PC_COMPOSITE_SCHUR) {
1955:     PetscInt nn;

1957:     PetscCheck(jac->schur, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONGSTATE, "Must call KSPSetUp() or PCSetUp() before calling PCFieldSplitSchurGetSubKSP()");
1958:     PetscCheck(jac->nsplits == 2, PetscObjectComm((PetscObject)pc), PETSC_ERR_PLIB, "Unexpected number of splits %" PetscInt_FMT " != 2", jac->nsplits);
1959:     nn = jac->nsplits + (jac->kspupper != jac->head->ksp ? 1 : 0);
1960:     PetscCall(PetscMalloc1(nn, subksp));
1961:     (*subksp)[0] = jac->head->ksp;
1962:     (*subksp)[1] = jac->kspschur;
1963:     if (jac->kspupper != jac->head->ksp) (*subksp)[2] = jac->kspupper;
1964:     if (n) *n = nn;
1965:   }
1966:   PetscFunctionReturn(PETSC_SUCCESS);
1967: }

1969: static PetscErrorCode PCFieldSplitGetSubKSP_FieldSplit_Schur(PC pc, PetscInt *n, KSP **subksp)
1970: {
1971:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

1973:   PetscFunctionBegin;
1974:   PetscCheck(jac->schur, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONGSTATE, "Must call KSPSetUp() or PCSetUp() before calling PCFieldSplitGetSubKSP()");
1975:   PetscCall(PetscMalloc1(jac->nsplits, subksp));
1976:   PetscCall(MatSchurComplementGetKSP(jac->schur, *subksp));

1978:   (*subksp)[1] = jac->kspschur;
1979:   if (n) *n = jac->nsplits;
1980:   PetscFunctionReturn(PETSC_SUCCESS);
1981: }

1983: static PetscErrorCode PCFieldSplitGetSubKSP_FieldSplit(PC pc, PetscInt *n, KSP **subksp)
1984: {
1985:   PC_FieldSplit    *jac   = (PC_FieldSplit *)pc->data;
1986:   PetscInt          cnt   = 0;
1987:   PC_FieldSplitLink ilink = jac->head;

1989:   PetscFunctionBegin;
1990:   PetscCall(PetscMalloc1(jac->nsplits, subksp));
1991:   while (ilink) {
1992:     (*subksp)[cnt++] = ilink->ksp;
1993:     ilink            = ilink->next;
1994:   }
1995:   PetscCheck(cnt == jac->nsplits, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Corrupt PCFIELDSPLIT object: number of splits in linked list %" PetscInt_FMT " does not match number in object %" PetscInt_FMT, cnt, jac->nsplits);
1996:   if (n) *n = jac->nsplits;
1997:   PetscFunctionReturn(PETSC_SUCCESS);
1998: }

2000: /*@
2001:   PCFieldSplitRestrictIS - Restricts the fieldsplit `IS`s to be within a given `IS`.

2003:   Input Parameters:
2004: + pc  - the preconditioner context
2005: - isy - the index set that defines the indices to which the fieldsplit is to be restricted

2007:   Level: advanced

2009:   Developer Notes:
2010:   It seems the resulting `IS`s will not cover the entire space, so
2011:   how can they define a convergent preconditioner? Needs explaining.

2013: .seealso: [](sec_block_matrices), `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSetIS()`
2014: @*/
2015: PetscErrorCode PCFieldSplitRestrictIS(PC pc, IS isy)
2016: {
2017:   PetscFunctionBegin;
2020:   PetscTryMethod(pc, "PCFieldSplitRestrictIS_C", (PC, IS), (pc, isy));
2021:   PetscFunctionReturn(PETSC_SUCCESS);
2022: }

2024: static PetscErrorCode PCFieldSplitRestrictIS_FieldSplit(PC pc, IS isy)
2025: {
2026:   PC_FieldSplit    *jac   = (PC_FieldSplit *)pc->data;
2027:   PC_FieldSplitLink ilink = jac->head, next;
2028:   PetscInt          localsize, size, sizez, i;
2029:   const PetscInt   *ind, *indz;
2030:   PetscInt         *indc, *indcz;
2031:   PetscBool         flg;

2033:   PetscFunctionBegin;
2034:   PetscCall(ISGetLocalSize(isy, &localsize));
2035:   PetscCallMPI(MPI_Scan(&localsize, &size, 1, MPIU_INT, MPI_SUM, PetscObjectComm((PetscObject)isy)));
2036:   size -= localsize;
2037:   while (ilink) {
2038:     IS isrl, isr;
2039:     PC subpc;
2040:     PetscCall(ISEmbed(ilink->is, isy, PETSC_TRUE, &isrl));
2041:     PetscCall(ISGetLocalSize(isrl, &localsize));
2042:     PetscCall(PetscMalloc1(localsize, &indc));
2043:     PetscCall(ISGetIndices(isrl, &ind));
2044:     PetscCall(PetscArraycpy(indc, ind, localsize));
2045:     PetscCall(ISRestoreIndices(isrl, &ind));
2046:     PetscCall(ISDestroy(&isrl));
2047:     for (i = 0; i < localsize; i++) *(indc + i) += size;
2048:     PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)isy), localsize, indc, PETSC_OWN_POINTER, &isr));
2049:     PetscCall(PetscObjectReference((PetscObject)isr));
2050:     PetscCall(ISDestroy(&ilink->is));
2051:     ilink->is = isr;
2052:     PetscCall(PetscObjectReference((PetscObject)isr));
2053:     PetscCall(ISDestroy(&ilink->is_col));
2054:     ilink->is_col = isr;
2055:     PetscCall(ISDestroy(&isr));
2056:     PetscCall(KSPGetPC(ilink->ksp, &subpc));
2057:     PetscCall(PetscObjectTypeCompare((PetscObject)subpc, PCFIELDSPLIT, &flg));
2058:     if (flg) {
2059:       IS       iszl, isz;
2060:       MPI_Comm comm;
2061:       PetscCall(ISGetLocalSize(ilink->is, &localsize));
2062:       comm = PetscObjectComm((PetscObject)ilink->is);
2063:       PetscCall(ISEmbed(isy, ilink->is, PETSC_TRUE, &iszl));
2064:       PetscCallMPI(MPI_Scan(&localsize, &sizez, 1, MPIU_INT, MPI_SUM, comm));
2065:       sizez -= localsize;
2066:       PetscCall(ISGetLocalSize(iszl, &localsize));
2067:       PetscCall(PetscMalloc1(localsize, &indcz));
2068:       PetscCall(ISGetIndices(iszl, &indz));
2069:       PetscCall(PetscArraycpy(indcz, indz, localsize));
2070:       PetscCall(ISRestoreIndices(iszl, &indz));
2071:       PetscCall(ISDestroy(&iszl));
2072:       for (i = 0; i < localsize; i++) *(indcz + i) += sizez;
2073:       PetscCall(ISCreateGeneral(comm, localsize, indcz, PETSC_OWN_POINTER, &isz));
2074:       PetscCall(PCFieldSplitRestrictIS(subpc, isz));
2075:       PetscCall(ISDestroy(&isz));
2076:     }
2077:     next  = ilink->next;
2078:     ilink = next;
2079:   }
2080:   jac->isrestrict = PETSC_TRUE;
2081:   PetscFunctionReturn(PETSC_SUCCESS);
2082: }

2084: static PetscErrorCode PCFieldSplitSetIS_FieldSplit(PC pc, const char splitname[], IS is)
2085: {
2086:   PC_FieldSplit    *jac = (PC_FieldSplit *)pc->data;
2087:   PC_FieldSplitLink ilink, next = jac->head;
2088:   char              prefix[128];
2089:   PetscLogEvent     nse;

2091:   PetscFunctionBegin;
2092:   if (jac->splitdefined) {
2093:     PetscCall(PetscInfo(pc, "Ignoring new split \"%s\" because the splits have already been defined\n", splitname));
2094:     PetscFunctionReturn(PETSC_SUCCESS);
2095:   }
2096:   PetscCall(PetscNew(&ilink));
2097:   if (splitname) {
2098:     PetscCall(PetscStrallocpy(splitname, &ilink->splitname));
2099:   } else {
2100:     PetscCall(PetscMalloc1(8, &ilink->splitname));
2101:     PetscCall(PetscSNPrintf(ilink->splitname, 7, "%" PetscInt_FMT, jac->nsplits));
2102:   }
2103:   PetscCall(PetscMPIIntCast(jac->nsplits, &nse));
2104:   ilink->event = jac->nsplits < 5 ? KSP_Solve_FS_0 + nse : KSP_Solve_FS_0 + 4; /* Splits greater than 4 logged in 4th split */
2105:   PetscCall(PetscObjectReference((PetscObject)is));
2106:   PetscCall(ISDestroy(&ilink->is));
2107:   ilink->is = is;
2108:   PetscCall(PetscObjectReference((PetscObject)is));
2109:   PetscCall(ISDestroy(&ilink->is_col));
2110:   ilink->is_col = is;
2111:   ilink->next   = NULL;
2112:   PetscCall(KSPCreate(PetscObjectComm((PetscObject)pc), &ilink->ksp));
2113:   PetscCall(KSPSetNestLevel(ilink->ksp, pc->kspnestlevel));
2114:   PetscCall(KSPSetErrorIfNotConverged(ilink->ksp, pc->erroriffailure));
2115:   PetscCall(PetscObjectIncrementTabLevel((PetscObject)ilink->ksp, (PetscObject)pc, 1));
2116:   PetscCall(KSPSetType(ilink->ksp, KSPPREONLY));

2118:   PetscCall(PetscSNPrintf(prefix, sizeof(prefix), "%sfieldsplit_%s_", ((PetscObject)pc)->prefix ? ((PetscObject)pc)->prefix : "", ilink->splitname));
2119:   PetscCall(KSPSetOptionsPrefix(ilink->ksp, prefix));

2121:   if (!next) {
2122:     jac->head       = ilink;
2123:     ilink->previous = NULL;
2124:   } else {
2125:     while (next->next) next = next->next;
2126:     next->next      = ilink;
2127:     ilink->previous = next;
2128:   }
2129:   jac->nsplits++;
2130:   PetscFunctionReturn(PETSC_SUCCESS);
2131: }

2133: /*@
2134:   PCFieldSplitSetFields - Sets the fields that define one particular split in `PCFIELDSPLIT`

2136:   Logically Collective

2138:   Input Parameters:
2139: + pc         - the preconditioner context
2140: . splitname  - name of this split, if `NULL` the number of the split is used
2141: . n          - the number of fields in this split
2142: . fields     - the fields in this split
2143: - fields_col - generally the same as `fields`, if it does not match `fields` then the submatrix that is solved for this set of fields comes from an off-diagonal block
2144:                of the matrix and `fields_col` provides the column indices for that block

2146:   Options Database Key:
2147: . -pc_fieldsplit_%d_fields <a,b,..> - indicates the fields to be used in the `%d`'th split

2149:   Level: intermediate

2151:   Notes:
2152:   Use `PCFieldSplitSetIS()` to set a  general set of indices as a split.

2154:   If the matrix used to construct the preconditioner is `MATNEST` then field i refers to the `is_row[i]` `IS` passed to `MatCreateNest()`.

2156:   If the matrix used to construct the preconditioner is not `MATNEST` then
2157:   `PCFieldSplitSetFields()` is for defining fields as strided blocks (based on the block size provided to the matrix with `MatSetBlockSize()` or
2158:   to the `PC` with `PCFieldSplitSetBlockSize()`). For example, if the block
2159:   size is three then one can define a split as 0, or 1 or 2 or 0,1 or 0,2 or 1,2 which mean
2160:   0xx3xx6xx9xx12 ... x1xx4xx7xx ... xx2xx5xx8xx.. 01x34x67x... 0x23x56x8.. x12x45x78x....
2161:   where the numbered entries indicate what is in the split.

2163:   This function is called once per split (it creates a new split each time).  Solve options
2164:   for this split will be available under the prefix `-fieldsplit_SPLITNAME_`.

2166:   `PCFieldSplitSetIS()` does not support having a `fields_col` different from `fields`

2168:   Developer Notes:
2169:   This routine does not actually create the `IS` representing the split, that is delayed
2170:   until `PCSetUp_FieldSplit()`, because information about the vector/matrix layouts may not be
2171:   available when this routine is called.

2173: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSetBlockSize()`, `PCFieldSplitSetIS()`, `PCFieldSplitRestrictIS()`,
2174:           `MatSetBlockSize()`, `MatCreateNest()`
2175: @*/
2176: PetscErrorCode PCFieldSplitSetFields(PC pc, const char splitname[], PetscInt n, const PetscInt fields[], const PetscInt fields_col[])
2177: {
2178:   PetscFunctionBegin;
2180:   PetscAssertPointer(splitname, 2);
2181:   PetscCheck(n >= 1, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_OUTOFRANGE, "Provided number of fields %" PetscInt_FMT " in split \"%s\" not positive", n, splitname);
2182:   PetscAssertPointer(fields, 4);
2183:   PetscTryMethod(pc, "PCFieldSplitSetFields_C", (PC, const char[], PetscInt, const PetscInt *, const PetscInt *), (pc, splitname, n, fields, fields_col));
2184:   PetscFunctionReturn(PETSC_SUCCESS);
2185: }

2187: /*@
2188:   PCFieldSplitSetDiagUseAmat - set flag indicating whether to extract diagonal blocks from Amat (rather than Pmat) to build
2189:   the sub-matrices associated with each split. Where `KSPSetOperators`(ksp,Amat,Pmat) was used to supply the operators.

2191:   Logically Collective

2193:   Input Parameters:
2194: + pc  - the preconditioner object
2195: - flg - boolean flag indicating whether or not to use Amat to extract the diagonal blocks from

2197:   Options Database Key:
2198: . -pc_fieldsplit_diag_use_amat - use the Amat to provide the diagonal blocks

2200:   Level: intermediate

2202: .seealso: [](sec_block_matrices), `PC`, `PCSetOperators()`, `KSPSetOperators()`, `PCFieldSplitGetDiagUseAmat()`, `PCFieldSplitSetOffDiagUseAmat()`, `PCFIELDSPLIT`
2203: @*/
2204: PetscErrorCode PCFieldSplitSetDiagUseAmat(PC pc, PetscBool flg)
2205: {
2206:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
2207:   PetscBool      isfs;

2209:   PetscFunctionBegin;
2211:   PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCFIELDSPLIT, &isfs));
2212:   PetscCheck(isfs, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "PC not of type %s", PCFIELDSPLIT);
2213:   jac->diag_use_amat = flg;
2214:   PetscFunctionReturn(PETSC_SUCCESS);
2215: }

2217: /*@
2218:   PCFieldSplitGetDiagUseAmat - get the flag indicating whether to extract diagonal blocks from Amat (rather than Pmat) to build
2219:   the sub-matrices associated with each split.  Where `KSPSetOperators`(ksp,Amat,Pmat) was used to supply the operators.

2221:   Logically Collective

2223:   Input Parameter:
2224: . pc - the preconditioner object

2226:   Output Parameter:
2227: . flg - boolean flag indicating whether or not to use Amat to extract the diagonal blocks from

2229:   Level: intermediate

2231: .seealso: [](sec_block_matrices), `PC`, `PCSetOperators()`, `KSPSetOperators()`, `PCFieldSplitSetDiagUseAmat()`, `PCFieldSplitGetOffDiagUseAmat()`, `PCFIELDSPLIT`
2232: @*/
2233: PetscErrorCode PCFieldSplitGetDiagUseAmat(PC pc, PetscBool *flg)
2234: {
2235:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
2236:   PetscBool      isfs;

2238:   PetscFunctionBegin;
2240:   PetscAssertPointer(flg, 2);
2241:   PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCFIELDSPLIT, &isfs));
2242:   PetscCheck(isfs, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "PC not of type %s", PCFIELDSPLIT);
2243:   *flg = jac->diag_use_amat;
2244:   PetscFunctionReturn(PETSC_SUCCESS);
2245: }

2247: /*@
2248:   PCFieldSplitSetOffDiagUseAmat - set flag indicating whether to extract off-diagonal blocks from Amat (rather than Pmat) to build
2249:   the sub-matrices associated with each split.  Where `KSPSetOperators`(ksp,Amat,Pmat) was used to supply the operators.

2251:   Logically Collective

2253:   Input Parameters:
2254: + pc  - the preconditioner object
2255: - flg - boolean flag indicating whether or not to use Amat to extract the off-diagonal blocks from

2257:   Options Database Key:
2258: . -pc_fieldsplit_off_diag_use_amat <bool> - use the Amat to extract the off-diagonal blocks

2260:   Level: intermediate

2262: .seealso: [](sec_block_matrices), `PC`, `PCSetOperators()`, `KSPSetOperators()`, `PCFieldSplitGetOffDiagUseAmat()`, `PCFieldSplitSetDiagUseAmat()`, `PCFIELDSPLIT`
2263: @*/
2264: PetscErrorCode PCFieldSplitSetOffDiagUseAmat(PC pc, PetscBool flg)
2265: {
2266:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
2267:   PetscBool      isfs;

2269:   PetscFunctionBegin;
2271:   PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCFIELDSPLIT, &isfs));
2272:   PetscCheck(isfs, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "PC not of type %s", PCFIELDSPLIT);
2273:   jac->offdiag_use_amat = flg;
2274:   PetscFunctionReturn(PETSC_SUCCESS);
2275: }

2277: /*@
2278:   PCFieldSplitGetOffDiagUseAmat - get the flag indicating whether to extract off-diagonal blocks from Amat (rather than Pmat) to build
2279:   the sub-matrices associated with each split.  Where `KSPSetOperators`(ksp,Amat,Pmat) was used to supply the operators.

2281:   Logically Collective

2283:   Input Parameter:
2284: . pc - the preconditioner object

2286:   Output Parameter:
2287: . flg - boolean flag indicating whether or not to use Amat to extract the off-diagonal blocks from

2289:   Level: intermediate

2291: .seealso: [](sec_block_matrices), `PC`, `PCSetOperators()`, `KSPSetOperators()`, `PCFieldSplitSetOffDiagUseAmat()`, `PCFieldSplitGetDiagUseAmat()`, `PCFIELDSPLIT`
2292: @*/
2293: PetscErrorCode PCFieldSplitGetOffDiagUseAmat(PC pc, PetscBool *flg)
2294: {
2295:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
2296:   PetscBool      isfs;

2298:   PetscFunctionBegin;
2300:   PetscAssertPointer(flg, 2);
2301:   PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCFIELDSPLIT, &isfs));
2302:   PetscCheck(isfs, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "PC not of type %s", PCFIELDSPLIT);
2303:   *flg = jac->offdiag_use_amat;
2304:   PetscFunctionReturn(PETSC_SUCCESS);
2305: }

2307: /*@
2308:   PCFieldSplitSetIS - Sets the exact elements for a split in a `PCFIELDSPLIT`

2310:   Logically Collective

2312:   Input Parameters:
2313: + pc        - the preconditioner context
2314: . splitname - name of this split, if `NULL` the number of the split is used
2315: - is        - the index set that defines the elements in this split

2317:   Level: intermediate

2319:   Notes:
2320:   Use `PCFieldSplitSetFields()`, for splits defined by strided `IS` based on the matrix block size or the `is_rows[]` passed into `MATNEST`

2322:   This function is called once per split (it creates a new split each time).  Solve options
2323:   for this split will be available under the prefix -fieldsplit_SPLITNAME_.

2325: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSetBlockSize()`, `PCFieldSplitSetFields()`
2326: @*/
2327: PetscErrorCode PCFieldSplitSetIS(PC pc, const char splitname[], IS is)
2328: {
2329:   PetscFunctionBegin;
2331:   if (splitname) PetscAssertPointer(splitname, 2);
2333:   PetscTryMethod(pc, "PCFieldSplitSetIS_C", (PC, const char[], IS), (pc, splitname, is));
2334:   PetscFunctionReturn(PETSC_SUCCESS);
2335: }

2337: /*@
2338:   PCFieldSplitGetIS - Retrieves the elements for a split as an `IS`

2340:   Logically Collective

2342:   Input Parameters:
2343: + pc        - the preconditioner context
2344: - splitname - name of this split

2346:   Output Parameter:
2347: . is - the index set that defines the elements in this split, or `NULL` if the split is not found

2349:   Level: intermediate

2351: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSetIS()`, `PCFieldSplitGetISByIndex()`
2352: @*/
2353: PetscErrorCode PCFieldSplitGetIS(PC pc, const char splitname[], IS *is)
2354: {
2355:   PetscFunctionBegin;
2357:   PetscAssertPointer(splitname, 2);
2358:   PetscAssertPointer(is, 3);
2359:   {
2360:     PC_FieldSplit    *jac   = (PC_FieldSplit *)pc->data;
2361:     PC_FieldSplitLink ilink = jac->head;
2362:     PetscBool         found;

2364:     *is = NULL;
2365:     while (ilink) {
2366:       PetscCall(PetscStrcmp(ilink->splitname, splitname, &found));
2367:       if (found) {
2368:         *is = ilink->is;
2369:         break;
2370:       }
2371:       ilink = ilink->next;
2372:     }
2373:   }
2374:   PetscFunctionReturn(PETSC_SUCCESS);
2375: }

2377: /*@
2378:   PCFieldSplitGetISByIndex - Retrieves the elements for a given split as an `IS`

2380:   Logically Collective

2382:   Input Parameters:
2383: + pc    - the preconditioner context
2384: - index - index of this split

2386:   Output Parameter:
2387: . is - the index set that defines the elements in this split

2389:   Level: intermediate

2391: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitGetIS()`, `PCFieldSplitSetIS()`,

2393: @*/
2394: PetscErrorCode PCFieldSplitGetISByIndex(PC pc, PetscInt index, IS *is)
2395: {
2396:   PetscFunctionBegin;
2397:   PetscCheck(index >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Negative field %" PetscInt_FMT " requested", index);
2399:   PetscAssertPointer(is, 3);
2400:   {
2401:     PC_FieldSplit    *jac   = (PC_FieldSplit *)pc->data;
2402:     PC_FieldSplitLink ilink = jac->head;
2403:     PetscInt          i     = 0;
2404:     PetscCheck(index < jac->nsplits, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Field %" PetscInt_FMT " requested but only %" PetscInt_FMT " exist", index, jac->nsplits);

2406:     while (i < index) {
2407:       ilink = ilink->next;
2408:       ++i;
2409:     }
2410:     PetscCall(PCFieldSplitGetIS(pc, ilink->splitname, is));
2411:   }
2412:   PetscFunctionReturn(PETSC_SUCCESS);
2413: }

2415: /*@
2416:   PCFieldSplitSetBlockSize - Sets the block size for defining where fields start in the
2417:   fieldsplit preconditioner when calling `PCFieldSplitSetFields()`. If not set the matrix block size is used.

2419:   Logically Collective

2421:   Input Parameters:
2422: + pc - the preconditioner context
2423: - bs - the block size

2425:   Level: intermediate

2427:   Note:
2428:   If the matrix is a `MATNEST` then the `is_rows[]` passed to `MatCreateNest()` determines the fields.

2430: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSetIS()`
2431: @*/
2432: PetscErrorCode PCFieldSplitSetBlockSize(PC pc, PetscInt bs)
2433: {
2434:   PetscFunctionBegin;
2437:   PetscTryMethod(pc, "PCFieldSplitSetBlockSize_C", (PC, PetscInt), (pc, bs));
2438:   PetscFunctionReturn(PETSC_SUCCESS);
2439: }

2441: /*@C
2442:   PCFieldSplitGetSubKSP - Gets the `KSP` contexts for all splits

2444:   Collective

2446:   Input Parameter:
2447: . pc - the preconditioner context

2449:   Output Parameters:
2450: + n      - the number of splits
2451: - subksp - the array of `KSP` contexts

2453:   Level: advanced

2455:   Notes:
2456:   After `PCFieldSplitGetSubKSP()` the array of `KSP`s is to be freed by the user with `PetscFree()`
2457:   (not the `KSP`, just the array that contains them).

2459:   You must call `PCSetUp()` before calling `PCFieldSplitGetSubKSP()`.

2461:   If the fieldsplit is of type `PC_COMPOSITE_SCHUR`, it returns the `KSP` object used inside the
2462:   Schur complement and the `KSP` object used to iterate over the Schur complement.
2463:   To access all the `KSP` objects used in `PC_COMPOSITE_SCHUR`, use `PCFieldSplitSchurGetSubKSP()`.

2465:   If the fieldsplit is of type `PC_COMPOSITE_GKB`, it returns the `KSP` object used to solve the
2466:   inner linear system defined by the matrix H in each loop.

2468:   Fortran Note:
2469:   Call `PCFieldSplitRestoreSubKSP()` when the array of `KSP` is no longer needed

2471:   Developer Notes:
2472:   There should be a `PCFieldSplitRestoreSubKSP()` instead of requiring the user to call `PetscFree()`

2474: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSetIS()`, `PCFieldSplitSchurGetSubKSP()`
2475: @*/
2476: PetscErrorCode PCFieldSplitGetSubKSP(PC pc, PetscInt *n, KSP *subksp[])
2477: {
2478:   PetscFunctionBegin;
2480:   if (n) PetscAssertPointer(n, 2);
2481:   PetscUseMethod(pc, "PCFieldSplitGetSubKSP_C", (PC, PetscInt *, KSP **), (pc, n, subksp));
2482:   PetscFunctionReturn(PETSC_SUCCESS);
2483: }

2485: /*@C
2486:   PCFieldSplitSchurGetSubKSP - Gets the `KSP` contexts used inside the Schur complement based `PCFIELDSPLIT`

2488:   Collective

2490:   Input Parameter:
2491: . pc - the preconditioner context

2493:   Output Parameters:
2494: + n      - the number of splits
2495: - subksp - the array of `KSP` contexts

2497:   Level: advanced

2499:   Notes:
2500:   After `PCFieldSplitSchurGetSubKSP()` the array of `KSP`s is to be freed by the user with `PetscFree()`
2501:   (not the `KSP` just the array that contains them).

2503:   You must call `PCSetUp()` before calling `PCFieldSplitSchurGetSubKSP()`.

2505:   If the fieldsplit type is of type `PC_COMPOSITE_SCHUR`, it returns (in order)
2506: +  1  - the `KSP` used for the (1,1) block
2507: .  2  - the `KSP` used for the Schur complement (not the one used for the interior Schur solver)
2508: -  3  - the `KSP` used for the (1,1) block in the upper triangular factor (if different from that of the (1,1) block).

2510:   It returns a null array if the fieldsplit is not of type `PC_COMPOSITE_SCHUR`; in this case, you should use `PCFieldSplitGetSubKSP()`.

2512:   Fortran Note:
2513:   Call `PCFieldSplitSchurRestoreSubKSP()` when the array of `KSP` is no longer needed

2515:   Developer Notes:
2516:   There should be a `PCFieldSplitRestoreSubKSP()` instead of requiring the user to call `PetscFree()`

2518:   Should the functionality of `PCFieldSplitSchurGetSubKSP()` and `PCFieldSplitGetSubKSP()` be merged?

2520: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSetIS()`, `PCFieldSplitGetSubKSP()`
2521: @*/
2522: PetscErrorCode PCFieldSplitSchurGetSubKSP(PC pc, PetscInt *n, KSP *subksp[])
2523: {
2524:   PetscFunctionBegin;
2526:   if (n) PetscAssertPointer(n, 2);
2527:   PetscUseMethod(pc, "PCFieldSplitSchurGetSubKSP_C", (PC, PetscInt *, KSP **), (pc, n, subksp));
2528:   PetscFunctionReturn(PETSC_SUCCESS);
2529: }

2531: /*@
2532:   PCFieldSplitSetSchurPre -  Indicates from what operator the preconditioner is constructed for the Schur complement.
2533:   The default is the A11 matrix.

2535:   Collective

2537:   Input Parameters:
2538: + pc    - the preconditioner context
2539: . ptype - which matrix to use for preconditioning the Schur complement: `PC_FIELDSPLIT_SCHUR_PRE_A11` (default),
2540:               `PC_FIELDSPLIT_SCHUR_PRE_SELF`, `PC_FIELDSPLIT_SCHUR_PRE_USER`,
2541:               `PC_FIELDSPLIT_SCHUR_PRE_SELFP`, and `PC_FIELDSPLIT_SCHUR_PRE_FULL`
2542: - pre   - matrix to use for preconditioning, or `NULL`

2544:   Options Database Keys:
2545: + -pc_fieldsplit_schur_precondition <self,selfp,user,a11,full> - default is `a11`. See notes for meaning of various arguments
2546: - -fieldsplit_1_pc_type <pctype>                               - the preconditioner algorithm that is used to construct the preconditioner from the operator

2548:   Level: intermediate

2550:   Notes:
2551:   If ptype is
2552: +     a11 - the preconditioner for the Schur complement is generated from the block diagonal part of the preconditioner
2553:   matrix associated with the Schur complement (i.e. A11), not the Schur complement matrix
2554: .     self - the preconditioner for the Schur complement is generated from the symbolic representation of the Schur complement matrix:
2555:   The only preconditioners that currently work with this symbolic representation matrix object are `PCLSC` and `PCHPDDM`
2556: .     user - the preconditioner for the Schur complement is generated from the user provided matrix (pre argument
2557:   to this function).
2558: .     selfp - the preconditioning for the Schur complement is generated from an explicitly-assembled approximation $ Sp = A11 - A10 inv(diag(A00)) A01 $
2559:   This is only a good preconditioner when diag(A00) is a good preconditioner for A00. Optionally, A00 can be
2560:   lumped before extracting the diagonal using the additional option `-fieldsplit_1_mat_schur_complement_ainv_type lump`
2561: -     full - the preconditioner for the Schur complement is generated from the exact Schur complement matrix representation
2562:   computed internally by `PCFIELDSPLIT` (this is expensive)
2563:   useful mostly as a test that the Schur complement approach can work for your problem

2565:   When solving a saddle point problem, where the A11 block is identically zero, using `a11` as the ptype only makes sense
2566:   with the additional option `-fieldsplit_1_pc_type none`. Usually for saddle point problems one would use a `ptype` of `self` and
2567:   `-fieldsplit_1_pc_type lsc` which uses the least squares commutator to compute a preconditioner for the Schur complement.

2569:   Developer Note:
2570:   The name of this function and the option `-pc_fieldsplit_schur_precondition` are inconsistent; precondition should be used everywhere.

2572: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSchurPre()`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSchurPreType`,
2573:           `MatSchurComplementSetAinvType()`, `PCLSC`, `PCFieldSplitSetSchurFactType()`
2574: @*/
2575: PetscErrorCode PCFieldSplitSetSchurPre(PC pc, PCFieldSplitSchurPreType ptype, Mat pre)
2576: {
2577:   PetscFunctionBegin;
2579:   PetscTryMethod(pc, "PCFieldSplitSetSchurPre_C", (PC, PCFieldSplitSchurPreType, Mat), (pc, ptype, pre));
2580:   PetscFunctionReturn(PETSC_SUCCESS);
2581: }

2583: PetscErrorCode PCFieldSplitSchurPrecondition(PC pc, PCFieldSplitSchurPreType ptype, Mat pre)
2584: {
2585:   return PCFieldSplitSetSchurPre(pc, ptype, pre);
2586: } /* Deprecated name */

2588: /*@
2589:   PCFieldSplitGetSchurPre - For Schur complement fieldsplit, determine how the Schur complement will be
2590:   preconditioned.  See `PCFieldSplitSetSchurPre()` for details.

2592:   Logically Collective

2594:   Input Parameter:
2595: . pc - the preconditioner context

2597:   Output Parameters:
2598: + ptype - which matrix to use for preconditioning the Schur complement: `PC_FIELDSPLIT_SCHUR_PRE_A11`, `PC_FIELDSPLIT_SCHUR_PRE_SELF`, `PC_FIELDSPLIT_SCHUR_PRE_USER`
2599: - pre   - matrix to use for preconditioning (with `PC_FIELDSPLIT_SCHUR_PRE_USER`), or `NULL`

2601:   Level: intermediate

2603: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitSetSchurPre()`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSchurPreType`, `PCLSC`
2604: @*/
2605: PetscErrorCode PCFieldSplitGetSchurPre(PC pc, PCFieldSplitSchurPreType *ptype, Mat *pre)
2606: {
2607:   PetscFunctionBegin;
2609:   PetscUseMethod(pc, "PCFieldSplitGetSchurPre_C", (PC, PCFieldSplitSchurPreType *, Mat *), (pc, ptype, pre));
2610:   PetscFunctionReturn(PETSC_SUCCESS);
2611: }

2613: /*@
2614:   PCFieldSplitSchurGetS -  extract the `MATSCHURCOMPLEMENT` object used by this `PCFIELDSPLIT` in case it needs to be configured separately

2616:   Not Collective

2618:   Input Parameter:
2619: . pc - the preconditioner context

2621:   Output Parameter:
2622: . S - the Schur complement matrix

2624:   Level: advanced

2626:   Note:
2627:   This matrix should not be destroyed using `MatDestroy()`; rather, use `PCFieldSplitSchurRestoreS()`.

2629: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSchurPreType`, `PCFieldSplitSetSchurPre()`, `MATSCHURCOMPLEMENT`, `PCFieldSplitSchurRestoreS()`,
2630:           `MatCreateSchurComplement()`, `MatSchurComplementGetKSP()`, `MatSchurComplementComputeExplicitOperator()`, `MatGetSchurComplement()`
2631: @*/
2632: PetscErrorCode PCFieldSplitSchurGetS(PC pc, Mat *S)
2633: {
2634:   const char    *t;
2635:   PetscBool      isfs;
2636:   PC_FieldSplit *jac;

2638:   PetscFunctionBegin;
2640:   PetscCall(PetscObjectGetType((PetscObject)pc, &t));
2641:   PetscCall(PetscStrcmp(t, PCFIELDSPLIT, &isfs));
2642:   PetscCheck(isfs, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Expected PC of type PCFIELDSPLIT, got %s instead", t);
2643:   jac = (PC_FieldSplit *)pc->data;
2644:   PetscCheck(jac->type == PC_COMPOSITE_SCHUR, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Expected PCFIELDSPLIT of type SCHUR, got %d instead", jac->type);
2645:   if (S) *S = jac->schur;
2646:   PetscFunctionReturn(PETSC_SUCCESS);
2647: }

2649: /*@
2650:   PCFieldSplitSchurRestoreS -  returns the `MATSCHURCOMPLEMENT` matrix used by this `PC`

2652:   Not Collective

2654:   Input Parameters:
2655: + pc - the preconditioner context
2656: - S  - the Schur complement matrix

2658:   Level: advanced

2660: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSchurPreType`, `PCFieldSplitSetSchurPre()`, `MatSchurComplement`, `PCFieldSplitSchurGetS()`
2661: @*/
2662: PetscErrorCode PCFieldSplitSchurRestoreS(PC pc, Mat *S)
2663: {
2664:   const char    *t;
2665:   PetscBool      isfs;
2666:   PC_FieldSplit *jac;

2668:   PetscFunctionBegin;
2670:   PetscCall(PetscObjectGetType((PetscObject)pc, &t));
2671:   PetscCall(PetscStrcmp(t, PCFIELDSPLIT, &isfs));
2672:   PetscCheck(isfs, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Expected PC of type PCFIELDSPLIT, got %s instead", t);
2673:   jac = (PC_FieldSplit *)pc->data;
2674:   PetscCheck(jac->type == PC_COMPOSITE_SCHUR, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Expected PCFIELDSPLIT of type SCHUR, got %d instead", jac->type);
2675:   PetscCheck(S && (*S == jac->schur), PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "MatSchurComplement restored is not the same as gotten");
2676:   PetscFunctionReturn(PETSC_SUCCESS);
2677: }

2679: static PetscErrorCode PCFieldSplitSetSchurPre_FieldSplit(PC pc, PCFieldSplitSchurPreType ptype, Mat pre)
2680: {
2681:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

2683:   PetscFunctionBegin;
2684:   jac->schurpre = ptype;
2685:   if (ptype == PC_FIELDSPLIT_SCHUR_PRE_USER && pre) {
2686:     PetscCall(MatDestroy(&jac->schur_user));
2687:     jac->schur_user = pre;
2688:     PetscCall(PetscObjectReference((PetscObject)jac->schur_user));
2689:   }
2690:   PetscFunctionReturn(PETSC_SUCCESS);
2691: }

2693: static PetscErrorCode PCFieldSplitGetSchurPre_FieldSplit(PC pc, PCFieldSplitSchurPreType *ptype, Mat *pre)
2694: {
2695:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

2697:   PetscFunctionBegin;
2698:   if (ptype) *ptype = jac->schurpre;
2699:   if (pre) *pre = jac->schur_user;
2700:   PetscFunctionReturn(PETSC_SUCCESS);
2701: }

2703: /*@
2704:   PCFieldSplitSetSchurFactType -  sets which blocks of the approximate block factorization to retain in the preconditioner {cite}`murphy2000note` and {cite}`ipsen2001note`

2706:   Collective

2708:   Input Parameters:
2709: + pc    - the preconditioner context
2710: - ftype - which blocks of factorization to retain, `PC_FIELDSPLIT_SCHUR_FACT_FULL` is default

2712:   Options Database Key:
2713: . -pc_fieldsplit_schur_fact_type <diag,lower,upper,full> - default is `full`

2715:   Level: intermediate

2717:   Notes:
2718:   The `full` factorization is

2720:   ```{math}
2721:   \left(\begin{array}{cc} A & B \\
2722:   C & E \\
2723:   \end{array}\right) =
2724:   \left(\begin{array}{cc} I & 0 \\
2725:   C A^{-1} & I \\
2726:   \end{array}\right)
2727:   \left(\begin{array}{cc} A & 0 \\
2728:   0 & S \\
2729:   \end{array}\right)
2730:   \left(\begin{array}{cc} I & A^{-1}B \\
2731:   0 & I \\
2732:   \end{array}\right) = L D U,
2733:   ```

2735:   where $ S = E - C A^{-1} B $. In practice, the full factorization is applied via block triangular solves with the grouping $L(DU)$. `upper` uses $DU$, `lower` uses $LD$,
2736:   and `diag` is the diagonal part with the sign of $S$ flipped (because this makes the preconditioner positive definite for many formulations,
2737:   thus allowing the use of `KSPMINRES)`. Sign flipping of $S$ can be turned off with `PCFieldSplitSetSchurScale()`.

2739:   If $A$ and $S$ are solved exactly
2740: +  1 - `full` factorization is a direct solver.
2741: .  2 - The preconditioned operator with `lower` or `upper` has all eigenvalues equal to 1 and minimal polynomial of degree 2, so `KSPGMRES` converges in 2 iterations.
2742: -  3 - With `diag`, the preconditioned operator has three distinct nonzero eigenvalues and minimal polynomial of degree at most 4, so `KSPGMRES` converges in at most 4 iterations.

2744:   If the iteration count is very low, consider using `KSPFGMRES` or `KSPGCR` which can use one less preconditioner
2745:   application in this case. Note that the preconditioned operator may be highly non-normal, so such fast convergence may not be observed in practice.

2747:   For symmetric problems in which $A$ is positive definite and $S$ is negative definite, `diag` can be used with `KSPMINRES`.

2749:   A flexible method like `KSPFGMRES` or `KSPGCR`, [](sec_flexibleksp), must be used if the fieldsplit preconditioner is nonlinear (e.g., a few iterations of a Krylov method is used to solve with $A$ or $S$).

2751: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSchurPreType`, `PCFieldSplitSetSchurScale()`,
2752:           [](sec_flexibleksp), `PCFieldSplitSetSchurPre()`
2753: @*/
2754: PetscErrorCode PCFieldSplitSetSchurFactType(PC pc, PCFieldSplitSchurFactType ftype)
2755: {
2756:   PetscFunctionBegin;
2758:   PetscTryMethod(pc, "PCFieldSplitSetSchurFactType_C", (PC, PCFieldSplitSchurFactType), (pc, ftype));
2759:   PetscFunctionReturn(PETSC_SUCCESS);
2760: }

2762: static PetscErrorCode PCFieldSplitSetSchurFactType_FieldSplit(PC pc, PCFieldSplitSchurFactType ftype)
2763: {
2764:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

2766:   PetscFunctionBegin;
2767:   jac->schurfactorization = ftype;
2768:   PetscFunctionReturn(PETSC_SUCCESS);
2769: }

2771: /*@
2772:   PCFieldSplitSetSchurScale -  Controls the sign flip of S for `PC_FIELDSPLIT_SCHUR_FACT_DIAG`.

2774:   Collective

2776:   Input Parameters:
2777: + pc    - the preconditioner context
2778: - scale - scaling factor for the Schur complement

2780:   Options Database Key:
2781: . -pc_fieldsplit_schur_scale <scale> - default is -1.0

2783:   Level: intermediate

2785: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSchurFactType`, `PCFieldSplitSetSchurFactType()`
2786: @*/
2787: PetscErrorCode PCFieldSplitSetSchurScale(PC pc, PetscScalar scale)
2788: {
2789:   PetscFunctionBegin;
2792:   PetscTryMethod(pc, "PCFieldSplitSetSchurScale_C", (PC, PetscScalar), (pc, scale));
2793:   PetscFunctionReturn(PETSC_SUCCESS);
2794: }

2796: static PetscErrorCode PCFieldSplitSetSchurScale_FieldSplit(PC pc, PetscScalar scale)
2797: {
2798:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

2800:   PetscFunctionBegin;
2801:   jac->schurscale = scale;
2802:   PetscFunctionReturn(PETSC_SUCCESS);
2803: }

2805: /*@C
2806:   PCFieldSplitGetSchurBlocks - Gets all matrix blocks for the Schur complement

2808:   Collective

2810:   Input Parameter:
2811: . pc - the preconditioner context

2813:   Output Parameters:
2814: + A00 - the (0,0) block
2815: . A01 - the (0,1) block
2816: . A10 - the (1,0) block
2817: - A11 - the (1,1) block

2819:   Level: advanced

2821:   Note:
2822:   Use `NULL` for any unneeded output arguments

2824: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `MatSchurComplementGetSubMatrices()`, `MatSchurComplementSetSubMatrices()`
2825: @*/
2826: PetscErrorCode PCFieldSplitGetSchurBlocks(PC pc, Mat *A00, Mat *A01, Mat *A10, Mat *A11)
2827: {
2828:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

2830:   PetscFunctionBegin;
2832:   PetscCheck(jac->type == PC_COMPOSITE_SCHUR, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONG, "FieldSplit is not using a Schur complement approach.");
2833:   if (A00) *A00 = jac->pmat[0];
2834:   if (A01) *A01 = jac->B;
2835:   if (A10) *A10 = jac->C;
2836:   if (A11) *A11 = jac->pmat[1];
2837:   PetscFunctionReturn(PETSC_SUCCESS);
2838: }

2840: /*@
2841:   PCFieldSplitSetGKBTol -  Sets the solver tolerance for the generalized Golub-Kahan bidiagonalization preconditioner {cite}`arioli2013` in `PCFIELDSPLIT`

2843:   Collective

2845:   Input Parameters:
2846: + pc        - the preconditioner context
2847: - tolerance - the solver tolerance

2849:   Options Database Key:
2850: . -pc_fieldsplit_gkb_tol <tolerance> - default is 1e-5

2852:   Level: intermediate

2854:   Note:
2855:   The generalized GKB algorithm {cite}`arioli2013` uses a lower bound estimate of the error in energy norm as stopping criterion.
2856:   It stops once the lower bound estimate undershoots the required solver tolerance. Although the actual error might be bigger than
2857:   this estimate, the stopping criterion is satisfactory in practical cases.

2859: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetGKBDelay()`, `PCFieldSplitSetGKBNu()`, `PCFieldSplitSetGKBMaxit()`
2860: @*/
2861: PetscErrorCode PCFieldSplitSetGKBTol(PC pc, PetscReal tolerance)
2862: {
2863:   PetscFunctionBegin;
2866:   PetscTryMethod(pc, "PCFieldSplitSetGKBTol_C", (PC, PetscReal), (pc, tolerance));
2867:   PetscFunctionReturn(PETSC_SUCCESS);
2868: }

2870: static PetscErrorCode PCFieldSplitSetGKBTol_FieldSplit(PC pc, PetscReal tolerance)
2871: {
2872:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

2874:   PetscFunctionBegin;
2875:   jac->gkbtol = tolerance;
2876:   PetscFunctionReturn(PETSC_SUCCESS);
2877: }

2879: /*@
2880:   PCFieldSplitSetGKBMaxit -  Sets the maximum number of iterations for the generalized Golub-Kahan bidiagonalization preconditioner {cite}`arioli2013` in `PCFIELDSPLIT`

2882:   Collective

2884:   Input Parameters:
2885: + pc    - the preconditioner context
2886: - maxit - the maximum number of iterations

2888:   Options Database Key:
2889: . -pc_fieldsplit_gkb_maxit <maxit> - default is 100

2891:   Level: intermediate

2893: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetGKBDelay()`, `PCFieldSplitSetGKBTol()`, `PCFieldSplitSetGKBNu()`
2894: @*/
2895: PetscErrorCode PCFieldSplitSetGKBMaxit(PC pc, PetscInt maxit)
2896: {
2897:   PetscFunctionBegin;
2900:   PetscTryMethod(pc, "PCFieldSplitSetGKBMaxit_C", (PC, PetscInt), (pc, maxit));
2901:   PetscFunctionReturn(PETSC_SUCCESS);
2902: }

2904: static PetscErrorCode PCFieldSplitSetGKBMaxit_FieldSplit(PC pc, PetscInt maxit)
2905: {
2906:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

2908:   PetscFunctionBegin;
2909:   jac->gkbmaxit = maxit;
2910:   PetscFunctionReturn(PETSC_SUCCESS);
2911: }

2913: /*@
2914:   PCFieldSplitSetGKBDelay -  Sets the delay in the lower bound error estimate in the generalized Golub-Kahan bidiagonalization {cite}`arioli2013` in `PCFIELDSPLIT`
2915:   preconditioner.

2917:   Collective

2919:   Input Parameters:
2920: + pc    - the preconditioner context
2921: - delay - the delay window in the lower bound estimate

2923:   Options Database Key:
2924: . -pc_fieldsplit_gkb_delay <delay> - default is 5

2926:   Level: intermediate

2928:   Notes:
2929:   The algorithm uses a lower bound estimate of the error in energy norm as stopping criterion. The lower bound of the error $ ||u-u^k||_H $
2930:   is expressed as a truncated sum. The error at iteration k can only be measured at iteration (k + `delay`), and thus the algorithm needs
2931:   at least (`delay` + 1) iterations to stop.

2933:   For more details on the generalized Golub-Kahan bidiagonalization method and its lower bound stopping criterion, please refer to {cite}`arioli2013`

2935: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetGKBNu()`, `PCFieldSplitSetGKBTol()`, `PCFieldSplitSetGKBMaxit()`
2936: @*/
2937: PetscErrorCode PCFieldSplitSetGKBDelay(PC pc, PetscInt delay)
2938: {
2939:   PetscFunctionBegin;
2942:   PetscTryMethod(pc, "PCFieldSplitSetGKBDelay_C", (PC, PetscInt), (pc, delay));
2943:   PetscFunctionReturn(PETSC_SUCCESS);
2944: }

2946: static PetscErrorCode PCFieldSplitSetGKBDelay_FieldSplit(PC pc, PetscInt delay)
2947: {
2948:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

2950:   PetscFunctionBegin;
2951:   jac->gkbdelay = delay;
2952:   PetscFunctionReturn(PETSC_SUCCESS);
2953: }

2955: /*@
2956:   PCFieldSplitSetGKBNu -  Sets the scalar value nu >= 0 in the transformation H = A00 + nu*A01*A01' of the (1,1) block in the
2957:   Golub-Kahan bidiagonalization preconditioner {cite}`arioli2013` in `PCFIELDSPLIT`

2959:   Collective

2961:   Input Parameters:
2962: + pc - the preconditioner context
2963: - nu - the shift parameter

2965:   Options Database Key:
2966: . -pc_fieldsplit_gkb_nu <nu> - default is 1

2968:   Level: intermediate

2970:   Notes:
2971:   This shift is in general done to obtain better convergence properties for the outer loop of the algorithm. This is often achieved by choosing `nu` sufficiently large. However,
2972:   if `nu` is chosen too large, the matrix H might be badly conditioned and the solution of the linear system $Hx = b$ in the inner loop becomes difficult. It is therefore
2973:   necessary to find a good balance in between the convergence of the inner and outer loop.

2975:   For `nu` = 0, no shift is done. In this case A00 has to be positive definite. The matrix N in {cite}`arioli2013` is then chosen as identity.

2977: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetGKBDelay()`, `PCFieldSplitSetGKBTol()`, `PCFieldSplitSetGKBMaxit()`
2978: @*/
2979: PetscErrorCode PCFieldSplitSetGKBNu(PC pc, PetscReal nu)
2980: {
2981:   PetscFunctionBegin;
2984:   PetscTryMethod(pc, "PCFieldSplitSetGKBNu_C", (PC, PetscReal), (pc, nu));
2985:   PetscFunctionReturn(PETSC_SUCCESS);
2986: }

2988: static PetscErrorCode PCFieldSplitSetGKBNu_FieldSplit(PC pc, PetscReal nu)
2989: {
2990:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

2992:   PetscFunctionBegin;
2993:   jac->gkbnu = nu;
2994:   PetscFunctionReturn(PETSC_SUCCESS);
2995: }

2997: static PetscErrorCode PCFieldSplitSetType_FieldSplit(PC pc, PCCompositeType type)
2998: {
2999:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

3001:   PetscFunctionBegin;
3002:   jac->type = type;
3003:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSubKSP_C", NULL));
3004:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurPre_C", NULL));
3005:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSchurPre_C", NULL));
3006:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurFactType_C", NULL));
3007:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurScale_C", NULL));
3008:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBTol_C", NULL));
3009:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBMaxit_C", NULL));
3010:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBNu_C", NULL));
3011:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBDelay_C", NULL));

3013:   if (type == PC_COMPOSITE_SCHUR) {
3014:     pc->ops->apply          = PCApply_FieldSplit_Schur;
3015:     pc->ops->applytranspose = PCApplyTranspose_FieldSplit_Schur;
3016:     pc->ops->view           = PCView_FieldSplit_Schur;
3017:     pc->ops->setuponblocks  = PCSetUpOnBlocks_FieldSplit_Schur;

3019:     PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSubKSP_C", PCFieldSplitGetSubKSP_FieldSplit_Schur));
3020:     PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurPre_C", PCFieldSplitSetSchurPre_FieldSplit));
3021:     PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSchurPre_C", PCFieldSplitGetSchurPre_FieldSplit));
3022:     PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurFactType_C", PCFieldSplitSetSchurFactType_FieldSplit));
3023:     PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurScale_C", PCFieldSplitSetSchurScale_FieldSplit));
3024:   } else if (type == PC_COMPOSITE_GKB) {
3025:     pc->ops->apply          = PCApply_FieldSplit_GKB;
3026:     pc->ops->applytranspose = NULL;
3027:     pc->ops->view           = PCView_FieldSplit_GKB;
3028:     pc->ops->setuponblocks  = PCSetUpOnBlocks_FieldSplit_GKB;

3030:     PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSubKSP_C", PCFieldSplitGetSubKSP_FieldSplit));
3031:     PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBTol_C", PCFieldSplitSetGKBTol_FieldSplit));
3032:     PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBMaxit_C", PCFieldSplitSetGKBMaxit_FieldSplit));
3033:     PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBNu_C", PCFieldSplitSetGKBNu_FieldSplit));
3034:     PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBDelay_C", PCFieldSplitSetGKBDelay_FieldSplit));
3035:   } else {
3036:     pc->ops->apply          = PCApply_FieldSplit;
3037:     pc->ops->applytranspose = PCApplyTranspose_FieldSplit;
3038:     pc->ops->view           = PCView_FieldSplit;
3039:     pc->ops->setuponblocks  = PCSetUpOnBlocks_FieldSplit;

3041:     PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSubKSP_C", PCFieldSplitGetSubKSP_FieldSplit));
3042:   }
3043:   PetscFunctionReturn(PETSC_SUCCESS);
3044: }

3046: static PetscErrorCode PCFieldSplitSetBlockSize_FieldSplit(PC pc, PetscInt bs)
3047: {
3048:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

3050:   PetscFunctionBegin;
3051:   PetscCheck(bs >= 1, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_OUTOFRANGE, "Blocksize must be positive, you gave %" PetscInt_FMT, bs);
3052:   PetscCheck(jac->bs <= 0 || jac->bs == bs, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONGSTATE, "Cannot change fieldsplit blocksize from %" PetscInt_FMT " to %" PetscInt_FMT " after it has been set", jac->bs, bs);
3053:   jac->bs = bs;
3054:   PetscFunctionReturn(PETSC_SUCCESS);
3055: }

3057: static PetscErrorCode PCSetCoordinates_FieldSplit(PC pc, PetscInt dim, PetscInt nloc, PetscReal coords[])
3058: {
3059:   PC_FieldSplit    *jac           = (PC_FieldSplit *)pc->data;
3060:   PC_FieldSplitLink ilink_current = jac->head;
3061:   IS                is_owned;

3063:   PetscFunctionBegin;
3064:   jac->coordinates_set = PETSC_TRUE; // Internal flag
3065:   PetscCall(MatGetOwnershipIS(pc->mat, &is_owned, NULL));

3067:   while (ilink_current) {
3068:     // For each IS, embed it to get local coords indces
3069:     IS              is_coords;
3070:     PetscInt        ndofs_block;
3071:     const PetscInt *block_dofs_enumeration; // Numbering of the dofs relevant to the current block

3073:     // Setting drop to true for safety. It should make no difference.
3074:     PetscCall(ISEmbed(ilink_current->is, is_owned, PETSC_TRUE, &is_coords));
3075:     PetscCall(ISGetLocalSize(is_coords, &ndofs_block));
3076:     PetscCall(ISGetIndices(is_coords, &block_dofs_enumeration));

3078:     // Allocate coordinates vector and set it directly
3079:     PetscCall(PetscMalloc1(ndofs_block * dim, &ilink_current->coords));
3080:     for (PetscInt dof = 0; dof < ndofs_block; ++dof) {
3081:       for (PetscInt d = 0; d < dim; ++d) (ilink_current->coords)[dim * dof + d] = coords[dim * block_dofs_enumeration[dof] + d];
3082:     }
3083:     ilink_current->dim   = dim;
3084:     ilink_current->ndofs = ndofs_block;
3085:     PetscCall(ISRestoreIndices(is_coords, &block_dofs_enumeration));
3086:     PetscCall(ISDestroy(&is_coords));
3087:     ilink_current = ilink_current->next;
3088:   }
3089:   PetscCall(ISDestroy(&is_owned));
3090:   PetscFunctionReturn(PETSC_SUCCESS);
3091: }

3093: /*@
3094:   PCFieldSplitSetType - Sets the type, `PCCompositeType`, of a `PCFIELDSPLIT`

3096:   Collective

3098:   Input Parameters:
3099: + pc   - the preconditioner context
3100: - type - `PC_COMPOSITE_ADDITIVE`, `PC_COMPOSITE_MULTIPLICATIVE` (default), `PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE`, `PC_COMPOSITE_SPECIAL`, `PC_COMPOSITE_SCHUR`,
3101:          `PC_COMPOSITE_GKB`

3103:   Options Database Key:
3104: . -pc_fieldsplit_type <one of multiplicative, additive, symmetric_multiplicative, special, schur> - Sets fieldsplit preconditioner type

3106:   Level: intermediate

3108: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCCompositeType`, `PCCompositeGetType()`, `PC_COMPOSITE_ADDITIVE`, `PC_COMPOSITE_MULTIPLICATIVE`,
3109:           `PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE`, `PC_COMPOSITE_SPECIAL`, `PC_COMPOSITE_SCHUR`, `PCFieldSplitSetSchurFactType()`
3110: @*/
3111: PetscErrorCode PCFieldSplitSetType(PC pc, PCCompositeType type)
3112: {
3113:   PetscFunctionBegin;
3115:   PetscTryMethod(pc, "PCFieldSplitSetType_C", (PC, PCCompositeType), (pc, type));
3116:   PetscFunctionReturn(PETSC_SUCCESS);
3117: }

3119: /*@
3120:   PCFieldSplitGetType - Gets the type, `PCCompositeType`, of a `PCFIELDSPLIT`

3122:   Not collective

3124:   Input Parameter:
3125: . pc - the preconditioner context

3127:   Output Parameter:
3128: . type - `PC_COMPOSITE_ADDITIVE`, `PC_COMPOSITE_MULTIPLICATIVE` (default), `PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE`, `PC_COMPOSITE_SPECIAL`, `PC_COMPOSITE_SCHUR`

3130:   Level: intermediate

3132: .seealso: [](sec_block_matrices), `PC`, `PCCompositeSetType()`, `PCFIELDSPLIT`, `PCCompositeType`, `PC_COMPOSITE_ADDITIVE`, `PC_COMPOSITE_MULTIPLICATIVE`,
3133:           `PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE`, `PC_COMPOSITE_SPECIAL`, `PC_COMPOSITE_SCHUR`
3134: @*/
3135: PetscErrorCode PCFieldSplitGetType(PC pc, PCCompositeType *type)
3136: {
3137:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

3139:   PetscFunctionBegin;
3141:   PetscAssertPointer(type, 2);
3142:   *type = jac->type;
3143:   PetscFunctionReturn(PETSC_SUCCESS);
3144: }

3146: /*@
3147:   PCFieldSplitSetDMSplits - Flags whether `DMCreateFieldDecomposition()` should be used to define the splits in a `PCFIELDSPLIT`, whenever possible.

3149:   Logically Collective

3151:   Input Parameters:
3152: + pc  - the preconditioner context
3153: - flg - boolean indicating whether to use field splits defined by the `DM`

3155:   Options Database Key:
3156: . -pc_fieldsplit_dm_splits <bool> - use the field splits defined by the `DM`

3158:   Level: intermediate

3160:   Developer Note:
3161:   The name should be `PCFieldSplitSetUseDMSplits()`, similar change to options database

3163: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitGetDMSplits()`, `DMCreateFieldDecomposition()`, `PCFieldSplitSetFields()`, `PCFieldSplitSetIS()`
3164: @*/
3165: PetscErrorCode PCFieldSplitSetDMSplits(PC pc, PetscBool flg)
3166: {
3167:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
3168:   PetscBool      isfs;

3170:   PetscFunctionBegin;
3173:   PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCFIELDSPLIT, &isfs));
3174:   if (isfs) jac->dm_splits = flg;
3175:   PetscFunctionReturn(PETSC_SUCCESS);
3176: }

3178: /*@
3179:   PCFieldSplitGetDMSplits - Returns flag indicating whether `DMCreateFieldDecomposition()` should be used to define the splits in a `PCFIELDSPLIT`, whenever possible.

3181:   Logically Collective

3183:   Input Parameter:
3184: . pc - the preconditioner context

3186:   Output Parameter:
3187: . flg - boolean indicating whether to use field splits defined by the `DM`

3189:   Level: intermediate

3191:   Developer Note:
3192:   The name should be `PCFieldSplitGetUseDMSplits()`

3194: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetDMSplits()`, `DMCreateFieldDecomposition()`, `PCFieldSplitSetFields()`, `PCFieldSplitSetIS()`
3195: @*/
3196: PetscErrorCode PCFieldSplitGetDMSplits(PC pc, PetscBool *flg)
3197: {
3198:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
3199:   PetscBool      isfs;

3201:   PetscFunctionBegin;
3203:   PetscAssertPointer(flg, 2);
3204:   PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCFIELDSPLIT, &isfs));
3205:   if (isfs) {
3206:     if (flg) *flg = jac->dm_splits;
3207:   }
3208:   PetscFunctionReturn(PETSC_SUCCESS);
3209: }

3211: /*@
3212:   PCFieldSplitGetDetectSaddlePoint - Returns flag indicating whether `PCFIELDSPLIT` will attempt to automatically determine fields based on zero diagonal entries.

3214:   Logically Collective

3216:   Input Parameter:
3217: . pc - the preconditioner context

3219:   Output Parameter:
3220: . flg - boolean indicating whether to detect fields or not

3222:   Level: intermediate

3224: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetDetectSaddlePoint()`
3225: @*/
3226: PetscErrorCode PCFieldSplitGetDetectSaddlePoint(PC pc, PetscBool *flg)
3227: {
3228:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

3230:   PetscFunctionBegin;
3231:   *flg = jac->detect;
3232:   PetscFunctionReturn(PETSC_SUCCESS);
3233: }

3235: /*@
3236:   PCFieldSplitSetDetectSaddlePoint - Sets flag indicating whether `PCFIELDSPLIT` will attempt to automatically determine fields based on zero diagonal entries.

3238:   Logically Collective

3240:   Input Parameter:
3241: . pc - the preconditioner context

3243:   Output Parameter:
3244: . flg - boolean indicating whether to detect fields or not

3246:   Options Database Key:
3247: . -pc_fieldsplit_detect_saddle_point <bool> - detect and use the saddle point

3249:   Level: intermediate

3251:   Note:
3252:   Also sets the split type to `PC_COMPOSITE_SCHUR` (see `PCFieldSplitSetType()`) and the Schur preconditioner type to `PC_FIELDSPLIT_SCHUR_PRE_SELF` (see `PCFieldSplitSetSchurPre()`).

3254: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitGetDetectSaddlePoint()`, `PCFieldSplitSetType()`, `PCFieldSplitSetSchurPre()`, `PC_FIELDSPLIT_SCHUR_PRE_SELF`
3255: @*/
3256: PetscErrorCode PCFieldSplitSetDetectSaddlePoint(PC pc, PetscBool flg)
3257: {
3258:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

3260:   PetscFunctionBegin;
3261:   jac->detect = flg;
3262:   if (jac->detect) {
3263:     PetscCall(PCFieldSplitSetType(pc, PC_COMPOSITE_SCHUR));
3264:     PetscCall(PCFieldSplitSetSchurPre(pc, PC_FIELDSPLIT_SCHUR_PRE_SELF, NULL));
3265:   }
3266:   PetscFunctionReturn(PETSC_SUCCESS);
3267: }

3269: /*MC
3270:   PCFIELDSPLIT - Preconditioner created by combining separate preconditioners for individual
3271:   collections of variables (that may overlap) called fields or splits. Each field often represents a different continuum variable
3272:   represented on a grid, such as velocity, pressure, or temperature.
3273:   In the literature these are sometimes called block preconditioners; but should not be confused with `PCBJACOBI`.
3274:   See [the users manual section on "Solving Block Matrices"](sec_block_matrices) for more details.

3276:   Options Database Keys:
3277: +   -pc_fieldsplit_%d_fields <a,b,..>                                                - indicates the fields to be used in the `%d`'th split
3278: .   -pc_fieldsplit_default                                                           - automatically add any fields to additional splits that have not
3279:                                                                                        been supplied explicitly by `-pc_fieldsplit_%d_fields`
3280: .   -pc_fieldsplit_block_size <bs>                                                   - size of block that defines fields (i.e. there are bs fields)
3281:                                                                                        when the matrix is not of `MatType` `MATNEST`
3282: .   -pc_fieldsplit_type <additive,multiplicative,symmetric_multiplicative,schur,gkb> - type of relaxation or factorization splitting
3283: .   -pc_fieldsplit_schur_precondition <self,selfp,user,a11,full>                     - default is `a11`; see `PCFieldSplitSetSchurPre()`
3284: .   -pc_fieldsplit_schur_fact_type <diag,lower,upper,full>                           - set factorization type when using `-pc_fieldsplit_type schur`;
3285:                                                                                        see `PCFieldSplitSetSchurFactType()`
3286: .   -pc_fieldsplit_dm_splits <true,false> (default is true)                          - Whether to use `DMCreateFieldDecomposition()` for splits
3287: -   -pc_fieldsplit_detect_saddle_point                                               - automatically finds rows with zero diagonal and uses Schur complement with no preconditioner as the solver

3289:   Options prefixes for inner solvers when using the Schur complement preconditioner are `-fieldsplit_0_` and `-fieldsplit_1_` .
3290:   The options prefix for the inner solver when using the Golub-Kahan biadiagonalization preconditioner is `-fieldsplit_0_`
3291:   For all other solvers they are `-fieldsplit_%d_` for the `%d`'th field; use `-fieldsplit_` for all fields.

3293:   To set options on the solvers for all blocks, prepend `-fieldsplit_` to all the `PC`
3294:   options database keys. For example, `-fieldsplit_pc_type ilu` `-fieldsplit_pc_factor_levels 1`.

3296:   To set the options on the solvers separate for each block call `PCFieldSplitGetSubKSP()`
3297:   and set the options directly on the resulting `KSP` object

3299:   Level: intermediate

3301:   Notes:
3302:   Use `PCFieldSplitSetFields()` to set splits defined by "strided" entries or with a `MATNEST` and `PCFieldSplitSetIS()`
3303:   to define a split by an arbitrary collection of entries.

3305:   If no splits are set, the default is used. If a `DM` is associated with the `PC` and it supports
3306:   `DMCreateFieldDecomposition()`, then that is used for the default. Otherwise if the matrix is not `MATNEST`, the splits are defined by entries strided by bs,
3307:   beginning at 0 then 1, etc to bs-1. The block size can be set with `PCFieldSplitSetBlockSize()`,
3308:   if this is not called the block size defaults to the blocksize of the second matrix passed
3309:   to `KSPSetOperators()`/`PCSetOperators()`.

3311:   For the Schur complement preconditioner if
3312:   ```{math}
3313:     J = \left[\begin{array}{cc} A_{00} & A_{01} \\ A_{10} & A_{11} \end{array}\right]
3314:   ```

3316:   the preconditioner using `full` factorization is logically
3317:   ```{math}
3318:     \left[\begin{array}{cc} I & -\text{ksp}(A_{00}) A_{01} \\ 0 & I \end{array}\right] \left[\begin{array}{cc} \text{ksp}(A_{00}) & 0 \\ 0 & \text{ksp}(S) \end{array}\right] \left[\begin{array}{cc} I & 0 \\ -A_{10} \text{ksp}(A_{00}) & I \end{array}\right]
3319:       ```
3320:   where the action of $\text{ksp}(A_{00})$ is applied using the `KSP` solver with prefix `-fieldsplit_0_`.  $S$ is the Schur complement
3321:   ```{math}
3322:      S = A_{11} - A_{10} \text{ksp}(A_{00}) A_{01}
3323:   ```
3324:   which is usually dense and not stored explicitly.  The action of $\text{ksp}(S)$ is computed using the `KSP` solver with prefix `-fieldsplit_splitname_` (where `splitname`
3325:   was given in providing the SECOND split or 1 if not given). Accordingly, if using `PCFieldSplitGetSubKSP()`, the array of sub-`KSP` contexts will hold two `KSP`s: at its
3326:   0th index, the `KSP` associated with `-fieldsplit_0_`, and at its 1st index, the `KSP` corresponding to `-fieldsplit_1_`.
3327:   By default, $A_{11}$ is used to construct a preconditioner for $S$, use `PCFieldSplitSetSchurPre()` for all the possible ways to construct the preconditioner for $S$.

3329:   The factorization type is set using `-pc_fieldsplit_schur_fact_type <diag, lower, upper, full>`. `full` is shown above,
3330:   `diag` gives
3331:   ```{math}
3332:     \left[\begin{array}{cc} \text{ksp}(A_{00}) & 0 \\  0 & -\text{ksp}(S) \end{array}\right]
3333:   ```
3334:   Note that, slightly counter intuitively, there is a negative in front of the $\text{ksp}(S)$  so that the preconditioner is positive definite. For SPD matrices $J$, the sign flip
3335:   can be turned off with `PCFieldSplitSetSchurScale()` or by command line `-pc_fieldsplit_schur_scale 1.0`. The `lower` factorization is the inverse of
3336:   ```{math}
3337:     \left[\begin{array}{cc} A_{00} & 0 \\  A_{10} & S \end{array}\right]
3338:   ```
3339:   where the inverses of $A_{00}$ and $S$ are applied using `KSP`s. The upper factorization is the inverse of
3340:   ```{math}
3341:     \left[\begin{array}{cc} A_{00} & A_{01} \\  0 & S \end{array}\right]
3342:   ```
3343:   where again the inverses of $A_{00}$ and $S$ are applied using `KSP`s.

3345:   If only one set of indices (one `IS`) is provided with `PCFieldSplitSetIS()` then the complement of that `IS`
3346:   is used automatically for a second submatrix.

3348:   The fieldsplit preconditioner cannot currently be used with the `MATBAIJ` or `MATSBAIJ` data formats if the blocksize is larger than 1.
3349:   Generally it should be used with the `MATAIJ` or `MATNEST` `MatType`

3351:   The forms of these preconditioners are closely related, if not identical, to forms derived as "Distributive Iterations", see,
3352:   for example, page 294 in "Principles of Computational Fluid Dynamics" by Pieter Wesseling {cite}`wesseling2009`.
3353:   One can also use `PCFIELDSPLIT` inside a smoother resulting in "Distributive Smoothers".

3355:   See "A taxonomy and comparison of parallel block multi-level preconditioners for the incompressible Navier-Stokes equations" {cite}`elman2008tcp`.

3357:   The Constrained Pressure Preconditioner (CPR) can be implemented using `PCCOMPOSITE` with `PCGALERKIN`. CPR first solves an $R A P$ subsystem, updates the
3358:   residual on all variables (`PCCompositeSetType(pc,PC_COMPOSITE_MULTIPLICATIVE)`), and then applies a simple ILU like preconditioner on all the variables.

3360:   The generalized Golub-Kahan bidiagonalization preconditioner (GKB) can be applied to symmetric $2 \times 2$ block matrices of the shape
3361:   ```{math}
3362:     \left[\begin{array}{cc} A_{00} & A_{01} \\ A_{01}' & 0 \end{array}\right]
3363:   ```
3364:   with $A_{00}$ positive semi-definite. The implementation follows {cite}`arioli2013`. Therein, we choose $N := 1/\nu * I$ and the $(1,1)$-block of the matrix is modified to $H = _{A00} + \nu*A_{01}*A_{01}'$.
3365:   A linear system $Hx = b$ has to be solved in each iteration of the GKB algorithm. This solver is chosen with the option prefix `-fieldsplit_0_`.

3367:   Some `PCFIELDSPLIT` variants are called physics-based preconditioners, since the preconditioner takes into account the underlying physics of the
3368:   problem. But this nomenclature is not well-defined.

3370:   Developer Note:
3371:   The Schur complement functionality of `PCFIELDSPLIT` should likely be factored into its own `PC` thus simplifying the implementation of the preconditioners and their
3372:   user API.

3374: .seealso: [](sec_block_matrices), `PC`, `PCCreate()`, `PCSetType()`, `PCType`, `PC`, `PCLSC`,
3375:           `PCFieldSplitGetSubKSP()`, `PCFieldSplitSchurGetSubKSP()`, `PCFieldSplitSetFields()`,
3376:           `PCFieldSplitSetType()`, `PCFieldSplitSetIS()`, `PCFieldSplitSetSchurPre()`, `PCFieldSplitSetSchurFactType()`,
3377:           `MatSchurComplementSetAinvType()`, `PCFieldSplitSetSchurScale()`, `PCFieldSplitSetDetectSaddlePoint()`
3378: M*/

3380: PETSC_EXTERN PetscErrorCode PCCreate_FieldSplit(PC pc)
3381: {
3382:   PC_FieldSplit *jac;

3384:   PetscFunctionBegin;
3385:   PetscCall(PetscNew(&jac));

3387:   jac->bs                 = -1;
3388:   jac->type               = PC_COMPOSITE_MULTIPLICATIVE;
3389:   jac->schurpre           = PC_FIELDSPLIT_SCHUR_PRE_USER; /* Try user preconditioner first, fall back on diagonal */
3390:   jac->schurfactorization = PC_FIELDSPLIT_SCHUR_FACT_FULL;
3391:   jac->schurscale         = -1.0;
3392:   jac->dm_splits          = PETSC_TRUE;
3393:   jac->gkbtol             = 1e-5;
3394:   jac->gkbdelay           = 5;
3395:   jac->gkbnu              = 1;
3396:   jac->gkbmaxit           = 100;

3398:   pc->data = (void *)jac;

3400:   pc->ops->setup           = PCSetUp_FieldSplit;
3401:   pc->ops->reset           = PCReset_FieldSplit;
3402:   pc->ops->destroy         = PCDestroy_FieldSplit;
3403:   pc->ops->setfromoptions  = PCSetFromOptions_FieldSplit;
3404:   pc->ops->applyrichardson = NULL;

3406:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSchurGetSubKSP_C", PCFieldSplitSchurGetSubKSP_FieldSplit));
3407:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetFields_C", PCFieldSplitSetFields_FieldSplit));
3408:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetIS_C", PCFieldSplitSetIS_FieldSplit));
3409:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetType_C", PCFieldSplitSetType_FieldSplit));
3410:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetBlockSize_C", PCFieldSplitSetBlockSize_FieldSplit));
3411:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitRestrictIS_C", PCFieldSplitRestrictIS_FieldSplit));
3412:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCSetCoordinates_C", PCSetCoordinates_FieldSplit));

3414:   /* Initialize function pointers */
3415:   PetscCall(PCFieldSplitSetType(pc, jac->type));
3416:   PetscFunctionReturn(PETSC_SUCCESS);
3417: }