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:           {
453:             PetscErrorCode (*func)(KSP, Mat, Mat, void *);
454:             void *ctx;

456:             PetscCall(DMKSPGetComputeOperators(pc->dm, &func, &ctx));
457:             PetscCall(DMKSPSetComputeOperators(dms[i], func, ctx));
458:           }
459:           PetscCall(PetscObjectIncrementTabLevel((PetscObject)dms[i], (PetscObject)ilink->ksp, 0));
460:           PetscCall(DMDestroy(&dms[i]));
461:         }
462:         PetscCall(PetscFree(dms));
463:       }
464:     } else {
465:       if (jac->bs <= 0) {
466:         if (pc->pmat) {
467:           PetscCall(MatGetBlockSize(pc->pmat, &jac->bs));
468:         } else jac->bs = 1;
469:       }

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

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

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

514:           PetscCall(PetscInfo(pc, "Using default splitting of fields\n"));
515:           PetscCall(PetscObjectTypeCompare((PetscObject)pc->pmat, MATNEST, &isnest));
516:           if (!isnest) {
517:             M = pc->mat;
518:             PetscCall(PetscObjectTypeCompare((PetscObject)pc->mat, MATNEST, &isnest));
519:           }
520:           if (isnest) {
521:             IS      *fields;
522:             PetscInt nf;

524:             PetscCall(MatNestGetSize(M, &nf, NULL));
525:             PetscCall(PetscMalloc1(nf, &fields));
526:             PetscCall(MatNestGetISs(M, fields, NULL));
527:             for (i = 0; i < nf; i++) PetscCall(PCFieldSplitSetIS(pc, NULL, fields[i]));
528:             PetscCall(PetscFree(fields));
529:           } else {
530:             for (i = 0; i < jac->bs; i++) {
531:               char splitname[8];
532:               PetscCall(PetscSNPrintf(splitname, sizeof(splitname), "%" PetscInt_FMT, i));
533:               PetscCall(PCFieldSplitSetFields(pc, splitname, 1, &i, &i));
534:             }
535:             jac->defaultsplit = PETSC_TRUE;
536:           }
537:         }
538:       }
539:     }
540:   } else if (jac->nsplits == 1) {
541:     IS       is2;
542:     PetscInt nmin, nmax;

544:     PetscCheck(ilink->is, PetscObjectComm((PetscObject)pc), PETSC_ERR_SUP, "Must provide at least two sets of fields to PCFieldSplit()");
545:     PetscCall(MatGetOwnershipRange(pc->mat, &nmin, &nmax));
546:     PetscCall(ISComplement(ilink->is, nmin, nmax, &is2));
547:     PetscCall(PCFieldSplitSetIS(pc, "1", is2));
548:     PetscCall(ISDestroy(&is2));
549:   }

551:   PetscCheck(jac->nsplits >= 2, PetscObjectComm((PetscObject)pc), PETSC_ERR_PLIB, "Unhandled case, must have at least two fields, not %" PetscInt_FMT, jac->nsplits);
552:   PetscFunctionReturn(PETSC_SUCCESS);
553: }

555: static PetscErrorCode MatGolubKahanComputeExplicitOperator(Mat A, Mat B, Mat C, Mat *H, PetscReal gkbnu)
556: {
557:   Mat       BT, T;
558:   PetscReal nrmT, nrmB;

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

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

573:   PetscCall(MatDestroy(&BT));
574:   PetscCall(MatDestroy(&T));
575:   PetscFunctionReturn(PETSC_SUCCESS);
576: }

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

580: static PetscErrorCode PCSetUp_FieldSplit(PC pc)
581: {
582:   PC_FieldSplit    *jac = (PC_FieldSplit *)pc->data;
583:   PC_FieldSplitLink ilink;
584:   PetscInt          i, nsplit;
585:   PetscBool         sorted, sorted_col;

587:   PetscFunctionBegin;
588:   pc->failedreason = PC_NOERROR;
589:   PetscCall(PCFieldSplitSetDefaults(pc));
590:   nsplit = jac->nsplits;
591:   ilink  = jac->head;

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

597:     jac->issetup = PETSC_TRUE;

599:     /* This is done here instead of in PCFieldSplitSetFields() because may not have matrix at that point */
600:     if (jac->defaultsplit || !ilink->is) {
601:       if (jac->bs <= 0) jac->bs = nsplit;
602:     }

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

609:       PetscCall(PetscObjectTypeCompareAny((PetscObject)pc->pmat, &blk, MATBAIJ, MATSBAIJ, MATSEQBAIJ, MATSEQSBAIJ, MATMPIBAIJ, MATMPISBAIJ, NULL));
610:       PetscCheck(!blk, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONG, "Cannot use MATBAIJ with PCFIELDSPLIT and currently set matrix and PC blocksizes");
611:     }

613:     bs = jac->bs;
614:     PetscCall(MatGetOwnershipRange(pc->pmat, &rstart, &rend));
615:     nslots = (rend - rstart) / bs;
616:     for (i = 0; i < nsplit; i++) {
617:       if (jac->defaultsplit) {
618:         PetscCall(ISCreateStride(PetscObjectComm((PetscObject)pc), nslots, rstart + i, nsplit, &ilink->is));
619:         PetscCall(ISDuplicate(ilink->is, &ilink->is_col));
620:       } else if (!ilink->is) {
621:         if (ilink->nfields > 1) {
622:           PetscInt *ii, *jj, j, k, nfields = ilink->nfields, *fields = ilink->fields, *fields_col = ilink->fields_col;
623:           PetscCall(PetscMalloc1(ilink->nfields * nslots, &ii));
624:           PetscCall(PetscMalloc1(ilink->nfields * nslots, &jj));
625:           for (j = 0; j < nslots; j++) {
626:             for (k = 0; k < nfields; k++) {
627:               ii[nfields * j + k] = rstart + bs * j + fields[k];
628:               jj[nfields * j + k] = rstart + bs * j + fields_col[k];
629:             }
630:           }
631:           PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)pc), nslots * nfields, ii, PETSC_OWN_POINTER, &ilink->is));
632:           PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)pc), nslots * nfields, jj, PETSC_OWN_POINTER, &ilink->is_col));
633:           PetscCall(ISSetBlockSize(ilink->is, nfields));
634:           PetscCall(ISSetBlockSize(ilink->is_col, nfields));
635:         } else {
636:           PetscCall(ISCreateStride(PetscObjectComm((PetscObject)pc), nslots, rstart + ilink->fields[0], bs, &ilink->is));
637:           PetscCall(ISCreateStride(PetscObjectComm((PetscObject)pc), nslots, rstart + ilink->fields_col[0], bs, &ilink->is_col));
638:         }
639:       }
640:       PetscCall(ISSorted(ilink->is, &sorted));
641:       if (ilink->is_col) PetscCall(ISSorted(ilink->is_col, &sorted_col));
642:       PetscCheck(sorted && sorted_col, PETSC_COMM_SELF, PETSC_ERR_USER, "Fields must be sorted when creating split");
643:       ilink = ilink->next;
644:     }
645:   }

647:   ilink = jac->head;
648:   if (!jac->pmat) {
649:     Vec xtmp;

651:     PetscCall(MatCreateVecs(pc->pmat, &xtmp, NULL));
652:     PetscCall(PetscMalloc1(nsplit, &jac->pmat));
653:     PetscCall(PetscMalloc2(nsplit, &jac->x, nsplit, &jac->y));
654:     for (i = 0; i < nsplit; i++) {
655:       MatNullSpace sp;

657:       /* Check for preconditioning matrix attached to IS */
658:       PetscCall(PetscObjectQuery((PetscObject)ilink->is, "pmat", (PetscObject *)&jac->pmat[i]));
659:       if (jac->pmat[i]) {
660:         PetscCall(PetscObjectReference((PetscObject)jac->pmat[i]));
661:         if (jac->type == PC_COMPOSITE_SCHUR) {
662:           jac->schur_user = jac->pmat[i];

664:           PetscCall(PetscObjectReference((PetscObject)jac->schur_user));
665:         }
666:       } else {
667:         const char *prefix;
668:         PetscCall(MatCreateSubMatrix(pc->pmat, ilink->is, ilink->is_col, MAT_INITIAL_MATRIX, &jac->pmat[i]));
669:         PetscCall(MatGetOptionsPrefix(jac->pmat[i], &prefix));
670:         if (!prefix) {
671:           PetscCall(KSPGetOptionsPrefix(ilink->ksp, &prefix));
672:           PetscCall(MatSetOptionsPrefix(jac->pmat[i], prefix));
673:         }
674:         PetscCall(MatSetFromOptions(jac->pmat[i]));
675:         PetscCall(MatViewFromOptions(jac->pmat[i], NULL, "-mat_view"));
676:       }
677:       /* create work vectors for each split */
678:       PetscCall(MatCreateVecs(jac->pmat[i], &jac->x[i], &jac->y[i]));
679:       ilink->x = jac->x[i];
680:       ilink->y = jac->y[i];
681:       ilink->z = NULL;
682:       /* compute scatter contexts needed by multiplicative versions and non-default splits */
683:       PetscCall(VecScatterCreate(xtmp, ilink->is, jac->x[i], NULL, &ilink->sctx));
684:       PetscCall(PetscObjectQuery((PetscObject)ilink->is, "nearnullspace", (PetscObject *)&sp));
685:       if (sp) PetscCall(MatSetNearNullSpace(jac->pmat[i], sp));
686:       ilink = ilink->next;
687:     }
688:     PetscCall(VecDestroy(&xtmp));
689:   } else {
690:     MatReuse      scall;
691:     MatNullSpace *nullsp = NULL;

693:     if (pc->flag == DIFFERENT_NONZERO_PATTERN) {
694:       PetscCall(MatGetNullSpaces(nsplit, jac->pmat, &nullsp));
695:       for (i = 0; i < nsplit; i++) PetscCall(MatDestroy(&jac->pmat[i]));
696:       scall = MAT_INITIAL_MATRIX;
697:     } else scall = MAT_REUSE_MATRIX;

699:     for (i = 0; i < nsplit; i++) {
700:       Mat pmat;

702:       /* Check for preconditioning matrix attached to IS */
703:       PetscCall(PetscObjectQuery((PetscObject)ilink->is, "pmat", (PetscObject *)&pmat));
704:       if (!pmat) PetscCall(MatCreateSubMatrix(pc->pmat, ilink->is, ilink->is_col, scall, &jac->pmat[i]));
705:       ilink = ilink->next;
706:     }
707:     if (nullsp) PetscCall(MatRestoreNullSpaces(nsplit, jac->pmat, &nullsp));
708:   }
709:   if (jac->diag_use_amat) {
710:     ilink = jac->head;
711:     if (!jac->mat) {
712:       PetscCall(PetscMalloc1(nsplit, &jac->mat));
713:       for (i = 0; i < nsplit; i++) {
714:         PetscCall(MatCreateSubMatrix(pc->mat, ilink->is, ilink->is_col, MAT_INITIAL_MATRIX, &jac->mat[i]));
715:         ilink = ilink->next;
716:       }
717:     } else {
718:       MatReuse      scall;
719:       MatNullSpace *nullsp = NULL;

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

727:       for (i = 0; i < nsplit; i++) {
728:         PetscCall(MatCreateSubMatrix(pc->mat, ilink->is, ilink->is_col, scall, &jac->mat[i]));
729:         ilink = ilink->next;
730:       }
731:       if (nullsp) PetscCall(MatRestoreNullSpaces(nsplit, jac->mat, &nullsp));
732:     }
733:   } else {
734:     jac->mat = jac->pmat;
735:   }

737:   /* Check for null space attached to IS */
738:   ilink = jac->head;
739:   for (i = 0; i < nsplit; i++) {
740:     MatNullSpace sp;

742:     PetscCall(PetscObjectQuery((PetscObject)ilink->is, "nullspace", (PetscObject *)&sp));
743:     if (sp) PetscCall(MatSetNullSpace(jac->mat[i], sp));
744:     ilink = ilink->next;
745:   }

747:   if (jac->type != PC_COMPOSITE_ADDITIVE && jac->type != PC_COMPOSITE_SCHUR && jac->type != PC_COMPOSITE_GKB) {
748:     /* extract the rows of the matrix associated with each field: used for efficient computation of residual inside algorithm */
749:     /* FIXME: Can/should we reuse jac->mat whenever (jac->diag_use_amat) is true? */
750:     ilink = jac->head;
751:     if (nsplit == 2 && jac->type == PC_COMPOSITE_MULTIPLICATIVE) {
752:       /* 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 */
753:       if (!jac->Afield) {
754:         PetscCall(PetscCalloc1(nsplit, &jac->Afield));
755:         if (jac->offdiag_use_amat) {
756:           PetscCall(MatCreateSubMatrix(pc->mat, ilink->next->is, ilink->is, MAT_INITIAL_MATRIX, &jac->Afield[1]));
757:         } else {
758:           PetscCall(MatCreateSubMatrix(pc->pmat, ilink->next->is, ilink->is, MAT_INITIAL_MATRIX, &jac->Afield[1]));
759:         }
760:       } else {
761:         MatReuse scall;

763:         if (pc->flag == DIFFERENT_NONZERO_PATTERN) {
764:           PetscCall(MatDestroy(&jac->Afield[1]));
765:           scall = MAT_INITIAL_MATRIX;
766:         } else scall = MAT_REUSE_MATRIX;

768:         if (jac->offdiag_use_amat) {
769:           PetscCall(MatCreateSubMatrix(pc->mat, ilink->next->is, ilink->is, scall, &jac->Afield[1]));
770:         } else {
771:           PetscCall(MatCreateSubMatrix(pc->pmat, ilink->next->is, ilink->is, scall, &jac->Afield[1]));
772:         }
773:       }
774:     } else {
775:       if (!jac->Afield) {
776:         PetscCall(PetscMalloc1(nsplit, &jac->Afield));
777:         for (i = 0; i < nsplit; i++) {
778:           if (jac->offdiag_use_amat) {
779:             PetscCall(MatCreateSubMatrix(pc->mat, ilink->is, NULL, MAT_INITIAL_MATRIX, &jac->Afield[i]));
780:           } else {
781:             PetscCall(MatCreateSubMatrix(pc->pmat, ilink->is, NULL, MAT_INITIAL_MATRIX, &jac->Afield[i]));
782:           }
783:           ilink = ilink->next;
784:         }
785:       } else {
786:         MatReuse scall;
787:         if (pc->flag == DIFFERENT_NONZERO_PATTERN) {
788:           for (i = 0; i < nsplit; i++) PetscCall(MatDestroy(&jac->Afield[i]));
789:           scall = MAT_INITIAL_MATRIX;
790:         } else scall = MAT_REUSE_MATRIX;

792:         for (i = 0; i < nsplit; i++) {
793:           if (jac->offdiag_use_amat) {
794:             PetscCall(MatCreateSubMatrix(pc->mat, ilink->is, NULL, scall, &jac->Afield[i]));
795:           } else {
796:             PetscCall(MatCreateSubMatrix(pc->pmat, ilink->is, NULL, scall, &jac->Afield[i]));
797:           }
798:           ilink = ilink->next;
799:         }
800:       }
801:     }
802:   }

804:   if (jac->type == PC_COMPOSITE_SCHUR) {
805:     IS          ccis;
806:     PetscBool   isset, isspd;
807:     PetscInt    rstart, rend;
808:     char        lscname[256];
809:     PetscObject LSC_L;
810:     PetscBool   set, flg;

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

814:     /* If pc->mat is SPD, don't scale by -1 the Schur complement */
815:     if (jac->schurscale == (PetscScalar)-1.0) {
816:       PetscCall(MatIsSPDKnown(pc->pmat, &isset, &isspd));
817:       jac->schurscale = (isset && isspd) ? 1.0 : -1.0;
818:     }

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

824:     if (jac->schur) {
825:       KSP      kspA = jac->head->ksp, kspInner = NULL, kspUpper = jac->kspupper;
826:       MatReuse scall;

828:       if (pc->flag == DIFFERENT_NONZERO_PATTERN) {
829:         scall = MAT_INITIAL_MATRIX;
830:         PetscCall(MatDestroy(&jac->B));
831:         PetscCall(MatDestroy(&jac->C));
832:       } else scall = MAT_REUSE_MATRIX;

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

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

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

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

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

924:         /* Set DM for new solver */
925:         PetscCall(KSPGetDM(jac->head->ksp, &dmInner));
926:         PetscCall(KSPSetDM(kspInner, dmInner));
927:         PetscCall(KSPSetDMActive(kspInner, PETSC_FALSE));

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

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

952:         PetscCall(MatSchurComplementGetKSP(jac->schur, &kspInner));
953:         PetscCall(KSPGetPC(kspInner, &pcInner));
954:         PetscCall(PetscObjectTypeCompare((PetscObject)pcInner, PCKSP, &flg));
955:         if (flg) {
956:           KSP ksp;

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

967:         PetscCall(PetscSNPrintf(schurprefix, sizeof(schurprefix), "%sfieldsplit_%s_upper_", ((PetscObject)pc)->prefix ? ((PetscObject)pc)->prefix : "", ilink->splitname));
968:         PetscCall(KSPCreate(PetscObjectComm((PetscObject)pc), &jac->kspupper));
969:         PetscCall(KSPSetNestLevel(jac->kspupper, pc->kspnestlevel));
970:         PetscCall(KSPSetErrorIfNotConverged(jac->kspupper, pc->erroriffailure));
971:         PetscCall(KSPSetOptionsPrefix(jac->kspupper, schurprefix));
972:         PetscCall(PetscObjectIncrementTabLevel((PetscObject)jac->kspupper, (PetscObject)pc, 1));
973:         PetscCall(PetscObjectIncrementTabLevel((PetscObject)jac->kspupper->pc, (PetscObject)pc, 1));
974:         PetscCall(KSPGetDM(jac->head->ksp, &dmInner));
975:         PetscCall(KSPSetDM(jac->kspupper, dmInner));
976:         PetscCall(KSPSetDMActive(jac->kspupper, PETSC_FALSE));
977:         PetscCall(KSPSetFromOptions(jac->kspupper));
978:         PetscCall(KSPSetOperators(jac->kspupper, jac->mat[0], jac->pmat[0]));
979:         PetscCall(VecDuplicate(jac->head->x, &jac->head->z));
980:       } else {
981:         jac->kspupper = jac->head->ksp;
982:         PetscCall(PetscObjectReference((PetscObject)jac->head->ksp));
983:       }

985:       if (jac->schurpre == PC_FIELDSPLIT_SCHUR_PRE_SELFP) PetscCall(MatSchurComplementGetPmat(jac->schur, MAT_INITIAL_MATRIX, &jac->schurp));
986:       PetscCall(KSPCreate(PetscObjectComm((PetscObject)pc), &jac->kspschur));
987:       PetscCall(KSPSetNestLevel(jac->kspschur, pc->kspnestlevel));
988:       PetscCall(KSPSetErrorIfNotConverged(jac->kspschur, pc->erroriffailure));
989:       PetscCall(PetscObjectIncrementTabLevel((PetscObject)jac->kspschur, (PetscObject)pc, 1));
990:       if (jac->schurpre == PC_FIELDSPLIT_SCHUR_PRE_SELF) {
991:         PC pcschur;
992:         PetscCall(KSPGetPC(jac->kspschur, &pcschur));
993:         PetscCall(PCSetType(pcschur, PCNONE));
994:         /* Note: This is bad if there exist preconditioners for MATSCHURCOMPLEMENT */
995:       } else if (jac->schurpre == PC_FIELDSPLIT_SCHUR_PRE_FULL) {
996:         PetscCall(MatSchurComplementComputeExplicitOperator(jac->schur, &jac->schur_user));
997:       }
998:       PetscCall(KSPSetOperators(jac->kspschur, jac->schur, FieldSplitSchurPre(jac)));
999:       PetscCall(KSPGetOptionsPrefix(jac->head->next->ksp, &Dprefix));
1000:       PetscCall(KSPSetOptionsPrefix(jac->kspschur, Dprefix));
1001:       /* propagate DM */
1002:       {
1003:         DM sdm;
1004:         PetscCall(KSPGetDM(jac->head->next->ksp, &sdm));
1005:         if (sdm) {
1006:           PetscCall(KSPSetDM(jac->kspschur, sdm));
1007:           PetscCall(KSPSetDMActive(jac->kspschur, PETSC_FALSE));
1008:         }
1009:       }
1010:       /* really want setfromoptions called in PCSetFromOptions_FieldSplit(), but it is not ready yet */
1011:       /* need to call this every time, since the jac->kspschur is freshly created, otherwise its options never get set */
1012:       PetscCall(KSPSetFromOptions(jac->kspschur));
1013:     }
1014:     PetscCall(MatAssemblyBegin(jac->schur, MAT_FINAL_ASSEMBLY));
1015:     PetscCall(MatAssemblyEnd(jac->schur, MAT_FINAL_ASSEMBLY));

1017:     /* HACK: special support to forward L and Lp matrices that might be used by PCLSC */
1018:     PetscCall(PetscSNPrintf(lscname, sizeof(lscname), "%s_LSC_L", ilink->splitname));
1019:     PetscCall(PetscObjectQuery((PetscObject)pc->mat, lscname, (PetscObject *)&LSC_L));
1020:     if (!LSC_L) PetscCall(PetscObjectQuery((PetscObject)pc->pmat, lscname, (PetscObject *)&LSC_L));
1021:     if (LSC_L) PetscCall(PetscObjectCompose((PetscObject)jac->schur, "LSC_L", (PetscObject)LSC_L));
1022:     PetscCall(PetscSNPrintf(lscname, sizeof(lscname), "%s_LSC_Lp", ilink->splitname));
1023:     PetscCall(PetscObjectQuery((PetscObject)pc->pmat, lscname, (PetscObject *)&LSC_L));
1024:     if (!LSC_L) PetscCall(PetscObjectQuery((PetscObject)pc->mat, lscname, (PetscObject *)&LSC_L));
1025:     if (LSC_L) PetscCall(PetscObjectCompose((PetscObject)jac->schur, "LSC_Lp", (PetscObject)LSC_L));
1026:   } else if (jac->type == PC_COMPOSITE_GKB) {
1027:     IS       ccis;
1028:     PetscInt rstart, rend;

1030:     PetscCheck(nsplit == 2, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_INCOMP, "To use GKB preconditioner you must have exactly 2 fields");

1032:     ilink = jac->head;

1034:     /* When extracting off-diagonal submatrices, we take complements from this range */
1035:     PetscCall(MatGetOwnershipRangeColumn(pc->mat, &rstart, &rend));

1037:     PetscCall(ISComplement(ilink->is_col, rstart, rend, &ccis));
1038:     if (jac->offdiag_use_amat) {
1039:       PetscCall(MatCreateSubMatrix(pc->mat, ilink->is, ccis, MAT_INITIAL_MATRIX, &jac->B));
1040:     } else {
1041:       PetscCall(MatCreateSubMatrix(pc->pmat, ilink->is, ccis, MAT_INITIAL_MATRIX, &jac->B));
1042:     }
1043:     PetscCall(ISDestroy(&ccis));
1044:     /* Create work vectors for GKB algorithm */
1045:     PetscCall(VecDuplicate(ilink->x, &jac->u));
1046:     PetscCall(VecDuplicate(ilink->x, &jac->Hu));
1047:     PetscCall(VecDuplicate(ilink->x, &jac->w2));
1048:     ilink = ilink->next;
1049:     PetscCall(ISComplement(ilink->is_col, rstart, rend, &ccis));
1050:     if (jac->offdiag_use_amat) {
1051:       PetscCall(MatCreateSubMatrix(pc->mat, ilink->is, ccis, MAT_INITIAL_MATRIX, &jac->C));
1052:     } else {
1053:       PetscCall(MatCreateSubMatrix(pc->pmat, ilink->is, ccis, MAT_INITIAL_MATRIX, &jac->C));
1054:     }
1055:     PetscCall(ISDestroy(&ccis));
1056:     /* Create work vectors for GKB algorithm */
1057:     PetscCall(VecDuplicate(ilink->x, &jac->v));
1058:     PetscCall(VecDuplicate(ilink->x, &jac->d));
1059:     PetscCall(VecDuplicate(ilink->x, &jac->w1));
1060:     PetscCall(MatGolubKahanComputeExplicitOperator(jac->mat[0], jac->B, jac->C, &jac->H, jac->gkbnu));
1061:     PetscCall(PetscCalloc1(jac->gkbdelay, &jac->vecz));

1063:     ilink = jac->head;
1064:     PetscCall(KSPSetOperators(ilink->ksp, jac->H, jac->H));
1065:     if (!jac->suboptionsset) PetscCall(KSPSetFromOptions(ilink->ksp));
1066:     /* Create gkb_monitor context */
1067:     if (jac->gkbmonitor) {
1068:       PetscInt tablevel;
1069:       PetscCall(PetscViewerCreate(PETSC_COMM_WORLD, &jac->gkbviewer));
1070:       PetscCall(PetscViewerSetType(jac->gkbviewer, PETSCVIEWERASCII));
1071:       PetscCall(PetscObjectGetTabLevel((PetscObject)ilink->ksp, &tablevel));
1072:       PetscCall(PetscViewerASCIISetTab(jac->gkbviewer, tablevel));
1073:       PetscCall(PetscObjectIncrementTabLevel((PetscObject)ilink->ksp, (PetscObject)ilink->ksp, 1));
1074:     }
1075:   } else {
1076:     /* set up the individual splits' PCs */
1077:     i     = 0;
1078:     ilink = jac->head;
1079:     while (ilink) {
1080:       PetscCall(KSPSetOperators(ilink->ksp, jac->mat[i], jac->pmat[i]));
1081:       /* really want setfromoptions called in PCSetFromOptions_FieldSplit(), but it is not ready yet */
1082:       if (!jac->suboptionsset) PetscCall(KSPSetFromOptions(ilink->ksp));
1083:       i++;
1084:       ilink = ilink->next;
1085:     }
1086:   }

1088:   /* Set coordinates to the sub PC objects whenever these are set */
1089:   if (jac->coordinates_set) {
1090:     PC pc_coords;
1091:     if (jac->type == PC_COMPOSITE_SCHUR) {
1092:       // Head is first block.
1093:       PetscCall(KSPGetPC(jac->head->ksp, &pc_coords));
1094:       PetscCall(PCSetCoordinates(pc_coords, jac->head->dim, jac->head->ndofs, jac->head->coords));
1095:       // Second one is Schur block, but its KSP object is in kspschur.
1096:       PetscCall(KSPGetPC(jac->kspschur, &pc_coords));
1097:       PetscCall(PCSetCoordinates(pc_coords, jac->head->next->dim, jac->head->next->ndofs, jac->head->next->coords));
1098:     } else if (jac->type == PC_COMPOSITE_GKB) {
1099:       PetscCall(PetscInfo(pc, "Warning: Setting coordinates does nothing for the GKB Fieldpslit preconditioner\n"));
1100:     } else {
1101:       ilink = jac->head;
1102:       while (ilink) {
1103:         PetscCall(KSPGetPC(ilink->ksp, &pc_coords));
1104:         PetscCall(PCSetCoordinates(pc_coords, ilink->dim, ilink->ndofs, ilink->coords));
1105:         ilink = ilink->next;
1106:       }
1107:     }
1108:   }

1110:   jac->suboptionsset = PETSC_TRUE;
1111:   PetscFunctionReturn(PETSC_SUCCESS);
1112: }

1114: #define FieldSplitSplitSolveAdd(ilink, xx, yy) \
1115:   ((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) || \
1116:                     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) || \
1117:                     VecScatterEnd(ilink->sctx, ilink->y, yy, ADD_VALUES, SCATTER_REVERSE)))

1119: static PetscErrorCode PCApply_FieldSplit_Schur(PC pc, Vec x, Vec y)
1120: {
1121:   PC_FieldSplit    *jac    = (PC_FieldSplit *)pc->data;
1122:   PC_FieldSplitLink ilinkA = jac->head, ilinkD = ilinkA->next;
1123:   KSP               kspA = ilinkA->ksp, kspLower = kspA, kspUpper = jac->kspupper;

1125:   PetscFunctionBegin;
1126:   switch (jac->schurfactorization) {
1127:   case PC_FIELDSPLIT_SCHUR_FACT_DIAG:
1128:     /* [A00 0; 0 -S], positive definite, suitable for MINRES */
1129:     PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1130:     PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1131:     PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1132:     PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1133:     PetscCall(KSPSolve(kspA, ilinkA->x, ilinkA->y));
1134:     PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1135:     PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1136:     PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1137:     PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1138:     PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1139:     PetscCall(KSPSolve(jac->kspschur, ilinkD->x, ilinkD->y));
1140:     PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y));
1141:     PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1142:     PetscCall(VecScale(ilinkD->y, jac->schurscale));
1143:     PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1144:     PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1145:     PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1146:     break;
1147:   case PC_FIELDSPLIT_SCHUR_FACT_LOWER:
1148:     /* [A00 0; A10 S], suitable for left preconditioning */
1149:     PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1150:     PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1151:     PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1152:     PetscCall(KSPSolve(kspA, ilinkA->x, ilinkA->y));
1153:     PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1154:     PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1155:     PetscCall(MatMult(jac->C, ilinkA->y, ilinkD->x));
1156:     PetscCall(VecScale(ilinkD->x, -1.));
1157:     PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD));
1158:     PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1159:     PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD));
1160:     PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1161:     PetscCall(KSPSolve(jac->kspschur, ilinkD->x, ilinkD->y));
1162:     PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y));
1163:     PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1164:     PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1165:     PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1166:     PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1167:     break;
1168:   case PC_FIELDSPLIT_SCHUR_FACT_UPPER:
1169:     /* [A00 A01; 0 S], suitable for right preconditioning */
1170:     PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1171:     PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1172:     PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1173:     PetscCall(KSPSolve(jac->kspschur, ilinkD->x, ilinkD->y));
1174:     PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y));
1175:     PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1176:     PetscCall(MatMult(jac->B, ilinkD->y, ilinkA->x));
1177:     PetscCall(VecScale(ilinkA->x, -1.));
1178:     PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, ADD_VALUES, SCATTER_FORWARD));
1179:     PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1180:     PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, ADD_VALUES, SCATTER_FORWARD));
1181:     PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1182:     PetscCall(KSPSolve(kspA, ilinkA->x, ilinkA->y));
1183:     PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1184:     PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1185:     PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1186:     PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1187:     PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1188:     break;
1189:   case PC_FIELDSPLIT_SCHUR_FACT_FULL:
1190:     /* [1 0; A10 A00^{-1} 1] [A00 0; 0 S] [1 A00^{-1}A01; 0 1] */
1191:     PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1192:     PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1193:     PetscCall(PetscLogEventBegin(KSP_Solve_FS_L, kspLower, ilinkA->x, ilinkA->y, NULL));
1194:     PetscCall(KSPSolve(kspLower, ilinkA->x, ilinkA->y));
1195:     PetscCall(KSPCheckSolve(kspLower, pc, ilinkA->y));
1196:     PetscCall(PetscLogEventEnd(KSP_Solve_FS_L, kspLower, ilinkA->x, ilinkA->y, NULL));
1197:     PetscCall(MatMult(jac->C, ilinkA->y, ilinkD->x));
1198:     PetscCall(VecScale(ilinkD->x, -1.0));
1199:     PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD));
1200:     PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD));

1202:     PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1203:     PetscCall(KSPSolve(jac->kspschur, ilinkD->x, ilinkD->y));
1204:     PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y));
1205:     PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1206:     PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));

1208:     if (kspUpper == kspA) {
1209:       PetscCall(MatMult(jac->B, ilinkD->y, ilinkA->y));
1210:       PetscCall(VecAXPY(ilinkA->x, -1.0, ilinkA->y));
1211:       PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1212:       PetscCall(KSPSolve(kspA, ilinkA->x, ilinkA->y));
1213:       PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1214:       PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1215:     } else {
1216:       PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1217:       PetscCall(KSPSolve(kspA, ilinkA->x, ilinkA->y));
1218:       PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1219:       PetscCall(MatMult(jac->B, ilinkD->y, ilinkA->x));
1220:       PetscCall(PetscLogEventBegin(KSP_Solve_FS_U, kspUpper, ilinkA->x, ilinkA->z, NULL));
1221:       PetscCall(KSPSolve(kspUpper, ilinkA->x, ilinkA->z));
1222:       PetscCall(KSPCheckSolve(kspUpper, pc, ilinkA->z));
1223:       PetscCall(PetscLogEventEnd(KSP_Solve_FS_U, kspUpper, ilinkA->x, ilinkA->z, NULL));
1224:       PetscCall(VecAXPY(ilinkA->y, -1.0, ilinkA->z));
1225:     }
1226:     PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1227:     PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1228:     PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1229:   }
1230:   PetscFunctionReturn(PETSC_SUCCESS);
1231: }

1233: static PetscErrorCode PCApplyTranspose_FieldSplit_Schur(PC pc, Vec x, Vec y)
1234: {
1235:   PC_FieldSplit    *jac    = (PC_FieldSplit *)pc->data;
1236:   PC_FieldSplitLink ilinkA = jac->head, ilinkD = ilinkA->next;
1237:   KSP               kspA = ilinkA->ksp, kspLower = kspA, kspUpper = jac->kspupper;

1239:   PetscFunctionBegin;
1240:   switch (jac->schurfactorization) {
1241:   case PC_FIELDSPLIT_SCHUR_FACT_DIAG:
1242:     /* [A00 0; 0 -S], positive definite, suitable for MINRES */
1243:     PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1244:     PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1245:     PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1246:     PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1247:     PetscCall(KSPSolveTranspose(kspA, ilinkA->x, ilinkA->y));
1248:     PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1249:     PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1250:     PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1251:     PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1252:     PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1253:     PetscCall(KSPSolveTranspose(jac->kspschur, ilinkD->x, ilinkD->y));
1254:     PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y));
1255:     PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1256:     PetscCall(VecScale(ilinkD->y, jac->schurscale));
1257:     PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1258:     PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1259:     PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1260:     break;
1261:   case PC_FIELDSPLIT_SCHUR_FACT_UPPER:
1262:     PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1263:     PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1264:     PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1265:     PetscCall(KSPSolveTranspose(kspA, ilinkA->x, ilinkA->y));
1266:     PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1267:     PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1268:     PetscCall(MatMultTranspose(jac->B, ilinkA->y, ilinkD->x));
1269:     PetscCall(VecScale(ilinkD->x, -1.));
1270:     PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD));
1271:     PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1272:     PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD));
1273:     PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1274:     PetscCall(KSPSolveTranspose(jac->kspschur, ilinkD->x, ilinkD->y));
1275:     PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y));
1276:     PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1277:     PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1278:     PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1279:     PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1280:     break;
1281:   case PC_FIELDSPLIT_SCHUR_FACT_LOWER:
1282:     PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1283:     PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1284:     PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1285:     PetscCall(KSPSolveTranspose(jac->kspschur, ilinkD->x, ilinkD->y));
1286:     PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y));
1287:     PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1288:     PetscCall(MatMultTranspose(jac->C, ilinkD->y, ilinkA->x));
1289:     PetscCall(VecScale(ilinkA->x, -1.));
1290:     PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, ADD_VALUES, SCATTER_FORWARD));
1291:     PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1292:     PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, ADD_VALUES, SCATTER_FORWARD));
1293:     PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1294:     PetscCall(KSPSolveTranspose(kspA, ilinkA->x, ilinkA->y));
1295:     PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1296:     PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1297:     PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1298:     PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1299:     PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1300:     break;
1301:   case PC_FIELDSPLIT_SCHUR_FACT_FULL:
1302:     PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1303:     PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1304:     PetscCall(PetscLogEventBegin(KSP_Solve_FS_U, kspUpper, ilinkA->x, ilinkA->y, NULL));
1305:     PetscCall(KSPSolveTranspose(kspUpper, ilinkA->x, ilinkA->y));
1306:     PetscCall(KSPCheckSolve(kspUpper, pc, ilinkA->y));
1307:     PetscCall(PetscLogEventEnd(KSP_Solve_FS_U, kspUpper, ilinkA->x, ilinkA->y, NULL));
1308:     PetscCall(MatMultTranspose(jac->B, ilinkA->y, ilinkD->x));
1309:     PetscCall(VecScale(ilinkD->x, -1.0));
1310:     PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD));
1311:     PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD));

1313:     PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1314:     PetscCall(KSPSolveTranspose(jac->kspschur, ilinkD->x, ilinkD->y));
1315:     PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y));
1316:     PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1317:     PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));

1319:     if (kspLower == kspA) {
1320:       PetscCall(MatMultTranspose(jac->C, ilinkD->y, ilinkA->y));
1321:       PetscCall(VecAXPY(ilinkA->x, -1.0, ilinkA->y));
1322:       PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1323:       PetscCall(KSPSolveTranspose(kspA, ilinkA->x, ilinkA->y));
1324:       PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1325:       PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1326:     } else {
1327:       PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1328:       PetscCall(KSPSolveTranspose(kspA, ilinkA->x, ilinkA->y));
1329:       PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1330:       PetscCall(MatMultTranspose(jac->C, ilinkD->y, ilinkA->x));
1331:       PetscCall(PetscLogEventBegin(KSP_Solve_FS_L, kspLower, ilinkA->x, ilinkA->z, NULL));
1332:       PetscCall(KSPSolveTranspose(kspLower, ilinkA->x, ilinkA->z));
1333:       PetscCall(KSPCheckSolve(kspLower, pc, ilinkA->z));
1334:       PetscCall(PetscLogEventEnd(KSP_Solve_FS_L, kspLower, ilinkA->x, ilinkA->z, NULL));
1335:       PetscCall(VecAXPY(ilinkA->y, -1.0, ilinkA->z));
1336:     }
1337:     PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1338:     PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1339:     PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1340:   }
1341:   PetscFunctionReturn(PETSC_SUCCESS);
1342: }

1344: static PetscErrorCode PCApply_FieldSplit(PC pc, Vec x, Vec y)
1345: {
1346:   PC_FieldSplit    *jac   = (PC_FieldSplit *)pc->data;
1347:   PC_FieldSplitLink ilink = jac->head;
1348:   PetscInt          cnt, bs;

1350:   PetscFunctionBegin;
1351:   if (jac->type == PC_COMPOSITE_ADDITIVE) {
1352:     if (jac->defaultsplit) {
1353:       PetscCall(VecGetBlockSize(x, &bs));
1354:       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);
1355:       PetscCall(VecGetBlockSize(y, &bs));
1356:       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);
1357:       PetscCall(VecStrideGatherAll(x, jac->x, INSERT_VALUES));
1358:       while (ilink) {
1359:         PetscCall(PetscLogEventBegin(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1360:         PetscCall(KSPSolve(ilink->ksp, ilink->x, ilink->y));
1361:         PetscCall(KSPCheckSolve(ilink->ksp, pc, ilink->y));
1362:         PetscCall(PetscLogEventEnd(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1363:         ilink = ilink->next;
1364:       }
1365:       PetscCall(VecStrideScatterAll(jac->y, y, INSERT_VALUES));
1366:     } else {
1367:       PetscCall(VecSet(y, 0.0));
1368:       while (ilink) {
1369:         PetscCall(FieldSplitSplitSolveAdd(ilink, x, y));
1370:         ilink = ilink->next;
1371:       }
1372:     }
1373:   } else if (jac->type == PC_COMPOSITE_MULTIPLICATIVE && jac->nsplits == 2) {
1374:     PetscCall(VecSet(y, 0.0));
1375:     /* solve on first block for first block variables */
1376:     PetscCall(VecScatterBegin(ilink->sctx, x, ilink->x, INSERT_VALUES, SCATTER_FORWARD));
1377:     PetscCall(VecScatterEnd(ilink->sctx, x, ilink->x, INSERT_VALUES, SCATTER_FORWARD));
1378:     PetscCall(PetscLogEventBegin(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1379:     PetscCall(KSPSolve(ilink->ksp, ilink->x, ilink->y));
1380:     PetscCall(KSPCheckSolve(ilink->ksp, pc, ilink->y));
1381:     PetscCall(PetscLogEventEnd(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1382:     PetscCall(VecScatterBegin(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE));
1383:     PetscCall(VecScatterEnd(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE));

1385:     /* compute the residual only onto second block variables using first block variables */
1386:     PetscCall(MatMult(jac->Afield[1], ilink->y, ilink->next->x));
1387:     ilink = ilink->next;
1388:     PetscCall(VecScale(ilink->x, -1.0));
1389:     PetscCall(VecScatterBegin(ilink->sctx, x, ilink->x, ADD_VALUES, SCATTER_FORWARD));
1390:     PetscCall(VecScatterEnd(ilink->sctx, x, ilink->x, ADD_VALUES, SCATTER_FORWARD));

1392:     /* solve on second block variables */
1393:     PetscCall(PetscLogEventBegin(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1394:     PetscCall(KSPSolve(ilink->ksp, ilink->x, ilink->y));
1395:     PetscCall(KSPCheckSolve(ilink->ksp, pc, ilink->y));
1396:     PetscCall(PetscLogEventEnd(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1397:     PetscCall(VecScatterBegin(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE));
1398:     PetscCall(VecScatterEnd(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE));
1399:   } else if (jac->type == PC_COMPOSITE_MULTIPLICATIVE || jac->type == PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE) {
1400:     if (!jac->w1) {
1401:       PetscCall(VecDuplicate(x, &jac->w1));
1402:       PetscCall(VecDuplicate(x, &jac->w2));
1403:     }
1404:     PetscCall(VecSet(y, 0.0));
1405:     PetscCall(FieldSplitSplitSolveAdd(ilink, x, y));
1406:     cnt = 1;
1407:     while (ilink->next) {
1408:       ilink = ilink->next;
1409:       /* compute the residual only over the part of the vector needed */
1410:       PetscCall(MatMult(jac->Afield[cnt++], y, ilink->x));
1411:       PetscCall(VecScale(ilink->x, -1.0));
1412:       PetscCall(VecScatterBegin(ilink->sctx, x, ilink->x, ADD_VALUES, SCATTER_FORWARD));
1413:       PetscCall(VecScatterEnd(ilink->sctx, x, ilink->x, ADD_VALUES, SCATTER_FORWARD));
1414:       PetscCall(PetscLogEventBegin(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1415:       PetscCall(KSPSolve(ilink->ksp, ilink->x, ilink->y));
1416:       PetscCall(KSPCheckSolve(ilink->ksp, pc, ilink->y));
1417:       PetscCall(PetscLogEventEnd(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1418:       PetscCall(VecScatterBegin(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE));
1419:       PetscCall(VecScatterEnd(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE));
1420:     }
1421:     if (jac->type == PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE) {
1422:       cnt -= 2;
1423:       while (ilink->previous) {
1424:         ilink = ilink->previous;
1425:         /* compute the residual only over the part of the vector needed */
1426:         PetscCall(MatMult(jac->Afield[cnt--], y, ilink->x));
1427:         PetscCall(VecScale(ilink->x, -1.0));
1428:         PetscCall(VecScatterBegin(ilink->sctx, x, ilink->x, ADD_VALUES, SCATTER_FORWARD));
1429:         PetscCall(VecScatterEnd(ilink->sctx, x, ilink->x, ADD_VALUES, SCATTER_FORWARD));
1430:         PetscCall(PetscLogEventBegin(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1431:         PetscCall(KSPSolve(ilink->ksp, ilink->x, ilink->y));
1432:         PetscCall(KSPCheckSolve(ilink->ksp, pc, ilink->y));
1433:         PetscCall(PetscLogEventEnd(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1434:         PetscCall(VecScatterBegin(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE));
1435:         PetscCall(VecScatterEnd(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE));
1436:       }
1437:     }
1438:   } else SETERRQ(PetscObjectComm((PetscObject)pc), PETSC_ERR_SUP, "Unsupported or unknown composition %d", (int)jac->type);
1439:   PetscFunctionReturn(PETSC_SUCCESS);
1440: }

1442: static PetscErrorCode PCApply_FieldSplit_GKB(PC pc, Vec x, Vec y)
1443: {
1444:   PC_FieldSplit    *jac    = (PC_FieldSplit *)pc->data;
1445:   PC_FieldSplitLink ilinkA = jac->head, ilinkD = ilinkA->next;
1446:   KSP               ksp = ilinkA->ksp;
1447:   Vec               u, v, Hu, d, work1, work2;
1448:   PetscScalar       alpha, z, nrmz2, *vecz;
1449:   PetscReal         lowbnd, nu, beta;
1450:   PetscInt          j, iterGKB;

1452:   PetscFunctionBegin;
1453:   PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1454:   PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1455:   PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1456:   PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));

1458:   u     = jac->u;
1459:   v     = jac->v;
1460:   Hu    = jac->Hu;
1461:   d     = jac->d;
1462:   work1 = jac->w1;
1463:   work2 = jac->w2;
1464:   vecz  = jac->vecz;

1466:   /* Change RHS to comply with matrix regularization H = A + nu*B*B' */
1467:   /* Add q = q + nu*B*b */
1468:   if (jac->gkbnu) {
1469:     nu = jac->gkbnu;
1470:     PetscCall(VecScale(ilinkD->x, jac->gkbnu));
1471:     PetscCall(MatMultAdd(jac->B, ilinkD->x, ilinkA->x, ilinkA->x)); /* q = q + nu*B*b */
1472:   } else {
1473:     /* Situation when no augmented Lagrangian is used. Then we set inner  */
1474:     /* matrix N = I in [Ar13], and thus nu = 1.                           */
1475:     nu = 1;
1476:   }

1478:   /* Transform rhs from [q,tilde{b}] to [0,b] */
1479:   PetscCall(PetscLogEventBegin(ilinkA->event, ksp, ilinkA->x, ilinkA->y, NULL));
1480:   PetscCall(KSPSolve(ksp, ilinkA->x, ilinkA->y));
1481:   PetscCall(KSPCheckSolve(ksp, pc, ilinkA->y));
1482:   PetscCall(PetscLogEventEnd(ilinkA->event, ksp, ilinkA->x, ilinkA->y, NULL));
1483:   PetscCall(MatMultHermitianTranspose(jac->B, ilinkA->y, work1));
1484:   PetscCall(VecAXPBY(work1, 1.0 / nu, -1.0, ilinkD->x)); /* c = b - B'*x        */

1486:   /* First step of algorithm */
1487:   PetscCall(VecNorm(work1, NORM_2, &beta)); /* beta = sqrt(nu*c'*c)*/
1488:   KSPCheckDot(ksp, beta);
1489:   beta = PetscSqrtReal(nu) * beta;
1490:   PetscCall(VecAXPBY(v, nu / beta, 0.0, work1)); /* v = nu/beta *c      */
1491:   PetscCall(MatMult(jac->B, v, work2));          /* u = H^{-1}*B*v      */
1492:   PetscCall(PetscLogEventBegin(ilinkA->event, ksp, work2, u, NULL));
1493:   PetscCall(KSPSolve(ksp, work2, u));
1494:   PetscCall(KSPCheckSolve(ksp, pc, u));
1495:   PetscCall(PetscLogEventEnd(ilinkA->event, ksp, work2, u, NULL));
1496:   PetscCall(MatMult(jac->H, u, Hu)); /* alpha = u'*H*u      */
1497:   PetscCall(VecDot(Hu, u, &alpha));
1498:   KSPCheckDot(ksp, alpha);
1499:   PetscCheck(PetscRealPart(alpha) > 0.0, PETSC_COMM_SELF, PETSC_ERR_NOT_CONVERGED, "GKB preconditioner diverged, H is not positive definite");
1500:   alpha = PetscSqrtReal(PetscAbsScalar(alpha));
1501:   PetscCall(VecScale(u, 1.0 / alpha));
1502:   PetscCall(VecAXPBY(d, 1.0 / alpha, 0.0, v)); /* v = nu/beta *c      */

1504:   z       = beta / alpha;
1505:   vecz[1] = z;

1507:   /* Computation of first iterate x(1) and p(1) */
1508:   PetscCall(VecAXPY(ilinkA->y, z, u));
1509:   PetscCall(VecCopy(d, ilinkD->y));
1510:   PetscCall(VecScale(ilinkD->y, -z));

1512:   iterGKB = 1;
1513:   lowbnd  = 2 * jac->gkbtol;
1514:   if (jac->gkbmonitor) PetscCall(PetscViewerASCIIPrintf(jac->gkbviewer, "%3" PetscInt_FMT " GKB Lower bound estimate %14.12e\n", iterGKB, (double)lowbnd));

1516:   while (iterGKB < jac->gkbmaxit && lowbnd > jac->gkbtol) {
1517:     iterGKB += 1;
1518:     PetscCall(MatMultHermitianTranspose(jac->B, u, work1)); /* v <- nu*(B'*u-alpha/nu*v) */
1519:     PetscCall(VecAXPBY(v, nu, -alpha, work1));
1520:     PetscCall(VecNorm(v, NORM_2, &beta)); /* beta = sqrt(nu)*v'*v      */
1521:     beta = beta / PetscSqrtReal(nu);
1522:     PetscCall(VecScale(v, 1.0 / beta));
1523:     PetscCall(MatMult(jac->B, v, work2)); /* u <- H^{-1}*(B*v-beta*H*u) */
1524:     PetscCall(MatMult(jac->H, u, Hu));
1525:     PetscCall(VecAXPY(work2, -beta, Hu));
1526:     PetscCall(PetscLogEventBegin(ilinkA->event, ksp, work2, u, NULL));
1527:     PetscCall(KSPSolve(ksp, work2, u));
1528:     PetscCall(KSPCheckSolve(ksp, pc, u));
1529:     PetscCall(PetscLogEventEnd(ilinkA->event, ksp, work2, u, NULL));
1530:     PetscCall(MatMult(jac->H, u, Hu)); /* alpha = u'*H*u            */
1531:     PetscCall(VecDot(Hu, u, &alpha));
1532:     KSPCheckDot(ksp, alpha);
1533:     PetscCheck(PetscRealPart(alpha) > 0.0, PETSC_COMM_SELF, PETSC_ERR_NOT_CONVERGED, "GKB preconditioner diverged, H is not positive definite");
1534:     alpha = PetscSqrtReal(PetscAbsScalar(alpha));
1535:     PetscCall(VecScale(u, 1.0 / alpha));

1537:     z       = -beta / alpha * z; /* z <- beta/alpha*z     */
1538:     vecz[0] = z;

1540:     /* Computation of new iterate x(i+1) and p(i+1) */
1541:     PetscCall(VecAXPBY(d, 1.0 / alpha, -beta / alpha, v)); /* d = (v-beta*d)/alpha */
1542:     PetscCall(VecAXPY(ilinkA->y, z, u));                   /* r = r + z*u          */
1543:     PetscCall(VecAXPY(ilinkD->y, -z, d));                  /* p = p - z*d          */
1544:     PetscCall(MatMult(jac->H, ilinkA->y, Hu));             /* ||u||_H = u'*H*u     */
1545:     PetscCall(VecDot(Hu, ilinkA->y, &nrmz2));

1547:     /* Compute Lower Bound estimate */
1548:     if (iterGKB > jac->gkbdelay) {
1549:       lowbnd = 0.0;
1550:       for (j = 0; j < jac->gkbdelay; j++) lowbnd += PetscAbsScalar(vecz[j] * vecz[j]);
1551:       lowbnd = PetscSqrtReal(lowbnd / PetscAbsScalar(nrmz2));
1552:     }

1554:     for (j = 0; j < jac->gkbdelay - 1; j++) vecz[jac->gkbdelay - j - 1] = vecz[jac->gkbdelay - j - 2];
1555:     if (jac->gkbmonitor) PetscCall(PetscViewerASCIIPrintf(jac->gkbviewer, "%3" PetscInt_FMT " GKB Lower bound estimate %14.12e\n", iterGKB, (double)lowbnd));
1556:   }

1558:   PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1559:   PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1560:   PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1561:   PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1562:   PetscFunctionReturn(PETSC_SUCCESS);
1563: }

1565: #define FieldSplitSplitSolveAddTranspose(ilink, xx, yy) \
1566:   ((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) || \
1567:                     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) || \
1568:                     VecScatterEnd(ilink->sctx, ilink->x, yy, ADD_VALUES, SCATTER_REVERSE)))

1570: static PetscErrorCode PCApplyTranspose_FieldSplit(PC pc, Vec x, Vec y)
1571: {
1572:   PC_FieldSplit    *jac   = (PC_FieldSplit *)pc->data;
1573:   PC_FieldSplitLink ilink = jac->head;
1574:   PetscInt          bs;

1576:   PetscFunctionBegin;
1577:   if (jac->type == PC_COMPOSITE_ADDITIVE) {
1578:     if (jac->defaultsplit) {
1579:       PetscCall(VecGetBlockSize(x, &bs));
1580:       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);
1581:       PetscCall(VecGetBlockSize(y, &bs));
1582:       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);
1583:       PetscCall(VecStrideGatherAll(x, jac->x, INSERT_VALUES));
1584:       while (ilink) {
1585:         PetscCall(PetscLogEventBegin(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1586:         PetscCall(KSPSolveTranspose(ilink->ksp, ilink->x, ilink->y));
1587:         PetscCall(KSPCheckSolve(ilink->ksp, pc, ilink->y));
1588:         PetscCall(PetscLogEventEnd(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1589:         ilink = ilink->next;
1590:       }
1591:       PetscCall(VecStrideScatterAll(jac->y, y, INSERT_VALUES));
1592:     } else {
1593:       PetscCall(VecSet(y, 0.0));
1594:       while (ilink) {
1595:         PetscCall(FieldSplitSplitSolveAddTranspose(ilink, x, y));
1596:         ilink = ilink->next;
1597:       }
1598:     }
1599:   } else {
1600:     if (!jac->w1) {
1601:       PetscCall(VecDuplicate(x, &jac->w1));
1602:       PetscCall(VecDuplicate(x, &jac->w2));
1603:     }
1604:     PetscCall(VecSet(y, 0.0));
1605:     if (jac->type == PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE) {
1606:       PetscCall(FieldSplitSplitSolveAddTranspose(ilink, x, y));
1607:       while (ilink->next) {
1608:         ilink = ilink->next;
1609:         PetscCall(MatMultTranspose(pc->mat, y, jac->w1));
1610:         PetscCall(VecWAXPY(jac->w2, -1.0, jac->w1, x));
1611:         PetscCall(FieldSplitSplitSolveAddTranspose(ilink, jac->w2, y));
1612:       }
1613:       while (ilink->previous) {
1614:         ilink = ilink->previous;
1615:         PetscCall(MatMultTranspose(pc->mat, y, jac->w1));
1616:         PetscCall(VecWAXPY(jac->w2, -1.0, jac->w1, x));
1617:         PetscCall(FieldSplitSplitSolveAddTranspose(ilink, jac->w2, y));
1618:       }
1619:     } else {
1620:       while (ilink->next) { /* get to last entry in linked list */
1621:         ilink = ilink->next;
1622:       }
1623:       PetscCall(FieldSplitSplitSolveAddTranspose(ilink, x, y));
1624:       while (ilink->previous) {
1625:         ilink = ilink->previous;
1626:         PetscCall(MatMultTranspose(pc->mat, y, jac->w1));
1627:         PetscCall(VecWAXPY(jac->w2, -1.0, jac->w1, x));
1628:         PetscCall(FieldSplitSplitSolveAddTranspose(ilink, jac->w2, y));
1629:       }
1630:     }
1631:   }
1632:   PetscFunctionReturn(PETSC_SUCCESS);
1633: }

1635: static PetscErrorCode PCReset_FieldSplit(PC pc)
1636: {
1637:   PC_FieldSplit    *jac   = (PC_FieldSplit *)pc->data;
1638:   PC_FieldSplitLink ilink = jac->head, next;

1640:   PetscFunctionBegin;
1641:   while (ilink) {
1642:     PetscCall(KSPDestroy(&ilink->ksp));
1643:     PetscCall(VecDestroy(&ilink->x));
1644:     PetscCall(VecDestroy(&ilink->y));
1645:     PetscCall(VecDestroy(&ilink->z));
1646:     PetscCall(VecScatterDestroy(&ilink->sctx));
1647:     PetscCall(ISDestroy(&ilink->is));
1648:     PetscCall(ISDestroy(&ilink->is_col));
1649:     PetscCall(PetscFree(ilink->splitname));
1650:     PetscCall(PetscFree(ilink->fields));
1651:     PetscCall(PetscFree(ilink->fields_col));
1652:     next = ilink->next;
1653:     PetscCall(PetscFree(ilink));
1654:     ilink = next;
1655:   }
1656:   jac->head = NULL;
1657:   PetscCall(PetscFree2(jac->x, jac->y));
1658:   if (jac->mat && jac->mat != jac->pmat) {
1659:     PetscCall(MatDestroyMatrices(jac->nsplits, &jac->mat));
1660:   } else if (jac->mat) {
1661:     jac->mat = NULL;
1662:   }
1663:   if (jac->pmat) PetscCall(MatDestroyMatrices(jac->nsplits, &jac->pmat));
1664:   if (jac->Afield) PetscCall(MatDestroyMatrices(jac->nsplits, &jac->Afield));
1665:   jac->nsplits = 0;
1666:   PetscCall(VecDestroy(&jac->w1));
1667:   PetscCall(VecDestroy(&jac->w2));
1668:   PetscCall(MatDestroy(&jac->schur));
1669:   PetscCall(MatDestroy(&jac->schurp));
1670:   PetscCall(MatDestroy(&jac->schur_user));
1671:   PetscCall(KSPDestroy(&jac->kspschur));
1672:   PetscCall(KSPDestroy(&jac->kspupper));
1673:   PetscCall(MatDestroy(&jac->B));
1674:   PetscCall(MatDestroy(&jac->C));
1675:   PetscCall(MatDestroy(&jac->H));
1676:   PetscCall(VecDestroy(&jac->u));
1677:   PetscCall(VecDestroy(&jac->v));
1678:   PetscCall(VecDestroy(&jac->Hu));
1679:   PetscCall(VecDestroy(&jac->d));
1680:   PetscCall(PetscFree(jac->vecz));
1681:   PetscCall(PetscViewerDestroy(&jac->gkbviewer));
1682:   jac->isrestrict = PETSC_FALSE;
1683:   PetscFunctionReturn(PETSC_SUCCESS);
1684: }

1686: static PetscErrorCode PCDestroy_FieldSplit(PC pc)
1687: {
1688:   PetscFunctionBegin;
1689:   PetscCall(PCReset_FieldSplit(pc));
1690:   PetscCall(PetscFree(pc->data));
1691:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCSetCoordinates_C", NULL));
1692:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetFields_C", NULL));
1693:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetIS_C", NULL));
1694:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetType_C", NULL));
1695:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetBlockSize_C", NULL));
1696:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitRestrictIS_C", NULL));
1697:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSchurGetSubKSP_C", NULL));
1698:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSubKSP_C", NULL));

1700:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBTol_C", NULL));
1701:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBMaxit_C", NULL));
1702:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBNu_C", NULL));
1703:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBDelay_C", NULL));
1704:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSubKSP_C", NULL));
1705:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurPre_C", NULL));
1706:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSchurPre_C", NULL));
1707:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurFactType_C", NULL));
1708:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurScale_C", NULL));
1709:   PetscFunctionReturn(PETSC_SUCCESS);
1710: }

1712: static PetscErrorCode PCSetFromOptions_FieldSplit(PC pc, PetscOptionItems *PetscOptionsObject)
1713: {
1714:   PetscInt        bs;
1715:   PetscBool       flg;
1716:   PC_FieldSplit  *jac = (PC_FieldSplit *)pc->data;
1717:   PCCompositeType ctype;

1719:   PetscFunctionBegin;
1720:   PetscOptionsHeadBegin(PetscOptionsObject, "FieldSplit options");
1721:   PetscCall(PetscOptionsBool("-pc_fieldsplit_dm_splits", "Whether to use DMCreateFieldDecomposition() for splits", "PCFieldSplitSetDMSplits", jac->dm_splits, &jac->dm_splits, NULL));
1722:   PetscCall(PetscOptionsInt("-pc_fieldsplit_block_size", "Blocksize that defines number of fields", "PCFieldSplitSetBlockSize", jac->bs, &bs, &flg));
1723:   if (flg) PetscCall(PCFieldSplitSetBlockSize(pc, bs));
1724:   jac->diag_use_amat = pc->useAmat;
1725:   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));
1726:   jac->offdiag_use_amat = pc->useAmat;
1727:   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));
1728:   PetscCall(PetscOptionsBool("-pc_fieldsplit_detect_saddle_point", "Form 2-way split by detecting zero diagonal entries", "PCFieldSplitSetDetectSaddlePoint", jac->detect, &jac->detect, NULL));
1729:   PetscCall(PCFieldSplitSetDetectSaddlePoint(pc, jac->detect)); /* Sets split type and Schur PC type */
1730:   PetscCall(PetscOptionsEnum("-pc_fieldsplit_type", "Type of composition", "PCFieldSplitSetType", PCCompositeTypes, (PetscEnum)jac->type, (PetscEnum *)&ctype, &flg));
1731:   if (flg) PetscCall(PCFieldSplitSetType(pc, ctype));
1732:   /* Only setup fields once */
1733:   if ((jac->bs > 0) && (jac->nsplits == 0)) {
1734:     /* only allow user to set fields from command line if bs is already known.
1735:        otherwise user can set them in PCFieldSplitSetDefaults() */
1736:     PetscCall(PCFieldSplitSetRuntimeSplits_Private(pc));
1737:     if (jac->splitdefined) PetscCall(PetscInfo(pc, "Splits defined using the options database\n"));
1738:   }
1739:   if (jac->type == PC_COMPOSITE_SCHUR) {
1740:     PetscCall(PetscOptionsGetEnum(((PetscObject)pc)->options, ((PetscObject)pc)->prefix, "-pc_fieldsplit_schur_factorization_type", PCFieldSplitSchurFactTypes, (PetscEnum *)&jac->schurfactorization, &flg));
1741:     if (flg) PetscCall(PetscInfo(pc, "Deprecated use of -pc_fieldsplit_schur_factorization_type\n"));
1742:     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));
1743:     PetscCall(PetscOptionsEnum("-pc_fieldsplit_schur_precondition", "How to build preconditioner for Schur complement", "PCFieldSplitSetSchurPre", PCFieldSplitSchurPreTypes, (PetscEnum)jac->schurpre, (PetscEnum *)&jac->schurpre, NULL));
1744:     PetscCall(PetscOptionsScalar("-pc_fieldsplit_schur_scale", "Scale Schur complement", "PCFieldSplitSetSchurScale", jac->schurscale, &jac->schurscale, NULL));
1745:   } else if (jac->type == PC_COMPOSITE_GKB) {
1746:     PetscCall(PetscOptionsReal("-pc_fieldsplit_gkb_tol", "The tolerance for the lower bound stopping criterion", "PCFieldSplitGKBTol", jac->gkbtol, &jac->gkbtol, NULL));
1747:     PetscCall(PetscOptionsInt("-pc_fieldsplit_gkb_delay", "The delay value for lower bound criterion", "PCFieldSplitGKBDelay", jac->gkbdelay, &jac->gkbdelay, NULL));
1748:     PetscCall(PetscOptionsBoundedReal("-pc_fieldsplit_gkb_nu", "Parameter in augmented Lagrangian approach", "PCFieldSplitGKBNu", jac->gkbnu, &jac->gkbnu, NULL, 0.0));
1749:     PetscCall(PetscOptionsInt("-pc_fieldsplit_gkb_maxit", "Maximum allowed number of iterations", "PCFieldSplitGKBMaxit", jac->gkbmaxit, &jac->gkbmaxit, NULL));
1750:     PetscCall(PetscOptionsBool("-pc_fieldsplit_gkb_monitor", "Prints number of GKB iterations and error", "PCFieldSplitGKB", jac->gkbmonitor, &jac->gkbmonitor, NULL));
1751:   }
1752:   /*
1753:     In the initial call to this routine the sub-solver data structures do not exist so we cannot call KSPSetFromOptions() on them yet.
1754:     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
1755:     is called on the outer solver in case changes were made in the options database

1757:     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()
1758:     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.
1759:     Without this extra check test p2p1fetidp_olof_full and others fail with incorrect matrix types.

1761:     There could be a negative side effect of calling the KSPSetFromOptions() below.

1763:     If one captured the PetscObjectState of the options database one could skip these calls if the database has not changed from the previous call
1764:   */
1765:   if (jac->issetup) {
1766:     PC_FieldSplitLink ilink = jac->head;
1767:     if (jac->type == PC_COMPOSITE_SCHUR) {
1768:       if (jac->kspupper && jac->kspupper->totalits > 0) PetscCall(KSPSetFromOptions(jac->kspupper));
1769:       if (jac->kspschur && jac->kspschur->totalits > 0) PetscCall(KSPSetFromOptions(jac->kspschur));
1770:     }
1771:     while (ilink) {
1772:       if (ilink->ksp->totalits > 0) PetscCall(KSPSetFromOptions(ilink->ksp));
1773:       ilink = ilink->next;
1774:     }
1775:   }
1776:   PetscOptionsHeadEnd();
1777:   PetscFunctionReturn(PETSC_SUCCESS);
1778: }

1780: static PetscErrorCode PCFieldSplitSetFields_FieldSplit(PC pc, const char splitname[], PetscInt n, const PetscInt *fields, const PetscInt *fields_col)
1781: {
1782:   PC_FieldSplit    *jac = (PC_FieldSplit *)pc->data;
1783:   PC_FieldSplitLink ilink, next = jac->head;
1784:   char              prefix[128];
1785:   PetscInt          i;

1787:   PetscFunctionBegin;
1788:   if (jac->splitdefined) {
1789:     PetscCall(PetscInfo(pc, "Ignoring new split \"%s\" because the splits have already been defined\n", splitname));
1790:     PetscFunctionReturn(PETSC_SUCCESS);
1791:   }
1792:   for (i = 0; i < n; i++) {
1793:     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);
1794:     PetscCheck(fields[i] >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Negative field %" PetscInt_FMT " requested", fields[i]);
1795:   }
1796:   PetscCall(PetscNew(&ilink));
1797:   if (splitname) {
1798:     PetscCall(PetscStrallocpy(splitname, &ilink->splitname));
1799:   } else {
1800:     PetscCall(PetscMalloc1(3, &ilink->splitname));
1801:     PetscCall(PetscSNPrintf(ilink->splitname, 2, "%" PetscInt_FMT, jac->nsplits));
1802:   }
1803:   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 */
1804:   PetscCall(PetscMalloc1(n, &ilink->fields));
1805:   PetscCall(PetscArraycpy(ilink->fields, fields, n));
1806:   PetscCall(PetscMalloc1(n, &ilink->fields_col));
1807:   PetscCall(PetscArraycpy(ilink->fields_col, fields_col, n));

1809:   ilink->nfields = n;
1810:   ilink->next    = NULL;
1811:   PetscCall(KSPCreate(PetscObjectComm((PetscObject)pc), &ilink->ksp));
1812:   PetscCall(KSPSetNestLevel(ilink->ksp, pc->kspnestlevel));
1813:   PetscCall(KSPSetErrorIfNotConverged(ilink->ksp, pc->erroriffailure));
1814:   PetscCall(PetscObjectIncrementTabLevel((PetscObject)ilink->ksp, (PetscObject)pc, 1));
1815:   PetscCall(KSPSetType(ilink->ksp, KSPPREONLY));

1817:   PetscCall(PetscSNPrintf(prefix, sizeof(prefix), "%sfieldsplit_%s_", ((PetscObject)pc)->prefix ? ((PetscObject)pc)->prefix : "", ilink->splitname));
1818:   PetscCall(KSPSetOptionsPrefix(ilink->ksp, prefix));

1820:   if (!next) {
1821:     jac->head       = ilink;
1822:     ilink->previous = NULL;
1823:   } else {
1824:     while (next->next) next = next->next;
1825:     next->next      = ilink;
1826:     ilink->previous = next;
1827:   }
1828:   jac->nsplits++;
1829:   PetscFunctionReturn(PETSC_SUCCESS);
1830: }

1832: static PetscErrorCode PCFieldSplitSchurGetSubKSP_FieldSplit(PC pc, PetscInt *n, KSP **subksp)
1833: {
1834:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

1836:   PetscFunctionBegin;
1837:   *subksp = NULL;
1838:   if (n) *n = 0;
1839:   if (jac->type == PC_COMPOSITE_SCHUR) {
1840:     PetscInt nn;

1842:     PetscCheck(jac->schur, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONGSTATE, "Must call KSPSetUp() or PCSetUp() before calling PCFieldSplitSchurGetSubKSP()");
1843:     PetscCheck(jac->nsplits == 2, PetscObjectComm((PetscObject)pc), PETSC_ERR_PLIB, "Unexpected number of splits %" PetscInt_FMT " != 2", jac->nsplits);
1844:     nn = jac->nsplits + (jac->kspupper != jac->head->ksp ? 1 : 0);
1845:     PetscCall(PetscMalloc1(nn, subksp));
1846:     (*subksp)[0] = jac->head->ksp;
1847:     (*subksp)[1] = jac->kspschur;
1848:     if (jac->kspupper != jac->head->ksp) (*subksp)[2] = jac->kspupper;
1849:     if (n) *n = nn;
1850:   }
1851:   PetscFunctionReturn(PETSC_SUCCESS);
1852: }

1854: static PetscErrorCode PCFieldSplitGetSubKSP_FieldSplit_Schur(PC pc, PetscInt *n, KSP **subksp)
1855: {
1856:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

1858:   PetscFunctionBegin;
1859:   PetscCheck(jac->schur, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONGSTATE, "Must call KSPSetUp() or PCSetUp() before calling PCFieldSplitGetSubKSP()");
1860:   PetscCall(PetscMalloc1(jac->nsplits, subksp));
1861:   PetscCall(MatSchurComplementGetKSP(jac->schur, *subksp));

1863:   (*subksp)[1] = jac->kspschur;
1864:   if (n) *n = jac->nsplits;
1865:   PetscFunctionReturn(PETSC_SUCCESS);
1866: }

1868: static PetscErrorCode PCFieldSplitGetSubKSP_FieldSplit(PC pc, PetscInt *n, KSP **subksp)
1869: {
1870:   PC_FieldSplit    *jac   = (PC_FieldSplit *)pc->data;
1871:   PetscInt          cnt   = 0;
1872:   PC_FieldSplitLink ilink = jac->head;

1874:   PetscFunctionBegin;
1875:   PetscCall(PetscMalloc1(jac->nsplits, subksp));
1876:   while (ilink) {
1877:     (*subksp)[cnt++] = ilink->ksp;
1878:     ilink            = ilink->next;
1879:   }
1880:   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);
1881:   if (n) *n = jac->nsplits;
1882:   PetscFunctionReturn(PETSC_SUCCESS);
1883: }

1885: /*@C
1886:   PCFieldSplitRestrictIS - Restricts the fieldsplit `IS`s to be within a given `IS`.

1888:   Input Parameters:
1889: + pc  - the preconditioner context
1890: - isy - the index set that defines the indices to which the fieldsplit is to be restricted

1892:   Level: advanced

1894:   Developer Notes:
1895:   It seems the resulting `IS`s will not cover the entire space, so
1896:   how can they define a convergent preconditioner? Needs explaining.

1898: .seealso: [](sec_block_matrices), `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSetIS()`
1899: @*/
1900: PetscErrorCode PCFieldSplitRestrictIS(PC pc, IS isy)
1901: {
1902:   PetscFunctionBegin;
1905:   PetscTryMethod(pc, "PCFieldSplitRestrictIS_C", (PC, IS), (pc, isy));
1906:   PetscFunctionReturn(PETSC_SUCCESS);
1907: }

1909: static PetscErrorCode PCFieldSplitRestrictIS_FieldSplit(PC pc, IS isy)
1910: {
1911:   PC_FieldSplit    *jac   = (PC_FieldSplit *)pc->data;
1912:   PC_FieldSplitLink ilink = jac->head, next;
1913:   PetscInt          localsize, size, sizez, i;
1914:   const PetscInt   *ind, *indz;
1915:   PetscInt         *indc, *indcz;
1916:   PetscBool         flg;

1918:   PetscFunctionBegin;
1919:   PetscCall(ISGetLocalSize(isy, &localsize));
1920:   PetscCallMPI(MPI_Scan(&localsize, &size, 1, MPIU_INT, MPI_SUM, PetscObjectComm((PetscObject)isy)));
1921:   size -= localsize;
1922:   while (ilink) {
1923:     IS isrl, isr;
1924:     PC subpc;
1925:     PetscCall(ISEmbed(ilink->is, isy, PETSC_TRUE, &isrl));
1926:     PetscCall(ISGetLocalSize(isrl, &localsize));
1927:     PetscCall(PetscMalloc1(localsize, &indc));
1928:     PetscCall(ISGetIndices(isrl, &ind));
1929:     PetscCall(PetscArraycpy(indc, ind, localsize));
1930:     PetscCall(ISRestoreIndices(isrl, &ind));
1931:     PetscCall(ISDestroy(&isrl));
1932:     for (i = 0; i < localsize; i++) *(indc + i) += size;
1933:     PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)isy), localsize, indc, PETSC_OWN_POINTER, &isr));
1934:     PetscCall(PetscObjectReference((PetscObject)isr));
1935:     PetscCall(ISDestroy(&ilink->is));
1936:     ilink->is = isr;
1937:     PetscCall(PetscObjectReference((PetscObject)isr));
1938:     PetscCall(ISDestroy(&ilink->is_col));
1939:     ilink->is_col = isr;
1940:     PetscCall(ISDestroy(&isr));
1941:     PetscCall(KSPGetPC(ilink->ksp, &subpc));
1942:     PetscCall(PetscObjectTypeCompare((PetscObject)subpc, PCFIELDSPLIT, &flg));
1943:     if (flg) {
1944:       IS       iszl, isz;
1945:       MPI_Comm comm;
1946:       PetscCall(ISGetLocalSize(ilink->is, &localsize));
1947:       comm = PetscObjectComm((PetscObject)ilink->is);
1948:       PetscCall(ISEmbed(isy, ilink->is, PETSC_TRUE, &iszl));
1949:       PetscCallMPI(MPI_Scan(&localsize, &sizez, 1, MPIU_INT, MPI_SUM, comm));
1950:       sizez -= localsize;
1951:       PetscCall(ISGetLocalSize(iszl, &localsize));
1952:       PetscCall(PetscMalloc1(localsize, &indcz));
1953:       PetscCall(ISGetIndices(iszl, &indz));
1954:       PetscCall(PetscArraycpy(indcz, indz, localsize));
1955:       PetscCall(ISRestoreIndices(iszl, &indz));
1956:       PetscCall(ISDestroy(&iszl));
1957:       for (i = 0; i < localsize; i++) *(indcz + i) += sizez;
1958:       PetscCall(ISCreateGeneral(comm, localsize, indcz, PETSC_OWN_POINTER, &isz));
1959:       PetscCall(PCFieldSplitRestrictIS(subpc, isz));
1960:       PetscCall(ISDestroy(&isz));
1961:     }
1962:     next  = ilink->next;
1963:     ilink = next;
1964:   }
1965:   jac->isrestrict = PETSC_TRUE;
1966:   PetscFunctionReturn(PETSC_SUCCESS);
1967: }

1969: static PetscErrorCode PCFieldSplitSetIS_FieldSplit(PC pc, const char splitname[], IS is)
1970: {
1971:   PC_FieldSplit    *jac = (PC_FieldSplit *)pc->data;
1972:   PC_FieldSplitLink ilink, next = jac->head;
1973:   char              prefix[128];

1975:   PetscFunctionBegin;
1976:   if (jac->splitdefined) {
1977:     PetscCall(PetscInfo(pc, "Ignoring new split \"%s\" because the splits have already been defined\n", splitname));
1978:     PetscFunctionReturn(PETSC_SUCCESS);
1979:   }
1980:   PetscCall(PetscNew(&ilink));
1981:   if (splitname) {
1982:     PetscCall(PetscStrallocpy(splitname, &ilink->splitname));
1983:   } else {
1984:     PetscCall(PetscMalloc1(8, &ilink->splitname));
1985:     PetscCall(PetscSNPrintf(ilink->splitname, 7, "%" PetscInt_FMT, jac->nsplits));
1986:   }
1987:   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 */
1988:   PetscCall(PetscObjectReference((PetscObject)is));
1989:   PetscCall(ISDestroy(&ilink->is));
1990:   ilink->is = is;
1991:   PetscCall(PetscObjectReference((PetscObject)is));
1992:   PetscCall(ISDestroy(&ilink->is_col));
1993:   ilink->is_col = is;
1994:   ilink->next   = NULL;
1995:   PetscCall(KSPCreate(PetscObjectComm((PetscObject)pc), &ilink->ksp));
1996:   PetscCall(KSPSetNestLevel(ilink->ksp, pc->kspnestlevel));
1997:   PetscCall(KSPSetErrorIfNotConverged(ilink->ksp, pc->erroriffailure));
1998:   PetscCall(PetscObjectIncrementTabLevel((PetscObject)ilink->ksp, (PetscObject)pc, 1));
1999:   PetscCall(KSPSetType(ilink->ksp, KSPPREONLY));

2001:   PetscCall(PetscSNPrintf(prefix, sizeof(prefix), "%sfieldsplit_%s_", ((PetscObject)pc)->prefix ? ((PetscObject)pc)->prefix : "", ilink->splitname));
2002:   PetscCall(KSPSetOptionsPrefix(ilink->ksp, prefix));

2004:   if (!next) {
2005:     jac->head       = ilink;
2006:     ilink->previous = NULL;
2007:   } else {
2008:     while (next->next) next = next->next;
2009:     next->next      = ilink;
2010:     ilink->previous = next;
2011:   }
2012:   jac->nsplits++;
2013:   PetscFunctionReturn(PETSC_SUCCESS);
2014: }

2016: /*@C
2017:   PCFieldSplitSetFields - Sets the fields that define one particular split in `PCFIELDSPLIT`

2019:   Logically Collective

2021:   Input Parameters:
2022: + pc         - the preconditioner context
2023: . splitname  - name of this split, if `NULL` the number of the split is used
2024: . n          - the number of fields in this split
2025: . fields     - the fields in this split
2026: - 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
2027:                  of the matrix and fields_col provides the column indices for that block

2029:   Level: intermediate

2031:   Notes:
2032:   Use `PCFieldSplitSetIS()` to set a  general set of indices as a split.

2034:   `PCFieldSplitSetFields()` is for defining fields as strided blocks. For example, if the block
2035:   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
2036:   0xx3xx6xx9xx12 ... x1xx4xx7xx ... xx2xx5xx8xx.. 01x34x67x... 0x1x3x5x7.. x12x45x78x....
2037:   where the numbered entries indicate what is in the split.

2039:   This function is called once per split (it creates a new split each time).  Solve options
2040:   for this split will be available under the prefix `-fieldsplit_SPLITNAME_`.

2042:   `PCFieldSplitSetIS()` does not support having a fields_col different from fields

2044:   Developer Notes:
2045:   This routine does not actually create the `IS` representing the split, that is delayed
2046:   until `PCSetUp_FieldSplit()`, because information about the vector/matrix layouts may not be
2047:   available when this routine is called.

2049: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSetBlockSize()`, `PCFieldSplitSetIS()`, `PCFieldSplitRestrictIS()`
2050: @*/
2051: PetscErrorCode PCFieldSplitSetFields(PC pc, const char splitname[], PetscInt n, const PetscInt *fields, const PetscInt *fields_col)
2052: {
2053:   PetscFunctionBegin;
2055:   PetscAssertPointer(splitname, 2);
2056:   PetscCheck(n >= 1, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_OUTOFRANGE, "Provided number of fields %" PetscInt_FMT " in split \"%s\" not positive", n, splitname);
2057:   PetscAssertPointer(fields, 4);
2058:   PetscTryMethod(pc, "PCFieldSplitSetFields_C", (PC, const char[], PetscInt, const PetscInt *, const PetscInt *), (pc, splitname, n, fields, fields_col));
2059:   PetscFunctionReturn(PETSC_SUCCESS);
2060: }

2062: /*@
2063:   PCFieldSplitSetDiagUseAmat - set flag indicating whether to extract diagonal blocks from Amat (rather than Pmat) to build
2064:   the sub-matrices associated with each split. Where `KSPSetOperators`(ksp,Amat,Pmat) was used to supply the operators.

2066:   Logically Collective

2068:   Input Parameters:
2069: + pc  - the preconditioner object
2070: - flg - boolean flag indicating whether or not to use Amat to extract the diagonal blocks from

2072:   Options Database Key:
2073: . -pc_fieldsplit_diag_use_amat - use the Amat to provide the diagonal blocks

2075:   Level: intermediate

2077: .seealso: [](sec_block_matrices), `PC`, `PCSetOperators()`, `KSPSetOperators()`, `PCFieldSplitGetDiagUseAmat()`, `PCFieldSplitSetOffDiagUseAmat()`, `PCFIELDSPLIT`
2078: @*/
2079: PetscErrorCode PCFieldSplitSetDiagUseAmat(PC pc, PetscBool flg)
2080: {
2081:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
2082:   PetscBool      isfs;

2084:   PetscFunctionBegin;
2086:   PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCFIELDSPLIT, &isfs));
2087:   PetscCheck(isfs, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "PC not of type %s", PCFIELDSPLIT);
2088:   jac->diag_use_amat = flg;
2089:   PetscFunctionReturn(PETSC_SUCCESS);
2090: }

2092: /*@
2093:   PCFieldSplitGetDiagUseAmat - get the flag indicating whether to extract diagonal blocks from Amat (rather than Pmat) to build
2094:   the sub-matrices associated with each split.  Where `KSPSetOperators`(ksp,Amat,Pmat) was used to supply the operators.

2096:   Logically Collective

2098:   Input Parameter:
2099: . pc - the preconditioner object

2101:   Output Parameter:
2102: . flg - boolean flag indicating whether or not to use Amat to extract the diagonal blocks from

2104:   Level: intermediate

2106: .seealso: [](sec_block_matrices), `PC`, `PCSetOperators()`, `KSPSetOperators()`, `PCFieldSplitSetDiagUseAmat()`, `PCFieldSplitGetOffDiagUseAmat()`, `PCFIELDSPLIT`
2107: @*/
2108: PetscErrorCode PCFieldSplitGetDiagUseAmat(PC pc, PetscBool *flg)
2109: {
2110:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
2111:   PetscBool      isfs;

2113:   PetscFunctionBegin;
2115:   PetscAssertPointer(flg, 2);
2116:   PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCFIELDSPLIT, &isfs));
2117:   PetscCheck(isfs, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "PC not of type %s", PCFIELDSPLIT);
2118:   *flg = jac->diag_use_amat;
2119:   PetscFunctionReturn(PETSC_SUCCESS);
2120: }

2122: /*@
2123:   PCFieldSplitSetOffDiagUseAmat - set flag indicating whether to extract off-diagonal blocks from Amat (rather than Pmat) to build
2124:   the sub-matrices associated with each split.  Where `KSPSetOperators`(ksp,Amat,Pmat) was used to supply the operators.

2126:   Logically Collective

2128:   Input Parameters:
2129: + pc  - the preconditioner object
2130: - flg - boolean flag indicating whether or not to use Amat to extract the off-diagonal blocks from

2132:   Options Database Key:
2133: . -pc_fieldsplit_off_diag_use_amat <bool> - use the Amat to extract the off-diagonal blocks

2135:   Level: intermediate

2137: .seealso: [](sec_block_matrices), `PC`, `PCSetOperators()`, `KSPSetOperators()`, `PCFieldSplitGetOffDiagUseAmat()`, `PCFieldSplitSetDiagUseAmat()`, `PCFIELDSPLIT`
2138: @*/
2139: PetscErrorCode PCFieldSplitSetOffDiagUseAmat(PC pc, PetscBool flg)
2140: {
2141:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
2142:   PetscBool      isfs;

2144:   PetscFunctionBegin;
2146:   PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCFIELDSPLIT, &isfs));
2147:   PetscCheck(isfs, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "PC not of type %s", PCFIELDSPLIT);
2148:   jac->offdiag_use_amat = flg;
2149:   PetscFunctionReturn(PETSC_SUCCESS);
2150: }

2152: /*@
2153:   PCFieldSplitGetOffDiagUseAmat - get the flag indicating whether to extract off-diagonal blocks from Amat (rather than Pmat) to build
2154:   the sub-matrices associated with each split.  Where `KSPSetOperators`(ksp,Amat,Pmat) was used to supply the operators.

2156:   Logically Collective

2158:   Input Parameter:
2159: . pc - the preconditioner object

2161:   Output Parameter:
2162: . flg - boolean flag indicating whether or not to use Amat to extract the off-diagonal blocks from

2164:   Level: intermediate

2166: .seealso: [](sec_block_matrices), `PC`, `PCSetOperators()`, `KSPSetOperators()`, `PCFieldSplitSetOffDiagUseAmat()`, `PCFieldSplitGetDiagUseAmat()`, `PCFIELDSPLIT`
2167: @*/
2168: PetscErrorCode PCFieldSplitGetOffDiagUseAmat(PC pc, PetscBool *flg)
2169: {
2170:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
2171:   PetscBool      isfs;

2173:   PetscFunctionBegin;
2175:   PetscAssertPointer(flg, 2);
2176:   PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCFIELDSPLIT, &isfs));
2177:   PetscCheck(isfs, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "PC not of type %s", PCFIELDSPLIT);
2178:   *flg = jac->offdiag_use_amat;
2179:   PetscFunctionReturn(PETSC_SUCCESS);
2180: }

2182: /*@C
2183:   PCFieldSplitSetIS - Sets the exact elements for a split in a `PCFIELDSPLIT`

2185:   Logically Collective

2187:   Input Parameters:
2188: + pc        - the preconditioner context
2189: . splitname - name of this split, if `NULL` the number of the split is used
2190: - is        - the index set that defines the elements in this split

2192:   Level: intermediate

2194:   Notes:
2195:   Use `PCFieldSplitSetFields()`, for splits defined by strided types.

2197:   This function is called once per split (it creates a new split each time).  Solve options
2198:   for this split will be available under the prefix -fieldsplit_SPLITNAME_.

2200: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSetBlockSize()`
2201: @*/
2202: PetscErrorCode PCFieldSplitSetIS(PC pc, const char splitname[], IS is)
2203: {
2204:   PetscFunctionBegin;
2206:   if (splitname) PetscAssertPointer(splitname, 2);
2208:   PetscTryMethod(pc, "PCFieldSplitSetIS_C", (PC, const char[], IS), (pc, splitname, is));
2209:   PetscFunctionReturn(PETSC_SUCCESS);
2210: }

2212: /*@C
2213:   PCFieldSplitGetIS - Retrieves the elements for a split as an `IS`

2215:   Logically Collective

2217:   Input Parameters:
2218: + pc        - the preconditioner context
2219: - splitname - name of this split

2221:   Output Parameter:
2222: . is - the index set that defines the elements in this split, or `NULL` if the split is not found

2224:   Level: intermediate

2226: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSetIS()`
2227: @*/
2228: PetscErrorCode PCFieldSplitGetIS(PC pc, const char splitname[], IS *is)
2229: {
2230:   PetscFunctionBegin;
2232:   PetscAssertPointer(splitname, 2);
2233:   PetscAssertPointer(is, 3);
2234:   {
2235:     PC_FieldSplit    *jac   = (PC_FieldSplit *)pc->data;
2236:     PC_FieldSplitLink ilink = jac->head;
2237:     PetscBool         found;

2239:     *is = NULL;
2240:     while (ilink) {
2241:       PetscCall(PetscStrcmp(ilink->splitname, splitname, &found));
2242:       if (found) {
2243:         *is = ilink->is;
2244:         break;
2245:       }
2246:       ilink = ilink->next;
2247:     }
2248:   }
2249:   PetscFunctionReturn(PETSC_SUCCESS);
2250: }

2252: /*@C
2253:   PCFieldSplitGetISByIndex - Retrieves the elements for a given split as an `IS`

2255:   Logically Collective

2257:   Input Parameters:
2258: + pc    - the preconditioner context
2259: - index - index of this split

2261:   Output Parameter:
2262: . is - the index set that defines the elements in this split

2264:   Level: intermediate

2266: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitGetIS()`, `PCFieldSplitSetIS()`
2267: @*/
2268: PetscErrorCode PCFieldSplitGetISByIndex(PC pc, PetscInt index, IS *is)
2269: {
2270:   PetscFunctionBegin;
2271:   PetscCheck(index >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Negative field %" PetscInt_FMT " requested", index);
2273:   PetscAssertPointer(is, 3);
2274:   {
2275:     PC_FieldSplit    *jac   = (PC_FieldSplit *)pc->data;
2276:     PC_FieldSplitLink ilink = jac->head;
2277:     PetscInt          i     = 0;
2278:     PetscCheck(index < jac->nsplits, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Field %" PetscInt_FMT " requested but only %" PetscInt_FMT " exist", index, jac->nsplits);

2280:     while (i < index) {
2281:       ilink = ilink->next;
2282:       ++i;
2283:     }
2284:     PetscCall(PCFieldSplitGetIS(pc, ilink->splitname, is));
2285:   }
2286:   PetscFunctionReturn(PETSC_SUCCESS);
2287: }

2289: /*@
2290:   PCFieldSplitSetBlockSize - Sets the block size for defining where fields start in the
2291:   fieldsplit preconditioner when calling `PCFieldSplitSetIS()`. If not set the matrix block size is used.

2293:   Logically Collective

2295:   Input Parameters:
2296: + pc - the preconditioner context
2297: - bs - the block size

2299:   Level: intermediate

2301: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSetIS()`
2302: @*/
2303: PetscErrorCode PCFieldSplitSetBlockSize(PC pc, PetscInt bs)
2304: {
2305:   PetscFunctionBegin;
2308:   PetscTryMethod(pc, "PCFieldSplitSetBlockSize_C", (PC, PetscInt), (pc, bs));
2309:   PetscFunctionReturn(PETSC_SUCCESS);
2310: }

2312: /*@C
2313:   PCFieldSplitGetSubKSP - Gets the `KSP` contexts for all splits

2315:   Collective

2317:   Input Parameter:
2318: . pc - the preconditioner context

2320:   Output Parameters:
2321: + n      - the number of splits
2322: - subksp - the array of `KSP` contexts

2324:   Level: advanced

2326:   Notes:
2327:   After `PCFieldSplitGetSubKSP()` the array of `KSP`s is to be freed by the user with `PetscFree()`
2328:   (not the `KSP`, just the array that contains them).

2330:   You must call `PCSetUp()` before calling `PCFieldSplitGetSubKSP()`.

2332:   If the fieldsplit is of type `PC_COMPOSITE_SCHUR`, it returns the `KSP` object used inside the
2333:   Schur complement and the `KSP` object used to iterate over the Schur complement.
2334:   To access all the `KSP` objects used in `PC_COMPOSITE_SCHUR`, use `PCFieldSplitSchurGetSubKSP()`.

2336:   If the fieldsplit is of type `PC_COMPOSITE_GKB`, it returns the `KSP` object used to solve the
2337:   inner linear system defined by the matrix H in each loop.

2339:   Fortran Notes:
2340:   You must pass in a `KSP` array that is large enough to contain all the `KSP`s.
2341:   You can call `PCFieldSplitGetSubKSP`(pc,n,`PETSC_NULL_KSP`,ierr) to determine how large the
2342:   `KSP` array must be.

2344:   Developer Notes:
2345:   There should be a `PCFieldSplitRestoreSubKSP()` instead of requiring the user to call `PetscFree()`

2347:   The Fortran interface should be modernized to return directly the array of values.

2349: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSetIS()`, `PCFieldSplitSchurGetSubKSP()`
2350: @*/
2351: PetscErrorCode PCFieldSplitGetSubKSP(PC pc, PetscInt *n, KSP *subksp[])
2352: {
2353:   PetscFunctionBegin;
2355:   if (n) PetscAssertPointer(n, 2);
2356:   PetscUseMethod(pc, "PCFieldSplitGetSubKSP_C", (PC, PetscInt *, KSP **), (pc, n, subksp));
2357:   PetscFunctionReturn(PETSC_SUCCESS);
2358: }

2360: /*@C
2361:   PCFieldSplitSchurGetSubKSP - Gets the `KSP` contexts used inside the Schur complement based `PCFIELDSPLIT`

2363:   Collective

2365:   Input Parameter:
2366: . pc - the preconditioner context

2368:   Output Parameters:
2369: + n      - the number of splits
2370: - subksp - the array of `KSP` contexts

2372:   Level: advanced

2374:   Notes:
2375:   After `PCFieldSplitSchurGetSubKSP()` the array of `KSP`s is to be freed by the user with `PetscFree()`
2376:   (not the `KSP` just the array that contains them).

2378:   You must call `PCSetUp()` before calling `PCFieldSplitSchurGetSubKSP()`.

2380:   If the fieldsplit type is of type `PC_COMPOSITE_SCHUR`, it returns (in order)
2381: +  1  - the `KSP` used for the (1,1) block
2382: .  2  - the `KSP` used for the Schur complement (not the one used for the interior Schur solver)
2383: -  3  - the `KSP` used for the (1,1) block in the upper triangular factor (if different from that of the (1,1) block).

2385:   It returns a null array if the fieldsplit is not of type `PC_COMPOSITE_SCHUR`; in this case, you should use `PCFieldSplitGetSubKSP()`.

2387:   Fortran Notes:
2388:   You must pass in a `KSP` array that is large enough to contain all the local `KSP`s.
2389:   You can call `PCFieldSplitSchurGetSubKSP`(pc,n,`PETSC_NULL_KSP`,ierr) to determine how large the
2390:   `KSP` array must be.

2392:   Developer Notes:
2393:   There should be a `PCFieldSplitRestoreSubKSP()` instead of requiring the user to call `PetscFree()`

2395:   Should the functionality of `PCFieldSplitSchurGetSubKSP()` and `PCFieldSplitGetSubKSP()` be merged?

2397:   The Fortran interface should be modernized to return directly the array of values.

2399: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSetIS()`, `PCFieldSplitGetSubKSP()`
2400: @*/
2401: PetscErrorCode PCFieldSplitSchurGetSubKSP(PC pc, PetscInt *n, KSP *subksp[])
2402: {
2403:   PetscFunctionBegin;
2405:   if (n) PetscAssertPointer(n, 2);
2406:   PetscUseMethod(pc, "PCFieldSplitSchurGetSubKSP_C", (PC, PetscInt *, KSP **), (pc, n, subksp));
2407:   PetscFunctionReturn(PETSC_SUCCESS);
2408: }

2410: /*@
2411:   PCFieldSplitSetSchurPre -  Indicates from what operator the preconditioner is constructed for the Schur complement.
2412:   The default is the A11 matrix.

2414:   Collective

2416:   Input Parameters:
2417: + pc    - the preconditioner context
2418: . ptype - which matrix to use for preconditioning the Schur complement: `PC_FIELDSPLIT_SCHUR_PRE_A11` (default),
2419:               `PC_FIELDSPLIT_SCHUR_PRE_SELF`, `PC_FIELDSPLIT_SCHUR_PRE_USER`,
2420:               `PC_FIELDSPLIT_SCHUR_PRE_SELFP`, and `PC_FIELDSPLIT_SCHUR_PRE_FULL`
2421: - pre   - matrix to use for preconditioning, or `NULL`

2423:   Options Database Keys:
2424: + -pc_fieldsplit_schur_precondition <self,selfp,user,a11,full> - default is `a11`. See notes for meaning of various arguments
2425: - -fieldsplit_1_pc_type <pctype>                               - the preconditioner algorithm that is used to construct the preconditioner from the operator

2427:   Level: intermediate

2429:   Notes:
2430:   If ptype is
2431: +     a11 - the preconditioner for the Schur complement is generated from the block diagonal part of the preconditioner
2432:   matrix associated with the Schur complement (i.e. A11), not the Schur complement matrix
2433: .     self - the preconditioner for the Schur complement is generated from the symbolic representation of the Schur complement matrix:
2434:   The only preconditioners that currently work with this symbolic representation matrix object are `PCLSC` and `PCHPDDM`
2435: .     user - the preconditioner for the Schur complement is generated from the user provided matrix (pre argument
2436:   to this function).
2437: .     selfp - the preconditioning for the Schur complement is generated from an explicitly-assembled approximation Sp = A11 - A10 inv(diag(A00)) A01
2438:   This is only a good preconditioner when diag(A00) is a good preconditioner for A00. Optionally, A00 can be
2439:   lumped before extracting the diagonal using the additional option `-fieldsplit_1_mat_schur_complement_ainv_type lump`
2440: -     full - the preconditioner for the Schur complement is generated from the exact Schur complement matrix representation
2441:   computed internally by `PCFIELDSPLIT` (this is expensive)
2442:   useful mostly as a test that the Schur complement approach can work for your problem

2444:   When solving a saddle point problem, where the A11 block is identically zero, using `a11` as the ptype only makes sense
2445:   with the additional option `-fieldsplit_1_pc_type none`. Usually for saddle point problems one would use a ptype of self and
2446:   `-fieldsplit_1_pc_type lsc` which uses the least squares commutator to compute a preconditioner for the Schur complement.

2448: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSchurPre()`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSchurPreType`,
2449:           `MatSchurComplementSetAinvType()`, `PCLSC`

2451: @*/
2452: PetscErrorCode PCFieldSplitSetSchurPre(PC pc, PCFieldSplitSchurPreType ptype, Mat pre)
2453: {
2454:   PetscFunctionBegin;
2456:   PetscTryMethod(pc, "PCFieldSplitSetSchurPre_C", (PC, PCFieldSplitSchurPreType, Mat), (pc, ptype, pre));
2457:   PetscFunctionReturn(PETSC_SUCCESS);
2458: }

2460: PetscErrorCode PCFieldSplitSchurPrecondition(PC pc, PCFieldSplitSchurPreType ptype, Mat pre)
2461: {
2462:   return PCFieldSplitSetSchurPre(pc, ptype, pre);
2463: } /* Deprecated name */

2465: /*@
2466:   PCFieldSplitGetSchurPre - For Schur complement fieldsplit, determine how the Schur complement will be
2467:   preconditioned.  See `PCFieldSplitSetSchurPre()` for details.

2469:   Logically Collective

2471:   Input Parameter:
2472: . pc - the preconditioner context

2474:   Output Parameters:
2475: + 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`
2476: - pre   - matrix to use for preconditioning (with `PC_FIELDSPLIT_SCHUR_PRE_USER`), or `NULL`

2478:   Level: intermediate

2480: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitSetSchurPre()`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSchurPreType`, `PCLSC`

2482: @*/
2483: PetscErrorCode PCFieldSplitGetSchurPre(PC pc, PCFieldSplitSchurPreType *ptype, Mat *pre)
2484: {
2485:   PetscFunctionBegin;
2487:   PetscUseMethod(pc, "PCFieldSplitGetSchurPre_C", (PC, PCFieldSplitSchurPreType *, Mat *), (pc, ptype, pre));
2488:   PetscFunctionReturn(PETSC_SUCCESS);
2489: }

2491: /*@
2492:   PCFieldSplitSchurGetS -  extract the `MATSCHURCOMPLEMENT` object used by this `PCFIELDSPLIT` in case it needs to be configured separately

2494:   Not Collective

2496:   Input Parameter:
2497: . pc - the preconditioner context

2499:   Output Parameter:
2500: . S - the Schur complement matrix

2502:   Level: advanced

2504:   Note:
2505:   This matrix should not be destroyed using `MatDestroy()`; rather, use `PCFieldSplitSchurRestoreS()`.

2507: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSchurPreType`, `PCFieldSplitSetSchurPre()`, `MATSCHURCOMPLEMENT`, `PCFieldSplitSchurRestoreS()`,
2508:           `MatCreateSchurComplement()`, `MatSchurComplementGetKSP()`, `MatSchurComplementComputeExplicitOperator()`, `MatGetSchurComplement()`
2509: @*/
2510: PetscErrorCode PCFieldSplitSchurGetS(PC pc, Mat *S)
2511: {
2512:   const char    *t;
2513:   PetscBool      isfs;
2514:   PC_FieldSplit *jac;

2516:   PetscFunctionBegin;
2518:   PetscCall(PetscObjectGetType((PetscObject)pc, &t));
2519:   PetscCall(PetscStrcmp(t, PCFIELDSPLIT, &isfs));
2520:   PetscCheck(isfs, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Expected PC of type PCFIELDSPLIT, got %s instead", t);
2521:   jac = (PC_FieldSplit *)pc->data;
2522:   PetscCheck(jac->type == PC_COMPOSITE_SCHUR, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Expected PCFIELDSPLIT of type SCHUR, got %d instead", jac->type);
2523:   if (S) *S = jac->schur;
2524:   PetscFunctionReturn(PETSC_SUCCESS);
2525: }

2527: /*@
2528:   PCFieldSplitSchurRestoreS -  returns the `MATSCHURCOMPLEMENT` matrix used by this `PC`

2530:   Not Collective

2532:   Input Parameters:
2533: + pc - the preconditioner context
2534: - S  - the Schur complement matrix

2536:   Level: advanced

2538: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSchurPreType`, `PCFieldSplitSetSchurPre()`, `MatSchurComplement`, `PCFieldSplitSchurGetS()`
2539: @*/
2540: PetscErrorCode PCFieldSplitSchurRestoreS(PC pc, Mat *S)
2541: {
2542:   const char    *t;
2543:   PetscBool      isfs;
2544:   PC_FieldSplit *jac;

2546:   PetscFunctionBegin;
2548:   PetscCall(PetscObjectGetType((PetscObject)pc, &t));
2549:   PetscCall(PetscStrcmp(t, PCFIELDSPLIT, &isfs));
2550:   PetscCheck(isfs, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Expected PC of type PCFIELDSPLIT, got %s instead", t);
2551:   jac = (PC_FieldSplit *)pc->data;
2552:   PetscCheck(jac->type == PC_COMPOSITE_SCHUR, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Expected PCFIELDSPLIT of type SCHUR, got %d instead", jac->type);
2553:   PetscCheck(S && (*S == jac->schur), PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "MatSchurComplement restored is not the same as gotten");
2554:   PetscFunctionReturn(PETSC_SUCCESS);
2555: }

2557: static PetscErrorCode PCFieldSplitSetSchurPre_FieldSplit(PC pc, PCFieldSplitSchurPreType ptype, Mat pre)
2558: {
2559:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

2561:   PetscFunctionBegin;
2562:   jac->schurpre = ptype;
2563:   if (ptype == PC_FIELDSPLIT_SCHUR_PRE_USER && pre) {
2564:     PetscCall(MatDestroy(&jac->schur_user));
2565:     jac->schur_user = pre;
2566:     PetscCall(PetscObjectReference((PetscObject)jac->schur_user));
2567:   }
2568:   PetscFunctionReturn(PETSC_SUCCESS);
2569: }

2571: static PetscErrorCode PCFieldSplitGetSchurPre_FieldSplit(PC pc, PCFieldSplitSchurPreType *ptype, Mat *pre)
2572: {
2573:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

2575:   PetscFunctionBegin;
2576:   if (ptype) *ptype = jac->schurpre;
2577:   if (pre) *pre = jac->schur_user;
2578:   PetscFunctionReturn(PETSC_SUCCESS);
2579: }

2581: /*@
2582:   PCFieldSplitSetSchurFactType -  sets which blocks of the approximate block factorization to retain in the preconditioner {cite}`murphy2000note` and {cite}`ipsen2001note`

2584:   Collective

2586:   Input Parameters:
2587: + pc    - the preconditioner context
2588: - ftype - which blocks of factorization to retain, `PC_FIELDSPLIT_SCHUR_FACT_FULL` is default

2590:   Options Database Key:
2591: . -pc_fieldsplit_schur_fact_type <diag,lower,upper,full> - default is `full`

2593:   Level: intermediate

2595:   Notes:
2596:   The FULL factorization is
2597: .vb
2598:   (A   B)  = (1       0) (A   0) (1  Ainv*B)  = L D U
2599:   (C   E)    (C*Ainv  1) (0   S) (0       1)
2600: .vb
2601:   where S = E - C*Ainv*B. In practice, the full factorization is applied via block triangular solves with the grouping $L*(D*U)$. UPPER uses $D*U$, LOWER uses $L*D$,
2602:   and DIAG is the diagonal part with the sign of S flipped (because this makes the preconditioner positive definite for many formulations,
2603:   thus allowing the use of `KSPMINRES)`. Sign flipping of S can be turned off with `PCFieldSplitSetSchurScale()`.

2605:   If A and S are solved exactly
2606: .vb
2607:   *) FULL factorization is a direct solver.
2608:   *) 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.
2609:   *) 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.
2610: .ve

2612:   If the iteration count is very low, consider using `KSPFGMRES` or `KSPGCR` which can use one less preconditioner
2613:   application in this case. Note that the preconditioned operator may be highly non-normal, so such fast convergence may not be observed in practice.

2615:   For symmetric problems in which A is positive definite and S is negative definite, DIAG can be used with `KSPMINRES`.

2617:   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).

2619: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSchurPreType`, `PCFieldSplitSetSchurScale()`,
2620:           [](sec_flexibleksp)
2621: @*/
2622: PetscErrorCode PCFieldSplitSetSchurFactType(PC pc, PCFieldSplitSchurFactType ftype)
2623: {
2624:   PetscFunctionBegin;
2626:   PetscTryMethod(pc, "PCFieldSplitSetSchurFactType_C", (PC, PCFieldSplitSchurFactType), (pc, ftype));
2627:   PetscFunctionReturn(PETSC_SUCCESS);
2628: }

2630: static PetscErrorCode PCFieldSplitSetSchurFactType_FieldSplit(PC pc, PCFieldSplitSchurFactType ftype)
2631: {
2632:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

2634:   PetscFunctionBegin;
2635:   jac->schurfactorization = ftype;
2636:   PetscFunctionReturn(PETSC_SUCCESS);
2637: }

2639: /*@
2640:   PCFieldSplitSetSchurScale -  Controls the sign flip of S for `PC_FIELDSPLIT_SCHUR_FACT_DIAG`.

2642:   Collective

2644:   Input Parameters:
2645: + pc    - the preconditioner context
2646: - scale - scaling factor for the Schur complement

2648:   Options Database Key:
2649: . -pc_fieldsplit_schur_scale <scale> - default is -1.0

2651:   Level: intermediate

2653: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSchurFactType`, `PCFieldSplitSetSchurFactType()`
2654: @*/
2655: PetscErrorCode PCFieldSplitSetSchurScale(PC pc, PetscScalar scale)
2656: {
2657:   PetscFunctionBegin;
2660:   PetscTryMethod(pc, "PCFieldSplitSetSchurScale_C", (PC, PetscScalar), (pc, scale));
2661:   PetscFunctionReturn(PETSC_SUCCESS);
2662: }

2664: static PetscErrorCode PCFieldSplitSetSchurScale_FieldSplit(PC pc, PetscScalar scale)
2665: {
2666:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

2668:   PetscFunctionBegin;
2669:   jac->schurscale = scale;
2670:   PetscFunctionReturn(PETSC_SUCCESS);
2671: }

2673: /*@C
2674:   PCFieldSplitGetSchurBlocks - Gets all matrix blocks for the Schur complement

2676:   Collective

2678:   Input Parameter:
2679: . pc - the preconditioner context

2681:   Output Parameters:
2682: + A00 - the (0,0) block
2683: . A01 - the (0,1) block
2684: . A10 - the (1,0) block
2685: - A11 - the (1,1) block

2687:   Level: advanced

2689: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `MatSchurComplementGetSubMatrices()`, `MatSchurComplementSetSubMatrices()`
2690: @*/
2691: PetscErrorCode PCFieldSplitGetSchurBlocks(PC pc, Mat *A00, Mat *A01, Mat *A10, Mat *A11)
2692: {
2693:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

2695:   PetscFunctionBegin;
2697:   PetscCheck(jac->type == PC_COMPOSITE_SCHUR, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONG, "FieldSplit is not using a Schur complement approach.");
2698:   if (A00) *A00 = jac->pmat[0];
2699:   if (A01) *A01 = jac->B;
2700:   if (A10) *A10 = jac->C;
2701:   if (A11) *A11 = jac->pmat[1];
2702:   PetscFunctionReturn(PETSC_SUCCESS);
2703: }

2705: /*@
2706:   PCFieldSplitSetGKBTol -  Sets the solver tolerance for the generalized Golub-Kahan bidiagonalization preconditioner {cite}`arioli2013` in `PCFIELDSPLIT`

2708:   Collective

2710:   Input Parameters:
2711: + pc        - the preconditioner context
2712: - tolerance - the solver tolerance

2714:   Options Database Key:
2715: . -pc_fieldsplit_gkb_tol <tolerance> - default is 1e-5

2717:   Level: intermediate

2719:   Note:
2720:   The generalized GKB algorithm {cite}`arioli2013` uses a lower bound estimate of the error in energy norm as stopping criterion.
2721:   It stops once the lower bound estimate undershoots the required solver tolerance. Although the actual error might be bigger than
2722:   this estimate, the stopping criterion is satisfactory in practical cases.

2724: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetGKBDelay()`, `PCFieldSplitSetGKBNu()`, `PCFieldSplitSetGKBMaxit()`
2725: @*/
2726: PetscErrorCode PCFieldSplitSetGKBTol(PC pc, PetscReal tolerance)
2727: {
2728:   PetscFunctionBegin;
2731:   PetscTryMethod(pc, "PCFieldSplitSetGKBTol_C", (PC, PetscReal), (pc, tolerance));
2732:   PetscFunctionReturn(PETSC_SUCCESS);
2733: }

2735: static PetscErrorCode PCFieldSplitSetGKBTol_FieldSplit(PC pc, PetscReal tolerance)
2736: {
2737:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

2739:   PetscFunctionBegin;
2740:   jac->gkbtol = tolerance;
2741:   PetscFunctionReturn(PETSC_SUCCESS);
2742: }

2744: /*@
2745:   PCFieldSplitSetGKBMaxit -  Sets the maximum number of iterations for the generalized Golub-Kahan bidiagonalization preconditioner in `PCFIELDSPLIT`

2747:   Collective

2749:   Input Parameters:
2750: + pc    - the preconditioner context
2751: - maxit - the maximum number of iterations

2753:   Options Database Key:
2754: . -pc_fieldsplit_gkb_maxit <maxit> - default is 100

2756:   Level: intermediate

2758: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetGKBDelay()`, `PCFieldSplitSetGKBTol()`, `PCFieldSplitSetGKBNu()`
2759: @*/
2760: PetscErrorCode PCFieldSplitSetGKBMaxit(PC pc, PetscInt maxit)
2761: {
2762:   PetscFunctionBegin;
2765:   PetscTryMethod(pc, "PCFieldSplitSetGKBMaxit_C", (PC, PetscInt), (pc, maxit));
2766:   PetscFunctionReturn(PETSC_SUCCESS);
2767: }

2769: static PetscErrorCode PCFieldSplitSetGKBMaxit_FieldSplit(PC pc, PetscInt maxit)
2770: {
2771:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

2773:   PetscFunctionBegin;
2774:   jac->gkbmaxit = maxit;
2775:   PetscFunctionReturn(PETSC_SUCCESS);
2776: }

2778: /*@
2779:   PCFieldSplitSetGKBDelay -  Sets the delay in the lower bound error estimate in the generalized Golub-Kahan bidiagonalization {cite}`arioli2013` in `PCFIELDSPLIT`
2780:   preconditioner.

2782:   Collective

2784:   Input Parameters:
2785: + pc    - the preconditioner context
2786: - delay - the delay window in the lower bound estimate

2788:   Options Database Key:
2789: . -pc_fieldsplit_gkb_delay <delay> - default is 5

2791:   Level: intermediate

2793:   Notes:
2794:   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 $
2795:   is expressed as a truncated sum. The error at iteration k can only be measured at iteration (k + `delay`), and thus the algorithm needs
2796:   at least (`delay` + 1) iterations to stop.

2798:   For more details on the generalized Golub-Kahan bidiagonalization method and its lower bound stopping criterion, please refer to {cite}`arioli2013`

2800: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetGKBNu()`, `PCFieldSplitSetGKBTol()`, `PCFieldSplitSetGKBMaxit()`
2801: @*/
2802: PetscErrorCode PCFieldSplitSetGKBDelay(PC pc, PetscInt delay)
2803: {
2804:   PetscFunctionBegin;
2807:   PetscTryMethod(pc, "PCFieldSplitSetGKBDelay_C", (PC, PetscInt), (pc, delay));
2808:   PetscFunctionReturn(PETSC_SUCCESS);
2809: }

2811: static PetscErrorCode PCFieldSplitSetGKBDelay_FieldSplit(PC pc, PetscInt delay)
2812: {
2813:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

2815:   PetscFunctionBegin;
2816:   jac->gkbdelay = delay;
2817:   PetscFunctionReturn(PETSC_SUCCESS);
2818: }

2820: /*@
2821:   PCFieldSplitSetGKBNu -  Sets the scalar value nu >= 0 in the transformation H = A00 + nu*A01*A01' of the (1,1) block in the
2822:   Golub-Kahan bidiagonalization preconditioner {cite}`arioli2013` in `PCFIELDSPLIT`

2824:   Collective

2826:   Input Parameters:
2827: + pc - the preconditioner context
2828: - nu - the shift parameter

2830:   Options Database Key:
2831: . -pc_fieldsplit_gkb_nu <nu> - default is 1

2833:   Level: intermediate

2835:   Notes:
2836:   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,
2837:   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
2838:   necessary to find a good balance in between the convergence of the inner and outer loop.

2840:   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.

2842: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetGKBDelay()`, `PCFieldSplitSetGKBTol()`, `PCFieldSplitSetGKBMaxit()`
2843: @*/
2844: PetscErrorCode PCFieldSplitSetGKBNu(PC pc, PetscReal nu)
2845: {
2846:   PetscFunctionBegin;
2849:   PetscTryMethod(pc, "PCFieldSplitSetGKBNu_C", (PC, PetscReal), (pc, nu));
2850:   PetscFunctionReturn(PETSC_SUCCESS);
2851: }

2853: static PetscErrorCode PCFieldSplitSetGKBNu_FieldSplit(PC pc, PetscReal nu)
2854: {
2855:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

2857:   PetscFunctionBegin;
2858:   jac->gkbnu = nu;
2859:   PetscFunctionReturn(PETSC_SUCCESS);
2860: }

2862: static PetscErrorCode PCFieldSplitSetType_FieldSplit(PC pc, PCCompositeType type)
2863: {
2864:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

2866:   PetscFunctionBegin;
2867:   jac->type = type;
2868:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSubKSP_C", NULL));
2869:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurPre_C", NULL));
2870:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSchurPre_C", NULL));
2871:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurFactType_C", NULL));
2872:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurScale_C", NULL));
2873:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBTol_C", NULL));
2874:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBMaxit_C", NULL));
2875:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBNu_C", NULL));
2876:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBDelay_C", NULL));

2878:   if (type == PC_COMPOSITE_SCHUR) {
2879:     pc->ops->apply          = PCApply_FieldSplit_Schur;
2880:     pc->ops->applytranspose = PCApplyTranspose_FieldSplit_Schur;
2881:     pc->ops->view           = PCView_FieldSplit_Schur;

2883:     PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSubKSP_C", PCFieldSplitGetSubKSP_FieldSplit_Schur));
2884:     PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurPre_C", PCFieldSplitSetSchurPre_FieldSplit));
2885:     PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSchurPre_C", PCFieldSplitGetSchurPre_FieldSplit));
2886:     PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurFactType_C", PCFieldSplitSetSchurFactType_FieldSplit));
2887:     PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurScale_C", PCFieldSplitSetSchurScale_FieldSplit));
2888:   } else if (type == PC_COMPOSITE_GKB) {
2889:     pc->ops->apply = PCApply_FieldSplit_GKB;
2890:     pc->ops->view  = PCView_FieldSplit_GKB;

2892:     PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSubKSP_C", PCFieldSplitGetSubKSP_FieldSplit));
2893:     PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBTol_C", PCFieldSplitSetGKBTol_FieldSplit));
2894:     PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBMaxit_C", PCFieldSplitSetGKBMaxit_FieldSplit));
2895:     PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBNu_C", PCFieldSplitSetGKBNu_FieldSplit));
2896:     PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBDelay_C", PCFieldSplitSetGKBDelay_FieldSplit));
2897:   } else {
2898:     pc->ops->apply = PCApply_FieldSplit;
2899:     pc->ops->view  = PCView_FieldSplit;

2901:     PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSubKSP_C", PCFieldSplitGetSubKSP_FieldSplit));
2902:   }
2903:   PetscFunctionReturn(PETSC_SUCCESS);
2904: }

2906: static PetscErrorCode PCFieldSplitSetBlockSize_FieldSplit(PC pc, PetscInt bs)
2907: {
2908:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

2910:   PetscFunctionBegin;
2911:   PetscCheck(bs >= 1, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_OUTOFRANGE, "Blocksize must be positive, you gave %" PetscInt_FMT, bs);
2912:   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);
2913:   jac->bs = bs;
2914:   PetscFunctionReturn(PETSC_SUCCESS);
2915: }

2917: static PetscErrorCode PCSetCoordinates_FieldSplit(PC pc, PetscInt dim, PetscInt nloc, PetscReal coords[])
2918: {
2919:   PC_FieldSplit    *jac           = (PC_FieldSplit *)pc->data;
2920:   PC_FieldSplitLink ilink_current = jac->head;
2921:   IS                is_owned;

2923:   PetscFunctionBegin;
2924:   jac->coordinates_set = PETSC_TRUE; // Internal flag
2925:   PetscCall(MatGetOwnershipIS(pc->mat, &is_owned, NULL));

2927:   while (ilink_current) {
2928:     // For each IS, embed it to get local coords indces
2929:     IS              is_coords;
2930:     PetscInt        ndofs_block;
2931:     const PetscInt *block_dofs_enumeration; // Numbering of the dofs relevant to the current block

2933:     // Setting drop to true for safety. It should make no difference.
2934:     PetscCall(ISEmbed(ilink_current->is, is_owned, PETSC_TRUE, &is_coords));
2935:     PetscCall(ISGetLocalSize(is_coords, &ndofs_block));
2936:     PetscCall(ISGetIndices(is_coords, &block_dofs_enumeration));

2938:     // Allocate coordinates vector and set it directly
2939:     PetscCall(PetscMalloc1(ndofs_block * dim, &ilink_current->coords));
2940:     for (PetscInt dof = 0; dof < ndofs_block; ++dof) {
2941:       for (PetscInt d = 0; d < dim; ++d) (ilink_current->coords)[dim * dof + d] = coords[dim * block_dofs_enumeration[dof] + d];
2942:     }
2943:     ilink_current->dim   = dim;
2944:     ilink_current->ndofs = ndofs_block;
2945:     PetscCall(ISRestoreIndices(is_coords, &block_dofs_enumeration));
2946:     PetscCall(ISDestroy(&is_coords));
2947:     ilink_current = ilink_current->next;
2948:   }
2949:   PetscCall(ISDestroy(&is_owned));
2950:   PetscFunctionReturn(PETSC_SUCCESS);
2951: }

2953: /*@
2954:   PCFieldSplitSetType - Sets the type, `PCCompositeType`, of a `PCFIELDSPLIT`

2956:   Collective

2958:   Input Parameters:
2959: + pc   - the preconditioner context
2960: - type - `PC_COMPOSITE_ADDITIVE`, `PC_COMPOSITE_MULTIPLICATIVE` (default), `PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE`, `PC_COMPOSITE_SPECIAL`, `PC_COMPOSITE_SCHUR`

2962:   Options Database Key:
2963: . -pc_fieldsplit_type <one of multiplicative, additive, symmetric_multiplicative, special, schur> - Sets fieldsplit preconditioner type

2965:   Level: intermediate

2967: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCCompositeType`, `PCCompositeGetType()`, `PC_COMPOSITE_ADDITIVE`, `PC_COMPOSITE_MULTIPLICATIVE`,
2968:           `PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE`, `PC_COMPOSITE_SPECIAL`, `PC_COMPOSITE_SCHUR`
2969: @*/
2970: PetscErrorCode PCFieldSplitSetType(PC pc, PCCompositeType type)
2971: {
2972:   PetscFunctionBegin;
2974:   PetscTryMethod(pc, "PCFieldSplitSetType_C", (PC, PCCompositeType), (pc, type));
2975:   PetscFunctionReturn(PETSC_SUCCESS);
2976: }

2978: /*@
2979:   PCFieldSplitGetType - Gets the type, `PCCompositeType`, of a `PCFIELDSPLIT`

2981:   Not collective

2983:   Input Parameter:
2984: . pc - the preconditioner context

2986:   Output Parameter:
2987: . type - `PC_COMPOSITE_ADDITIVE`, `PC_COMPOSITE_MULTIPLICATIVE` (default), `PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE`, `PC_COMPOSITE_SPECIAL`, `PC_COMPOSITE_SCHUR`

2989:   Level: intermediate

2991: .seealso: [](sec_block_matrices), `PC`, `PCCompositeSetType()`, `PCFIELDSPLIT`, `PCCompositeType`, `PC_COMPOSITE_ADDITIVE`, `PC_COMPOSITE_MULTIPLICATIVE`,
2992:           `PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE`, `PC_COMPOSITE_SPECIAL`, `PC_COMPOSITE_SCHUR`
2993: @*/
2994: PetscErrorCode PCFieldSplitGetType(PC pc, PCCompositeType *type)
2995: {
2996:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

2998:   PetscFunctionBegin;
3000:   PetscAssertPointer(type, 2);
3001:   *type = jac->type;
3002:   PetscFunctionReturn(PETSC_SUCCESS);
3003: }

3005: /*@
3006:   PCFieldSplitSetDMSplits - Flags whether `DMCreateFieldDecomposition()` should be used to define the splits in a `PCFIELDSPLIT`, whenever possible.

3008:   Logically Collective

3010:   Input Parameters:
3011: + pc  - the preconditioner context
3012: - flg - boolean indicating whether to use field splits defined by the `DM`

3014:   Options Database Key:
3015: . -pc_fieldsplit_dm_splits <bool> - use the field splits defined by the `DM`

3017:   Level: intermediate

3019:   Developer Note:
3020:   The name should be `PCFieldSplitSetUseDMSplits()`, similar change to options database

3022: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitGetDMSplits()`, `DMCreateFieldDecomposition()`, `PCFieldSplitSetFields()`, `PCFieldsplitSetIS()`
3023: @*/
3024: PetscErrorCode PCFieldSplitSetDMSplits(PC pc, PetscBool flg)
3025: {
3026:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
3027:   PetscBool      isfs;

3029:   PetscFunctionBegin;
3032:   PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCFIELDSPLIT, &isfs));
3033:   if (isfs) jac->dm_splits = flg;
3034:   PetscFunctionReturn(PETSC_SUCCESS);
3035: }

3037: /*@
3038:   PCFieldSplitGetDMSplits - Returns flag indicating whether `DMCreateFieldDecomposition()` should be used to define the splits in a `PCFIELDSPLIT`, whenever possible.

3040:   Logically Collective

3042:   Input Parameter:
3043: . pc - the preconditioner context

3045:   Output Parameter:
3046: . flg - boolean indicating whether to use field splits defined by the `DM`

3048:   Level: intermediate

3050:   Developer Note:
3051:   The name should be `PCFieldSplitGetUseDMSplits()`

3053: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetDMSplits()`, `DMCreateFieldDecomposition()`, `PCFieldSplitSetFields()`, `PCFieldsplitSetIS()`
3054: @*/
3055: PetscErrorCode PCFieldSplitGetDMSplits(PC pc, PetscBool *flg)
3056: {
3057:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
3058:   PetscBool      isfs;

3060:   PetscFunctionBegin;
3062:   PetscAssertPointer(flg, 2);
3063:   PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCFIELDSPLIT, &isfs));
3064:   if (isfs) {
3065:     if (flg) *flg = jac->dm_splits;
3066:   }
3067:   PetscFunctionReturn(PETSC_SUCCESS);
3068: }

3070: /*@
3071:   PCFieldSplitGetDetectSaddlePoint - Returns flag indicating whether `PCFIELDSPLIT` will attempt to automatically determine fields based on zero diagonal entries.

3073:   Logically Collective

3075:   Input Parameter:
3076: . pc - the preconditioner context

3078:   Output Parameter:
3079: . flg - boolean indicating whether to detect fields or not

3081:   Level: intermediate

3083: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetDetectSaddlePoint()`
3084: @*/
3085: PetscErrorCode PCFieldSplitGetDetectSaddlePoint(PC pc, PetscBool *flg)
3086: {
3087:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

3089:   PetscFunctionBegin;
3090:   *flg = jac->detect;
3091:   PetscFunctionReturn(PETSC_SUCCESS);
3092: }

3094: /*@
3095:   PCFieldSplitSetDetectSaddlePoint - Sets flag indicating whether `PCFIELDSPLIT` will attempt to automatically determine fields based on zero diagonal entries.

3097:   Logically Collective

3099:   Input Parameter:
3100: . pc - the preconditioner context

3102:   Output Parameter:
3103: . flg - boolean indicating whether to detect fields or not

3105:   Options Database Key:
3106: . -pc_fieldsplit_detect_saddle_point <bool> - detect and use the saddle point

3108:   Level: intermediate

3110:   Note:
3111:   Also sets the split type to `PC_COMPOSITE_SCHUR` (see `PCFieldSplitSetType()`) and the Schur preconditioner type to `PC_FIELDSPLIT_SCHUR_PRE_SELF` (see `PCFieldSplitSetSchurPre()`).

3113: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitGetDetectSaddlePoint()`, `PCFieldSplitSetType()`, `PCFieldSplitSetSchurPre()`, `PC_FIELDSPLIT_SCHUR_PRE_SELF`
3114: @*/
3115: PetscErrorCode PCFieldSplitSetDetectSaddlePoint(PC pc, PetscBool flg)
3116: {
3117:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

3119:   PetscFunctionBegin;
3120:   jac->detect = flg;
3121:   if (jac->detect) {
3122:     PetscCall(PCFieldSplitSetType(pc, PC_COMPOSITE_SCHUR));
3123:     PetscCall(PCFieldSplitSetSchurPre(pc, PC_FIELDSPLIT_SCHUR_PRE_SELF, NULL));
3124:   }
3125:   PetscFunctionReturn(PETSC_SUCCESS);
3126: }

3128: /*MC
3129:    PCFIELDSPLIT - Preconditioner created by combining separate preconditioners for individual
3130:    collections of variables (that may overlap) called splits. See [the users manual section on "Solving Block Matrices"](sec_block_matrices) for more details.

3132:    Options Database Keys:
3133: +   -pc_fieldsplit_%d_fields <a,b,..>                                                - indicates the fields to be used in the `%d`'th split
3134: .   -pc_fieldsplit_default                                                           - automatically add any fields to additional splits that have not
3135:                                                                                      been supplied explicitly by `-pc_fieldsplit_%d_fields`
3136: .   -pc_fieldsplit_block_size <bs>                                                   - size of block that defines fields (i.e. there are bs fields)
3137: .   -pc_fieldsplit_type <additive,multiplicative,symmetric_multiplicative,schur,gkb> - type of relaxation or factorization splitting
3138: .   -pc_fieldsplit_schur_precondition <self,selfp,user,a11,full>                     - default is `a11`; see `PCFieldSplitSetSchurPre()`
3139: .   -pc_fieldsplit_schur_fact_type <diag,lower,upper,full>                           - set factorization type when using `-pc_fieldsplit_type schur`;
3140:                                                                                      see `PCFieldSplitSetSchurFactType()`
3141: .   -pc_fieldsplit_dm_splits <true,false> (default is true)                          - Whether to use `DMCreateFieldDecomposition()` for splits
3142: -   -pc_fieldsplit_detect_saddle_point                                               - automatically finds rows with zero diagonal and uses Schur complement with no preconditioner as the solver

3144:      Options prefixes for inner solvers when using the Schur complement preconditioner are `-fieldsplit_0_` and `-fieldsplit_1_` .
3145:      The options prefix for the inner solver when using the Golub-Kahan biadiagonalization preconditioner is `-fieldsplit_0_`
3146:      For all other solvers they are `-fieldsplit_%d_` for the `%d`'th field; use `-fieldsplit_` for all fields.

3148:      To set options on the solvers for each block append `-fieldsplit_` to all the `PC`
3149:      options database keys. For example, `-fieldsplit_pc_type ilu` `-fieldsplit_pc_factor_levels 1`

3151:      To set the options on the solvers separate for each block call `PCFieldSplitGetSubKSP()`
3152:       and set the options directly on the resulting `KSP` object

3154:     Level: intermediate

3156:    Notes:
3157:     Use `PCFieldSplitSetFields()` to set splits defined by "strided" entries and `PCFieldSplitSetIS()`
3158:      to define a split by an arbitrary collection of entries.

3160:       If no splits are set, the default is used. If a `DM` is associated with the `PC` and it supports
3161:       `DMCreateFieldDecomposition()`, then that is used for the default. Otherwise, the splits are defined by entries strided by bs,
3162:       beginning at 0 then 1, etc to bs-1. The block size can be set with `PCFieldSplitSetBlockSize()`,
3163:       if this is not called the block size defaults to the blocksize of the second matrix passed
3164:       to `KSPSetOperators()`/`PCSetOperators()`.

3166:       For the Schur complement preconditioner if

3168:       ```{math}
3169:       J = \left[\begin{array}{cc} A_{00} & A_{01} \\ A_{10} & A_{11} \end{array}\right]
3170:       ```

3172:       the preconditioner using `full` factorization is logically
3173:       ```{math}
3174:       \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]
3175:       ```
3176:      where the action of $\text{inv}(A_{00})$ is applied using the KSP solver with prefix `-fieldsplit_0_`.  $S$ is the Schur complement
3177:      ```{math}
3178:      S = A_{11} - A_{10} \text{ksp}(A_{00}) A_{01}
3179:      ```
3180:      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
3181:      in providing the SECOND split or 1 if not given). For `PCFieldSplitGetSubKSP()` when field number is 0,
3182:      it returns the KSP associated with `-fieldsplit_0_` while field number 1 gives `-fieldsplit_1_` KSP. By default
3183:      $A_{11}$ is used to construct a preconditioner for $S$, use `PCFieldSplitSetSchurPre()` for all the possible ways to construct the preconditioner for $S$.

3185:      The factorization type is set using `-pc_fieldsplit_schur_fact_type <diag, lower, upper, full>`. `full` is shown above,
3186:      `diag` gives
3187:       ```{math}
3188:       \left[\begin{array}{cc} \text{inv}(A_{00}) & 0 \\  0 & -\text{ksp}(S) \end{array}\right]
3189:       ```
3190:      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
3191:      can be turned off with `PCFieldSplitSetSchurScale()` or by command line `-pc_fieldsplit_schur_scale 1.0`. The `lower` factorization is the inverse of
3192:       ```{math}
3193:       \left[\begin{array}{cc} A_{00} & 0 \\  A_{10} & S \end{array}\right]
3194:       ```
3195:      where the inverses of A_{00} and S are applied using KSPs. The upper factorization is the inverse of
3196:       ```{math}
3197:       \left[\begin{array}{cc} A_{00} & A_{01} \\  0 & S \end{array}\right]
3198:       ```
3199:      where again the inverses of $A_{00}$ and $S$ are applied using `KSP`s.

3201:      If only one set of indices (one `IS`) is provided with `PCFieldSplitSetIS()` then the complement of that `IS`
3202:      is used automatically for a second block.

3204:      The fieldsplit preconditioner cannot currently be used with the `MATBAIJ` or `MATSBAIJ` data formats if the blocksize is larger than 1.
3205:      Generally it should be used with the `MATAIJ` format.

3207:      The forms of these preconditioners are closely related if not identical to forms derived as "Distributive Iterations", see,
3208:      for example, page 294 in "Principles of Computational Fluid Dynamics" by Pieter Wesseling {cite}`wesseling2009`.
3209:      One can also use `PCFIELDSPLIT`
3210:      inside a smoother resulting in "Distributive Smoothers".

3212:      See "A taxonomy and comparison of parallel block multi-level preconditioners for the incompressible Navier-Stokes equations" {cite}`elman2008tcp`.

3214:      The Constrained Pressure Preconditioner (CPR) can be implemented using `PCCOMPOSITE` with `PCGALERKIN`. CPR first solves an $R A P$ subsystem, updates the
3215:      residual on all variables (`PCCompositeSetType(pc,PC_COMPOSITE_MULTIPLICATIVE)`), and then applies a simple ILU like preconditioner on all the variables.

3217:      The generalized Golub-Kahan bidiagonalization preconditioner (GKB) can be applied to symmetric $2 \times 2$ block matrices of the shape
3218:      ```{math}
3219:      \left[\begin{array}{cc} A_{00} & A_{01} \\ A_{01}' & 0 \end{array}\right]
3220:      ```
3221:      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 $H = _{A00} + \nu*A_{01}*A_{01}'$.
3222:      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_`.

3224:    Developer Note:
3225:    The Schur complement functionality of `PCFIELDSPLIT` should likely be factored into its own `PC` thus simplifying the implementation of the preconditioners and their
3226:    user API.

3228: .seealso: [](sec_block_matrices), `PC`, `PCCreate()`, `PCSetType()`, `PCType`, `PC`, `PCLSC`,
3229:           `PCFieldSplitGetSubKSP()`, `PCFieldSplitSchurGetSubKSP()`, `PCFieldSplitSetFields()`,
3230:           `PCFieldSplitSetType()`, `PCFieldSplitSetIS()`, `PCFieldSplitSetSchurPre()`, `PCFieldSplitSetSchurFactType()`,
3231:           `MatSchurComplementSetAinvType()`, `PCFieldSplitSetSchurScale()`, `PCFieldSplitSetDetectSaddlePoint()`
3232: M*/

3234: PETSC_EXTERN PetscErrorCode PCCreate_FieldSplit(PC pc)
3235: {
3236:   PC_FieldSplit *jac;

3238:   PetscFunctionBegin;
3239:   PetscCall(PetscNew(&jac));

3241:   jac->bs                 = -1;
3242:   jac->nsplits            = 0;
3243:   jac->type               = PC_COMPOSITE_MULTIPLICATIVE;
3244:   jac->schurpre           = PC_FIELDSPLIT_SCHUR_PRE_USER; /* Try user preconditioner first, fall back on diagonal */
3245:   jac->schurfactorization = PC_FIELDSPLIT_SCHUR_FACT_FULL;
3246:   jac->schurscale         = -1.0;
3247:   jac->dm_splits          = PETSC_TRUE;
3248:   jac->detect             = PETSC_FALSE;
3249:   jac->gkbtol             = 1e-5;
3250:   jac->gkbdelay           = 5;
3251:   jac->gkbnu              = 1;
3252:   jac->gkbmaxit           = 100;
3253:   jac->gkbmonitor         = PETSC_FALSE;
3254:   jac->coordinates_set    = PETSC_FALSE;

3256:   pc->data = (void *)jac;

3258:   pc->ops->apply           = PCApply_FieldSplit;
3259:   pc->ops->applytranspose  = PCApplyTranspose_FieldSplit;
3260:   pc->ops->setup           = PCSetUp_FieldSplit;
3261:   pc->ops->reset           = PCReset_FieldSplit;
3262:   pc->ops->destroy         = PCDestroy_FieldSplit;
3263:   pc->ops->setfromoptions  = PCSetFromOptions_FieldSplit;
3264:   pc->ops->view            = PCView_FieldSplit;
3265:   pc->ops->applyrichardson = NULL;

3267:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSchurGetSubKSP_C", PCFieldSplitSchurGetSubKSP_FieldSplit));
3268:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSubKSP_C", PCFieldSplitGetSubKSP_FieldSplit));
3269:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetFields_C", PCFieldSplitSetFields_FieldSplit));
3270:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetIS_C", PCFieldSplitSetIS_FieldSplit));
3271:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetType_C", PCFieldSplitSetType_FieldSplit));
3272:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetBlockSize_C", PCFieldSplitSetBlockSize_FieldSplit));
3273:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitRestrictIS_C", PCFieldSplitRestrictIS_FieldSplit));
3274:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCSetCoordinates_C", PCSetCoordinates_FieldSplit));
3275:   PetscFunctionReturn(PETSC_SUCCESS);
3276: }