Actual source code: fieldsplit.c

  1: #include <petsc/private/pcimpl.h>
  2: #include <petsc/private/kspimpl.h>
  3: #include <petscdm.h>

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

  8: 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;

 10: typedef struct _PC_FieldSplitLink *PC_FieldSplitLink;
 11: struct _PC_FieldSplitLink {
 12:   KSP               ksp;
 13:   Vec               x, y, z;
 14:   char             *splitname;
 15:   PetscInt          nfields;
 16:   PetscInt         *fields, *fields_col;
 17:   VecScatter        sctx;
 18:   IS                is, is_col;
 19:   PC_FieldSplitLink next, previous;
 20:   PetscLogEvent     event;

 22:   /* Used only when setting coordinates with PCSetCoordinates */
 23:   PetscInt   dim;
 24:   PetscInt   ndofs;
 25:   PetscReal *coords;
 26: };

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

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

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

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

 73: /*
 74:     Note:
 75:     there is no particular reason that pmat, x, and y are stored as arrays in PC_FieldSplit instead of
 76:    inside PC_FieldSplitLink, just historical. If you want to be able to add new fields after already using the
 77:    PC you could change this.
 78: */

 80: /* This helper is so that setting a user-provided preconditioning matrix is orthogonal to choosing to use it.  This way the
 81: * application-provided FormJacobian can provide this matrix without interfering with the user's (command-line) choices. */
 82: static Mat FieldSplitSchurPre(PC_FieldSplit *jac)
 83: {
 84:   switch (jac->schurpre) {
 85:   case PC_FIELDSPLIT_SCHUR_PRE_SELF:
 86:     return jac->schur;
 87:   case PC_FIELDSPLIT_SCHUR_PRE_SELFP:
 88:     return jac->schurp;
 89:   case PC_FIELDSPLIT_SCHUR_PRE_A11:
 90:     return jac->pmat[1];
 91:   case PC_FIELDSPLIT_SCHUR_PRE_FULL: /* We calculate this and store it in schur_user */
 92:   case PC_FIELDSPLIT_SCHUR_PRE_USER: /* Use a user-provided matrix if it is given, otherwise diagonal block */
 93:   default:
 94:     return jac->schur_user ? jac->schur_user : jac->pmat[1];
 95:   }
 96: }

 98: #include <petscdraw.h>
 99: static PetscErrorCode PCView_FieldSplit(PC pc, PetscViewer viewer)
100: {
101:   PC_FieldSplit    *jac = (PC_FieldSplit *)pc->data;
102:   PetscBool         iascii, isdraw;
103:   PetscInt          i, j;
104:   PC_FieldSplitLink ilink = jac->head;

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

137:   if (isdraw) {
138:     PetscDraw draw;
139:     PetscReal x, y, w, wd;

141:     PetscCall(PetscViewerDrawGetDraw(viewer, 0, &draw));
142:     PetscCall(PetscDrawGetCurrentPoint(draw, &x, &y));
143:     w  = 2 * PetscMin(1.0 - x, x);
144:     wd = w / (jac->nsplits + 1);
145:     x  = x - wd * (jac->nsplits - 1) / 2.0;
146:     for (i = 0; i < jac->nsplits; i++) {
147:       PetscCall(PetscDrawPushCurrentPoint(draw, x, y));
148:       PetscCall(KSPView(ilink->ksp, viewer));
149:       PetscCall(PetscDrawPopCurrentPoint(draw));
150:       x += wd;
151:       ilink = ilink->next;
152:     }
153:   }
154:   PetscFunctionReturn(PETSC_SUCCESS);
155: }

157: static PetscErrorCode PCView_FieldSplit_Schur(PC pc, PetscViewer viewer)
158: {
159:   PC_FieldSplit             *jac = (PC_FieldSplit *)pc->data;
160:   PetscBool                  iascii, isdraw;
161:   PetscInt                   i, j;
162:   PC_FieldSplitLink          ilink = jac->head;
163:   MatSchurComplementAinvType atype;

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

246:     PetscCall(PetscViewerDrawGetDraw(viewer, 0, &draw));
247:     PetscCall(PetscDrawGetCurrentPoint(draw, &x, &y));
248:     if (jac->kspupper != jac->head->ksp) cnt++;
249:     w  = 2 * PetscMin(1.0 - x, x);
250:     wd = w / (cnt + 1);

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

264:     PetscCall(PetscDrawPushCurrentPoint(draw, x, y));
265:     PetscCall(KSPView(jac->head->ksp, viewer));
266:     PetscCall(PetscDrawPopCurrentPoint(draw));
267:     if (jac->kspupper != jac->head->ksp) {
268:       x += wd;
269:       PetscCall(PetscDrawPushCurrentPoint(draw, x, y));
270:       PetscCall(KSPView(jac->kspupper, viewer));
271:       PetscCall(PetscDrawPopCurrentPoint(draw));
272:     }
273:     x += wd;
274:     PetscCall(PetscDrawPushCurrentPoint(draw, x, y));
275:     PetscCall(KSPView(jac->kspschur, viewer));
276:     PetscCall(PetscDrawPopCurrentPoint(draw));
277:   }
278:   PetscFunctionReturn(PETSC_SUCCESS);
279: }

281: static PetscErrorCode PCView_FieldSplit_GKB(PC pc, PetscViewer viewer)
282: {
283:   PC_FieldSplit    *jac = (PC_FieldSplit *)pc->data;
284:   PetscBool         iascii, isdraw;
285:   PetscInt          i, j;
286:   PC_FieldSplitLink ilink = jac->head;

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

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

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

319:     PetscCall(PetscViewerASCIIPopTab(viewer));
320:   }

322:   if (isdraw) {
323:     PetscDraw draw;
324:     PetscReal x, y, w, wd;

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

342: /* Precondition: jac->bs is set to a meaningful value */
343: static PetscErrorCode PCFieldSplitSetRuntimeSplits_Private(PC pc)
344: {
345:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
346:   PetscInt       i, nfields, *ifields, nfields_col, *ifields_col;
347:   PetscBool      flg, flg_col;
348:   char           optionname[128], splitname[8], optionname_col[128];

350:   PetscFunctionBegin;
351:   PetscCall(PetscMalloc1(jac->bs, &ifields));
352:   PetscCall(PetscMalloc1(jac->bs, &ifields_col));
353:   for (i = 0, flg = PETSC_TRUE;; i++) {
354:     PetscCall(PetscSNPrintf(splitname, sizeof(splitname), "%" PetscInt_FMT, i));
355:     PetscCall(PetscSNPrintf(optionname, sizeof(optionname), "-pc_fieldsplit_%" PetscInt_FMT "_fields", i));
356:     PetscCall(PetscSNPrintf(optionname_col, sizeof(optionname_col), "-pc_fieldsplit_%" PetscInt_FMT "_fields_col", i));
357:     nfields     = jac->bs;
358:     nfields_col = jac->bs;
359:     PetscCall(PetscOptionsGetIntArray(((PetscObject)pc)->options, ((PetscObject)pc)->prefix, optionname, ifields, &nfields, &flg));
360:     PetscCall(PetscOptionsGetIntArray(((PetscObject)pc)->options, ((PetscObject)pc)->prefix, optionname_col, ifields_col, &nfields_col, &flg_col));
361:     if (!flg) break;
362:     else if (flg && !flg_col) {
363:       PetscCheck(nfields, PETSC_COMM_SELF, PETSC_ERR_USER, "Cannot list zero fields");
364:       PetscCall(PCFieldSplitSetFields(pc, splitname, nfields, ifields, ifields));
365:     } else {
366:       PetscCheck(nfields && nfields_col, PETSC_COMM_SELF, PETSC_ERR_USER, "Cannot list zero fields");
367:       PetscCheck(nfields == nfields_col, PETSC_COMM_SELF, PETSC_ERR_USER, "Number of row and column fields must match");
368:       PetscCall(PCFieldSplitSetFields(pc, splitname, nfields, ifields, ifields_col));
369:     }
370:   }
371:   if (i > 0) {
372:     /* Makes command-line setting of splits take precedence over setting them in code.
373:        Otherwise subsequent calls to PCFieldSplitSetIS() or PCFieldSplitSetFields() would
374:        create new splits, which would probably not be what the user wanted. */
375:     jac->splitdefined = PETSC_TRUE;
376:   }
377:   PetscCall(PetscFree(ifields));
378:   PetscCall(PetscFree(ifields_col));
379:   PetscFunctionReturn(PETSC_SUCCESS);
380: }

382: static PetscErrorCode PCFieldSplitSetDefaults(PC pc)
383: {
384:   PC_FieldSplit    *jac                = (PC_FieldSplit *)pc->data;
385:   PC_FieldSplitLink ilink              = jac->head;
386:   PetscBool         fieldsplit_default = PETSC_FALSE, coupling = PETSC_FALSE;
387:   PetscInt          i;

389:   PetscFunctionBegin;
390:   /*
391:    Kinda messy, but at least this now uses DMCreateFieldDecomposition().
392:    Should probably be rewritten.
393:    */
394:   if (!ilink) {
395:     PetscCall(PetscOptionsGetBool(((PetscObject)pc)->options, ((PetscObject)pc)->prefix, "-pc_fieldsplit_detect_coupling", &coupling, NULL));
396:     if (pc->dm && jac->dm_splits && !jac->detect && !coupling) {
397:       PetscInt  numFields, f, i, j;
398:       char    **fieldNames;
399:       IS       *fields;
400:       DM       *dms;
401:       DM        subdm[128];
402:       PetscBool flg;

404:       PetscCall(DMCreateFieldDecomposition(pc->dm, &numFields, &fieldNames, &fields, &dms));
405:       /* Allow the user to prescribe the splits */
406:       for (i = 0, flg = PETSC_TRUE;; i++) {
407:         PetscInt ifields[128];
408:         IS       compField;
409:         char     optionname[128], splitname[8];
410:         PetscInt nfields = numFields;

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

464:       if (jac->detect) {
465:         IS       zerodiags, rest;
466:         PetscInt nmin, nmax;

468:         PetscCall(MatGetOwnershipRange(pc->mat, &nmin, &nmax));
469:         if (jac->diag_use_amat) {
470:           PetscCall(MatFindZeroDiagonals(pc->mat, &zerodiags));
471:         } else {
472:           PetscCall(MatFindZeroDiagonals(pc->pmat, &zerodiags));
473:         }
474:         PetscCall(ISComplement(zerodiags, nmin, nmax, &rest));
475:         PetscCall(PCFieldSplitSetIS(pc, "0", rest));
476:         PetscCall(PCFieldSplitSetIS(pc, "1", zerodiags));
477:         PetscCall(ISDestroy(&zerodiags));
478:         PetscCall(ISDestroy(&rest));
479:       } else if (coupling) {
480:         IS       coupling, rest;
481:         PetscInt nmin, nmax;

483:         PetscCall(MatGetOwnershipRange(pc->mat, &nmin, &nmax));
484:         if (jac->offdiag_use_amat) {
485:           PetscCall(MatFindOffBlockDiagonalEntries(pc->mat, &coupling));
486:         } else {
487:           PetscCall(MatFindOffBlockDiagonalEntries(pc->pmat, &coupling));
488:         }
489:         PetscCall(ISCreateStride(PetscObjectComm((PetscObject)pc->mat), nmax - nmin, nmin, 1, &rest));
490:         PetscCall(ISSetIdentity(rest));
491:         PetscCall(PCFieldSplitSetIS(pc, "0", rest));
492:         PetscCall(PCFieldSplitSetIS(pc, "1", coupling));
493:         PetscCall(ISDestroy(&coupling));
494:         PetscCall(ISDestroy(&rest));
495:       } else {
496:         PetscCall(PetscOptionsGetBool(((PetscObject)pc)->options, ((PetscObject)pc)->prefix, "-pc_fieldsplit_default", &fieldsplit_default, NULL));
497:         if (!fieldsplit_default) {
498:           /* Allow user to set fields from command line,  if bs was known at the time of PCSetFromOptions_FieldSplit()
499:            then it is set there. This is not ideal because we should only have options set in XXSetFromOptions(). */
500:           PetscCall(PCFieldSplitSetRuntimeSplits_Private(pc));
501:           if (jac->splitdefined) PetscCall(PetscInfo(pc, "Splits defined using the options database\n"));
502:         }
503:         if ((fieldsplit_default || !jac->splitdefined) && !jac->isrestrict) {
504:           Mat       M = pc->pmat;
505:           PetscBool isnest;

507:           PetscCall(PetscInfo(pc, "Using default splitting of fields\n"));
508:           PetscCall(PetscObjectTypeCompare((PetscObject)pc->pmat, MATNEST, &isnest));
509:           if (!isnest) {
510:             M = pc->mat;
511:             PetscCall(PetscObjectTypeCompare((PetscObject)pc->mat, MATNEST, &isnest));
512:           }
513:           if (isnest) {
514:             IS      *fields;
515:             PetscInt nf;

517:             PetscCall(MatNestGetSize(M, &nf, NULL));
518:             PetscCall(PetscMalloc1(nf, &fields));
519:             PetscCall(MatNestGetISs(M, fields, NULL));
520:             for (i = 0; i < nf; i++) PetscCall(PCFieldSplitSetIS(pc, NULL, fields[i]));
521:             PetscCall(PetscFree(fields));
522:           } else {
523:             for (i = 0; i < jac->bs; i++) {
524:               char splitname[8];
525:               PetscCall(PetscSNPrintf(splitname, sizeof(splitname), "%" PetscInt_FMT, i));
526:               PetscCall(PCFieldSplitSetFields(pc, splitname, 1, &i, &i));
527:             }
528:             jac->defaultsplit = PETSC_TRUE;
529:           }
530:         }
531:       }
532:     }
533:   } else if (jac->nsplits == 1) {
534:     IS       is2;
535:     PetscInt nmin, nmax;

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

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

548: static PetscErrorCode MatGolubKahanComputeExplicitOperator(Mat A, Mat B, Mat C, Mat *H, PetscReal gkbnu)
549: {
550:   Mat       BT, T;
551:   PetscReal nrmT, nrmB;

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

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

566:   PetscCall(MatDestroy(&BT));
567:   PetscCall(MatDestroy(&T));
568:   PetscFunctionReturn(PETSC_SUCCESS);
569: }

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

573: static PetscErrorCode PCSetUp_FieldSplit(PC pc)
574: {
575:   PC_FieldSplit    *jac = (PC_FieldSplit *)pc->data;
576:   PC_FieldSplitLink ilink;
577:   PetscInt          i, nsplit;
578:   PetscBool         sorted, sorted_col;

580:   PetscFunctionBegin;
581:   pc->failedreason = PC_NOERROR;
582:   PetscCall(PCFieldSplitSetDefaults(pc));
583:   nsplit = jac->nsplits;
584:   ilink  = jac->head;

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

590:     jac->issetup = PETSC_TRUE;

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

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

602:       PetscCall(PetscObjectTypeCompareAny((PetscObject)pc->pmat, &blk, MATBAIJ, MATSBAIJ, MATSEQBAIJ, MATSEQSBAIJ, MATMPIBAIJ, MATMPISBAIJ, NULL));
603:       PetscCheck(!blk, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONG, "Cannot use MATBAIJ with PCFIELDSPLIT and currently set matrix and PC blocksizes");
604:     }

606:     bs = jac->bs;
607:     PetscCall(MatGetOwnershipRange(pc->pmat, &rstart, &rend));
608:     nslots = (rend - rstart) / bs;
609:     for (i = 0; i < nsplit; i++) {
610:       if (jac->defaultsplit) {
611:         PetscCall(ISCreateStride(PetscObjectComm((PetscObject)pc), nslots, rstart + i, nsplit, &ilink->is));
612:         PetscCall(ISDuplicate(ilink->is, &ilink->is_col));
613:       } else if (!ilink->is) {
614:         if (ilink->nfields > 1) {
615:           PetscInt *ii, *jj, j, k, nfields = ilink->nfields, *fields = ilink->fields, *fields_col = ilink->fields_col;
616:           PetscCall(PetscMalloc1(ilink->nfields * nslots, &ii));
617:           PetscCall(PetscMalloc1(ilink->nfields * nslots, &jj));
618:           for (j = 0; j < nslots; j++) {
619:             for (k = 0; k < nfields; k++) {
620:               ii[nfields * j + k] = rstart + bs * j + fields[k];
621:               jj[nfields * j + k] = rstart + bs * j + fields_col[k];
622:             }
623:           }
624:           PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)pc), nslots * nfields, ii, PETSC_OWN_POINTER, &ilink->is));
625:           PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)pc), nslots * nfields, jj, PETSC_OWN_POINTER, &ilink->is_col));
626:           PetscCall(ISSetBlockSize(ilink->is, nfields));
627:           PetscCall(ISSetBlockSize(ilink->is_col, nfields));
628:         } else {
629:           PetscCall(ISCreateStride(PetscObjectComm((PetscObject)pc), nslots, rstart + ilink->fields[0], bs, &ilink->is));
630:           PetscCall(ISCreateStride(PetscObjectComm((PetscObject)pc), nslots, rstart + ilink->fields_col[0], bs, &ilink->is_col));
631:         }
632:       }
633:       PetscCall(ISSorted(ilink->is, &sorted));
634:       if (ilink->is_col) PetscCall(ISSorted(ilink->is_col, &sorted_col));
635:       PetscCheck(sorted && sorted_col, PETSC_COMM_SELF, PETSC_ERR_USER, "Fields must be sorted when creating split");
636:       ilink = ilink->next;
637:     }
638:   }

640:   ilink = jac->head;
641:   if (!jac->pmat) {
642:     Vec xtmp;

644:     PetscCall(MatCreateVecs(pc->pmat, &xtmp, NULL));
645:     PetscCall(PetscMalloc1(nsplit, &jac->pmat));
646:     PetscCall(PetscMalloc2(nsplit, &jac->x, nsplit, &jac->y));
647:     for (i = 0; i < nsplit; i++) {
648:       MatNullSpace sp;

650:       /* Check for preconditioning matrix attached to IS */
651:       PetscCall(PetscObjectQuery((PetscObject)ilink->is, "pmat", (PetscObject *)&jac->pmat[i]));
652:       if (jac->pmat[i]) {
653:         PetscCall(PetscObjectReference((PetscObject)jac->pmat[i]));
654:         if (jac->type == PC_COMPOSITE_SCHUR) {
655:           jac->schur_user = jac->pmat[i];

657:           PetscCall(PetscObjectReference((PetscObject)jac->schur_user));
658:         }
659:       } else {
660:         const char *prefix;
661:         PetscCall(MatCreateSubMatrix(pc->pmat, ilink->is, ilink->is_col, MAT_INITIAL_MATRIX, &jac->pmat[i]));
662:         PetscCall(MatGetOptionsPrefix(jac->pmat[i], &prefix));
663:         if (!prefix) {
664:           PetscCall(KSPGetOptionsPrefix(ilink->ksp, &prefix));
665:           PetscCall(MatSetOptionsPrefix(jac->pmat[i], prefix));
666:         }
667:         PetscCall(MatSetFromOptions(jac->pmat[i]));
668:         PetscCall(MatViewFromOptions(jac->pmat[i], NULL, "-mat_view"));
669:       }
670:       /* create work vectors for each split */
671:       PetscCall(MatCreateVecs(jac->pmat[i], &jac->x[i], &jac->y[i]));
672:       ilink->x = jac->x[i];
673:       ilink->y = jac->y[i];
674:       ilink->z = NULL;
675:       /* compute scatter contexts needed by multiplicative versions and non-default splits */
676:       PetscCall(VecScatterCreate(xtmp, ilink->is, jac->x[i], NULL, &ilink->sctx));
677:       PetscCall(PetscObjectQuery((PetscObject)ilink->is, "nearnullspace", (PetscObject *)&sp));
678:       if (sp) PetscCall(MatSetNearNullSpace(jac->pmat[i], sp));
679:       ilink = ilink->next;
680:     }
681:     PetscCall(VecDestroy(&xtmp));
682:   } else {
683:     MatReuse      scall;
684:     MatNullSpace *nullsp = NULL;

686:     if (pc->flag == DIFFERENT_NONZERO_PATTERN) {
687:       PetscCall(MatGetNullSpaces(nsplit, jac->pmat, &nullsp));
688:       for (i = 0; i < nsplit; i++) PetscCall(MatDestroy(&jac->pmat[i]));
689:       scall = MAT_INITIAL_MATRIX;
690:     } else scall = MAT_REUSE_MATRIX;

692:     for (i = 0; i < nsplit; i++) {
693:       Mat pmat;

695:       /* Check for preconditioning matrix attached to IS */
696:       PetscCall(PetscObjectQuery((PetscObject)ilink->is, "pmat", (PetscObject *)&pmat));
697:       if (!pmat) PetscCall(MatCreateSubMatrix(pc->pmat, ilink->is, ilink->is_col, scall, &jac->pmat[i]));
698:       ilink = ilink->next;
699:     }
700:     if (nullsp) PetscCall(MatRestoreNullSpaces(nsplit, jac->pmat, &nullsp));
701:   }
702:   if (jac->diag_use_amat) {
703:     ilink = jac->head;
704:     if (!jac->mat) {
705:       PetscCall(PetscMalloc1(nsplit, &jac->mat));
706:       for (i = 0; i < nsplit; i++) {
707:         PetscCall(MatCreateSubMatrix(pc->mat, ilink->is, ilink->is_col, MAT_INITIAL_MATRIX, &jac->mat[i]));
708:         ilink = ilink->next;
709:       }
710:     } else {
711:       MatReuse      scall;
712:       MatNullSpace *nullsp = NULL;

714:       if (pc->flag == DIFFERENT_NONZERO_PATTERN) {
715:         PetscCall(MatGetNullSpaces(nsplit, jac->mat, &nullsp));
716:         for (i = 0; i < nsplit; i++) PetscCall(MatDestroy(&jac->mat[i]));
717:         scall = MAT_INITIAL_MATRIX;
718:       } else scall = MAT_REUSE_MATRIX;

720:       for (i = 0; i < nsplit; i++) {
721:         PetscCall(MatCreateSubMatrix(pc->mat, ilink->is, ilink->is_col, scall, &jac->mat[i]));
722:         ilink = ilink->next;
723:       }
724:       if (nullsp) PetscCall(MatRestoreNullSpaces(nsplit, jac->mat, &nullsp));
725:     }
726:   } else {
727:     jac->mat = jac->pmat;
728:   }

730:   /* Check for null space attached to IS */
731:   ilink = jac->head;
732:   for (i = 0; i < nsplit; i++) {
733:     MatNullSpace sp;

735:     PetscCall(PetscObjectQuery((PetscObject)ilink->is, "nullspace", (PetscObject *)&sp));
736:     if (sp) PetscCall(MatSetNullSpace(jac->mat[i], sp));
737:     ilink = ilink->next;
738:   }

740:   if (jac->type != PC_COMPOSITE_ADDITIVE && jac->type != PC_COMPOSITE_SCHUR && jac->type != PC_COMPOSITE_GKB) {
741:     /* extract the rows of the matrix associated with each field: used for efficient computation of residual inside algorithm */
742:     /* FIXME: Can/should we reuse jac->mat whenever (jac->diag_use_amat) is true? */
743:     ilink = jac->head;
744:     if (nsplit == 2 && jac->type == PC_COMPOSITE_MULTIPLICATIVE) {
745:       /* 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 */
746:       if (!jac->Afield) {
747:         PetscCall(PetscCalloc1(nsplit, &jac->Afield));
748:         if (jac->offdiag_use_amat) {
749:           PetscCall(MatCreateSubMatrix(pc->mat, ilink->next->is, ilink->is, MAT_INITIAL_MATRIX, &jac->Afield[1]));
750:         } else {
751:           PetscCall(MatCreateSubMatrix(pc->pmat, ilink->next->is, ilink->is, MAT_INITIAL_MATRIX, &jac->Afield[1]));
752:         }
753:       } else {
754:         MatReuse scall;

756:         if (pc->flag == DIFFERENT_NONZERO_PATTERN) {
757:           PetscCall(MatDestroy(&jac->Afield[1]));
758:           scall = MAT_INITIAL_MATRIX;
759:         } else scall = MAT_REUSE_MATRIX;

761:         if (jac->offdiag_use_amat) {
762:           PetscCall(MatCreateSubMatrix(pc->mat, ilink->next->is, ilink->is, scall, &jac->Afield[1]));
763:         } else {
764:           PetscCall(MatCreateSubMatrix(pc->pmat, ilink->next->is, ilink->is, scall, &jac->Afield[1]));
765:         }
766:       }
767:     } else {
768:       if (!jac->Afield) {
769:         PetscCall(PetscMalloc1(nsplit, &jac->Afield));
770:         for (i = 0; i < nsplit; i++) {
771:           if (jac->offdiag_use_amat) {
772:             PetscCall(MatCreateSubMatrix(pc->mat, ilink->is, NULL, MAT_INITIAL_MATRIX, &jac->Afield[i]));
773:           } else {
774:             PetscCall(MatCreateSubMatrix(pc->pmat, ilink->is, NULL, MAT_INITIAL_MATRIX, &jac->Afield[i]));
775:           }
776:           ilink = ilink->next;
777:         }
778:       } else {
779:         MatReuse scall;
780:         if (pc->flag == DIFFERENT_NONZERO_PATTERN) {
781:           for (i = 0; i < nsplit; i++) PetscCall(MatDestroy(&jac->Afield[i]));
782:           scall = MAT_INITIAL_MATRIX;
783:         } else scall = MAT_REUSE_MATRIX;

785:         for (i = 0; i < nsplit; i++) {
786:           if (jac->offdiag_use_amat) {
787:             PetscCall(MatCreateSubMatrix(pc->mat, ilink->is, NULL, scall, &jac->Afield[i]));
788:           } else {
789:             PetscCall(MatCreateSubMatrix(pc->pmat, ilink->is, NULL, scall, &jac->Afield[i]));
790:           }
791:           ilink = ilink->next;
792:         }
793:       }
794:     }
795:   }

797:   if (jac->type == PC_COMPOSITE_SCHUR) {
798:     IS          ccis;
799:     PetscBool   isset, isspd;
800:     PetscInt    rstart, rend;
801:     char        lscname[256];
802:     PetscObject LSC_L;
803:     PetscBool   set, flg;

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

807:     /* If pc->mat is SPD, don't scale by -1 the Schur complement */
808:     if (jac->schurscale == (PetscScalar)-1.0) {
809:       PetscCall(MatIsSPDKnown(pc->pmat, &isset, &isspd));
810:       jac->schurscale = (isset && isspd) ? 1.0 : -1.0;
811:     }

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

817:     if (jac->schur) {
818:       KSP      kspA = jac->head->ksp, kspInner = NULL, kspUpper = jac->kspupper;
819:       MatReuse scall;

821:       if (pc->flag == DIFFERENT_NONZERO_PATTERN) {
822:         scall = MAT_INITIAL_MATRIX;
823:         PetscCall(MatDestroy(&jac->B));
824:         PetscCall(MatDestroy(&jac->C));
825:       } else scall = MAT_REUSE_MATRIX;

827:       PetscCall(MatSchurComplementGetKSP(jac->schur, &kspInner));
828:       ilink = jac->head;
829:       PetscCall(ISComplement(ilink->is_col, rstart, rend, &ccis));
830:       if (jac->offdiag_use_amat) {
831:         PetscCall(MatCreateSubMatrix(pc->mat, ilink->is, ccis, scall, &jac->B));
832:       } else {
833:         PetscCall(MatCreateSubMatrix(pc->pmat, ilink->is, ccis, scall, &jac->B));
834:       }
835:       PetscCall(ISDestroy(&ccis));
836:       if (!flg) {
837:         ilink = ilink->next;
838:         PetscCall(ISComplement(ilink->is_col, rstart, rend, &ccis));
839:         if (jac->offdiag_use_amat) {
840:           PetscCall(MatCreateSubMatrix(pc->mat, ilink->is, ccis, scall, &jac->C));
841:         } else {
842:           PetscCall(MatCreateSubMatrix(pc->pmat, ilink->is, ccis, scall, &jac->C));
843:         }
844:         PetscCall(ISDestroy(&ccis));
845:       } else {
846:         PetscCall(MatIsHermitianKnown(jac->offdiag_use_amat ? pc->mat : pc->pmat, &set, &flg));
847:         if (set && flg) PetscCall(MatCreateHermitianTranspose(jac->B, &jac->C));
848:         else PetscCall(MatCreateTranspose(jac->B, &jac->C));
849:       }
850:       PetscCall(MatSchurComplementUpdateSubMatrices(jac->schur, jac->mat[0], jac->pmat[0], jac->B, jac->C, jac->mat[1]));
851:       if (jac->schurpre == PC_FIELDSPLIT_SCHUR_PRE_SELFP) {
852:         PetscCall(MatDestroy(&jac->schurp));
853:         PetscCall(MatSchurComplementGetPmat(jac->schur, MAT_INITIAL_MATRIX, &jac->schurp));
854:       } else if (jac->schurpre == PC_FIELDSPLIT_SCHUR_PRE_FULL) {
855:         PetscCall(MatDestroy(&jac->schur_user));
856:         PetscCall(MatSchurComplementComputeExplicitOperator(jac->schur, &jac->schur_user));
857:       }
858:       if (kspA != kspInner) PetscCall(KSPSetOperators(kspA, jac->mat[0], jac->pmat[0]));
859:       if (kspUpper != kspA) PetscCall(KSPSetOperators(kspUpper, jac->mat[0], jac->pmat[0]));
860:       PetscCall(KSPSetOperators(jac->kspschur, jac->schur, FieldSplitSchurPre(jac)));
861:     } else {
862:       const char  *Dprefix;
863:       char         schurprefix[256], schurmatprefix[256];
864:       char         schurtestoption[256];
865:       MatNullSpace sp;
866:       KSP          kspt;

868:       /* extract the A01 and A10 matrices */
869:       ilink = jac->head;
870:       PetscCall(ISComplement(ilink->is_col, rstart, rend, &ccis));
871:       if (jac->offdiag_use_amat) {
872:         PetscCall(MatCreateSubMatrix(pc->mat, ilink->is, ccis, MAT_INITIAL_MATRIX, &jac->B));
873:       } else {
874:         PetscCall(MatCreateSubMatrix(pc->pmat, ilink->is, ccis, MAT_INITIAL_MATRIX, &jac->B));
875:       }
876:       PetscCall(ISDestroy(&ccis));
877:       ilink = ilink->next;
878:       if (!flg) {
879:         PetscCall(ISComplement(ilink->is_col, rstart, rend, &ccis));
880:         if (jac->offdiag_use_amat) {
881:           PetscCall(MatCreateSubMatrix(pc->mat, ilink->is, ccis, MAT_INITIAL_MATRIX, &jac->C));
882:         } else {
883:           PetscCall(MatCreateSubMatrix(pc->pmat, ilink->is, ccis, MAT_INITIAL_MATRIX, &jac->C));
884:         }
885:         PetscCall(ISDestroy(&ccis));
886:       } else {
887:         PetscCall(MatIsHermitianKnown(jac->offdiag_use_amat ? pc->mat : pc->pmat, &set, &flg));
888:         if (set && flg) PetscCall(MatCreateHermitianTranspose(jac->B, &jac->C));
889:         else PetscCall(MatCreateTranspose(jac->B, &jac->C));
890:       }
891:       /* Use mat[0] (diagonal block of Amat) preconditioned by pmat[0] to define Schur complement */
892:       PetscCall(MatCreate(((PetscObject)jac->mat[0])->comm, &jac->schur));
893:       PetscCall(MatSetType(jac->schur, MATSCHURCOMPLEMENT));
894:       PetscCall(MatSchurComplementSetSubMatrices(jac->schur, jac->mat[0], jac->pmat[0], jac->B, jac->C, jac->mat[1]));
895:       PetscCall(PetscSNPrintf(schurmatprefix, sizeof(schurmatprefix), "%sfieldsplit_%s_", ((PetscObject)pc)->prefix ? ((PetscObject)pc)->prefix : "", ilink->splitname));
896:       PetscCall(MatSetOptionsPrefix(jac->schur, schurmatprefix));
897:       PetscCall(MatSchurComplementGetKSP(jac->schur, &kspt));
898:       PetscCall(KSPSetOptionsPrefix(kspt, schurmatprefix));

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

904:       PetscCall(PetscSNPrintf(schurtestoption, sizeof(schurtestoption), "-fieldsplit_%s_inner_", ilink->splitname));
905:       PetscCall(PetscOptionsFindPairPrefix_Private(((PetscObject)pc)->options, ((PetscObject)pc)->prefix, schurtestoption, NULL, NULL, &flg));
906:       if (flg) {
907:         DM  dmInner;
908:         KSP kspInner;
909:         PC  pcInner;

911:         PetscCall(MatSchurComplementGetKSP(jac->schur, &kspInner));
912:         PetscCall(KSPReset(kspInner));
913:         PetscCall(KSPSetOperators(kspInner, jac->mat[0], jac->pmat[0]));
914:         PetscCall(PetscSNPrintf(schurprefix, sizeof(schurprefix), "%sfieldsplit_%s_inner_", ((PetscObject)pc)->prefix ? ((PetscObject)pc)->prefix : "", ilink->splitname));
915:         /* Indent this deeper to emphasize the "inner" nature of this solver. */
916:         PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspInner, (PetscObject)pc, 2));
917:         PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspInner->pc, (PetscObject)pc, 2));
918:         PetscCall(KSPSetOptionsPrefix(kspInner, schurprefix));

920:         /* Set DM for new solver */
921:         PetscCall(KSPGetDM(jac->head->ksp, &dmInner));
922:         PetscCall(KSPSetDM(kspInner, dmInner));
923:         PetscCall(KSPSetDMActive(kspInner, PETSC_FALSE));

925:         /* Defaults to PCKSP as preconditioner */
926:         PetscCall(KSPGetPC(kspInner, &pcInner));
927:         PetscCall(PCSetType(pcInner, PCKSP));
928:         PetscCall(PCKSPSetKSP(pcInner, jac->head->ksp));
929:       } else {
930:         /* Use the outer solver for the inner solve, but revert the KSPPREONLY from PCFieldSplitSetFields_FieldSplit or
931:           * PCFieldSplitSetIS_FieldSplit. We don't want KSPPREONLY because it makes the Schur complement inexact,
932:           * preventing Schur complement reduction to be an accurate solve. Usually when an iterative solver is used for
933:           * S = D - C A_inner^{-1} B, we expect S to be defined using an accurate definition of A_inner^{-1}, so we make
934:           * GMRES the default. Note that it is also common to use PREONLY for S, in which case S may not be used
935:           * directly, and the user is responsible for setting an inexact method for fieldsplit's A^{-1}. */
936:         PetscCall(KSPSetType(jac->head->ksp, KSPGMRES));
937:         PetscCall(MatSchurComplementSetKSP(jac->schur, jac->head->ksp));
938:       }
939:       PetscCall(KSPSetOperators(jac->head->ksp, jac->mat[0], jac->pmat[0]));
940:       PetscCall(KSPSetFromOptions(jac->head->ksp));
941:       PetscCall(MatSetFromOptions(jac->schur));

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

948:         PetscCall(MatSchurComplementGetKSP(jac->schur, &kspInner));
949:         PetscCall(KSPGetPC(kspInner, &pcInner));
950:         PetscCall(PetscObjectTypeCompare((PetscObject)pcInner, PCKSP, &flg));
951:         if (flg) {
952:           KSP ksp;

954:           PetscCall(PCKSPGetKSP(pcInner, &ksp));
955:           if (ksp == jac->head->ksp) PetscCall(PCSetUseAmat(pcInner, PETSC_TRUE));
956:         }
957:       }
958:       PetscCall(PetscSNPrintf(schurtestoption, sizeof(schurtestoption), "-fieldsplit_%s_upper_", ilink->splitname));
959:       PetscCall(PetscOptionsFindPairPrefix_Private(((PetscObject)pc)->options, ((PetscObject)pc)->prefix, schurtestoption, NULL, NULL, &flg));
960:       if (flg) {
961:         DM dmInner;

963:         PetscCall(PetscSNPrintf(schurprefix, sizeof(schurprefix), "%sfieldsplit_%s_upper_", ((PetscObject)pc)->prefix ? ((PetscObject)pc)->prefix : "", ilink->splitname));
964:         PetscCall(KSPCreate(PetscObjectComm((PetscObject)pc), &jac->kspupper));
965:         PetscCall(KSPSetNestLevel(jac->kspupper, pc->kspnestlevel));
966:         PetscCall(KSPSetErrorIfNotConverged(jac->kspupper, pc->erroriffailure));
967:         PetscCall(KSPSetOptionsPrefix(jac->kspupper, schurprefix));
968:         PetscCall(PetscObjectIncrementTabLevel((PetscObject)jac->kspupper, (PetscObject)pc, 1));
969:         PetscCall(PetscObjectIncrementTabLevel((PetscObject)jac->kspupper->pc, (PetscObject)pc, 1));
970:         PetscCall(KSPGetDM(jac->head->ksp, &dmInner));
971:         PetscCall(KSPSetDM(jac->kspupper, dmInner));
972:         PetscCall(KSPSetDMActive(jac->kspupper, PETSC_FALSE));
973:         PetscCall(KSPSetFromOptions(jac->kspupper));
974:         PetscCall(KSPSetOperators(jac->kspupper, jac->mat[0], jac->pmat[0]));
975:         PetscCall(VecDuplicate(jac->head->x, &jac->head->z));
976:       } else {
977:         jac->kspupper = jac->head->ksp;
978:         PetscCall(PetscObjectReference((PetscObject)jac->head->ksp));
979:       }

981:       if (jac->schurpre == PC_FIELDSPLIT_SCHUR_PRE_SELFP) PetscCall(MatSchurComplementGetPmat(jac->schur, MAT_INITIAL_MATRIX, &jac->schurp));
982:       PetscCall(KSPCreate(PetscObjectComm((PetscObject)pc), &jac->kspschur));
983:       PetscCall(KSPSetNestLevel(jac->kspschur, pc->kspnestlevel));
984:       PetscCall(KSPSetErrorIfNotConverged(jac->kspschur, pc->erroriffailure));
985:       PetscCall(PetscObjectIncrementTabLevel((PetscObject)jac->kspschur, (PetscObject)pc, 1));
986:       if (jac->schurpre == PC_FIELDSPLIT_SCHUR_PRE_SELF) {
987:         PC pcschur;
988:         PetscCall(KSPGetPC(jac->kspschur, &pcschur));
989:         PetscCall(PCSetType(pcschur, PCNONE));
990:         /* Note: This is bad if there exist preconditioners for MATSCHURCOMPLEMENT */
991:       } else if (jac->schurpre == PC_FIELDSPLIT_SCHUR_PRE_FULL) {
992:         PetscCall(MatSchurComplementComputeExplicitOperator(jac->schur, &jac->schur_user));
993:       }
994:       PetscCall(KSPSetOperators(jac->kspschur, jac->schur, FieldSplitSchurPre(jac)));
995:       PetscCall(KSPGetOptionsPrefix(jac->head->next->ksp, &Dprefix));
996:       PetscCall(KSPSetOptionsPrefix(jac->kspschur, Dprefix));
997:       /* propagate DM */
998:       {
999:         DM sdm;
1000:         PetscCall(KSPGetDM(jac->head->next->ksp, &sdm));
1001:         if (sdm) {
1002:           PetscCall(KSPSetDM(jac->kspschur, sdm));
1003:           PetscCall(KSPSetDMActive(jac->kspschur, PETSC_FALSE));
1004:         }
1005:       }
1006:       /* really want setfromoptions called in PCSetFromOptions_FieldSplit(), but it is not ready yet */
1007:       /* need to call this every time, since the jac->kspschur is freshly created, otherwise its options never get set */
1008:       PetscCall(KSPSetFromOptions(jac->kspschur));
1009:     }
1010:     PetscCall(MatAssemblyBegin(jac->schur, MAT_FINAL_ASSEMBLY));
1011:     PetscCall(MatAssemblyEnd(jac->schur, MAT_FINAL_ASSEMBLY));

1013:     /* HACK: special support to forward L and Lp matrices that might be used by PCLSC */
1014:     PetscCall(PetscSNPrintf(lscname, sizeof(lscname), "%s_LSC_L", ilink->splitname));
1015:     PetscCall(PetscObjectQuery((PetscObject)pc->mat, lscname, (PetscObject *)&LSC_L));
1016:     if (!LSC_L) PetscCall(PetscObjectQuery((PetscObject)pc->pmat, lscname, (PetscObject *)&LSC_L));
1017:     if (LSC_L) PetscCall(PetscObjectCompose((PetscObject)jac->schur, "LSC_L", (PetscObject)LSC_L));
1018:     PetscCall(PetscSNPrintf(lscname, sizeof(lscname), "%s_LSC_Lp", ilink->splitname));
1019:     PetscCall(PetscObjectQuery((PetscObject)pc->pmat, lscname, (PetscObject *)&LSC_L));
1020:     if (!LSC_L) PetscCall(PetscObjectQuery((PetscObject)pc->mat, lscname, (PetscObject *)&LSC_L));
1021:     if (LSC_L) PetscCall(PetscObjectCompose((PetscObject)jac->schur, "LSC_Lp", (PetscObject)LSC_L));
1022:   } else if (jac->type == PC_COMPOSITE_GKB) {
1023:     IS       ccis;
1024:     PetscInt rstart, rend;

1026:     PetscCheck(nsplit == 2, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_INCOMP, "To use GKB preconditioner you must have exactly 2 fields");

1028:     ilink = jac->head;

1030:     /* When extracting off-diagonal submatrices, we take complements from this range */
1031:     PetscCall(MatGetOwnershipRangeColumn(pc->mat, &rstart, &rend));

1033:     PetscCall(ISComplement(ilink->is_col, rstart, rend, &ccis));
1034:     if (jac->offdiag_use_amat) {
1035:       PetscCall(MatCreateSubMatrix(pc->mat, ilink->is, ccis, MAT_INITIAL_MATRIX, &jac->B));
1036:     } else {
1037:       PetscCall(MatCreateSubMatrix(pc->pmat, ilink->is, ccis, MAT_INITIAL_MATRIX, &jac->B));
1038:     }
1039:     PetscCall(ISDestroy(&ccis));
1040:     /* Create work vectors for GKB algorithm */
1041:     PetscCall(VecDuplicate(ilink->x, &jac->u));
1042:     PetscCall(VecDuplicate(ilink->x, &jac->Hu));
1043:     PetscCall(VecDuplicate(ilink->x, &jac->w2));
1044:     ilink = ilink->next;
1045:     PetscCall(ISComplement(ilink->is_col, rstart, rend, &ccis));
1046:     if (jac->offdiag_use_amat) {
1047:       PetscCall(MatCreateSubMatrix(pc->mat, ilink->is, ccis, MAT_INITIAL_MATRIX, &jac->C));
1048:     } else {
1049:       PetscCall(MatCreateSubMatrix(pc->pmat, ilink->is, ccis, MAT_INITIAL_MATRIX, &jac->C));
1050:     }
1051:     PetscCall(ISDestroy(&ccis));
1052:     /* Create work vectors for GKB algorithm */
1053:     PetscCall(VecDuplicate(ilink->x, &jac->v));
1054:     PetscCall(VecDuplicate(ilink->x, &jac->d));
1055:     PetscCall(VecDuplicate(ilink->x, &jac->w1));
1056:     PetscCall(MatGolubKahanComputeExplicitOperator(jac->mat[0], jac->B, jac->C, &jac->H, jac->gkbnu));
1057:     PetscCall(PetscCalloc1(jac->gkbdelay, &jac->vecz));

1059:     ilink = jac->head;
1060:     PetscCall(KSPSetOperators(ilink->ksp, jac->H, jac->H));
1061:     if (!jac->suboptionsset) PetscCall(KSPSetFromOptions(ilink->ksp));
1062:     /* Create gkb_monitor context */
1063:     if (jac->gkbmonitor) {
1064:       PetscInt tablevel;
1065:       PetscCall(PetscViewerCreate(PETSC_COMM_WORLD, &jac->gkbviewer));
1066:       PetscCall(PetscViewerSetType(jac->gkbviewer, PETSCVIEWERASCII));
1067:       PetscCall(PetscObjectGetTabLevel((PetscObject)ilink->ksp, &tablevel));
1068:       PetscCall(PetscViewerASCIISetTab(jac->gkbviewer, tablevel));
1069:       PetscCall(PetscObjectIncrementTabLevel((PetscObject)ilink->ksp, (PetscObject)ilink->ksp, 1));
1070:     }
1071:   } else {
1072:     /* set up the individual splits' PCs */
1073:     i     = 0;
1074:     ilink = jac->head;
1075:     while (ilink) {
1076:       PetscCall(KSPSetOperators(ilink->ksp, jac->mat[i], jac->pmat[i]));
1077:       /* really want setfromoptions called in PCSetFromOptions_FieldSplit(), but it is not ready yet */
1078:       if (!jac->suboptionsset) PetscCall(KSPSetFromOptions(ilink->ksp));
1079:       i++;
1080:       ilink = ilink->next;
1081:     }
1082:   }

1084:   /* Set coordinates to the sub PC objects whenever these are set */
1085:   if (jac->coordinates_set) {
1086:     PC pc_coords;
1087:     if (jac->type == PC_COMPOSITE_SCHUR) {
1088:       // Head is first block.
1089:       PetscCall(KSPGetPC(jac->head->ksp, &pc_coords));
1090:       PetscCall(PCSetCoordinates(pc_coords, jac->head->dim, jac->head->ndofs, jac->head->coords));
1091:       // Second one is Schur block, but its KSP object is in kspschur.
1092:       PetscCall(KSPGetPC(jac->kspschur, &pc_coords));
1093:       PetscCall(PCSetCoordinates(pc_coords, jac->head->next->dim, jac->head->next->ndofs, jac->head->next->coords));
1094:     } else if (jac->type == PC_COMPOSITE_GKB) {
1095:       PetscCall(PetscInfo(pc, "Warning: Setting coordinates does nothing for the GKB Fieldpslit preconditioner\n"));
1096:     } else {
1097:       ilink = jac->head;
1098:       while (ilink) {
1099:         PetscCall(KSPGetPC(ilink->ksp, &pc_coords));
1100:         PetscCall(PCSetCoordinates(pc_coords, ilink->dim, ilink->ndofs, ilink->coords));
1101:         ilink = ilink->next;
1102:       }
1103:     }
1104:   }

1106:   jac->suboptionsset = PETSC_TRUE;
1107:   PetscFunctionReturn(PETSC_SUCCESS);
1108: }

1110: #define FieldSplitSplitSolveAdd(ilink, xx, yy) \
1111:   ((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) || \
1112:                     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) || \
1113:                     VecScatterEnd(ilink->sctx, ilink->y, yy, ADD_VALUES, SCATTER_REVERSE)))

1115: static PetscErrorCode PCApply_FieldSplit_Schur(PC pc, Vec x, Vec y)
1116: {
1117:   PC_FieldSplit    *jac    = (PC_FieldSplit *)pc->data;
1118:   PC_FieldSplitLink ilinkA = jac->head, ilinkD = ilinkA->next;
1119:   KSP               kspA = ilinkA->ksp, kspLower = kspA, kspUpper = jac->kspupper;

1121:   PetscFunctionBegin;
1122:   switch (jac->schurfactorization) {
1123:   case PC_FIELDSPLIT_SCHUR_FACT_DIAG:
1124:     /* [A00 0; 0 -S], positive definite, suitable for MINRES */
1125:     PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1126:     PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1127:     PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1128:     PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1129:     PetscCall(KSPSolve(kspA, ilinkA->x, ilinkA->y));
1130:     PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1131:     PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1132:     PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1133:     PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1134:     PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1135:     PetscCall(KSPSolve(jac->kspschur, ilinkD->x, ilinkD->y));
1136:     PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y));
1137:     PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1138:     PetscCall(VecScale(ilinkD->y, jac->schurscale));
1139:     PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1140:     PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1141:     PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1142:     break;
1143:   case PC_FIELDSPLIT_SCHUR_FACT_LOWER:
1144:     /* [A00 0; A10 S], suitable for left preconditioning */
1145:     PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1146:     PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1147:     PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1148:     PetscCall(KSPSolve(kspA, ilinkA->x, ilinkA->y));
1149:     PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1150:     PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1151:     PetscCall(MatMult(jac->C, ilinkA->y, ilinkD->x));
1152:     PetscCall(VecScale(ilinkD->x, -1.));
1153:     PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD));
1154:     PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1155:     PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD));
1156:     PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1157:     PetscCall(KSPSolve(jac->kspschur, ilinkD->x, ilinkD->y));
1158:     PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y));
1159:     PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1160:     PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1161:     PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1162:     PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1163:     break;
1164:   case PC_FIELDSPLIT_SCHUR_FACT_UPPER:
1165:     /* [A00 A01; 0 S], suitable for right preconditioning */
1166:     PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1167:     PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1168:     PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1169:     PetscCall(KSPSolve(jac->kspschur, ilinkD->x, ilinkD->y));
1170:     PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y));
1171:     PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1172:     PetscCall(MatMult(jac->B, ilinkD->y, ilinkA->x));
1173:     PetscCall(VecScale(ilinkA->x, -1.));
1174:     PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, ADD_VALUES, SCATTER_FORWARD));
1175:     PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1176:     PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, ADD_VALUES, SCATTER_FORWARD));
1177:     PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1178:     PetscCall(KSPSolve(kspA, ilinkA->x, ilinkA->y));
1179:     PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1180:     PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1181:     PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1182:     PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1183:     PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1184:     break;
1185:   case PC_FIELDSPLIT_SCHUR_FACT_FULL:
1186:     /* [1 0; A10 A00^{-1} 1] [A00 0; 0 S] [1 A00^{-1}A01; 0 1] */
1187:     PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1188:     PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1189:     PetscCall(PetscLogEventBegin(KSP_Solve_FS_L, kspLower, ilinkA->x, ilinkA->y, NULL));
1190:     PetscCall(KSPSolve(kspLower, ilinkA->x, ilinkA->y));
1191:     PetscCall(KSPCheckSolve(kspLower, pc, ilinkA->y));
1192:     PetscCall(PetscLogEventEnd(KSP_Solve_FS_L, kspLower, ilinkA->x, ilinkA->y, NULL));
1193:     PetscCall(MatMult(jac->C, ilinkA->y, ilinkD->x));
1194:     PetscCall(VecScale(ilinkD->x, -1.0));
1195:     PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD));
1196:     PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD));

1198:     PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1199:     PetscCall(KSPSolve(jac->kspschur, ilinkD->x, ilinkD->y));
1200:     PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y));
1201:     PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1202:     PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));

1204:     if (kspUpper == kspA) {
1205:       PetscCall(MatMult(jac->B, ilinkD->y, ilinkA->y));
1206:       PetscCall(VecAXPY(ilinkA->x, -1.0, ilinkA->y));
1207:       PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1208:       PetscCall(KSPSolve(kspA, ilinkA->x, ilinkA->y));
1209:       PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1210:       PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1211:     } else {
1212:       PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1213:       PetscCall(KSPSolve(kspA, ilinkA->x, ilinkA->y));
1214:       PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1215:       PetscCall(MatMult(jac->B, ilinkD->y, ilinkA->x));
1216:       PetscCall(PetscLogEventBegin(KSP_Solve_FS_U, kspUpper, ilinkA->x, ilinkA->z, NULL));
1217:       PetscCall(KSPSolve(kspUpper, ilinkA->x, ilinkA->z));
1218:       PetscCall(KSPCheckSolve(kspUpper, pc, ilinkA->z));
1219:       PetscCall(PetscLogEventEnd(KSP_Solve_FS_U, kspUpper, ilinkA->x, ilinkA->z, NULL));
1220:       PetscCall(VecAXPY(ilinkA->y, -1.0, ilinkA->z));
1221:     }
1222:     PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1223:     PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1224:     PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1225:   }
1226:   PetscFunctionReturn(PETSC_SUCCESS);
1227: }

1229: static PetscErrorCode PCApplyTranspose_FieldSplit_Schur(PC pc, Vec x, Vec y)
1230: {
1231:   PC_FieldSplit    *jac    = (PC_FieldSplit *)pc->data;
1232:   PC_FieldSplitLink ilinkA = jac->head, ilinkD = ilinkA->next;
1233:   KSP               kspA = ilinkA->ksp, kspLower = kspA, kspUpper = jac->kspupper;

1235:   PetscFunctionBegin;
1236:   switch (jac->schurfactorization) {
1237:   case PC_FIELDSPLIT_SCHUR_FACT_DIAG:
1238:     /* [A00 0; 0 -S], positive definite, suitable for MINRES */
1239:     PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1240:     PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1241:     PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1242:     PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1243:     PetscCall(KSPSolveTranspose(kspA, ilinkA->x, ilinkA->y));
1244:     PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1245:     PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1246:     PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1247:     PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1248:     PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1249:     PetscCall(KSPSolveTranspose(jac->kspschur, ilinkD->x, ilinkD->y));
1250:     PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y));
1251:     PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1252:     PetscCall(VecScale(ilinkD->y, jac->schurscale));
1253:     PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1254:     PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1255:     PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1256:     break;
1257:   case PC_FIELDSPLIT_SCHUR_FACT_UPPER:
1258:     PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1259:     PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1260:     PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1261:     PetscCall(KSPSolveTranspose(kspA, ilinkA->x, ilinkA->y));
1262:     PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1263:     PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1264:     PetscCall(MatMultTranspose(jac->B, ilinkA->y, ilinkD->x));
1265:     PetscCall(VecScale(ilinkD->x, -1.));
1266:     PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD));
1267:     PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1268:     PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD));
1269:     PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1270:     PetscCall(KSPSolveTranspose(jac->kspschur, ilinkD->x, ilinkD->y));
1271:     PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y));
1272:     PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1273:     PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1274:     PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1275:     PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1276:     break;
1277:   case PC_FIELDSPLIT_SCHUR_FACT_LOWER:
1278:     PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1279:     PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1280:     PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1281:     PetscCall(KSPSolveTranspose(jac->kspschur, ilinkD->x, ilinkD->y));
1282:     PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y));
1283:     PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1284:     PetscCall(MatMultTranspose(jac->C, ilinkD->y, ilinkA->x));
1285:     PetscCall(VecScale(ilinkA->x, -1.));
1286:     PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, ADD_VALUES, SCATTER_FORWARD));
1287:     PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1288:     PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, ADD_VALUES, SCATTER_FORWARD));
1289:     PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1290:     PetscCall(KSPSolveTranspose(kspA, ilinkA->x, ilinkA->y));
1291:     PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1292:     PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1293:     PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1294:     PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1295:     PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1296:     break;
1297:   case PC_FIELDSPLIT_SCHUR_FACT_FULL:
1298:     PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1299:     PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1300:     PetscCall(PetscLogEventBegin(KSP_Solve_FS_U, kspUpper, ilinkA->x, ilinkA->y, NULL));
1301:     PetscCall(KSPSolveTranspose(kspUpper, ilinkA->x, ilinkA->y));
1302:     PetscCall(KSPCheckSolve(kspUpper, pc, ilinkA->y));
1303:     PetscCall(PetscLogEventEnd(KSP_Solve_FS_U, kspUpper, ilinkA->x, ilinkA->y, NULL));
1304:     PetscCall(MatMultTranspose(jac->B, ilinkA->y, ilinkD->x));
1305:     PetscCall(VecScale(ilinkD->x, -1.0));
1306:     PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD));
1307:     PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD));

1309:     PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1310:     PetscCall(KSPSolveTranspose(jac->kspschur, ilinkD->x, ilinkD->y));
1311:     PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y));
1312:     PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1313:     PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));

1315:     if (kspLower == kspA) {
1316:       PetscCall(MatMultTranspose(jac->C, ilinkD->y, ilinkA->y));
1317:       PetscCall(VecAXPY(ilinkA->x, -1.0, ilinkA->y));
1318:       PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1319:       PetscCall(KSPSolveTranspose(kspA, ilinkA->x, ilinkA->y));
1320:       PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1321:       PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1322:     } else {
1323:       PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1324:       PetscCall(KSPSolveTranspose(kspA, ilinkA->x, ilinkA->y));
1325:       PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1326:       PetscCall(MatMultTranspose(jac->C, ilinkD->y, ilinkA->x));
1327:       PetscCall(PetscLogEventBegin(KSP_Solve_FS_L, kspLower, ilinkA->x, ilinkA->z, NULL));
1328:       PetscCall(KSPSolveTranspose(kspLower, ilinkA->x, ilinkA->z));
1329:       PetscCall(KSPCheckSolve(kspLower, pc, ilinkA->z));
1330:       PetscCall(PetscLogEventEnd(KSP_Solve_FS_L, kspLower, ilinkA->x, ilinkA->z, NULL));
1331:       PetscCall(VecAXPY(ilinkA->y, -1.0, ilinkA->z));
1332:     }
1333:     PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1334:     PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1335:     PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1336:   }
1337:   PetscFunctionReturn(PETSC_SUCCESS);
1338: }

1340: static PetscErrorCode PCApply_FieldSplit(PC pc, Vec x, Vec y)
1341: {
1342:   PC_FieldSplit    *jac   = (PC_FieldSplit *)pc->data;
1343:   PC_FieldSplitLink ilink = jac->head;
1344:   PetscInt          cnt, bs;

1346:   PetscFunctionBegin;
1347:   if (jac->type == PC_COMPOSITE_ADDITIVE) {
1348:     if (jac->defaultsplit) {
1349:       PetscCall(VecGetBlockSize(x, &bs));
1350:       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);
1351:       PetscCall(VecGetBlockSize(y, &bs));
1352:       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);
1353:       PetscCall(VecStrideGatherAll(x, jac->x, INSERT_VALUES));
1354:       while (ilink) {
1355:         PetscCall(PetscLogEventBegin(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1356:         PetscCall(KSPSolve(ilink->ksp, ilink->x, ilink->y));
1357:         PetscCall(KSPCheckSolve(ilink->ksp, pc, ilink->y));
1358:         PetscCall(PetscLogEventEnd(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1359:         ilink = ilink->next;
1360:       }
1361:       PetscCall(VecStrideScatterAll(jac->y, y, INSERT_VALUES));
1362:     } else {
1363:       PetscCall(VecSet(y, 0.0));
1364:       while (ilink) {
1365:         PetscCall(FieldSplitSplitSolveAdd(ilink, x, y));
1366:         ilink = ilink->next;
1367:       }
1368:     }
1369:   } else if (jac->type == PC_COMPOSITE_MULTIPLICATIVE && jac->nsplits == 2) {
1370:     PetscCall(VecSet(y, 0.0));
1371:     /* solve on first block for first block variables */
1372:     PetscCall(VecScatterBegin(ilink->sctx, x, ilink->x, INSERT_VALUES, SCATTER_FORWARD));
1373:     PetscCall(VecScatterEnd(ilink->sctx, x, ilink->x, INSERT_VALUES, SCATTER_FORWARD));
1374:     PetscCall(PetscLogEventBegin(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1375:     PetscCall(KSPSolve(ilink->ksp, ilink->x, ilink->y));
1376:     PetscCall(KSPCheckSolve(ilink->ksp, pc, ilink->y));
1377:     PetscCall(PetscLogEventEnd(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1378:     PetscCall(VecScatterBegin(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE));
1379:     PetscCall(VecScatterEnd(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE));

1381:     /* compute the residual only onto second block variables using first block variables */
1382:     PetscCall(MatMult(jac->Afield[1], ilink->y, ilink->next->x));
1383:     ilink = ilink->next;
1384:     PetscCall(VecScale(ilink->x, -1.0));
1385:     PetscCall(VecScatterBegin(ilink->sctx, x, ilink->x, ADD_VALUES, SCATTER_FORWARD));
1386:     PetscCall(VecScatterEnd(ilink->sctx, x, ilink->x, ADD_VALUES, SCATTER_FORWARD));

1388:     /* solve on second block variables */
1389:     PetscCall(PetscLogEventBegin(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1390:     PetscCall(KSPSolve(ilink->ksp, ilink->x, ilink->y));
1391:     PetscCall(KSPCheckSolve(ilink->ksp, pc, ilink->y));
1392:     PetscCall(PetscLogEventEnd(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1393:     PetscCall(VecScatterBegin(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE));
1394:     PetscCall(VecScatterEnd(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE));
1395:   } else if (jac->type == PC_COMPOSITE_MULTIPLICATIVE || jac->type == PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE) {
1396:     if (!jac->w1) {
1397:       PetscCall(VecDuplicate(x, &jac->w1));
1398:       PetscCall(VecDuplicate(x, &jac->w2));
1399:     }
1400:     PetscCall(VecSet(y, 0.0));
1401:     PetscCall(FieldSplitSplitSolveAdd(ilink, x, y));
1402:     cnt = 1;
1403:     while (ilink->next) {
1404:       ilink = ilink->next;
1405:       /* compute the residual only over the part of the vector needed */
1406:       PetscCall(MatMult(jac->Afield[cnt++], y, ilink->x));
1407:       PetscCall(VecScale(ilink->x, -1.0));
1408:       PetscCall(VecScatterBegin(ilink->sctx, x, ilink->x, ADD_VALUES, SCATTER_FORWARD));
1409:       PetscCall(VecScatterEnd(ilink->sctx, x, ilink->x, ADD_VALUES, SCATTER_FORWARD));
1410:       PetscCall(PetscLogEventBegin(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1411:       PetscCall(KSPSolve(ilink->ksp, ilink->x, ilink->y));
1412:       PetscCall(KSPCheckSolve(ilink->ksp, pc, ilink->y));
1413:       PetscCall(PetscLogEventEnd(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1414:       PetscCall(VecScatterBegin(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE));
1415:       PetscCall(VecScatterEnd(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE));
1416:     }
1417:     if (jac->type == PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE) {
1418:       cnt -= 2;
1419:       while (ilink->previous) {
1420:         ilink = ilink->previous;
1421:         /* compute the residual only over the part of the vector needed */
1422:         PetscCall(MatMult(jac->Afield[cnt--], y, ilink->x));
1423:         PetscCall(VecScale(ilink->x, -1.0));
1424:         PetscCall(VecScatterBegin(ilink->sctx, x, ilink->x, ADD_VALUES, SCATTER_FORWARD));
1425:         PetscCall(VecScatterEnd(ilink->sctx, x, ilink->x, ADD_VALUES, SCATTER_FORWARD));
1426:         PetscCall(PetscLogEventBegin(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1427:         PetscCall(KSPSolve(ilink->ksp, ilink->x, ilink->y));
1428:         PetscCall(KSPCheckSolve(ilink->ksp, pc, ilink->y));
1429:         PetscCall(PetscLogEventEnd(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1430:         PetscCall(VecScatterBegin(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE));
1431:         PetscCall(VecScatterEnd(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE));
1432:       }
1433:     }
1434:   } else SETERRQ(PetscObjectComm((PetscObject)pc), PETSC_ERR_SUP, "Unsupported or unknown composition %d", (int)jac->type);
1435:   PetscFunctionReturn(PETSC_SUCCESS);
1436: }

1438: static PetscErrorCode PCApply_FieldSplit_GKB(PC pc, Vec x, Vec y)
1439: {
1440:   PC_FieldSplit    *jac    = (PC_FieldSplit *)pc->data;
1441:   PC_FieldSplitLink ilinkA = jac->head, ilinkD = ilinkA->next;
1442:   KSP               ksp = ilinkA->ksp;
1443:   Vec               u, v, Hu, d, work1, work2;
1444:   PetscScalar       alpha, z, nrmz2, *vecz;
1445:   PetscReal         lowbnd, nu, beta;
1446:   PetscInt          j, iterGKB;

1448:   PetscFunctionBegin;
1449:   PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1450:   PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1451:   PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1452:   PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));

1454:   u     = jac->u;
1455:   v     = jac->v;
1456:   Hu    = jac->Hu;
1457:   d     = jac->d;
1458:   work1 = jac->w1;
1459:   work2 = jac->w2;
1460:   vecz  = jac->vecz;

1462:   /* Change RHS to comply with matrix regularization H = A + nu*B*B' */
1463:   /* Add q = q + nu*B*b */
1464:   if (jac->gkbnu) {
1465:     nu = jac->gkbnu;
1466:     PetscCall(VecScale(ilinkD->x, jac->gkbnu));
1467:     PetscCall(MatMultAdd(jac->B, ilinkD->x, ilinkA->x, ilinkA->x)); /* q = q + nu*B*b */
1468:   } else {
1469:     /* Situation when no augmented Lagrangian is used. Then we set inner  */
1470:     /* matrix N = I in [Ar13], and thus nu = 1.                           */
1471:     nu = 1;
1472:   }

1474:   /* Transform rhs from [q,tilde{b}] to [0,b] */
1475:   PetscCall(PetscLogEventBegin(ilinkA->event, ksp, ilinkA->x, ilinkA->y, NULL));
1476:   PetscCall(KSPSolve(ksp, ilinkA->x, ilinkA->y));
1477:   PetscCall(KSPCheckSolve(ksp, pc, ilinkA->y));
1478:   PetscCall(PetscLogEventEnd(ilinkA->event, ksp, ilinkA->x, ilinkA->y, NULL));
1479:   PetscCall(MatMultHermitianTranspose(jac->B, ilinkA->y, work1));
1480:   PetscCall(VecAXPBY(work1, 1.0 / nu, -1.0, ilinkD->x)); /* c = b - B'*x        */

1482:   /* First step of algorithm */
1483:   PetscCall(VecNorm(work1, NORM_2, &beta)); /* beta = sqrt(nu*c'*c)*/
1484:   KSPCheckDot(ksp, beta);
1485:   beta = PetscSqrtReal(nu) * beta;
1486:   PetscCall(VecAXPBY(v, nu / beta, 0.0, work1)); /* v = nu/beta *c      */
1487:   PetscCall(MatMult(jac->B, v, work2));          /* u = H^{-1}*B*v      */
1488:   PetscCall(PetscLogEventBegin(ilinkA->event, ksp, work2, u, NULL));
1489:   PetscCall(KSPSolve(ksp, work2, u));
1490:   PetscCall(KSPCheckSolve(ksp, pc, u));
1491:   PetscCall(PetscLogEventEnd(ilinkA->event, ksp, work2, u, NULL));
1492:   PetscCall(MatMult(jac->H, u, Hu)); /* alpha = u'*H*u      */
1493:   PetscCall(VecDot(Hu, u, &alpha));
1494:   KSPCheckDot(ksp, alpha);
1495:   PetscCheck(PetscRealPart(alpha) > 0.0, PETSC_COMM_SELF, PETSC_ERR_NOT_CONVERGED, "GKB preconditioner diverged, H is not positive definite");
1496:   alpha = PetscSqrtReal(PetscAbsScalar(alpha));
1497:   PetscCall(VecScale(u, 1.0 / alpha));
1498:   PetscCall(VecAXPBY(d, 1.0 / alpha, 0.0, v)); /* v = nu/beta *c      */

1500:   z       = beta / alpha;
1501:   vecz[1] = z;

1503:   /* Computation of first iterate x(1) and p(1) */
1504:   PetscCall(VecAXPY(ilinkA->y, z, u));
1505:   PetscCall(VecCopy(d, ilinkD->y));
1506:   PetscCall(VecScale(ilinkD->y, -z));

1508:   iterGKB = 1;
1509:   lowbnd  = 2 * jac->gkbtol;
1510:   if (jac->gkbmonitor) PetscCall(PetscViewerASCIIPrintf(jac->gkbviewer, "%3" PetscInt_FMT " GKB Lower bound estimate %14.12e\n", iterGKB, (double)lowbnd));

1512:   while (iterGKB < jac->gkbmaxit && lowbnd > jac->gkbtol) {
1513:     iterGKB += 1;
1514:     PetscCall(MatMultHermitianTranspose(jac->B, u, work1)); /* v <- nu*(B'*u-alpha/nu*v) */
1515:     PetscCall(VecAXPBY(v, nu, -alpha, work1));
1516:     PetscCall(VecNorm(v, NORM_2, &beta)); /* beta = sqrt(nu)*v'*v      */
1517:     beta = beta / PetscSqrtReal(nu);
1518:     PetscCall(VecScale(v, 1.0 / beta));
1519:     PetscCall(MatMult(jac->B, v, work2)); /* u <- H^{-1}*(B*v-beta*H*u) */
1520:     PetscCall(MatMult(jac->H, u, Hu));
1521:     PetscCall(VecAXPY(work2, -beta, Hu));
1522:     PetscCall(PetscLogEventBegin(ilinkA->event, ksp, work2, u, NULL));
1523:     PetscCall(KSPSolve(ksp, work2, u));
1524:     PetscCall(KSPCheckSolve(ksp, pc, u));
1525:     PetscCall(PetscLogEventEnd(ilinkA->event, ksp, work2, u, NULL));
1526:     PetscCall(MatMult(jac->H, u, Hu)); /* alpha = u'*H*u            */
1527:     PetscCall(VecDot(Hu, u, &alpha));
1528:     KSPCheckDot(ksp, alpha);
1529:     PetscCheck(PetscRealPart(alpha) > 0.0, PETSC_COMM_SELF, PETSC_ERR_NOT_CONVERGED, "GKB preconditioner diverged, H is not positive definite");
1530:     alpha = PetscSqrtReal(PetscAbsScalar(alpha));
1531:     PetscCall(VecScale(u, 1.0 / alpha));

1533:     z       = -beta / alpha * z; /* z <- beta/alpha*z     */
1534:     vecz[0] = z;

1536:     /* Computation of new iterate x(i+1) and p(i+1) */
1537:     PetscCall(VecAXPBY(d, 1.0 / alpha, -beta / alpha, v)); /* d = (v-beta*d)/alpha */
1538:     PetscCall(VecAXPY(ilinkA->y, z, u));                   /* r = r + z*u          */
1539:     PetscCall(VecAXPY(ilinkD->y, -z, d));                  /* p = p - z*d          */
1540:     PetscCall(MatMult(jac->H, ilinkA->y, Hu));             /* ||u||_H = u'*H*u     */
1541:     PetscCall(VecDot(Hu, ilinkA->y, &nrmz2));

1543:     /* Compute Lower Bound estimate */
1544:     if (iterGKB > jac->gkbdelay) {
1545:       lowbnd = 0.0;
1546:       for (j = 0; j < jac->gkbdelay; j++) lowbnd += PetscAbsScalar(vecz[j] * vecz[j]);
1547:       lowbnd = PetscSqrtReal(lowbnd / PetscAbsScalar(nrmz2));
1548:     }

1550:     for (j = 0; j < jac->gkbdelay - 1; j++) vecz[jac->gkbdelay - j - 1] = vecz[jac->gkbdelay - j - 2];
1551:     if (jac->gkbmonitor) PetscCall(PetscViewerASCIIPrintf(jac->gkbviewer, "%3" PetscInt_FMT " GKB Lower bound estimate %14.12e\n", iterGKB, (double)lowbnd));
1552:   }

1554:   PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1555:   PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1556:   PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1557:   PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1558:   PetscFunctionReturn(PETSC_SUCCESS);
1559: }

1561: #define FieldSplitSplitSolveAddTranspose(ilink, xx, yy) \
1562:   ((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) || \
1563:                     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) || \
1564:                     VecScatterEnd(ilink->sctx, ilink->x, yy, ADD_VALUES, SCATTER_REVERSE)))

1566: static PetscErrorCode PCApplyTranspose_FieldSplit(PC pc, Vec x, Vec y)
1567: {
1568:   PC_FieldSplit    *jac   = (PC_FieldSplit *)pc->data;
1569:   PC_FieldSplitLink ilink = jac->head;
1570:   PetscInt          bs;

1572:   PetscFunctionBegin;
1573:   if (jac->type == PC_COMPOSITE_ADDITIVE) {
1574:     if (jac->defaultsplit) {
1575:       PetscCall(VecGetBlockSize(x, &bs));
1576:       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);
1577:       PetscCall(VecGetBlockSize(y, &bs));
1578:       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);
1579:       PetscCall(VecStrideGatherAll(x, jac->x, INSERT_VALUES));
1580:       while (ilink) {
1581:         PetscCall(PetscLogEventBegin(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1582:         PetscCall(KSPSolveTranspose(ilink->ksp, ilink->x, ilink->y));
1583:         PetscCall(KSPCheckSolve(ilink->ksp, pc, ilink->y));
1584:         PetscCall(PetscLogEventEnd(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1585:         ilink = ilink->next;
1586:       }
1587:       PetscCall(VecStrideScatterAll(jac->y, y, INSERT_VALUES));
1588:     } else {
1589:       PetscCall(VecSet(y, 0.0));
1590:       while (ilink) {
1591:         PetscCall(FieldSplitSplitSolveAddTranspose(ilink, x, y));
1592:         ilink = ilink->next;
1593:       }
1594:     }
1595:   } else {
1596:     if (!jac->w1) {
1597:       PetscCall(VecDuplicate(x, &jac->w1));
1598:       PetscCall(VecDuplicate(x, &jac->w2));
1599:     }
1600:     PetscCall(VecSet(y, 0.0));
1601:     if (jac->type == PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE) {
1602:       PetscCall(FieldSplitSplitSolveAddTranspose(ilink, x, y));
1603:       while (ilink->next) {
1604:         ilink = ilink->next;
1605:         PetscCall(MatMultTranspose(pc->mat, y, jac->w1));
1606:         PetscCall(VecWAXPY(jac->w2, -1.0, jac->w1, x));
1607:         PetscCall(FieldSplitSplitSolveAddTranspose(ilink, jac->w2, y));
1608:       }
1609:       while (ilink->previous) {
1610:         ilink = ilink->previous;
1611:         PetscCall(MatMultTranspose(pc->mat, y, jac->w1));
1612:         PetscCall(VecWAXPY(jac->w2, -1.0, jac->w1, x));
1613:         PetscCall(FieldSplitSplitSolveAddTranspose(ilink, jac->w2, y));
1614:       }
1615:     } else {
1616:       while (ilink->next) { /* get to last entry in linked list */
1617:         ilink = ilink->next;
1618:       }
1619:       PetscCall(FieldSplitSplitSolveAddTranspose(ilink, x, y));
1620:       while (ilink->previous) {
1621:         ilink = ilink->previous;
1622:         PetscCall(MatMultTranspose(pc->mat, y, jac->w1));
1623:         PetscCall(VecWAXPY(jac->w2, -1.0, jac->w1, x));
1624:         PetscCall(FieldSplitSplitSolveAddTranspose(ilink, jac->w2, y));
1625:       }
1626:     }
1627:   }
1628:   PetscFunctionReturn(PETSC_SUCCESS);
1629: }

1631: static PetscErrorCode PCReset_FieldSplit(PC pc)
1632: {
1633:   PC_FieldSplit    *jac   = (PC_FieldSplit *)pc->data;
1634:   PC_FieldSplitLink ilink = jac->head, next;

1636:   PetscFunctionBegin;
1637:   while (ilink) {
1638:     PetscCall(KSPDestroy(&ilink->ksp));
1639:     PetscCall(VecDestroy(&ilink->x));
1640:     PetscCall(VecDestroy(&ilink->y));
1641:     PetscCall(VecDestroy(&ilink->z));
1642:     PetscCall(VecScatterDestroy(&ilink->sctx));
1643:     PetscCall(ISDestroy(&ilink->is));
1644:     PetscCall(ISDestroy(&ilink->is_col));
1645:     PetscCall(PetscFree(ilink->splitname));
1646:     PetscCall(PetscFree(ilink->fields));
1647:     PetscCall(PetscFree(ilink->fields_col));
1648:     next = ilink->next;
1649:     PetscCall(PetscFree(ilink));
1650:     ilink = next;
1651:   }
1652:   jac->head = NULL;
1653:   PetscCall(PetscFree2(jac->x, jac->y));
1654:   if (jac->mat && jac->mat != jac->pmat) {
1655:     PetscCall(MatDestroyMatrices(jac->nsplits, &jac->mat));
1656:   } else if (jac->mat) {
1657:     jac->mat = NULL;
1658:   }
1659:   if (jac->pmat) PetscCall(MatDestroyMatrices(jac->nsplits, &jac->pmat));
1660:   if (jac->Afield) PetscCall(MatDestroyMatrices(jac->nsplits, &jac->Afield));
1661:   jac->nsplits = 0;
1662:   PetscCall(VecDestroy(&jac->w1));
1663:   PetscCall(VecDestroy(&jac->w2));
1664:   PetscCall(MatDestroy(&jac->schur));
1665:   PetscCall(MatDestroy(&jac->schurp));
1666:   PetscCall(MatDestroy(&jac->schur_user));
1667:   PetscCall(KSPDestroy(&jac->kspschur));
1668:   PetscCall(KSPDestroy(&jac->kspupper));
1669:   PetscCall(MatDestroy(&jac->B));
1670:   PetscCall(MatDestroy(&jac->C));
1671:   PetscCall(MatDestroy(&jac->H));
1672:   PetscCall(VecDestroy(&jac->u));
1673:   PetscCall(VecDestroy(&jac->v));
1674:   PetscCall(VecDestroy(&jac->Hu));
1675:   PetscCall(VecDestroy(&jac->d));
1676:   PetscCall(PetscFree(jac->vecz));
1677:   PetscCall(PetscViewerDestroy(&jac->gkbviewer));
1678:   jac->isrestrict = PETSC_FALSE;
1679:   PetscFunctionReturn(PETSC_SUCCESS);
1680: }

1682: static PetscErrorCode PCDestroy_FieldSplit(PC pc)
1683: {
1684:   PetscFunctionBegin;
1685:   PetscCall(PCReset_FieldSplit(pc));
1686:   PetscCall(PetscFree(pc->data));
1687:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCSetCoordinates_C", NULL));
1688:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetFields_C", NULL));
1689:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetIS_C", NULL));
1690:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetType_C", NULL));
1691:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetBlockSize_C", NULL));
1692:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitRestrictIS_C", NULL));
1693:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSchurGetSubKSP_C", NULL));
1694:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSubKSP_C", NULL));

1696:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBTol_C", NULL));
1697:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBMaxit_C", NULL));
1698:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBNu_C", NULL));
1699:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBDelay_C", NULL));
1700:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSubKSP_C", NULL));
1701:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurPre_C", NULL));
1702:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSchurPre_C", NULL));
1703:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurFactType_C", NULL));
1704:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurScale_C", NULL));
1705:   PetscFunctionReturn(PETSC_SUCCESS);
1706: }

1708: static PetscErrorCode PCSetFromOptions_FieldSplit(PC pc, PetscOptionItems *PetscOptionsObject)
1709: {
1710:   PetscInt        bs;
1711:   PetscBool       flg;
1712:   PC_FieldSplit  *jac = (PC_FieldSplit *)pc->data;
1713:   PCCompositeType ctype;

1715:   PetscFunctionBegin;
1716:   PetscOptionsHeadBegin(PetscOptionsObject, "FieldSplit options");
1717:   PetscCall(PetscOptionsBool("-pc_fieldsplit_dm_splits", "Whether to use DMCreateFieldDecomposition() for splits", "PCFieldSplitSetDMSplits", jac->dm_splits, &jac->dm_splits, NULL));
1718:   PetscCall(PetscOptionsInt("-pc_fieldsplit_block_size", "Blocksize that defines number of fields", "PCFieldSplitSetBlockSize", jac->bs, &bs, &flg));
1719:   if (flg) PetscCall(PCFieldSplitSetBlockSize(pc, bs));
1720:   jac->diag_use_amat = pc->useAmat;
1721:   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));
1722:   jac->offdiag_use_amat = pc->useAmat;
1723:   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));
1724:   PetscCall(PetscOptionsBool("-pc_fieldsplit_detect_saddle_point", "Form 2-way split by detecting zero diagonal entries", "PCFieldSplitSetDetectSaddlePoint", jac->detect, &jac->detect, NULL));
1725:   PetscCall(PCFieldSplitSetDetectSaddlePoint(pc, jac->detect)); /* Sets split type and Schur PC type */
1726:   PetscCall(PetscOptionsEnum("-pc_fieldsplit_type", "Type of composition", "PCFieldSplitSetType", PCCompositeTypes, (PetscEnum)jac->type, (PetscEnum *)&ctype, &flg));
1727:   if (flg) PetscCall(PCFieldSplitSetType(pc, ctype));
1728:   /* Only setup fields once */
1729:   if ((jac->bs > 0) && (jac->nsplits == 0)) {
1730:     /* only allow user to set fields from command line if bs is already known.
1731:        otherwise user can set them in PCFieldSplitSetDefaults() */
1732:     PetscCall(PCFieldSplitSetRuntimeSplits_Private(pc));
1733:     if (jac->splitdefined) PetscCall(PetscInfo(pc, "Splits defined using the options database\n"));
1734:   }
1735:   if (jac->type == PC_COMPOSITE_SCHUR) {
1736:     PetscCall(PetscOptionsGetEnum(((PetscObject)pc)->options, ((PetscObject)pc)->prefix, "-pc_fieldsplit_schur_factorization_type", PCFieldSplitSchurFactTypes, (PetscEnum *)&jac->schurfactorization, &flg));
1737:     if (flg) PetscCall(PetscInfo(pc, "Deprecated use of -pc_fieldsplit_schur_factorization_type\n"));
1738:     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));
1739:     PetscCall(PetscOptionsEnum("-pc_fieldsplit_schur_precondition", "How to build preconditioner for Schur complement", "PCFieldSplitSetSchurPre", PCFieldSplitSchurPreTypes, (PetscEnum)jac->schurpre, (PetscEnum *)&jac->schurpre, NULL));
1740:     PetscCall(PetscOptionsScalar("-pc_fieldsplit_schur_scale", "Scale Schur complement", "PCFieldSplitSetSchurScale", jac->schurscale, &jac->schurscale, NULL));
1741:   } else if (jac->type == PC_COMPOSITE_GKB) {
1742:     PetscCall(PetscOptionsReal("-pc_fieldsplit_gkb_tol", "The tolerance for the lower bound stopping criterion", "PCFieldSplitSetGKBTol", jac->gkbtol, &jac->gkbtol, NULL));
1743:     PetscCall(PetscOptionsInt("-pc_fieldsplit_gkb_delay", "The delay value for lower bound criterion", "PCFieldSplitSetGKBDelay", jac->gkbdelay, &jac->gkbdelay, NULL));
1744:     PetscCall(PetscOptionsBoundedReal("-pc_fieldsplit_gkb_nu", "Parameter in augmented Lagrangian approach", "PCFieldSplitSetGKBNu", jac->gkbnu, &jac->gkbnu, NULL, 0.0));
1745:     PetscCall(PetscOptionsInt("-pc_fieldsplit_gkb_maxit", "Maximum allowed number of iterations", "PCFieldSplitSetGKBMaxit", jac->gkbmaxit, &jac->gkbmaxit, NULL));
1746:     PetscCall(PetscOptionsBool("-pc_fieldsplit_gkb_monitor", "Prints number of GKB iterations and error", "PCFieldSplitGKB", jac->gkbmonitor, &jac->gkbmonitor, NULL));
1747:   }
1748:   /*
1749:     In the initial call to this routine the sub-solver data structures do not exist so we cannot call KSPSetFromOptions() on them yet.
1750:     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
1751:     is called on the outer solver in case changes were made in the options database

1753:     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()
1754:     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.
1755:     Without this extra check test p2p1fetidp_olof_full and others fail with incorrect matrix types.

1757:     There could be a negative side effect of calling the KSPSetFromOptions() below.

1759:     If one captured the PetscObjectState of the options database one could skip these calls if the database has not changed from the previous call
1760:   */
1761:   if (jac->issetup) {
1762:     PC_FieldSplitLink ilink = jac->head;
1763:     if (jac->type == PC_COMPOSITE_SCHUR) {
1764:       if (jac->kspupper && jac->kspupper->totalits > 0) PetscCall(KSPSetFromOptions(jac->kspupper));
1765:       if (jac->kspschur && jac->kspschur->totalits > 0) PetscCall(KSPSetFromOptions(jac->kspschur));
1766:     }
1767:     while (ilink) {
1768:       if (ilink->ksp->totalits > 0) PetscCall(KSPSetFromOptions(ilink->ksp));
1769:       ilink = ilink->next;
1770:     }
1771:   }
1772:   PetscOptionsHeadEnd();
1773:   PetscFunctionReturn(PETSC_SUCCESS);
1774: }

1776: static PetscErrorCode PCFieldSplitSetFields_FieldSplit(PC pc, const char splitname[], PetscInt n, const PetscInt *fields, const PetscInt *fields_col)
1777: {
1778:   PC_FieldSplit    *jac = (PC_FieldSplit *)pc->data;
1779:   PC_FieldSplitLink ilink, next = jac->head;
1780:   char              prefix[128];
1781:   PetscInt          i;

1783:   PetscFunctionBegin;
1784:   if (jac->splitdefined) {
1785:     PetscCall(PetscInfo(pc, "Ignoring new split \"%s\" because the splits have already been defined\n", splitname));
1786:     PetscFunctionReturn(PETSC_SUCCESS);
1787:   }
1788:   for (i = 0; i < n; i++) {
1789:     PetscCheck(fields[i] < jac->bs, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Field %" PetscInt_FMT " requested but only %" PetscInt_FMT " exist", fields[i], jac->bs);
1790:     PetscCheck(fields[i] >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Negative field %" PetscInt_FMT " requested", fields[i]);
1791:   }
1792:   PetscCall(PetscNew(&ilink));
1793:   if (splitname) {
1794:     PetscCall(PetscStrallocpy(splitname, &ilink->splitname));
1795:   } else {
1796:     PetscCall(PetscMalloc1(3, &ilink->splitname));
1797:     PetscCall(PetscSNPrintf(ilink->splitname, 2, "%" PetscInt_FMT, jac->nsplits));
1798:   }
1799:   ilink->event = jac->nsplits < 5 ? KSP_Solve_FS_0 + jac->nsplits : KSP_Solve_FS_0 + 4; /* Any split great than 4 gets logged in the 4th split */
1800:   PetscCall(PetscMalloc1(n, &ilink->fields));
1801:   PetscCall(PetscArraycpy(ilink->fields, fields, n));
1802:   PetscCall(PetscMalloc1(n, &ilink->fields_col));
1803:   PetscCall(PetscArraycpy(ilink->fields_col, fields_col, n));

1805:   ilink->nfields = n;
1806:   ilink->next    = NULL;
1807:   PetscCall(KSPCreate(PetscObjectComm((PetscObject)pc), &ilink->ksp));
1808:   PetscCall(KSPSetNestLevel(ilink->ksp, pc->kspnestlevel));
1809:   PetscCall(KSPSetErrorIfNotConverged(ilink->ksp, pc->erroriffailure));
1810:   PetscCall(PetscObjectIncrementTabLevel((PetscObject)ilink->ksp, (PetscObject)pc, 1));
1811:   PetscCall(KSPSetType(ilink->ksp, KSPPREONLY));

1813:   PetscCall(PetscSNPrintf(prefix, sizeof(prefix), "%sfieldsplit_%s_", ((PetscObject)pc)->prefix ? ((PetscObject)pc)->prefix : "", ilink->splitname));
1814:   PetscCall(KSPSetOptionsPrefix(ilink->ksp, prefix));

1816:   if (!next) {
1817:     jac->head       = ilink;
1818:     ilink->previous = NULL;
1819:   } else {
1820:     while (next->next) next = next->next;
1821:     next->next      = ilink;
1822:     ilink->previous = next;
1823:   }
1824:   jac->nsplits++;
1825:   PetscFunctionReturn(PETSC_SUCCESS);
1826: }

1828: static PetscErrorCode PCFieldSplitSchurGetSubKSP_FieldSplit(PC pc, PetscInt *n, KSP **subksp)
1829: {
1830:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

1832:   PetscFunctionBegin;
1833:   *subksp = NULL;
1834:   if (n) *n = 0;
1835:   if (jac->type == PC_COMPOSITE_SCHUR) {
1836:     PetscInt nn;

1838:     PetscCheck(jac->schur, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONGSTATE, "Must call KSPSetUp() or PCSetUp() before calling PCFieldSplitSchurGetSubKSP()");
1839:     PetscCheck(jac->nsplits == 2, PetscObjectComm((PetscObject)pc), PETSC_ERR_PLIB, "Unexpected number of splits %" PetscInt_FMT " != 2", jac->nsplits);
1840:     nn = jac->nsplits + (jac->kspupper != jac->head->ksp ? 1 : 0);
1841:     PetscCall(PetscMalloc1(nn, subksp));
1842:     (*subksp)[0] = jac->head->ksp;
1843:     (*subksp)[1] = jac->kspschur;
1844:     if (jac->kspupper != jac->head->ksp) (*subksp)[2] = jac->kspupper;
1845:     if (n) *n = nn;
1846:   }
1847:   PetscFunctionReturn(PETSC_SUCCESS);
1848: }

1850: static PetscErrorCode PCFieldSplitGetSubKSP_FieldSplit_Schur(PC pc, PetscInt *n, KSP **subksp)
1851: {
1852:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

1854:   PetscFunctionBegin;
1855:   PetscCheck(jac->schur, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONGSTATE, "Must call KSPSetUp() or PCSetUp() before calling PCFieldSplitGetSubKSP()");
1856:   PetscCall(PetscMalloc1(jac->nsplits, subksp));
1857:   PetscCall(MatSchurComplementGetKSP(jac->schur, *subksp));

1859:   (*subksp)[1] = jac->kspschur;
1860:   if (n) *n = jac->nsplits;
1861:   PetscFunctionReturn(PETSC_SUCCESS);
1862: }

1864: static PetscErrorCode PCFieldSplitGetSubKSP_FieldSplit(PC pc, PetscInt *n, KSP **subksp)
1865: {
1866:   PC_FieldSplit    *jac   = (PC_FieldSplit *)pc->data;
1867:   PetscInt          cnt   = 0;
1868:   PC_FieldSplitLink ilink = jac->head;

1870:   PetscFunctionBegin;
1871:   PetscCall(PetscMalloc1(jac->nsplits, subksp));
1872:   while (ilink) {
1873:     (*subksp)[cnt++] = ilink->ksp;
1874:     ilink            = ilink->next;
1875:   }
1876:   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);
1877:   if (n) *n = jac->nsplits;
1878:   PetscFunctionReturn(PETSC_SUCCESS);
1879: }

1881: /*@C
1882:   PCFieldSplitRestrictIS - Restricts the fieldsplit `IS`s to be within a given `IS`.

1884:   Input Parameters:
1885: + pc  - the preconditioner context
1886: - isy - the index set that defines the indices to which the fieldsplit is to be restricted

1888:   Level: advanced

1890:   Developer Notes:
1891:   It seems the resulting `IS`s will not cover the entire space, so
1892:   how can they define a convergent preconditioner? Needs explaining.

1894: .seealso: [](sec_block_matrices), `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSetIS()`
1895: @*/
1896: PetscErrorCode PCFieldSplitRestrictIS(PC pc, IS isy)
1897: {
1898:   PetscFunctionBegin;
1901:   PetscTryMethod(pc, "PCFieldSplitRestrictIS_C", (PC, IS), (pc, isy));
1902:   PetscFunctionReturn(PETSC_SUCCESS);
1903: }

1905: static PetscErrorCode PCFieldSplitRestrictIS_FieldSplit(PC pc, IS isy)
1906: {
1907:   PC_FieldSplit    *jac   = (PC_FieldSplit *)pc->data;
1908:   PC_FieldSplitLink ilink = jac->head, next;
1909:   PetscInt          localsize, size, sizez, i;
1910:   const PetscInt   *ind, *indz;
1911:   PetscInt         *indc, *indcz;
1912:   PetscBool         flg;

1914:   PetscFunctionBegin;
1915:   PetscCall(ISGetLocalSize(isy, &localsize));
1916:   PetscCallMPI(MPI_Scan(&localsize, &size, 1, MPIU_INT, MPI_SUM, PetscObjectComm((PetscObject)isy)));
1917:   size -= localsize;
1918:   while (ilink) {
1919:     IS isrl, isr;
1920:     PC subpc;
1921:     PetscCall(ISEmbed(ilink->is, isy, PETSC_TRUE, &isrl));
1922:     PetscCall(ISGetLocalSize(isrl, &localsize));
1923:     PetscCall(PetscMalloc1(localsize, &indc));
1924:     PetscCall(ISGetIndices(isrl, &ind));
1925:     PetscCall(PetscArraycpy(indc, ind, localsize));
1926:     PetscCall(ISRestoreIndices(isrl, &ind));
1927:     PetscCall(ISDestroy(&isrl));
1928:     for (i = 0; i < localsize; i++) *(indc + i) += size;
1929:     PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)isy), localsize, indc, PETSC_OWN_POINTER, &isr));
1930:     PetscCall(PetscObjectReference((PetscObject)isr));
1931:     PetscCall(ISDestroy(&ilink->is));
1932:     ilink->is = isr;
1933:     PetscCall(PetscObjectReference((PetscObject)isr));
1934:     PetscCall(ISDestroy(&ilink->is_col));
1935:     ilink->is_col = isr;
1936:     PetscCall(ISDestroy(&isr));
1937:     PetscCall(KSPGetPC(ilink->ksp, &subpc));
1938:     PetscCall(PetscObjectTypeCompare((PetscObject)subpc, PCFIELDSPLIT, &flg));
1939:     if (flg) {
1940:       IS       iszl, isz;
1941:       MPI_Comm comm;
1942:       PetscCall(ISGetLocalSize(ilink->is, &localsize));
1943:       comm = PetscObjectComm((PetscObject)ilink->is);
1944:       PetscCall(ISEmbed(isy, ilink->is, PETSC_TRUE, &iszl));
1945:       PetscCallMPI(MPI_Scan(&localsize, &sizez, 1, MPIU_INT, MPI_SUM, comm));
1946:       sizez -= localsize;
1947:       PetscCall(ISGetLocalSize(iszl, &localsize));
1948:       PetscCall(PetscMalloc1(localsize, &indcz));
1949:       PetscCall(ISGetIndices(iszl, &indz));
1950:       PetscCall(PetscArraycpy(indcz, indz, localsize));
1951:       PetscCall(ISRestoreIndices(iszl, &indz));
1952:       PetscCall(ISDestroy(&iszl));
1953:       for (i = 0; i < localsize; i++) *(indcz + i) += sizez;
1954:       PetscCall(ISCreateGeneral(comm, localsize, indcz, PETSC_OWN_POINTER, &isz));
1955:       PetscCall(PCFieldSplitRestrictIS(subpc, isz));
1956:       PetscCall(ISDestroy(&isz));
1957:     }
1958:     next  = ilink->next;
1959:     ilink = next;
1960:   }
1961:   jac->isrestrict = PETSC_TRUE;
1962:   PetscFunctionReturn(PETSC_SUCCESS);
1963: }

1965: static PetscErrorCode PCFieldSplitSetIS_FieldSplit(PC pc, const char splitname[], IS is)
1966: {
1967:   PC_FieldSplit    *jac = (PC_FieldSplit *)pc->data;
1968:   PC_FieldSplitLink ilink, next = jac->head;
1969:   char              prefix[128];

1971:   PetscFunctionBegin;
1972:   if (jac->splitdefined) {
1973:     PetscCall(PetscInfo(pc, "Ignoring new split \"%s\" because the splits have already been defined\n", splitname));
1974:     PetscFunctionReturn(PETSC_SUCCESS);
1975:   }
1976:   PetscCall(PetscNew(&ilink));
1977:   if (splitname) {
1978:     PetscCall(PetscStrallocpy(splitname, &ilink->splitname));
1979:   } else {
1980:     PetscCall(PetscMalloc1(8, &ilink->splitname));
1981:     PetscCall(PetscSNPrintf(ilink->splitname, 7, "%" PetscInt_FMT, jac->nsplits));
1982:   }
1983:   ilink->event = jac->nsplits < 5 ? KSP_Solve_FS_0 + jac->nsplits : KSP_Solve_FS_0 + 4; /* Any split great than 4 gets logged in the 4th split */
1984:   PetscCall(PetscObjectReference((PetscObject)is));
1985:   PetscCall(ISDestroy(&ilink->is));
1986:   ilink->is = is;
1987:   PetscCall(PetscObjectReference((PetscObject)is));
1988:   PetscCall(ISDestroy(&ilink->is_col));
1989:   ilink->is_col = is;
1990:   ilink->next   = NULL;
1991:   PetscCall(KSPCreate(PetscObjectComm((PetscObject)pc), &ilink->ksp));
1992:   PetscCall(KSPSetNestLevel(ilink->ksp, pc->kspnestlevel));
1993:   PetscCall(KSPSetErrorIfNotConverged(ilink->ksp, pc->erroriffailure));
1994:   PetscCall(PetscObjectIncrementTabLevel((PetscObject)ilink->ksp, (PetscObject)pc, 1));
1995:   PetscCall(KSPSetType(ilink->ksp, KSPPREONLY));

1997:   PetscCall(PetscSNPrintf(prefix, sizeof(prefix), "%sfieldsplit_%s_", ((PetscObject)pc)->prefix ? ((PetscObject)pc)->prefix : "", ilink->splitname));
1998:   PetscCall(KSPSetOptionsPrefix(ilink->ksp, prefix));

2000:   if (!next) {
2001:     jac->head       = ilink;
2002:     ilink->previous = NULL;
2003:   } else {
2004:     while (next->next) next = next->next;
2005:     next->next      = ilink;
2006:     ilink->previous = next;
2007:   }
2008:   jac->nsplits++;
2009:   PetscFunctionReturn(PETSC_SUCCESS);
2010: }

2012: /*@C
2013:   PCFieldSplitSetFields - Sets the fields that define one particular split in `PCFIELDSPLIT`

2015:   Logically Collective

2017:   Input Parameters:
2018: + pc         - the preconditioner context
2019: . splitname  - name of this split, if `NULL` the number of the split is used
2020: . n          - the number of fields in this split
2021: . fields     - the fields in this split
2022: - fields_col - generally the same as fields, if it does not match fields then the matrix block that is solved for this set of fields comes from an off-diagonal block
2023:                  of the matrix and fields_col provides the column indices for that block

2025:   Level: intermediate

2027:   Notes:
2028:   Use `PCFieldSplitSetIS()` to set a  general set of indices as a split.

2030:   `PCFieldSplitSetFields()` is for defining fields as strided blocks. For example, if the block
2031:   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
2032:   0xx3xx6xx9xx12 ... x1xx4xx7xx ... xx2xx5xx8xx.. 01x34x67x... 0x1x3x5x7.. x12x45x78x....
2033:   where the numbered entries indicate what is in the split.

2035:   This function is called once per split (it creates a new split each time).  Solve options
2036:   for this split will be available under the prefix `-fieldsplit_SPLITNAME_`.

2038:   `PCFieldSplitSetIS()` does not support having a fields_col different from fields

2040:   Developer Notes:
2041:   This routine does not actually create the `IS` representing the split, that is delayed
2042:   until `PCSetUp_FieldSplit()`, because information about the vector/matrix layouts may not be
2043:   available when this routine is called.

2045: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSetBlockSize()`, `PCFieldSplitSetIS()`, `PCFieldSplitRestrictIS()`
2046: @*/
2047: PetscErrorCode PCFieldSplitSetFields(PC pc, const char splitname[], PetscInt n, const PetscInt *fields, const PetscInt *fields_col)
2048: {
2049:   PetscFunctionBegin;
2051:   PetscAssertPointer(splitname, 2);
2052:   PetscCheck(n >= 1, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_OUTOFRANGE, "Provided number of fields %" PetscInt_FMT " in split \"%s\" not positive", n, splitname);
2053:   PetscAssertPointer(fields, 4);
2054:   PetscTryMethod(pc, "PCFieldSplitSetFields_C", (PC, const char[], PetscInt, const PetscInt *, const PetscInt *), (pc, splitname, n, fields, fields_col));
2055:   PetscFunctionReturn(PETSC_SUCCESS);
2056: }

2058: /*@
2059:   PCFieldSplitSetDiagUseAmat - set flag indicating whether to extract diagonal blocks from Amat (rather than Pmat) to build
2060:   the sub-matrices associated with each split. Where `KSPSetOperators`(ksp,Amat,Pmat) was used to supply the operators.

2062:   Logically Collective

2064:   Input Parameters:
2065: + pc  - the preconditioner object
2066: - flg - boolean flag indicating whether or not to use Amat to extract the diagonal blocks from

2068:   Options Database Key:
2069: . -pc_fieldsplit_diag_use_amat - use the Amat to provide the diagonal blocks

2071:   Level: intermediate

2073: .seealso: [](sec_block_matrices), `PC`, `PCSetOperators()`, `KSPSetOperators()`, `PCFieldSplitGetDiagUseAmat()`, `PCFieldSplitSetOffDiagUseAmat()`, `PCFIELDSPLIT`
2074: @*/
2075: PetscErrorCode PCFieldSplitSetDiagUseAmat(PC pc, PetscBool flg)
2076: {
2077:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
2078:   PetscBool      isfs;

2080:   PetscFunctionBegin;
2082:   PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCFIELDSPLIT, &isfs));
2083:   PetscCheck(isfs, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "PC not of type %s", PCFIELDSPLIT);
2084:   jac->diag_use_amat = flg;
2085:   PetscFunctionReturn(PETSC_SUCCESS);
2086: }

2088: /*@
2089:   PCFieldSplitGetDiagUseAmat - get the flag indicating whether to extract diagonal blocks from Amat (rather than Pmat) to build
2090:   the sub-matrices associated with each split.  Where `KSPSetOperators`(ksp,Amat,Pmat) was used to supply the operators.

2092:   Logically Collective

2094:   Input Parameter:
2095: . pc - the preconditioner object

2097:   Output Parameter:
2098: . flg - boolean flag indicating whether or not to use Amat to extract the diagonal blocks from

2100:   Level: intermediate

2102: .seealso: [](sec_block_matrices), `PC`, `PCSetOperators()`, `KSPSetOperators()`, `PCFieldSplitSetDiagUseAmat()`, `PCFieldSplitGetOffDiagUseAmat()`, `PCFIELDSPLIT`
2103: @*/
2104: PetscErrorCode PCFieldSplitGetDiagUseAmat(PC pc, PetscBool *flg)
2105: {
2106:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
2107:   PetscBool      isfs;

2109:   PetscFunctionBegin;
2111:   PetscAssertPointer(flg, 2);
2112:   PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCFIELDSPLIT, &isfs));
2113:   PetscCheck(isfs, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "PC not of type %s", PCFIELDSPLIT);
2114:   *flg = jac->diag_use_amat;
2115:   PetscFunctionReturn(PETSC_SUCCESS);
2116: }

2118: /*@
2119:   PCFieldSplitSetOffDiagUseAmat - set flag indicating whether to extract off-diagonal blocks from Amat (rather than Pmat) to build
2120:   the sub-matrices associated with each split.  Where `KSPSetOperators`(ksp,Amat,Pmat) was used to supply the operators.

2122:   Logically Collective

2124:   Input Parameters:
2125: + pc  - the preconditioner object
2126: - flg - boolean flag indicating whether or not to use Amat to extract the off-diagonal blocks from

2128:   Options Database Key:
2129: . -pc_fieldsplit_off_diag_use_amat <bool> - use the Amat to extract the off-diagonal blocks

2131:   Level: intermediate

2133: .seealso: [](sec_block_matrices), `PC`, `PCSetOperators()`, `KSPSetOperators()`, `PCFieldSplitGetOffDiagUseAmat()`, `PCFieldSplitSetDiagUseAmat()`, `PCFIELDSPLIT`
2134: @*/
2135: PetscErrorCode PCFieldSplitSetOffDiagUseAmat(PC pc, PetscBool flg)
2136: {
2137:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
2138:   PetscBool      isfs;

2140:   PetscFunctionBegin;
2142:   PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCFIELDSPLIT, &isfs));
2143:   PetscCheck(isfs, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "PC not of type %s", PCFIELDSPLIT);
2144:   jac->offdiag_use_amat = flg;
2145:   PetscFunctionReturn(PETSC_SUCCESS);
2146: }

2148: /*@
2149:   PCFieldSplitGetOffDiagUseAmat - get the flag indicating whether to extract off-diagonal blocks from Amat (rather than Pmat) to build
2150:   the sub-matrices associated with each split.  Where `KSPSetOperators`(ksp,Amat,Pmat) was used to supply the operators.

2152:   Logically Collective

2154:   Input Parameter:
2155: . pc - the preconditioner object

2157:   Output Parameter:
2158: . flg - boolean flag indicating whether or not to use Amat to extract the off-diagonal blocks from

2160:   Level: intermediate

2162: .seealso: [](sec_block_matrices), `PC`, `PCSetOperators()`, `KSPSetOperators()`, `PCFieldSplitSetOffDiagUseAmat()`, `PCFieldSplitGetDiagUseAmat()`, `PCFIELDSPLIT`
2163: @*/
2164: PetscErrorCode PCFieldSplitGetOffDiagUseAmat(PC pc, PetscBool *flg)
2165: {
2166:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
2167:   PetscBool      isfs;

2169:   PetscFunctionBegin;
2171:   PetscAssertPointer(flg, 2);
2172:   PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCFIELDSPLIT, &isfs));
2173:   PetscCheck(isfs, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "PC not of type %s", PCFIELDSPLIT);
2174:   *flg = jac->offdiag_use_amat;
2175:   PetscFunctionReturn(PETSC_SUCCESS);
2176: }

2178: /*@C
2179:   PCFieldSplitSetIS - Sets the exact elements for a split in a `PCFIELDSPLIT`

2181:   Logically Collective

2183:   Input Parameters:
2184: + pc        - the preconditioner context
2185: . splitname - name of this split, if `NULL` the number of the split is used
2186: - is        - the index set that defines the elements in this split

2188:   Level: intermediate

2190:   Notes:
2191:   Use `PCFieldSplitSetFields()`, for splits defined by strided types.

2193:   This function is called once per split (it creates a new split each time).  Solve options
2194:   for this split will be available under the prefix -fieldsplit_SPLITNAME_.

2196: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSetBlockSize()`
2197: @*/
2198: PetscErrorCode PCFieldSplitSetIS(PC pc, const char splitname[], IS is)
2199: {
2200:   PetscFunctionBegin;
2202:   if (splitname) PetscAssertPointer(splitname, 2);
2204:   PetscTryMethod(pc, "PCFieldSplitSetIS_C", (PC, const char[], IS), (pc, splitname, is));
2205:   PetscFunctionReturn(PETSC_SUCCESS);
2206: }

2208: /*@C
2209:   PCFieldSplitGetIS - Retrieves the elements for a split as an `IS`

2211:   Logically Collective

2213:   Input Parameters:
2214: + pc        - the preconditioner context
2215: - splitname - name of this split

2217:   Output Parameter:
2218: . is - the index set that defines the elements in this split, or `NULL` if the split is not found

2220:   Level: intermediate

2222: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSetIS()`
2223: @*/
2224: PetscErrorCode PCFieldSplitGetIS(PC pc, const char splitname[], IS *is)
2225: {
2226:   PetscFunctionBegin;
2228:   PetscAssertPointer(splitname, 2);
2229:   PetscAssertPointer(is, 3);
2230:   {
2231:     PC_FieldSplit    *jac   = (PC_FieldSplit *)pc->data;
2232:     PC_FieldSplitLink ilink = jac->head;
2233:     PetscBool         found;

2235:     *is = NULL;
2236:     while (ilink) {
2237:       PetscCall(PetscStrcmp(ilink->splitname, splitname, &found));
2238:       if (found) {
2239:         *is = ilink->is;
2240:         break;
2241:       }
2242:       ilink = ilink->next;
2243:     }
2244:   }
2245:   PetscFunctionReturn(PETSC_SUCCESS);
2246: }

2248: /*@C
2249:   PCFieldSplitGetISByIndex - Retrieves the elements for a given split as an `IS`

2251:   Logically Collective

2253:   Input Parameters:
2254: + pc    - the preconditioner context
2255: - index - index of this split

2257:   Output Parameter:
2258: . is - the index set that defines the elements in this split

2260:   Level: intermediate

2262: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitGetIS()`, `PCFieldSplitSetIS()`
2263: @*/
2264: PetscErrorCode PCFieldSplitGetISByIndex(PC pc, PetscInt index, IS *is)
2265: {
2266:   PetscFunctionBegin;
2267:   PetscCheck(index >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Negative field %" PetscInt_FMT " requested", index);
2269:   PetscAssertPointer(is, 3);
2270:   {
2271:     PC_FieldSplit    *jac   = (PC_FieldSplit *)pc->data;
2272:     PC_FieldSplitLink ilink = jac->head;
2273:     PetscInt          i     = 0;
2274:     PetscCheck(index < jac->nsplits, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Field %" PetscInt_FMT " requested but only %" PetscInt_FMT " exist", index, jac->nsplits);

2276:     while (i < index) {
2277:       ilink = ilink->next;
2278:       ++i;
2279:     }
2280:     PetscCall(PCFieldSplitGetIS(pc, ilink->splitname, is));
2281:   }
2282:   PetscFunctionReturn(PETSC_SUCCESS);
2283: }

2285: /*@
2286:   PCFieldSplitSetBlockSize - Sets the block size for defining where fields start in the
2287:   fieldsplit preconditioner when calling `PCFieldSplitSetIS()`. If not set the matrix block size is used.

2289:   Logically Collective

2291:   Input Parameters:
2292: + pc - the preconditioner context
2293: - bs - the block size

2295:   Level: intermediate

2297: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSetIS()`
2298: @*/
2299: PetscErrorCode PCFieldSplitSetBlockSize(PC pc, PetscInt bs)
2300: {
2301:   PetscFunctionBegin;
2304:   PetscTryMethod(pc, "PCFieldSplitSetBlockSize_C", (PC, PetscInt), (pc, bs));
2305:   PetscFunctionReturn(PETSC_SUCCESS);
2306: }

2308: /*@C
2309:   PCFieldSplitGetSubKSP - Gets the `KSP` contexts for all splits

2311:   Collective

2313:   Input Parameter:
2314: . pc - the preconditioner context

2316:   Output Parameters:
2317: + n      - the number of splits
2318: - subksp - the array of `KSP` contexts

2320:   Level: advanced

2322:   Notes:
2323:   After `PCFieldSplitGetSubKSP()` the array of `KSP`s is to be freed by the user with `PetscFree()`
2324:   (not the `KSP`, just the array that contains them).

2326:   You must call `PCSetUp()` before calling `PCFieldSplitGetSubKSP()`.

2328:   If the fieldsplit is of type `PC_COMPOSITE_SCHUR`, it returns the `KSP` object used inside the
2329:   Schur complement and the `KSP` object used to iterate over the Schur complement.
2330:   To access all the `KSP` objects used in `PC_COMPOSITE_SCHUR`, use `PCFieldSplitSchurGetSubKSP()`.

2332:   If the fieldsplit is of type `PC_COMPOSITE_GKB`, it returns the `KSP` object used to solve the
2333:   inner linear system defined by the matrix H in each loop.

2335:   Fortran Notes:
2336:   You must pass in a `KSP` array that is large enough to contain all the `KSP`s.
2337:   You can call `PCFieldSplitGetSubKSP`(pc,n,`PETSC_NULL_KSP`,ierr) to determine how large the
2338:   `KSP` array must be.

2340:   Developer Notes:
2341:   There should be a `PCFieldSplitRestoreSubKSP()` instead of requiring the user to call `PetscFree()`

2343:   The Fortran interface should be modernized to return directly the array of values.

2345: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSetIS()`, `PCFieldSplitSchurGetSubKSP()`
2346: @*/
2347: PetscErrorCode PCFieldSplitGetSubKSP(PC pc, PetscInt *n, KSP *subksp[])
2348: {
2349:   PetscFunctionBegin;
2351:   if (n) PetscAssertPointer(n, 2);
2352:   PetscUseMethod(pc, "PCFieldSplitGetSubKSP_C", (PC, PetscInt *, KSP **), (pc, n, subksp));
2353:   PetscFunctionReturn(PETSC_SUCCESS);
2354: }

2356: /*@C
2357:   PCFieldSplitSchurGetSubKSP - Gets the `KSP` contexts used inside the Schur complement based `PCFIELDSPLIT`

2359:   Collective

2361:   Input Parameter:
2362: . pc - the preconditioner context

2364:   Output Parameters:
2365: + n      - the number of splits
2366: - subksp - the array of `KSP` contexts

2368:   Level: advanced

2370:   Notes:
2371:   After `PCFieldSplitSchurGetSubKSP()` the array of `KSP`s is to be freed by the user with `PetscFree()`
2372:   (not the `KSP` just the array that contains them).

2374:   You must call `PCSetUp()` before calling `PCFieldSplitSchurGetSubKSP()`.

2376:   If the fieldsplit type is of type `PC_COMPOSITE_SCHUR`, it returns (in order)
2377: +  1  - the `KSP` used for the (1,1) block
2378: .  2  - the `KSP` used for the Schur complement (not the one used for the interior Schur solver)
2379: -  3  - the `KSP` used for the (1,1) block in the upper triangular factor (if different from that of the (1,1) block).

2381:   It returns a null array if the fieldsplit is not of type `PC_COMPOSITE_SCHUR`; in this case, you should use `PCFieldSplitGetSubKSP()`.

2383:   Fortran Notes:
2384:   You must pass in a `KSP` array that is large enough to contain all the local `KSP`s.
2385:   You can call `PCFieldSplitSchurGetSubKSP`(pc,n,`PETSC_NULL_KSP`,ierr) to determine how large the
2386:   `KSP` array must be.

2388:   Developer Notes:
2389:   There should be a `PCFieldSplitRestoreSubKSP()` instead of requiring the user to call `PetscFree()`

2391:   Should the functionality of `PCFieldSplitSchurGetSubKSP()` and `PCFieldSplitGetSubKSP()` be merged?

2393:   The Fortran interface should be modernized to return directly the array of values.

2395: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSetIS()`, `PCFieldSplitGetSubKSP()`
2396: @*/
2397: PetscErrorCode PCFieldSplitSchurGetSubKSP(PC pc, PetscInt *n, KSP *subksp[])
2398: {
2399:   PetscFunctionBegin;
2401:   if (n) PetscAssertPointer(n, 2);
2402:   PetscUseMethod(pc, "PCFieldSplitSchurGetSubKSP_C", (PC, PetscInt *, KSP **), (pc, n, subksp));
2403:   PetscFunctionReturn(PETSC_SUCCESS);
2404: }

2406: /*@
2407:   PCFieldSplitSetSchurPre -  Indicates from what operator the preconditioner is constructed for the Schur complement.
2408:   The default is the A11 matrix.

2410:   Collective

2412:   Input Parameters:
2413: + pc    - the preconditioner context
2414: . ptype - which matrix to use for preconditioning the Schur complement: `PC_FIELDSPLIT_SCHUR_PRE_A11` (default),
2415:               `PC_FIELDSPLIT_SCHUR_PRE_SELF`, `PC_FIELDSPLIT_SCHUR_PRE_USER`,
2416:               `PC_FIELDSPLIT_SCHUR_PRE_SELFP`, and `PC_FIELDSPLIT_SCHUR_PRE_FULL`
2417: - pre   - matrix to use for preconditioning, or `NULL`

2419:   Options Database Keys:
2420: + -pc_fieldsplit_schur_precondition <self,selfp,user,a11,full> - default is `a11`. See notes for meaning of various arguments
2421: - -fieldsplit_1_pc_type <pctype>                               - the preconditioner algorithm that is used to construct the preconditioner from the operator

2423:   Level: intermediate

2425:   Notes:
2426:   If ptype is
2427: +     a11 - the preconditioner for the Schur complement is generated from the block diagonal part of the preconditioner
2428:   matrix associated with the Schur complement (i.e. A11), not the Schur complement matrix
2429: .     self - the preconditioner for the Schur complement is generated from the symbolic representation of the Schur complement matrix:
2430:   The only preconditioners that currently work with this symbolic representation matrix object are `PCLSC` and `PCHPDDM`
2431: .     user - the preconditioner for the Schur complement is generated from the user provided matrix (pre argument
2432:   to this function).
2433: .     selfp - the preconditioning for the Schur complement is generated from an explicitly-assembled approximation $ Sp = A11 - A10 inv(diag(A00)) A01 $
2434:   This is only a good preconditioner when diag(A00) is a good preconditioner for A00. Optionally, A00 can be
2435:   lumped before extracting the diagonal using the additional option `-fieldsplit_1_mat_schur_complement_ainv_type lump`
2436: -     full - the preconditioner for the Schur complement is generated from the exact Schur complement matrix representation
2437:   computed internally by `PCFIELDSPLIT` (this is expensive)
2438:   useful mostly as a test that the Schur complement approach can work for your problem

2440:   When solving a saddle point problem, where the A11 block is identically zero, using `a11` as the ptype only makes sense
2441:   with the additional option `-fieldsplit_1_pc_type none`. Usually for saddle point problems one would use a `ptype` of `self` and
2442:   `-fieldsplit_1_pc_type lsc` which uses the least squares commutator to compute a preconditioner for the Schur complement.

2444:   Developer Note:
2445:   The name of this function and the option `-pc_fieldsplit_schur_precondition` are inconsistent; precondition should be used everywhere.

2447: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSchurPre()`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSchurPreType`,
2448:           `MatSchurComplementSetAinvType()`, `PCLSC`, `PCFieldSplitSetSchurFactType()`
2449: @*/
2450: PetscErrorCode PCFieldSplitSetSchurPre(PC pc, PCFieldSplitSchurPreType ptype, Mat pre)
2451: {
2452:   PetscFunctionBegin;
2454:   PetscTryMethod(pc, "PCFieldSplitSetSchurPre_C", (PC, PCFieldSplitSchurPreType, Mat), (pc, ptype, pre));
2455:   PetscFunctionReturn(PETSC_SUCCESS);
2456: }

2458: PetscErrorCode PCFieldSplitSchurPrecondition(PC pc, PCFieldSplitSchurPreType ptype, Mat pre)
2459: {
2460:   return PCFieldSplitSetSchurPre(pc, ptype, pre);
2461: } /* Deprecated name */

2463: /*@
2464:   PCFieldSplitGetSchurPre - For Schur complement fieldsplit, determine how the Schur complement will be
2465:   preconditioned.  See `PCFieldSplitSetSchurPre()` for details.

2467:   Logically Collective

2469:   Input Parameter:
2470: . pc - the preconditioner context

2472:   Output Parameters:
2473: + 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`
2474: - pre   - matrix to use for preconditioning (with `PC_FIELDSPLIT_SCHUR_PRE_USER`), or `NULL`

2476:   Level: intermediate

2478: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitSetSchurPre()`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSchurPreType`, `PCLSC`
2479: @*/
2480: PetscErrorCode PCFieldSplitGetSchurPre(PC pc, PCFieldSplitSchurPreType *ptype, Mat *pre)
2481: {
2482:   PetscFunctionBegin;
2484:   PetscUseMethod(pc, "PCFieldSplitGetSchurPre_C", (PC, PCFieldSplitSchurPreType *, Mat *), (pc, ptype, pre));
2485:   PetscFunctionReturn(PETSC_SUCCESS);
2486: }

2488: /*@
2489:   PCFieldSplitSchurGetS -  extract the `MATSCHURCOMPLEMENT` object used by this `PCFIELDSPLIT` in case it needs to be configured separately

2491:   Not Collective

2493:   Input Parameter:
2494: . pc - the preconditioner context

2496:   Output Parameter:
2497: . S - the Schur complement matrix

2499:   Level: advanced

2501:   Note:
2502:   This matrix should not be destroyed using `MatDestroy()`; rather, use `PCFieldSplitSchurRestoreS()`.

2504: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSchurPreType`, `PCFieldSplitSetSchurPre()`, `MATSCHURCOMPLEMENT`, `PCFieldSplitSchurRestoreS()`,
2505:           `MatCreateSchurComplement()`, `MatSchurComplementGetKSP()`, `MatSchurComplementComputeExplicitOperator()`, `MatGetSchurComplement()`
2506: @*/
2507: PetscErrorCode PCFieldSplitSchurGetS(PC pc, Mat *S)
2508: {
2509:   const char    *t;
2510:   PetscBool      isfs;
2511:   PC_FieldSplit *jac;

2513:   PetscFunctionBegin;
2515:   PetscCall(PetscObjectGetType((PetscObject)pc, &t));
2516:   PetscCall(PetscStrcmp(t, PCFIELDSPLIT, &isfs));
2517:   PetscCheck(isfs, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Expected PC of type PCFIELDSPLIT, got %s instead", t);
2518:   jac = (PC_FieldSplit *)pc->data;
2519:   PetscCheck(jac->type == PC_COMPOSITE_SCHUR, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Expected PCFIELDSPLIT of type SCHUR, got %d instead", jac->type);
2520:   if (S) *S = jac->schur;
2521:   PetscFunctionReturn(PETSC_SUCCESS);
2522: }

2524: /*@
2525:   PCFieldSplitSchurRestoreS -  returns the `MATSCHURCOMPLEMENT` matrix used by this `PC`

2527:   Not Collective

2529:   Input Parameters:
2530: + pc - the preconditioner context
2531: - S  - the Schur complement matrix

2533:   Level: advanced

2535: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSchurPreType`, `PCFieldSplitSetSchurPre()`, `MatSchurComplement`, `PCFieldSplitSchurGetS()`
2536: @*/
2537: PetscErrorCode PCFieldSplitSchurRestoreS(PC pc, Mat *S)
2538: {
2539:   const char    *t;
2540:   PetscBool      isfs;
2541:   PC_FieldSplit *jac;

2543:   PetscFunctionBegin;
2545:   PetscCall(PetscObjectGetType((PetscObject)pc, &t));
2546:   PetscCall(PetscStrcmp(t, PCFIELDSPLIT, &isfs));
2547:   PetscCheck(isfs, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Expected PC of type PCFIELDSPLIT, got %s instead", t);
2548:   jac = (PC_FieldSplit *)pc->data;
2549:   PetscCheck(jac->type == PC_COMPOSITE_SCHUR, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Expected PCFIELDSPLIT of type SCHUR, got %d instead", jac->type);
2550:   PetscCheck(S && (*S == jac->schur), PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "MatSchurComplement restored is not the same as gotten");
2551:   PetscFunctionReturn(PETSC_SUCCESS);
2552: }

2554: static PetscErrorCode PCFieldSplitSetSchurPre_FieldSplit(PC pc, PCFieldSplitSchurPreType ptype, Mat pre)
2555: {
2556:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

2558:   PetscFunctionBegin;
2559:   jac->schurpre = ptype;
2560:   if (ptype == PC_FIELDSPLIT_SCHUR_PRE_USER && pre) {
2561:     PetscCall(MatDestroy(&jac->schur_user));
2562:     jac->schur_user = pre;
2563:     PetscCall(PetscObjectReference((PetscObject)jac->schur_user));
2564:   }
2565:   PetscFunctionReturn(PETSC_SUCCESS);
2566: }

2568: static PetscErrorCode PCFieldSplitGetSchurPre_FieldSplit(PC pc, PCFieldSplitSchurPreType *ptype, Mat *pre)
2569: {
2570:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

2572:   PetscFunctionBegin;
2573:   if (ptype) *ptype = jac->schurpre;
2574:   if (pre) *pre = jac->schur_user;
2575:   PetscFunctionReturn(PETSC_SUCCESS);
2576: }

2578: /*@
2579:   PCFieldSplitSetSchurFactType -  sets which blocks of the approximate block factorization to retain in the preconditioner {cite}`murphy2000note` and {cite}`ipsen2001note`

2581:   Collective

2583:   Input Parameters:
2584: + pc    - the preconditioner context
2585: - ftype - which blocks of factorization to retain, `PC_FIELDSPLIT_SCHUR_FACT_FULL` is default

2587:   Options Database Key:
2588: . -pc_fieldsplit_schur_fact_type <diag,lower,upper,full> - default is `full`

2590:   Level: intermediate

2592:   Notes:
2593:   The FULL factorization is

2595:   ```{math}
2596:   \left(\begin{array}{cc} A & B \\
2597:   C & E \\
2598:   \end{array}\right) =
2599:   \left(\begin{array}{cc} 1 & 0 \\
2600:   C*A^{-1} & I \\
2601:   \end{array}\right)
2602:   \left(\begin{array}{cc} A & 0 \\
2603:   0 & S \\
2604:   \end{array}\right)
2605:   \left(\begin{array}{cc} I & A^{-1}B \\
2606:   0 & I \\
2607:   \end{array}\right) = L D U.
2608:   ```

2610:   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 $L*D$,
2611:   and DIAG is the diagonal part with the sign of $ S $ flipped (because this makes the preconditioner positive definite for many formulations,
2612:   thus allowing the use of `KSPMINRES)`. Sign flipping of $ S $ can be turned off with `PCFieldSplitSetSchurScale()`.

2614:   If $A$ and $S$ are solved exactly
2615: +  1 - FULL factorization is a direct solver.
2616: .  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.
2617: -  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.

2619:   If the iteration count is very low, consider using `KSPFGMRES` or `KSPGCR` which can use one less preconditioner
2620:   application in this case. Note that the preconditioned operator may be highly non-normal, so such fast convergence may not be observed in practice.

2622:   For symmetric problems in which $A$ is positive definite and $S$ is negative definite, DIAG can be used with `KSPMINRES`.

2624:   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).

2626: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSchurPreType`, `PCFieldSplitSetSchurScale()`,
2627:           [](sec_flexibleksp), `PCFieldSplitSetSchurPre()`
2628: @*/
2629: PetscErrorCode PCFieldSplitSetSchurFactType(PC pc, PCFieldSplitSchurFactType ftype)
2630: {
2631:   PetscFunctionBegin;
2633:   PetscTryMethod(pc, "PCFieldSplitSetSchurFactType_C", (PC, PCFieldSplitSchurFactType), (pc, ftype));
2634:   PetscFunctionReturn(PETSC_SUCCESS);
2635: }

2637: static PetscErrorCode PCFieldSplitSetSchurFactType_FieldSplit(PC pc, PCFieldSplitSchurFactType ftype)
2638: {
2639:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

2641:   PetscFunctionBegin;
2642:   jac->schurfactorization = ftype;
2643:   PetscFunctionReturn(PETSC_SUCCESS);
2644: }

2646: /*@
2647:   PCFieldSplitSetSchurScale -  Controls the sign flip of S for `PC_FIELDSPLIT_SCHUR_FACT_DIAG`.

2649:   Collective

2651:   Input Parameters:
2652: + pc    - the preconditioner context
2653: - scale - scaling factor for the Schur complement

2655:   Options Database Key:
2656: . -pc_fieldsplit_schur_scale <scale> - default is -1.0

2658:   Level: intermediate

2660: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSchurFactType`, `PCFieldSplitSetSchurFactType()`
2661: @*/
2662: PetscErrorCode PCFieldSplitSetSchurScale(PC pc, PetscScalar scale)
2663: {
2664:   PetscFunctionBegin;
2667:   PetscTryMethod(pc, "PCFieldSplitSetSchurScale_C", (PC, PetscScalar), (pc, scale));
2668:   PetscFunctionReturn(PETSC_SUCCESS);
2669: }

2671: static PetscErrorCode PCFieldSplitSetSchurScale_FieldSplit(PC pc, PetscScalar scale)
2672: {
2673:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

2675:   PetscFunctionBegin;
2676:   jac->schurscale = scale;
2677:   PetscFunctionReturn(PETSC_SUCCESS);
2678: }

2680: /*@C
2681:   PCFieldSplitGetSchurBlocks - Gets all matrix blocks for the Schur complement

2683:   Collective

2685:   Input Parameter:
2686: . pc - the preconditioner context

2688:   Output Parameters:
2689: + A00 - the (0,0) block
2690: . A01 - the (0,1) block
2691: . A10 - the (1,0) block
2692: - A11 - the (1,1) block

2694:   Level: advanced

2696: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `MatSchurComplementGetSubMatrices()`, `MatSchurComplementSetSubMatrices()`
2697: @*/
2698: PetscErrorCode PCFieldSplitGetSchurBlocks(PC pc, Mat *A00, Mat *A01, Mat *A10, Mat *A11)
2699: {
2700:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

2702:   PetscFunctionBegin;
2704:   PetscCheck(jac->type == PC_COMPOSITE_SCHUR, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONG, "FieldSplit is not using a Schur complement approach.");
2705:   if (A00) *A00 = jac->pmat[0];
2706:   if (A01) *A01 = jac->B;
2707:   if (A10) *A10 = jac->C;
2708:   if (A11) *A11 = jac->pmat[1];
2709:   PetscFunctionReturn(PETSC_SUCCESS);
2710: }

2712: /*@
2713:   PCFieldSplitSetGKBTol -  Sets the solver tolerance for the generalized Golub-Kahan bidiagonalization preconditioner {cite}`arioli2013` in `PCFIELDSPLIT`

2715:   Collective

2717:   Input Parameters:
2718: + pc        - the preconditioner context
2719: - tolerance - the solver tolerance

2721:   Options Database Key:
2722: . -pc_fieldsplit_gkb_tol <tolerance> - default is 1e-5

2724:   Level: intermediate

2726:   Note:
2727:   The generalized GKB algorithm {cite}`arioli2013` uses a lower bound estimate of the error in energy norm as stopping criterion.
2728:   It stops once the lower bound estimate undershoots the required solver tolerance. Although the actual error might be bigger than
2729:   this estimate, the stopping criterion is satisfactory in practical cases.

2731: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetGKBDelay()`, `PCFieldSplitSetGKBNu()`, `PCFieldSplitSetGKBMaxit()`
2732: @*/
2733: PetscErrorCode PCFieldSplitSetGKBTol(PC pc, PetscReal tolerance)
2734: {
2735:   PetscFunctionBegin;
2738:   PetscTryMethod(pc, "PCFieldSplitSetGKBTol_C", (PC, PetscReal), (pc, tolerance));
2739:   PetscFunctionReturn(PETSC_SUCCESS);
2740: }

2742: static PetscErrorCode PCFieldSplitSetGKBTol_FieldSplit(PC pc, PetscReal tolerance)
2743: {
2744:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

2746:   PetscFunctionBegin;
2747:   jac->gkbtol = tolerance;
2748:   PetscFunctionReturn(PETSC_SUCCESS);
2749: }

2751: /*@
2752:   PCFieldSplitSetGKBMaxit -  Sets the maximum number of iterations for the generalized Golub-Kahan bidiagonalization preconditioner in `PCFIELDSPLIT`

2754:   Collective

2756:   Input Parameters:
2757: + pc    - the preconditioner context
2758: - maxit - the maximum number of iterations

2760:   Options Database Key:
2761: . -pc_fieldsplit_gkb_maxit <maxit> - default is 100

2763:   Level: intermediate

2765: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetGKBDelay()`, `PCFieldSplitSetGKBTol()`, `PCFieldSplitSetGKBNu()`
2766: @*/
2767: PetscErrorCode PCFieldSplitSetGKBMaxit(PC pc, PetscInt maxit)
2768: {
2769:   PetscFunctionBegin;
2772:   PetscTryMethod(pc, "PCFieldSplitSetGKBMaxit_C", (PC, PetscInt), (pc, maxit));
2773:   PetscFunctionReturn(PETSC_SUCCESS);
2774: }

2776: static PetscErrorCode PCFieldSplitSetGKBMaxit_FieldSplit(PC pc, PetscInt maxit)
2777: {
2778:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

2780:   PetscFunctionBegin;
2781:   jac->gkbmaxit = maxit;
2782:   PetscFunctionReturn(PETSC_SUCCESS);
2783: }

2785: /*@
2786:   PCFieldSplitSetGKBDelay -  Sets the delay in the lower bound error estimate in the generalized Golub-Kahan bidiagonalization {cite}`arioli2013` in `PCFIELDSPLIT`
2787:   preconditioner.

2789:   Collective

2791:   Input Parameters:
2792: + pc    - the preconditioner context
2793: - delay - the delay window in the lower bound estimate

2795:   Options Database Key:
2796: . -pc_fieldsplit_gkb_delay <delay> - default is 5

2798:   Level: intermediate

2800:   Notes:
2801:   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 $
2802:   is expressed as a truncated sum. The error at iteration k can only be measured at iteration (k + `delay`), and thus the algorithm needs
2803:   at least (`delay` + 1) iterations to stop.

2805:   For more details on the generalized Golub-Kahan bidiagonalization method and its lower bound stopping criterion, please refer to {cite}`arioli2013`

2807: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetGKBNu()`, `PCFieldSplitSetGKBTol()`, `PCFieldSplitSetGKBMaxit()`
2808: @*/
2809: PetscErrorCode PCFieldSplitSetGKBDelay(PC pc, PetscInt delay)
2810: {
2811:   PetscFunctionBegin;
2814:   PetscTryMethod(pc, "PCFieldSplitSetGKBDelay_C", (PC, PetscInt), (pc, delay));
2815:   PetscFunctionReturn(PETSC_SUCCESS);
2816: }

2818: static PetscErrorCode PCFieldSplitSetGKBDelay_FieldSplit(PC pc, PetscInt delay)
2819: {
2820:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

2822:   PetscFunctionBegin;
2823:   jac->gkbdelay = delay;
2824:   PetscFunctionReturn(PETSC_SUCCESS);
2825: }

2827: /*@
2828:   PCFieldSplitSetGKBNu -  Sets the scalar value nu >= 0 in the transformation H = A00 + nu*A01*A01' of the (1,1) block in the
2829:   Golub-Kahan bidiagonalization preconditioner {cite}`arioli2013` in `PCFIELDSPLIT`

2831:   Collective

2833:   Input Parameters:
2834: + pc - the preconditioner context
2835: - nu - the shift parameter

2837:   Options Database Key:
2838: . -pc_fieldsplit_gkb_nu <nu> - default is 1

2840:   Level: intermediate

2842:   Notes:
2843:   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,
2844:   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
2845:   necessary to find a good balance in between the convergence of the inner and outer loop.

2847:   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.

2849: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetGKBDelay()`, `PCFieldSplitSetGKBTol()`, `PCFieldSplitSetGKBMaxit()`
2850: @*/
2851: PetscErrorCode PCFieldSplitSetGKBNu(PC pc, PetscReal nu)
2852: {
2853:   PetscFunctionBegin;
2856:   PetscTryMethod(pc, "PCFieldSplitSetGKBNu_C", (PC, PetscReal), (pc, nu));
2857:   PetscFunctionReturn(PETSC_SUCCESS);
2858: }

2860: static PetscErrorCode PCFieldSplitSetGKBNu_FieldSplit(PC pc, PetscReal nu)
2861: {
2862:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

2864:   PetscFunctionBegin;
2865:   jac->gkbnu = nu;
2866:   PetscFunctionReturn(PETSC_SUCCESS);
2867: }

2869: static PetscErrorCode PCFieldSplitSetType_FieldSplit(PC pc, PCCompositeType type)
2870: {
2871:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

2873:   PetscFunctionBegin;
2874:   jac->type = type;
2875:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSubKSP_C", NULL));
2876:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurPre_C", NULL));
2877:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSchurPre_C", NULL));
2878:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurFactType_C", NULL));
2879:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurScale_C", NULL));
2880:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBTol_C", NULL));
2881:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBMaxit_C", NULL));
2882:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBNu_C", NULL));
2883:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBDelay_C", NULL));

2885:   if (type == PC_COMPOSITE_SCHUR) {
2886:     pc->ops->apply          = PCApply_FieldSplit_Schur;
2887:     pc->ops->applytranspose = PCApplyTranspose_FieldSplit_Schur;
2888:     pc->ops->view           = PCView_FieldSplit_Schur;

2890:     PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSubKSP_C", PCFieldSplitGetSubKSP_FieldSplit_Schur));
2891:     PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurPre_C", PCFieldSplitSetSchurPre_FieldSplit));
2892:     PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSchurPre_C", PCFieldSplitGetSchurPre_FieldSplit));
2893:     PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurFactType_C", PCFieldSplitSetSchurFactType_FieldSplit));
2894:     PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurScale_C", PCFieldSplitSetSchurScale_FieldSplit));
2895:   } else if (type == PC_COMPOSITE_GKB) {
2896:     pc->ops->apply = PCApply_FieldSplit_GKB;
2897:     pc->ops->view  = PCView_FieldSplit_GKB;

2899:     PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSubKSP_C", PCFieldSplitGetSubKSP_FieldSplit));
2900:     PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBTol_C", PCFieldSplitSetGKBTol_FieldSplit));
2901:     PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBMaxit_C", PCFieldSplitSetGKBMaxit_FieldSplit));
2902:     PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBNu_C", PCFieldSplitSetGKBNu_FieldSplit));
2903:     PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBDelay_C", PCFieldSplitSetGKBDelay_FieldSplit));
2904:   } else {
2905:     pc->ops->apply = PCApply_FieldSplit;
2906:     pc->ops->view  = PCView_FieldSplit;

2908:     PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSubKSP_C", PCFieldSplitGetSubKSP_FieldSplit));
2909:   }
2910:   PetscFunctionReturn(PETSC_SUCCESS);
2911: }

2913: static PetscErrorCode PCFieldSplitSetBlockSize_FieldSplit(PC pc, PetscInt bs)
2914: {
2915:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

2917:   PetscFunctionBegin;
2918:   PetscCheck(bs >= 1, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_OUTOFRANGE, "Blocksize must be positive, you gave %" PetscInt_FMT, bs);
2919:   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);
2920:   jac->bs = bs;
2921:   PetscFunctionReturn(PETSC_SUCCESS);
2922: }

2924: static PetscErrorCode PCSetCoordinates_FieldSplit(PC pc, PetscInt dim, PetscInt nloc, PetscReal coords[])
2925: {
2926:   PC_FieldSplit    *jac           = (PC_FieldSplit *)pc->data;
2927:   PC_FieldSplitLink ilink_current = jac->head;
2928:   IS                is_owned;

2930:   PetscFunctionBegin;
2931:   jac->coordinates_set = PETSC_TRUE; // Internal flag
2932:   PetscCall(MatGetOwnershipIS(pc->mat, &is_owned, NULL));

2934:   while (ilink_current) {
2935:     // For each IS, embed it to get local coords indces
2936:     IS              is_coords;
2937:     PetscInt        ndofs_block;
2938:     const PetscInt *block_dofs_enumeration; // Numbering of the dofs relevant to the current block

2940:     // Setting drop to true for safety. It should make no difference.
2941:     PetscCall(ISEmbed(ilink_current->is, is_owned, PETSC_TRUE, &is_coords));
2942:     PetscCall(ISGetLocalSize(is_coords, &ndofs_block));
2943:     PetscCall(ISGetIndices(is_coords, &block_dofs_enumeration));

2945:     // Allocate coordinates vector and set it directly
2946:     PetscCall(PetscMalloc1(ndofs_block * dim, &ilink_current->coords));
2947:     for (PetscInt dof = 0; dof < ndofs_block; ++dof) {
2948:       for (PetscInt d = 0; d < dim; ++d) (ilink_current->coords)[dim * dof + d] = coords[dim * block_dofs_enumeration[dof] + d];
2949:     }
2950:     ilink_current->dim   = dim;
2951:     ilink_current->ndofs = ndofs_block;
2952:     PetscCall(ISRestoreIndices(is_coords, &block_dofs_enumeration));
2953:     PetscCall(ISDestroy(&is_coords));
2954:     ilink_current = ilink_current->next;
2955:   }
2956:   PetscCall(ISDestroy(&is_owned));
2957:   PetscFunctionReturn(PETSC_SUCCESS);
2958: }

2960: /*@
2961:   PCFieldSplitSetType - Sets the type, `PCCompositeType`, of a `PCFIELDSPLIT`

2963:   Collective

2965:   Input Parameters:
2966: + pc   - the preconditioner context
2967: - type - `PC_COMPOSITE_ADDITIVE`, `PC_COMPOSITE_MULTIPLICATIVE` (default), `PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE`, `PC_COMPOSITE_SPECIAL`, `PC_COMPOSITE_SCHUR`,
2968:          `PC_COMPOSITE_GKB`

2970:   Options Database Key:
2971: . -pc_fieldsplit_type <one of multiplicative, additive, symmetric_multiplicative, special, schur> - Sets fieldsplit preconditioner type

2973:   Level: intermediate

2975: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCCompositeType`, `PCCompositeGetType()`, `PC_COMPOSITE_ADDITIVE`, `PC_COMPOSITE_MULTIPLICATIVE`,
2976:           `PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE`, `PC_COMPOSITE_SPECIAL`, `PC_COMPOSITE_SCHUR`, `PCFieldSplitSetSchurFactType()`
2977: @*/
2978: PetscErrorCode PCFieldSplitSetType(PC pc, PCCompositeType type)
2979: {
2980:   PetscFunctionBegin;
2982:   PetscTryMethod(pc, "PCFieldSplitSetType_C", (PC, PCCompositeType), (pc, type));
2983:   PetscFunctionReturn(PETSC_SUCCESS);
2984: }

2986: /*@
2987:   PCFieldSplitGetType - Gets the type, `PCCompositeType`, of a `PCFIELDSPLIT`

2989:   Not collective

2991:   Input Parameter:
2992: . pc - the preconditioner context

2994:   Output Parameter:
2995: . type - `PC_COMPOSITE_ADDITIVE`, `PC_COMPOSITE_MULTIPLICATIVE` (default), `PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE`, `PC_COMPOSITE_SPECIAL`, `PC_COMPOSITE_SCHUR`

2997:   Level: intermediate

2999: .seealso: [](sec_block_matrices), `PC`, `PCCompositeSetType()`, `PCFIELDSPLIT`, `PCCompositeType`, `PC_COMPOSITE_ADDITIVE`, `PC_COMPOSITE_MULTIPLICATIVE`,
3000:           `PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE`, `PC_COMPOSITE_SPECIAL`, `PC_COMPOSITE_SCHUR`
3001: @*/
3002: PetscErrorCode PCFieldSplitGetType(PC pc, PCCompositeType *type)
3003: {
3004:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

3006:   PetscFunctionBegin;
3008:   PetscAssertPointer(type, 2);
3009:   *type = jac->type;
3010:   PetscFunctionReturn(PETSC_SUCCESS);
3011: }

3013: /*@
3014:   PCFieldSplitSetDMSplits - Flags whether `DMCreateFieldDecomposition()` should be used to define the splits in a `PCFIELDSPLIT`, whenever possible.

3016:   Logically Collective

3018:   Input Parameters:
3019: + pc  - the preconditioner context
3020: - flg - boolean indicating whether to use field splits defined by the `DM`

3022:   Options Database Key:
3023: . -pc_fieldsplit_dm_splits <bool> - use the field splits defined by the `DM`

3025:   Level: intermediate

3027:   Developer Note:
3028:   The name should be `PCFieldSplitSetUseDMSplits()`, similar change to options database

3030: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitGetDMSplits()`, `DMCreateFieldDecomposition()`, `PCFieldSplitSetFields()`, `PCFieldsplitSetIS()`
3031: @*/
3032: PetscErrorCode PCFieldSplitSetDMSplits(PC pc, PetscBool flg)
3033: {
3034:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
3035:   PetscBool      isfs;

3037:   PetscFunctionBegin;
3040:   PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCFIELDSPLIT, &isfs));
3041:   if (isfs) jac->dm_splits = flg;
3042:   PetscFunctionReturn(PETSC_SUCCESS);
3043: }

3045: /*@
3046:   PCFieldSplitGetDMSplits - Returns flag indicating whether `DMCreateFieldDecomposition()` should be used to define the splits in a `PCFIELDSPLIT`, whenever possible.

3048:   Logically Collective

3050:   Input Parameter:
3051: . pc - the preconditioner context

3053:   Output Parameter:
3054: . flg - boolean indicating whether to use field splits defined by the `DM`

3056:   Level: intermediate

3058:   Developer Note:
3059:   The name should be `PCFieldSplitGetUseDMSplits()`

3061: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetDMSplits()`, `DMCreateFieldDecomposition()`, `PCFieldSplitSetFields()`, `PCFieldsplitSetIS()`
3062: @*/
3063: PetscErrorCode PCFieldSplitGetDMSplits(PC pc, PetscBool *flg)
3064: {
3065:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
3066:   PetscBool      isfs;

3068:   PetscFunctionBegin;
3070:   PetscAssertPointer(flg, 2);
3071:   PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCFIELDSPLIT, &isfs));
3072:   if (isfs) {
3073:     if (flg) *flg = jac->dm_splits;
3074:   }
3075:   PetscFunctionReturn(PETSC_SUCCESS);
3076: }

3078: /*@
3079:   PCFieldSplitGetDetectSaddlePoint - Returns flag indicating whether `PCFIELDSPLIT` will attempt to automatically determine fields based on zero diagonal entries.

3081:   Logically Collective

3083:   Input Parameter:
3084: . pc - the preconditioner context

3086:   Output Parameter:
3087: . flg - boolean indicating whether to detect fields or not

3089:   Level: intermediate

3091: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetDetectSaddlePoint()`
3092: @*/
3093: PetscErrorCode PCFieldSplitGetDetectSaddlePoint(PC pc, PetscBool *flg)
3094: {
3095:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

3097:   PetscFunctionBegin;
3098:   *flg = jac->detect;
3099:   PetscFunctionReturn(PETSC_SUCCESS);
3100: }

3102: /*@
3103:   PCFieldSplitSetDetectSaddlePoint - Sets flag indicating whether `PCFIELDSPLIT` will attempt to automatically determine fields based on zero diagonal entries.

3105:   Logically Collective

3107:   Input Parameter:
3108: . pc - the preconditioner context

3110:   Output Parameter:
3111: . flg - boolean indicating whether to detect fields or not

3113:   Options Database Key:
3114: . -pc_fieldsplit_detect_saddle_point <bool> - detect and use the saddle point

3116:   Level: intermediate

3118:   Note:
3119:   Also sets the split type to `PC_COMPOSITE_SCHUR` (see `PCFieldSplitSetType()`) and the Schur preconditioner type to `PC_FIELDSPLIT_SCHUR_PRE_SELF` (see `PCFieldSplitSetSchurPre()`).

3121: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitGetDetectSaddlePoint()`, `PCFieldSplitSetType()`, `PCFieldSplitSetSchurPre()`, `PC_FIELDSPLIT_SCHUR_PRE_SELF`
3122: @*/
3123: PetscErrorCode PCFieldSplitSetDetectSaddlePoint(PC pc, PetscBool flg)
3124: {
3125:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

3127:   PetscFunctionBegin;
3128:   jac->detect = flg;
3129:   if (jac->detect) {
3130:     PetscCall(PCFieldSplitSetType(pc, PC_COMPOSITE_SCHUR));
3131:     PetscCall(PCFieldSplitSetSchurPre(pc, PC_FIELDSPLIT_SCHUR_PRE_SELF, NULL));
3132:   }
3133:   PetscFunctionReturn(PETSC_SUCCESS);
3134: }

3136: /*MC
3137:    PCFIELDSPLIT - Preconditioner created by combining separate preconditioners for individual
3138:    collections of variables (that may overlap) called splits. See [the users manual section on "Solving Block Matrices"](sec_block_matrices) for more details.

3140:    Options Database Keys:
3141: +   -pc_fieldsplit_%d_fields <a,b,..>                                                - indicates the fields to be used in the `%d`'th split
3142: .   -pc_fieldsplit_default                                                           - automatically add any fields to additional splits that have not
3143:                                                                                      been supplied explicitly by `-pc_fieldsplit_%d_fields`
3144: .   -pc_fieldsplit_block_size <bs>                                                   - size of block that defines fields (i.e. there are bs fields)
3145: .   -pc_fieldsplit_type <additive,multiplicative,symmetric_multiplicative,schur,gkb> - type of relaxation or factorization splitting
3146: .   -pc_fieldsplit_schur_precondition <self,selfp,user,a11,full>                     - default is `a11`; see `PCFieldSplitSetSchurPre()`
3147: .   -pc_fieldsplit_schur_fact_type <diag,lower,upper,full>                           - set factorization type when using `-pc_fieldsplit_type schur`;
3148:                                                                                      see `PCFieldSplitSetSchurFactType()`
3149: .   -pc_fieldsplit_dm_splits <true,false> (default is true)                          - Whether to use `DMCreateFieldDecomposition()` for splits
3150: -   -pc_fieldsplit_detect_saddle_point                                               - automatically finds rows with zero diagonal and uses Schur complement with no preconditioner as the solver

3152:      Options prefixes for inner solvers when using the Schur complement preconditioner are `-fieldsplit_0_` and `-fieldsplit_1_` .
3153:      The options prefix for the inner solver when using the Golub-Kahan biadiagonalization preconditioner is `-fieldsplit_0_`
3154:      For all other solvers they are `-fieldsplit_%d_` for the `%d`'th field; use `-fieldsplit_` for all fields.

3156:      To set options on the solvers for each block append `-fieldsplit_` to all the `PC`
3157:      options database keys. For example, `-fieldsplit_pc_type ilu` `-fieldsplit_pc_factor_levels 1`

3159:      To set the options on the solvers separate for each block call `PCFieldSplitGetSubKSP()`
3160:       and set the options directly on the resulting `KSP` object

3162:     Level: intermediate

3164:    Notes:
3165:     Use `PCFieldSplitSetFields()` to set splits defined by "strided" entries and `PCFieldSplitSetIS()`
3166:      to define a split by an arbitrary collection of entries.

3168:       If no splits are set, the default is used. If a `DM` is associated with the `PC` and it supports
3169:       `DMCreateFieldDecomposition()`, then that is used for the default. Otherwise, the splits are defined by entries strided by bs,
3170:       beginning at 0 then 1, etc to bs-1. The block size can be set with `PCFieldSplitSetBlockSize()`,
3171:       if this is not called the block size defaults to the blocksize of the second matrix passed
3172:       to `KSPSetOperators()`/`PCSetOperators()`.

3174:       For the Schur complement preconditioner if

3176:       ```{math}
3177:       J = \left[\begin{array}{cc} A_{00} & A_{01} \\ A_{10} & A_{11} \end{array}\right]
3178:       ```

3180:       the preconditioner using `full` factorization is logically
3181:       ```{math}
3182:       \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]
3183:       ```
3184:      where the action of $\text{inv}(A_{00})$ is applied using the KSP solver with prefix `-fieldsplit_0_`.  $S$ is the Schur complement
3185:      ```{math}
3186:      S = A_{11} - A_{10} \text{ksp}(A_{00}) A_{01}
3187:      ```
3188:      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
3189:      in providing the SECOND split or 1 if not given). For `PCFieldSplitGetSubKSP()` when field number is 0,
3190:      it returns the KSP associated with `-fieldsplit_0_` while field number 1 gives `-fieldsplit_1_` KSP. By default
3191:      $A_{11}$ is used to construct a preconditioner for $S$, use `PCFieldSplitSetSchurPre()` for all the possible ways to construct the preconditioner for $S$.

3193:      The factorization type is set using `-pc_fieldsplit_schur_fact_type <diag, lower, upper, full>`. `full` is shown above,
3194:      `diag` gives
3195:       ```{math}
3196:       \left[\begin{array}{cc} \text{inv}(A_{00}) & 0 \\  0 & -\text{ksp}(S) \end{array}\right]
3197:       ```
3198:      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
3199:      can be turned off with `PCFieldSplitSetSchurScale()` or by command line `-pc_fieldsplit_schur_scale 1.0`. The `lower` factorization is the inverse of
3200:       ```{math}
3201:       \left[\begin{array}{cc} A_{00} & 0 \\  A_{10} & S \end{array}\right]
3202:       ```
3203:      where the inverses of A_{00} and S are applied using KSPs. The upper factorization is the inverse of
3204:       ```{math}
3205:       \left[\begin{array}{cc} A_{00} & A_{01} \\  0 & S \end{array}\right]
3206:       ```
3207:      where again the inverses of $A_{00}$ and $S$ are applied using `KSP`s.

3209:      If only one set of indices (one `IS`) is provided with `PCFieldSplitSetIS()` then the complement of that `IS`
3210:      is used automatically for a second block.

3212:      The fieldsplit preconditioner cannot currently be used with the `MATBAIJ` or `MATSBAIJ` data formats if the blocksize is larger than 1.
3213:      Generally it should be used with the `MATAIJ` format.

3215:      The forms of these preconditioners are closely related if not identical to forms derived as "Distributive Iterations", see,
3216:      for example, page 294 in "Principles of Computational Fluid Dynamics" by Pieter Wesseling {cite}`wesseling2009`.
3217:      One can also use `PCFIELDSPLIT`
3218:      inside a smoother resulting in "Distributive Smoothers".

3220:      See "A taxonomy and comparison of parallel block multi-level preconditioners for the incompressible Navier-Stokes equations" {cite}`elman2008tcp`.

3222:      The Constrained Pressure Preconditioner (CPR) can be implemented using `PCCOMPOSITE` with `PCGALERKIN`. CPR first solves an $R A P$ subsystem, updates the
3223:      residual on all variables (`PCCompositeSetType(pc,PC_COMPOSITE_MULTIPLICATIVE)`), and then applies a simple ILU like preconditioner on all the variables.

3225:      The generalized Golub-Kahan bidiagonalization preconditioner (GKB) can be applied to symmetric $2 \times 2$ block matrices of the shape
3226:      ```{math}
3227:      \left[\begin{array}{cc} A_{00} & A_{01} \\ A_{01}' & 0 \end{array}\right]
3228:      ```
3229:      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 $H = _{A00} + \nu*A_{01}*A_{01}'$.
3230:      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_`.

3232:    Developer Note:
3233:    The Schur complement functionality of `PCFIELDSPLIT` should likely be factored into its own `PC` thus simplifying the implementation of the preconditioners and their
3234:    user API.

3236: .seealso: [](sec_block_matrices), `PC`, `PCCreate()`, `PCSetType()`, `PCType`, `PC`, `PCLSC`,
3237:           `PCFieldSplitGetSubKSP()`, `PCFieldSplitSchurGetSubKSP()`, `PCFieldSplitSetFields()`,
3238:           `PCFieldSplitSetType()`, `PCFieldSplitSetIS()`, `PCFieldSplitSetSchurPre()`, `PCFieldSplitSetSchurFactType()`,
3239:           `MatSchurComplementSetAinvType()`, `PCFieldSplitSetSchurScale()`, `PCFieldSplitSetDetectSaddlePoint()`
3240: M*/

3242: PETSC_EXTERN PetscErrorCode PCCreate_FieldSplit(PC pc)
3243: {
3244:   PC_FieldSplit *jac;

3246:   PetscFunctionBegin;
3247:   PetscCall(PetscNew(&jac));

3249:   jac->bs                 = -1;
3250:   jac->nsplits            = 0;
3251:   jac->type               = PC_COMPOSITE_MULTIPLICATIVE;
3252:   jac->schurpre           = PC_FIELDSPLIT_SCHUR_PRE_USER; /* Try user preconditioner first, fall back on diagonal */
3253:   jac->schurfactorization = PC_FIELDSPLIT_SCHUR_FACT_FULL;
3254:   jac->schurscale         = -1.0;
3255:   jac->dm_splits          = PETSC_TRUE;
3256:   jac->detect             = PETSC_FALSE;
3257:   jac->gkbtol             = 1e-5;
3258:   jac->gkbdelay           = 5;
3259:   jac->gkbnu              = 1;
3260:   jac->gkbmaxit           = 100;
3261:   jac->gkbmonitor         = PETSC_FALSE;
3262:   jac->coordinates_set    = PETSC_FALSE;

3264:   pc->data = (void *)jac;

3266:   pc->ops->apply           = PCApply_FieldSplit;
3267:   pc->ops->applytranspose  = PCApplyTranspose_FieldSplit;
3268:   pc->ops->setup           = PCSetUp_FieldSplit;
3269:   pc->ops->reset           = PCReset_FieldSplit;
3270:   pc->ops->destroy         = PCDestroy_FieldSplit;
3271:   pc->ops->setfromoptions  = PCSetFromOptions_FieldSplit;
3272:   pc->ops->view            = PCView_FieldSplit;
3273:   pc->ops->applyrichardson = NULL;

3275:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSchurGetSubKSP_C", PCFieldSplitSchurGetSubKSP_FieldSplit));
3276:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSubKSP_C", PCFieldSplitGetSubKSP_FieldSplit));
3277:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetFields_C", PCFieldSplitSetFields_FieldSplit));
3278:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetIS_C", PCFieldSplitSetIS_FieldSplit));
3279:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetType_C", PCFieldSplitSetType_FieldSplit));
3280:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetBlockSize_C", PCFieldSplitSetBlockSize_FieldSplit));
3281:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitRestrictIS_C", PCFieldSplitRestrictIS_FieldSplit));
3282:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCSetCoordinates_C", PCSetCoordinates_FieldSplit));
3283:   PetscFunctionReturn(PETSC_SUCCESS);
3284: }