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 preconditioning matrix when solving with S */
 52:   Mat                       schur_user; /* User-provided preconditioning matrix for the Schur complement */
 53:   PCFieldSplitSchurPreType  schurpre;   /* Determines which preconditioning 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 preconditioning 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         iascii, isdraw;
110:   PetscInt          i, j;
111:   PC_FieldSplitLink ilink = jac->head;

113:   PetscFunctionBegin;
114:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &iascii));
115:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERDRAW, &isdraw));
116:   if (iascii) {
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                  iascii, isdraw;
168:   PetscInt                   i, j;
169:   PC_FieldSplitLink          ilink = jac->head;
170:   MatSchurComplementAinvType atype;

172:   PetscFunctionBegin;
173:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &iascii));
174:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERDRAW, &isdraw));
175:   if (iascii) {
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) {
228:       PetscCall(KSPView(jac->head->ksp, viewer));
229:     } else PetscCall(PetscViewerASCIIPrintf(viewer, "  not yet available\n"));
230:     PetscCall(PetscViewerASCIIPopTab(viewer));
231:     if (jac->head && jac->kspupper != jac->head->ksp) {
232:       PetscCall(PetscViewerASCIIPrintf(viewer, "KSP solver for upper A00 in upper triangular factor\n"));
233:       PetscCall(PetscViewerASCIIPushTab(viewer));
234:       if (jac->kspupper) PetscCall(KSPView(jac->kspupper, viewer));
235:       else PetscCall(PetscViewerASCIIPrintf(viewer, "  not yet available\n"));
236:       PetscCall(PetscViewerASCIIPopTab(viewer));
237:     }
238:     PetscCall(PetscViewerASCIIPrintf(viewer, "KSP solver for S = A11 - A10 inv(A00) A01\n"));
239:     PetscCall(PetscViewerASCIIPushTab(viewer));
240:     if (jac->kspschur) {
241:       PetscCall(KSPView(jac->kspschur, viewer));
242:     } else {
243:       PetscCall(PetscViewerASCIIPrintf(viewer, "  not yet available\n"));
244:     }
245:     PetscCall(PetscViewerASCIIPopTab(viewer));
246:     PetscCall(PetscViewerASCIIPopTab(viewer));
247:   } else if (isdraw && jac->head) {
248:     PetscDraw draw;
249:     PetscReal x, y, w, wd, h;
250:     PetscInt  cnt = 2;
251:     char      str[32];

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

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

271:     PetscCall(PetscDrawPushCurrentPoint(draw, x, y));
272:     PetscCall(KSPView(jac->head->ksp, viewer));
273:     PetscCall(PetscDrawPopCurrentPoint(draw));
274:     if (jac->kspupper != jac->head->ksp) {
275:       x += wd;
276:       PetscCall(PetscDrawPushCurrentPoint(draw, x, y));
277:       PetscCall(KSPView(jac->kspupper, viewer));
278:       PetscCall(PetscDrawPopCurrentPoint(draw));
279:     }
280:     x += wd;
281:     PetscCall(PetscDrawPushCurrentPoint(draw, x, y));
282:     PetscCall(KSPView(jac->kspschur, viewer));
283:     PetscCall(PetscDrawPopCurrentPoint(draw));
284:   }
285:   PetscFunctionReturn(PETSC_SUCCESS);
286: }

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

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

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

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

326:     PetscCall(PetscViewerASCIIPopTab(viewer));
327:   }

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

333:     PetscCall(PetscViewerDrawGetDraw(viewer, 0, &draw));
334:     PetscCall(PetscDrawGetCurrentPoint(draw, &x, &y));
335:     w  = 2 * PetscMin(1.0 - x, x);
336:     wd = w / (jac->nsplits + 1);
337:     x  = x - wd * (jac->nsplits - 1) / 2.0;
338:     for (i = 0; i < jac->nsplits; i++) {
339:       PetscCall(PetscDrawPushCurrentPoint(draw, x, y));
340:       PetscCall(KSPView(ilink->ksp, viewer));
341:       PetscCall(PetscDrawPopCurrentPoint(draw));
342:       x += wd;
343:       ilink = ilink->next;
344:     }
345:   }
346:   PetscFunctionReturn(PETSC_SUCCESS);
347: }

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

357:   PetscFunctionBegin;
358:   PetscCall(PetscObjectTypeCompare((PetscObject)pc->mat, MATNEST, &mnest));
359:   if (mnest) {
360:     PetscCall(MatNestGetSize(pc->pmat, &bs, NULL));
361:   } else {
362:     bs = jac->bs;
363:   }
364:   PetscCall(PetscMalloc2(bs, &ifields, bs, &ifields_col));
365:   for (i = 0, flg = PETSC_TRUE;; i++) {
366:     PetscCall(PetscSNPrintf(splitname, sizeof(splitname), "%" PetscInt_FMT, i));
367:     PetscCall(PetscSNPrintf(optionname, sizeof(optionname), "-pc_fieldsplit_%" PetscInt_FMT "_fields", i));
368:     PetscCall(PetscSNPrintf(optionname_col, sizeof(optionname_col), "-pc_fieldsplit_%" PetscInt_FMT "_fields_col", i));
369:     nfields     = bs;
370:     nfields_col = bs;
371:     PetscCall(PetscOptionsGetIntArray(((PetscObject)pc)->options, ((PetscObject)pc)->prefix, optionname, ifields, &nfields, &flg));
372:     PetscCall(PetscOptionsGetIntArray(((PetscObject)pc)->options, ((PetscObject)pc)->prefix, optionname_col, ifields_col, &nfields_col, &flg_col));
373:     if (!flg) break;
374:     else if (flg && !flg_col) {
375:       PetscCheck(nfields, PETSC_COMM_SELF, PETSC_ERR_USER, "Cannot list zero fields");
376:       PetscCall(PCFieldSplitSetFields(pc, splitname, nfields, ifields, ifields));
377:     } else {
378:       PetscCheck(nfields && nfields_col, PETSC_COMM_SELF, PETSC_ERR_USER, "Cannot list zero fields");
379:       PetscCheck(nfields == nfields_col, PETSC_COMM_SELF, PETSC_ERR_USER, "Number of row and column fields must match");
380:       PetscCall(PCFieldSplitSetFields(pc, splitname, nfields, ifields, ifields_col));
381:     }
382:   }
383:   if (i > 0) {
384:     /* Makes command-line setting of splits take precedence over setting them in code.
385:        Otherwise subsequent calls to PCFieldSplitSetIS() or PCFieldSplitSetFields() would
386:        create new splits, which would probably not be what the user wanted. */
387:     jac->splitdefined = PETSC_TRUE;
388:   }
389:   PetscCall(PetscFree2(ifields, ifields_col));
390:   PetscFunctionReturn(PETSC_SUCCESS);
391: }

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

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

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

423:         PetscCall(PetscSNPrintf(optionname, sizeof(optionname), "-pc_fieldsplit_%" PetscInt_FMT "_fields", i));
424:         PetscCall(PetscOptionsGetIntArray(((PetscObject)pc)->options, ((PetscObject)pc)->prefix, optionname, ifields, &nfields, &flg));
425:         if (!flg) break;
426:         PetscCheck(numFields <= 128, PetscObjectComm((PetscObject)pc), PETSC_ERR_SUP, "Cannot currently support %" PetscInt_FMT " > 128 fields", numFields);
427:         PetscCall(DMCreateSubDM(pc->dm, nfields, ifields, &compField, &subdm[i]));
428:         if (nfields == 1) {
429:           PetscCall(PCFieldSplitSetIS(pc, fieldNames[ifields[0]], compField));
430:         } else {
431:           PetscCall(PetscSNPrintf(splitname, sizeof(splitname), "%" PetscInt_FMT, i));
432:           PetscCall(PCFieldSplitSetIS(pc, splitname, compField));
433:         }
434:         PetscCall(ISDestroy(&compField));
435:         for (j = 0; j < nfields; ++j) {
436:           f = ifields[j];
437:           PetscCall(PetscFree(fieldNames[f]));
438:           PetscCall(ISDestroy(&fields[f]));
439:         }
440:       }
441:       if (i == 0) {
442:         for (f = 0; f < numFields; ++f) {
443:           PetscCall(PCFieldSplitSetIS(pc, fieldNames[f], fields[f]));
444:           PetscCall(PetscFree(fieldNames[f]));
445:           PetscCall(ISDestroy(&fields[f]));
446:         }
447:       } else {
448:         for (j = 0; j < numFields; j++) PetscCall(DMDestroy(dms + j));
449:         PetscCall(PetscFree(dms));
450:         PetscCall(PetscMalloc1(i, &dms));
451:         for (j = 0; j < i; ++j) dms[j] = subdm[j];
452:       }
453:       PetscCall(PetscFree(fieldNames));
454:       PetscCall(PetscFree(fields));
455:       if (dms) {
456:         PetscCall(PetscInfo(pc, "Setting up physics based fieldsplit preconditioner using the embedded DM\n"));
457:         for (ilink = jac->head, i = 0; ilink; ilink = ilink->next, ++i) {
458:           const char *prefix;
459:           PetscCall(PetscObjectGetOptionsPrefix((PetscObject)ilink->ksp, &prefix));
460:           PetscCall(PetscObjectSetOptionsPrefix((PetscObject)dms[i], prefix));
461:           PetscCall(KSPSetDM(ilink->ksp, dms[i]));
462:           PetscCall(KSPSetDMActive(ilink->ksp, PETSC_FALSE));
463:           PetscCall(PetscObjectIncrementTabLevel((PetscObject)dms[i], (PetscObject)ilink->ksp, 0));
464:           PetscCall(DMDestroy(&dms[i]));
465:         }
466:         PetscCall(PetscFree(dms));
467:       }
468:     } else {
469:       if (jac->bs <= 0) {
470:         if (pc->pmat) {
471:           PetscCall(MatGetBlockSize(pc->pmat, &jac->bs));
472:         } else jac->bs = 1;
473:       }

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

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

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

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

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

541:     PetscCheck(ilink->is, PetscObjectComm((PetscObject)pc), PETSC_ERR_SUP, "Must provide at least two sets of fields to PCFieldSplit()");
542:     PetscCall(MatGetOwnershipRange(pc->mat, &nmin, &nmax));
543:     PetscCall(ISComplement(ilink->is, nmin, nmax, &is2));
544:     PetscCall(PCFieldSplitSetIS(pc, "1", is2));
545:     PetscCall(ISDestroy(&is2));
546:   }

548:   PetscCheck(jac->nsplits >= 2, PetscObjectComm((PetscObject)pc), PETSC_ERR_PLIB, "Unhandled case, must have at least two fields, not %" PetscInt_FMT, jac->nsplits);
549:   PetscFunctionReturn(PETSC_SUCCESS);
550: }

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

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

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

570:   PetscCall(MatDestroy(&BT));
571:   PetscCall(MatDestroy(&T));
572:   PetscFunctionReturn(PETSC_SUCCESS);
573: }

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

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

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

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

595:     jac->issetup = PETSC_TRUE;

597:     /* This is done here instead of in PCFieldSplitSetFields() because may not have matrix at that point */
598:     if (jac->defaultsplit || !ilink->is) {
599:       if (jac->bs <= 0) jac->bs = nsplit;
600:     }

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

607:       PetscCall(PetscObjectTypeCompareAny((PetscObject)pc->pmat, &blk, MATBAIJ, MATSBAIJ, MATSEQBAIJ, MATSEQSBAIJ, MATMPIBAIJ, MATMPISBAIJ, NULL));
608:       PetscCheck(!blk, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONG, "Cannot use MATBAIJ with PCFIELDSPLIT and currently set matrix and PC blocksizes");
609:     }

611:     if (!matnest) { /* use the matrix blocksize and stride IS to determine the index sets that define the submatrices */
612:       bs = jac->bs;
613:       PetscCall(MatGetOwnershipRange(pc->pmat, &rstart, &rend));
614:       nslots = (rend - rstart) / bs;
615:       for (i = 0; i < nsplit; i++) {
616:         if (jac->defaultsplit) {
617:           PetscCall(ISCreateStride(PetscObjectComm((PetscObject)pc), nslots, rstart + i, nsplit, &ilink->is));
618:           PetscCall(ISDuplicate(ilink->is, &ilink->is_col));
619:         } else if (!ilink->is) {
620:           if (ilink->nfields > 1) {
621:             PetscInt *ii, *jj, j, k, nfields = ilink->nfields, *fields = ilink->fields, *fields_col = ilink->fields_col;

623:             PetscCall(PetscMalloc1(ilink->nfields * nslots, &ii));
624:             PetscCall(PetscMalloc1(ilink->nfields * nslots, &jj));
625:             for (j = 0; j < nslots; j++) {
626:               for (k = 0; k < nfields; k++) {
627:                 ii[nfields * j + k] = rstart + bs * j + fields[k];
628:                 jj[nfields * j + k] = rstart + bs * j + fields_col[k];
629:               }
630:             }
631:             PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)pc), nslots * nfields, ii, PETSC_OWN_POINTER, &ilink->is));
632:             PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)pc), nslots * nfields, jj, PETSC_OWN_POINTER, &ilink->is_col));
633:             PetscCall(ISSetBlockSize(ilink->is, nfields));
634:             PetscCall(ISSetBlockSize(ilink->is_col, nfields));
635:           } else {
636:             PetscCall(ISCreateStride(PetscObjectComm((PetscObject)pc), nslots, rstart + ilink->fields[0], bs, &ilink->is));
637:             PetscCall(ISCreateStride(PetscObjectComm((PetscObject)pc), nslots, rstart + ilink->fields_col[0], bs, &ilink->is_col));
638:           }
639:         }
640:         PetscCall(ISSorted(ilink->is, &sorted));
641:         if (ilink->is_col) PetscCall(ISSorted(ilink->is_col, &sorted_col));
642:         PetscCheck(sorted && sorted_col, PETSC_COMM_SELF, PETSC_ERR_USER, "Fields must be sorted when creating split");
643:         ilink = ilink->next;
644:       }
645:     } else { /* use the IS that define the MATNEST to determine the index sets that define the submatrices */
646:       IS      *rowis, *colis, *ises = NULL;
647:       PetscInt mis, nis;

649:       PetscCall(MatNestGetSize(pc->pmat, &mis, &nis));
650:       PetscCall(PetscMalloc2(mis, &rowis, nis, &colis));
651:       PetscCall(MatNestGetISs(pc->pmat, rowis, colis));
652:       if (!jac->defaultsplit) PetscCall(PetscMalloc1(mis, &ises));

654:       for (i = 0; i < nsplit; i++) {
655:         if (jac->defaultsplit) {
656:           PetscCall(ISDuplicate(rowis[i], &ilink->is));
657:           PetscCall(ISDuplicate(ilink->is, &ilink->is_col));
658:         } else if (!ilink->is) {
659:           if (ilink->nfields > 1) {
660:             for (PetscInt j = 0; j < ilink->nfields; j++) ises[j] = rowis[ilink->fields[j]];
661:             PetscCall(ISConcatenate(PetscObjectComm((PetscObject)pc), ilink->nfields, ises, &ilink->is));
662:           } else {
663:             PetscCall(ISDuplicate(rowis[ilink->fields[0]], &ilink->is));
664:           }
665:           PetscCall(ISDuplicate(ilink->is, &ilink->is_col));
666:         }
667:         ilink = ilink->next;
668:       }
669:       PetscCall(PetscFree2(rowis, colis));
670:       PetscCall(PetscFree(ises));
671:     }
672:   }

674:   ilink = jac->head;
675:   if (!jac->pmat) {
676:     Vec xtmp;

678:     PetscCall(MatCreateVecs(pc->pmat, &xtmp, NULL));
679:     PetscCall(PetscMalloc1(nsplit, &jac->pmat));
680:     PetscCall(PetscMalloc2(nsplit, &jac->x, nsplit, &jac->y));
681:     for (i = 0; i < nsplit; i++) {
682:       MatNullSpace sp;

684:       /* Check for preconditioning matrix attached to IS */
685:       PetscCall(PetscObjectQuery((PetscObject)ilink->is, "pmat", (PetscObject *)&jac->pmat[i]));
686:       if (jac->pmat[i]) {
687:         PetscCall(PetscObjectReference((PetscObject)jac->pmat[i]));
688:         if (jac->type == PC_COMPOSITE_SCHUR) {
689:           jac->schur_user = jac->pmat[i];

691:           PetscCall(PetscObjectReference((PetscObject)jac->schur_user));
692:         }
693:       } else {
694:         const char *prefix;
695:         PetscCall(MatCreateSubMatrix(pc->pmat, ilink->is, ilink->is_col, MAT_INITIAL_MATRIX, &jac->pmat[i]));
696:         PetscCall(MatGetOptionsPrefix(jac->pmat[i], &prefix));
697:         if (!prefix) {
698:           PetscCall(KSPGetOptionsPrefix(ilink->ksp, &prefix));
699:           PetscCall(MatSetOptionsPrefix(jac->pmat[i], prefix));
700:         }
701:         PetscCall(MatSetFromOptions(jac->pmat[i]));
702:         PetscCall(MatViewFromOptions(jac->pmat[i], NULL, "-mat_view"));
703:       }
704:       /* create work vectors for each split */
705:       PetscCall(MatCreateVecs(jac->pmat[i], &jac->x[i], &jac->y[i]));
706:       ilink->x = jac->x[i];
707:       ilink->y = jac->y[i];
708:       ilink->z = NULL;
709:       /* compute scatter contexts needed by multiplicative versions and non-default splits */
710:       PetscCall(VecScatterCreate(xtmp, ilink->is, jac->x[i], NULL, &ilink->sctx));
711:       PetscCall(PetscObjectQuery((PetscObject)ilink->is, "nearnullspace", (PetscObject *)&sp));
712:       if (sp) PetscCall(MatSetNearNullSpace(jac->pmat[i], sp));
713:       ilink = ilink->next;
714:     }
715:     PetscCall(VecDestroy(&xtmp));
716:   } else {
717:     MatReuse      scall;
718:     MatNullSpace *nullsp = NULL;

720:     if (pc->flag == DIFFERENT_NONZERO_PATTERN) {
721:       PetscCall(MatGetNullSpaces(nsplit, jac->pmat, &nullsp));
722:       for (i = 0; i < nsplit; i++) PetscCall(MatDestroy(&jac->pmat[i]));
723:       scall = MAT_INITIAL_MATRIX;
724:     } else scall = MAT_REUSE_MATRIX;

726:     for (i = 0; i < nsplit; i++) {
727:       Mat pmat;

729:       /* Check for preconditioning matrix attached to IS */
730:       PetscCall(PetscObjectQuery((PetscObject)ilink->is, "pmat", (PetscObject *)&pmat));
731:       if (!pmat) PetscCall(MatCreateSubMatrix(pc->pmat, ilink->is, ilink->is_col, scall, &jac->pmat[i]));
732:       ilink = ilink->next;
733:     }
734:     if (nullsp) PetscCall(MatRestoreNullSpaces(nsplit, jac->pmat, &nullsp));
735:   }
736:   if (jac->diag_use_amat) {
737:     ilink = jac->head;
738:     if (!jac->mat) {
739:       PetscCall(PetscMalloc1(nsplit, &jac->mat));
740:       for (i = 0; i < nsplit; i++) {
741:         PetscCall(MatCreateSubMatrix(pc->mat, ilink->is, ilink->is_col, MAT_INITIAL_MATRIX, &jac->mat[i]));
742:         ilink = ilink->next;
743:       }
744:     } else {
745:       MatReuse      scall;
746:       MatNullSpace *nullsp = NULL;

748:       if (pc->flag == DIFFERENT_NONZERO_PATTERN) {
749:         PetscCall(MatGetNullSpaces(nsplit, jac->mat, &nullsp));
750:         for (i = 0; i < nsplit; i++) PetscCall(MatDestroy(&jac->mat[i]));
751:         scall = MAT_INITIAL_MATRIX;
752:       } else scall = MAT_REUSE_MATRIX;

754:       for (i = 0; i < nsplit; i++) {
755:         PetscCall(MatCreateSubMatrix(pc->mat, ilink->is, ilink->is_col, scall, &jac->mat[i]));
756:         ilink = ilink->next;
757:       }
758:       if (nullsp) PetscCall(MatRestoreNullSpaces(nsplit, jac->mat, &nullsp));
759:     }
760:   } else {
761:     jac->mat = jac->pmat;
762:   }

764:   /* Check for null space attached to IS */
765:   ilink = jac->head;
766:   for (i = 0; i < nsplit; i++) {
767:     MatNullSpace sp;

769:     PetscCall(PetscObjectQuery((PetscObject)ilink->is, "nullspace", (PetscObject *)&sp));
770:     if (sp) PetscCall(MatSetNullSpace(jac->mat[i], sp));
771:     ilink = ilink->next;
772:   }

774:   if (jac->type != PC_COMPOSITE_ADDITIVE && jac->type != PC_COMPOSITE_SCHUR && jac->type != PC_COMPOSITE_GKB) {
775:     /* extract the rows of the matrix associated with each field: used for efficient computation of residual inside algorithm */
776:     /* FIXME: Can/should we reuse jac->mat whenever (jac->diag_use_amat) is true? */
777:     ilink = jac->head;
778:     if (nsplit == 2 && jac->type == PC_COMPOSITE_MULTIPLICATIVE) {
779:       /* 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 */
780:       if (!jac->Afield) {
781:         PetscCall(PetscCalloc1(nsplit, &jac->Afield));
782:         if (jac->offdiag_use_amat) {
783:           PetscCall(MatCreateSubMatrix(pc->mat, ilink->next->is, ilink->is, MAT_INITIAL_MATRIX, &jac->Afield[1]));
784:         } else {
785:           PetscCall(MatCreateSubMatrix(pc->pmat, ilink->next->is, ilink->is, MAT_INITIAL_MATRIX, &jac->Afield[1]));
786:         }
787:       } else {
788:         MatReuse scall;

790:         if (pc->flag == DIFFERENT_NONZERO_PATTERN) {
791:           PetscCall(MatDestroy(&jac->Afield[1]));
792:           scall = MAT_INITIAL_MATRIX;
793:         } else scall = MAT_REUSE_MATRIX;

795:         if (jac->offdiag_use_amat) {
796:           PetscCall(MatCreateSubMatrix(pc->mat, ilink->next->is, ilink->is, scall, &jac->Afield[1]));
797:         } else {
798:           PetscCall(MatCreateSubMatrix(pc->pmat, ilink->next->is, ilink->is, scall, &jac->Afield[1]));
799:         }
800:       }
801:     } else {
802:       if (!jac->Afield) {
803:         PetscCall(PetscMalloc1(nsplit, &jac->Afield));
804:         for (i = 0; i < nsplit; i++) {
805:           if (jac->offdiag_use_amat) {
806:             PetscCall(MatCreateSubMatrix(pc->mat, ilink->is, NULL, MAT_INITIAL_MATRIX, &jac->Afield[i]));
807:           } else {
808:             PetscCall(MatCreateSubMatrix(pc->pmat, ilink->is, NULL, MAT_INITIAL_MATRIX, &jac->Afield[i]));
809:           }
810:           ilink = ilink->next;
811:         }
812:       } else {
813:         MatReuse scall;
814:         if (pc->flag == DIFFERENT_NONZERO_PATTERN) {
815:           for (i = 0; i < nsplit; i++) PetscCall(MatDestroy(&jac->Afield[i]));
816:           scall = MAT_INITIAL_MATRIX;
817:         } else scall = MAT_REUSE_MATRIX;

819:         for (i = 0; i < nsplit; i++) {
820:           if (jac->offdiag_use_amat) {
821:             PetscCall(MatCreateSubMatrix(pc->mat, ilink->is, NULL, scall, &jac->Afield[i]));
822:           } else {
823:             PetscCall(MatCreateSubMatrix(pc->pmat, ilink->is, NULL, scall, &jac->Afield[i]));
824:           }
825:           ilink = ilink->next;
826:         }
827:       }
828:     }
829:   }

831:   if (jac->type == PC_COMPOSITE_SCHUR) {
832:     IS          ccis;
833:     PetscBool   isset, isspd;
834:     PetscInt    rstart, rend;
835:     char        lscname[256];
836:     PetscObject LSC_L;
837:     PetscBool   set, flg;

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

841:     /* If pc->mat is SPD, don't scale by -1 the Schur complement */
842:     if (jac->schurscale == (PetscScalar)-1.0) {
843:       PetscCall(MatIsSPDKnown(pc->pmat, &isset, &isspd));
844:       jac->schurscale = (isset && isspd) ? 1.0 : -1.0;
845:     }

847:     /* When extracting off-diagonal submatrices, we take complements from this range */
848:     PetscCall(MatGetOwnershipRangeColumn(pc->mat, &rstart, &rend));
849:     PetscCall(PetscObjectTypeCompareAny(jac->offdiag_use_amat ? (PetscObject)pc->mat : (PetscObject)pc->pmat, &flg, MATSEQSBAIJ, MATMPISBAIJ, ""));

851:     if (jac->schur) {
852:       KSP      kspA = jac->head->ksp, kspInner = NULL, kspUpper = jac->kspupper;
853:       MatReuse scall;

855:       if (pc->flag == DIFFERENT_NONZERO_PATTERN) {
856:         scall = MAT_INITIAL_MATRIX;
857:         PetscCall(MatDestroy(&jac->B));
858:         PetscCall(MatDestroy(&jac->C));
859:       } else scall = MAT_REUSE_MATRIX;

861:       PetscCall(MatSchurComplementGetKSP(jac->schur, &kspInner));
862:       ilink = jac->head;
863:       PetscCall(ISComplement(ilink->is_col, rstart, rend, &ccis));
864:       if (jac->offdiag_use_amat) {
865:         PetscCall(MatCreateSubMatrix(pc->mat, ilink->is, ccis, scall, &jac->B));
866:       } else {
867:         PetscCall(MatCreateSubMatrix(pc->pmat, ilink->is, ccis, scall, &jac->B));
868:       }
869:       PetscCall(ISDestroy(&ccis));
870:       if (!flg) {
871:         ilink = ilink->next;
872:         PetscCall(ISComplement(ilink->is_col, rstart, rend, &ccis));
873:         if (jac->offdiag_use_amat) {
874:           PetscCall(MatCreateSubMatrix(pc->mat, ilink->is, ccis, scall, &jac->C));
875:         } else {
876:           PetscCall(MatCreateSubMatrix(pc->pmat, ilink->is, ccis, scall, &jac->C));
877:         }
878:         PetscCall(ISDestroy(&ccis));
879:       } else {
880:         PetscCall(MatIsHermitianKnown(jac->offdiag_use_amat ? pc->mat : pc->pmat, &set, &flg));
881:         if (set && flg) PetscCall(MatCreateHermitianTranspose(jac->B, &jac->C));
882:         else PetscCall(MatCreateTranspose(jac->B, &jac->C));
883:       }
884:       PetscCall(MatSchurComplementUpdateSubMatrices(jac->schur, jac->mat[0], jac->pmat[0], jac->B, jac->C, jac->mat[1]));
885:       if (jac->schurpre == PC_FIELDSPLIT_SCHUR_PRE_SELFP) {
886:         PetscCall(MatDestroy(&jac->schurp));
887:         PetscCall(MatSchurComplementGetPmat(jac->schur, MAT_INITIAL_MATRIX, &jac->schurp));
888:       } else if (jac->schurpre == PC_FIELDSPLIT_SCHUR_PRE_FULL) {
889:         PetscCall(MatDestroy(&jac->schur_user));
890:         if (jac->kspupper == jac->head->ksp) {
891:           Mat AinvB;

893:           PetscCall(MatCreate(PetscObjectComm((PetscObject)jac->schur), &AinvB));
894:           PetscCall(PetscObjectCompose((PetscObject)jac->schur, "AinvB", (PetscObject)AinvB));
895:           PetscCall(MatDestroy(&AinvB));
896:         }
897:         PetscCall(MatSchurComplementComputeExplicitOperator(jac->schur, &jac->schur_user));
898:       }
899:       if (kspA != kspInner) PetscCall(KSPSetOperators(kspA, jac->mat[0], jac->pmat[0]));
900:       if (kspUpper != kspA) PetscCall(KSPSetOperators(kspUpper, jac->mat[0], jac->pmat[0]));
901:       PetscCall(KSPSetOperators(jac->kspschur, jac->schur, FieldSplitSchurPre(jac)));
902:     } else {
903:       const char  *Dprefix;
904:       char         schurprefix[256], schurmatprefix[256];
905:       char         schurtestoption[256];
906:       MatNullSpace sp;
907:       KSP          kspt;

909:       /* extract the A01 and A10 matrices */
910:       ilink = jac->head;
911:       PetscCall(ISComplement(ilink->is_col, rstart, rend, &ccis));
912:       if (jac->offdiag_use_amat) {
913:         PetscCall(MatCreateSubMatrix(pc->mat, ilink->is, ccis, MAT_INITIAL_MATRIX, &jac->B));
914:       } else {
915:         PetscCall(MatCreateSubMatrix(pc->pmat, ilink->is, ccis, MAT_INITIAL_MATRIX, &jac->B));
916:       }
917:       PetscCall(ISDestroy(&ccis));
918:       ilink = ilink->next;
919:       if (!flg) {
920:         PetscCall(ISComplement(ilink->is_col, rstart, rend, &ccis));
921:         if (jac->offdiag_use_amat) {
922:           PetscCall(MatCreateSubMatrix(pc->mat, ilink->is, ccis, MAT_INITIAL_MATRIX, &jac->C));
923:         } else {
924:           PetscCall(MatCreateSubMatrix(pc->pmat, ilink->is, ccis, MAT_INITIAL_MATRIX, &jac->C));
925:         }
926:         PetscCall(ISDestroy(&ccis));
927:       } else {
928:         PetscCall(MatIsHermitianKnown(jac->offdiag_use_amat ? pc->mat : pc->pmat, &set, &flg));
929:         if (set && flg) PetscCall(MatCreateHermitianTranspose(jac->B, &jac->C));
930:         else PetscCall(MatCreateTranspose(jac->B, &jac->C));
931:       }
932:       /* Use mat[0] (diagonal block of Amat) preconditioned by pmat[0] to define Schur complement */
933:       PetscCall(MatCreate(((PetscObject)jac->mat[0])->comm, &jac->schur));
934:       PetscCall(MatSetType(jac->schur, MATSCHURCOMPLEMENT));
935:       PetscCall(MatSchurComplementSetSubMatrices(jac->schur, jac->mat[0], jac->pmat[0], jac->B, jac->C, jac->mat[1]));
936:       PetscCall(PetscSNPrintf(schurmatprefix, sizeof(schurmatprefix), "%sfieldsplit_%s_", ((PetscObject)pc)->prefix ? ((PetscObject)pc)->prefix : "", ilink->splitname));
937:       PetscCall(MatSetOptionsPrefix(jac->schur, schurmatprefix));
938:       PetscCall(MatSchurComplementGetKSP(jac->schur, &kspt));
939:       PetscCall(KSPSetOptionsPrefix(kspt, schurmatprefix));

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

945:       PetscCall(PetscSNPrintf(schurtestoption, sizeof(schurtestoption), "-fieldsplit_%s_inner_", ilink->splitname));
946:       PetscCall(PetscOptionsFindPairPrefix_Private(((PetscObject)pc)->options, ((PetscObject)pc)->prefix, schurtestoption, NULL, NULL, &flg));
947:       if (flg) {
948:         DM  dmInner;
949:         KSP kspInner;
950:         PC  pcInner;

952:         PetscCall(MatSchurComplementGetKSP(jac->schur, &kspInner));
953:         PetscCall(KSPReset(kspInner));
954:         PetscCall(KSPSetOperators(kspInner, jac->mat[0], jac->pmat[0]));
955:         PetscCall(PetscSNPrintf(schurprefix, sizeof(schurprefix), "%sfieldsplit_%s_inner_", ((PetscObject)pc)->prefix ? ((PetscObject)pc)->prefix : "", ilink->splitname));
956:         /* Indent this deeper to emphasize the "inner" nature of this solver. */
957:         PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspInner, (PetscObject)pc, 2));
958:         PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspInner->pc, (PetscObject)pc, 2));
959:         PetscCall(KSPSetOptionsPrefix(kspInner, schurprefix));

961:         /* Set DM for new solver */
962:         PetscCall(KSPGetDM(jac->head->ksp, &dmInner));
963:         PetscCall(KSPSetDM(kspInner, dmInner));
964:         PetscCall(KSPSetDMActive(kspInner, PETSC_FALSE));

966:         /* Defaults to PCKSP as preconditioner */
967:         PetscCall(KSPGetPC(kspInner, &pcInner));
968:         PetscCall(PCSetType(pcInner, PCKSP));
969:         PetscCall(PCKSPSetKSP(pcInner, jac->head->ksp));
970:       } else {
971:         /* Use the outer solver for the inner solve, but revert the KSPPREONLY from PCFieldSplitSetFields_FieldSplit or
972:           * PCFieldSplitSetIS_FieldSplit. We don't want KSPPREONLY because it makes the Schur complement inexact,
973:           * preventing Schur complement reduction to be an accurate solve. Usually when an iterative solver is used for
974:           * S = D - C A_inner^{-1} B, we expect S to be defined using an accurate definition of A_inner^{-1}, so we make
975:           * GMRES the default. Note that it is also common to use PREONLY for S, in which case S may not be used
976:           * directly, and the user is responsible for setting an inexact method for fieldsplit's A^{-1}. */
977:         PetscCall(KSPSetType(jac->head->ksp, KSPGMRES));
978:         PetscCall(MatSchurComplementSetKSP(jac->schur, jac->head->ksp));
979:       }
980:       PetscCall(KSPSetOperators(jac->head->ksp, jac->mat[0], jac->pmat[0]));
981:       PetscCall(KSPSetFromOptions(jac->head->ksp));
982:       PetscCall(MatSetFromOptions(jac->schur));

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

989:         PetscCall(MatSchurComplementGetKSP(jac->schur, &kspInner));
990:         PetscCall(KSPGetPC(kspInner, &pcInner));
991:         PetscCall(PetscObjectTypeCompare((PetscObject)pcInner, PCKSP, &flg));
992:         if (flg) {
993:           KSP ksp;

995:           PetscCall(PCKSPGetKSP(pcInner, &ksp));
996:           if (ksp == jac->head->ksp) PetscCall(PCSetUseAmat(pcInner, PETSC_TRUE));
997:         }
998:       }
999:       PetscCall(PetscSNPrintf(schurtestoption, sizeof(schurtestoption), "-fieldsplit_%s_upper_", ilink->splitname));
1000:       PetscCall(PetscOptionsFindPairPrefix_Private(((PetscObject)pc)->options, ((PetscObject)pc)->prefix, schurtestoption, NULL, NULL, &flg));
1001:       if (flg) {
1002:         DM dmInner;

1004:         PetscCall(PetscSNPrintf(schurprefix, sizeof(schurprefix), "%sfieldsplit_%s_upper_", ((PetscObject)pc)->prefix ? ((PetscObject)pc)->prefix : "", ilink->splitname));
1005:         PetscCall(KSPCreate(PetscObjectComm((PetscObject)pc), &jac->kspupper));
1006:         PetscCall(KSPSetNestLevel(jac->kspupper, pc->kspnestlevel));
1007:         PetscCall(KSPSetErrorIfNotConverged(jac->kspupper, pc->erroriffailure));
1008:         PetscCall(KSPSetOptionsPrefix(jac->kspupper, schurprefix));
1009:         PetscCall(PetscObjectIncrementTabLevel((PetscObject)jac->kspupper, (PetscObject)pc, 1));
1010:         PetscCall(PetscObjectIncrementTabLevel((PetscObject)jac->kspupper->pc, (PetscObject)pc, 1));
1011:         PetscCall(KSPGetDM(jac->head->ksp, &dmInner));
1012:         PetscCall(KSPSetDM(jac->kspupper, dmInner));
1013:         PetscCall(KSPSetDMActive(jac->kspupper, PETSC_FALSE));
1014:         PetscCall(KSPSetFromOptions(jac->kspupper));
1015:         PetscCall(KSPSetOperators(jac->kspupper, jac->mat[0], jac->pmat[0]));
1016:         PetscCall(VecDuplicate(jac->head->x, &jac->head->z));
1017:       } else {
1018:         jac->kspupper = jac->head->ksp;
1019:         PetscCall(PetscObjectReference((PetscObject)jac->head->ksp));
1020:       }

1022:       if (jac->schurpre == PC_FIELDSPLIT_SCHUR_PRE_SELFP) PetscCall(MatSchurComplementGetPmat(jac->schur, MAT_INITIAL_MATRIX, &jac->schurp));
1023:       PetscCall(KSPCreate(PetscObjectComm((PetscObject)pc), &jac->kspschur));
1024:       PetscCall(KSPSetNestLevel(jac->kspschur, pc->kspnestlevel));
1025:       PetscCall(KSPSetErrorIfNotConverged(jac->kspschur, pc->erroriffailure));
1026:       PetscCall(PetscObjectIncrementTabLevel((PetscObject)jac->kspschur, (PetscObject)pc, 1));
1027:       if (jac->schurpre == PC_FIELDSPLIT_SCHUR_PRE_SELF) {
1028:         PC pcschur;
1029:         PetscCall(KSPGetPC(jac->kspschur, &pcschur));
1030:         PetscCall(PCSetType(pcschur, PCNONE));
1031:         /* Note: This is bad if there exist preconditioners for MATSCHURCOMPLEMENT */
1032:       } else if (jac->schurpre == PC_FIELDSPLIT_SCHUR_PRE_FULL) {
1033:         if (jac->schurfactorization == PC_FIELDSPLIT_SCHUR_FACT_FULL && jac->kspupper == jac->head->ksp) {
1034:           Mat AinvB;

1036:           PetscCall(MatCreate(PetscObjectComm((PetscObject)jac->schur), &AinvB));
1037:           PetscCall(PetscObjectCompose((PetscObject)jac->schur, "AinvB", (PetscObject)AinvB));
1038:           PetscCall(MatDestroy(&AinvB));
1039:         }
1040:         PetscCall(MatSchurComplementComputeExplicitOperator(jac->schur, &jac->schur_user));
1041:       }
1042:       PetscCall(KSPSetOperators(jac->kspschur, jac->schur, FieldSplitSchurPre(jac)));
1043:       PetscCall(KSPGetOptionsPrefix(jac->head->next->ksp, &Dprefix));
1044:       PetscCall(KSPSetOptionsPrefix(jac->kspschur, Dprefix));
1045:       /* propagate DM */
1046:       {
1047:         DM sdm;
1048:         PetscCall(KSPGetDM(jac->head->next->ksp, &sdm));
1049:         if (sdm) {
1050:           PetscCall(KSPSetDM(jac->kspschur, sdm));
1051:           PetscCall(KSPSetDMActive(jac->kspschur, PETSC_FALSE));
1052:         }
1053:       }
1054:       /* really want setfromoptions called in PCSetFromOptions_FieldSplit(), but it is not ready yet */
1055:       /* need to call this every time, since the jac->kspschur is freshly created, otherwise its options never get set */
1056:       PetscCall(KSPSetFromOptions(jac->kspschur));
1057:     }
1058:     PetscCall(MatAssemblyBegin(jac->schur, MAT_FINAL_ASSEMBLY));
1059:     PetscCall(MatAssemblyEnd(jac->schur, MAT_FINAL_ASSEMBLY));

1061:     /* HACK: special support to forward L and Lp matrices that might be used by PCLSC */
1062:     PetscCall(PetscSNPrintf(lscname, sizeof(lscname), "%s_LSC_L", ilink->splitname));
1063:     PetscCall(PetscObjectQuery((PetscObject)pc->mat, lscname, &LSC_L));
1064:     if (!LSC_L) PetscCall(PetscObjectQuery((PetscObject)pc->pmat, lscname, &LSC_L));
1065:     if (LSC_L) PetscCall(PetscObjectCompose((PetscObject)jac->schur, "LSC_L", LSC_L));
1066:     PetscCall(PetscSNPrintf(lscname, sizeof(lscname), "%s_LSC_Lp", ilink->splitname));
1067:     PetscCall(PetscObjectQuery((PetscObject)pc->pmat, lscname, &LSC_L));
1068:     if (!LSC_L) PetscCall(PetscObjectQuery((PetscObject)pc->mat, lscname, &LSC_L));
1069:     if (LSC_L) PetscCall(PetscObjectCompose((PetscObject)jac->schur, "LSC_Lp", LSC_L));
1070:   } else if (jac->type == PC_COMPOSITE_GKB) {
1071:     IS       ccis;
1072:     PetscInt rstart, rend;

1074:     PetscCheck(nsplit == 2, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_INCOMP, "To use GKB preconditioner you must have exactly 2 fields");

1076:     ilink = jac->head;

1078:     /* When extracting off-diagonal submatrices, we take complements from this range */
1079:     PetscCall(MatGetOwnershipRangeColumn(pc->mat, &rstart, &rend));

1081:     PetscCall(ISComplement(ilink->is_col, rstart, rend, &ccis));
1082:     if (jac->offdiag_use_amat) {
1083:       PetscCall(MatCreateSubMatrix(pc->mat, ilink->is, ccis, MAT_INITIAL_MATRIX, &jac->B));
1084:     } else {
1085:       PetscCall(MatCreateSubMatrix(pc->pmat, ilink->is, ccis, MAT_INITIAL_MATRIX, &jac->B));
1086:     }
1087:     PetscCall(ISDestroy(&ccis));
1088:     /* Create work vectors for GKB algorithm */
1089:     PetscCall(VecDuplicate(ilink->x, &jac->u));
1090:     PetscCall(VecDuplicate(ilink->x, &jac->Hu));
1091:     PetscCall(VecDuplicate(ilink->x, &jac->w2));
1092:     ilink = ilink->next;
1093:     PetscCall(ISComplement(ilink->is_col, rstart, rend, &ccis));
1094:     if (jac->offdiag_use_amat) {
1095:       PetscCall(MatCreateSubMatrix(pc->mat, ilink->is, ccis, MAT_INITIAL_MATRIX, &jac->C));
1096:     } else {
1097:       PetscCall(MatCreateSubMatrix(pc->pmat, ilink->is, ccis, MAT_INITIAL_MATRIX, &jac->C));
1098:     }
1099:     PetscCall(ISDestroy(&ccis));
1100:     /* Create work vectors for GKB algorithm */
1101:     PetscCall(VecDuplicate(ilink->x, &jac->v));
1102:     PetscCall(VecDuplicate(ilink->x, &jac->d));
1103:     PetscCall(VecDuplicate(ilink->x, &jac->w1));
1104:     PetscCall(MatGolubKahanComputeExplicitOperator(jac->mat[0], jac->B, jac->C, &jac->H, jac->gkbnu));
1105:     PetscCall(PetscCalloc1(jac->gkbdelay, &jac->vecz));

1107:     ilink = jac->head;
1108:     PetscCall(KSPSetOperators(ilink->ksp, jac->H, jac->H));
1109:     if (!jac->suboptionsset) PetscCall(KSPSetFromOptions(ilink->ksp));
1110:     /* Create gkb_monitor context */
1111:     if (jac->gkbmonitor) {
1112:       PetscInt tablevel;
1113:       PetscCall(PetscViewerCreate(PETSC_COMM_WORLD, &jac->gkbviewer));
1114:       PetscCall(PetscViewerSetType(jac->gkbviewer, PETSCVIEWERASCII));
1115:       PetscCall(PetscObjectGetTabLevel((PetscObject)ilink->ksp, &tablevel));
1116:       PetscCall(PetscViewerASCIISetTab(jac->gkbviewer, tablevel));
1117:       PetscCall(PetscObjectIncrementTabLevel((PetscObject)ilink->ksp, (PetscObject)ilink->ksp, 1));
1118:     }
1119:   } else {
1120:     /* set up the individual splits' PCs */
1121:     i     = 0;
1122:     ilink = jac->head;
1123:     while (ilink) {
1124:       PetscCall(KSPSetOperators(ilink->ksp, jac->mat[i], jac->pmat[i]));
1125:       /* really want setfromoptions called in PCSetFromOptions_FieldSplit(), but it is not ready yet */
1126:       if (!jac->suboptionsset) PetscCall(KSPSetFromOptions(ilink->ksp));
1127:       i++;
1128:       ilink = ilink->next;
1129:     }
1130:   }

1132:   /* Set coordinates to the sub PC objects whenever these are set */
1133:   if (jac->coordinates_set) {
1134:     PC pc_coords;
1135:     if (jac->type == PC_COMPOSITE_SCHUR) {
1136:       // Head is first block.
1137:       PetscCall(KSPGetPC(jac->head->ksp, &pc_coords));
1138:       PetscCall(PCSetCoordinates(pc_coords, jac->head->dim, jac->head->ndofs, jac->head->coords));
1139:       // Second one is Schur block, but its KSP object is in kspschur.
1140:       PetscCall(KSPGetPC(jac->kspschur, &pc_coords));
1141:       PetscCall(PCSetCoordinates(pc_coords, jac->head->next->dim, jac->head->next->ndofs, jac->head->next->coords));
1142:     } else if (jac->type == PC_COMPOSITE_GKB) {
1143:       PetscCall(PetscInfo(pc, "Warning: Setting coordinates does nothing for the GKB Fieldpslit preconditioner\n"));
1144:     } else {
1145:       ilink = jac->head;
1146:       while (ilink) {
1147:         PetscCall(KSPGetPC(ilink->ksp, &pc_coords));
1148:         PetscCall(PCSetCoordinates(pc_coords, ilink->dim, ilink->ndofs, ilink->coords));
1149:         ilink = ilink->next;
1150:       }
1151:     }
1152:   }

1154:   jac->suboptionsset = PETSC_TRUE;
1155:   PetscFunctionReturn(PETSC_SUCCESS);
1156: }

1158: #define FieldSplitSplitSolveAdd(ilink, xx, yy) \
1159:   ((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) || \
1160:                     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) || \
1161:                     VecScatterEnd(ilink->sctx, ilink->y, yy, ADD_VALUES, SCATTER_REVERSE)))

1163: static PetscErrorCode PCSetUpOnBlocks_FieldSplit_Schur(PC pc)
1164: {
1165:   PC_FieldSplit    *jac    = (PC_FieldSplit *)pc->data;
1166:   PC_FieldSplitLink ilinkA = jac->head;
1167:   KSP               kspA = ilinkA->ksp, kspUpper = jac->kspupper;

1169:   PetscFunctionBegin;
1170:   if (jac->schurfactorization == PC_FIELDSPLIT_SCHUR_FACT_FULL && kspUpper != kspA) {
1171:     PetscCall(KSPSetUp(kspUpper));
1172:     PetscCall(KSPSetUpOnBlocks(kspUpper));
1173:   }
1174:   PetscCall(KSPSetUp(kspA));
1175:   PetscCall(KSPSetUpOnBlocks(kspA));
1176:   if (jac->schurpre != PC_FIELDSPLIT_SCHUR_PRE_FULL) {
1177:     PetscCall(KSPSetUp(jac->kspschur));
1178:     PetscCall(KSPSetUpOnBlocks(jac->kspschur));
1179:   } else if (kspUpper == kspA) {
1180:     Mat      AinvB, A;
1181:     PetscInt m, M, N;

1183:     PetscCall(PetscObjectQuery((PetscObject)jac->schur, "AinvB", (PetscObject *)&AinvB));
1184:     if (AinvB) {
1185:       PetscCall(MatGetSize(AinvB, NULL, &N));
1186:       if (N == -1) { // first time PCSetUpOnBlocks_FieldSplit_Schur() is called
1187:         VecType      vtype;
1188:         PetscMemType mtype;
1189:         PetscScalar *array;

1191:         PetscCall(MatGetSize(jac->B, &M, &N));
1192:         PetscCall(MatGetLocalSize(jac->B, &m, NULL));
1193:         PetscCall(MatGetVecType(jac->B, &vtype));
1194:         PetscCall(VecGetArrayAndMemType(ilinkA->x, &array, &mtype));
1195:         PetscCall(VecRestoreArrayAndMemType(ilinkA->x, &array));
1196:         if (PetscMemTypeHost(mtype) || (!PetscDefined(HAVE_CUDA) && !PetscDefined(HAVE_HIP))) PetscCall(PetscMalloc1(m * (N + 1), &array));
1197: #if PetscDefined(HAVE_CUDA)
1198:         else if (PetscMemTypeCUDA(mtype)) PetscCallCUDA(cudaMalloc((void **)&array, sizeof(PetscScalar) * m * (N + 1)));
1199: #endif
1200: #if PetscDefined(HAVE_HIP)
1201:         else if (PetscMemTypeHIP(mtype)) PetscCallHIP(hipMalloc((void **)&array, sizeof(PetscScalar) * m * (N + 1)));
1202: #endif
1203:         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
1204:         PetscCall(MatHeaderReplace(AinvB, &A));
1205:       }
1206:     }
1207:   }
1208:   PetscFunctionReturn(PETSC_SUCCESS);
1209: }

1211: static PetscErrorCode PCSetUpOnBlocks_FieldSplit(PC pc)
1212: {
1213:   PC_FieldSplit    *jac   = (PC_FieldSplit *)pc->data;
1214:   PC_FieldSplitLink ilink = jac->head;

1216:   PetscFunctionBegin;
1217:   while (ilink) {
1218:     PetscCall(KSPSetUp(ilink->ksp));
1219:     PetscCall(KSPSetUpOnBlocks(ilink->ksp));
1220:     ilink = ilink->next;
1221:   }
1222:   PetscFunctionReturn(PETSC_SUCCESS);
1223: }

1225: static PetscErrorCode PCSetUpOnBlocks_FieldSplit_GKB(PC pc)
1226: {
1227:   PC_FieldSplit    *jac    = (PC_FieldSplit *)pc->data;
1228:   PC_FieldSplitLink ilinkA = jac->head;
1229:   KSP               ksp    = ilinkA->ksp;

1231:   PetscFunctionBegin;
1232:   PetscCall(KSPSetUp(ksp));
1233:   PetscCall(KSPSetUpOnBlocks(ksp));
1234:   PetscFunctionReturn(PETSC_SUCCESS);
1235: }

1237: static PetscErrorCode PCApply_FieldSplit_Schur(PC pc, Vec x, Vec y)
1238: {
1239:   PC_FieldSplit    *jac    = (PC_FieldSplit *)pc->data;
1240:   PC_FieldSplitLink ilinkA = jac->head, ilinkD = ilinkA->next;
1241:   KSP               kspA = ilinkA->ksp, kspLower = kspA, kspUpper = jac->kspupper;
1242:   Mat               AinvB = NULL;
1243:   PetscInt          N, P;

1245:   PetscFunctionBegin;
1246:   switch (jac->schurfactorization) {
1247:   case PC_FIELDSPLIT_SCHUR_FACT_DIAG:
1248:     /* [A00 0; 0 -S], positive definite, suitable for MINRES */
1249:     PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1250:     PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1251:     PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1252:     PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1253:     PetscCall(KSPSolve(kspA, ilinkA->x, ilinkA->y));
1254:     PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1255:     PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1256:     PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1257:     PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1258:     PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1259:     PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, 1));
1260:     PetscCall(KSPSolve(jac->kspschur, ilinkD->x, ilinkD->y));
1261:     PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y));
1262:     PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, -1));
1263:     PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1264:     PetscCall(VecScale(ilinkD->y, jac->schurscale));
1265:     PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1266:     PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1267:     PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1268:     break;
1269:   case PC_FIELDSPLIT_SCHUR_FACT_LOWER:
1270:     /* [A00 0; A10 S], suitable for left preconditioning */
1271:     PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1272:     PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1273:     PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1274:     PetscCall(KSPSolve(kspA, ilinkA->x, ilinkA->y));
1275:     PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1276:     PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1277:     PetscCall(MatMult(jac->C, ilinkA->y, ilinkD->x));
1278:     PetscCall(VecScale(ilinkD->x, -1.));
1279:     PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD));
1280:     PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1281:     PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD));
1282:     PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1283:     PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, 1));
1284:     PetscCall(KSPSolve(jac->kspschur, ilinkD->x, ilinkD->y));
1285:     PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, -1));
1286:     PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y));
1287:     PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1288:     PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1289:     PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1290:     PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1291:     break;
1292:   case PC_FIELDSPLIT_SCHUR_FACT_UPPER:
1293:     /* [A00 A01; 0 S], suitable for right preconditioning */
1294:     PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1295:     PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, INSERT_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(MatMult(jac->B, ilinkD->y, ilinkA->x));
1303:     PetscCall(VecScale(ilinkA->x, -1.));
1304:     PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, ADD_VALUES, SCATTER_FORWARD));
1305:     PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1306:     PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, ADD_VALUES, SCATTER_FORWARD));
1307:     PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1308:     PetscCall(KSPSolve(kspA, ilinkA->x, ilinkA->y));
1309:     PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1310:     PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1311:     PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1312:     PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1313:     PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1314:     break;
1315:   case PC_FIELDSPLIT_SCHUR_FACT_FULL:
1316:     /* [1 0; A10 A00^{-1} 1] [A00 0; 0 S] [1 A00^{-1}A01; 0 1] */
1317:     PetscCall(MatGetSize(jac->B, NULL, &P));
1318:     N = P;
1319:     PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1320:     PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1321:     PetscCall(PetscLogEventBegin(KSP_Solve_FS_L, kspLower, ilinkA->x, ilinkA->y, NULL));
1322:     if (kspUpper == kspA) {
1323:       PetscCall(PetscObjectQuery((PetscObject)jac->schur, "AinvB", (PetscObject *)&AinvB));
1324:       if (AinvB) {
1325:         PetscCall(MatGetSize(AinvB, NULL, &N));
1326:         if (N > P) { // first time PCApply_FieldSplit_Schur() is called
1327:           PetscMemType mtype;
1328:           Vec          c = NULL;
1329:           PetscScalar *array;
1330:           PetscInt     m, M;

1332:           PetscCall(MatGetSize(jac->B, &M, NULL));
1333:           PetscCall(MatGetLocalSize(jac->B, &m, NULL));
1334:           PetscCall(MatDenseGetArrayAndMemType(AinvB, &array, &mtype));
1335:           if (PetscMemTypeHost(mtype) || (!PetscDefined(HAVE_CUDA) && !PetscDefined(HAVE_HIP))) PetscCall(VecCreateMPIWithArray(PetscObjectComm((PetscObject)jac->schur), 1, m, M, array + m * P, &c));
1336: #if PetscDefined(HAVE_CUDA)
1337:           else if (PetscMemTypeCUDA(mtype)) PetscCall(VecCreateMPICUDAWithArray(PetscObjectComm((PetscObject)jac->schur), 1, m, M, array + m * P, &c));
1338: #endif
1339: #if PetscDefined(HAVE_HIP)
1340:           else if (PetscMemTypeHIP(mtype)) PetscCall(VecCreateMPIHIPWithArray(PetscObjectComm((PetscObject)jac->schur), 1, m, M, array + m * P, &c));
1341: #endif
1342:           PetscCall(MatDenseRestoreArrayAndMemType(AinvB, &array));
1343:           PetscCall(VecCopy(ilinkA->x, c));
1344:           PetscCall(MatSchurComplementComputeExplicitOperator(jac->schur, &jac->schur_user));
1345:           PetscCall(KSPSetOperators(jac->kspschur, jac->schur, jac->schur_user));
1346:           PetscCall(VecCopy(c, ilinkA->y)); // retrieve the solution as the last column of the composed Mat
1347:           PetscCall(VecDestroy(&c));
1348:         }
1349:       }
1350:     }
1351:     if (N == P) PetscCall(KSPSolve(kspLower, ilinkA->x, ilinkA->y));
1352:     PetscCall(KSPCheckSolve(kspLower, pc, ilinkA->y));
1353:     PetscCall(PetscLogEventEnd(KSP_Solve_FS_L, kspLower, ilinkA->x, ilinkA->y, NULL));
1354:     PetscCall(MatMult(jac->C, ilinkA->y, ilinkD->x));
1355:     PetscCall(VecScale(ilinkD->x, -1.0));
1356:     PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD));
1357:     PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD));

1359:     PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1360:     PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, 1));
1361:     PetscCall(KSPSolve(jac->kspschur, ilinkD->x, ilinkD->y));
1362:     PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, -1));
1363:     PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y));
1364:     PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1365:     PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));

1367:     if (kspUpper == kspA) {
1368:       if (!AinvB) {
1369:         PetscCall(MatMult(jac->B, ilinkD->y, ilinkA->y));
1370:         PetscCall(VecAXPY(ilinkA->x, -1.0, ilinkA->y));
1371:         PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1372:         PetscCall(KSPSolve(kspA, ilinkA->x, ilinkA->y));
1373:         PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1374:         PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1375:       } else PetscCall(MatMultAdd(AinvB, ilinkD->y, ilinkA->y, ilinkA->y));
1376:     } else {
1377:       PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1378:       PetscCall(KSPSolve(kspA, ilinkA->x, ilinkA->y));
1379:       PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1380:       PetscCall(MatMult(jac->B, ilinkD->y, ilinkA->x));
1381:       PetscCall(PetscLogEventBegin(KSP_Solve_FS_U, kspUpper, ilinkA->x, ilinkA->z, NULL));
1382:       PetscCall(KSPSolve(kspUpper, ilinkA->x, ilinkA->z));
1383:       PetscCall(KSPCheckSolve(kspUpper, pc, ilinkA->z));
1384:       PetscCall(PetscLogEventEnd(KSP_Solve_FS_U, kspUpper, ilinkA->x, ilinkA->z, NULL));
1385:       PetscCall(VecAXPY(ilinkA->y, -1.0, ilinkA->z));
1386:     }
1387:     PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1388:     PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1389:     PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1390:   }
1391:   PetscFunctionReturn(PETSC_SUCCESS);
1392: }

1394: static PetscErrorCode PCApplyTranspose_FieldSplit_Schur(PC pc, Vec x, Vec y)
1395: {
1396:   PC_FieldSplit    *jac    = (PC_FieldSplit *)pc->data;
1397:   PC_FieldSplitLink ilinkA = jac->head, ilinkD = ilinkA->next;
1398:   KSP               kspA = ilinkA->ksp, kspLower = kspA, kspUpper = jac->kspupper;

1400:   PetscFunctionBegin;
1401:   switch (jac->schurfactorization) {
1402:   case PC_FIELDSPLIT_SCHUR_FACT_DIAG:
1403:     /* [A00 0; 0 -S], positive definite, suitable for MINRES */
1404:     PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1405:     PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1406:     PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1407:     PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1408:     PetscCall(KSPSolveTranspose(kspA, ilinkA->x, ilinkA->y));
1409:     PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1410:     PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1411:     PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1412:     PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1413:     PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1414:     PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, 1));
1415:     PetscCall(KSPSolveTranspose(jac->kspschur, ilinkD->x, ilinkD->y));
1416:     PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, -1));
1417:     PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y));
1418:     PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1419:     PetscCall(VecScale(ilinkD->y, jac->schurscale));
1420:     PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1421:     PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1422:     PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1423:     break;
1424:   case PC_FIELDSPLIT_SCHUR_FACT_UPPER:
1425:     PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1426:     PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1427:     PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1428:     PetscCall(KSPSolveTranspose(kspA, ilinkA->x, ilinkA->y));
1429:     PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1430:     PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1431:     PetscCall(MatMultTranspose(jac->B, ilinkA->y, ilinkD->x));
1432:     PetscCall(VecScale(ilinkD->x, -1.));
1433:     PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD));
1434:     PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1435:     PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD));
1436:     PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1437:     PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, 1));
1438:     PetscCall(KSPSolveTranspose(jac->kspschur, ilinkD->x, ilinkD->y));
1439:     PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, -1));
1440:     PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y));
1441:     PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1442:     PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1443:     PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1444:     PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1445:     break;
1446:   case PC_FIELDSPLIT_SCHUR_FACT_LOWER:
1447:     PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1448:     PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1449:     PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1450:     PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, 1));
1451:     PetscCall(KSPSolveTranspose(jac->kspschur, ilinkD->x, ilinkD->y));
1452:     PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, -1));
1453:     PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y));
1454:     PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1455:     PetscCall(MatMultTranspose(jac->C, ilinkD->y, ilinkA->x));
1456:     PetscCall(VecScale(ilinkA->x, -1.));
1457:     PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, ADD_VALUES, SCATTER_FORWARD));
1458:     PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1459:     PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, ADD_VALUES, SCATTER_FORWARD));
1460:     PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1461:     PetscCall(KSPSolveTranspose(kspA, ilinkA->x, ilinkA->y));
1462:     PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1463:     PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1464:     PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1465:     PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1466:     PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1467:     break;
1468:   case PC_FIELDSPLIT_SCHUR_FACT_FULL:
1469:     PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1470:     PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1471:     PetscCall(PetscLogEventBegin(KSP_Solve_FS_U, kspUpper, ilinkA->x, ilinkA->y, NULL));
1472:     PetscCall(KSPSolveTranspose(kspUpper, ilinkA->x, ilinkA->y));
1473:     PetscCall(KSPCheckSolve(kspUpper, pc, ilinkA->y));
1474:     PetscCall(PetscLogEventEnd(KSP_Solve_FS_U, kspUpper, ilinkA->x, ilinkA->y, NULL));
1475:     PetscCall(MatMultTranspose(jac->B, ilinkA->y, ilinkD->x));
1476:     PetscCall(VecScale(ilinkD->x, -1.0));
1477:     PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD));
1478:     PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD));

1480:     PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1481:     PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, 1));
1482:     PetscCall(KSPSolveTranspose(jac->kspschur, ilinkD->x, ilinkD->y));
1483:     PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, -1));
1484:     PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y));
1485:     PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1486:     PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));

1488:     if (kspLower == kspA) {
1489:       PetscCall(MatMultTranspose(jac->C, ilinkD->y, ilinkA->y));
1490:       PetscCall(VecAXPY(ilinkA->x, -1.0, ilinkA->y));
1491:       PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1492:       PetscCall(KSPSolveTranspose(kspA, ilinkA->x, ilinkA->y));
1493:       PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1494:       PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1495:     } else {
1496:       PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1497:       PetscCall(KSPSolveTranspose(kspA, ilinkA->x, ilinkA->y));
1498:       PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1499:       PetscCall(MatMultTranspose(jac->C, ilinkD->y, ilinkA->x));
1500:       PetscCall(PetscLogEventBegin(KSP_Solve_FS_L, kspLower, ilinkA->x, ilinkA->z, NULL));
1501:       PetscCall(KSPSolveTranspose(kspLower, ilinkA->x, ilinkA->z));
1502:       PetscCall(KSPCheckSolve(kspLower, pc, ilinkA->z));
1503:       PetscCall(PetscLogEventEnd(KSP_Solve_FS_L, kspLower, ilinkA->x, ilinkA->z, NULL));
1504:       PetscCall(VecAXPY(ilinkA->y, -1.0, ilinkA->z));
1505:     }
1506:     PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1507:     PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1508:     PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1509:   }
1510:   PetscFunctionReturn(PETSC_SUCCESS);
1511: }

1513: static PetscErrorCode PCApply_FieldSplit(PC pc, Vec x, Vec y)
1514: {
1515:   PC_FieldSplit    *jac   = (PC_FieldSplit *)pc->data;
1516:   PC_FieldSplitLink ilink = jac->head;
1517:   PetscInt          cnt, bs;

1519:   PetscFunctionBegin;
1520:   if (jac->type == PC_COMPOSITE_ADDITIVE) {
1521:     PetscBool matnest;

1523:     PetscCall(PetscObjectTypeCompare((PetscObject)pc->pmat, MATNEST, &matnest));
1524:     if (jac->defaultsplit && !matnest) {
1525:       PetscCall(VecGetBlockSize(x, &bs));
1526:       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);
1527:       PetscCall(VecGetBlockSize(y, &bs));
1528:       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);
1529:       PetscCall(VecStrideGatherAll(x, jac->x, INSERT_VALUES));
1530:       while (ilink) {
1531:         PetscCall(PetscLogEventBegin(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1532:         PetscCall(KSPSolve(ilink->ksp, ilink->x, ilink->y));
1533:         PetscCall(KSPCheckSolve(ilink->ksp, pc, ilink->y));
1534:         PetscCall(PetscLogEventEnd(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1535:         ilink = ilink->next;
1536:       }
1537:       PetscCall(VecStrideScatterAll(jac->y, y, INSERT_VALUES));
1538:     } else {
1539:       PetscCall(VecSet(y, 0.0));
1540:       while (ilink) {
1541:         PetscCall(FieldSplitSplitSolveAdd(ilink, x, y));
1542:         ilink = ilink->next;
1543:       }
1544:     }
1545:   } else if (jac->type == PC_COMPOSITE_MULTIPLICATIVE && jac->nsplits == 2) {
1546:     PetscCall(VecSet(y, 0.0));
1547:     /* solve on first block for first block variables */
1548:     PetscCall(VecScatterBegin(ilink->sctx, x, ilink->x, INSERT_VALUES, SCATTER_FORWARD));
1549:     PetscCall(VecScatterEnd(ilink->sctx, x, ilink->x, INSERT_VALUES, SCATTER_FORWARD));
1550:     PetscCall(PetscLogEventBegin(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1551:     PetscCall(KSPSolve(ilink->ksp, ilink->x, ilink->y));
1552:     PetscCall(KSPCheckSolve(ilink->ksp, pc, ilink->y));
1553:     PetscCall(PetscLogEventEnd(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1554:     PetscCall(VecScatterBegin(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE));
1555:     PetscCall(VecScatterEnd(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE));

1557:     /* compute the residual only onto second block variables using first block variables */
1558:     PetscCall(MatMult(jac->Afield[1], ilink->y, ilink->next->x));
1559:     ilink = ilink->next;
1560:     PetscCall(VecScale(ilink->x, -1.0));
1561:     PetscCall(VecScatterBegin(ilink->sctx, x, ilink->x, ADD_VALUES, SCATTER_FORWARD));
1562:     PetscCall(VecScatterEnd(ilink->sctx, x, ilink->x, ADD_VALUES, SCATTER_FORWARD));

1564:     /* solve on second block variables */
1565:     PetscCall(PetscLogEventBegin(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1566:     PetscCall(KSPSolve(ilink->ksp, ilink->x, ilink->y));
1567:     PetscCall(KSPCheckSolve(ilink->ksp, pc, ilink->y));
1568:     PetscCall(PetscLogEventEnd(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1569:     PetscCall(VecScatterBegin(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE));
1570:     PetscCall(VecScatterEnd(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE));
1571:   } else if (jac->type == PC_COMPOSITE_MULTIPLICATIVE || jac->type == PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE) {
1572:     if (!jac->w1) {
1573:       PetscCall(VecDuplicate(x, &jac->w1));
1574:       PetscCall(VecDuplicate(x, &jac->w2));
1575:     }
1576:     PetscCall(VecSet(y, 0.0));
1577:     PetscCall(FieldSplitSplitSolveAdd(ilink, x, y));
1578:     cnt = 1;
1579:     while (ilink->next) {
1580:       ilink = ilink->next;
1581:       /* compute the residual only over the part of the vector needed */
1582:       PetscCall(MatMult(jac->Afield[cnt++], y, ilink->x));
1583:       PetscCall(VecScale(ilink->x, -1.0));
1584:       PetscCall(VecScatterBegin(ilink->sctx, x, ilink->x, ADD_VALUES, SCATTER_FORWARD));
1585:       PetscCall(VecScatterEnd(ilink->sctx, x, ilink->x, ADD_VALUES, SCATTER_FORWARD));
1586:       PetscCall(PetscLogEventBegin(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1587:       PetscCall(KSPSolve(ilink->ksp, ilink->x, ilink->y));
1588:       PetscCall(KSPCheckSolve(ilink->ksp, pc, ilink->y));
1589:       PetscCall(PetscLogEventEnd(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1590:       PetscCall(VecScatterBegin(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE));
1591:       PetscCall(VecScatterEnd(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE));
1592:     }
1593:     if (jac->type == PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE) {
1594:       cnt -= 2;
1595:       while (ilink->previous) {
1596:         ilink = ilink->previous;
1597:         /* compute the residual only over the part of the vector needed */
1598:         PetscCall(MatMult(jac->Afield[cnt--], y, ilink->x));
1599:         PetscCall(VecScale(ilink->x, -1.0));
1600:         PetscCall(VecScatterBegin(ilink->sctx, x, ilink->x, ADD_VALUES, SCATTER_FORWARD));
1601:         PetscCall(VecScatterEnd(ilink->sctx, x, ilink->x, ADD_VALUES, SCATTER_FORWARD));
1602:         PetscCall(PetscLogEventBegin(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1603:         PetscCall(KSPSolve(ilink->ksp, ilink->x, ilink->y));
1604:         PetscCall(KSPCheckSolve(ilink->ksp, pc, ilink->y));
1605:         PetscCall(PetscLogEventEnd(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1606:         PetscCall(VecScatterBegin(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE));
1607:         PetscCall(VecScatterEnd(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE));
1608:       }
1609:     }
1610:   } else SETERRQ(PetscObjectComm((PetscObject)pc), PETSC_ERR_SUP, "Unsupported or unknown composition %d", (int)jac->type);
1611:   PetscFunctionReturn(PETSC_SUCCESS);
1612: }

1614: static PetscErrorCode PCApply_FieldSplit_GKB(PC pc, Vec x, Vec y)
1615: {
1616:   PC_FieldSplit    *jac    = (PC_FieldSplit *)pc->data;
1617:   PC_FieldSplitLink ilinkA = jac->head, ilinkD = ilinkA->next;
1618:   KSP               ksp = ilinkA->ksp;
1619:   Vec               u, v, Hu, d, work1, work2;
1620:   PetscScalar       alpha, z, nrmz2, *vecz;
1621:   PetscReal         lowbnd, nu, beta;
1622:   PetscInt          j, iterGKB;

1624:   PetscFunctionBegin;
1625:   PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1626:   PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1627:   PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1628:   PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));

1630:   u     = jac->u;
1631:   v     = jac->v;
1632:   Hu    = jac->Hu;
1633:   d     = jac->d;
1634:   work1 = jac->w1;
1635:   work2 = jac->w2;
1636:   vecz  = jac->vecz;

1638:   /* Change RHS to comply with matrix regularization H = A + nu*B*B' */
1639:   /* Add q = q + nu*B*b */
1640:   if (jac->gkbnu) {
1641:     nu = jac->gkbnu;
1642:     PetscCall(VecScale(ilinkD->x, jac->gkbnu));
1643:     PetscCall(MatMultAdd(jac->B, ilinkD->x, ilinkA->x, ilinkA->x)); /* q = q + nu*B*b */
1644:   } else {
1645:     /* Situation when no augmented Lagrangian is used. Then we set inner  */
1646:     /* matrix N = I in [Ar13], and thus nu = 1.                           */
1647:     nu = 1;
1648:   }

1650:   /* Transform rhs from [q,tilde{b}] to [0,b] */
1651:   PetscCall(PetscLogEventBegin(ilinkA->event, ksp, ilinkA->x, ilinkA->y, NULL));
1652:   PetscCall(KSPSolve(ksp, ilinkA->x, ilinkA->y));
1653:   PetscCall(KSPCheckSolve(ksp, pc, ilinkA->y));
1654:   PetscCall(PetscLogEventEnd(ilinkA->event, ksp, ilinkA->x, ilinkA->y, NULL));
1655:   PetscCall(MatMultHermitianTranspose(jac->B, ilinkA->y, work1));
1656:   PetscCall(VecAXPBY(work1, 1.0 / nu, -1.0, ilinkD->x)); /* c = b - B'*x        */

1658:   /* First step of algorithm */
1659:   PetscCall(VecNorm(work1, NORM_2, &beta)); /* beta = sqrt(nu*c'*c)*/
1660:   KSPCheckDot(ksp, beta);
1661:   beta = PetscSqrtReal(nu) * beta;
1662:   PetscCall(VecAXPBY(v, nu / beta, 0.0, work1)); /* v = nu/beta *c      */
1663:   PetscCall(MatMult(jac->B, v, work2));          /* u = H^{-1}*B*v      */
1664:   PetscCall(PetscLogEventBegin(ilinkA->event, ksp, work2, u, NULL));
1665:   PetscCall(KSPSolve(ksp, work2, u));
1666:   PetscCall(KSPCheckSolve(ksp, pc, u));
1667:   PetscCall(PetscLogEventEnd(ilinkA->event, ksp, work2, u, NULL));
1668:   PetscCall(MatMult(jac->H, u, Hu)); /* alpha = u'*H*u      */
1669:   PetscCall(VecDot(Hu, u, &alpha));
1670:   KSPCheckDot(ksp, alpha);
1671:   PetscCheck(PetscRealPart(alpha) > 0.0, PETSC_COMM_SELF, PETSC_ERR_NOT_CONVERGED, "GKB preconditioner diverged, H is not positive definite");
1672:   alpha = PetscSqrtReal(PetscAbsScalar(alpha));
1673:   PetscCall(VecScale(u, 1.0 / alpha));
1674:   PetscCall(VecAXPBY(d, 1.0 / alpha, 0.0, v)); /* v = nu/beta *c      */

1676:   z       = beta / alpha;
1677:   vecz[1] = z;

1679:   /* Computation of first iterate x(1) and p(1) */
1680:   PetscCall(VecAXPY(ilinkA->y, z, u));
1681:   PetscCall(VecCopy(d, ilinkD->y));
1682:   PetscCall(VecScale(ilinkD->y, -z));

1684:   iterGKB = 1;
1685:   lowbnd  = 2 * jac->gkbtol;
1686:   if (jac->gkbmonitor) PetscCall(PetscViewerASCIIPrintf(jac->gkbviewer, "%3" PetscInt_FMT " GKB Lower bound estimate %14.12e\n", iterGKB, (double)lowbnd));

1688:   while (iterGKB < jac->gkbmaxit && lowbnd > jac->gkbtol) {
1689:     iterGKB += 1;
1690:     PetscCall(MatMultHermitianTranspose(jac->B, u, work1)); /* v <- nu*(B'*u-alpha/nu*v) */
1691:     PetscCall(VecAXPBY(v, nu, -alpha, work1));
1692:     PetscCall(VecNorm(v, NORM_2, &beta)); /* beta = sqrt(nu)*v'*v      */
1693:     beta = beta / PetscSqrtReal(nu);
1694:     PetscCall(VecScale(v, 1.0 / beta));
1695:     PetscCall(MatMult(jac->B, v, work2)); /* u <- H^{-1}*(B*v-beta*H*u) */
1696:     PetscCall(MatMult(jac->H, u, Hu));
1697:     PetscCall(VecAXPY(work2, -beta, Hu));
1698:     PetscCall(PetscLogEventBegin(ilinkA->event, ksp, work2, u, NULL));
1699:     PetscCall(KSPSolve(ksp, work2, u));
1700:     PetscCall(KSPCheckSolve(ksp, pc, u));
1701:     PetscCall(PetscLogEventEnd(ilinkA->event, ksp, work2, u, NULL));
1702:     PetscCall(MatMult(jac->H, u, Hu)); /* alpha = u'*H*u            */
1703:     PetscCall(VecDot(Hu, u, &alpha));
1704:     KSPCheckDot(ksp, alpha);
1705:     PetscCheck(PetscRealPart(alpha) > 0.0, PETSC_COMM_SELF, PETSC_ERR_NOT_CONVERGED, "GKB preconditioner diverged, H is not positive definite");
1706:     alpha = PetscSqrtReal(PetscAbsScalar(alpha));
1707:     PetscCall(VecScale(u, 1.0 / alpha));

1709:     z       = -beta / alpha * z; /* z <- beta/alpha*z     */
1710:     vecz[0] = z;

1712:     /* Computation of new iterate x(i+1) and p(i+1) */
1713:     PetscCall(VecAXPBY(d, 1.0 / alpha, -beta / alpha, v)); /* d = (v-beta*d)/alpha */
1714:     PetscCall(VecAXPY(ilinkA->y, z, u));                   /* r = r + z*u          */
1715:     PetscCall(VecAXPY(ilinkD->y, -z, d));                  /* p = p - z*d          */
1716:     PetscCall(MatMult(jac->H, ilinkA->y, Hu));             /* ||u||_H = u'*H*u     */
1717:     PetscCall(VecDot(Hu, ilinkA->y, &nrmz2));

1719:     /* Compute Lower Bound estimate */
1720:     if (iterGKB > jac->gkbdelay) {
1721:       lowbnd = 0.0;
1722:       for (j = 0; j < jac->gkbdelay; j++) lowbnd += PetscAbsScalar(vecz[j] * vecz[j]);
1723:       lowbnd = PetscSqrtReal(lowbnd / PetscAbsScalar(nrmz2));
1724:     }

1726:     for (j = 0; j < jac->gkbdelay - 1; j++) vecz[jac->gkbdelay - j - 1] = vecz[jac->gkbdelay - j - 2];
1727:     if (jac->gkbmonitor) PetscCall(PetscViewerASCIIPrintf(jac->gkbviewer, "%3" PetscInt_FMT " GKB Lower bound estimate %14.12e\n", iterGKB, (double)lowbnd));
1728:   }

1730:   PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1731:   PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1732:   PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1733:   PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1734:   PetscFunctionReturn(PETSC_SUCCESS);
1735: }

1737: #define FieldSplitSplitSolveAddTranspose(ilink, xx, yy) \
1738:   ((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) || \
1739:                     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) || \
1740:                     VecScatterEnd(ilink->sctx, ilink->x, yy, ADD_VALUES, SCATTER_REVERSE)))

1742: static PetscErrorCode PCApplyTranspose_FieldSplit(PC pc, Vec x, Vec y)
1743: {
1744:   PC_FieldSplit    *jac   = (PC_FieldSplit *)pc->data;
1745:   PC_FieldSplitLink ilink = jac->head;
1746:   PetscInt          bs;

1748:   PetscFunctionBegin;
1749:   if (jac->type == PC_COMPOSITE_ADDITIVE) {
1750:     PetscBool matnest;

1752:     PetscCall(PetscObjectTypeCompare((PetscObject)pc->pmat, MATNEST, &matnest));
1753:     if (jac->defaultsplit && !matnest) {
1754:       PetscCall(VecGetBlockSize(x, &bs));
1755:       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);
1756:       PetscCall(VecGetBlockSize(y, &bs));
1757:       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);
1758:       PetscCall(VecStrideGatherAll(x, jac->x, INSERT_VALUES));
1759:       while (ilink) {
1760:         PetscCall(PetscLogEventBegin(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1761:         PetscCall(KSPSolveTranspose(ilink->ksp, ilink->x, ilink->y));
1762:         PetscCall(KSPCheckSolve(ilink->ksp, pc, ilink->y));
1763:         PetscCall(PetscLogEventEnd(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1764:         ilink = ilink->next;
1765:       }
1766:       PetscCall(VecStrideScatterAll(jac->y, y, INSERT_VALUES));
1767:     } else {
1768:       PetscCall(VecSet(y, 0.0));
1769:       while (ilink) {
1770:         PetscCall(FieldSplitSplitSolveAddTranspose(ilink, x, y));
1771:         ilink = ilink->next;
1772:       }
1773:     }
1774:   } else {
1775:     if (!jac->w1) {
1776:       PetscCall(VecDuplicate(x, &jac->w1));
1777:       PetscCall(VecDuplicate(x, &jac->w2));
1778:     }
1779:     PetscCall(VecSet(y, 0.0));
1780:     if (jac->type == PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE) {
1781:       PetscCall(FieldSplitSplitSolveAddTranspose(ilink, x, y));
1782:       while (ilink->next) {
1783:         ilink = ilink->next;
1784:         PetscCall(MatMultTranspose(pc->mat, y, jac->w1));
1785:         PetscCall(VecWAXPY(jac->w2, -1.0, jac->w1, x));
1786:         PetscCall(FieldSplitSplitSolveAddTranspose(ilink, jac->w2, y));
1787:       }
1788:       while (ilink->previous) {
1789:         ilink = ilink->previous;
1790:         PetscCall(MatMultTranspose(pc->mat, y, jac->w1));
1791:         PetscCall(VecWAXPY(jac->w2, -1.0, jac->w1, x));
1792:         PetscCall(FieldSplitSplitSolveAddTranspose(ilink, jac->w2, y));
1793:       }
1794:     } else {
1795:       while (ilink->next) { /* get to last entry in linked list */
1796:         ilink = ilink->next;
1797:       }
1798:       PetscCall(FieldSplitSplitSolveAddTranspose(ilink, x, y));
1799:       while (ilink->previous) {
1800:         ilink = ilink->previous;
1801:         PetscCall(MatMultTranspose(pc->mat, y, jac->w1));
1802:         PetscCall(VecWAXPY(jac->w2, -1.0, jac->w1, x));
1803:         PetscCall(FieldSplitSplitSolveAddTranspose(ilink, jac->w2, y));
1804:       }
1805:     }
1806:   }
1807:   PetscFunctionReturn(PETSC_SUCCESS);
1808: }

1810: static PetscErrorCode PCReset_FieldSplit(PC pc)
1811: {
1812:   PC_FieldSplit    *jac   = (PC_FieldSplit *)pc->data;
1813:   PC_FieldSplitLink ilink = jac->head, next;

1815:   PetscFunctionBegin;
1816:   while (ilink) {
1817:     PetscCall(KSPDestroy(&ilink->ksp));
1818:     PetscCall(VecDestroy(&ilink->x));
1819:     PetscCall(VecDestroy(&ilink->y));
1820:     PetscCall(VecDestroy(&ilink->z));
1821:     PetscCall(VecScatterDestroy(&ilink->sctx));
1822:     PetscCall(ISDestroy(&ilink->is));
1823:     PetscCall(ISDestroy(&ilink->is_col));
1824:     PetscCall(PetscFree(ilink->splitname));
1825:     PetscCall(PetscFree(ilink->fields));
1826:     PetscCall(PetscFree(ilink->fields_col));
1827:     next = ilink->next;
1828:     PetscCall(PetscFree(ilink));
1829:     ilink = next;
1830:   }
1831:   jac->head = NULL;
1832:   PetscCall(PetscFree2(jac->x, jac->y));
1833:   if (jac->mat && jac->mat != jac->pmat) {
1834:     PetscCall(MatDestroyMatrices(jac->nsplits, &jac->mat));
1835:   } else if (jac->mat) {
1836:     jac->mat = NULL;
1837:   }
1838:   if (jac->pmat) PetscCall(MatDestroyMatrices(jac->nsplits, &jac->pmat));
1839:   if (jac->Afield) PetscCall(MatDestroyMatrices(jac->nsplits, &jac->Afield));
1840:   jac->nsplits = 0;
1841:   PetscCall(VecDestroy(&jac->w1));
1842:   PetscCall(VecDestroy(&jac->w2));
1843:   if (jac->schur) PetscCall(PetscObjectCompose((PetscObject)jac->schur, "AinvB", NULL));
1844:   PetscCall(MatDestroy(&jac->schur));
1845:   PetscCall(MatDestroy(&jac->schurp));
1846:   PetscCall(MatDestroy(&jac->schur_user));
1847:   PetscCall(KSPDestroy(&jac->kspschur));
1848:   PetscCall(KSPDestroy(&jac->kspupper));
1849:   PetscCall(MatDestroy(&jac->B));
1850:   PetscCall(MatDestroy(&jac->C));
1851:   PetscCall(MatDestroy(&jac->H));
1852:   PetscCall(VecDestroy(&jac->u));
1853:   PetscCall(VecDestroy(&jac->v));
1854:   PetscCall(VecDestroy(&jac->Hu));
1855:   PetscCall(VecDestroy(&jac->d));
1856:   PetscCall(PetscFree(jac->vecz));
1857:   PetscCall(PetscViewerDestroy(&jac->gkbviewer));
1858:   jac->isrestrict = PETSC_FALSE;
1859:   PetscFunctionReturn(PETSC_SUCCESS);
1860: }

1862: static PetscErrorCode PCDestroy_FieldSplit(PC pc)
1863: {
1864:   PetscFunctionBegin;
1865:   PetscCall(PCReset_FieldSplit(pc));
1866:   PetscCall(PetscFree(pc->data));
1867:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCSetCoordinates_C", NULL));
1868:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetFields_C", NULL));
1869:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetIS_C", NULL));
1870:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetType_C", NULL));
1871:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetBlockSize_C", NULL));
1872:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitRestrictIS_C", NULL));
1873:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSchurGetSubKSP_C", NULL));
1874:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSubKSP_C", NULL));
1875:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBTol_C", NULL));
1876:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBMaxit_C", NULL));
1877:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBNu_C", NULL));
1878:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBDelay_C", NULL));
1879:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurPre_C", NULL));
1880:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSchurPre_C", NULL));
1881:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurFactType_C", NULL));
1882:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurScale_C", NULL));
1883:   PetscFunctionReturn(PETSC_SUCCESS);
1884: }

1886: static PetscErrorCode PCSetFromOptions_FieldSplit(PC pc, PetscOptionItems *PetscOptionsObject)
1887: {
1888:   PetscInt        bs;
1889:   PetscBool       flg;
1890:   PC_FieldSplit  *jac = (PC_FieldSplit *)pc->data;
1891:   PCCompositeType ctype;

1893:   PetscFunctionBegin;
1894:   PetscOptionsHeadBegin(PetscOptionsObject, "FieldSplit options");
1895:   PetscCall(PetscOptionsBool("-pc_fieldsplit_dm_splits", "Whether to use DMCreateFieldDecomposition() for splits", "PCFieldSplitSetDMSplits", jac->dm_splits, &jac->dm_splits, NULL));
1896:   PetscCall(PetscOptionsInt("-pc_fieldsplit_block_size", "Blocksize that defines number of fields", "PCFieldSplitSetBlockSize", jac->bs, &bs, &flg));
1897:   if (flg) PetscCall(PCFieldSplitSetBlockSize(pc, bs));
1898:   jac->diag_use_amat = pc->useAmat;
1899:   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));
1900:   jac->offdiag_use_amat = pc->useAmat;
1901:   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));
1902:   PetscCall(PetscOptionsBool("-pc_fieldsplit_detect_saddle_point", "Form 2-way split by detecting zero diagonal entries", "PCFieldSplitSetDetectSaddlePoint", jac->detect, &jac->detect, NULL));
1903:   PetscCall(PCFieldSplitSetDetectSaddlePoint(pc, jac->detect)); /* Sets split type and Schur PC type */
1904:   PetscCall(PetscOptionsEnum("-pc_fieldsplit_type", "Type of composition", "PCFieldSplitSetType", PCCompositeTypes, (PetscEnum)jac->type, (PetscEnum *)&ctype, &flg));
1905:   if (flg) PetscCall(PCFieldSplitSetType(pc, ctype));
1906:   /* Only setup fields once */
1907:   if ((jac->bs > 0) && (jac->nsplits == 0)) {
1908:     /* only allow user to set fields from command line.
1909:        otherwise user can set them in PCFieldSplitSetDefaults() */
1910:     PetscCall(PCFieldSplitSetRuntimeSplits_Private(pc));
1911:     if (jac->splitdefined) PetscCall(PetscInfo(pc, "Splits defined using the options database\n"));
1912:   }
1913:   if (jac->type == PC_COMPOSITE_SCHUR) {
1914:     PetscCall(PetscOptionsGetEnum(((PetscObject)pc)->options, ((PetscObject)pc)->prefix, "-pc_fieldsplit_schur_factorization_type", PCFieldSplitSchurFactTypes, (PetscEnum *)&jac->schurfactorization, &flg));
1915:     if (flg) PetscCall(PetscInfo(pc, "Deprecated use of -pc_fieldsplit_schur_factorization_type\n"));
1916:     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));
1917:     PetscCall(PetscOptionsEnum("-pc_fieldsplit_schur_precondition", "How to build preconditioner for Schur complement", "PCFieldSplitSetSchurPre", PCFieldSplitSchurPreTypes, (PetscEnum)jac->schurpre, (PetscEnum *)&jac->schurpre, NULL));
1918:     PetscCall(PetscOptionsScalar("-pc_fieldsplit_schur_scale", "Scale Schur complement", "PCFieldSplitSetSchurScale", jac->schurscale, &jac->schurscale, NULL));
1919:   } else if (jac->type == PC_COMPOSITE_GKB) {
1920:     PetscCall(PetscOptionsReal("-pc_fieldsplit_gkb_tol", "The tolerance for the lower bound stopping criterion", "PCFieldSplitSetGKBTol", jac->gkbtol, &jac->gkbtol, NULL));
1921:     PetscCall(PetscOptionsInt("-pc_fieldsplit_gkb_delay", "The delay value for lower bound criterion", "PCFieldSplitSetGKBDelay", jac->gkbdelay, &jac->gkbdelay, NULL));
1922:     PetscCall(PetscOptionsBoundedReal("-pc_fieldsplit_gkb_nu", "Parameter in augmented Lagrangian approach", "PCFieldSplitSetGKBNu", jac->gkbnu, &jac->gkbnu, NULL, 0.0));
1923:     PetscCall(PetscOptionsInt("-pc_fieldsplit_gkb_maxit", "Maximum allowed number of iterations", "PCFieldSplitSetGKBMaxit", jac->gkbmaxit, &jac->gkbmaxit, NULL));
1924:     PetscCall(PetscOptionsBool("-pc_fieldsplit_gkb_monitor", "Prints number of GKB iterations and error", "PCFieldSplitGKB", jac->gkbmonitor, &jac->gkbmonitor, NULL));
1925:   }
1926:   /*
1927:     In the initial call to this routine the sub-solver data structures do not exist so we cannot call KSPSetFromOptions() on them yet.
1928:     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
1929:     is called on the outer solver in case changes were made in the options database

1931:     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()
1932:     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.
1933:     Without this extra check test p2p1fetidp_olof_full and others fail with incorrect matrix types.

1935:     There could be a negative side effect of calling the KSPSetFromOptions() below.

1937:     If one captured the PetscObjectState of the options database one could skip these calls if the database has not changed from the previous call
1938:   */
1939:   if (jac->issetup) {
1940:     PC_FieldSplitLink ilink = jac->head;
1941:     if (jac->type == PC_COMPOSITE_SCHUR) {
1942:       if (jac->kspupper && jac->kspupper->totalits > 0) PetscCall(KSPSetFromOptions(jac->kspupper));
1943:       if (jac->kspschur && jac->kspschur->totalits > 0) PetscCall(KSPSetFromOptions(jac->kspschur));
1944:     }
1945:     while (ilink) {
1946:       if (ilink->ksp->totalits > 0) PetscCall(KSPSetFromOptions(ilink->ksp));
1947:       ilink = ilink->next;
1948:     }
1949:   }
1950:   PetscOptionsHeadEnd();
1951:   PetscFunctionReturn(PETSC_SUCCESS);
1952: }

1954: static PetscErrorCode PCFieldSplitSetFields_FieldSplit(PC pc, const char splitname[], PetscInt n, const PetscInt *fields, const PetscInt *fields_col)
1955: {
1956:   PC_FieldSplit    *jac = (PC_FieldSplit *)pc->data;
1957:   PC_FieldSplitLink ilink, next = jac->head;
1958:   char              prefix[128];
1959:   PetscInt          i;
1960:   PetscLogEvent     nse;

1962:   PetscFunctionBegin;
1963:   if (jac->splitdefined) {
1964:     PetscCall(PetscInfo(pc, "Ignoring new split \"%s\" because the splits have already been defined\n", splitname));
1965:     PetscFunctionReturn(PETSC_SUCCESS);
1966:   }
1967:   for (i = 0; i < n; i++) { PetscCheck(fields[i] >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Negative field %" PetscInt_FMT " requested", fields[i]); }
1968:   PetscCall(PetscNew(&ilink));
1969:   if (splitname) {
1970:     PetscCall(PetscStrallocpy(splitname, &ilink->splitname));
1971:   } else {
1972:     PetscCall(PetscMalloc1(3, &ilink->splitname));
1973:     PetscCall(PetscSNPrintf(ilink->splitname, 2, "%" PetscInt_FMT, jac->nsplits));
1974:   }
1975:   PetscCall(PetscMPIIntCast(jac->nsplits, &nse));
1976:   ilink->event = jac->nsplits < 5 ? KSP_Solve_FS_0 + nse : KSP_Solve_FS_0 + 4; /* Splits greater than 4 logged in 4th split */
1977:   PetscCall(PetscMalloc1(n, &ilink->fields));
1978:   PetscCall(PetscArraycpy(ilink->fields, fields, n));
1979:   PetscCall(PetscMalloc1(n, &ilink->fields_col));
1980:   PetscCall(PetscArraycpy(ilink->fields_col, fields_col, n));

1982:   ilink->nfields = n;
1983:   ilink->next    = NULL;
1984:   PetscCall(KSPCreate(PetscObjectComm((PetscObject)pc), &ilink->ksp));
1985:   PetscCall(KSPSetNestLevel(ilink->ksp, pc->kspnestlevel));
1986:   PetscCall(KSPSetErrorIfNotConverged(ilink->ksp, pc->erroriffailure));
1987:   PetscCall(PetscObjectIncrementTabLevel((PetscObject)ilink->ksp, (PetscObject)pc, 1));
1988:   PetscCall(KSPSetType(ilink->ksp, KSPPREONLY));

1990:   PetscCall(PetscSNPrintf(prefix, sizeof(prefix), "%sfieldsplit_%s_", ((PetscObject)pc)->prefix ? ((PetscObject)pc)->prefix : "", ilink->splitname));
1991:   PetscCall(KSPSetOptionsPrefix(ilink->ksp, prefix));

1993:   if (!next) {
1994:     jac->head       = ilink;
1995:     ilink->previous = NULL;
1996:   } else {
1997:     while (next->next) next = next->next;
1998:     next->next      = ilink;
1999:     ilink->previous = next;
2000:   }
2001:   jac->nsplits++;
2002:   PetscFunctionReturn(PETSC_SUCCESS);
2003: }

2005: static PetscErrorCode PCFieldSplitSchurGetSubKSP_FieldSplit(PC pc, PetscInt *n, KSP **subksp)
2006: {
2007:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

2009:   PetscFunctionBegin;
2010:   *subksp = NULL;
2011:   if (n) *n = 0;
2012:   if (jac->type == PC_COMPOSITE_SCHUR) {
2013:     PetscInt nn;

2015:     PetscCheck(jac->schur, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONGSTATE, "Must call KSPSetUp() or PCSetUp() before calling PCFieldSplitSchurGetSubKSP()");
2016:     PetscCheck(jac->nsplits == 2, PetscObjectComm((PetscObject)pc), PETSC_ERR_PLIB, "Unexpected number of splits %" PetscInt_FMT " != 2", jac->nsplits);
2017:     nn = jac->nsplits + (jac->kspupper != jac->head->ksp ? 1 : 0);
2018:     PetscCall(PetscMalloc1(nn, subksp));
2019:     (*subksp)[0] = jac->head->ksp;
2020:     (*subksp)[1] = jac->kspschur;
2021:     if (jac->kspupper != jac->head->ksp) (*subksp)[2] = jac->kspupper;
2022:     if (n) *n = nn;
2023:   }
2024:   PetscFunctionReturn(PETSC_SUCCESS);
2025: }

2027: static PetscErrorCode PCFieldSplitGetSubKSP_FieldSplit_Schur(PC pc, PetscInt *n, KSP **subksp)
2028: {
2029:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

2031:   PetscFunctionBegin;
2032:   PetscCheck(jac->schur, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONGSTATE, "Must call KSPSetUp() or PCSetUp() before calling PCFieldSplitGetSubKSP()");
2033:   PetscCall(PetscMalloc1(jac->nsplits, subksp));
2034:   PetscCall(MatSchurComplementGetKSP(jac->schur, *subksp));

2036:   (*subksp)[1] = jac->kspschur;
2037:   if (n) *n = jac->nsplits;
2038:   PetscFunctionReturn(PETSC_SUCCESS);
2039: }

2041: static PetscErrorCode PCFieldSplitGetSubKSP_FieldSplit(PC pc, PetscInt *n, KSP **subksp)
2042: {
2043:   PC_FieldSplit    *jac   = (PC_FieldSplit *)pc->data;
2044:   PetscInt          cnt   = 0;
2045:   PC_FieldSplitLink ilink = jac->head;

2047:   PetscFunctionBegin;
2048:   PetscCall(PetscMalloc1(jac->nsplits, subksp));
2049:   while (ilink) {
2050:     (*subksp)[cnt++] = ilink->ksp;
2051:     ilink            = ilink->next;
2052:   }
2053:   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);
2054:   if (n) *n = jac->nsplits;
2055:   PetscFunctionReturn(PETSC_SUCCESS);
2056: }

2058: /*@
2059:   PCFieldSplitRestrictIS - Restricts the fieldsplit `IS`s to be within a given `IS`.

2061:   Input Parameters:
2062: + pc  - the preconditioner context
2063: - isy - the index set that defines the indices to which the fieldsplit is to be restricted

2065:   Level: advanced

2067:   Developer Notes:
2068:   It seems the resulting `IS`s will not cover the entire space, so
2069:   how can they define a convergent preconditioner? Needs explaining.

2071: .seealso: [](sec_block_matrices), `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSetIS()`
2072: @*/
2073: PetscErrorCode PCFieldSplitRestrictIS(PC pc, IS isy)
2074: {
2075:   PetscFunctionBegin;
2078:   PetscTryMethod(pc, "PCFieldSplitRestrictIS_C", (PC, IS), (pc, isy));
2079:   PetscFunctionReturn(PETSC_SUCCESS);
2080: }

2082: static PetscErrorCode PCFieldSplitRestrictIS_FieldSplit(PC pc, IS isy)
2083: {
2084:   PC_FieldSplit    *jac   = (PC_FieldSplit *)pc->data;
2085:   PC_FieldSplitLink ilink = jac->head, next;
2086:   PetscInt          localsize, size, sizez, i;
2087:   const PetscInt   *ind, *indz;
2088:   PetscInt         *indc, *indcz;
2089:   PetscBool         flg;

2091:   PetscFunctionBegin;
2092:   PetscCall(ISGetLocalSize(isy, &localsize));
2093:   PetscCallMPI(MPI_Scan(&localsize, &size, 1, MPIU_INT, MPI_SUM, PetscObjectComm((PetscObject)isy)));
2094:   size -= localsize;
2095:   while (ilink) {
2096:     IS isrl, isr;
2097:     PC subpc;
2098:     PetscCall(ISEmbed(ilink->is, isy, PETSC_TRUE, &isrl));
2099:     PetscCall(ISGetLocalSize(isrl, &localsize));
2100:     PetscCall(PetscMalloc1(localsize, &indc));
2101:     PetscCall(ISGetIndices(isrl, &ind));
2102:     PetscCall(PetscArraycpy(indc, ind, localsize));
2103:     PetscCall(ISRestoreIndices(isrl, &ind));
2104:     PetscCall(ISDestroy(&isrl));
2105:     for (i = 0; i < localsize; i++) *(indc + i) += size;
2106:     PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)isy), localsize, indc, PETSC_OWN_POINTER, &isr));
2107:     PetscCall(PetscObjectReference((PetscObject)isr));
2108:     PetscCall(ISDestroy(&ilink->is));
2109:     ilink->is = isr;
2110:     PetscCall(PetscObjectReference((PetscObject)isr));
2111:     PetscCall(ISDestroy(&ilink->is_col));
2112:     ilink->is_col = isr;
2113:     PetscCall(ISDestroy(&isr));
2114:     PetscCall(KSPGetPC(ilink->ksp, &subpc));
2115:     PetscCall(PetscObjectTypeCompare((PetscObject)subpc, PCFIELDSPLIT, &flg));
2116:     if (flg) {
2117:       IS       iszl, isz;
2118:       MPI_Comm comm;
2119:       PetscCall(ISGetLocalSize(ilink->is, &localsize));
2120:       comm = PetscObjectComm((PetscObject)ilink->is);
2121:       PetscCall(ISEmbed(isy, ilink->is, PETSC_TRUE, &iszl));
2122:       PetscCallMPI(MPI_Scan(&localsize, &sizez, 1, MPIU_INT, MPI_SUM, comm));
2123:       sizez -= localsize;
2124:       PetscCall(ISGetLocalSize(iszl, &localsize));
2125:       PetscCall(PetscMalloc1(localsize, &indcz));
2126:       PetscCall(ISGetIndices(iszl, &indz));
2127:       PetscCall(PetscArraycpy(indcz, indz, localsize));
2128:       PetscCall(ISRestoreIndices(iszl, &indz));
2129:       PetscCall(ISDestroy(&iszl));
2130:       for (i = 0; i < localsize; i++) *(indcz + i) += sizez;
2131:       PetscCall(ISCreateGeneral(comm, localsize, indcz, PETSC_OWN_POINTER, &isz));
2132:       PetscCall(PCFieldSplitRestrictIS(subpc, isz));
2133:       PetscCall(ISDestroy(&isz));
2134:     }
2135:     next  = ilink->next;
2136:     ilink = next;
2137:   }
2138:   jac->isrestrict = PETSC_TRUE;
2139:   PetscFunctionReturn(PETSC_SUCCESS);
2140: }

2142: static PetscErrorCode PCFieldSplitSetIS_FieldSplit(PC pc, const char splitname[], IS is)
2143: {
2144:   PC_FieldSplit    *jac = (PC_FieldSplit *)pc->data;
2145:   PC_FieldSplitLink ilink, next = jac->head;
2146:   char              prefix[128];
2147:   PetscLogEvent     nse;

2149:   PetscFunctionBegin;
2150:   if (jac->splitdefined) {
2151:     PetscCall(PetscInfo(pc, "Ignoring new split \"%s\" because the splits have already been defined\n", splitname));
2152:     PetscFunctionReturn(PETSC_SUCCESS);
2153:   }
2154:   PetscCall(PetscNew(&ilink));
2155:   if (splitname) {
2156:     PetscCall(PetscStrallocpy(splitname, &ilink->splitname));
2157:   } else {
2158:     PetscCall(PetscMalloc1(8, &ilink->splitname));
2159:     PetscCall(PetscSNPrintf(ilink->splitname, 7, "%" PetscInt_FMT, jac->nsplits));
2160:   }
2161:   PetscCall(PetscMPIIntCast(jac->nsplits, &nse));
2162:   ilink->event = jac->nsplits < 5 ? KSP_Solve_FS_0 + nse : KSP_Solve_FS_0 + 4; /* Splits greater than 4 logged in 4th split */
2163:   PetscCall(PetscObjectReference((PetscObject)is));
2164:   PetscCall(ISDestroy(&ilink->is));
2165:   ilink->is = is;
2166:   PetscCall(PetscObjectReference((PetscObject)is));
2167:   PetscCall(ISDestroy(&ilink->is_col));
2168:   ilink->is_col = is;
2169:   ilink->next   = NULL;
2170:   PetscCall(KSPCreate(PetscObjectComm((PetscObject)pc), &ilink->ksp));
2171:   PetscCall(KSPSetNestLevel(ilink->ksp, pc->kspnestlevel));
2172:   PetscCall(KSPSetErrorIfNotConverged(ilink->ksp, pc->erroriffailure));
2173:   PetscCall(PetscObjectIncrementTabLevel((PetscObject)ilink->ksp, (PetscObject)pc, 1));
2174:   PetscCall(KSPSetType(ilink->ksp, KSPPREONLY));

2176:   PetscCall(PetscSNPrintf(prefix, sizeof(prefix), "%sfieldsplit_%s_", ((PetscObject)pc)->prefix ? ((PetscObject)pc)->prefix : "", ilink->splitname));
2177:   PetscCall(KSPSetOptionsPrefix(ilink->ksp, prefix));

2179:   if (!next) {
2180:     jac->head       = ilink;
2181:     ilink->previous = NULL;
2182:   } else {
2183:     while (next->next) next = next->next;
2184:     next->next      = ilink;
2185:     ilink->previous = next;
2186:   }
2187:   jac->nsplits++;
2188:   PetscFunctionReturn(PETSC_SUCCESS);
2189: }

2191: /*@
2192:   PCFieldSplitSetFields - Sets the fields that define one particular split in `PCFIELDSPLIT`

2194:   Logically Collective

2196:   Input Parameters:
2197: + pc         - the preconditioner context
2198: . splitname  - name of this split, if `NULL` the number of the split is used
2199: . n          - the number of fields in this split
2200: . fields     - the fields in this split
2201: - 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
2202:                of the matrix and `fields_col` provides the column indices for that block

2204:   Options Database Key:
2205: . -pc_fieldsplit_%d_fields <a,b,..> - indicates the fields to be used in the `%d`'th split

2207:   Level: intermediate

2209:   Notes:
2210:   Use `PCFieldSplitSetIS()` to set a  general set of indices as a split.

2212:   If the matrix used to construct the preconditioner is `MATNEST` then field i refers to the `is_row[i]` `IS` passed to `MatCreateNest()`.

2214:   If the matrix used to construct the preconditioner is not `MATNEST` then
2215:   `PCFieldSplitSetFields()` is for defining fields as strided blocks (based on the block size provided to the matrix with `MatSetBlocksize()` or
2216:   to the `PC` with `PCFieldSplitSetBlockSize()`). For example, if the block
2217:   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
2218:   0xx3xx6xx9xx12 ... x1xx4xx7xx ... xx2xx5xx8xx.. 01x34x67x... 0x1x3x5x7.. x12x45x78x....
2219:   where the numbered entries indicate what is in the split.

2221:   This function is called once per split (it creates a new split each time).  Solve options
2222:   for this split will be available under the prefix `-fieldsplit_SPLITNAME_`.

2224:   `PCFieldSplitSetIS()` does not support having a `fields_col` different from `fields`

2226:   Developer Notes:
2227:   This routine does not actually create the `IS` representing the split, that is delayed
2228:   until `PCSetUp_FieldSplit()`, because information about the vector/matrix layouts may not be
2229:   available when this routine is called.

2231: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSetBlockSize()`, `PCFieldSplitSetIS()`, `PCFieldSplitRestrictIS()`,
2232:           `MatSetBlocksize()`, `MatCreateNest()`
2233: @*/
2234: PetscErrorCode PCFieldSplitSetFields(PC pc, const char splitname[], PetscInt n, const PetscInt fields[], const PetscInt fields_col[])
2235: {
2236:   PetscFunctionBegin;
2238:   PetscAssertPointer(splitname, 2);
2239:   PetscCheck(n >= 1, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_OUTOFRANGE, "Provided number of fields %" PetscInt_FMT " in split \"%s\" not positive", n, splitname);
2240:   PetscAssertPointer(fields, 4);
2241:   PetscTryMethod(pc, "PCFieldSplitSetFields_C", (PC, const char[], PetscInt, const PetscInt *, const PetscInt *), (pc, splitname, n, fields, fields_col));
2242:   PetscFunctionReturn(PETSC_SUCCESS);
2243: }

2245: /*@
2246:   PCFieldSplitSetDiagUseAmat - set flag indicating whether to extract diagonal blocks from Amat (rather than Pmat) to build
2247:   the sub-matrices associated with each split. Where `KSPSetOperators`(ksp,Amat,Pmat) was used to supply the operators.

2249:   Logically Collective

2251:   Input Parameters:
2252: + pc  - the preconditioner object
2253: - flg - boolean flag indicating whether or not to use Amat to extract the diagonal blocks from

2255:   Options Database Key:
2256: . -pc_fieldsplit_diag_use_amat - use the Amat to provide the diagonal blocks

2258:   Level: intermediate

2260: .seealso: [](sec_block_matrices), `PC`, `PCSetOperators()`, `KSPSetOperators()`, `PCFieldSplitGetDiagUseAmat()`, `PCFieldSplitSetOffDiagUseAmat()`, `PCFIELDSPLIT`
2261: @*/
2262: PetscErrorCode PCFieldSplitSetDiagUseAmat(PC pc, PetscBool flg)
2263: {
2264:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
2265:   PetscBool      isfs;

2267:   PetscFunctionBegin;
2269:   PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCFIELDSPLIT, &isfs));
2270:   PetscCheck(isfs, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "PC not of type %s", PCFIELDSPLIT);
2271:   jac->diag_use_amat = flg;
2272:   PetscFunctionReturn(PETSC_SUCCESS);
2273: }

2275: /*@
2276:   PCFieldSplitGetDiagUseAmat - get the flag indicating whether to extract diagonal blocks from Amat (rather than Pmat) to build
2277:   the sub-matrices associated with each split.  Where `KSPSetOperators`(ksp,Amat,Pmat) was used to supply the operators.

2279:   Logically Collective

2281:   Input Parameter:
2282: . pc - the preconditioner object

2284:   Output Parameter:
2285: . flg - boolean flag indicating whether or not to use Amat to extract the diagonal blocks from

2287:   Level: intermediate

2289: .seealso: [](sec_block_matrices), `PC`, `PCSetOperators()`, `KSPSetOperators()`, `PCFieldSplitSetDiagUseAmat()`, `PCFieldSplitGetOffDiagUseAmat()`, `PCFIELDSPLIT`
2290: @*/
2291: PetscErrorCode PCFieldSplitGetDiagUseAmat(PC pc, PetscBool *flg)
2292: {
2293:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
2294:   PetscBool      isfs;

2296:   PetscFunctionBegin;
2298:   PetscAssertPointer(flg, 2);
2299:   PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCFIELDSPLIT, &isfs));
2300:   PetscCheck(isfs, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "PC not of type %s", PCFIELDSPLIT);
2301:   *flg = jac->diag_use_amat;
2302:   PetscFunctionReturn(PETSC_SUCCESS);
2303: }

2305: /*@
2306:   PCFieldSplitSetOffDiagUseAmat - set flag indicating whether to extract off-diagonal blocks from Amat (rather than Pmat) to build
2307:   the sub-matrices associated with each split.  Where `KSPSetOperators`(ksp,Amat,Pmat) was used to supply the operators.

2309:   Logically Collective

2311:   Input Parameters:
2312: + pc  - the preconditioner object
2313: - flg - boolean flag indicating whether or not to use Amat to extract the off-diagonal blocks from

2315:   Options Database Key:
2316: . -pc_fieldsplit_off_diag_use_amat <bool> - use the Amat to extract the off-diagonal blocks

2318:   Level: intermediate

2320: .seealso: [](sec_block_matrices), `PC`, `PCSetOperators()`, `KSPSetOperators()`, `PCFieldSplitGetOffDiagUseAmat()`, `PCFieldSplitSetDiagUseAmat()`, `PCFIELDSPLIT`
2321: @*/
2322: PetscErrorCode PCFieldSplitSetOffDiagUseAmat(PC pc, PetscBool flg)
2323: {
2324:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
2325:   PetscBool      isfs;

2327:   PetscFunctionBegin;
2329:   PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCFIELDSPLIT, &isfs));
2330:   PetscCheck(isfs, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "PC not of type %s", PCFIELDSPLIT);
2331:   jac->offdiag_use_amat = flg;
2332:   PetscFunctionReturn(PETSC_SUCCESS);
2333: }

2335: /*@
2336:   PCFieldSplitGetOffDiagUseAmat - get the flag indicating whether to extract off-diagonal blocks from Amat (rather than Pmat) to build
2337:   the sub-matrices associated with each split.  Where `KSPSetOperators`(ksp,Amat,Pmat) was used to supply the operators.

2339:   Logically Collective

2341:   Input Parameter:
2342: . pc - the preconditioner object

2344:   Output Parameter:
2345: . flg - boolean flag indicating whether or not to use Amat to extract the off-diagonal blocks from

2347:   Level: intermediate

2349: .seealso: [](sec_block_matrices), `PC`, `PCSetOperators()`, `KSPSetOperators()`, `PCFieldSplitSetOffDiagUseAmat()`, `PCFieldSplitGetDiagUseAmat()`, `PCFIELDSPLIT`
2350: @*/
2351: PetscErrorCode PCFieldSplitGetOffDiagUseAmat(PC pc, PetscBool *flg)
2352: {
2353:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
2354:   PetscBool      isfs;

2356:   PetscFunctionBegin;
2358:   PetscAssertPointer(flg, 2);
2359:   PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCFIELDSPLIT, &isfs));
2360:   PetscCheck(isfs, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "PC not of type %s", PCFIELDSPLIT);
2361:   *flg = jac->offdiag_use_amat;
2362:   PetscFunctionReturn(PETSC_SUCCESS);
2363: }

2365: /*@
2366:   PCFieldSplitSetIS - Sets the exact elements for a split in a `PCFIELDSPLIT`

2368:   Logically Collective

2370:   Input Parameters:
2371: + pc        - the preconditioner context
2372: . splitname - name of this split, if `NULL` the number of the split is used
2373: - is        - the index set that defines the elements in this split

2375:   Level: intermediate

2377:   Notes:
2378:   Use `PCFieldSplitSetFields()`, for splits defined by strided `IS` based on the matrix block size or the `is_rows[]` passed into `MATNEST`

2380:   This function is called once per split (it creates a new split each time).  Solve options
2381:   for this split will be available under the prefix -fieldsplit_SPLITNAME_.

2383: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSetBlockSize()`, `PCFieldSplitSetFields()`
2384: @*/
2385: PetscErrorCode PCFieldSplitSetIS(PC pc, const char splitname[], IS is)
2386: {
2387:   PetscFunctionBegin;
2389:   if (splitname) PetscAssertPointer(splitname, 2);
2391:   PetscTryMethod(pc, "PCFieldSplitSetIS_C", (PC, const char[], IS), (pc, splitname, is));
2392:   PetscFunctionReturn(PETSC_SUCCESS);
2393: }

2395: /*@
2396:   PCFieldSplitGetIS - Retrieves the elements for a split as an `IS`

2398:   Logically Collective

2400:   Input Parameters:
2401: + pc        - the preconditioner context
2402: - splitname - name of this split

2404:   Output Parameter:
2405: . is - the index set that defines the elements in this split, or `NULL` if the split is not found

2407:   Level: intermediate

2409: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSetIS()`, `PCFieldSplitGetISByIndex()`
2410: @*/
2411: PetscErrorCode PCFieldSplitGetIS(PC pc, const char splitname[], IS *is)
2412: {
2413:   PetscFunctionBegin;
2415:   PetscAssertPointer(splitname, 2);
2416:   PetscAssertPointer(is, 3);
2417:   {
2418:     PC_FieldSplit    *jac   = (PC_FieldSplit *)pc->data;
2419:     PC_FieldSplitLink ilink = jac->head;
2420:     PetscBool         found;

2422:     *is = NULL;
2423:     while (ilink) {
2424:       PetscCall(PetscStrcmp(ilink->splitname, splitname, &found));
2425:       if (found) {
2426:         *is = ilink->is;
2427:         break;
2428:       }
2429:       ilink = ilink->next;
2430:     }
2431:   }
2432:   PetscFunctionReturn(PETSC_SUCCESS);
2433: }

2435: /*@
2436:   PCFieldSplitGetISByIndex - Retrieves the elements for a given split as an `IS`

2438:   Logically Collective

2440:   Input Parameters:
2441: + pc    - the preconditioner context
2442: - index - index of this split

2444:   Output Parameter:
2445: . is - the index set that defines the elements in this split

2447:   Level: intermediate

2449: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitGetIS()`, `PCFieldSplitSetIS()`,

2451: @*/
2452: PetscErrorCode PCFieldSplitGetISByIndex(PC pc, PetscInt index, IS *is)
2453: {
2454:   PetscFunctionBegin;
2455:   PetscCheck(index >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Negative field %" PetscInt_FMT " requested", index);
2457:   PetscAssertPointer(is, 3);
2458:   {
2459:     PC_FieldSplit    *jac   = (PC_FieldSplit *)pc->data;
2460:     PC_FieldSplitLink ilink = jac->head;
2461:     PetscInt          i     = 0;
2462:     PetscCheck(index < jac->nsplits, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Field %" PetscInt_FMT " requested but only %" PetscInt_FMT " exist", index, jac->nsplits);

2464:     while (i < index) {
2465:       ilink = ilink->next;
2466:       ++i;
2467:     }
2468:     PetscCall(PCFieldSplitGetIS(pc, ilink->splitname, is));
2469:   }
2470:   PetscFunctionReturn(PETSC_SUCCESS);
2471: }

2473: /*@
2474:   PCFieldSplitSetBlockSize - Sets the block size for defining where fields start in the
2475:   fieldsplit preconditioner when calling `PCFieldSplitSetFields()`. If not set the matrix block size is used.

2477:   Logically Collective

2479:   Input Parameters:
2480: + pc - the preconditioner context
2481: - bs - the block size

2483:   Level: intermediate

2485:   Note:
2486:   If the matrix is a `MATNEST` then the `is_rows[]` passed to `MatCreateNest()` determines the fields.

2488: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSetIS()`
2489: @*/
2490: PetscErrorCode PCFieldSplitSetBlockSize(PC pc, PetscInt bs)
2491: {
2492:   PetscFunctionBegin;
2495:   PetscTryMethod(pc, "PCFieldSplitSetBlockSize_C", (PC, PetscInt), (pc, bs));
2496:   PetscFunctionReturn(PETSC_SUCCESS);
2497: }

2499: /*@C
2500:   PCFieldSplitGetSubKSP - Gets the `KSP` contexts for all splits

2502:   Collective

2504:   Input Parameter:
2505: . pc - the preconditioner context

2507:   Output Parameters:
2508: + n      - the number of splits
2509: - subksp - the array of `KSP` contexts

2511:   Level: advanced

2513:   Notes:
2514:   After `PCFieldSplitGetSubKSP()` the array of `KSP`s is to be freed by the user with `PetscFree()`
2515:   (not the `KSP`, just the array that contains them).

2517:   You must call `PCSetUp()` before calling `PCFieldSplitGetSubKSP()`.

2519:   If the fieldsplit is of type `PC_COMPOSITE_SCHUR`, it returns the `KSP` object used inside the
2520:   Schur complement and the `KSP` object used to iterate over the Schur complement.
2521:   To access all the `KSP` objects used in `PC_COMPOSITE_SCHUR`, use `PCFieldSplitSchurGetSubKSP()`.

2523:   If the fieldsplit is of type `PC_COMPOSITE_GKB`, it returns the `KSP` object used to solve the
2524:   inner linear system defined by the matrix H in each loop.

2526:   Fortran Notes:
2527:   You must pass in a `KSP` array that is large enough to contain all the `KSP`s.
2528:   You can call `PCFieldSplitGetSubKSP`(pc,n,`PETSC_NULL_KSP`,ierr) to determine how large the
2529:   `KSP` array must be.

2531:   Developer Notes:
2532:   There should be a `PCFieldSplitRestoreSubKSP()` instead of requiring the user to call `PetscFree()`

2534:   The Fortran interface could be modernized to return directly the array of values.

2536: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSetIS()`, `PCFieldSplitSchurGetSubKSP()`
2537: @*/
2538: PetscErrorCode PCFieldSplitGetSubKSP(PC pc, PetscInt *n, KSP *subksp[])
2539: {
2540:   PetscFunctionBegin;
2542:   if (n) PetscAssertPointer(n, 2);
2543:   PetscUseMethod(pc, "PCFieldSplitGetSubKSP_C", (PC, PetscInt *, KSP **), (pc, n, subksp));
2544:   PetscFunctionReturn(PETSC_SUCCESS);
2545: }

2547: /*@C
2548:   PCFieldSplitSchurGetSubKSP - Gets the `KSP` contexts used inside the Schur complement based `PCFIELDSPLIT`

2550:   Collective

2552:   Input Parameter:
2553: . pc - the preconditioner context

2555:   Output Parameters:
2556: + n      - the number of splits
2557: - subksp - the array of `KSP` contexts

2559:   Level: advanced

2561:   Notes:
2562:   After `PCFieldSplitSchurGetSubKSP()` the array of `KSP`s is to be freed by the user with `PetscFree()`
2563:   (not the `KSP` just the array that contains them).

2565:   You must call `PCSetUp()` before calling `PCFieldSplitSchurGetSubKSP()`.

2567:   If the fieldsplit type is of type `PC_COMPOSITE_SCHUR`, it returns (in order)
2568: +  1  - the `KSP` used for the (1,1) block
2569: .  2  - the `KSP` used for the Schur complement (not the one used for the interior Schur solver)
2570: -  3  - the `KSP` used for the (1,1) block in the upper triangular factor (if different from that of the (1,1) block).

2572:   It returns a null array if the fieldsplit is not of type `PC_COMPOSITE_SCHUR`; in this case, you should use `PCFieldSplitGetSubKSP()`.

2574:   Fortran Notes:
2575:   You must pass in a `KSP` array that is large enough to contain all the local `KSP`s.
2576:   You can call `PCFieldSplitSchurGetSubKSP`(pc,n,`PETSC_NULL_KSP`,ierr) to determine how large the
2577:   `KSP` array must be.

2579:   Developer Notes:
2580:   There should be a `PCFieldSplitRestoreSubKSP()` instead of requiring the user to call `PetscFree()`

2582:   Should the functionality of `PCFieldSplitSchurGetSubKSP()` and `PCFieldSplitGetSubKSP()` be merged?

2584:   The Fortran interface should be modernized to return directly the array of values.

2586: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSetIS()`, `PCFieldSplitGetSubKSP()`
2587: @*/
2588: PetscErrorCode PCFieldSplitSchurGetSubKSP(PC pc, PetscInt *n, KSP *subksp[])
2589: {
2590:   PetscFunctionBegin;
2592:   if (n) PetscAssertPointer(n, 2);
2593:   PetscUseMethod(pc, "PCFieldSplitSchurGetSubKSP_C", (PC, PetscInt *, KSP **), (pc, n, subksp));
2594:   PetscFunctionReturn(PETSC_SUCCESS);
2595: }

2597: /*@
2598:   PCFieldSplitSetSchurPre -  Indicates from what operator the preconditioner is constructed for the Schur complement.
2599:   The default is the A11 matrix.

2601:   Collective

2603:   Input Parameters:
2604: + pc    - the preconditioner context
2605: . ptype - which matrix to use for preconditioning the Schur complement: `PC_FIELDSPLIT_SCHUR_PRE_A11` (default),
2606:               `PC_FIELDSPLIT_SCHUR_PRE_SELF`, `PC_FIELDSPLIT_SCHUR_PRE_USER`,
2607:               `PC_FIELDSPLIT_SCHUR_PRE_SELFP`, and `PC_FIELDSPLIT_SCHUR_PRE_FULL`
2608: - pre   - matrix to use for preconditioning, or `NULL`

2610:   Options Database Keys:
2611: + -pc_fieldsplit_schur_precondition <self,selfp,user,a11,full> - default is `a11`. See notes for meaning of various arguments
2612: - -fieldsplit_1_pc_type <pctype>                               - the preconditioner algorithm that is used to construct the preconditioner from the operator

2614:   Level: intermediate

2616:   Notes:
2617:   If ptype is
2618: +     a11 - the preconditioner for the Schur complement is generated from the block diagonal part of the preconditioner
2619:   matrix associated with the Schur complement (i.e. A11), not the Schur complement matrix
2620: .     self - the preconditioner for the Schur complement is generated from the symbolic representation of the Schur complement matrix:
2621:   The only preconditioners that currently work with this symbolic representation matrix object are `PCLSC` and `PCHPDDM`
2622: .     user - the preconditioner for the Schur complement is generated from the user provided matrix (pre argument
2623:   to this function).
2624: .     selfp - the preconditioning for the Schur complement is generated from an explicitly-assembled approximation $ Sp = A11 - A10 inv(diag(A00)) A01 $
2625:   This is only a good preconditioner when diag(A00) is a good preconditioner for A00. Optionally, A00 can be
2626:   lumped before extracting the diagonal using the additional option `-fieldsplit_1_mat_schur_complement_ainv_type lump`
2627: -     full - the preconditioner for the Schur complement is generated from the exact Schur complement matrix representation
2628:   computed internally by `PCFIELDSPLIT` (this is expensive)
2629:   useful mostly as a test that the Schur complement approach can work for your problem

2631:   When solving a saddle point problem, where the A11 block is identically zero, using `a11` as the ptype only makes sense
2632:   with the additional option `-fieldsplit_1_pc_type none`. Usually for saddle point problems one would use a `ptype` of `self` and
2633:   `-fieldsplit_1_pc_type lsc` which uses the least squares commutator to compute a preconditioner for the Schur complement.

2635:   Developer Note:
2636:   The name of this function and the option `-pc_fieldsplit_schur_precondition` are inconsistent; precondition should be used everywhere.

2638: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSchurPre()`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSchurPreType`,
2639:           `MatSchurComplementSetAinvType()`, `PCLSC`, `PCFieldSplitSetSchurFactType()`
2640: @*/
2641: PetscErrorCode PCFieldSplitSetSchurPre(PC pc, PCFieldSplitSchurPreType ptype, Mat pre)
2642: {
2643:   PetscFunctionBegin;
2645:   PetscTryMethod(pc, "PCFieldSplitSetSchurPre_C", (PC, PCFieldSplitSchurPreType, Mat), (pc, ptype, pre));
2646:   PetscFunctionReturn(PETSC_SUCCESS);
2647: }

2649: PetscErrorCode PCFieldSplitSchurPrecondition(PC pc, PCFieldSplitSchurPreType ptype, Mat pre)
2650: {
2651:   return PCFieldSplitSetSchurPre(pc, ptype, pre);
2652: } /* Deprecated name */

2654: /*@
2655:   PCFieldSplitGetSchurPre - For Schur complement fieldsplit, determine how the Schur complement will be
2656:   preconditioned.  See `PCFieldSplitSetSchurPre()` for details.

2658:   Logically Collective

2660:   Input Parameter:
2661: . pc - the preconditioner context

2663:   Output Parameters:
2664: + 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`
2665: - pre   - matrix to use for preconditioning (with `PC_FIELDSPLIT_SCHUR_PRE_USER`), or `NULL`

2667:   Level: intermediate

2669: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitSetSchurPre()`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSchurPreType`, `PCLSC`
2670: @*/
2671: PetscErrorCode PCFieldSplitGetSchurPre(PC pc, PCFieldSplitSchurPreType *ptype, Mat *pre)
2672: {
2673:   PetscFunctionBegin;
2675:   PetscUseMethod(pc, "PCFieldSplitGetSchurPre_C", (PC, PCFieldSplitSchurPreType *, Mat *), (pc, ptype, pre));
2676:   PetscFunctionReturn(PETSC_SUCCESS);
2677: }

2679: /*@
2680:   PCFieldSplitSchurGetS -  extract the `MATSCHURCOMPLEMENT` object used by this `PCFIELDSPLIT` in case it needs to be configured separately

2682:   Not Collective

2684:   Input Parameter:
2685: . pc - the preconditioner context

2687:   Output Parameter:
2688: . S - the Schur complement matrix

2690:   Level: advanced

2692:   Note:
2693:   This matrix should not be destroyed using `MatDestroy()`; rather, use `PCFieldSplitSchurRestoreS()`.

2695: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSchurPreType`, `PCFieldSplitSetSchurPre()`, `MATSCHURCOMPLEMENT`, `PCFieldSplitSchurRestoreS()`,
2696:           `MatCreateSchurComplement()`, `MatSchurComplementGetKSP()`, `MatSchurComplementComputeExplicitOperator()`, `MatGetSchurComplement()`
2697: @*/
2698: PetscErrorCode PCFieldSplitSchurGetS(PC pc, Mat *S)
2699: {
2700:   const char    *t;
2701:   PetscBool      isfs;
2702:   PC_FieldSplit *jac;

2704:   PetscFunctionBegin;
2706:   PetscCall(PetscObjectGetType((PetscObject)pc, &t));
2707:   PetscCall(PetscStrcmp(t, PCFIELDSPLIT, &isfs));
2708:   PetscCheck(isfs, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Expected PC of type PCFIELDSPLIT, got %s instead", t);
2709:   jac = (PC_FieldSplit *)pc->data;
2710:   PetscCheck(jac->type == PC_COMPOSITE_SCHUR, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Expected PCFIELDSPLIT of type SCHUR, got %d instead", jac->type);
2711:   if (S) *S = jac->schur;
2712:   PetscFunctionReturn(PETSC_SUCCESS);
2713: }

2715: /*@
2716:   PCFieldSplitSchurRestoreS -  returns the `MATSCHURCOMPLEMENT` matrix used by this `PC`

2718:   Not Collective

2720:   Input Parameters:
2721: + pc - the preconditioner context
2722: - S  - the Schur complement matrix

2724:   Level: advanced

2726: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSchurPreType`, `PCFieldSplitSetSchurPre()`, `MatSchurComplement`, `PCFieldSplitSchurGetS()`
2727: @*/
2728: PetscErrorCode PCFieldSplitSchurRestoreS(PC pc, Mat *S)
2729: {
2730:   const char    *t;
2731:   PetscBool      isfs;
2732:   PC_FieldSplit *jac;

2734:   PetscFunctionBegin;
2736:   PetscCall(PetscObjectGetType((PetscObject)pc, &t));
2737:   PetscCall(PetscStrcmp(t, PCFIELDSPLIT, &isfs));
2738:   PetscCheck(isfs, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Expected PC of type PCFIELDSPLIT, got %s instead", t);
2739:   jac = (PC_FieldSplit *)pc->data;
2740:   PetscCheck(jac->type == PC_COMPOSITE_SCHUR, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Expected PCFIELDSPLIT of type SCHUR, got %d instead", jac->type);
2741:   PetscCheck(S && (*S == jac->schur), PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "MatSchurComplement restored is not the same as gotten");
2742:   PetscFunctionReturn(PETSC_SUCCESS);
2743: }

2745: static PetscErrorCode PCFieldSplitSetSchurPre_FieldSplit(PC pc, PCFieldSplitSchurPreType ptype, Mat pre)
2746: {
2747:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

2749:   PetscFunctionBegin;
2750:   jac->schurpre = ptype;
2751:   if (ptype == PC_FIELDSPLIT_SCHUR_PRE_USER && pre) {
2752:     PetscCall(MatDestroy(&jac->schur_user));
2753:     jac->schur_user = pre;
2754:     PetscCall(PetscObjectReference((PetscObject)jac->schur_user));
2755:   }
2756:   PetscFunctionReturn(PETSC_SUCCESS);
2757: }

2759: static PetscErrorCode PCFieldSplitGetSchurPre_FieldSplit(PC pc, PCFieldSplitSchurPreType *ptype, Mat *pre)
2760: {
2761:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

2763:   PetscFunctionBegin;
2764:   if (ptype) *ptype = jac->schurpre;
2765:   if (pre) *pre = jac->schur_user;
2766:   PetscFunctionReturn(PETSC_SUCCESS);
2767: }

2769: /*@
2770:   PCFieldSplitSetSchurFactType -  sets which blocks of the approximate block factorization to retain in the preconditioner {cite}`murphy2000note` and {cite}`ipsen2001note`

2772:   Collective

2774:   Input Parameters:
2775: + pc    - the preconditioner context
2776: - ftype - which blocks of factorization to retain, `PC_FIELDSPLIT_SCHUR_FACT_FULL` is default

2778:   Options Database Key:
2779: . -pc_fieldsplit_schur_fact_type <diag,lower,upper,full> - default is `full`

2781:   Level: intermediate

2783:   Notes:
2784:   The FULL factorization is

2786:   ```{math}
2787:   \left(\begin{array}{cc} A & B \\
2788:   C & E \\
2789:   \end{array}\right) =
2790:   \left(\begin{array}{cc} 1 & 0 \\
2791:   C*A^{-1} & I \\
2792:   \end{array}\right)
2793:   \left(\begin{array}{cc} A & 0 \\
2794:   0 & S \\
2795:   \end{array}\right)
2796:   \left(\begin{array}{cc} I & A^{-1}B \\
2797:   0 & I \\
2798:   \end{array}\right) = L D U.
2799:   ```

2801:   where $ S = E - C*A^{-1}*B $. In practice, the full factorization is applied via block triangular solves with the grouping $L*(D*U)$. UPPER uses $D*U$, LOWER uses $L*D$,
2802:   and DIAG is the diagonal part with the sign of $ S $ flipped (because this makes the preconditioner positive definite for many formulations,
2803:   thus allowing the use of `KSPMINRES)`. Sign flipping of $ S $ can be turned off with `PCFieldSplitSetSchurScale()`.

2805:   If $A$ and $S$ are solved exactly
2806: +  1 - FULL factorization is a direct solver.
2807: .  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.
2808: -  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.

2810:   If the iteration count is very low, consider using `KSPFGMRES` or `KSPGCR` which can use one less preconditioner
2811:   application in this case. Note that the preconditioned operator may be highly non-normal, so such fast convergence may not be observed in practice.

2813:   For symmetric problems in which $A$ is positive definite and $S$ is negative definite, DIAG can be used with `KSPMINRES`.

2815:   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).

2817: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSchurPreType`, `PCFieldSplitSetSchurScale()`,
2818:           [](sec_flexibleksp), `PCFieldSplitSetSchurPre()`
2819: @*/
2820: PetscErrorCode PCFieldSplitSetSchurFactType(PC pc, PCFieldSplitSchurFactType ftype)
2821: {
2822:   PetscFunctionBegin;
2824:   PetscTryMethod(pc, "PCFieldSplitSetSchurFactType_C", (PC, PCFieldSplitSchurFactType), (pc, ftype));
2825:   PetscFunctionReturn(PETSC_SUCCESS);
2826: }

2828: static PetscErrorCode PCFieldSplitSetSchurFactType_FieldSplit(PC pc, PCFieldSplitSchurFactType ftype)
2829: {
2830:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

2832:   PetscFunctionBegin;
2833:   jac->schurfactorization = ftype;
2834:   PetscFunctionReturn(PETSC_SUCCESS);
2835: }

2837: /*@
2838:   PCFieldSplitSetSchurScale -  Controls the sign flip of S for `PC_FIELDSPLIT_SCHUR_FACT_DIAG`.

2840:   Collective

2842:   Input Parameters:
2843: + pc    - the preconditioner context
2844: - scale - scaling factor for the Schur complement

2846:   Options Database Key:
2847: . -pc_fieldsplit_schur_scale <scale> - default is -1.0

2849:   Level: intermediate

2851: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSchurFactType`, `PCFieldSplitSetSchurFactType()`
2852: @*/
2853: PetscErrorCode PCFieldSplitSetSchurScale(PC pc, PetscScalar scale)
2854: {
2855:   PetscFunctionBegin;
2858:   PetscTryMethod(pc, "PCFieldSplitSetSchurScale_C", (PC, PetscScalar), (pc, scale));
2859:   PetscFunctionReturn(PETSC_SUCCESS);
2860: }

2862: static PetscErrorCode PCFieldSplitSetSchurScale_FieldSplit(PC pc, PetscScalar scale)
2863: {
2864:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

2866:   PetscFunctionBegin;
2867:   jac->schurscale = scale;
2868:   PetscFunctionReturn(PETSC_SUCCESS);
2869: }

2871: /*@C
2872:   PCFieldSplitGetSchurBlocks - Gets all matrix blocks for the Schur complement

2874:   Collective

2876:   Input Parameter:
2877: . pc - the preconditioner context

2879:   Output Parameters:
2880: + A00 - the (0,0) block
2881: . A01 - the (0,1) block
2882: . A10 - the (1,0) block
2883: - A11 - the (1,1) block

2885:   Level: advanced

2887:   Note:
2888:   Use `NULL` for any unneeded output arguments

2890: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `MatSchurComplementGetSubMatrices()`, `MatSchurComplementSetSubMatrices()`
2891: @*/
2892: PetscErrorCode PCFieldSplitGetSchurBlocks(PC pc, Mat *A00, Mat *A01, Mat *A10, Mat *A11)
2893: {
2894:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

2896:   PetscFunctionBegin;
2898:   PetscCheck(jac->type == PC_COMPOSITE_SCHUR, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONG, "FieldSplit is not using a Schur complement approach.");
2899:   if (A00) *A00 = jac->pmat[0];
2900:   if (A01) *A01 = jac->B;
2901:   if (A10) *A10 = jac->C;
2902:   if (A11) *A11 = jac->pmat[1];
2903:   PetscFunctionReturn(PETSC_SUCCESS);
2904: }

2906: /*@
2907:   PCFieldSplitSetGKBTol -  Sets the solver tolerance for the generalized Golub-Kahan bidiagonalization preconditioner {cite}`arioli2013` in `PCFIELDSPLIT`

2909:   Collective

2911:   Input Parameters:
2912: + pc        - the preconditioner context
2913: - tolerance - the solver tolerance

2915:   Options Database Key:
2916: . -pc_fieldsplit_gkb_tol <tolerance> - default is 1e-5

2918:   Level: intermediate

2920:   Note:
2921:   The generalized GKB algorithm {cite}`arioli2013` uses a lower bound estimate of the error in energy norm as stopping criterion.
2922:   It stops once the lower bound estimate undershoots the required solver tolerance. Although the actual error might be bigger than
2923:   this estimate, the stopping criterion is satisfactory in practical cases.

2925: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetGKBDelay()`, `PCFieldSplitSetGKBNu()`, `PCFieldSplitSetGKBMaxit()`
2926: @*/
2927: PetscErrorCode PCFieldSplitSetGKBTol(PC pc, PetscReal tolerance)
2928: {
2929:   PetscFunctionBegin;
2932:   PetscTryMethod(pc, "PCFieldSplitSetGKBTol_C", (PC, PetscReal), (pc, tolerance));
2933:   PetscFunctionReturn(PETSC_SUCCESS);
2934: }

2936: static PetscErrorCode PCFieldSplitSetGKBTol_FieldSplit(PC pc, PetscReal tolerance)
2937: {
2938:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

2940:   PetscFunctionBegin;
2941:   jac->gkbtol = tolerance;
2942:   PetscFunctionReturn(PETSC_SUCCESS);
2943: }

2945: /*@
2946:   PCFieldSplitSetGKBMaxit -  Sets the maximum number of iterations for the generalized Golub-Kahan bidiagonalization preconditioner {cite}`arioli2013` in `PCFIELDSPLIT`

2948:   Collective

2950:   Input Parameters:
2951: + pc    - the preconditioner context
2952: - maxit - the maximum number of iterations

2954:   Options Database Key:
2955: . -pc_fieldsplit_gkb_maxit <maxit> - default is 100

2957:   Level: intermediate

2959: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetGKBDelay()`, `PCFieldSplitSetGKBTol()`, `PCFieldSplitSetGKBNu()`
2960: @*/
2961: PetscErrorCode PCFieldSplitSetGKBMaxit(PC pc, PetscInt maxit)
2962: {
2963:   PetscFunctionBegin;
2966:   PetscTryMethod(pc, "PCFieldSplitSetGKBMaxit_C", (PC, PetscInt), (pc, maxit));
2967:   PetscFunctionReturn(PETSC_SUCCESS);
2968: }

2970: static PetscErrorCode PCFieldSplitSetGKBMaxit_FieldSplit(PC pc, PetscInt maxit)
2971: {
2972:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

2974:   PetscFunctionBegin;
2975:   jac->gkbmaxit = maxit;
2976:   PetscFunctionReturn(PETSC_SUCCESS);
2977: }

2979: /*@
2980:   PCFieldSplitSetGKBDelay -  Sets the delay in the lower bound error estimate in the generalized Golub-Kahan bidiagonalization {cite}`arioli2013` in `PCFIELDSPLIT`
2981:   preconditioner.

2983:   Collective

2985:   Input Parameters:
2986: + pc    - the preconditioner context
2987: - delay - the delay window in the lower bound estimate

2989:   Options Database Key:
2990: . -pc_fieldsplit_gkb_delay <delay> - default is 5

2992:   Level: intermediate

2994:   Notes:
2995:   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 $
2996:   is expressed as a truncated sum. The error at iteration k can only be measured at iteration (k + `delay`), and thus the algorithm needs
2997:   at least (`delay` + 1) iterations to stop.

2999:   For more details on the generalized Golub-Kahan bidiagonalization method and its lower bound stopping criterion, please refer to {cite}`arioli2013`

3001: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetGKBNu()`, `PCFieldSplitSetGKBTol()`, `PCFieldSplitSetGKBMaxit()`
3002: @*/
3003: PetscErrorCode PCFieldSplitSetGKBDelay(PC pc, PetscInt delay)
3004: {
3005:   PetscFunctionBegin;
3008:   PetscTryMethod(pc, "PCFieldSplitSetGKBDelay_C", (PC, PetscInt), (pc, delay));
3009:   PetscFunctionReturn(PETSC_SUCCESS);
3010: }

3012: static PetscErrorCode PCFieldSplitSetGKBDelay_FieldSplit(PC pc, PetscInt delay)
3013: {
3014:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

3016:   PetscFunctionBegin;
3017:   jac->gkbdelay = delay;
3018:   PetscFunctionReturn(PETSC_SUCCESS);
3019: }

3021: /*@
3022:   PCFieldSplitSetGKBNu -  Sets the scalar value nu >= 0 in the transformation H = A00 + nu*A01*A01' of the (1,1) block in the
3023:   Golub-Kahan bidiagonalization preconditioner {cite}`arioli2013` in `PCFIELDSPLIT`

3025:   Collective

3027:   Input Parameters:
3028: + pc - the preconditioner context
3029: - nu - the shift parameter

3031:   Options Database Key:
3032: . -pc_fieldsplit_gkb_nu <nu> - default is 1

3034:   Level: intermediate

3036:   Notes:
3037:   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,
3038:   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
3039:   necessary to find a good balance in between the convergence of the inner and outer loop.

3041:   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.

3043: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetGKBDelay()`, `PCFieldSplitSetGKBTol()`, `PCFieldSplitSetGKBMaxit()`
3044: @*/
3045: PetscErrorCode PCFieldSplitSetGKBNu(PC pc, PetscReal nu)
3046: {
3047:   PetscFunctionBegin;
3050:   PetscTryMethod(pc, "PCFieldSplitSetGKBNu_C", (PC, PetscReal), (pc, nu));
3051:   PetscFunctionReturn(PETSC_SUCCESS);
3052: }

3054: static PetscErrorCode PCFieldSplitSetGKBNu_FieldSplit(PC pc, PetscReal nu)
3055: {
3056:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

3058:   PetscFunctionBegin;
3059:   jac->gkbnu = nu;
3060:   PetscFunctionReturn(PETSC_SUCCESS);
3061: }

3063: static PetscErrorCode PCFieldSplitSetType_FieldSplit(PC pc, PCCompositeType type)
3064: {
3065:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

3067:   PetscFunctionBegin;
3068:   jac->type = type;
3069:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSubKSP_C", NULL));
3070:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurPre_C", NULL));
3071:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSchurPre_C", NULL));
3072:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurFactType_C", NULL));
3073:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurScale_C", NULL));
3074:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBTol_C", NULL));
3075:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBMaxit_C", NULL));
3076:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBNu_C", NULL));
3077:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBDelay_C", NULL));

3079:   if (type == PC_COMPOSITE_SCHUR) {
3080:     pc->ops->apply          = PCApply_FieldSplit_Schur;
3081:     pc->ops->applytranspose = PCApplyTranspose_FieldSplit_Schur;
3082:     pc->ops->view           = PCView_FieldSplit_Schur;
3083:     pc->ops->setuponblocks  = PCSetUpOnBlocks_FieldSplit_Schur;

3085:     PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSubKSP_C", PCFieldSplitGetSubKSP_FieldSplit_Schur));
3086:     PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurPre_C", PCFieldSplitSetSchurPre_FieldSplit));
3087:     PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSchurPre_C", PCFieldSplitGetSchurPre_FieldSplit));
3088:     PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurFactType_C", PCFieldSplitSetSchurFactType_FieldSplit));
3089:     PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurScale_C", PCFieldSplitSetSchurScale_FieldSplit));
3090:   } else if (type == PC_COMPOSITE_GKB) {
3091:     pc->ops->apply          = PCApply_FieldSplit_GKB;
3092:     pc->ops->applytranspose = NULL;
3093:     pc->ops->view           = PCView_FieldSplit_GKB;
3094:     pc->ops->setuponblocks  = PCSetUpOnBlocks_FieldSplit_GKB;

3096:     PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSubKSP_C", PCFieldSplitGetSubKSP_FieldSplit));
3097:     PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBTol_C", PCFieldSplitSetGKBTol_FieldSplit));
3098:     PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBMaxit_C", PCFieldSplitSetGKBMaxit_FieldSplit));
3099:     PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBNu_C", PCFieldSplitSetGKBNu_FieldSplit));
3100:     PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBDelay_C", PCFieldSplitSetGKBDelay_FieldSplit));
3101:   } else {
3102:     pc->ops->apply          = PCApply_FieldSplit;
3103:     pc->ops->applytranspose = PCApplyTranspose_FieldSplit;
3104:     pc->ops->view           = PCView_FieldSplit;
3105:     pc->ops->setuponblocks  = PCSetUpOnBlocks_FieldSplit;

3107:     PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSubKSP_C", PCFieldSplitGetSubKSP_FieldSplit));
3108:   }
3109:   PetscFunctionReturn(PETSC_SUCCESS);
3110: }

3112: static PetscErrorCode PCFieldSplitSetBlockSize_FieldSplit(PC pc, PetscInt bs)
3113: {
3114:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

3116:   PetscFunctionBegin;
3117:   PetscCheck(bs >= 1, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_OUTOFRANGE, "Blocksize must be positive, you gave %" PetscInt_FMT, bs);
3118:   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);
3119:   jac->bs = bs;
3120:   PetscFunctionReturn(PETSC_SUCCESS);
3121: }

3123: static PetscErrorCode PCSetCoordinates_FieldSplit(PC pc, PetscInt dim, PetscInt nloc, PetscReal coords[])
3124: {
3125:   PC_FieldSplit    *jac           = (PC_FieldSplit *)pc->data;
3126:   PC_FieldSplitLink ilink_current = jac->head;
3127:   IS                is_owned;

3129:   PetscFunctionBegin;
3130:   jac->coordinates_set = PETSC_TRUE; // Internal flag
3131:   PetscCall(MatGetOwnershipIS(pc->mat, &is_owned, NULL));

3133:   while (ilink_current) {
3134:     // For each IS, embed it to get local coords indces
3135:     IS              is_coords;
3136:     PetscInt        ndofs_block;
3137:     const PetscInt *block_dofs_enumeration; // Numbering of the dofs relevant to the current block

3139:     // Setting drop to true for safety. It should make no difference.
3140:     PetscCall(ISEmbed(ilink_current->is, is_owned, PETSC_TRUE, &is_coords));
3141:     PetscCall(ISGetLocalSize(is_coords, &ndofs_block));
3142:     PetscCall(ISGetIndices(is_coords, &block_dofs_enumeration));

3144:     // Allocate coordinates vector and set it directly
3145:     PetscCall(PetscMalloc1(ndofs_block * dim, &ilink_current->coords));
3146:     for (PetscInt dof = 0; dof < ndofs_block; ++dof) {
3147:       for (PetscInt d = 0; d < dim; ++d) (ilink_current->coords)[dim * dof + d] = coords[dim * block_dofs_enumeration[dof] + d];
3148:     }
3149:     ilink_current->dim   = dim;
3150:     ilink_current->ndofs = ndofs_block;
3151:     PetscCall(ISRestoreIndices(is_coords, &block_dofs_enumeration));
3152:     PetscCall(ISDestroy(&is_coords));
3153:     ilink_current = ilink_current->next;
3154:   }
3155:   PetscCall(ISDestroy(&is_owned));
3156:   PetscFunctionReturn(PETSC_SUCCESS);
3157: }

3159: /*@
3160:   PCFieldSplitSetType - Sets the type, `PCCompositeType`, of a `PCFIELDSPLIT`

3162:   Collective

3164:   Input Parameters:
3165: + pc   - the preconditioner context
3166: - type - `PC_COMPOSITE_ADDITIVE`, `PC_COMPOSITE_MULTIPLICATIVE` (default), `PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE`, `PC_COMPOSITE_SPECIAL`, `PC_COMPOSITE_SCHUR`,
3167:          `PC_COMPOSITE_GKB`

3169:   Options Database Key:
3170: . -pc_fieldsplit_type <one of multiplicative, additive, symmetric_multiplicative, special, schur> - Sets fieldsplit preconditioner type

3172:   Level: intermediate

3174: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCCompositeType`, `PCCompositeGetType()`, `PC_COMPOSITE_ADDITIVE`, `PC_COMPOSITE_MULTIPLICATIVE`,
3175:           `PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE`, `PC_COMPOSITE_SPECIAL`, `PC_COMPOSITE_SCHUR`, `PCFieldSplitSetSchurFactType()`
3176: @*/
3177: PetscErrorCode PCFieldSplitSetType(PC pc, PCCompositeType type)
3178: {
3179:   PetscFunctionBegin;
3181:   PetscTryMethod(pc, "PCFieldSplitSetType_C", (PC, PCCompositeType), (pc, type));
3182:   PetscFunctionReturn(PETSC_SUCCESS);
3183: }

3185: /*@
3186:   PCFieldSplitGetType - Gets the type, `PCCompositeType`, of a `PCFIELDSPLIT`

3188:   Not collective

3190:   Input Parameter:
3191: . pc - the preconditioner context

3193:   Output Parameter:
3194: . type - `PC_COMPOSITE_ADDITIVE`, `PC_COMPOSITE_MULTIPLICATIVE` (default), `PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE`, `PC_COMPOSITE_SPECIAL`, `PC_COMPOSITE_SCHUR`

3196:   Level: intermediate

3198: .seealso: [](sec_block_matrices), `PC`, `PCCompositeSetType()`, `PCFIELDSPLIT`, `PCCompositeType`, `PC_COMPOSITE_ADDITIVE`, `PC_COMPOSITE_MULTIPLICATIVE`,
3199:           `PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE`, `PC_COMPOSITE_SPECIAL`, `PC_COMPOSITE_SCHUR`
3200: @*/
3201: PetscErrorCode PCFieldSplitGetType(PC pc, PCCompositeType *type)
3202: {
3203:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

3205:   PetscFunctionBegin;
3207:   PetscAssertPointer(type, 2);
3208:   *type = jac->type;
3209:   PetscFunctionReturn(PETSC_SUCCESS);
3210: }

3212: /*@
3213:   PCFieldSplitSetDMSplits - Flags whether `DMCreateFieldDecomposition()` should be used to define the splits in a `PCFIELDSPLIT`, whenever possible.

3215:   Logically Collective

3217:   Input Parameters:
3218: + pc  - the preconditioner context
3219: - flg - boolean indicating whether to use field splits defined by the `DM`

3221:   Options Database Key:
3222: . -pc_fieldsplit_dm_splits <bool> - use the field splits defined by the `DM`

3224:   Level: intermediate

3226:   Developer Note:
3227:   The name should be `PCFieldSplitSetUseDMSplits()`, similar change to options database

3229: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitGetDMSplits()`, `DMCreateFieldDecomposition()`, `PCFieldSplitSetFields()`, `PCFieldsplitSetIS()`
3230: @*/
3231: PetscErrorCode PCFieldSplitSetDMSplits(PC pc, PetscBool flg)
3232: {
3233:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
3234:   PetscBool      isfs;

3236:   PetscFunctionBegin;
3239:   PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCFIELDSPLIT, &isfs));
3240:   if (isfs) jac->dm_splits = flg;
3241:   PetscFunctionReturn(PETSC_SUCCESS);
3242: }

3244: /*@
3245:   PCFieldSplitGetDMSplits - Returns flag indicating whether `DMCreateFieldDecomposition()` should be used to define the splits in a `PCFIELDSPLIT`, whenever possible.

3247:   Logically Collective

3249:   Input Parameter:
3250: . pc - the preconditioner context

3252:   Output Parameter:
3253: . flg - boolean indicating whether to use field splits defined by the `DM`

3255:   Level: intermediate

3257:   Developer Note:
3258:   The name should be `PCFieldSplitGetUseDMSplits()`

3260: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetDMSplits()`, `DMCreateFieldDecomposition()`, `PCFieldSplitSetFields()`, `PCFieldsplitSetIS()`
3261: @*/
3262: PetscErrorCode PCFieldSplitGetDMSplits(PC pc, PetscBool *flg)
3263: {
3264:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
3265:   PetscBool      isfs;

3267:   PetscFunctionBegin;
3269:   PetscAssertPointer(flg, 2);
3270:   PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCFIELDSPLIT, &isfs));
3271:   if (isfs) {
3272:     if (flg) *flg = jac->dm_splits;
3273:   }
3274:   PetscFunctionReturn(PETSC_SUCCESS);
3275: }

3277: /*@
3278:   PCFieldSplitGetDetectSaddlePoint - Returns flag indicating whether `PCFIELDSPLIT` will attempt to automatically determine fields based on zero diagonal entries.

3280:   Logically Collective

3282:   Input Parameter:
3283: . pc - the preconditioner context

3285:   Output Parameter:
3286: . flg - boolean indicating whether to detect fields or not

3288:   Level: intermediate

3290: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetDetectSaddlePoint()`
3291: @*/
3292: PetscErrorCode PCFieldSplitGetDetectSaddlePoint(PC pc, PetscBool *flg)
3293: {
3294:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

3296:   PetscFunctionBegin;
3297:   *flg = jac->detect;
3298:   PetscFunctionReturn(PETSC_SUCCESS);
3299: }

3301: /*@
3302:   PCFieldSplitSetDetectSaddlePoint - Sets flag indicating whether `PCFIELDSPLIT` will attempt to automatically determine fields based on zero diagonal entries.

3304:   Logically Collective

3306:   Input Parameter:
3307: . pc - the preconditioner context

3309:   Output Parameter:
3310: . flg - boolean indicating whether to detect fields or not

3312:   Options Database Key:
3313: . -pc_fieldsplit_detect_saddle_point <bool> - detect and use the saddle point

3315:   Level: intermediate

3317:   Note:
3318:   Also sets the split type to `PC_COMPOSITE_SCHUR` (see `PCFieldSplitSetType()`) and the Schur preconditioner type to `PC_FIELDSPLIT_SCHUR_PRE_SELF` (see `PCFieldSplitSetSchurPre()`).

3320: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitGetDetectSaddlePoint()`, `PCFieldSplitSetType()`, `PCFieldSplitSetSchurPre()`, `PC_FIELDSPLIT_SCHUR_PRE_SELF`
3321: @*/
3322: PetscErrorCode PCFieldSplitSetDetectSaddlePoint(PC pc, PetscBool flg)
3323: {
3324:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

3326:   PetscFunctionBegin;
3327:   jac->detect = flg;
3328:   if (jac->detect) {
3329:     PetscCall(PCFieldSplitSetType(pc, PC_COMPOSITE_SCHUR));
3330:     PetscCall(PCFieldSplitSetSchurPre(pc, PC_FIELDSPLIT_SCHUR_PRE_SELF, NULL));
3331:   }
3332:   PetscFunctionReturn(PETSC_SUCCESS);
3333: }

3335: /*MC
3336:   PCFIELDSPLIT - Preconditioner created by combining separate preconditioners for individual
3337:   collections of variables (that may overlap) called splits. See [the users manual section on "Solving Block Matrices"](sec_block_matrices) for more details.

3339:   Options Database Keys:
3340: +   -pc_fieldsplit_%d_fields <a,b,..>                                                - indicates the fields to be used in the `%d`'th split
3341: .   -pc_fieldsplit_default                                                           - automatically add any fields to additional splits that have not
3342:                                                                                        been supplied explicitly by `-pc_fieldsplit_%d_fields`
3343: .   -pc_fieldsplit_block_size <bs>                                                   - size of block that defines fields (i.e. there are bs fields)
3344:                                                                                        when the matrix is not of `MatType` `MATNEST`
3345: .   -pc_fieldsplit_type <additive,multiplicative,symmetric_multiplicative,schur,gkb> - type of relaxation or factorization splitting
3346: .   -pc_fieldsplit_schur_precondition <self,selfp,user,a11,full>                     - default is `a11`; see `PCFieldSplitSetSchurPre()`
3347: .   -pc_fieldsplit_schur_fact_type <diag,lower,upper,full>                           - set factorization type when using `-pc_fieldsplit_type schur`;
3348:                                                                                        see `PCFieldSplitSetSchurFactType()`
3349: .   -pc_fieldsplit_dm_splits <true,false> (default is true)                          - Whether to use `DMCreateFieldDecomposition()` for splits
3350: -   -pc_fieldsplit_detect_saddle_point                                               - automatically finds rows with zero diagonal and uses Schur complement with no preconditioner as the solver

3352:   Options prefixes for inner solvers when using the Schur complement preconditioner are `-fieldsplit_0_` and `-fieldsplit_1_` .
3353:   The options prefix for the inner solver when using the Golub-Kahan biadiagonalization preconditioner is `-fieldsplit_0_`
3354:   For all other solvers they are `-fieldsplit_%d_` for the `%d`'th field; use `-fieldsplit_` for all fields.

3356:   To set options on the solvers for each block append `-fieldsplit_` to all the `PC`
3357:   options database keys. For example, `-fieldsplit_pc_type ilu` `-fieldsplit_pc_factor_levels 1`

3359:   To set the options on the solvers separate for each block call `PCFieldSplitGetSubKSP()`
3360:   and set the options directly on the resulting `KSP` object

3362:   Level: intermediate

3364:   Notes:
3365:   Use `PCFieldSplitSetFields()` to set splits defined by "strided" entries or with a `MATNEST` and `PCFieldSplitSetIS()`
3366:   to define a split by an arbitrary collection of entries.

3368:   If no splits are set, the default is used. If a `DM` is associated with the `PC` and it supports
3369:   `DMCreateFieldDecomposition()`, then that is used for the default. Otherwise if the matrix is not `MATNEST`, the splits are defined by entries strided by bs,
3370:   beginning at 0 then 1, etc to bs-1. The block size can be set with `PCFieldSplitSetBlockSize()`,
3371:   if this is not called the block size defaults to the blocksize of the second matrix passed
3372:   to `KSPSetOperators()`/`PCSetOperators()`.

3374:   For the Schur complement preconditioner if
3375:   ```{math}
3376:     J = \left[\begin{array}{cc} A_{00} & A_{01} \\ A_{10} & A_{11} \end{array}\right]
3377:   ```

3379:   the preconditioner using `full` factorization is logically
3380:   ```{math}
3381:     \left[\begin{array}{cc} I & -\text{ksp}(A_{00}) A_{01} \\ 0 & I \end{array}\right] \left[\begin{array}{cc} \text{inv}(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]
3382:       ```
3383:   where the action of $\text{inv}(A_{00})$ is applied using the KSP solver with prefix `-fieldsplit_0_`.  $S$ is the Schur complement
3384:   ```{math}
3385:      S = A_{11} - A_{10} \text{ksp}(A_{00}) A_{01}
3386:   ```
3387:   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` was given
3388:   in providing the SECOND split or 1 if not given). For `PCFieldSplitGetSubKSP()` when field number is 0,
3389:   it returns the `KSP` associated with `-fieldsplit_0_` while field number 1 gives `-fieldsplit_1_` KSP. By default
3390:   $A_{11}$ is used to construct a preconditioner for $S$, use `PCFieldSplitSetSchurPre()` for all the possible ways to construct the preconditioner for $S$.

3392:   The factorization type is set using `-pc_fieldsplit_schur_fact_type <diag, lower, upper, full>`. `full` is shown above,
3393:   `diag` gives
3394:   ```{math}
3395:     \left[\begin{array}{cc} \text{inv}(A_{00}) & 0 \\  0 & -\text{ksp}(S) \end{array}\right]
3396:   ```
3397:   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
3398:   can be turned off with `PCFieldSplitSetSchurScale()` or by command line `-pc_fieldsplit_schur_scale 1.0`. The `lower` factorization is the inverse of
3399:   ```{math}
3400:     \left[\begin{array}{cc} A_{00} & 0 \\  A_{10} & S \end{array}\right]
3401:   ```
3402:   where the inverses of A_{00} and S are applied using KSPs. The upper factorization is the inverse of
3403:   ```{math}
3404:     \left[\begin{array}{cc} A_{00} & A_{01} \\  0 & S \end{array}\right]
3405:   ```
3406:   where again the inverses of $A_{00}$ and $S$ are applied using `KSP`s.

3408:   If only one set of indices (one `IS`) is provided with `PCFieldSplitSetIS()` then the complement of that `IS`
3409:   is used automatically for a second submatrix.

3411:   The fieldsplit preconditioner cannot currently be used with the `MATBAIJ` or `MATSBAIJ` data formats if the blocksize is larger than 1.
3412:   Generally it should be used with the `MATAIJ` or `MATNEST` `MatType`

3414:   The forms of these preconditioners are closely related, if not identical, to forms derived as "Distributive Iterations", see,
3415:   for example, page 294 in "Principles of Computational Fluid Dynamics" by Pieter Wesseling {cite}`wesseling2009`.
3416:   One can also use `PCFIELDSPLIT` inside a smoother resulting in "Distributive Smoothers".

3418:   See "A taxonomy and comparison of parallel block multi-level preconditioners for the incompressible Navier-Stokes equations" {cite}`elman2008tcp`.

3420:   The Constrained Pressure Preconditioner (CPR) can be implemented using `PCCOMPOSITE` with `PCGALERKIN`. CPR first solves an $R A P$ subsystem, updates the
3421:   residual on all variables (`PCCompositeSetType(pc,PC_COMPOSITE_MULTIPLICATIVE)`), and then applies a simple ILU like preconditioner on all the variables.

3423:   The generalized Golub-Kahan bidiagonalization preconditioner (GKB) can be applied to symmetric $2 \times 2$ block matrices of the shape
3424:   ```{math}
3425:     \left[\begin{array}{cc} A_{00} & A_{01} \\ A_{01}' & 0 \end{array}\right]
3426:   ```
3427:   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 $H = _{A00} + \nu*A_{01}*A_{01}'$.
3428:   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_`.

3430:   Developer Note:
3431:   The Schur complement functionality of `PCFIELDSPLIT` should likely be factored into its own `PC` thus simplifying the implementation of the preconditioners and their
3432:   user API.

3434: .seealso: [](sec_block_matrices), `PC`, `PCCreate()`, `PCSetType()`, `PCType`, `PC`, `PCLSC`,
3435:           `PCFieldSplitGetSubKSP()`, `PCFieldSplitSchurGetSubKSP()`, `PCFieldSplitSetFields()`,
3436:           `PCFieldSplitSetType()`, `PCFieldSplitSetIS()`, `PCFieldSplitSetSchurPre()`, `PCFieldSplitSetSchurFactType()`,
3437:           `MatSchurComplementSetAinvType()`, `PCFieldSplitSetSchurScale()`, `PCFieldSplitSetDetectSaddlePoint()`
3438: M*/

3440: PETSC_EXTERN PetscErrorCode PCCreate_FieldSplit(PC pc)
3441: {
3442:   PC_FieldSplit *jac;

3444:   PetscFunctionBegin;
3445:   PetscCall(PetscNew(&jac));

3447:   jac->bs                 = -1;
3448:   jac->type               = PC_COMPOSITE_MULTIPLICATIVE;
3449:   jac->schurpre           = PC_FIELDSPLIT_SCHUR_PRE_USER; /* Try user preconditioner first, fall back on diagonal */
3450:   jac->schurfactorization = PC_FIELDSPLIT_SCHUR_FACT_FULL;
3451:   jac->schurscale         = -1.0;
3452:   jac->dm_splits          = PETSC_TRUE;
3453:   jac->gkbtol             = 1e-5;
3454:   jac->gkbdelay           = 5;
3455:   jac->gkbnu              = 1;
3456:   jac->gkbmaxit           = 100;

3458:   pc->data = (void *)jac;

3460:   pc->ops->setup           = PCSetUp_FieldSplit;
3461:   pc->ops->reset           = PCReset_FieldSplit;
3462:   pc->ops->destroy         = PCDestroy_FieldSplit;
3463:   pc->ops->setfromoptions  = PCSetFromOptions_FieldSplit;
3464:   pc->ops->applyrichardson = NULL;

3466:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSchurGetSubKSP_C", PCFieldSplitSchurGetSubKSP_FieldSplit));
3467:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetFields_C", PCFieldSplitSetFields_FieldSplit));
3468:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetIS_C", PCFieldSplitSetIS_FieldSplit));
3469:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetType_C", PCFieldSplitSetType_FieldSplit));
3470:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetBlockSize_C", PCFieldSplitSetBlockSize_FieldSplit));
3471:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitRestrictIS_C", PCFieldSplitRestrictIS_FieldSplit));
3472:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCSetCoordinates_C", PCSetCoordinates_FieldSplit));

3474:   /* Initialize function pointers */
3475:   PetscCall(PCFieldSplitSetType(pc, jac->type));
3476:   PetscFunctionReturn(PETSC_SUCCESS);
3477: }