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

696:     for (i = 0; i < nsplit; i++) {
697:       Mat pmat;

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

916:         /* Set DM for new solver */
917:         PetscCall(KSPGetDM(jac->head->ksp, &dmInner));
918:         PetscCall(KSPSetDM(kspInner, dmInner));
919:         PetscCall(KSPSetDMActive(kspInner, PETSC_FALSE));

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

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

944:         PetscCall(MatSchurComplementGetKSP(jac->schur, &kspInner));
945:         PetscCall(KSPGetPC(kspInner, &pcInner));
946:         PetscCall(PetscObjectTypeCompare((PetscObject)pcInner, PCKSP, &flg));
947:         if (flg) {
948:           KSP ksp;

950:           PetscCall(PCKSPGetKSP(pcInner, &ksp));
951:           if (ksp == jac->head->ksp) PetscCall(PCSetUseAmat(pcInner, PETSC_TRUE));
952:         }
953:       }
954:       PetscCall(PetscSNPrintf(schurtestoption, sizeof(schurtestoption), "-fieldsplit_%s_upper_", ilink->splitname));
955:       PetscCall(PetscOptionsFindPairPrefix_Private(((PetscObject)pc)->options, ((PetscObject)pc)->prefix, schurtestoption, NULL, &flg));
956:       if (flg) {
957:         DM dmInner;

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

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

1009:     /* HACK: special support to forward L and Lp matrices that might be used by PCLSC */
1010:     PetscCall(PetscSNPrintf(lscname, sizeof(lscname), "%s_LSC_L", ilink->splitname));
1011:     PetscCall(PetscObjectQuery((PetscObject)pc->mat, lscname, (PetscObject *)&LSC_L));
1012:     if (!LSC_L) PetscCall(PetscObjectQuery((PetscObject)pc->pmat, lscname, (PetscObject *)&LSC_L));
1013:     if (LSC_L) PetscCall(PetscObjectCompose((PetscObject)jac->schur, "LSC_L", (PetscObject)LSC_L));
1014:     PetscCall(PetscSNPrintf(lscname, sizeof(lscname), "%s_LSC_Lp", ilink->splitname));
1015:     PetscCall(PetscObjectQuery((PetscObject)pc->pmat, lscname, (PetscObject *)&LSC_L));
1016:     if (!LSC_L) PetscCall(PetscObjectQuery((PetscObject)pc->mat, lscname, (PetscObject *)&LSC_L));
1017:     if (LSC_L) PetscCall(PetscObjectCompose((PetscObject)jac->schur, "LSC_Lp", (PetscObject)LSC_L));
1018:   } else if (jac->type == PC_COMPOSITE_GKB) {
1019:     IS       ccis;
1020:     PetscInt rstart, rend;

1022:     PetscCheck(nsplit == 2, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_INCOMP, "To use GKB preconditioner you must have exactly 2 fields");

1024:     ilink = jac->head;

1026:     /* When extracting off-diagonal submatrices, we take complements from this range */
1027:     PetscCall(MatGetOwnershipRangeColumn(pc->mat, &rstart, &rend));

1029:     PetscCall(ISComplement(ilink->is_col, rstart, rend, &ccis));
1030:     if (jac->offdiag_use_amat) {
1031:       PetscCall(MatCreateSubMatrix(pc->mat, ilink->is, ccis, MAT_INITIAL_MATRIX, &jac->B));
1032:     } else {
1033:       PetscCall(MatCreateSubMatrix(pc->pmat, ilink->is, ccis, MAT_INITIAL_MATRIX, &jac->B));
1034:     }
1035:     PetscCall(ISDestroy(&ccis));
1036:     /* Create work vectors for GKB algorithm */
1037:     PetscCall(VecDuplicate(ilink->x, &jac->u));
1038:     PetscCall(VecDuplicate(ilink->x, &jac->Hu));
1039:     PetscCall(VecDuplicate(ilink->x, &jac->w2));
1040:     ilink = ilink->next;
1041:     PetscCall(ISComplement(ilink->is_col, rstart, rend, &ccis));
1042:     if (jac->offdiag_use_amat) {
1043:       PetscCall(MatCreateSubMatrix(pc->mat, ilink->is, ccis, MAT_INITIAL_MATRIX, &jac->C));
1044:     } else {
1045:       PetscCall(MatCreateSubMatrix(pc->pmat, ilink->is, ccis, MAT_INITIAL_MATRIX, &jac->C));
1046:     }
1047:     PetscCall(ISDestroy(&ccis));
1048:     /* Create work vectors for GKB algorithm */
1049:     PetscCall(VecDuplicate(ilink->x, &jac->v));
1050:     PetscCall(VecDuplicate(ilink->x, &jac->d));
1051:     PetscCall(VecDuplicate(ilink->x, &jac->w1));
1052:     PetscCall(MatGolubKahanComputeExplicitOperator(jac->mat[0], jac->B, jac->C, &jac->H, jac->gkbnu));
1053:     PetscCall(PetscCalloc1(jac->gkbdelay, &jac->vecz));

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

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

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

1106: #define FieldSplitSplitSolveAdd(ilink, xx, yy) \
1107:   ((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) || \
1108:                     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) || \
1109:                     VecScatterEnd(ilink->sctx, ilink->y, yy, ADD_VALUES, SCATTER_REVERSE)))

1111: static PetscErrorCode PCApply_FieldSplit_Schur(PC pc, Vec x, Vec y)
1112: {
1113:   PC_FieldSplit    *jac    = (PC_FieldSplit *)pc->data;
1114:   PC_FieldSplitLink ilinkA = jac->head, ilinkD = ilinkA->next;
1115:   KSP               kspA = ilinkA->ksp, kspLower = kspA, kspUpper = jac->kspupper;

1117:   PetscFunctionBegin;
1118:   switch (jac->schurfactorization) {
1119:   case PC_FIELDSPLIT_SCHUR_FACT_DIAG:
1120:     /* [A00 0; 0 -S], positive definite, suitable for MINRES */
1121:     PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1122:     PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1123:     PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1124:     PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1125:     PetscCall(KSPSolve(kspA, ilinkA->x, ilinkA->y));
1126:     PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1127:     PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1128:     PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1129:     PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1130:     PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1131:     PetscCall(KSPSolve(jac->kspschur, ilinkD->x, ilinkD->y));
1132:     PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y));
1133:     PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1134:     PetscCall(VecScale(ilinkD->y, jac->schurscale));
1135:     PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1136:     PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1137:     PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1138:     break;
1139:   case PC_FIELDSPLIT_SCHUR_FACT_LOWER:
1140:     /* [A00 0; A10 S], suitable for left preconditioning */
1141:     PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1142:     PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1143:     PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1144:     PetscCall(KSPSolve(kspA, ilinkA->x, ilinkA->y));
1145:     PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1146:     PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1147:     PetscCall(MatMult(jac->C, ilinkA->y, ilinkD->x));
1148:     PetscCall(VecScale(ilinkD->x, -1.));
1149:     PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD));
1150:     PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1151:     PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD));
1152:     PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1153:     PetscCall(KSPSolve(jac->kspschur, ilinkD->x, ilinkD->y));
1154:     PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y));
1155:     PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1156:     PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1157:     PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1158:     PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1159:     break;
1160:   case PC_FIELDSPLIT_SCHUR_FACT_UPPER:
1161:     /* [A00 A01; 0 S], suitable for right preconditioning */
1162:     PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1163:     PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1164:     PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1165:     PetscCall(KSPSolve(jac->kspschur, ilinkD->x, ilinkD->y));
1166:     PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y));
1167:     PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1168:     PetscCall(MatMult(jac->B, ilinkD->y, ilinkA->x));
1169:     PetscCall(VecScale(ilinkA->x, -1.));
1170:     PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, ADD_VALUES, SCATTER_FORWARD));
1171:     PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1172:     PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, ADD_VALUES, SCATTER_FORWARD));
1173:     PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1174:     PetscCall(KSPSolve(kspA, ilinkA->x, ilinkA->y));
1175:     PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1176:     PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1177:     PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1178:     PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1179:     PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1180:     break;
1181:   case PC_FIELDSPLIT_SCHUR_FACT_FULL:
1182:     /* [1 0; A10 A00^{-1} 1] [A00 0; 0 S] [1 A00^{-1}A01; 0 1] */
1183:     PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1184:     PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1185:     PetscCall(PetscLogEventBegin(KSP_Solve_FS_L, kspLower, ilinkA->x, ilinkA->y, NULL));
1186:     PetscCall(KSPSolve(kspLower, ilinkA->x, ilinkA->y));
1187:     PetscCall(KSPCheckSolve(kspLower, pc, ilinkA->y));
1188:     PetscCall(PetscLogEventEnd(KSP_Solve_FS_L, kspLower, ilinkA->x, ilinkA->y, NULL));
1189:     PetscCall(MatMult(jac->C, ilinkA->y, ilinkD->x));
1190:     PetscCall(VecScale(ilinkD->x, -1.0));
1191:     PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD));
1192:     PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD));

1194:     PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1195:     PetscCall(KSPSolve(jac->kspschur, ilinkD->x, ilinkD->y));
1196:     PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y));
1197:     PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1198:     PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));

1200:     if (kspUpper == kspA) {
1201:       PetscCall(MatMult(jac->B, ilinkD->y, ilinkA->y));
1202:       PetscCall(VecAXPY(ilinkA->x, -1.0, ilinkA->y));
1203:       PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1204:       PetscCall(KSPSolve(kspA, ilinkA->x, ilinkA->y));
1205:       PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1206:       PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1207:     } else {
1208:       PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1209:       PetscCall(KSPSolve(kspA, ilinkA->x, ilinkA->y));
1210:       PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1211:       PetscCall(MatMult(jac->B, ilinkD->y, ilinkA->x));
1212:       PetscCall(PetscLogEventBegin(KSP_Solve_FS_U, kspUpper, ilinkA->x, ilinkA->z, NULL));
1213:       PetscCall(KSPSolve(kspUpper, ilinkA->x, ilinkA->z));
1214:       PetscCall(KSPCheckSolve(kspUpper, pc, ilinkA->z));
1215:       PetscCall(PetscLogEventEnd(KSP_Solve_FS_U, kspUpper, ilinkA->x, ilinkA->z, NULL));
1216:       PetscCall(VecAXPY(ilinkA->y, -1.0, ilinkA->z));
1217:     }
1218:     PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1219:     PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1220:     PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1221:   }
1222:   PetscFunctionReturn(PETSC_SUCCESS);
1223: }

1225: static PetscErrorCode PCApplyTranspose_FieldSplit_Schur(PC pc, Vec x, Vec y)
1226: {
1227:   PC_FieldSplit    *jac    = (PC_FieldSplit *)pc->data;
1228:   PC_FieldSplitLink ilinkA = jac->head, ilinkD = ilinkA->next;
1229:   KSP               kspA = ilinkA->ksp, kspLower = kspA, kspUpper = jac->kspupper;

1231:   PetscFunctionBegin;
1232:   switch (jac->schurfactorization) {
1233:   case PC_FIELDSPLIT_SCHUR_FACT_DIAG:
1234:     /* [A00 0; 0 -S], positive definite, suitable for MINRES */
1235:     PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1236:     PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1237:     PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1238:     PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1239:     PetscCall(KSPSolveTranspose(kspA, ilinkA->x, ilinkA->y));
1240:     PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1241:     PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1242:     PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1243:     PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1244:     PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1245:     PetscCall(KSPSolveTranspose(jac->kspschur, ilinkD->x, ilinkD->y));
1246:     PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y));
1247:     PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1248:     PetscCall(VecScale(ilinkD->y, jac->schurscale));
1249:     PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1250:     PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1251:     PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1252:     break;
1253:   case PC_FIELDSPLIT_SCHUR_FACT_UPPER:
1254:     PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1255:     PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1256:     PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1257:     PetscCall(KSPSolveTranspose(kspA, ilinkA->x, ilinkA->y));
1258:     PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1259:     PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1260:     PetscCall(MatMultTranspose(jac->B, ilinkA->y, ilinkD->x));
1261:     PetscCall(VecScale(ilinkD->x, -1.));
1262:     PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD));
1263:     PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1264:     PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD));
1265:     PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1266:     PetscCall(KSPSolveTranspose(jac->kspschur, ilinkD->x, ilinkD->y));
1267:     PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y));
1268:     PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1269:     PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1270:     PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1271:     PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1272:     break;
1273:   case PC_FIELDSPLIT_SCHUR_FACT_LOWER:
1274:     PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1275:     PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1276:     PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1277:     PetscCall(KSPSolveTranspose(jac->kspschur, ilinkD->x, ilinkD->y));
1278:     PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y));
1279:     PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1280:     PetscCall(MatMultTranspose(jac->C, ilinkD->y, ilinkA->x));
1281:     PetscCall(VecScale(ilinkA->x, -1.));
1282:     PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, ADD_VALUES, SCATTER_FORWARD));
1283:     PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1284:     PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, ADD_VALUES, SCATTER_FORWARD));
1285:     PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1286:     PetscCall(KSPSolveTranspose(kspA, ilinkA->x, ilinkA->y));
1287:     PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1288:     PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1289:     PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1290:     PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1291:     PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1292:     break;
1293:   case PC_FIELDSPLIT_SCHUR_FACT_FULL:
1294:     PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1295:     PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1296:     PetscCall(PetscLogEventBegin(KSP_Solve_FS_U, kspUpper, ilinkA->x, ilinkA->y, NULL));
1297:     PetscCall(KSPSolveTranspose(kspUpper, ilinkA->x, ilinkA->y));
1298:     PetscCall(KSPCheckSolve(kspUpper, pc, ilinkA->y));
1299:     PetscCall(PetscLogEventEnd(KSP_Solve_FS_U, kspUpper, ilinkA->x, ilinkA->y, NULL));
1300:     PetscCall(MatMultTranspose(jac->B, ilinkA->y, ilinkD->x));
1301:     PetscCall(VecScale(ilinkD->x, -1.0));
1302:     PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD));
1303:     PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD));

1305:     PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1306:     PetscCall(KSPSolveTranspose(jac->kspschur, ilinkD->x, ilinkD->y));
1307:     PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y));
1308:     PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1309:     PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));

1311:     if (kspLower == kspA) {
1312:       PetscCall(MatMultTranspose(jac->C, ilinkD->y, ilinkA->y));
1313:       PetscCall(VecAXPY(ilinkA->x, -1.0, ilinkA->y));
1314:       PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1315:       PetscCall(KSPSolveTranspose(kspA, ilinkA->x, ilinkA->y));
1316:       PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1317:       PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1318:     } else {
1319:       PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1320:       PetscCall(KSPSolveTranspose(kspA, ilinkA->x, ilinkA->y));
1321:       PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1322:       PetscCall(MatMultTranspose(jac->C, ilinkD->y, ilinkA->x));
1323:       PetscCall(PetscLogEventBegin(KSP_Solve_FS_L, kspLower, ilinkA->x, ilinkA->z, NULL));
1324:       PetscCall(KSPSolveTranspose(kspLower, ilinkA->x, ilinkA->z));
1325:       PetscCall(KSPCheckSolve(kspLower, pc, ilinkA->z));
1326:       PetscCall(PetscLogEventEnd(KSP_Solve_FS_L, kspLower, ilinkA->x, ilinkA->z, NULL));
1327:       PetscCall(VecAXPY(ilinkA->y, -1.0, ilinkA->z));
1328:     }
1329:     PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1330:     PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1331:     PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1332:   }
1333:   PetscFunctionReturn(PETSC_SUCCESS);
1334: }

1336: static PetscErrorCode PCApply_FieldSplit(PC pc, Vec x, Vec y)
1337: {
1338:   PC_FieldSplit    *jac   = (PC_FieldSplit *)pc->data;
1339:   PC_FieldSplitLink ilink = jac->head;
1340:   PetscInt          cnt, bs;

1342:   PetscFunctionBegin;
1343:   if (jac->type == PC_COMPOSITE_ADDITIVE) {
1344:     if (jac->defaultsplit) {
1345:       PetscCall(VecGetBlockSize(x, &bs));
1346:       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);
1347:       PetscCall(VecGetBlockSize(y, &bs));
1348:       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);
1349:       PetscCall(VecStrideGatherAll(x, jac->x, INSERT_VALUES));
1350:       while (ilink) {
1351:         PetscCall(PetscLogEventBegin(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1352:         PetscCall(KSPSolve(ilink->ksp, ilink->x, ilink->y));
1353:         PetscCall(KSPCheckSolve(ilink->ksp, pc, ilink->y));
1354:         PetscCall(PetscLogEventEnd(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1355:         ilink = ilink->next;
1356:       }
1357:       PetscCall(VecStrideScatterAll(jac->y, y, INSERT_VALUES));
1358:     } else {
1359:       PetscCall(VecSet(y, 0.0));
1360:       while (ilink) {
1361:         PetscCall(FieldSplitSplitSolveAdd(ilink, x, y));
1362:         ilink = ilink->next;
1363:       }
1364:     }
1365:   } else if (jac->type == PC_COMPOSITE_MULTIPLICATIVE && jac->nsplits == 2) {
1366:     PetscCall(VecSet(y, 0.0));
1367:     /* solve on first block for first block variables */
1368:     PetscCall(VecScatterBegin(ilink->sctx, x, ilink->x, INSERT_VALUES, SCATTER_FORWARD));
1369:     PetscCall(VecScatterEnd(ilink->sctx, x, ilink->x, INSERT_VALUES, SCATTER_FORWARD));
1370:     PetscCall(PetscLogEventBegin(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1371:     PetscCall(KSPSolve(ilink->ksp, ilink->x, ilink->y));
1372:     PetscCall(KSPCheckSolve(ilink->ksp, pc, ilink->y));
1373:     PetscCall(PetscLogEventEnd(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1374:     PetscCall(VecScatterBegin(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE));
1375:     PetscCall(VecScatterEnd(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE));

1377:     /* compute the residual only onto second block variables using first block variables */
1378:     PetscCall(MatMult(jac->Afield[1], ilink->y, ilink->next->x));
1379:     ilink = ilink->next;
1380:     PetscCall(VecScale(ilink->x, -1.0));
1381:     PetscCall(VecScatterBegin(ilink->sctx, x, ilink->x, ADD_VALUES, SCATTER_FORWARD));
1382:     PetscCall(VecScatterEnd(ilink->sctx, x, ilink->x, ADD_VALUES, SCATTER_FORWARD));

1384:     /* solve on second block variables */
1385:     PetscCall(PetscLogEventBegin(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1386:     PetscCall(KSPSolve(ilink->ksp, ilink->x, ilink->y));
1387:     PetscCall(KSPCheckSolve(ilink->ksp, pc, ilink->y));
1388:     PetscCall(PetscLogEventEnd(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1389:     PetscCall(VecScatterBegin(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE));
1390:     PetscCall(VecScatterEnd(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE));
1391:   } else if (jac->type == PC_COMPOSITE_MULTIPLICATIVE || jac->type == PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE) {
1392:     if (!jac->w1) {
1393:       PetscCall(VecDuplicate(x, &jac->w1));
1394:       PetscCall(VecDuplicate(x, &jac->w2));
1395:     }
1396:     PetscCall(VecSet(y, 0.0));
1397:     PetscCall(FieldSplitSplitSolveAdd(ilink, x, y));
1398:     cnt = 1;
1399:     while (ilink->next) {
1400:       ilink = ilink->next;
1401:       /* compute the residual only over the part of the vector needed */
1402:       PetscCall(MatMult(jac->Afield[cnt++], y, ilink->x));
1403:       PetscCall(VecScale(ilink->x, -1.0));
1404:       PetscCall(VecScatterBegin(ilink->sctx, x, ilink->x, ADD_VALUES, SCATTER_FORWARD));
1405:       PetscCall(VecScatterEnd(ilink->sctx, x, ilink->x, ADD_VALUES, SCATTER_FORWARD));
1406:       PetscCall(PetscLogEventBegin(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1407:       PetscCall(KSPSolve(ilink->ksp, ilink->x, ilink->y));
1408:       PetscCall(KSPCheckSolve(ilink->ksp, pc, ilink->y));
1409:       PetscCall(PetscLogEventEnd(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1410:       PetscCall(VecScatterBegin(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE));
1411:       PetscCall(VecScatterEnd(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE));
1412:     }
1413:     if (jac->type == PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE) {
1414:       cnt -= 2;
1415:       while (ilink->previous) {
1416:         ilink = ilink->previous;
1417:         /* compute the residual only over the part of the vector needed */
1418:         PetscCall(MatMult(jac->Afield[cnt--], y, ilink->x));
1419:         PetscCall(VecScale(ilink->x, -1.0));
1420:         PetscCall(VecScatterBegin(ilink->sctx, x, ilink->x, ADD_VALUES, SCATTER_FORWARD));
1421:         PetscCall(VecScatterEnd(ilink->sctx, x, ilink->x, ADD_VALUES, SCATTER_FORWARD));
1422:         PetscCall(PetscLogEventBegin(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1423:         PetscCall(KSPSolve(ilink->ksp, ilink->x, ilink->y));
1424:         PetscCall(KSPCheckSolve(ilink->ksp, pc, ilink->y));
1425:         PetscCall(PetscLogEventEnd(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1426:         PetscCall(VecScatterBegin(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE));
1427:         PetscCall(VecScatterEnd(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE));
1428:       }
1429:     }
1430:   } else SETERRQ(PetscObjectComm((PetscObject)pc), PETSC_ERR_SUP, "Unsupported or unknown composition %d", (int)jac->type);
1431:   PetscFunctionReturn(PETSC_SUCCESS);
1432: }

1434: static PetscErrorCode PCApply_FieldSplit_GKB(PC pc, Vec x, Vec y)
1435: {
1436:   PC_FieldSplit    *jac    = (PC_FieldSplit *)pc->data;
1437:   PC_FieldSplitLink ilinkA = jac->head, ilinkD = ilinkA->next;
1438:   KSP               ksp = ilinkA->ksp;
1439:   Vec               u, v, Hu, d, work1, work2;
1440:   PetscScalar       alpha, z, nrmz2, *vecz;
1441:   PetscReal         lowbnd, nu, beta;
1442:   PetscInt          j, iterGKB;

1444:   PetscFunctionBegin;
1445:   PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1446:   PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1447:   PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1448:   PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));

1450:   u     = jac->u;
1451:   v     = jac->v;
1452:   Hu    = jac->Hu;
1453:   d     = jac->d;
1454:   work1 = jac->w1;
1455:   work2 = jac->w2;
1456:   vecz  = jac->vecz;

1458:   /* Change RHS to comply with matrix regularization H = A + nu*B*B' */
1459:   /* Add q = q + nu*B*b */
1460:   if (jac->gkbnu) {
1461:     nu = jac->gkbnu;
1462:     PetscCall(VecScale(ilinkD->x, jac->gkbnu));
1463:     PetscCall(MatMultAdd(jac->B, ilinkD->x, ilinkA->x, ilinkA->x)); /* q = q + nu*B*b */
1464:   } else {
1465:     /* Situation when no augmented Lagrangian is used. Then we set inner  */
1466:     /* matrix N = I in [Ar13], and thus nu = 1.                           */
1467:     nu = 1;
1468:   }

1470:   /* Transform rhs from [q,tilde{b}] to [0,b] */
1471:   PetscCall(PetscLogEventBegin(ilinkA->event, ksp, ilinkA->x, ilinkA->y, NULL));
1472:   PetscCall(KSPSolve(ksp, ilinkA->x, ilinkA->y));
1473:   PetscCall(KSPCheckSolve(ksp, pc, ilinkA->y));
1474:   PetscCall(PetscLogEventEnd(ilinkA->event, ksp, ilinkA->x, ilinkA->y, NULL));
1475:   PetscCall(MatMultHermitianTranspose(jac->B, ilinkA->y, work1));
1476:   PetscCall(VecAXPBY(work1, 1.0 / nu, -1.0, ilinkD->x)); /* c = b - B'*x        */

1478:   /* First step of algorithm */
1479:   PetscCall(VecNorm(work1, NORM_2, &beta)); /* beta = sqrt(nu*c'*c)*/
1480:   KSPCheckDot(ksp, beta);
1481:   beta = PetscSqrtReal(nu) * beta;
1482:   PetscCall(VecAXPBY(v, nu / beta, 0.0, work1)); /* v = nu/beta *c      */
1483:   PetscCall(MatMult(jac->B, v, work2));          /* u = H^{-1}*B*v      */
1484:   PetscCall(PetscLogEventBegin(ilinkA->event, ksp, work2, u, NULL));
1485:   PetscCall(KSPSolve(ksp, work2, u));
1486:   PetscCall(KSPCheckSolve(ksp, pc, u));
1487:   PetscCall(PetscLogEventEnd(ilinkA->event, ksp, work2, u, NULL));
1488:   PetscCall(MatMult(jac->H, u, Hu)); /* alpha = u'*H*u      */
1489:   PetscCall(VecDot(Hu, u, &alpha));
1490:   KSPCheckDot(ksp, alpha);
1491:   PetscCheck(PetscRealPart(alpha) > 0.0, PETSC_COMM_SELF, PETSC_ERR_NOT_CONVERGED, "GKB preconditioner diverged, H is not positive definite");
1492:   alpha = PetscSqrtReal(PetscAbsScalar(alpha));
1493:   PetscCall(VecScale(u, 1.0 / alpha));
1494:   PetscCall(VecAXPBY(d, 1.0 / alpha, 0.0, v)); /* v = nu/beta *c      */

1496:   z       = beta / alpha;
1497:   vecz[1] = z;

1499:   /* Computation of first iterate x(1) and p(1) */
1500:   PetscCall(VecAXPY(ilinkA->y, z, u));
1501:   PetscCall(VecCopy(d, ilinkD->y));
1502:   PetscCall(VecScale(ilinkD->y, -z));

1504:   iterGKB = 1;
1505:   lowbnd  = 2 * jac->gkbtol;
1506:   if (jac->gkbmonitor) PetscCall(PetscViewerASCIIPrintf(jac->gkbviewer, "%3" PetscInt_FMT " GKB Lower bound estimate %14.12e\n", iterGKB, (double)lowbnd));

1508:   while (iterGKB < jac->gkbmaxit && lowbnd > jac->gkbtol) {
1509:     iterGKB += 1;
1510:     PetscCall(MatMultHermitianTranspose(jac->B, u, work1)); /* v <- nu*(B'*u-alpha/nu*v) */
1511:     PetscCall(VecAXPBY(v, nu, -alpha, work1));
1512:     PetscCall(VecNorm(v, NORM_2, &beta)); /* beta = sqrt(nu)*v'*v      */
1513:     beta = beta / PetscSqrtReal(nu);
1514:     PetscCall(VecScale(v, 1.0 / beta));
1515:     PetscCall(MatMult(jac->B, v, work2)); /* u <- H^{-1}*(B*v-beta*H*u) */
1516:     PetscCall(MatMult(jac->H, u, Hu));
1517:     PetscCall(VecAXPY(work2, -beta, Hu));
1518:     PetscCall(PetscLogEventBegin(ilinkA->event, ksp, work2, u, NULL));
1519:     PetscCall(KSPSolve(ksp, work2, u));
1520:     PetscCall(KSPCheckSolve(ksp, pc, u));
1521:     PetscCall(PetscLogEventEnd(ilinkA->event, ksp, work2, u, NULL));
1522:     PetscCall(MatMult(jac->H, u, Hu)); /* alpha = u'*H*u            */
1523:     PetscCall(VecDot(Hu, u, &alpha));
1524:     KSPCheckDot(ksp, alpha);
1525:     PetscCheck(PetscRealPart(alpha) > 0.0, PETSC_COMM_SELF, PETSC_ERR_NOT_CONVERGED, "GKB preconditioner diverged, H is not positive definite");
1526:     alpha = PetscSqrtReal(PetscAbsScalar(alpha));
1527:     PetscCall(VecScale(u, 1.0 / alpha));

1529:     z       = -beta / alpha * z; /* z <- beta/alpha*z     */
1530:     vecz[0] = z;

1532:     /* Computation of new iterate x(i+1) and p(i+1) */
1533:     PetscCall(VecAXPBY(d, 1.0 / alpha, -beta / alpha, v)); /* d = (v-beta*d)/alpha */
1534:     PetscCall(VecAXPY(ilinkA->y, z, u));                   /* r = r + z*u          */
1535:     PetscCall(VecAXPY(ilinkD->y, -z, d));                  /* p = p - z*d          */
1536:     PetscCall(MatMult(jac->H, ilinkA->y, Hu));             /* ||u||_H = u'*H*u     */
1537:     PetscCall(VecDot(Hu, ilinkA->y, &nrmz2));

1539:     /* Compute Lower Bound estimate */
1540:     if (iterGKB > jac->gkbdelay) {
1541:       lowbnd = 0.0;
1542:       for (j = 0; j < jac->gkbdelay; j++) lowbnd += PetscAbsScalar(vecz[j] * vecz[j]);
1543:       lowbnd = PetscSqrtReal(lowbnd / PetscAbsScalar(nrmz2));
1544:     }

1546:     for (j = 0; j < jac->gkbdelay - 1; j++) vecz[jac->gkbdelay - j - 1] = vecz[jac->gkbdelay - j - 2];
1547:     if (jac->gkbmonitor) PetscCall(PetscViewerASCIIPrintf(jac->gkbviewer, "%3" PetscInt_FMT " GKB Lower bound estimate %14.12e\n", iterGKB, (double)lowbnd));
1548:   }

1550:   PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1551:   PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1552:   PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1553:   PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));

1555:   PetscFunctionReturn(PETSC_SUCCESS);
1556: }

1558: #define FieldSplitSplitSolveAddTranspose(ilink, xx, yy) \
1559:   ((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) || \
1560:                     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) || \
1561:                     VecScatterEnd(ilink->sctx, ilink->x, yy, ADD_VALUES, SCATTER_REVERSE)))

1563: static PetscErrorCode PCApplyTranspose_FieldSplit(PC pc, Vec x, Vec y)
1564: {
1565:   PC_FieldSplit    *jac   = (PC_FieldSplit *)pc->data;
1566:   PC_FieldSplitLink ilink = jac->head;
1567:   PetscInt          bs;

1569:   PetscFunctionBegin;
1570:   if (jac->type == PC_COMPOSITE_ADDITIVE) {
1571:     if (jac->defaultsplit) {
1572:       PetscCall(VecGetBlockSize(x, &bs));
1573:       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);
1574:       PetscCall(VecGetBlockSize(y, &bs));
1575:       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);
1576:       PetscCall(VecStrideGatherAll(x, jac->x, INSERT_VALUES));
1577:       while (ilink) {
1578:         PetscCall(PetscLogEventBegin(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1579:         PetscCall(KSPSolveTranspose(ilink->ksp, ilink->x, ilink->y));
1580:         PetscCall(KSPCheckSolve(ilink->ksp, pc, ilink->y));
1581:         PetscCall(PetscLogEventEnd(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1582:         ilink = ilink->next;
1583:       }
1584:       PetscCall(VecStrideScatterAll(jac->y, y, INSERT_VALUES));
1585:     } else {
1586:       PetscCall(VecSet(y, 0.0));
1587:       while (ilink) {
1588:         PetscCall(FieldSplitSplitSolveAddTranspose(ilink, x, y));
1589:         ilink = ilink->next;
1590:       }
1591:     }
1592:   } else {
1593:     if (!jac->w1) {
1594:       PetscCall(VecDuplicate(x, &jac->w1));
1595:       PetscCall(VecDuplicate(x, &jac->w2));
1596:     }
1597:     PetscCall(VecSet(y, 0.0));
1598:     if (jac->type == PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE) {
1599:       PetscCall(FieldSplitSplitSolveAddTranspose(ilink, x, y));
1600:       while (ilink->next) {
1601:         ilink = ilink->next;
1602:         PetscCall(MatMultTranspose(pc->mat, y, jac->w1));
1603:         PetscCall(VecWAXPY(jac->w2, -1.0, jac->w1, x));
1604:         PetscCall(FieldSplitSplitSolveAddTranspose(ilink, jac->w2, y));
1605:       }
1606:       while (ilink->previous) {
1607:         ilink = ilink->previous;
1608:         PetscCall(MatMultTranspose(pc->mat, y, jac->w1));
1609:         PetscCall(VecWAXPY(jac->w2, -1.0, jac->w1, x));
1610:         PetscCall(FieldSplitSplitSolveAddTranspose(ilink, jac->w2, y));
1611:       }
1612:     } else {
1613:       while (ilink->next) { /* get to last entry in linked list */
1614:         ilink = ilink->next;
1615:       }
1616:       PetscCall(FieldSplitSplitSolveAddTranspose(ilink, x, y));
1617:       while (ilink->previous) {
1618:         ilink = ilink->previous;
1619:         PetscCall(MatMultTranspose(pc->mat, y, jac->w1));
1620:         PetscCall(VecWAXPY(jac->w2, -1.0, jac->w1, x));
1621:         PetscCall(FieldSplitSplitSolveAddTranspose(ilink, jac->w2, y));
1622:       }
1623:     }
1624:   }
1625:   PetscFunctionReturn(PETSC_SUCCESS);
1626: }

1628: static PetscErrorCode PCReset_FieldSplit(PC pc)
1629: {
1630:   PC_FieldSplit    *jac   = (PC_FieldSplit *)pc->data;
1631:   PC_FieldSplitLink ilink = jac->head, next;

1633:   PetscFunctionBegin;
1634:   while (ilink) {
1635:     PetscCall(KSPDestroy(&ilink->ksp));
1636:     PetscCall(VecDestroy(&ilink->x));
1637:     PetscCall(VecDestroy(&ilink->y));
1638:     PetscCall(VecDestroy(&ilink->z));
1639:     PetscCall(VecScatterDestroy(&ilink->sctx));
1640:     PetscCall(ISDestroy(&ilink->is));
1641:     PetscCall(ISDestroy(&ilink->is_col));
1642:     PetscCall(PetscFree(ilink->splitname));
1643:     PetscCall(PetscFree(ilink->fields));
1644:     PetscCall(PetscFree(ilink->fields_col));
1645:     next = ilink->next;
1646:     PetscCall(PetscFree(ilink));
1647:     ilink = next;
1648:   }
1649:   jac->head = NULL;
1650:   PetscCall(PetscFree2(jac->x, jac->y));
1651:   if (jac->mat && jac->mat != jac->pmat) {
1652:     PetscCall(MatDestroyMatrices(jac->nsplits, &jac->mat));
1653:   } else if (jac->mat) {
1654:     jac->mat = NULL;
1655:   }
1656:   if (jac->pmat) PetscCall(MatDestroyMatrices(jac->nsplits, &jac->pmat));
1657:   if (jac->Afield) PetscCall(MatDestroyMatrices(jac->nsplits, &jac->Afield));
1658:   jac->nsplits = 0;
1659:   PetscCall(VecDestroy(&jac->w1));
1660:   PetscCall(VecDestroy(&jac->w2));
1661:   PetscCall(MatDestroy(&jac->schur));
1662:   PetscCall(MatDestroy(&jac->schurp));
1663:   PetscCall(MatDestroy(&jac->schur_user));
1664:   PetscCall(KSPDestroy(&jac->kspschur));
1665:   PetscCall(KSPDestroy(&jac->kspupper));
1666:   PetscCall(MatDestroy(&jac->B));
1667:   PetscCall(MatDestroy(&jac->C));
1668:   PetscCall(MatDestroy(&jac->H));
1669:   PetscCall(VecDestroy(&jac->u));
1670:   PetscCall(VecDestroy(&jac->v));
1671:   PetscCall(VecDestroy(&jac->Hu));
1672:   PetscCall(VecDestroy(&jac->d));
1673:   PetscCall(PetscFree(jac->vecz));
1674:   PetscCall(PetscViewerDestroy(&jac->gkbviewer));
1675:   jac->isrestrict = PETSC_FALSE;
1676:   PetscFunctionReturn(PETSC_SUCCESS);
1677: }

1679: static PetscErrorCode PCDestroy_FieldSplit(PC pc)
1680: {
1681:   PetscFunctionBegin;
1682:   PetscCall(PCReset_FieldSplit(pc));
1683:   PetscCall(PetscFree(pc->data));
1684:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCSetCoordinates_C", NULL));
1685:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetFields_C", NULL));
1686:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetIS_C", NULL));
1687:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetType_C", NULL));
1688:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetBlockSize_C", NULL));
1689:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitRestrictIS_C", NULL));
1690:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSchurGetSubKSP_C", NULL));
1691:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSubKSP_C", NULL));

1693:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBTol_C", NULL));
1694:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBMaxit_C", NULL));
1695:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBNu_C", NULL));
1696:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBDelay_C", NULL));
1697:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSubKSP_C", NULL));
1698:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurPre_C", NULL));
1699:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSchurPre_C", NULL));
1700:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurFactType_C", NULL));
1701:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurScale_C", NULL));
1702:   PetscFunctionReturn(PETSC_SUCCESS);
1703: }

1705: static PetscErrorCode PCSetFromOptions_FieldSplit(PC pc, PetscOptionItems *PetscOptionsObject)
1706: {
1707:   PetscInt        bs;
1708:   PetscBool       flg;
1709:   PC_FieldSplit  *jac = (PC_FieldSplit *)pc->data;
1710:   PCCompositeType ctype;

1712:   PetscFunctionBegin;
1713:   PetscOptionsHeadBegin(PetscOptionsObject, "FieldSplit options");
1714:   PetscCall(PetscOptionsBool("-pc_fieldsplit_dm_splits", "Whether to use DMCreateFieldDecomposition() for splits", "PCFieldSplitSetDMSplits", jac->dm_splits, &jac->dm_splits, NULL));
1715:   PetscCall(PetscOptionsInt("-pc_fieldsplit_block_size", "Blocksize that defines number of fields", "PCFieldSplitSetBlockSize", jac->bs, &bs, &flg));
1716:   if (flg) PetscCall(PCFieldSplitSetBlockSize(pc, bs));
1717:   jac->diag_use_amat = pc->useAmat;
1718:   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));
1719:   jac->offdiag_use_amat = pc->useAmat;
1720:   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));
1721:   PetscCall(PetscOptionsBool("-pc_fieldsplit_detect_saddle_point", "Form 2-way split by detecting zero diagonal entries", "PCFieldSplitSetDetectSaddlePoint", jac->detect, &jac->detect, NULL));
1722:   PetscCall(PCFieldSplitSetDetectSaddlePoint(pc, jac->detect)); /* Sets split type and Schur PC type */
1723:   PetscCall(PetscOptionsEnum("-pc_fieldsplit_type", "Type of composition", "PCFieldSplitSetType", PCCompositeTypes, (PetscEnum)jac->type, (PetscEnum *)&ctype, &flg));
1724:   if (flg) PetscCall(PCFieldSplitSetType(pc, ctype));
1725:   /* Only setup fields once */
1726:   if ((jac->bs > 0) && (jac->nsplits == 0)) {
1727:     /* only allow user to set fields from command line if bs is already known.
1728:        otherwise user can set them in PCFieldSplitSetDefaults() */
1729:     PetscCall(PCFieldSplitSetRuntimeSplits_Private(pc));
1730:     if (jac->splitdefined) PetscCall(PetscInfo(pc, "Splits defined using the options database\n"));
1731:   }
1732:   if (jac->type == PC_COMPOSITE_SCHUR) {
1733:     PetscCall(PetscOptionsGetEnum(((PetscObject)pc)->options, ((PetscObject)pc)->prefix, "-pc_fieldsplit_schur_factorization_type", PCFieldSplitSchurFactTypes, (PetscEnum *)&jac->schurfactorization, &flg));
1734:     if (flg) PetscCall(PetscInfo(pc, "Deprecated use of -pc_fieldsplit_schur_factorization_type\n"));
1735:     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));
1736:     PetscCall(PetscOptionsEnum("-pc_fieldsplit_schur_precondition", "How to build preconditioner for Schur complement", "PCFieldSplitSetSchurPre", PCFieldSplitSchurPreTypes, (PetscEnum)jac->schurpre, (PetscEnum *)&jac->schurpre, NULL));
1737:     PetscCall(PetscOptionsScalar("-pc_fieldsplit_schur_scale", "Scale Schur complement", "PCFieldSplitSetSchurScale", jac->schurscale, &jac->schurscale, NULL));
1738:   } else if (jac->type == PC_COMPOSITE_GKB) {
1739:     PetscCall(PetscOptionsReal("-pc_fieldsplit_gkb_tol", "The tolerance for the lower bound stopping criterion", "PCFieldSplitGKBTol", jac->gkbtol, &jac->gkbtol, NULL));
1740:     PetscCall(PetscOptionsInt("-pc_fieldsplit_gkb_delay", "The delay value for lower bound criterion", "PCFieldSplitGKBDelay", jac->gkbdelay, &jac->gkbdelay, NULL));
1741:     PetscCall(PetscOptionsReal("-pc_fieldsplit_gkb_nu", "Parameter in augmented Lagrangian approach", "PCFieldSplitGKBNu", jac->gkbnu, &jac->gkbnu, NULL));
1742:     PetscCheck(jac->gkbnu >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "nu cannot be less than 0: value %g", (double)jac->gkbnu);
1743:     PetscCall(PetscOptionsInt("-pc_fieldsplit_gkb_maxit", "Maximum allowed number of iterations", "PCFieldSplitGKBMaxit", jac->gkbmaxit, &jac->gkbmaxit, NULL));
1744:     PetscCall(PetscOptionsBool("-pc_fieldsplit_gkb_monitor", "Prints number of GKB iterations and error", "PCFieldSplitGKB", jac->gkbmonitor, &jac->gkbmonitor, NULL));
1745:   }
1746:   /*
1747:     In the initial call to this routine the sub-solver data structures do not exist so we cannot call KSPSetFromOptions() on them yet.
1748:     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
1749:     is called on the outer solver in case changes were made in the options database

1751:     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()
1752:     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.
1753:     Without this extra check test p2p1fetidp_olof_full and others fail with incorrect matrix types.

1755:     There could be a negative side effect of calling the KSPSetFromOptions() below.

1757:     If one captured the PetscObjectState of the options database one could skip these calls if the database has not changed from the previous call
1758:   */
1759:   if (jac->issetup) {
1760:     PC_FieldSplitLink ilink = jac->head;
1761:     if (jac->type == PC_COMPOSITE_SCHUR) {
1762:       if (jac->kspupper && jac->kspupper->totalits > 0) PetscCall(KSPSetFromOptions(jac->kspupper));
1763:       if (jac->kspschur && jac->kspschur->totalits > 0) PetscCall(KSPSetFromOptions(jac->kspschur));
1764:     }
1765:     while (ilink) {
1766:       if (ilink->ksp->totalits > 0) PetscCall(KSPSetFromOptions(ilink->ksp));
1767:       ilink = ilink->next;
1768:     }
1769:   }
1770:   PetscOptionsHeadEnd();
1771:   PetscFunctionReturn(PETSC_SUCCESS);
1772: }

1774: static PetscErrorCode PCFieldSplitSetFields_FieldSplit(PC pc, const char splitname[], PetscInt n, const PetscInt *fields, const PetscInt *fields_col)
1775: {
1776:   PC_FieldSplit    *jac = (PC_FieldSplit *)pc->data;
1777:   PC_FieldSplitLink ilink, next = jac->head;
1778:   char              prefix[128];
1779:   PetscInt          i;

1781:   PetscFunctionBegin;
1782:   if (jac->splitdefined) {
1783:     PetscCall(PetscInfo(pc, "Ignoring new split \"%s\" because the splits have already been defined\n", splitname));
1784:     PetscFunctionReturn(PETSC_SUCCESS);
1785:   }
1786:   for (i = 0; i < n; i++) {
1787:     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);
1788:     PetscCheck(fields[i] >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Negative field %" PetscInt_FMT " requested", fields[i]);
1789:   }
1790:   PetscCall(PetscNew(&ilink));
1791:   if (splitname) {
1792:     PetscCall(PetscStrallocpy(splitname, &ilink->splitname));
1793:   } else {
1794:     PetscCall(PetscMalloc1(3, &ilink->splitname));
1795:     PetscCall(PetscSNPrintf(ilink->splitname, 2, "%" PetscInt_FMT, jac->nsplits));
1796:   }
1797:   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 */
1798:   PetscCall(PetscMalloc1(n, &ilink->fields));
1799:   PetscCall(PetscArraycpy(ilink->fields, fields, n));
1800:   PetscCall(PetscMalloc1(n, &ilink->fields_col));
1801:   PetscCall(PetscArraycpy(ilink->fields_col, fields_col, n));

1803:   ilink->nfields = n;
1804:   ilink->next    = NULL;
1805:   PetscCall(KSPCreate(PetscObjectComm((PetscObject)pc), &ilink->ksp));
1806:   PetscCall(KSPSetNestLevel(ilink->ksp, pc->kspnestlevel));
1807:   PetscCall(KSPSetErrorIfNotConverged(ilink->ksp, pc->erroriffailure));
1808:   PetscCall(PetscObjectIncrementTabLevel((PetscObject)ilink->ksp, (PetscObject)pc, 1));
1809:   PetscCall(KSPSetType(ilink->ksp, KSPPREONLY));

1811:   PetscCall(PetscSNPrintf(prefix, sizeof(prefix), "%sfieldsplit_%s_", ((PetscObject)pc)->prefix ? ((PetscObject)pc)->prefix : "", ilink->splitname));
1812:   PetscCall(KSPSetOptionsPrefix(ilink->ksp, prefix));

1814:   if (!next) {
1815:     jac->head       = ilink;
1816:     ilink->previous = NULL;
1817:   } else {
1818:     while (next->next) next = next->next;
1819:     next->next      = ilink;
1820:     ilink->previous = next;
1821:   }
1822:   jac->nsplits++;
1823:   PetscFunctionReturn(PETSC_SUCCESS);
1824: }

1826: static PetscErrorCode PCFieldSplitSchurGetSubKSP_FieldSplit(PC pc, PetscInt *n, KSP **subksp)
1827: {
1828:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

1830:   PetscFunctionBegin;
1831:   *subksp = NULL;
1832:   if (n) *n = 0;
1833:   if (jac->type == PC_COMPOSITE_SCHUR) {
1834:     PetscInt nn;

1836:     PetscCheck(jac->schur, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONGSTATE, "Must call KSPSetUp() or PCSetUp() before calling PCFieldSplitSchurGetSubKSP()");
1837:     PetscCheck(jac->nsplits == 2, PetscObjectComm((PetscObject)pc), PETSC_ERR_PLIB, "Unexpected number of splits %" PetscInt_FMT " != 2", jac->nsplits);
1838:     nn = jac->nsplits + (jac->kspupper != jac->head->ksp ? 1 : 0);
1839:     PetscCall(PetscMalloc1(nn, subksp));
1840:     (*subksp)[0] = jac->head->ksp;
1841:     (*subksp)[1] = jac->kspschur;
1842:     if (jac->kspupper != jac->head->ksp) (*subksp)[2] = jac->kspupper;
1843:     if (n) *n = nn;
1844:   }
1845:   PetscFunctionReturn(PETSC_SUCCESS);
1846: }

1848: static PetscErrorCode PCFieldSplitGetSubKSP_FieldSplit_Schur(PC pc, PetscInt *n, KSP **subksp)
1849: {
1850:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

1852:   PetscFunctionBegin;
1853:   PetscCheck(jac->schur, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONGSTATE, "Must call KSPSetUp() or PCSetUp() before calling PCFieldSplitGetSubKSP()");
1854:   PetscCall(PetscMalloc1(jac->nsplits, subksp));
1855:   PetscCall(MatSchurComplementGetKSP(jac->schur, *subksp));

1857:   (*subksp)[1] = jac->kspschur;
1858:   if (n) *n = jac->nsplits;
1859:   PetscFunctionReturn(PETSC_SUCCESS);
1860: }

1862: static PetscErrorCode PCFieldSplitGetSubKSP_FieldSplit(PC pc, PetscInt *n, KSP **subksp)
1863: {
1864:   PC_FieldSplit    *jac   = (PC_FieldSplit *)pc->data;
1865:   PetscInt          cnt   = 0;
1866:   PC_FieldSplitLink ilink = jac->head;

1868:   PetscFunctionBegin;
1869:   PetscCall(PetscMalloc1(jac->nsplits, subksp));
1870:   while (ilink) {
1871:     (*subksp)[cnt++] = ilink->ksp;
1872:     ilink            = ilink->next;
1873:   }
1874:   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);
1875:   if (n) *n = jac->nsplits;
1876:   PetscFunctionReturn(PETSC_SUCCESS);
1877: }

1879: /*@C
1880:   PCFieldSplitRestrictIS - Restricts the fieldsplit `IS`s to be within a given `IS`.

1882:   Input Parameters:
1883: + pc  - the preconditioner context
1884: - isy - the index set that defines the indices to which the fieldsplit is to be restricted

1886:   Level: advanced

1888:   Developer Notes:
1889:   It seems the resulting `IS`s will not cover the entire space, so
1890:   how can they define a convergent preconditioner? Needs explaining.

1892: .seealso: [](sec_block_matrices), `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSetIS()`
1893: @*/
1894: PetscErrorCode PCFieldSplitRestrictIS(PC pc, IS isy)
1895: {
1896:   PetscFunctionBegin;
1899:   PetscTryMethod(pc, "PCFieldSplitRestrictIS_C", (PC, IS), (pc, isy));
1900:   PetscFunctionReturn(PETSC_SUCCESS);
1901: }

1903: static PetscErrorCode PCFieldSplitRestrictIS_FieldSplit(PC pc, IS isy)
1904: {
1905:   PC_FieldSplit    *jac   = (PC_FieldSplit *)pc->data;
1906:   PC_FieldSplitLink ilink = jac->head, next;
1907:   PetscInt          localsize, size, sizez, i;
1908:   const PetscInt   *ind, *indz;
1909:   PetscInt         *indc, *indcz;
1910:   PetscBool         flg;

1912:   PetscFunctionBegin;
1913:   PetscCall(ISGetLocalSize(isy, &localsize));
1914:   PetscCallMPI(MPI_Scan(&localsize, &size, 1, MPIU_INT, MPI_SUM, PetscObjectComm((PetscObject)isy)));
1915:   size -= localsize;
1916:   while (ilink) {
1917:     IS isrl, isr;
1918:     PC subpc;
1919:     PetscCall(ISEmbed(ilink->is, isy, PETSC_TRUE, &isrl));
1920:     PetscCall(ISGetLocalSize(isrl, &localsize));
1921:     PetscCall(PetscMalloc1(localsize, &indc));
1922:     PetscCall(ISGetIndices(isrl, &ind));
1923:     PetscCall(PetscArraycpy(indc, ind, localsize));
1924:     PetscCall(ISRestoreIndices(isrl, &ind));
1925:     PetscCall(ISDestroy(&isrl));
1926:     for (i = 0; i < localsize; i++) *(indc + i) += size;
1927:     PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)isy), localsize, indc, PETSC_OWN_POINTER, &isr));
1928:     PetscCall(PetscObjectReference((PetscObject)isr));
1929:     PetscCall(ISDestroy(&ilink->is));
1930:     ilink->is = isr;
1931:     PetscCall(PetscObjectReference((PetscObject)isr));
1932:     PetscCall(ISDestroy(&ilink->is_col));
1933:     ilink->is_col = isr;
1934:     PetscCall(ISDestroy(&isr));
1935:     PetscCall(KSPGetPC(ilink->ksp, &subpc));
1936:     PetscCall(PetscObjectTypeCompare((PetscObject)subpc, PCFIELDSPLIT, &flg));
1937:     if (flg) {
1938:       IS       iszl, isz;
1939:       MPI_Comm comm;
1940:       PetscCall(ISGetLocalSize(ilink->is, &localsize));
1941:       comm = PetscObjectComm((PetscObject)ilink->is);
1942:       PetscCall(ISEmbed(isy, ilink->is, PETSC_TRUE, &iszl));
1943:       PetscCallMPI(MPI_Scan(&localsize, &sizez, 1, MPIU_INT, MPI_SUM, comm));
1944:       sizez -= localsize;
1945:       PetscCall(ISGetLocalSize(iszl, &localsize));
1946:       PetscCall(PetscMalloc1(localsize, &indcz));
1947:       PetscCall(ISGetIndices(iszl, &indz));
1948:       PetscCall(PetscArraycpy(indcz, indz, localsize));
1949:       PetscCall(ISRestoreIndices(iszl, &indz));
1950:       PetscCall(ISDestroy(&iszl));
1951:       for (i = 0; i < localsize; i++) *(indcz + i) += sizez;
1952:       PetscCall(ISCreateGeneral(comm, localsize, indcz, PETSC_OWN_POINTER, &isz));
1953:       PetscCall(PCFieldSplitRestrictIS(subpc, isz));
1954:       PetscCall(ISDestroy(&isz));
1955:     }
1956:     next  = ilink->next;
1957:     ilink = next;
1958:   }
1959:   jac->isrestrict = PETSC_TRUE;
1960:   PetscFunctionReturn(PETSC_SUCCESS);
1961: }

1963: static PetscErrorCode PCFieldSplitSetIS_FieldSplit(PC pc, const char splitname[], IS is)
1964: {
1965:   PC_FieldSplit    *jac = (PC_FieldSplit *)pc->data;
1966:   PC_FieldSplitLink ilink, next = jac->head;
1967:   char              prefix[128];

1969:   PetscFunctionBegin;
1970:   if (jac->splitdefined) {
1971:     PetscCall(PetscInfo(pc, "Ignoring new split \"%s\" because the splits have already been defined\n", splitname));
1972:     PetscFunctionReturn(PETSC_SUCCESS);
1973:   }
1974:   PetscCall(PetscNew(&ilink));
1975:   if (splitname) {
1976:     PetscCall(PetscStrallocpy(splitname, &ilink->splitname));
1977:   } else {
1978:     PetscCall(PetscMalloc1(8, &ilink->splitname));
1979:     PetscCall(PetscSNPrintf(ilink->splitname, 7, "%" PetscInt_FMT, jac->nsplits));
1980:   }
1981:   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 */
1982:   PetscCall(PetscObjectReference((PetscObject)is));
1983:   PetscCall(ISDestroy(&ilink->is));
1984:   ilink->is = is;
1985:   PetscCall(PetscObjectReference((PetscObject)is));
1986:   PetscCall(ISDestroy(&ilink->is_col));
1987:   ilink->is_col = is;
1988:   ilink->next   = NULL;
1989:   PetscCall(KSPCreate(PetscObjectComm((PetscObject)pc), &ilink->ksp));
1990:   PetscCall(KSPSetNestLevel(ilink->ksp, pc->kspnestlevel));
1991:   PetscCall(KSPSetErrorIfNotConverged(ilink->ksp, pc->erroriffailure));
1992:   PetscCall(PetscObjectIncrementTabLevel((PetscObject)ilink->ksp, (PetscObject)pc, 1));
1993:   PetscCall(KSPSetType(ilink->ksp, KSPPREONLY));

1995:   PetscCall(PetscSNPrintf(prefix, sizeof(prefix), "%sfieldsplit_%s_", ((PetscObject)pc)->prefix ? ((PetscObject)pc)->prefix : "", ilink->splitname));
1996:   PetscCall(KSPSetOptionsPrefix(ilink->ksp, prefix));

1998:   if (!next) {
1999:     jac->head       = ilink;
2000:     ilink->previous = NULL;
2001:   } else {
2002:     while (next->next) next = next->next;
2003:     next->next      = ilink;
2004:     ilink->previous = next;
2005:   }
2006:   jac->nsplits++;
2007:   PetscFunctionReturn(PETSC_SUCCESS);
2008: }

2010: /*@C
2011:   PCFieldSplitSetFields - Sets the fields that define one particular split in `PCFIELDSPLIT`

2013:   Logically Collective

2015:   Input Parameters:
2016: + pc         - the preconditioner context
2017: . splitname  - name of this split, if `NULL` the number of the split is used
2018: . n          - the number of fields in this split
2019: . fields     - the fields in this split
2020: - 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
2021:                  of the matrix and fields_col provides the column indices for that block

2023:   Level: intermediate

2025:   Notes:
2026:   Use `PCFieldSplitSetIS()` to set a  general set of indices as a split.

2028:   `PCFieldSplitSetFields()` is for defining fields as strided blocks. For example, if the block
2029:   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
2030:   0xx3xx6xx9xx12 ... x1xx4xx7xx ... xx2xx5xx8xx.. 01x34x67x... 0x1x3x5x7.. x12x45x78x....
2031:   where the numbered entries indicate what is in the split.

2033:   This function is called once per split (it creates a new split each time).  Solve options
2034:   for this split will be available under the prefix `-fieldsplit_SPLITNAME_`.

2036:   `PCFieldSplitSetIS()` does not support having a fields_col different from fields

2038:   Developer Notes:
2039:   This routine does not actually create the `IS` representing the split, that is delayed
2040:   until `PCSetUp_FieldSplit()`, because information about the vector/matrix layouts may not be
2041:   available when this routine is called.

2043: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSetBlockSize()`, `PCFieldSplitSetIS()`, `PCFieldSplitRestrictIS()`
2044: @*/
2045: PetscErrorCode PCFieldSplitSetFields(PC pc, const char splitname[], PetscInt n, const PetscInt *fields, const PetscInt *fields_col)
2046: {
2047:   PetscFunctionBegin;
2049:   PetscAssertPointer(splitname, 2);
2050:   PetscCheck(n >= 1, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_OUTOFRANGE, "Provided number of fields %" PetscInt_FMT " in split \"%s\" not positive", n, splitname);
2051:   PetscAssertPointer(fields, 4);
2052:   PetscTryMethod(pc, "PCFieldSplitSetFields_C", (PC, const char[], PetscInt, const PetscInt *, const PetscInt *), (pc, splitname, n, fields, fields_col));
2053:   PetscFunctionReturn(PETSC_SUCCESS);
2054: }

2056: /*@
2057:   PCFieldSplitSetDiagUseAmat - set flag indicating whether to extract diagonal blocks from Amat (rather than Pmat) to build
2058:   the sub-matrices associated with each split. Where `KSPSetOperators`(ksp,Amat,Pmat) was used to supply the operators.

2060:   Logically Collective

2062:   Input Parameters:
2063: + pc  - the preconditioner object
2064: - flg - boolean flag indicating whether or not to use Amat to extract the diagonal blocks from

2066:   Options Database Key:
2067: . -pc_fieldsplit_diag_use_amat - use the Amat to provide the diagonal blocks

2069:   Level: intermediate

2071: .seealso: [](sec_block_matrices), `PC`, `PCSetOperators()`, `KSPSetOperators()`, `PCFieldSplitGetDiagUseAmat()`, `PCFieldSplitSetOffDiagUseAmat()`, `PCFIELDSPLIT`
2072: @*/
2073: PetscErrorCode PCFieldSplitSetDiagUseAmat(PC pc, PetscBool flg)
2074: {
2075:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
2076:   PetscBool      isfs;

2078:   PetscFunctionBegin;
2080:   PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCFIELDSPLIT, &isfs));
2081:   PetscCheck(isfs, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "PC not of type %s", PCFIELDSPLIT);
2082:   jac->diag_use_amat = flg;
2083:   PetscFunctionReturn(PETSC_SUCCESS);
2084: }

2086: /*@
2087:   PCFieldSplitGetDiagUseAmat - get the flag indicating whether to extract diagonal blocks from Amat (rather than Pmat) to build
2088:   the sub-matrices associated with each split.  Where `KSPSetOperators`(ksp,Amat,Pmat) was used to supply the operators.

2090:   Logically Collective

2092:   Input Parameter:
2093: . pc - the preconditioner object

2095:   Output Parameter:
2096: . flg - boolean flag indicating whether or not to use Amat to extract the diagonal blocks from

2098:   Level: intermediate

2100: .seealso: [](sec_block_matrices), `PC`, `PCSetOperators()`, `KSPSetOperators()`, `PCFieldSplitSetDiagUseAmat()`, `PCFieldSplitGetOffDiagUseAmat()`, `PCFIELDSPLIT`
2101: @*/
2102: PetscErrorCode PCFieldSplitGetDiagUseAmat(PC pc, PetscBool *flg)
2103: {
2104:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
2105:   PetscBool      isfs;

2107:   PetscFunctionBegin;
2109:   PetscAssertPointer(flg, 2);
2110:   PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCFIELDSPLIT, &isfs));
2111:   PetscCheck(isfs, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "PC not of type %s", PCFIELDSPLIT);
2112:   *flg = jac->diag_use_amat;
2113:   PetscFunctionReturn(PETSC_SUCCESS);
2114: }

2116: /*@
2117:   PCFieldSplitSetOffDiagUseAmat - set flag indicating whether to extract off-diagonal blocks from Amat (rather than Pmat) to build
2118:   the sub-matrices associated with each split.  Where `KSPSetOperators`(ksp,Amat,Pmat) was used to supply the operators.

2120:   Logically Collective

2122:   Input Parameters:
2123: + pc  - the preconditioner object
2124: - flg - boolean flag indicating whether or not to use Amat to extract the off-diagonal blocks from

2126:   Options Database Key:
2127: . -pc_fieldsplit_off_diag_use_amat <bool> - use the Amat to extract the off-diagonal blocks

2129:   Level: intermediate

2131: .seealso: [](sec_block_matrices), `PC`, `PCSetOperators()`, `KSPSetOperators()`, `PCFieldSplitGetOffDiagUseAmat()`, `PCFieldSplitSetDiagUseAmat()`, `PCFIELDSPLIT`
2132: @*/
2133: PetscErrorCode PCFieldSplitSetOffDiagUseAmat(PC pc, PetscBool flg)
2134: {
2135:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
2136:   PetscBool      isfs;

2138:   PetscFunctionBegin;
2140:   PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCFIELDSPLIT, &isfs));
2141:   PetscCheck(isfs, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "PC not of type %s", PCFIELDSPLIT);
2142:   jac->offdiag_use_amat = flg;
2143:   PetscFunctionReturn(PETSC_SUCCESS);
2144: }

2146: /*@
2147:   PCFieldSplitGetOffDiagUseAmat - get the flag indicating whether to extract off-diagonal blocks from Amat (rather than Pmat) to build
2148:   the sub-matrices associated with each split.  Where `KSPSetOperators`(ksp,Amat,Pmat) was used to supply the operators.

2150:   Logically Collective

2152:   Input Parameter:
2153: . pc - the preconditioner object

2155:   Output Parameter:
2156: . flg - boolean flag indicating whether or not to use Amat to extract the off-diagonal blocks from

2158:   Level: intermediate

2160: .seealso: [](sec_block_matrices), `PC`, `PCSetOperators()`, `KSPSetOperators()`, `PCFieldSplitSetOffDiagUseAmat()`, `PCFieldSplitGetDiagUseAmat()`, `PCFIELDSPLIT`
2161: @*/
2162: PetscErrorCode PCFieldSplitGetOffDiagUseAmat(PC pc, PetscBool *flg)
2163: {
2164:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
2165:   PetscBool      isfs;

2167:   PetscFunctionBegin;
2169:   PetscAssertPointer(flg, 2);
2170:   PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCFIELDSPLIT, &isfs));
2171:   PetscCheck(isfs, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "PC not of type %s", PCFIELDSPLIT);
2172:   *flg = jac->offdiag_use_amat;
2173:   PetscFunctionReturn(PETSC_SUCCESS);
2174: }

2176: /*@C
2177:   PCFieldSplitSetIS - Sets the exact elements for a split in a `PCFIELDSPLIT`

2179:   Logically Collective

2181:   Input Parameters:
2182: + pc        - the preconditioner context
2183: . splitname - name of this split, if `NULL` the number of the split is used
2184: - is        - the index set that defines the elements in this split

2186:   Level: intermediate

2188:   Notes:
2189:   Use `PCFieldSplitSetFields()`, for splits defined by strided types.

2191:   This function is called once per split (it creates a new split each time).  Solve options
2192:   for this split will be available under the prefix -fieldsplit_SPLITNAME_.

2194: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSetBlockSize()`
2195: @*/
2196: PetscErrorCode PCFieldSplitSetIS(PC pc, const char splitname[], IS is)
2197: {
2198:   PetscFunctionBegin;
2200:   if (splitname) PetscAssertPointer(splitname, 2);
2202:   PetscTryMethod(pc, "PCFieldSplitSetIS_C", (PC, const char[], IS), (pc, splitname, is));
2203:   PetscFunctionReturn(PETSC_SUCCESS);
2204: }

2206: /*@C
2207:   PCFieldSplitGetIS - Retrieves the elements for a split as an `IS`

2209:   Logically Collective

2211:   Input Parameters:
2212: + pc        - the preconditioner context
2213: - splitname - name of this split

2215:   Output Parameter:
2216: . is - the index set that defines the elements in this split, or `NULL` if the split is not found

2218:   Level: intermediate

2220: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSetIS()`
2221: @*/
2222: PetscErrorCode PCFieldSplitGetIS(PC pc, const char splitname[], IS *is)
2223: {
2224:   PetscFunctionBegin;
2226:   PetscAssertPointer(splitname, 2);
2227:   PetscAssertPointer(is, 3);
2228:   {
2229:     PC_FieldSplit    *jac   = (PC_FieldSplit *)pc->data;
2230:     PC_FieldSplitLink ilink = jac->head;
2231:     PetscBool         found;

2233:     *is = NULL;
2234:     while (ilink) {
2235:       PetscCall(PetscStrcmp(ilink->splitname, splitname, &found));
2236:       if (found) {
2237:         *is = ilink->is;
2238:         break;
2239:       }
2240:       ilink = ilink->next;
2241:     }
2242:   }
2243:   PetscFunctionReturn(PETSC_SUCCESS);
2244: }

2246: /*@C
2247:   PCFieldSplitGetISByIndex - Retrieves the elements for a given split as an `IS`

2249:   Logically Collective

2251:   Input Parameters:
2252: + pc    - the preconditioner context
2253: - index - index of this split

2255:   Output Parameter:
2256: . is - the index set that defines the elements in this split

2258:   Level: intermediate

2260: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitGetIS()`, `PCFieldSplitSetIS()`
2261: @*/
2262: PetscErrorCode PCFieldSplitGetISByIndex(PC pc, PetscInt index, IS *is)
2263: {
2264:   PetscFunctionBegin;
2265:   PetscCheck(index >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Negative field %" PetscInt_FMT " requested", index);
2267:   PetscAssertPointer(is, 3);
2268:   {
2269:     PC_FieldSplit    *jac   = (PC_FieldSplit *)pc->data;
2270:     PC_FieldSplitLink ilink = jac->head;
2271:     PetscInt          i     = 0;
2272:     PetscCheck(index < jac->nsplits, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Field %" PetscInt_FMT " requested but only %" PetscInt_FMT " exist", index, jac->nsplits);

2274:     while (i < index) {
2275:       ilink = ilink->next;
2276:       ++i;
2277:     }
2278:     PetscCall(PCFieldSplitGetIS(pc, ilink->splitname, is));
2279:   }
2280:   PetscFunctionReturn(PETSC_SUCCESS);
2281: }

2283: /*@
2284:   PCFieldSplitSetBlockSize - Sets the block size for defining where fields start in the
2285:   fieldsplit preconditioner when calling `PCFieldSplitSetIS()`. If not set the matrix block size is used.

2287:   Logically Collective

2289:   Input Parameters:
2290: + pc - the preconditioner context
2291: - bs - the block size

2293:   Level: intermediate

2295: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSetIS()`
2296: @*/
2297: PetscErrorCode PCFieldSplitSetBlockSize(PC pc, PetscInt bs)
2298: {
2299:   PetscFunctionBegin;
2302:   PetscTryMethod(pc, "PCFieldSplitSetBlockSize_C", (PC, PetscInt), (pc, bs));
2303:   PetscFunctionReturn(PETSC_SUCCESS);
2304: }

2306: /*@C
2307:   PCFieldSplitGetSubKSP - Gets the `KSP` contexts for all splits

2309:   Collective

2311:   Input Parameter:
2312: . pc - the preconditioner context

2314:   Output Parameters:
2315: + n      - the number of splits
2316: - subksp - the array of `KSP` contexts

2318:   Level: advanced

2320:   Notes:
2321:   After `PCFieldSplitGetSubKSP()` the array of `KSP`s is to be freed by the user with `PetscFree()`
2322:   (not the `KSP`, just the array that contains them).

2324:   You must call `PCSetUp()` before calling `PCFieldSplitGetSubKSP()`.

2326:   If the fieldsplit is of type `PC_COMPOSITE_SCHUR`, it returns the `KSP` object used inside the
2327:   Schur complement and the `KSP` object used to iterate over the Schur complement.
2328:   To access all the `KSP` objects used in `PC_COMPOSITE_SCHUR`, use `PCFieldSplitSchurGetSubKSP()`.

2330:   If the fieldsplit is of type `PC_COMPOSITE_GKB`, it returns the `KSP` object used to solve the
2331:   inner linear system defined by the matrix H in each loop.

2333:   Fortran Notes:
2334:   You must pass in a `KSP` array that is large enough to contain all the `KSP`s.
2335:   You can call `PCFieldSplitGetSubKSP`(pc,n,`PETSC_NULL_KSP`,ierr) to determine how large the
2336:   `KSP` array must be.

2338:   Developer Notes:
2339:   There should be a `PCFieldSplitRestoreSubKSP()` instead of requiring the user to call `PetscFree()`

2341:   The Fortran interface should be modernized to return directly the array of values.

2343: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSetIS()`, `PCFieldSplitSchurGetSubKSP()`
2344: @*/
2345: PetscErrorCode PCFieldSplitGetSubKSP(PC pc, PetscInt *n, KSP *subksp[])
2346: {
2347:   PetscFunctionBegin;
2349:   if (n) PetscAssertPointer(n, 2);
2350:   PetscUseMethod(pc, "PCFieldSplitGetSubKSP_C", (PC, PetscInt *, KSP **), (pc, n, subksp));
2351:   PetscFunctionReturn(PETSC_SUCCESS);
2352: }

2354: /*@C
2355:   PCFieldSplitSchurGetSubKSP - Gets the `KSP` contexts used inside the Schur complement based `PCFIELDSPLIT`

2357:   Collective

2359:   Input Parameter:
2360: . pc - the preconditioner context

2362:   Output Parameters:
2363: + n      - the number of splits
2364: - subksp - the array of `KSP` contexts

2366:   Level: advanced

2368:   Notes:
2369:   After `PCFieldSplitSchurGetSubKSP()` the array of `KSP`s is to be freed by the user with `PetscFree()`
2370:   (not the `KSP` just the array that contains them).

2372:   You must call `PCSetUp()` before calling `PCFieldSplitSchurGetSubKSP()`.

2374:   If the fieldsplit type is of type `PC_COMPOSITE_SCHUR`, it returns (in order)
2375: +  1  - the `KSP` used for the (1,1) block
2376: .  2  - the `KSP` used for the Schur complement (not the one used for the interior Schur solver)
2377: -  3  - the `KSP` used for the (1,1) block in the upper triangular factor (if different from that of the (1,1) block).

2379:   It returns a null array if the fieldsplit is not of type `PC_COMPOSITE_SCHUR`; in this case, you should use `PCFieldSplitGetSubKSP()`.

2381:   Fortran Notes:
2382:   You must pass in a `KSP` array that is large enough to contain all the local `KSP`s.
2383:   You can call `PCFieldSplitSchurGetSubKSP`(pc,n,`PETSC_NULL_KSP`,ierr) to determine how large the
2384:   `KSP` array must be.

2386:   Developer Notes:
2387:   There should be a `PCFieldSplitRestoreSubKSP()` instead of requiring the user to call `PetscFree()`

2389:   Should the functionality of `PCFieldSplitSchurGetSubKSP()` and `PCFieldSplitGetSubKSP()` be merged?

2391:   The Fortran interface should be modernized to return directly the array of values.

2393: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSetIS()`, `PCFieldSplitGetSubKSP()`
2394: @*/
2395: PetscErrorCode PCFieldSplitSchurGetSubKSP(PC pc, PetscInt *n, KSP *subksp[])
2396: {
2397:   PetscFunctionBegin;
2399:   if (n) PetscAssertPointer(n, 2);
2400:   PetscUseMethod(pc, "PCFieldSplitSchurGetSubKSP_C", (PC, PetscInt *, KSP **), (pc, n, subksp));
2401:   PetscFunctionReturn(PETSC_SUCCESS);
2402: }

2404: /*@
2405:   PCFieldSplitSetSchurPre -  Indicates from what operator the preconditioner is constructed for the Schur complement.
2406:   The default is the A11 matrix.

2408:   Collective

2410:   Input Parameters:
2411: + pc    - the preconditioner context
2412: . ptype - which matrix to use for preconditioning the Schur complement: `PC_FIELDSPLIT_SCHUR_PRE_A11` (default),
2413:               `PC_FIELDSPLIT_SCHUR_PRE_SELF`, `PC_FIELDSPLIT_SCHUR_PRE_USER`,
2414:               `PC_FIELDSPLIT_SCHUR_PRE_SELFP`, and `PC_FIELDSPLIT_SCHUR_PRE_FULL`
2415: - pre   - matrix to use for preconditioning, or `NULL`

2417:   Options Database Keys:
2418: + -pc_fieldsplit_schur_precondition <self,selfp,user,a11,full> - default is `a11`. See notes for meaning of various arguments
2419: - -fieldsplit_1_pc_type <pctype>                               - the preconditioner algorithm that is used to construct the preconditioner from the operator

2421:   Level: intermediate

2423:   Notes:
2424:   If ptype is
2425: +     a11 - the preconditioner for the Schur complement is generated from the block diagonal part of the preconditioner
2426:   matrix associated with the Schur complement (i.e. A11), not the Schur complement matrix
2427: .     self - the preconditioner for the Schur complement is generated from the symbolic representation of the Schur complement matrix:
2428:   The only preconditioner that currently works with this symbolic representation matrix object is the `PCLSC`
2429:   preconditioner
2430: .     user - the preconditioner for the Schur complement is generated from the user provided matrix (pre argument
2431:   to this function).
2432: .     selfp - the preconditioning for the Schur complement is generated from an explicitly-assembled approximation Sp = A11 - A10 inv(diag(A00)) A01
2433:   This is only a good preconditioner when diag(A00) is a good preconditioner for A00. Optionally, A00 can be
2434:   lumped before extracting the diagonal using the additional option `-fieldsplit_1_mat_schur_complement_ainv_type lump`
2435: -     full - the preconditioner for the Schur complement is generated from the exact Schur complement matrix representation
2436:   computed internally by `PCFIELDSPLIT` (this is expensive)
2437:   useful mostly as a test that the Schur complement approach can work for your problem

2439:   When solving a saddle point problem, where the A11 block is identically zero, using `a11` as the ptype only makes sense
2440:   with the additional option `-fieldsplit_1_pc_type none`. Usually for saddle point problems one would use a ptype of self and
2441:   `-fieldsplit_1_pc_type lsc` which uses the least squares commutator to compute a preconditioner for the Schur complement.

2443: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSchurPre()`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSchurPreType`,
2444:           `MatSchurComplementSetAinvType()`, `PCLSC`,

2446: @*/
2447: PetscErrorCode PCFieldSplitSetSchurPre(PC pc, PCFieldSplitSchurPreType ptype, Mat pre)
2448: {
2449:   PetscFunctionBegin;
2451:   PetscTryMethod(pc, "PCFieldSplitSetSchurPre_C", (PC, PCFieldSplitSchurPreType, Mat), (pc, ptype, pre));
2452:   PetscFunctionReturn(PETSC_SUCCESS);
2453: }

2455: PetscErrorCode PCFieldSplitSchurPrecondition(PC pc, PCFieldSplitSchurPreType ptype, Mat pre)
2456: {
2457:   return PCFieldSplitSetSchurPre(pc, ptype, pre);
2458: } /* Deprecated name */

2460: /*@
2461:   PCFieldSplitGetSchurPre - For Schur complement fieldsplit, determine how the Schur complement will be
2462:   preconditioned.  See `PCFieldSplitSetSchurPre()` for details.

2464:   Logically Collective

2466:   Input Parameter:
2467: . pc - the preconditioner context

2469:   Output Parameters:
2470: + 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`
2471: - pre   - matrix to use for preconditioning (with `PC_FIELDSPLIT_SCHUR_PRE_USER`), or `NULL`

2473:   Level: intermediate

2475: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitSetSchurPre()`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSchurPreType`, `PCLSC`

2477: @*/
2478: PetscErrorCode PCFieldSplitGetSchurPre(PC pc, PCFieldSplitSchurPreType *ptype, Mat *pre)
2479: {
2480:   PetscFunctionBegin;
2482:   PetscUseMethod(pc, "PCFieldSplitGetSchurPre_C", (PC, PCFieldSplitSchurPreType *, Mat *), (pc, ptype, pre));
2483:   PetscFunctionReturn(PETSC_SUCCESS);
2484: }

2486: /*@
2487:   PCFieldSplitSchurGetS -  extract the `MATSCHURCOMPLEMENT` object used by this `PCFIELDSPLIT` in case it needs to be configured separately

2489:   Not Collective

2491:   Input Parameter:
2492: . pc - the preconditioner context

2494:   Output Parameter:
2495: . S - the Schur complement matrix

2497:   Level: advanced

2499:   Note:
2500:   This matrix should not be destroyed using `MatDestroy()`; rather, use `PCFieldSplitSchurRestoreS()`.

2502: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSchurPreType`, `PCFieldSplitSetSchurPre()`, `MATSCHURCOMPLEMENT`, `PCFieldSplitSchurRestoreS()`,
2503:           `MatCreateSchurComplement()`, `MatSchurComplementGetKSP()`, `MatSchurComplementComputeExplicitOperator()`, `MatGetSchurComplement()`
2504: @*/
2505: PetscErrorCode PCFieldSplitSchurGetS(PC pc, Mat *S)
2506: {
2507:   const char    *t;
2508:   PetscBool      isfs;
2509:   PC_FieldSplit *jac;

2511:   PetscFunctionBegin;
2513:   PetscCall(PetscObjectGetType((PetscObject)pc, &t));
2514:   PetscCall(PetscStrcmp(t, PCFIELDSPLIT, &isfs));
2515:   PetscCheck(isfs, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Expected PC of type PCFIELDSPLIT, got %s instead", t);
2516:   jac = (PC_FieldSplit *)pc->data;
2517:   PetscCheck(jac->type == PC_COMPOSITE_SCHUR, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Expected PCFIELDSPLIT of type SCHUR, got %d instead", jac->type);
2518:   if (S) *S = jac->schur;
2519:   PetscFunctionReturn(PETSC_SUCCESS);
2520: }

2522: /*@
2523:   PCFieldSplitSchurRestoreS -  returns the `MATSCHURCOMPLEMENT` matrix used by this `PC`

2525:   Not Collective

2527:   Input Parameters:
2528: + pc - the preconditioner context
2529: - S  - the Schur complement matrix

2531:   Level: advanced

2533: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSchurPreType`, `PCFieldSplitSetSchurPre()`, `MatSchurComplement`, `PCFieldSplitSchurGetS()`
2534: @*/
2535: PetscErrorCode PCFieldSplitSchurRestoreS(PC pc, Mat *S)
2536: {
2537:   const char    *t;
2538:   PetscBool      isfs;
2539:   PC_FieldSplit *jac;

2541:   PetscFunctionBegin;
2543:   PetscCall(PetscObjectGetType((PetscObject)pc, &t));
2544:   PetscCall(PetscStrcmp(t, PCFIELDSPLIT, &isfs));
2545:   PetscCheck(isfs, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Expected PC of type PCFIELDSPLIT, got %s instead", t);
2546:   jac = (PC_FieldSplit *)pc->data;
2547:   PetscCheck(jac->type == PC_COMPOSITE_SCHUR, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Expected PCFIELDSPLIT of type SCHUR, got %d instead", jac->type);
2548:   PetscCheck(S && (*S == jac->schur), PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "MatSchurComplement restored is not the same as gotten");
2549:   PetscFunctionReturn(PETSC_SUCCESS);
2550: }

2552: static PetscErrorCode PCFieldSplitSetSchurPre_FieldSplit(PC pc, PCFieldSplitSchurPreType ptype, Mat pre)
2553: {
2554:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

2556:   PetscFunctionBegin;
2557:   jac->schurpre = ptype;
2558:   if (ptype == PC_FIELDSPLIT_SCHUR_PRE_USER && pre) {
2559:     PetscCall(MatDestroy(&jac->schur_user));
2560:     jac->schur_user = pre;
2561:     PetscCall(PetscObjectReference((PetscObject)jac->schur_user));
2562:   }
2563:   PetscFunctionReturn(PETSC_SUCCESS);
2564: }

2566: static PetscErrorCode PCFieldSplitGetSchurPre_FieldSplit(PC pc, PCFieldSplitSchurPreType *ptype, Mat *pre)
2567: {
2568:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

2570:   PetscFunctionBegin;
2571:   if (ptype) *ptype = jac->schurpre;
2572:   if (pre) *pre = jac->schur_user;
2573:   PetscFunctionReturn(PETSC_SUCCESS);
2574: }

2576: /*@
2577:   PCFieldSplitSetSchurFactType -  sets which blocks of the approximate block factorization to retain in the preconditioner {cite}`murphy2000note` and {cite}`ipsen2001note`

2579:   Collective

2581:   Input Parameters:
2582: + pc    - the preconditioner context
2583: - ftype - which blocks of factorization to retain, `PC_FIELDSPLIT_SCHUR_FACT_FULL` is default

2585:   Options Database Key:
2586: . -pc_fieldsplit_schur_fact_type <diag,lower,upper,full> - default is `full`

2588:   Level: intermediate

2590:   Notes:
2591:   The FULL factorization is
2592: .vb
2593:   (A   B)  = (1       0) (A   0) (1  Ainv*B)  = L D U
2594:   (C   E)    (C*Ainv  1) (0   S) (0       1)
2595: .vb
2596:   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 $L*D$,
2597:   and DIAG is the diagonal part with the sign of S flipped (because this makes the preconditioner positive definite for many formulations,
2598:   thus allowing the use of `KSPMINRES)`. Sign flipping of S can be turned off with `PCFieldSplitSetSchurScale()`.

2600:   If A and S are solved exactly
2601: .vb
2602:   *) FULL factorization is a direct solver.
2603:   *) 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.
2604:   *) 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.
2605: .ve

2607:   If the iteration count is very low, consider using `KSPFGMRES` or `KSPGCR` which can use one less preconditioner
2608:   application in this case. Note that the preconditioned operator may be highly non-normal, so such fast convergence may not be observed in practice.

2610:   For symmetric problems in which A is positive definite and S is negative definite, DIAG can be used with `KSPMINRES`.

2612:   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).

2614: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSchurPreType`, `PCFieldSplitSetSchurScale()`,
2615:           [](sec_flexibleksp)
2616: @*/
2617: PetscErrorCode PCFieldSplitSetSchurFactType(PC pc, PCFieldSplitSchurFactType ftype)
2618: {
2619:   PetscFunctionBegin;
2621:   PetscTryMethod(pc, "PCFieldSplitSetSchurFactType_C", (PC, PCFieldSplitSchurFactType), (pc, ftype));
2622:   PetscFunctionReturn(PETSC_SUCCESS);
2623: }

2625: static PetscErrorCode PCFieldSplitSetSchurFactType_FieldSplit(PC pc, PCFieldSplitSchurFactType ftype)
2626: {
2627:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

2629:   PetscFunctionBegin;
2630:   jac->schurfactorization = ftype;
2631:   PetscFunctionReturn(PETSC_SUCCESS);
2632: }

2634: /*@
2635:   PCFieldSplitSetSchurScale -  Controls the sign flip of S for `PC_FIELDSPLIT_SCHUR_FACT_DIAG`.

2637:   Collective

2639:   Input Parameters:
2640: + pc    - the preconditioner context
2641: - scale - scaling factor for the Schur complement

2643:   Options Database Key:
2644: . -pc_fieldsplit_schur_scale <scale> - default is -1.0

2646:   Level: intermediate

2648: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSchurFactType`, `PCFieldSplitSetSchurFactType()`
2649: @*/
2650: PetscErrorCode PCFieldSplitSetSchurScale(PC pc, PetscScalar scale)
2651: {
2652:   PetscFunctionBegin;
2655:   PetscTryMethod(pc, "PCFieldSplitSetSchurScale_C", (PC, PetscScalar), (pc, scale));
2656:   PetscFunctionReturn(PETSC_SUCCESS);
2657: }

2659: static PetscErrorCode PCFieldSplitSetSchurScale_FieldSplit(PC pc, PetscScalar scale)
2660: {
2661:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

2663:   PetscFunctionBegin;
2664:   jac->schurscale = scale;
2665:   PetscFunctionReturn(PETSC_SUCCESS);
2666: }

2668: /*@C
2669:   PCFieldSplitGetSchurBlocks - Gets all matrix blocks for the Schur complement

2671:   Collective

2673:   Input Parameter:
2674: . pc - the preconditioner context

2676:   Output Parameters:
2677: + A00 - the (0,0) block
2678: . A01 - the (0,1) block
2679: . A10 - the (1,0) block
2680: - A11 - the (1,1) block

2682:   Level: advanced

2684: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `MatSchurComplementGetSubMatrices()`, `MatSchurComplementSetSubMatrices()`
2685: @*/
2686: PetscErrorCode PCFieldSplitGetSchurBlocks(PC pc, Mat *A00, Mat *A01, Mat *A10, Mat *A11)
2687: {
2688:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

2690:   PetscFunctionBegin;
2692:   PetscCheck(jac->type == PC_COMPOSITE_SCHUR, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONG, "FieldSplit is not using a Schur complement approach.");
2693:   if (A00) *A00 = jac->pmat[0];
2694:   if (A01) *A01 = jac->B;
2695:   if (A10) *A10 = jac->C;
2696:   if (A11) *A11 = jac->pmat[1];
2697:   PetscFunctionReturn(PETSC_SUCCESS);
2698: }

2700: /*@
2701:   PCFieldSplitSetGKBTol -  Sets the solver tolerance for the generalized Golub-Kahan bidiagonalization preconditioner {cite}`arioli2013` in `PCFIELDSPLIT`

2703:   Collective

2705:   Input Parameters:
2706: + pc        - the preconditioner context
2707: - tolerance - the solver tolerance

2709:   Options Database Key:
2710: . -pc_fieldsplit_gkb_tol <tolerance> - default is 1e-5

2712:   Level: intermediate

2714:   Note:
2715:   The generalized GKB algorithm {cite}`arioli2013` uses a lower bound estimate of the error in energy norm as stopping criterion.
2716:   It stops once the lower bound estimate undershoots the required solver tolerance. Although the actual error might be bigger than
2717:   this estimate, the stopping criterion is satisfactory in practical cases.

2719: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetGKBDelay()`, `PCFieldSplitSetGKBNu()`, `PCFieldSplitSetGKBMaxit()`
2720: @*/
2721: PetscErrorCode PCFieldSplitSetGKBTol(PC pc, PetscReal tolerance)
2722: {
2723:   PetscFunctionBegin;
2726:   PetscTryMethod(pc, "PCFieldSplitSetGKBTol_C", (PC, PetscReal), (pc, tolerance));
2727:   PetscFunctionReturn(PETSC_SUCCESS);
2728: }

2730: static PetscErrorCode PCFieldSplitSetGKBTol_FieldSplit(PC pc, PetscReal tolerance)
2731: {
2732:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

2734:   PetscFunctionBegin;
2735:   jac->gkbtol = tolerance;
2736:   PetscFunctionReturn(PETSC_SUCCESS);
2737: }

2739: /*@
2740:   PCFieldSplitSetGKBMaxit -  Sets the maximum number of iterations for the generalized Golub-Kahan bidiagonalization preconditioner in `PCFIELDSPLIT`

2742:   Collective

2744:   Input Parameters:
2745: + pc    - the preconditioner context
2746: - maxit - the maximum number of iterations

2748:   Options Database Key:
2749: . -pc_fieldsplit_gkb_maxit <maxit> - default is 100

2751:   Level: intermediate

2753: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetGKBDelay()`, `PCFieldSplitSetGKBTol()`, `PCFieldSplitSetGKBNu()`
2754: @*/
2755: PetscErrorCode PCFieldSplitSetGKBMaxit(PC pc, PetscInt maxit)
2756: {
2757:   PetscFunctionBegin;
2760:   PetscTryMethod(pc, "PCFieldSplitSetGKBMaxit_C", (PC, PetscInt), (pc, maxit));
2761:   PetscFunctionReturn(PETSC_SUCCESS);
2762: }

2764: static PetscErrorCode PCFieldSplitSetGKBMaxit_FieldSplit(PC pc, PetscInt maxit)
2765: {
2766:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

2768:   PetscFunctionBegin;
2769:   jac->gkbmaxit = maxit;
2770:   PetscFunctionReturn(PETSC_SUCCESS);
2771: }

2773: /*@
2774:   PCFieldSplitSetGKBDelay -  Sets the delay in the lower bound error estimate in the generalized Golub-Kahan bidiagonalization {cite}`arioli2013` in `PCFIELDSPLIT`
2775:   preconditioner.

2777:   Collective

2779:   Input Parameters:
2780: + pc    - the preconditioner context
2781: - delay - the delay window in the lower bound estimate

2783:   Options Database Key:
2784: . -pc_fieldsplit_gkb_delay <delay> - default is 5

2786:   Level: intermediate

2788:   Notes:
2789:   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 $
2790:   is expressed as a truncated sum. The error at iteration k can only be measured at iteration (k + `delay`), and thus the algorithm needs
2791:   at least (`delay` + 1) iterations to stop.

2793:   For more details on the generalized Golub-Kahan bidiagonalization method and its lower bound stopping criterion, please refer to {cite}`arioli2013`

2795: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetGKBNu()`, `PCFieldSplitSetGKBTol()`, `PCFieldSplitSetGKBMaxit()`
2796: @*/
2797: PetscErrorCode PCFieldSplitSetGKBDelay(PC pc, PetscInt delay)
2798: {
2799:   PetscFunctionBegin;
2802:   PetscTryMethod(pc, "PCFieldSplitSetGKBDelay_C", (PC, PetscInt), (pc, delay));
2803:   PetscFunctionReturn(PETSC_SUCCESS);
2804: }

2806: static PetscErrorCode PCFieldSplitSetGKBDelay_FieldSplit(PC pc, PetscInt delay)
2807: {
2808:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

2810:   PetscFunctionBegin;
2811:   jac->gkbdelay = delay;
2812:   PetscFunctionReturn(PETSC_SUCCESS);
2813: }

2815: /*@
2816:   PCFieldSplitSetGKBNu -  Sets the scalar value nu >= 0 in the transformation H = A00 + nu*A01*A01' of the (1,1) block in the
2817:   Golub-Kahan bidiagonalization preconditioner {cite}`arioli2013` in `PCFIELDSPLIT`

2819:   Collective

2821:   Input Parameters:
2822: + pc - the preconditioner context
2823: - nu - the shift parameter

2825:   Options Database Key:
2826: . -pc_fieldsplit_gkb_nu <nu> - default is 1

2828:   Level: intermediate

2830:   Notes:
2831:   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,
2832:   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
2833:   necessary to find a good balance in between the convergence of the inner and outer loop.

2835:   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.

2837: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetGKBDelay()`, `PCFieldSplitSetGKBTol()`, `PCFieldSplitSetGKBMaxit()`
2838: @*/
2839: PetscErrorCode PCFieldSplitSetGKBNu(PC pc, PetscReal nu)
2840: {
2841:   PetscFunctionBegin;
2844:   PetscTryMethod(pc, "PCFieldSplitSetGKBNu_C", (PC, PetscReal), (pc, nu));
2845:   PetscFunctionReturn(PETSC_SUCCESS);
2846: }

2848: static PetscErrorCode PCFieldSplitSetGKBNu_FieldSplit(PC pc, PetscReal nu)
2849: {
2850:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

2852:   PetscFunctionBegin;
2853:   jac->gkbnu = nu;
2854:   PetscFunctionReturn(PETSC_SUCCESS);
2855: }

2857: static PetscErrorCode PCFieldSplitSetType_FieldSplit(PC pc, PCCompositeType type)
2858: {
2859:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

2861:   PetscFunctionBegin;
2862:   jac->type = type;
2863:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSubKSP_C", NULL));
2864:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurPre_C", NULL));
2865:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSchurPre_C", NULL));
2866:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurFactType_C", NULL));
2867:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurScale_C", NULL));
2868:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBTol_C", NULL));
2869:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBMaxit_C", NULL));
2870:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBNu_C", NULL));
2871:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBDelay_C", NULL));

2873:   if (type == PC_COMPOSITE_SCHUR) {
2874:     pc->ops->apply          = PCApply_FieldSplit_Schur;
2875:     pc->ops->applytranspose = PCApplyTranspose_FieldSplit_Schur;
2876:     pc->ops->view           = PCView_FieldSplit_Schur;

2878:     PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSubKSP_C", PCFieldSplitGetSubKSP_FieldSplit_Schur));
2879:     PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurPre_C", PCFieldSplitSetSchurPre_FieldSplit));
2880:     PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSchurPre_C", PCFieldSplitGetSchurPre_FieldSplit));
2881:     PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurFactType_C", PCFieldSplitSetSchurFactType_FieldSplit));
2882:     PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurScale_C", PCFieldSplitSetSchurScale_FieldSplit));
2883:   } else if (type == PC_COMPOSITE_GKB) {
2884:     pc->ops->apply = PCApply_FieldSplit_GKB;
2885:     pc->ops->view  = PCView_FieldSplit_GKB;

2887:     PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSubKSP_C", PCFieldSplitGetSubKSP_FieldSplit));
2888:     PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBTol_C", PCFieldSplitSetGKBTol_FieldSplit));
2889:     PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBMaxit_C", PCFieldSplitSetGKBMaxit_FieldSplit));
2890:     PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBNu_C", PCFieldSplitSetGKBNu_FieldSplit));
2891:     PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBDelay_C", PCFieldSplitSetGKBDelay_FieldSplit));
2892:   } else {
2893:     pc->ops->apply = PCApply_FieldSplit;
2894:     pc->ops->view  = PCView_FieldSplit;

2896:     PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSubKSP_C", PCFieldSplitGetSubKSP_FieldSplit));
2897:   }
2898:   PetscFunctionReturn(PETSC_SUCCESS);
2899: }

2901: static PetscErrorCode PCFieldSplitSetBlockSize_FieldSplit(PC pc, PetscInt bs)
2902: {
2903:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

2905:   PetscFunctionBegin;
2906:   PetscCheck(bs >= 1, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_OUTOFRANGE, "Blocksize must be positive, you gave %" PetscInt_FMT, bs);
2907:   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);
2908:   jac->bs = bs;
2909:   PetscFunctionReturn(PETSC_SUCCESS);
2910: }

2912: static PetscErrorCode PCSetCoordinates_FieldSplit(PC pc, PetscInt dim, PetscInt nloc, PetscReal coords[])
2913: {
2914:   PC_FieldSplit    *jac           = (PC_FieldSplit *)pc->data;
2915:   PC_FieldSplitLink ilink_current = jac->head;
2916:   IS                is_owned;

2918:   PetscFunctionBegin;
2919:   jac->coordinates_set = PETSC_TRUE; // Internal flag
2920:   PetscCall(MatGetOwnershipIS(pc->mat, &is_owned, NULL));

2922:   while (ilink_current) {
2923:     // For each IS, embed it to get local coords indces
2924:     IS              is_coords;
2925:     PetscInt        ndofs_block;
2926:     const PetscInt *block_dofs_enumeration; // Numbering of the dofs relevant to the current block

2928:     // Setting drop to true for safety. It should make no difference.
2929:     PetscCall(ISEmbed(ilink_current->is, is_owned, PETSC_TRUE, &is_coords));
2930:     PetscCall(ISGetLocalSize(is_coords, &ndofs_block));
2931:     PetscCall(ISGetIndices(is_coords, &block_dofs_enumeration));

2933:     // Allocate coordinates vector and set it directly
2934:     PetscCall(PetscMalloc1(ndofs_block * dim, &(ilink_current->coords)));
2935:     for (PetscInt dof = 0; dof < ndofs_block; ++dof) {
2936:       for (PetscInt d = 0; d < dim; ++d) (ilink_current->coords)[dim * dof + d] = coords[dim * block_dofs_enumeration[dof] + d];
2937:     }
2938:     ilink_current->dim   = dim;
2939:     ilink_current->ndofs = ndofs_block;
2940:     PetscCall(ISRestoreIndices(is_coords, &block_dofs_enumeration));
2941:     PetscCall(ISDestroy(&is_coords));
2942:     ilink_current = ilink_current->next;
2943:   }
2944:   PetscCall(ISDestroy(&is_owned));
2945:   PetscFunctionReturn(PETSC_SUCCESS);
2946: }

2948: /*@
2949:   PCFieldSplitSetType - Sets the type, `PCCompositeType`, of a `PCFIELDSPLIT`

2951:   Collective

2953:   Input Parameters:
2954: + pc   - the preconditioner context
2955: - type - `PC_COMPOSITE_ADDITIVE`, `PC_COMPOSITE_MULTIPLICATIVE` (default), `PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE`, `PC_COMPOSITE_SPECIAL`, `PC_COMPOSITE_SCHUR`

2957:   Options Database Key:
2958: . -pc_fieldsplit_type <one of multiplicative, additive, symmetric_multiplicative, special, schur> - Sets fieldsplit preconditioner type

2960:   Level: intermediate

2962: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCCompositeType`, `PCCompositeGetType()`, `PC_COMPOSITE_ADDITIVE`, `PC_COMPOSITE_MULTIPLICATIVE`,
2963:           `PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE`, `PC_COMPOSITE_SPECIAL`, `PC_COMPOSITE_SCHUR`
2964: @*/
2965: PetscErrorCode PCFieldSplitSetType(PC pc, PCCompositeType type)
2966: {
2967:   PetscFunctionBegin;
2969:   PetscTryMethod(pc, "PCFieldSplitSetType_C", (PC, PCCompositeType), (pc, type));
2970:   PetscFunctionReturn(PETSC_SUCCESS);
2971: }

2973: /*@
2974:   PCFieldSplitGetType - Gets the type, `PCCompositeType`, of a `PCFIELDSPLIT`

2976:   Not collective

2978:   Input Parameter:
2979: . pc - the preconditioner context

2981:   Output Parameter:
2982: . type - `PC_COMPOSITE_ADDITIVE`, `PC_COMPOSITE_MULTIPLICATIVE` (default), `PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE`, `PC_COMPOSITE_SPECIAL`, `PC_COMPOSITE_SCHUR`

2984:   Level: intermediate

2986: .seealso: [](sec_block_matrices), `PC`, `PCCompositeSetType()`, `PCFIELDSPLIT`, `PCCompositeType`, `PC_COMPOSITE_ADDITIVE`, `PC_COMPOSITE_MULTIPLICATIVE`,
2987:           `PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE`, `PC_COMPOSITE_SPECIAL`, `PC_COMPOSITE_SCHUR`
2988: @*/
2989: PetscErrorCode PCFieldSplitGetType(PC pc, PCCompositeType *type)
2990: {
2991:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

2993:   PetscFunctionBegin;
2995:   PetscAssertPointer(type, 2);
2996:   *type = jac->type;
2997:   PetscFunctionReturn(PETSC_SUCCESS);
2998: }

3000: /*@
3001:   PCFieldSplitSetDMSplits - Flags whether `DMCreateFieldDecomposition()` should be used to define the splits in a `PCFIELDSPLIT`, whenever possible.

3003:   Logically Collective

3005:   Input Parameters:
3006: + pc  - the preconditioner context
3007: - flg - boolean indicating whether to use field splits defined by the `DM`

3009:   Options Database Key:
3010: . -pc_fieldsplit_dm_splits <bool> - use the field splits defined by the `DM`

3012:   Level: intermediate

3014: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitGetDMSplits()`, `PCFieldSplitSetFields()`, `PCFieldsplitSetIS()`
3015: @*/
3016: PetscErrorCode PCFieldSplitSetDMSplits(PC pc, PetscBool flg)
3017: {
3018:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
3019:   PetscBool      isfs;

3021:   PetscFunctionBegin;
3024:   PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCFIELDSPLIT, &isfs));
3025:   if (isfs) jac->dm_splits = flg;
3026:   PetscFunctionReturn(PETSC_SUCCESS);
3027: }

3029: /*@
3030:   PCFieldSplitGetDMSplits - Returns flag indicating whether `DMCreateFieldDecomposition()` should be used to define the splits in a `PCFIELDSPLIT`, whenever possible.

3032:   Logically Collective

3034:   Input Parameter:
3035: . pc - the preconditioner context

3037:   Output Parameter:
3038: . flg - boolean indicating whether to use field splits defined by the `DM`

3040:   Level: intermediate

3042: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetDMSplits()`, `PCFieldSplitSetFields()`, `PCFieldsplitSetIS()`
3043: @*/
3044: PetscErrorCode PCFieldSplitGetDMSplits(PC pc, PetscBool *flg)
3045: {
3046:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
3047:   PetscBool      isfs;

3049:   PetscFunctionBegin;
3051:   PetscAssertPointer(flg, 2);
3052:   PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCFIELDSPLIT, &isfs));
3053:   if (isfs) {
3054:     if (flg) *flg = jac->dm_splits;
3055:   }
3056:   PetscFunctionReturn(PETSC_SUCCESS);
3057: }

3059: /*@
3060:   PCFieldSplitGetDetectSaddlePoint - Returns flag indicating whether `PCFIELDSPLIT` will attempt to automatically determine fields based on zero diagonal entries.

3062:   Logically Collective

3064:   Input Parameter:
3065: . pc - the preconditioner context

3067:   Output Parameter:
3068: . flg - boolean indicating whether to detect fields or not

3070:   Level: intermediate

3072: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetDetectSaddlePoint()`
3073: @*/
3074: PetscErrorCode PCFieldSplitGetDetectSaddlePoint(PC pc, PetscBool *flg)
3075: {
3076:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

3078:   PetscFunctionBegin;
3079:   *flg = jac->detect;
3080:   PetscFunctionReturn(PETSC_SUCCESS);
3081: }

3083: /*@
3084:   PCFieldSplitSetDetectSaddlePoint - Sets flag indicating whether `PCFIELDSPLIT` will attempt to automatically determine fields based on zero diagonal entries.

3086:   Logically Collective

3088:   Input Parameter:
3089: . pc - the preconditioner context

3091:   Output Parameter:
3092: . flg - boolean indicating whether to detect fields or not

3094:   Options Database Key:
3095: . -pc_fieldsplit_detect_saddle_point <bool> - detect and use the saddle point

3097:   Level: intermediate

3099:   Note:
3100:   Also sets the split type to `PC_COMPOSITE_SCHUR` (see `PCFieldSplitSetType()`) and the Schur preconditioner type to `PC_FIELDSPLIT_SCHUR_PRE_SELF` (see `PCFieldSplitSetSchurPre()`).

3102: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitGetDetectSaddlePoint()`, `PCFieldSplitSetType()`, `PCFieldSplitSetSchurPre()`, `PC_FIELDSPLIT_SCHUR_PRE_SELF`
3103: @*/
3104: PetscErrorCode PCFieldSplitSetDetectSaddlePoint(PC pc, PetscBool flg)
3105: {
3106:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

3108:   PetscFunctionBegin;
3109:   jac->detect = flg;
3110:   if (jac->detect) {
3111:     PetscCall(PCFieldSplitSetType(pc, PC_COMPOSITE_SCHUR));
3112:     PetscCall(PCFieldSplitSetSchurPre(pc, PC_FIELDSPLIT_SCHUR_PRE_SELF, NULL));
3113:   }
3114:   PetscFunctionReturn(PETSC_SUCCESS);
3115: }

3117: /*MC
3118:    PCFIELDSPLIT - Preconditioner created by combining separate preconditioners for individual
3119:    collections of variables (that may overlap) called splits. See [the users manual section on "Solving Block Matrices"](sec_block_matrices) for more details.

3121:    Options Database Keys:
3122: +   -pc_fieldsplit_%d_fields <a,b,..>                                                - indicates the fields to be used in the `%d`'th split
3123: .   -pc_fieldsplit_default                                                           - automatically add any fields to additional splits that have not
3124:                                                                                      been supplied explicitly by `-pc_fieldsplit_%d_fields`
3125: .   -pc_fieldsplit_block_size <bs>                                                   - size of block that defines fields (i.e. there are bs fields)
3126: .   -pc_fieldsplit_type <additive,multiplicative,symmetric_multiplicative,schur,gkb> - type of relaxation or factorization splitting
3127: .   -pc_fieldsplit_schur_precondition <self,selfp,user,a11,full>                     - default is `a11`; see `PCFieldSplitSetSchurPre()`
3128: .   -pc_fieldsplit_schur_fact_type <diag,lower,upper,full>                           - set factorization type when using `-pc_fieldsplit_type schur`;
3129:                                                                                      see `PCFieldSplitSetSchurFactType()`
3130: -   -pc_fieldsplit_detect_saddle_point                                               - automatically finds rows with zero diagonal and uses Schur complement with no preconditioner as the solver

3132:      Options prefixes for inner solvers when using the Schur complement preconditioner are `-fieldsplit_0_` and `-fieldsplit_1_` .
3133:      The options prefix for the inner solver when using the Golub-Kahan biadiagonalization preconditioner is `-fieldsplit_0_`
3134:      For all other solvers they are `-fieldsplit_%d_` for the `%d`'th field; use `-fieldsplit_` for all fields.

3136:      To set options on the solvers for each block append `-fieldsplit_` to all the `PC`
3137:      options database keys. For example, `-fieldsplit_pc_type ilu` `-fieldsplit_pc_factor_levels 1`

3139:      To set the options on the solvers separate for each block call `PCFieldSplitGetSubKSP()`
3140:       and set the options directly on the resulting `KSP` object

3142:     Level: intermediate

3144:    Notes:
3145:     Use `PCFieldSplitSetFields()` to set splits defined by "strided" entries and `PCFieldSplitSetIS()`
3146:      to define a split by an arbitrary collection of entries.

3148:       If no splits are set the default is used. The splits are defined by entries strided by bs,
3149:       beginning at 0 then 1, etc to bs-1. The block size can be set with `PCFieldSplitSetBlockSize()`,
3150:       if this is not called the block size defaults to the blocksize of the second matrix passed
3151:       to `KSPSetOperators()`/`PCSetOperators()`.

3153:       For the Schur complement preconditioner if

3155:       ```{math}
3156:       J = \left[\begin{array}{cc} A_{00} & A_{01} \\ A_{10} & A_{11} \end{array}\right]
3157:       ```

3159:       the preconditioner using `full` factorization is logically
3160:       ```{math}
3161:       \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]
3162:       ```
3163:      where the action of $\text{inv}(A_{00})$ is applied using the KSP solver with prefix `-fieldsplit_0_`.  $S$ is the Schur complement
3164:      ```{math}
3165:      S = A_{11} - A_{10} \text{ksp}(A_{00}) A_{01}
3166:      ```
3167:      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
3168:      in providing the SECOND split or 1 if not given). For `PCFieldSplitGetSubKSP()` when field number is 0,
3169:      it returns the KSP associated with `-fieldsplit_0_` while field number 1 gives `-fieldsplit_1_` KSP. By default
3170:      $A_{11}$ is used to construct a preconditioner for $S$, use `PCFieldSplitSetSchurPre()` for all the possible ways to construct the preconditioner for $S$.

3172:      The factorization type is set using `-pc_fieldsplit_schur_fact_type <diag, lower, upper, full>`. `full` is shown above,
3173:      `diag` gives
3174:       ```{math}
3175:       \left[\begin{array}{cc} \text{inv}(A_{00}) & 0 \\  0 & -\text{ksp}(S) \end{array}\right]
3176:       ```
3177:      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
3178:      can be turned off with `PCFieldSplitSetSchurScale()` or by command line `-pc_fieldsplit_schur_scale 1.0`. The `lower` factorization is the inverse of
3179:       ```{math}
3180:       \left[\begin{array}{cc} A_{00} & 0 \\  A_{10} & S \end{array}\right]
3181:       ```
3182:      where the inverses of A_{00} and S are applied using KSPs. The upper factorization is the inverse of
3183:       ```{math}
3184:       \left[\begin{array}{cc} A_{00} & A_{01} \\  0 & S \end{array}\right]
3185:       ```
3186:      where again the inverses of $A_{00}$ and $S$ are applied using `KSP`s.

3188:      If only one set of indices (one `IS`) is provided with `PCFieldSplitSetIS()` then the complement of that `IS`
3189:      is used automatically for a second block.

3191:      The fieldsplit preconditioner cannot currently be used with the `MATBAIJ` or `MATSBAIJ` data formats if the blocksize is larger than 1.
3192:      Generally it should be used with the `MATAIJ` format.

3194:      The forms of these preconditioners are closely related if not identical to forms derived as "Distributive Iterations", see,
3195:      for example, page 294 in "Principles of Computational Fluid Dynamics" by Pieter Wesseling {cite}`wesseling2009`.
3196:      One can also use `PCFIELDSPLIT`
3197:      inside a smoother resulting in "Distributive Smoothers".

3199:      See "A taxonomy and comparison of parallel block multi-level preconditioners for the incompressible Navier-Stokes equations" {cite}`elman2008tcp`.

3201:      The Constrained Pressure Preconditioner (CPR) can be implemented using `PCCOMPOSITE` with `PCGALERKIN`. CPR first solves an $R A P$ subsystem, updates the
3202:      residual on all variables (`PCCompositeSetType(pc,PC_COMPOSITE_MULTIPLICATIVE)`), and then applies a simple ILU like preconditioner on all the variables.

3204:      The generalized Golub-Kahan bidiagonalization preconditioner (GKB) can be applied to symmetric $2 \times 2$ block matrices of the shape
3205:      ```{math}
3206:      \left[\begin{array}{cc} A_{00} & A_{01} \\ A_{01}' & 0 \end{array}\right]
3207:      ```
3208:      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 $H = _{A00} + \nu*A_{01}*A_{01}'$.
3209:      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_`.

3211:    Developer Note:
3212:    The Schur complement functionality of `PCFIELDSPLIT` should likely be factored into its own `PC` thus simplifying the implementation of the preconditioners and their
3213:    user API.

3215: .seealso: [](sec_block_matrices), `PC`, `PCCreate()`, `PCSetType()`, `PCType`, `PC`, `PCLSC`,
3216:           `PCFieldSplitGetSubKSP()`, `PCFieldSplitSchurGetSubKSP()`, `PCFieldSplitSetFields()`,
3217:           `PCFieldSplitSetType()`, `PCFieldSplitSetIS()`, `PCFieldSplitSetSchurPre()`, `PCFieldSplitSetSchurFactType()`,
3218:           `MatSchurComplementSetAinvType()`, `PCFieldSplitSetSchurScale()`, `PCFieldSplitSetDetectSaddlePoint()`
3219: M*/

3221: PETSC_EXTERN PetscErrorCode PCCreate_FieldSplit(PC pc)
3222: {
3223:   PC_FieldSplit *jac;

3225:   PetscFunctionBegin;
3226:   PetscCall(PetscNew(&jac));

3228:   jac->bs                 = -1;
3229:   jac->nsplits            = 0;
3230:   jac->type               = PC_COMPOSITE_MULTIPLICATIVE;
3231:   jac->schurpre           = PC_FIELDSPLIT_SCHUR_PRE_USER; /* Try user preconditioner first, fall back on diagonal */
3232:   jac->schurfactorization = PC_FIELDSPLIT_SCHUR_FACT_FULL;
3233:   jac->schurscale         = -1.0;
3234:   jac->dm_splits          = PETSC_TRUE;
3235:   jac->detect             = PETSC_FALSE;
3236:   jac->gkbtol             = 1e-5;
3237:   jac->gkbdelay           = 5;
3238:   jac->gkbnu              = 1;
3239:   jac->gkbmaxit           = 100;
3240:   jac->gkbmonitor         = PETSC_FALSE;
3241:   jac->coordinates_set    = PETSC_FALSE;

3243:   pc->data = (void *)jac;

3245:   pc->ops->apply           = PCApply_FieldSplit;
3246:   pc->ops->applytranspose  = PCApplyTranspose_FieldSplit;
3247:   pc->ops->setup           = PCSetUp_FieldSplit;
3248:   pc->ops->reset           = PCReset_FieldSplit;
3249:   pc->ops->destroy         = PCDestroy_FieldSplit;
3250:   pc->ops->setfromoptions  = PCSetFromOptions_FieldSplit;
3251:   pc->ops->view            = PCView_FieldSplit;
3252:   pc->ops->applyrichardson = NULL;

3254:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSchurGetSubKSP_C", PCFieldSplitSchurGetSubKSP_FieldSplit));
3255:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSubKSP_C", PCFieldSplitGetSubKSP_FieldSplit));
3256:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetFields_C", PCFieldSplitSetFields_FieldSplit));
3257:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetIS_C", PCFieldSplitSetIS_FieldSplit));
3258:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetType_C", PCFieldSplitSetType_FieldSplit));
3259:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetBlockSize_C", PCFieldSplitSetBlockSize_FieldSplit));
3260:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitRestrictIS_C", PCFieldSplitRestrictIS_FieldSplit));
3261:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCSetCoordinates_C", PCSetCoordinates_FieldSplit));
3262:   PetscFunctionReturn(PETSC_SUCCESS);
3263: }