Actual source code: fieldsplit.c

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

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

 16: 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;

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

 31:   /* Used only when setting coordinates with PCSetCoordinates */
 32:   PetscInt   dim;
 33:   PetscInt   ndofs;
 34:   PetscReal *coords;
 35: };

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

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

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

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

 82: /*
 83:     Note:
 84:     there is no particular reason that pmat, x, and y are stored as arrays in PC_FieldSplit instead of
 85:    inside PC_FieldSplitLink, just historical. If you want to be able to add new fields after already using the
 86:    PC you could change this.
 87: */

 89: /* This helper is so that setting a user-provided matrix is orthogonal to choosing to use it.  This way the
 90: * application-provided FormJacobian can provide this matrix without interfering with the user's (command-line) choices. */
 91: static Mat FieldSplitSchurPre(PC_FieldSplit *jac)
 92: {
 93:   switch (jac->schurpre) {
 94:   case PC_FIELDSPLIT_SCHUR_PRE_SELF:
 95:     return jac->schur;
 96:   case PC_FIELDSPLIT_SCHUR_PRE_SELFP:
 97:     return jac->schurp;
 98:   case PC_FIELDSPLIT_SCHUR_PRE_A11:
 99:     return jac->pmat[1];
100:   case PC_FIELDSPLIT_SCHUR_PRE_FULL: /* We calculate this and store it in schur_user */
101:   case PC_FIELDSPLIT_SCHUR_PRE_USER: /* Use a user-provided matrix if it is given, otherwise diagonal block */
102:   default:
103:     return jac->schur_user ? jac->schur_user : jac->pmat[1];
104:   }
105: }

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

115:   PetscFunctionBegin;
116:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &isascii));
117:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERDRAW, &isdraw));
118:   if (isascii) {
119:     if (jac->bs > 0) {
120:       PetscCall(PetscViewerASCIIPrintf(viewer, "  FieldSplit with %s composition: total splits = %" PetscInt_FMT ", blocksize = %" PetscInt_FMT "\n", PCCompositeTypes[jac->type], jac->nsplits, jac->bs));
121:     } else {
122:       PetscCall(PetscViewerASCIIPrintf(viewer, "  FieldSplit with %s composition: total splits = %" PetscInt_FMT "\n", PCCompositeTypes[jac->type], jac->nsplits));
123:     }
124:     if (pc->useAmat) PetscCall(PetscViewerASCIIPrintf(viewer, "  using Amat (not Pmat) as operator for blocks\n"));
125:     if (jac->diag_use_amat) PetscCall(PetscViewerASCIIPrintf(viewer, "  using Amat (not Pmat) as operator for diagonal blocks\n"));
126:     if (jac->offdiag_use_amat) PetscCall(PetscViewerASCIIPrintf(viewer, "  using Amat (not Pmat) as operator for off-diagonal blocks\n"));
127:     PetscCall(PetscViewerASCIIPrintf(viewer, "  Solver info for each split is in the following KSP objects:\n"));
128:     for (i = 0; i < jac->nsplits; i++) {
129:       if (ilink->fields) {
130:         PetscCall(PetscViewerASCIIPrintf(viewer, "Split number %" PetscInt_FMT " Fields ", i));
131:         PetscCall(PetscViewerASCIIUseTabs(viewer, PETSC_FALSE));
132:         for (j = 0; j < ilink->nfields; j++) {
133:           if (j > 0) PetscCall(PetscViewerASCIIPrintf(viewer, ","));
134:           PetscCall(PetscViewerASCIIPrintf(viewer, " %" PetscInt_FMT, ilink->fields[j]));
135:         }
136:         PetscCall(PetscViewerASCIIPrintf(viewer, "\n"));
137:         PetscCall(PetscViewerASCIIUseTabs(viewer, PETSC_TRUE));
138:       } else {
139:         PetscCall(PetscViewerASCIIPrintf(viewer, "Split number %" PetscInt_FMT " Defined by IS\n", i));
140:       }
141:       PetscCall(KSPView(ilink->ksp, viewer));
142:       ilink = ilink->next;
143:     }
144:   }

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

150:     PetscCall(PetscViewerDrawGetDraw(viewer, 0, &draw));
151:     PetscCall(PetscDrawGetCurrentPoint(draw, &x, &y));
152:     w  = 2 * PetscMin(1.0 - x, x);
153:     wd = w / (jac->nsplits + 1);
154:     x  = x - wd * (jac->nsplits - 1) / 2.0;
155:     for (i = 0; i < jac->nsplits; i++) {
156:       PetscCall(PetscDrawPushCurrentPoint(draw, x, y));
157:       PetscCall(KSPView(ilink->ksp, viewer));
158:       PetscCall(PetscDrawPopCurrentPoint(draw));
159:       x += wd;
160:       ilink = ilink->next;
161:     }
162:   }
163:   PetscFunctionReturn(PETSC_SUCCESS);
164: }

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

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

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

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

272:     PetscCall(PetscDrawPushCurrentPoint(draw, x, y));
273:     PetscCall(KSPView(jac->head->ksp, viewer));
274:     PetscCall(PetscDrawPopCurrentPoint(draw));
275:     if (jac->kspupper != jac->head->ksp) {
276:       x += wd;
277:       PetscCall(PetscDrawPushCurrentPoint(draw, x, y));
278:       PetscCall(KSPView(jac->kspupper, viewer));
279:       PetscCall(PetscDrawPopCurrentPoint(draw));
280:     }
281:     x += wd;
282:     PetscCall(PetscDrawPushCurrentPoint(draw, x, y));
283:     PetscCall(KSPView(jac->kspschur, viewer));
284:     PetscCall(PetscDrawPopCurrentPoint(draw));
285:   }
286:   PetscFunctionReturn(PETSC_SUCCESS);
287: }

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

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

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

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

327:     PetscCall(PetscViewerASCIIPopTab(viewer));
328:   }

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

334:     PetscCall(PetscViewerDrawGetDraw(viewer, 0, &draw));
335:     PetscCall(PetscDrawGetCurrentPoint(draw, &x, &y));
336:     w  = 2 * PetscMin(1.0 - x, x);
337:     wd = w / (jac->nsplits + 1);
338:     x  = x - wd * (jac->nsplits - 1) / 2.0;
339:     for (i = 0; i < jac->nsplits; i++) {
340:       PetscCall(PetscDrawPushCurrentPoint(draw, x, y));
341:       PetscCall(KSPView(ilink->ksp, viewer));
342:       PetscCall(PetscDrawPopCurrentPoint(draw));
343:       x += wd;
344:       ilink = ilink->next;
345:     }
346:   }
347:   PetscFunctionReturn(PETSC_SUCCESS);
348: }

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

358:   PetscFunctionBegin;
359:   PetscCall(PetscObjectTypeCompare((PetscObject)pc->mat, MATNEST, &mnest));
360:   if (mnest) {
361:     PetscCall(MatNestGetSize(pc->pmat, &bs, NULL));
362:   } else {
363:     bs = jac->bs;
364:   }
365:   PetscCall(PetscMalloc2(bs, &ifields, bs, &ifields_col));
366:   for (i = 0, flg = PETSC_TRUE;; i++) {
367:     PetscCall(PetscSNPrintf(splitname, sizeof(splitname), "%" PetscInt_FMT, i));
368:     PetscCall(PetscSNPrintf(optionname, sizeof(optionname), "-pc_fieldsplit_%" PetscInt_FMT "_fields", i));
369:     PetscCall(PetscSNPrintf(optionname_col, sizeof(optionname_col), "-pc_fieldsplit_%" PetscInt_FMT "_fields_col", i));
370:     nfields     = bs;
371:     nfields_col = bs;
372:     PetscCall(PetscOptionsGetIntArray(((PetscObject)pc)->options, ((PetscObject)pc)->prefix, optionname, ifields, &nfields, &flg));
373:     PetscCall(PetscOptionsGetIntArray(((PetscObject)pc)->options, ((PetscObject)pc)->prefix, optionname_col, ifields_col, &nfields_col, &flg_col));
374:     if (!flg) break;
375:     else if (flg && !flg_col) {
376:       PetscCheck(nfields, PETSC_COMM_SELF, PETSC_ERR_USER, "Cannot list zero fields");
377:       PetscCall(PCFieldSplitSetFields(pc, splitname, nfields, ifields, ifields));
378:     } else {
379:       PetscCheck(nfields && nfields_col, PETSC_COMM_SELF, PETSC_ERR_USER, "Cannot list zero fields");
380:       PetscCheck(nfields == nfields_col, PETSC_COMM_SELF, PETSC_ERR_USER, "Number of row and column fields must match");
381:       PetscCall(PCFieldSplitSetFields(pc, splitname, nfields, ifields, ifields_col));
382:     }
383:   }
384:   if (i > 0) {
385:     /* Makes command-line setting of splits take precedence over setting them in code.
386:        Otherwise subsequent calls to PCFieldSplitSetIS() or PCFieldSplitSetFields() would
387:        create new splits, which would probably not be what the user wanted. */
388:     jac->splitdefined = PETSC_TRUE;
389:   }
390:   PetscCall(PetscFree2(ifields, ifields_col));
391:   PetscFunctionReturn(PETSC_SUCCESS);
392: }

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

595:     jac->issetup = PETSC_TRUE;

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

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

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

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

623:           for (PetscInt k = 0; k < ilink->nfields; k++) {
624:             if (ilink->fields[k] != ilink->fields_col[k]) same_fields = PETSC_FALSE;
625:           }

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

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

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

666:       for (i = 0; i < nsplit; i++) {
667:         if (jac->defaultsplit) {
668:           PetscCall(ISDuplicate(rowis[i], &ilink->is));
669:           PetscCall(PetscObjectReference((PetscObject)ilink->is));
670:           ilink->is_col = ilink->is;
671:         } else if (!ilink->is) {
672:           if (ilink->nfields > 1) {
673:             for (PetscInt j = 0; j < ilink->nfields; j++) ises[j] = rowis[ilink->fields[j]];
674:             PetscCall(ISConcatenate(PetscObjectComm((PetscObject)pc), ilink->nfields, ises, &ilink->is));
675:           } else {
676:             PetscCall(ISDuplicate(rowis[ilink->fields[0]], &ilink->is));
677:           }
678:           PetscCall(PetscObjectReference((PetscObject)ilink->is));
679:           ilink->is_col = ilink->is;
680:         }
681:         ilink = ilink->next;
682:       }
683:       PetscCall(PetscFree2(rowis, colis));
684:       PetscCall(PetscFree(ises));
685:     }
686:   }

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

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

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

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

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

740:     for (i = 0; i < nsplit; i++) {
741:       Mat pmat;

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

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

768:       for (i = 0; i < nsplit; i++) {
769:         PetscCall(MatCreateSubMatrix(pc->mat, ilink->is, ilink->is_col, scall, &jac->mat[i]));
770:         ilink = ilink->next;
771:       }
772:       if (nullsp) PetscCall(MatRestoreNullSpaces(nsplit, jac->mat, &nullsp));
773:     }
774:   } else {
775:     jac->mat = jac->pmat;
776:   }

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

783:     PetscCall(PetscObjectQuery((PetscObject)ilink->is, "nullspace", (PetscObject *)&sp));
784:     if (sp) PetscCall(MatSetNullSpace(jac->mat[i], sp));
785:     ilink = ilink->next;
786:   }

788:   if (jac->type != PC_COMPOSITE_ADDITIVE && jac->type != PC_COMPOSITE_SCHUR && jac->type != PC_COMPOSITE_GKB) {
789:     /* extract the rows of the matrix associated with each field: used for efficient computation of residual inside algorithm */
790:     /* FIXME: Can/should we reuse jac->mat whenever (jac->diag_use_amat) is true? */
791:     ilink = jac->head;
792:     if (nsplit == 2 && jac->type == PC_COMPOSITE_MULTIPLICATIVE) {
793:       /* 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 */
794:       if (!jac->Afield) {
795:         PetscCall(PetscCalloc1(nsplit, &jac->Afield));
796:         if (jac->offdiag_use_amat) {
797:           PetscCall(MatCreateSubMatrix(pc->mat, ilink->next->is, ilink->is, MAT_INITIAL_MATRIX, &jac->Afield[1]));
798:         } else {
799:           PetscCall(MatCreateSubMatrix(pc->pmat, ilink->next->is, ilink->is, MAT_INITIAL_MATRIX, &jac->Afield[1]));
800:         }
801:       } else {
802:         MatReuse scall;

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

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

833:         for (i = 0; i < nsplit; i++) {
834:           if (jac->offdiag_use_amat) {
835:             PetscCall(MatCreateSubMatrix(pc->mat, ilink->is, NULL, scall, &jac->Afield[i]));
836:           } else {
837:             PetscCall(MatCreateSubMatrix(pc->pmat, ilink->is, NULL, scall, &jac->Afield[i]));
838:           }
839:           ilink = ilink->next;
840:         }
841:       }
842:     }
843:   }

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

979:         PetscCall(PetscSNPrintf(schurprefix, sizeof(schurprefix), "%sfieldsplit_%s_upper_", ((PetscObject)pc)->prefix ? ((PetscObject)pc)->prefix : "", ilink->splitname));
980:         PetscCall(KSPCreate(PetscObjectComm((PetscObject)pc), &jac->kspupper));
981:         PetscCall(KSPSetNestLevel(jac->kspupper, pc->kspnestlevel));
982:         PetscCall(KSPSetErrorIfNotConverged(jac->kspupper, pc->erroriffailure));
983:         PetscCall(KSPSetOptionsPrefix(jac->kspupper, schurprefix));
984:         PetscCall(PetscObjectIncrementTabLevel((PetscObject)jac->kspupper, (PetscObject)pc, 1));
985:         PetscCall(PetscObjectIncrementTabLevel((PetscObject)jac->kspupper->pc, (PetscObject)pc, 1));
986:         PetscCall(KSPGetDM(jac->head->ksp, &dmInner));
987:         PetscCall(KSPSetDM(jac->kspupper, dmInner));
988:         PetscCall(KSPSetDMActive(jac->kspupper, KSP_DMACTIVE_ALL, PETSC_FALSE));
989:         PetscCall(KSPSetFromOptions(jac->kspupper));
990:         PetscCall(KSPSetOperators(jac->kspupper, jac->mat[0], jac->pmat[0]));
991:         PetscCall(VecDuplicate(jac->head->x, &jac->head->z));
992:       } else {
993:         jac->kspupper = jac->head->ksp;
994:         PetscCall(PetscObjectReference((PetscObject)jac->head->ksp));
995:       }

997:       if (jac->schurpre == PC_FIELDSPLIT_SCHUR_PRE_SELFP) PetscCall(MatSchurComplementGetPmat(jac->schur, MAT_INITIAL_MATRIX, &jac->schurp));
998:       PetscCall(KSPCreate(PetscObjectComm((PetscObject)pc), &jac->kspschur));
999:       PetscCall(KSPSetNestLevel(jac->kspschur, pc->kspnestlevel));
1000:       PetscCall(KSPSetErrorIfNotConverged(jac->kspschur, pc->erroriffailure));
1001:       PetscCall(PetscObjectIncrementTabLevel((PetscObject)jac->kspschur, (PetscObject)pc, 1));
1002:       if (jac->schurpre == PC_FIELDSPLIT_SCHUR_PRE_SELF) {
1003:         PC pcschur;
1004:         PetscCall(KSPGetPC(jac->kspschur, &pcschur));
1005:         PetscCall(PCSetType(pcschur, PCNONE));
1006:         /* Note: This is bad if there exist preconditioners for MATSCHURCOMPLEMENT */
1007:       } else if (jac->schurpre == PC_FIELDSPLIT_SCHUR_PRE_FULL) {
1008:         if (jac->schurfactorization != PC_FIELDSPLIT_SCHUR_FACT_FULL || jac->kspupper != jac->head->ksp) PetscCall(MatSchurComplementComputeExplicitOperator(jac->schur, &jac->schur_user));
1009:       }
1010:       PetscCall(KSPSetOperators(jac->kspschur, jac->schur, FieldSplitSchurPre(jac)));
1011:       PetscCall(KSPGetOptionsPrefix(jac->head->next->ksp, &Dprefix));
1012:       PetscCall(KSPSetOptionsPrefix(jac->kspschur, Dprefix));
1013:       /* propagate DM */
1014:       {
1015:         DM sdm;
1016:         PetscCall(KSPGetDM(jac->head->next->ksp, &sdm));
1017:         if (sdm) {
1018:           PetscCall(KSPSetDM(jac->kspschur, sdm));
1019:           PetscCall(KSPSetDMActive(jac->kspschur, KSP_DMACTIVE_ALL, PETSC_FALSE));
1020:         }
1021:       }
1022:       /* really want setfromoptions called in PCSetFromOptions_FieldSplit(), but it is not ready yet */
1023:       /* need to call this every time, since the jac->kspschur is freshly created, otherwise its options never get set */
1024:       PetscCall(KSPSetFromOptions(jac->kspschur));
1025:     }
1026:     PetscCall(MatAssemblyBegin(jac->schur, MAT_FINAL_ASSEMBLY));
1027:     PetscCall(MatAssemblyEnd(jac->schur, MAT_FINAL_ASSEMBLY));
1028:     if (issym) PetscCall(MatSetOption(jac->schur, MAT_SYMMETRIC, PETSC_TRUE));
1029:     if (isspd) PetscCall(MatSetOption(jac->schur, MAT_SPD, PETSC_TRUE));

1031:     /* HACK: special support to forward L and Lp matrices that might be used by PCLSC */
1032:     PetscCall(PetscSNPrintf(lscname, sizeof(lscname), "%s_LSC_L", ilink->splitname));
1033:     PetscCall(PetscObjectQuery((PetscObject)pc->mat, lscname, &LSC_L));
1034:     if (!LSC_L) PetscCall(PetscObjectQuery((PetscObject)pc->pmat, lscname, &LSC_L));
1035:     if (LSC_L) PetscCall(PetscObjectCompose((PetscObject)jac->schur, "LSC_L", LSC_L));
1036:     PetscCall(PetscSNPrintf(lscname, sizeof(lscname), "%s_LSC_Lp", ilink->splitname));
1037:     PetscCall(PetscObjectQuery((PetscObject)pc->pmat, lscname, &LSC_L));
1038:     if (!LSC_L) PetscCall(PetscObjectQuery((PetscObject)pc->mat, lscname, &LSC_L));
1039:     if (LSC_L) PetscCall(PetscObjectCompose((PetscObject)jac->schur, "LSC_Lp", LSC_L));
1040:   } else if (jac->type == PC_COMPOSITE_GKB) {
1041:     PetscCheck(nsplit == 2, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_INCOMP, "To use GKB preconditioner you must have exactly 2 fields");
1042:     ilink = jac->head;
1043:     PetscCall(MatCreateSubMatrix(jac->offdiag_use_amat ? pc->mat : pc->pmat, ilink->is, ilink->next->is, MAT_INITIAL_MATRIX, &jac->B));
1044:     /* Create work vectors for GKB algorithm */
1045:     PetscCall(VecDuplicate(ilink->x, &jac->u));
1046:     PetscCall(VecDuplicate(ilink->x, &jac->Hu));
1047:     PetscCall(VecDuplicate(ilink->x, &jac->w2));
1048:     PetscCall(MatCreateSubMatrix(jac->offdiag_use_amat ? pc->mat : pc->pmat, ilink->next->is, ilink->is, MAT_INITIAL_MATRIX, &jac->C));
1049:     ilink = ilink->next;
1050:     /* Create work vectors for GKB algorithm */
1051:     PetscCall(VecDuplicate(ilink->x, &jac->v));
1052:     PetscCall(VecDuplicate(ilink->x, &jac->d));
1053:     PetscCall(VecDuplicate(ilink->x, &jac->w1));
1054:     PetscCall(MatGolubKahanComputeExplicitOperator(jac->mat[0], jac->B, jac->C, &jac->H, jac->gkbnu));
1055:     PetscCall(PetscCalloc1(jac->gkbdelay, &jac->vecz));

1057:     ilink = jac->head;
1058:     PetscCall(KSPSetOperators(ilink->ksp, jac->H, jac->H));
1059:     if (!jac->suboptionsset) PetscCall(KSPSetFromOptions(ilink->ksp));
1060:     /* Create gkb_monitor context */
1061:     if (jac->gkbmonitor) {
1062:       PetscInt tablevel;
1063:       PetscCall(PetscViewerCreate(PETSC_COMM_WORLD, &jac->gkbviewer));
1064:       PetscCall(PetscViewerSetType(jac->gkbviewer, PETSCVIEWERASCII));
1065:       PetscCall(PetscObjectGetTabLevel((PetscObject)ilink->ksp, &tablevel));
1066:       PetscCall(PetscViewerASCIISetTab(jac->gkbviewer, tablevel));
1067:       PetscCall(PetscObjectIncrementTabLevel((PetscObject)ilink->ksp, (PetscObject)ilink->ksp, 1));
1068:     }
1069:   } else {
1070:     /* set up the individual splits' PCs */
1071:     i     = 0;
1072:     ilink = jac->head;
1073:     while (ilink) {
1074:       PetscCall(KSPSetOperators(ilink->ksp, jac->mat[i], jac->pmat[i]));
1075:       /* really want setfromoptions called in PCSetFromOptions_FieldSplit(), but it is not ready yet */
1076:       if (!jac->suboptionsset) PetscCall(KSPSetFromOptions(ilink->ksp));
1077:       i++;
1078:       ilink = ilink->next;
1079:     }
1080:   }

1082:   /* Set coordinates to the sub PC objects whenever these are set */
1083:   if (jac->coordinates_set) {
1084:     PC pc_coords;
1085:     if (jac->type == PC_COMPOSITE_SCHUR) {
1086:       // Head is first block.
1087:       PetscCall(KSPGetPC(jac->head->ksp, &pc_coords));
1088:       PetscCall(PCSetCoordinates(pc_coords, jac->head->dim, jac->head->ndofs, jac->head->coords));
1089:       // Second one is Schur block, but its KSP object is in kspschur.
1090:       PetscCall(KSPGetPC(jac->kspschur, &pc_coords));
1091:       PetscCall(PCSetCoordinates(pc_coords, jac->head->next->dim, jac->head->next->ndofs, jac->head->next->coords));
1092:     } else if (jac->type == PC_COMPOSITE_GKB) {
1093:       PetscCall(PetscInfo(pc, "Warning: Setting coordinates does nothing for the GKB Fieldpslit preconditioner\n"));
1094:     } else {
1095:       ilink = jac->head;
1096:       while (ilink) {
1097:         PetscCall(KSPGetPC(ilink->ksp, &pc_coords));
1098:         PetscCall(PCSetCoordinates(pc_coords, ilink->dim, ilink->ndofs, ilink->coords));
1099:         ilink = ilink->next;
1100:       }
1101:     }
1102:   }

1104:   jac->suboptionsset = PETSC_TRUE;
1105:   PetscFunctionReturn(PETSC_SUCCESS);
1106: }

1108: static PetscErrorCode PCSetUpOnBlocks_FieldSplit_Schur(PC pc)
1109: {
1110:   PC_FieldSplit    *jac    = (PC_FieldSplit *)pc->data;
1111:   PC_FieldSplitLink ilinkA = jac->head;
1112:   KSP               kspA = ilinkA->ksp, kspUpper = jac->kspupper;

1114:   PetscFunctionBegin;
1115:   if (jac->schurfactorization == PC_FIELDSPLIT_SCHUR_FACT_FULL && kspUpper != kspA) {
1116:     PetscCall(KSPSetUp(kspUpper));
1117:     PetscCall(KSPSetUpOnBlocks(kspUpper));
1118:   }
1119:   PetscCall(KSPSetUp(kspA));
1120:   PetscCall(KSPSetUpOnBlocks(kspA));
1121:   if (jac->schurpre != PC_FIELDSPLIT_SCHUR_PRE_FULL) {
1122:     PetscCall(KSPSetUp(jac->kspschur));
1123:     PetscCall(KSPSetUpOnBlocks(jac->kspschur));
1124:   } else if (kspUpper == kspA && jac->schurfactorization == PC_FIELDSPLIT_SCHUR_FACT_FULL) {
1125:     Mat          A;
1126:     PetscInt     m, M, N;
1127:     VecType      vtype;
1128:     PetscMemType mtype;
1129:     PetscScalar *array;

1131:     PetscCall(MatGetSize(jac->B, &M, &N));
1132:     PetscCall(MatGetLocalSize(jac->B, &m, NULL));
1133:     PetscCall(MatGetVecType(jac->B, &vtype));
1134:     PetscCall(VecGetArrayAndMemType(ilinkA->x, &array, &mtype));
1135:     PetscCall(VecRestoreArrayAndMemType(ilinkA->x, &array));
1136:     PetscCall(PetscObjectQuery((PetscObject)jac->schur, "AinvB", (PetscObject *)&A));
1137:     if (A) {
1138:       PetscInt P;

1140:       PetscCall(MatGetSize(A, NULL, &P));
1141:       if (P < N + 1) { // need to recreate AinvB, otherwise, the Schur complement won't be updated
1142:         PetscCall(PetscObjectCompose((PetscObject)jac->schur, "AinvB", NULL));
1143:         A = NULL;
1144:       }
1145:     }
1146:     if (!A) {
1147:       if (PetscMemTypeHost(mtype) || (!PetscDefined(HAVE_CUDA) && !PetscDefined(HAVE_HIP))) PetscCall(PetscMalloc1(m * (N + 1), &array));
1148: #if PetscDefined(HAVE_CUDA)
1149:       else if (PetscMemTypeCUDA(mtype)) PetscCallCUDA(cudaMalloc((void **)&array, sizeof(PetscScalar) * m * (N + 1)));
1150: #endif
1151: #if PetscDefined(HAVE_HIP)
1152:       else if (PetscMemTypeHIP(mtype)) PetscCallHIP(hipMalloc((void **)&array, sizeof(PetscScalar) * m * (N + 1)));
1153: #endif
1154:       PetscCall(MatCreateDenseFromVecType(PetscObjectComm((PetscObject)jac->schur), vtype, m, PETSC_DECIDE, M, N + 1, PETSC_DECIDE, array, &A)); // number of columns of the Schur complement plus one
1155:       PetscCall(PetscObjectCompose((PetscObject)jac->schur, "AinvB", (PetscObject)A));
1156:       PetscCall(MatDestroy(&A));
1157:     }
1158:   }
1159:   PetscFunctionReturn(PETSC_SUCCESS);
1160: }

1162: static PetscErrorCode PCSetUpOnBlocks_FieldSplit(PC pc)
1163: {
1164:   PC_FieldSplit    *jac   = (PC_FieldSplit *)pc->data;
1165:   PC_FieldSplitLink ilink = jac->head;

1167:   PetscFunctionBegin;
1168:   while (ilink) {
1169:     PetscCall(KSPSetUp(ilink->ksp));
1170:     PetscCall(KSPSetUpOnBlocks(ilink->ksp));
1171:     ilink = ilink->next;
1172:   }
1173:   PetscFunctionReturn(PETSC_SUCCESS);
1174: }

1176: static PetscErrorCode PCSetUpOnBlocks_FieldSplit_GKB(PC pc)
1177: {
1178:   PC_FieldSplit    *jac    = (PC_FieldSplit *)pc->data;
1179:   PC_FieldSplitLink ilinkA = jac->head;
1180:   KSP               ksp    = ilinkA->ksp;

1182:   PetscFunctionBegin;
1183:   PetscCall(KSPSetUp(ksp));
1184:   PetscCall(KSPSetUpOnBlocks(ksp));
1185:   PetscFunctionReturn(PETSC_SUCCESS);
1186: }

1188: static PetscErrorCode PCApply_FieldSplit_Schur(PC pc, Vec x, Vec y)
1189: {
1190:   PC_FieldSplit    *jac    = (PC_FieldSplit *)pc->data;
1191:   PC_FieldSplitLink ilinkA = jac->head, ilinkD = ilinkA->next;
1192:   KSP               kspA = ilinkA->ksp, kspLower = kspA, kspUpper = jac->kspupper;
1193:   Mat               AinvB = NULL;
1194:   PetscInt          N, P;

1196:   PetscFunctionBegin;
1197:   switch (jac->schurfactorization) {
1198:   case PC_FIELDSPLIT_SCHUR_FACT_DIAG:
1199:     /* [A00 0; 0 -S], positive definite, suitable for MINRES */
1200:     PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1201:     PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1202:     PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
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:     PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1208:     PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1209:     PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1210:     PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, 1));
1211:     PetscCall(KSPSolve(jac->kspschur, ilinkD->x, ilinkD->y));
1212:     PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y));
1213:     PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, -1));
1214:     PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1215:     PetscCall(VecScale(ilinkD->y, jac->schurscale));
1216:     PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1217:     PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1218:     PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1219:     break;
1220:   case PC_FIELDSPLIT_SCHUR_FACT_LOWER:
1221:     /* [A00 0; A10 S], suitable for left preconditioning */
1222:     PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1223:     PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1224:     PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1225:     PetscCall(KSPSolve(kspA, ilinkA->x, ilinkA->y));
1226:     PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1227:     PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1228:     PetscCall(MatMult(jac->C, ilinkA->y, ilinkD->x));
1229:     PetscCall(VecScale(ilinkD->x, -1.));
1230:     PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD));
1231:     PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1232:     PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD));
1233:     PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1234:     PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, 1));
1235:     PetscCall(KSPSolve(jac->kspschur, ilinkD->x, ilinkD->y));
1236:     PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, -1));
1237:     PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y));
1238:     PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1239:     PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1240:     PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1241:     PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1242:     break;
1243:   case PC_FIELDSPLIT_SCHUR_FACT_UPPER:
1244:     /* [A00 A01; 0 S], suitable for right preconditioning */
1245:     PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1246:     PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1247:     PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1248:     PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, 1));
1249:     PetscCall(KSPSolve(jac->kspschur, ilinkD->x, ilinkD->y));
1250:     PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, -1));
1251:     PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y));
1252:     PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1253:     PetscCall(MatMult(jac->B, ilinkD->y, ilinkA->x));
1254:     PetscCall(VecScale(ilinkA->x, -1.));
1255:     PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, ADD_VALUES, SCATTER_FORWARD));
1256:     PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1257:     PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, ADD_VALUES, SCATTER_FORWARD));
1258:     PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1259:     PetscCall(KSPSolve(kspA, ilinkA->x, ilinkA->y));
1260:     PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1261:     PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1262:     PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1263:     PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1264:     PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1265:     break;
1266:   case PC_FIELDSPLIT_SCHUR_FACT_FULL:
1267:     /* [1 0; A10 A00^{-1} 1] [A00 0; 0 S] [1 A00^{-1}A01; 0 1] */
1268:     PetscCall(MatGetSize(jac->B, NULL, &P));
1269:     N = P;
1270:     PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1271:     PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1272:     PetscCall(PetscLogEventBegin(KSP_Solve_FS_L, kspLower, ilinkA->x, ilinkA->y, NULL));
1273:     if (kspUpper == kspA) {
1274:       PetscCall(PetscObjectQuery((PetscObject)jac->schur, "AinvB", (PetscObject *)&AinvB));
1275:       if (AinvB) {
1276:         PetscCall(MatGetSize(AinvB, NULL, &N));
1277:         if (N > P) { // first time PCApply_FieldSplit_Schur() is called
1278:           PetscMemType mtype;
1279:           Vec          c = NULL;
1280:           PetscScalar *array;
1281:           PetscInt     m, M;

1283:           PetscCall(MatGetSize(jac->B, &M, NULL));
1284:           PetscCall(MatGetLocalSize(jac->B, &m, NULL));
1285:           PetscCall(MatDenseGetArrayAndMemType(AinvB, &array, &mtype));
1286:           if (PetscMemTypeHost(mtype) || (!PetscDefined(HAVE_CUDA) && !PetscDefined(HAVE_HIP))) PetscCall(VecCreateMPIWithArray(PetscObjectComm((PetscObject)jac->schur), 1, m, M, array + m * P, &c));
1287: #if PetscDefined(HAVE_CUDA)
1288:           else if (PetscMemTypeCUDA(mtype)) PetscCall(VecCreateMPICUDAWithArray(PetscObjectComm((PetscObject)jac->schur), 1, m, M, array + m * P, &c));
1289: #endif
1290: #if PetscDefined(HAVE_HIP)
1291:           else if (PetscMemTypeHIP(mtype)) PetscCall(VecCreateMPIHIPWithArray(PetscObjectComm((PetscObject)jac->schur), 1, m, M, array + m * P, &c));
1292: #endif
1293:           PetscCall(MatDenseRestoreArrayAndMemType(AinvB, &array));
1294:           PetscCall(VecCopy(ilinkA->x, c));
1295:           PetscCall(MatSchurComplementComputeExplicitOperator(jac->schur, &jac->schur_user));
1296:           PetscCall(KSPSetOperators(jac->kspschur, jac->schur, jac->schur_user));
1297:           PetscCall(VecCopy(c, ilinkA->y)); // retrieve the solution as the last column of the composed Mat
1298:           PetscCall(VecDestroy(&c));
1299:         }
1300:       }
1301:     }
1302:     if (N == P) PetscCall(KSPSolve(kspLower, ilinkA->x, ilinkA->y));
1303:     PetscCall(KSPCheckSolve(kspLower, pc, ilinkA->y));
1304:     PetscCall(PetscLogEventEnd(KSP_Solve_FS_L, kspLower, ilinkA->x, ilinkA->y, NULL));
1305:     PetscCall(MatMult(jac->C, ilinkA->y, ilinkD->x));
1306:     PetscCall(VecScale(ilinkD->x, -1.0));
1307:     PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD));
1308:     PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD));

1310:     PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1311:     PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, 1));
1312:     PetscCall(KSPSolve(jac->kspschur, ilinkD->x, ilinkD->y));
1313:     PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, -1));
1314:     PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y));
1315:     PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1316:     PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));

1318:     if (kspUpper == kspA) {
1319:       if (!AinvB) {
1320:         PetscCall(MatMult(jac->B, ilinkD->y, ilinkA->y));
1321:         PetscCall(VecAXPY(ilinkA->x, -1.0, ilinkA->y));
1322:         PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1323:         PetscCall(KSPSolve(kspA, ilinkA->x, ilinkA->y));
1324:         PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1325:         PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1326:       } else PetscCall(MatMultAdd(AinvB, ilinkD->y, ilinkA->y, ilinkA->y));
1327:     } else {
1328:       PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1329:       PetscCall(KSPSolve(kspA, ilinkA->x, ilinkA->y));
1330:       PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1331:       PetscCall(MatMult(jac->B, ilinkD->y, ilinkA->x));
1332:       PetscCall(PetscLogEventBegin(KSP_Solve_FS_U, kspUpper, ilinkA->x, ilinkA->z, NULL));
1333:       PetscCall(KSPSolve(kspUpper, ilinkA->x, ilinkA->z));
1334:       PetscCall(KSPCheckSolve(kspUpper, pc, ilinkA->z));
1335:       PetscCall(PetscLogEventEnd(KSP_Solve_FS_U, kspUpper, ilinkA->x, ilinkA->z, NULL));
1336:       PetscCall(VecAXPY(ilinkA->y, -1.0, ilinkA->z));
1337:     }
1338:     PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1339:     PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1340:     PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1341:   }
1342:   PetscFunctionReturn(PETSC_SUCCESS);
1343: }

1345: /*
1346:   PCFieldSplitCreateWorkMats_Private - Allocate per-field dense work matrices for multi-RHS

1348:   Input Parameters:
1349: + pc - the PC context
1350: - X  - matrix to copy column-layout from

1352:   Notes:
1353:   If matrices already exist with correct column count, they are reused.
1354:   If column count changed, old matrices are destroyed and new ones created.
1355: */
1356: static PetscErrorCode PCFieldSplitCreateWorkMats_Private(PC pc, Mat X)
1357: {
1358:   PC_FieldSplit    *jac   = (PC_FieldSplit *)pc->data;
1359:   PC_FieldSplitLink ilink = jac->head;
1360:   PetscInt          mx, Mx, my, My, N;

1362:   PetscFunctionBegin;
1363:   while (ilink) {
1364:     /* check if reallocation needed (previous allocation with wrong column count) */
1365:     if (ilink->X) {
1366:       PetscCall(MatGetSize(ilink->X, NULL, &N));
1367:       if (N != X->cmap->N) {
1368:         PetscCall(MatDestroy(&ilink->X));
1369:         PetscCall(MatDestroy(&ilink->Y));
1370:         PetscCall(MatDestroy(&ilink->Z));
1371:       }
1372:     }
1373:     /* create if needed */
1374:     if (!ilink->X) {
1375:       VecType xtype, ytype;

1377:       PetscCall(VecGetType(ilink->x, &xtype));
1378:       PetscCall(VecGetType(ilink->y, &ytype));
1379:       PetscCall(VecGetLocalSize(ilink->x, &mx));
1380:       PetscCall(VecGetSize(ilink->x, &Mx));
1381:       PetscCall(VecGetLocalSize(ilink->y, &my));
1382:       PetscCall(VecGetSize(ilink->y, &My));
1383:       /* use default lda */
1384:       PetscCall(MatCreateDenseFromVecType(PetscObjectComm((PetscObject)pc), xtype, mx, X->cmap->n, Mx, X->cmap->N, PETSC_DECIDE, NULL, &ilink->X));
1385:       PetscCall(MatCreateDenseFromVecType(PetscObjectComm((PetscObject)pc), ytype, my, X->cmap->n, My, X->cmap->N, PETSC_DECIDE, NULL, &ilink->Y));
1386:     }
1387:     ilink = ilink->next;
1388:   }
1389:   PetscFunctionReturn(PETSC_SUCCESS);
1390: }

1392: static PetscErrorCode PCMatApply_FieldSplit_Schur(PC pc, Mat X, Mat Y)
1393: {
1394:   PC_FieldSplit    *jac    = (PC_FieldSplit *)pc->data;
1395:   PC_FieldSplitLink ilinkA = jac->head, ilinkD = ilinkA->next;
1396:   KSP               kspA = ilinkA->ksp, kspLower = kspA, kspUpper = jac->kspupper;
1397:   Mat               AinvB = NULL;
1398:   PetscInt          N, P;

1400:   PetscFunctionBegin;
1401:   /* create working matrices with the correct number of columns */
1402:   PetscCall(PCFieldSplitCreateWorkMats_Private(pc, X));
1403:   switch (jac->schurfactorization) {
1404:   case PC_FIELDSPLIT_SCHUR_FACT_DIAG:
1405:     /* [A00 0; 0 -S], positive definite, suitable for MINRES */
1406:     PetscCall(MatDenseScatter_Private(ilinkA->sctx, X, ilinkA->X, INSERT_VALUES, SCATTER_FORWARD));
1407:     PetscCall(MatDenseScatter_Private(ilinkD->sctx, X, ilinkD->X, INSERT_VALUES, SCATTER_FORWARD));
1408:     PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->X, ilinkA->Y, NULL));
1409:     PetscCall(KSPMatSolve(kspA, ilinkA->X, ilinkA->Y));
1410:     PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->X, ilinkA->Y, NULL));
1411:     PetscCall(MatDenseScatter_Private(ilinkA->sctx, ilinkA->Y, Y, INSERT_VALUES, SCATTER_REVERSE));
1412:     PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->X, ilinkD->Y, NULL));
1413:     PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, 1));
1414:     PetscCall(KSPMatSolve(jac->kspschur, ilinkD->X, ilinkD->Y));
1415:     PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, -1));
1416:     PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->X, ilinkD->Y, NULL));
1417:     PetscCall(MatScale(ilinkD->Y, jac->schurscale));
1418:     PetscCall(MatDenseScatter_Private(ilinkD->sctx, ilinkD->Y, Y, INSERT_VALUES, SCATTER_REVERSE));
1419:     break;
1420:   case PC_FIELDSPLIT_SCHUR_FACT_LOWER:
1421:     /* [A00 0; A10 S], suitable for left preconditioning */
1422:     PetscCall(MatDenseScatter_Private(ilinkA->sctx, X, ilinkA->X, INSERT_VALUES, SCATTER_FORWARD));
1423:     PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->X, ilinkA->Y, NULL));
1424:     PetscCall(KSPMatSolve(kspA, ilinkA->X, ilinkA->Y));
1425:     PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->X, ilinkA->Y, NULL));
1426:     PetscCall(MatMatMult(jac->C, ilinkA->Y, MAT_REUSE_MATRIX, PETSC_DETERMINE, &ilinkD->X));
1427:     PetscCall(MatScale(ilinkD->X, -1.0));
1428:     PetscCall(MatDenseScatter_Private(ilinkD->sctx, X, ilinkD->X, ADD_VALUES, SCATTER_FORWARD));
1429:     PetscCall(MatDenseScatter_Private(ilinkA->sctx, ilinkA->Y, Y, INSERT_VALUES, SCATTER_REVERSE));
1430:     PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->X, ilinkD->Y, NULL));
1431:     PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, 1));
1432:     PetscCall(KSPMatSolve(jac->kspschur, ilinkD->X, ilinkD->Y));
1433:     PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, -1));
1434:     PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->X, ilinkD->Y, NULL));
1435:     PetscCall(MatDenseScatter_Private(ilinkD->sctx, ilinkD->Y, Y, INSERT_VALUES, SCATTER_REVERSE));
1436:     break;
1437:   case PC_FIELDSPLIT_SCHUR_FACT_UPPER:
1438:     /* [A00 A01; 0 S], suitable for right preconditioning */
1439:     PetscCall(MatDenseScatter_Private(ilinkD->sctx, X, ilinkD->X, INSERT_VALUES, SCATTER_FORWARD));
1440:     PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->X, ilinkD->Y, NULL));
1441:     PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, 1));
1442:     PetscCall(KSPMatSolve(jac->kspschur, ilinkD->X, ilinkD->Y));
1443:     PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, -1));
1444:     PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->X, ilinkD->Y, NULL));
1445:     PetscCall(MatMatMult(jac->B, ilinkD->Y, MAT_REUSE_MATRIX, PETSC_DETERMINE, &ilinkA->X));
1446:     PetscCall(MatScale(ilinkA->X, -1.0));
1447:     PetscCall(MatDenseScatter_Private(ilinkA->sctx, X, ilinkA->X, ADD_VALUES, SCATTER_FORWARD));
1448:     PetscCall(MatDenseScatter_Private(ilinkD->sctx, ilinkD->Y, Y, INSERT_VALUES, SCATTER_REVERSE));
1449:     PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->X, ilinkA->Y, NULL));
1450:     PetscCall(KSPMatSolve(kspA, ilinkA->X, ilinkA->Y));
1451:     PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->X, ilinkA->Y, NULL));
1452:     PetscCall(MatDenseScatter_Private(ilinkA->sctx, ilinkA->Y, Y, INSERT_VALUES, SCATTER_REVERSE));
1453:     break;
1454:   case PC_FIELDSPLIT_SCHUR_FACT_FULL:
1455:     /* [1 0; A10 A00^{-1} 1] [A00 0; 0 S] [1 A00^{-1}A01; 0 1] */
1456:     PetscCall(MatGetSize(jac->B, NULL, &P));
1457:     N = P;
1458:     PetscCall(MatDenseScatter_Private(ilinkA->sctx, X, ilinkA->X, INSERT_VALUES, SCATTER_FORWARD));
1459:     PetscCall(PetscLogEventBegin(KSP_Solve_FS_L, kspLower, ilinkA->X, ilinkA->Y, NULL));
1460:     if (kspUpper == kspA) {
1461:       PetscCall(PetscObjectQuery((PetscObject)jac->schur, "AinvB", (PetscObject *)&AinvB));
1462:       if (AinvB) {
1463:         PetscCall(MatGetSize(AinvB, NULL, &N));
1464:         if (N > P) { // first time PCApply_FieldSplit_Schur() is called
1465:           PetscMemType mtype;
1466:           Mat          C = NULL;
1467:           PetscScalar *array;
1468:           PetscInt     m, M, q, Q, p;

1470:           PetscCall(MatGetSize(jac->B, &M, NULL));
1471:           PetscCall(MatGetLocalSize(jac->B, &m, NULL));
1472:           PetscCall(MatGetSize(X, NULL, &Q));
1473:           PetscCall(MatGetLocalSize(X, NULL, &q));
1474:           PetscCall(MatDenseGetArrayAndMemType(AinvB, &array, &mtype));
1475:           if (N != P + Q) {
1476:             Mat replace;

1478:             PetscCall(MatGetLocalSize(jac->B, NULL, &p));
1479:             if (PetscMemTypeCUDA(mtype)) {
1480: #if PetscDefined(HAVE_CUDA)
1481:               PetscCallCUDA(cudaFree(array));
1482:               PetscCallCUDA(cudaMalloc((void **)&array, sizeof(PetscScalar) * m * (P + Q)));
1483: #endif
1484:             } else if (PetscMemTypeHIP(mtype)) {
1485: #if PetscDefined(HAVE_HIP)
1486:               PetscCallHIP(hipFree(array));
1487:               PetscCallHIP(hipMalloc((void **)&array, sizeof(PetscScalar) * m * (P + Q)));
1488: #endif
1489:             } else {
1490:               PetscCheck(PetscMemTypeHost(mtype), PetscObjectComm((PetscObject)jac->schur), PETSC_ERR_SUP, "PetscMemType should be either PETSC_MEMTYPE_HOST, PETSC_MEMTYPE_CUDA, or PETSC_MEMTYPE_HIP");
1491:               PetscCall(PetscFree(array));
1492:               PetscCall(PetscMalloc1(m * (P + Q), &array));
1493:             }
1494:             PetscCall(MatCreateDenseWithMemType(PetscObjectComm((PetscObject)jac->schur), mtype, m, PETSC_DECIDE, M, P + Q, PETSC_DECIDE, array, &replace));
1495:             PetscCall(MatHeaderReplace(AinvB, &replace));
1496:           }
1497:           PetscCall(MatCreateDenseWithMemType(PetscObjectComm((PetscObject)jac->schur), mtype, m, q, M, Q, PETSC_DECIDE, array + m * P, &C));
1498:           PetscCall(MatDenseRestoreArrayAndMemType(AinvB, &array));
1499:           PetscCall(MatCopy(ilinkA->X, C, SAME_NONZERO_PATTERN));
1500:           PetscCall(MatSchurComplementComputeExplicitOperator(jac->schur, &jac->schur_user));
1501:           PetscCall(KSPSetOperators(jac->kspschur, jac->schur, jac->schur_user));
1502:           PetscCall(MatCopy(C, ilinkA->Y, SAME_NONZERO_PATTERN)); // retrieve solutions as last columns of the composed Mat
1503:           PetscCall(MatDestroy(&C));
1504:         }
1505:       }
1506:     }
1507:     if (N == P) PetscCall(KSPMatSolve(kspLower, ilinkA->X, ilinkA->Y));
1508:     PetscCall(PetscLogEventEnd(KSP_Solve_FS_L, kspLower, ilinkA->X, ilinkA->Y, NULL));
1509:     PetscCall(MatMatMult(jac->C, ilinkA->Y, MAT_REUSE_MATRIX, PETSC_DETERMINE, &ilinkD->X));
1510:     PetscCall(MatScale(ilinkD->X, -1.0));
1511:     PetscCall(MatDenseScatter_Private(ilinkD->sctx, X, ilinkD->X, ADD_VALUES, SCATTER_FORWARD));

1513:     PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->X, ilinkD->Y, NULL));
1514:     PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, 1));
1515:     PetscCall(KSPMatSolve(jac->kspschur, ilinkD->X, ilinkD->Y));
1516:     PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, -1));
1517:     PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->X, ilinkD->Y, NULL));
1518:     PetscCall(MatDenseScatter_Private(ilinkD->sctx, ilinkD->Y, Y, INSERT_VALUES, SCATTER_REVERSE));

1520:     if (kspUpper == kspA) {
1521:       if (!AinvB) {
1522:         PetscCall(MatMatMult(jac->B, ilinkD->Y, MAT_REUSE_MATRIX, PETSC_DETERMINE, &ilinkA->Y));
1523:         PetscCall(MatAXPY(ilinkA->X, -1.0, ilinkA->Y, SAME_NONZERO_PATTERN));
1524:         PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->X, ilinkA->Y, NULL));
1525:         PetscCall(KSPMatSolve(kspA, ilinkA->X, ilinkA->Y));
1526:         PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->X, ilinkA->Y, NULL));
1527:       } else {
1528:         PetscCall(MatMatMult(AinvB, ilinkD->Y, MAT_REUSE_MATRIX, PETSC_DETERMINE, &ilinkA->X));
1529:         PetscCall(MatAXPY(ilinkA->Y, 1.0, ilinkA->X, SAME_NONZERO_PATTERN));
1530:       }
1531:     } else {
1532:       PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->X, ilinkA->Y, NULL));
1533:       PetscCall(KSPMatSolve(kspA, ilinkA->X, ilinkA->Y));
1534:       PetscCall(MatMatMult(jac->B, ilinkD->Y, MAT_REUSE_MATRIX, PETSC_DETERMINE, &ilinkA->X));
1535:       if (!ilinkA->Z) PetscCall(MatDuplicate(ilinkA->X, MAT_DO_NOT_COPY_VALUES, &ilinkA->Z));
1536:       PetscCall(PetscLogEventBegin(KSP_Solve_FS_U, kspUpper, ilinkA->X, ilinkA->Z, NULL));
1537:       PetscCall(KSPMatSolve(kspUpper, ilinkA->X, ilinkA->Z));
1538:       PetscCall(PetscLogEventEnd(KSP_Solve_FS_U, kspUpper, ilinkA->X, ilinkA->Z, NULL));
1539:       PetscCall(MatAXPY(ilinkA->Y, -1.0, ilinkA->Z, SAME_NONZERO_PATTERN));
1540:     }
1541:     PetscCall(MatDenseScatter_Private(ilinkA->sctx, ilinkA->Y, Y, INSERT_VALUES, SCATTER_REVERSE));
1542:   }
1543:   PetscFunctionReturn(PETSC_SUCCESS);
1544: }

1546: static PetscErrorCode PCApplyTranspose_FieldSplit_Schur(PC pc, Vec x, Vec y)
1547: {
1548:   PC_FieldSplit    *jac    = (PC_FieldSplit *)pc->data;
1549:   PC_FieldSplitLink ilinkA = jac->head, ilinkD = ilinkA->next;
1550:   KSP               kspA = ilinkA->ksp, kspLower = kspA, kspUpper = jac->kspupper;

1552:   PetscFunctionBegin;
1553:   switch (jac->schurfactorization) {
1554:   case PC_FIELDSPLIT_SCHUR_FACT_DIAG:
1555:     /* [A00 0; 0 -S], positive definite, suitable for MINRES */
1556:     PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1557:     PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1558:     PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1559:     PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1560:     PetscCall(KSPSolveTranspose(kspA, ilinkA->x, ilinkA->y));
1561:     PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1562:     PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1563:     PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1564:     PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1565:     PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1566:     PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, 1));
1567:     PetscCall(KSPSolveTranspose(jac->kspschur, ilinkD->x, ilinkD->y));
1568:     PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, -1));
1569:     PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y));
1570:     PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1571:     PetscCall(VecScale(ilinkD->y, jac->schurscale));
1572:     PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1573:     PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1574:     PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1575:     break;
1576:   case PC_FIELDSPLIT_SCHUR_FACT_UPPER:
1577:     PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1578:     PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1579:     PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1580:     PetscCall(KSPSolveTranspose(kspA, ilinkA->x, ilinkA->y));
1581:     PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1582:     PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1583:     PetscCall(MatMultTranspose(jac->B, ilinkA->y, ilinkD->x));
1584:     PetscCall(VecScale(ilinkD->x, -1.));
1585:     PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD));
1586:     PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1587:     PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD));
1588:     PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1589:     PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, 1));
1590:     PetscCall(KSPSolveTranspose(jac->kspschur, ilinkD->x, ilinkD->y));
1591:     PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, -1));
1592:     PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y));
1593:     PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1594:     PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1595:     PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1596:     PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1597:     break;
1598:   case PC_FIELDSPLIT_SCHUR_FACT_LOWER:
1599:     PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1600:     PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1601:     PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1602:     PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, 1));
1603:     PetscCall(KSPSolveTranspose(jac->kspschur, ilinkD->x, ilinkD->y));
1604:     PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, -1));
1605:     PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y));
1606:     PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1607:     PetscCall(MatMultTranspose(jac->C, ilinkD->y, ilinkA->x));
1608:     PetscCall(VecScale(ilinkA->x, -1.));
1609:     PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, ADD_VALUES, SCATTER_FORWARD));
1610:     PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1611:     PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, ADD_VALUES, SCATTER_FORWARD));
1612:     PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1613:     PetscCall(KSPSolveTranspose(kspA, ilinkA->x, ilinkA->y));
1614:     PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1615:     PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1616:     PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1617:     PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1618:     PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1619:     break;
1620:   case PC_FIELDSPLIT_SCHUR_FACT_FULL:
1621:     PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1622:     PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1623:     PetscCall(PetscLogEventBegin(KSP_Solve_FS_U, kspUpper, ilinkA->x, ilinkA->y, NULL));
1624:     PetscCall(KSPSolveTranspose(kspUpper, ilinkA->x, ilinkA->y));
1625:     PetscCall(KSPCheckSolve(kspUpper, pc, ilinkA->y));
1626:     PetscCall(PetscLogEventEnd(KSP_Solve_FS_U, kspUpper, ilinkA->x, ilinkA->y, NULL));
1627:     PetscCall(MatMultTranspose(jac->B, ilinkA->y, ilinkD->x));
1628:     PetscCall(VecScale(ilinkD->x, -1.0));
1629:     PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD));
1630:     PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD));

1632:     PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1633:     PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, 1));
1634:     PetscCall(KSPSolveTranspose(jac->kspschur, ilinkD->x, ilinkD->y));
1635:     PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, -1));
1636:     PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y));
1637:     PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1638:     PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));

1640:     if (kspLower == kspA) {
1641:       PetscCall(MatMultTranspose(jac->C, ilinkD->y, ilinkA->y));
1642:       PetscCall(VecAXPY(ilinkA->x, -1.0, ilinkA->y));
1643:       PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1644:       PetscCall(KSPSolveTranspose(kspA, ilinkA->x, ilinkA->y));
1645:       PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1646:       PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1647:     } else {
1648:       PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1649:       PetscCall(KSPSolveTranspose(kspA, ilinkA->x, ilinkA->y));
1650:       PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1651:       PetscCall(MatMultTranspose(jac->C, ilinkD->y, ilinkA->x));
1652:       PetscCall(PetscLogEventBegin(KSP_Solve_FS_L, kspLower, ilinkA->x, ilinkA->z, NULL));
1653:       PetscCall(KSPSolveTranspose(kspLower, ilinkA->x, ilinkA->z));
1654:       PetscCall(KSPCheckSolve(kspLower, pc, ilinkA->z));
1655:       PetscCall(PetscLogEventEnd(KSP_Solve_FS_L, kspLower, ilinkA->x, ilinkA->z, NULL));
1656:       PetscCall(VecAXPY(ilinkA->y, -1.0, ilinkA->z));
1657:     }
1658:     PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1659:     PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1660:     PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1661:   }
1662:   PetscFunctionReturn(PETSC_SUCCESS);
1663: }

1665: #define FieldSplitSplitSolveAdd(ilink, xx, yy) \
1666:   ((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) || \
1667:                     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) || \
1668:                     VecScatterEnd(ilink->sctx, ilink->y, yy, ADD_VALUES, SCATTER_REVERSE)))

1670: static PetscErrorCode PCApply_FieldSplit(PC pc, Vec x, Vec y)
1671: {
1672:   PC_FieldSplit    *jac   = (PC_FieldSplit *)pc->data;
1673:   PC_FieldSplitLink ilink = jac->head;
1674:   PetscInt          cnt, bs;

1676:   PetscFunctionBegin;
1677:   if (jac->type == PC_COMPOSITE_ADDITIVE) {
1678:     PetscBool matnest;

1680:     PetscCall(PetscObjectTypeCompare((PetscObject)pc->pmat, MATNEST, &matnest));
1681:     if (jac->defaultsplit && !matnest) {
1682:       PetscCall(VecGetBlockSize(x, &bs));
1683:       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);
1684:       PetscCall(VecGetBlockSize(y, &bs));
1685:       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);
1686:       PetscCall(VecStrideGatherAll(x, jac->x, INSERT_VALUES));
1687:       while (ilink) {
1688:         PetscCall(PetscLogEventBegin(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1689:         PetscCall(KSPSolve(ilink->ksp, ilink->x, ilink->y));
1690:         PetscCall(KSPCheckSolve(ilink->ksp, pc, ilink->y));
1691:         PetscCall(PetscLogEventEnd(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1692:         ilink = ilink->next;
1693:       }
1694:       PetscCall(VecStrideScatterAll(jac->y, y, INSERT_VALUES));
1695:     } else {
1696:       PetscCall(VecSet(y, 0.0));
1697:       while (ilink) {
1698:         PetscCall(FieldSplitSplitSolveAdd(ilink, x, y));
1699:         ilink = ilink->next;
1700:       }
1701:     }
1702:   } else if (jac->type == PC_COMPOSITE_MULTIPLICATIVE && jac->nsplits == 2) {
1703:     PetscCall(VecSet(y, 0.0));
1704:     /* solve on first block for first block variables */
1705:     PetscCall(VecScatterBegin(ilink->sctx, x, ilink->x, INSERT_VALUES, SCATTER_FORWARD));
1706:     PetscCall(VecScatterEnd(ilink->sctx, x, ilink->x, INSERT_VALUES, SCATTER_FORWARD));
1707:     PetscCall(PetscLogEventBegin(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1708:     PetscCall(KSPSolve(ilink->ksp, ilink->x, ilink->y));
1709:     PetscCall(KSPCheckSolve(ilink->ksp, pc, ilink->y));
1710:     PetscCall(PetscLogEventEnd(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1711:     PetscCall(VecScatterBegin(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE));
1712:     PetscCall(VecScatterEnd(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE));

1714:     /* compute the residual only onto second block variables using first block variables */
1715:     PetscCall(MatMult(jac->Afield[1], ilink->y, ilink->next->x));
1716:     ilink = ilink->next;
1717:     PetscCall(VecScale(ilink->x, -1.0));
1718:     PetscCall(VecScatterBegin(ilink->sctx, x, ilink->x, ADD_VALUES, SCATTER_FORWARD));
1719:     PetscCall(VecScatterEnd(ilink->sctx, x, ilink->x, ADD_VALUES, SCATTER_FORWARD));

1721:     /* solve on second block variables */
1722:     PetscCall(PetscLogEventBegin(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1723:     PetscCall(KSPSolve(ilink->ksp, ilink->x, ilink->y));
1724:     PetscCall(KSPCheckSolve(ilink->ksp, pc, ilink->y));
1725:     PetscCall(PetscLogEventEnd(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1726:     PetscCall(VecScatterBegin(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE));
1727:     PetscCall(VecScatterEnd(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE));
1728:   } else if (jac->type == PC_COMPOSITE_MULTIPLICATIVE || jac->type == PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE) {
1729:     if (!jac->w1) {
1730:       PetscCall(VecDuplicate(x, &jac->w1));
1731:       PetscCall(VecDuplicate(x, &jac->w2));
1732:     }
1733:     PetscCall(VecSet(y, 0.0));
1734:     PetscCall(FieldSplitSplitSolveAdd(ilink, x, y));
1735:     cnt = 1;
1736:     while (ilink->next) {
1737:       ilink = ilink->next;
1738:       /* compute the residual only over the part of the vector needed */
1739:       PetscCall(MatMult(jac->Afield[cnt++], y, ilink->x));
1740:       PetscCall(VecScale(ilink->x, -1.0));
1741:       PetscCall(VecScatterBegin(ilink->sctx, x, ilink->x, ADD_VALUES, SCATTER_FORWARD));
1742:       PetscCall(VecScatterEnd(ilink->sctx, x, ilink->x, ADD_VALUES, SCATTER_FORWARD));
1743:       PetscCall(PetscLogEventBegin(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1744:       PetscCall(KSPSolve(ilink->ksp, ilink->x, ilink->y));
1745:       PetscCall(KSPCheckSolve(ilink->ksp, pc, ilink->y));
1746:       PetscCall(PetscLogEventEnd(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1747:       PetscCall(VecScatterBegin(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE));
1748:       PetscCall(VecScatterEnd(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE));
1749:     }
1750:     if (jac->type == PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE) {
1751:       cnt -= 2;
1752:       while (ilink->previous) {
1753:         ilink = ilink->previous;
1754:         /* compute the residual only over the part of the vector needed */
1755:         PetscCall(MatMult(jac->Afield[cnt--], y, ilink->x));
1756:         PetscCall(VecScale(ilink->x, -1.0));
1757:         PetscCall(VecScatterBegin(ilink->sctx, x, ilink->x, ADD_VALUES, SCATTER_FORWARD));
1758:         PetscCall(VecScatterEnd(ilink->sctx, x, ilink->x, ADD_VALUES, SCATTER_FORWARD));
1759:         PetscCall(PetscLogEventBegin(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1760:         PetscCall(KSPSolve(ilink->ksp, ilink->x, ilink->y));
1761:         PetscCall(KSPCheckSolve(ilink->ksp, pc, ilink->y));
1762:         PetscCall(PetscLogEventEnd(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1763:         PetscCall(VecScatterBegin(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE));
1764:         PetscCall(VecScatterEnd(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE));
1765:       }
1766:     }
1767:   } else SETERRQ(PetscObjectComm((PetscObject)pc), PETSC_ERR_SUP, "Unsupported or unknown composition %d", (int)jac->type);
1768:   PetscFunctionReturn(PETSC_SUCCESS);
1769: }

1771: static PetscErrorCode PCMatApply_FieldSplit(PC pc, Mat X, Mat Y)
1772: {
1773:   PC_FieldSplit    *jac   = (PC_FieldSplit *)pc->data;
1774:   PC_FieldSplitLink ilink = jac->head;
1775:   PetscInt          cnt;

1777:   PetscFunctionBegin;
1778:   /* create working matrices with the correct number of columns */
1779:   PetscCall(PCFieldSplitCreateWorkMats_Private(pc, X));
1780:   if (jac->type == PC_COMPOSITE_ADDITIVE) {
1781:     PetscCall(MatZeroEntries(Y));
1782:     while (ilink) {
1783:       PetscCall(MatDenseScatter_Private(ilink->sctx, X, ilink->X, INSERT_VALUES, SCATTER_FORWARD));
1784:       PetscCall(PetscLogEventBegin(ilink->event, ilink->ksp, ilink->X, ilink->Y, NULL));
1785:       PetscCall(KSPMatSolve(ilink->ksp, ilink->X, ilink->Y));
1786:       PetscCall(PetscLogEventEnd(ilink->event, ilink->ksp, ilink->X, ilink->Y, NULL));
1787:       PetscCall(MatDenseScatter_Private(ilink->sctx, ilink->Y, Y, ADD_VALUES, SCATTER_REVERSE));
1788:       ilink = ilink->next;
1789:     }
1790:   } else if (jac->type == PC_COMPOSITE_MULTIPLICATIVE && jac->nsplits == 2) {
1791:     PetscCall(MatZeroEntries(Y));
1792:     PetscCall(MatDenseScatter_Private(ilink->sctx, X, ilink->X, INSERT_VALUES, SCATTER_FORWARD));
1793:     PetscCall(PetscLogEventBegin(ilink->event, ilink->ksp, ilink->X, ilink->Y, NULL));
1794:     PetscCall(KSPMatSolve(ilink->ksp, ilink->X, ilink->Y));
1795:     PetscCall(PetscLogEventEnd(ilink->event, ilink->ksp, ilink->X, ilink->Y, NULL));
1796:     PetscCall(MatDenseScatter_Private(ilink->sctx, ilink->Y, Y, ADD_VALUES, SCATTER_REVERSE));

1798:     /* compute the residual only onto second block variables using first block variables */
1799:     PetscCall(MatMatMult(jac->Afield[1], ilink->Y, MAT_REUSE_MATRIX, PETSC_DETERMINE, &ilink->next->X));
1800:     ilink = ilink->next;
1801:     PetscCall(MatScale(ilink->X, -1.0));
1802:     PetscCall(MatDenseScatter_Private(ilink->sctx, X, ilink->X, ADD_VALUES, SCATTER_FORWARD));

1804:     /* solve on second block variables */
1805:     PetscCall(PetscLogEventBegin(ilink->event, ilink->ksp, ilink->X, ilink->Y, NULL));
1806:     PetscCall(KSPMatSolve(ilink->ksp, ilink->X, ilink->Y));
1807:     PetscCall(PetscLogEventEnd(ilink->event, ilink->ksp, ilink->X, ilink->Y, NULL));
1808:     PetscCall(MatDenseScatter_Private(ilink->sctx, ilink->Y, Y, ADD_VALUES, SCATTER_REVERSE));
1809:   } else if (jac->type == PC_COMPOSITE_MULTIPLICATIVE || jac->type == PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE) {
1810:     /* general multiplicative with any number of splits */
1811:     PetscCall(MatZeroEntries(Y));
1812:     /* first split */
1813:     PetscCall(MatDenseScatter_Private(ilink->sctx, X, ilink->X, INSERT_VALUES, SCATTER_FORWARD));
1814:     PetscCall(PetscLogEventBegin(ilink->event, ilink->ksp, ilink->X, ilink->Y, NULL));
1815:     PetscCall(KSPMatSolve(ilink->ksp, ilink->X, ilink->Y));
1816:     PetscCall(PetscLogEventEnd(ilink->event, ilink->ksp, ilink->X, ilink->Y, NULL));
1817:     PetscCall(MatDenseScatter_Private(ilink->sctx, ilink->Y, Y, ADD_VALUES, SCATTER_REVERSE));
1818:     cnt = 1;
1819:     /* forward sweep */
1820:     while (ilink->next) {
1821:       ilink = ilink->next;
1822:       /* compute the residual only over the part of the vector needed */
1823:       PetscCall(MatMatMult(jac->Afield[cnt++], Y, MAT_REUSE_MATRIX, PETSC_DETERMINE, &ilink->X));
1824:       PetscCall(MatScale(ilink->X, -1.0));
1825:       PetscCall(MatDenseScatter_Private(ilink->sctx, X, ilink->X, ADD_VALUES, SCATTER_FORWARD));
1826:       PetscCall(PetscLogEventBegin(ilink->event, ilink->ksp, ilink->X, ilink->Y, NULL));
1827:       PetscCall(KSPMatSolve(ilink->ksp, ilink->X, ilink->Y));
1828:       PetscCall(PetscLogEventEnd(ilink->event, ilink->ksp, ilink->X, ilink->Y, NULL));
1829:       PetscCall(MatDenseScatter_Private(ilink->sctx, ilink->Y, Y, ADD_VALUES, SCATTER_REVERSE));
1830:     }
1831:     /* backward sweep for symmetric multiplicative */
1832:     if (jac->type == PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE) {
1833:       cnt -= 2;
1834:       while (ilink->previous) {
1835:         ilink = ilink->previous;
1836:         /* compute the residual only over the part of the vector needed */
1837:         PetscCall(MatMatMult(jac->Afield[cnt--], Y, MAT_REUSE_MATRIX, PETSC_DETERMINE, &ilink->X));
1838:         PetscCall(MatScale(ilink->X, -1.0));
1839:         PetscCall(MatDenseScatter_Private(ilink->sctx, X, ilink->X, ADD_VALUES, SCATTER_FORWARD));
1840:         PetscCall(PetscLogEventBegin(ilink->event, ilink->ksp, ilink->X, ilink->Y, NULL));
1841:         PetscCall(KSPMatSolve(ilink->ksp, ilink->X, ilink->Y));
1842:         PetscCall(PetscLogEventEnd(ilink->event, ilink->ksp, ilink->X, ilink->Y, NULL));
1843:         PetscCall(MatDenseScatter_Private(ilink->sctx, ilink->Y, Y, ADD_VALUES, SCATTER_REVERSE));
1844:       }
1845:     }
1846:   } else SETERRQ(PetscObjectComm((PetscObject)pc), PETSC_ERR_SUP, "PCMatApply() not implemented for this fieldsplit type");
1847:   PetscFunctionReturn(PETSC_SUCCESS);
1848: }

1850: static PetscErrorCode PCApply_FieldSplit_GKB(PC pc, Vec x, Vec y)
1851: {
1852:   PC_FieldSplit    *jac    = (PC_FieldSplit *)pc->data;
1853:   PC_FieldSplitLink ilinkA = jac->head, ilinkD = ilinkA->next;
1854:   KSP               ksp = ilinkA->ksp;
1855:   Vec               u, v, Hu, d, work1, work2;
1856:   PetscScalar       alpha, z, nrmz2, *vecz;
1857:   PetscReal         lowbnd, nu, beta;
1858:   PetscInt          j, iterGKB;

1860:   PetscFunctionBegin;
1861:   PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1862:   PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1863:   PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1864:   PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));

1866:   u     = jac->u;
1867:   v     = jac->v;
1868:   Hu    = jac->Hu;
1869:   d     = jac->d;
1870:   work1 = jac->w1;
1871:   work2 = jac->w2;
1872:   vecz  = jac->vecz;

1874:   /* Change RHS to comply with matrix regularization H = A + nu*B*B' */
1875:   /* Add q = q + nu*B*b */
1876:   if (jac->gkbnu) {
1877:     nu = jac->gkbnu;
1878:     PetscCall(VecScale(ilinkD->x, jac->gkbnu));
1879:     PetscCall(MatMultAdd(jac->B, ilinkD->x, ilinkA->x, ilinkA->x)); /* q = q + nu*B*b */
1880:   } else {
1881:     /* Situation when no augmented Lagrangian is used. Then we set inner  */
1882:     /* matrix N = I in [Ar13], and thus nu = 1.                           */
1883:     nu = 1;
1884:   }

1886:   /* Transform rhs from [q,tilde{b}] to [0,b] */
1887:   PetscCall(PetscLogEventBegin(ilinkA->event, ksp, ilinkA->x, ilinkA->y, NULL));
1888:   PetscCall(KSPSolve(ksp, ilinkA->x, ilinkA->y));
1889:   PetscCall(KSPCheckSolve(ksp, pc, ilinkA->y));
1890:   PetscCall(PetscLogEventEnd(ilinkA->event, ksp, ilinkA->x, ilinkA->y, NULL));
1891:   PetscCall(MatMultHermitianTranspose(jac->B, ilinkA->y, work1));
1892:   PetscCall(VecAXPBY(work1, 1.0 / nu, -1.0, ilinkD->x)); /* c = b - B'*x        */

1894:   /* First step of algorithm */
1895:   PetscCall(VecNorm(work1, NORM_2, &beta)); /* beta = sqrt(nu*c'*c)*/
1896:   KSPCheckDot(ksp, beta);
1897:   beta = PetscSqrtReal(nu) * beta;
1898:   PetscCall(VecAXPBY(v, nu / beta, 0.0, work1)); /* v = nu/beta *c      */
1899:   PetscCall(MatMult(jac->B, v, work2));          /* u = H^{-1}*B*v      */
1900:   PetscCall(PetscLogEventBegin(ilinkA->event, ksp, work2, u, NULL));
1901:   PetscCall(KSPSolve(ksp, work2, u));
1902:   PetscCall(KSPCheckSolve(ksp, pc, u));
1903:   PetscCall(PetscLogEventEnd(ilinkA->event, ksp, work2, u, NULL));
1904:   PetscCall(MatMult(jac->H, u, Hu)); /* alpha = u'*H*u      */
1905:   PetscCall(VecDot(Hu, u, &alpha));
1906:   KSPCheckDot(ksp, alpha);
1907:   PetscCheck(PetscRealPart(alpha) > 0.0, PETSC_COMM_SELF, PETSC_ERR_NOT_CONVERGED, "GKB preconditioner diverged, H is not positive definite");
1908:   alpha = PetscSqrtReal(PetscAbsScalar(alpha));
1909:   PetscCall(VecScale(u, 1.0 / alpha));
1910:   PetscCall(VecAXPBY(d, 1.0 / alpha, 0.0, v)); /* v = nu/beta *c      */

1912:   z       = beta / alpha;
1913:   vecz[1] = z;

1915:   /* Computation of first iterate x(1) and p(1) */
1916:   PetscCall(VecAXPY(ilinkA->y, z, u));
1917:   PetscCall(VecCopy(d, ilinkD->y));
1918:   PetscCall(VecScale(ilinkD->y, -z));

1920:   iterGKB = 1;
1921:   lowbnd  = 2 * jac->gkbtol;
1922:   if (jac->gkbmonitor) PetscCall(PetscViewerASCIIPrintf(jac->gkbviewer, "%3" PetscInt_FMT " GKB Lower bound estimate %14.12e\n", iterGKB, (double)lowbnd));

1924:   while (iterGKB < jac->gkbmaxit && lowbnd > jac->gkbtol) {
1925:     iterGKB += 1;
1926:     PetscCall(MatMultHermitianTranspose(jac->B, u, work1)); /* v <- nu*(B'*u-alpha/nu*v) */
1927:     PetscCall(VecAXPBY(v, nu, -alpha, work1));
1928:     PetscCall(VecNorm(v, NORM_2, &beta)); /* beta = sqrt(nu)*v'*v      */
1929:     beta = beta / PetscSqrtReal(nu);
1930:     PetscCall(VecScale(v, 1.0 / beta));
1931:     PetscCall(MatMult(jac->B, v, work2)); /* u <- H^{-1}*(B*v-beta*H*u) */
1932:     PetscCall(MatMult(jac->H, u, Hu));
1933:     PetscCall(VecAXPY(work2, -beta, Hu));
1934:     PetscCall(PetscLogEventBegin(ilinkA->event, ksp, work2, u, NULL));
1935:     PetscCall(KSPSolve(ksp, work2, u));
1936:     PetscCall(KSPCheckSolve(ksp, pc, u));
1937:     PetscCall(PetscLogEventEnd(ilinkA->event, ksp, work2, u, NULL));
1938:     PetscCall(MatMult(jac->H, u, Hu)); /* alpha = u'*H*u            */
1939:     PetscCall(VecDot(Hu, u, &alpha));
1940:     KSPCheckDot(ksp, alpha);
1941:     PetscCheck(PetscRealPart(alpha) > 0.0, PETSC_COMM_SELF, PETSC_ERR_NOT_CONVERGED, "GKB preconditioner diverged, H is not positive definite");
1942:     alpha = PetscSqrtReal(PetscAbsScalar(alpha));
1943:     PetscCall(VecScale(u, 1.0 / alpha));

1945:     z       = -beta / alpha * z; /* z <- beta/alpha*z     */
1946:     vecz[0] = z;

1948:     /* Computation of new iterate x(i+1) and p(i+1) */
1949:     PetscCall(VecAXPBY(d, 1.0 / alpha, -beta / alpha, v)); /* d = (v-beta*d)/alpha */
1950:     PetscCall(VecAXPY(ilinkA->y, z, u));                   /* r = r + z*u          */
1951:     PetscCall(VecAXPY(ilinkD->y, -z, d));                  /* p = p - z*d          */
1952:     PetscCall(MatMult(jac->H, ilinkA->y, Hu));             /* ||u||_H = u'*H*u     */
1953:     PetscCall(VecDot(Hu, ilinkA->y, &nrmz2));

1955:     /* Compute Lower Bound estimate */
1956:     if (iterGKB > jac->gkbdelay) {
1957:       lowbnd = 0.0;
1958:       for (j = 0; j < jac->gkbdelay; j++) lowbnd += PetscAbsScalar(vecz[j] * vecz[j]);
1959:       lowbnd = PetscSqrtReal(lowbnd / PetscAbsScalar(nrmz2));
1960:     }

1962:     for (j = 0; j < jac->gkbdelay - 1; j++) vecz[jac->gkbdelay - j - 1] = vecz[jac->gkbdelay - j - 2];
1963:     if (jac->gkbmonitor) PetscCall(PetscViewerASCIIPrintf(jac->gkbviewer, "%3" PetscInt_FMT " GKB Lower bound estimate %14.12e\n", iterGKB, (double)lowbnd));
1964:   }

1966:   PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1967:   PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1968:   PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1969:   PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1970:   PetscFunctionReturn(PETSC_SUCCESS);
1971: }

1973: #define FieldSplitSplitSolveAddTranspose(ilink, xx, yy) \
1974:   ((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) || \
1975:                     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) || \
1976:                     VecScatterEnd(ilink->sctx, ilink->x, yy, ADD_VALUES, SCATTER_REVERSE)))

1978: static PetscErrorCode PCApplyTranspose_FieldSplit(PC pc, Vec x, Vec y)
1979: {
1980:   PC_FieldSplit    *jac   = (PC_FieldSplit *)pc->data;
1981:   PC_FieldSplitLink ilink = jac->head;
1982:   PetscInt          bs;

1984:   PetscFunctionBegin;
1985:   if (jac->type == PC_COMPOSITE_ADDITIVE) {
1986:     PetscBool matnest;

1988:     PetscCall(PetscObjectTypeCompare((PetscObject)pc->pmat, MATNEST, &matnest));
1989:     if (jac->defaultsplit && !matnest) {
1990:       PetscCall(VecGetBlockSize(x, &bs));
1991:       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);
1992:       PetscCall(VecGetBlockSize(y, &bs));
1993:       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);
1994:       PetscCall(VecStrideGatherAll(x, jac->x, INSERT_VALUES));
1995:       while (ilink) {
1996:         PetscCall(PetscLogEventBegin(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1997:         PetscCall(KSPSolveTranspose(ilink->ksp, ilink->x, ilink->y));
1998:         PetscCall(KSPCheckSolve(ilink->ksp, pc, ilink->y));
1999:         PetscCall(PetscLogEventEnd(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
2000:         ilink = ilink->next;
2001:       }
2002:       PetscCall(VecStrideScatterAll(jac->y, y, INSERT_VALUES));
2003:     } else {
2004:       PetscCall(VecSet(y, 0.0));
2005:       while (ilink) {
2006:         PetscCall(FieldSplitSplitSolveAddTranspose(ilink, x, y));
2007:         ilink = ilink->next;
2008:       }
2009:     }
2010:   } else {
2011:     if (!jac->w1) {
2012:       PetscCall(VecDuplicate(x, &jac->w1));
2013:       PetscCall(VecDuplicate(x, &jac->w2));
2014:     }
2015:     PetscCall(VecSet(y, 0.0));
2016:     if (jac->type == PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE) {
2017:       PetscCall(FieldSplitSplitSolveAddTranspose(ilink, x, y));
2018:       while (ilink->next) {
2019:         ilink = ilink->next;
2020:         PetscCall(MatMultTranspose(pc->mat, y, jac->w1));
2021:         PetscCall(VecWAXPY(jac->w2, -1.0, jac->w1, x));
2022:         PetscCall(FieldSplitSplitSolveAddTranspose(ilink, jac->w2, y));
2023:       }
2024:       while (ilink->previous) {
2025:         ilink = ilink->previous;
2026:         PetscCall(MatMultTranspose(pc->mat, y, jac->w1));
2027:         PetscCall(VecWAXPY(jac->w2, -1.0, jac->w1, x));
2028:         PetscCall(FieldSplitSplitSolveAddTranspose(ilink, jac->w2, y));
2029:       }
2030:     } else {
2031:       while (ilink->next) { /* get to last entry in linked list */
2032:         ilink = ilink->next;
2033:       }
2034:       PetscCall(FieldSplitSplitSolveAddTranspose(ilink, x, y));
2035:       while (ilink->previous) {
2036:         ilink = ilink->previous;
2037:         PetscCall(MatMultTranspose(pc->mat, y, jac->w1));
2038:         PetscCall(VecWAXPY(jac->w2, -1.0, jac->w1, x));
2039:         PetscCall(FieldSplitSplitSolveAddTranspose(ilink, jac->w2, y));
2040:       }
2041:     }
2042:   }
2043:   PetscFunctionReturn(PETSC_SUCCESS);
2044: }

2046: static PetscErrorCode PCReset_FieldSplit(PC pc)
2047: {
2048:   PC_FieldSplit    *jac   = (PC_FieldSplit *)pc->data;
2049:   PC_FieldSplitLink ilink = jac->head, next;

2051:   PetscFunctionBegin;
2052:   while (ilink) {
2053:     PetscCall(KSPDestroy(&ilink->ksp));
2054:     PetscCall(VecDestroy(&ilink->x));
2055:     PetscCall(VecDestroy(&ilink->y));
2056:     PetscCall(VecDestroy(&ilink->z));
2057:     PetscCall(MatDestroy(&ilink->X));
2058:     PetscCall(MatDestroy(&ilink->Y));
2059:     PetscCall(MatDestroy(&ilink->Z));
2060:     PetscCall(VecScatterDestroy(&ilink->sctx));
2061:     PetscCall(ISDestroy(&ilink->is));
2062:     PetscCall(ISDestroy(&ilink->is_col));
2063:     PetscCall(PetscFree(ilink->splitname));
2064:     PetscCall(PetscFree(ilink->fields));
2065:     PetscCall(PetscFree(ilink->fields_col));
2066:     next = ilink->next;
2067:     PetscCall(PetscFree(ilink));
2068:     ilink = next;
2069:   }
2070:   jac->head = NULL;
2071:   PetscCall(PetscFree2(jac->x, jac->y));
2072:   if (jac->mat && jac->mat != jac->pmat) {
2073:     PetscCall(MatDestroyMatrices(jac->nsplits, &jac->mat));
2074:   } else if (jac->mat) {
2075:     jac->mat = NULL;
2076:   }
2077:   if (jac->pmat) PetscCall(MatDestroyMatrices(jac->nsplits, &jac->pmat));
2078:   if (jac->Afield) PetscCall(MatDestroyMatrices(jac->nsplits, &jac->Afield));
2079:   jac->nsplits = 0;
2080:   PetscCall(VecDestroy(&jac->w1));
2081:   PetscCall(VecDestroy(&jac->w2));
2082:   if (jac->schur) PetscCall(PetscObjectCompose((PetscObject)jac->schur, "AinvB", NULL));
2083:   PetscCall(MatDestroy(&jac->schur));
2084:   PetscCall(MatDestroy(&jac->schurp));
2085:   PetscCall(MatDestroy(&jac->schur_user));
2086:   PetscCall(KSPDestroy(&jac->kspschur));
2087:   PetscCall(KSPDestroy(&jac->kspupper));
2088:   PetscCall(MatDestroy(&jac->B));
2089:   PetscCall(MatDestroy(&jac->C));
2090:   PetscCall(MatDestroy(&jac->H));
2091:   PetscCall(VecDestroy(&jac->u));
2092:   PetscCall(VecDestroy(&jac->v));
2093:   PetscCall(VecDestroy(&jac->Hu));
2094:   PetscCall(VecDestroy(&jac->d));
2095:   PetscCall(PetscFree(jac->vecz));
2096:   PetscCall(PetscViewerDestroy(&jac->gkbviewer));
2097:   jac->isrestrict = PETSC_FALSE;
2098:   PetscFunctionReturn(PETSC_SUCCESS);
2099: }

2101: static PetscErrorCode PCDestroy_FieldSplit(PC pc)
2102: {
2103:   PetscFunctionBegin;
2104:   PetscCall(PCReset_FieldSplit(pc));
2105:   PetscCall(PetscFree(pc->data));
2106:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCSetCoordinates_C", NULL));
2107:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetFields_C", NULL));
2108:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetIS_C", NULL));
2109:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetType_C", NULL));
2110:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetBlockSize_C", NULL));
2111:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitRestrictIS_C", NULL));
2112:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSchurGetSubKSP_C", NULL));
2113:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSubKSP_C", NULL));
2114:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBTol_C", NULL));
2115:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBMaxit_C", NULL));
2116:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBNu_C", NULL));
2117:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBDelay_C", NULL));
2118:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurPre_C", NULL));
2119:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSchurPre_C", NULL));
2120:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurFactType_C", NULL));
2121:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurScale_C", NULL));
2122:   PetscFunctionReturn(PETSC_SUCCESS);
2123: }

2125: static PetscErrorCode PCSetFromOptions_FieldSplit(PC pc, PetscOptionItems PetscOptionsObject)
2126: {
2127:   PetscInt        bs;
2128:   PetscBool       flg;
2129:   PC_FieldSplit  *jac = (PC_FieldSplit *)pc->data;
2130:   PCCompositeType ctype;

2132:   PetscFunctionBegin;
2133:   PetscOptionsHeadBegin(PetscOptionsObject, "FieldSplit options");
2134:   PetscCall(PetscOptionsBool("-pc_fieldsplit_dm_splits", "Whether to use DMCreateFieldDecomposition() for splits", "PCFieldSplitSetDMSplits", jac->dm_splits, &jac->dm_splits, NULL));
2135:   PetscCall(PetscOptionsInt("-pc_fieldsplit_block_size", "Blocksize that defines number of fields", "PCFieldSplitSetBlockSize", jac->bs, &bs, &flg));
2136:   if (flg) PetscCall(PCFieldSplitSetBlockSize(pc, bs));
2137:   jac->diag_use_amat = pc->useAmat;
2138:   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));
2139:   jac->offdiag_use_amat = pc->useAmat;
2140:   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));
2141:   PetscCall(PetscOptionsBool("-pc_fieldsplit_detect_saddle_point", "Form 2-way split by detecting zero diagonal entries", "PCFieldSplitSetDetectSaddlePoint", jac->detect, &jac->detect, NULL));
2142:   PetscCall(PCFieldSplitSetDetectSaddlePoint(pc, jac->detect)); /* Sets split type and Schur PC type */
2143:   PetscCall(PetscOptionsEnum("-pc_fieldsplit_type", "Type of composition", "PCFieldSplitSetType", PCCompositeTypes, (PetscEnum)jac->type, (PetscEnum *)&ctype, &flg));
2144:   if (flg) PetscCall(PCFieldSplitSetType(pc, ctype));
2145:   /* Only setup fields once */
2146:   if (jac->bs > 0 && jac->nsplits == 0) {
2147:     /* only allow user to set fields from command line.
2148:        otherwise user can set them in PCFieldSplitSetDefaults() */
2149:     PetscCall(PCFieldSplitSetRuntimeSplits_Private(pc));
2150:     if (jac->splitdefined) PetscCall(PetscInfo(pc, "Splits defined using the options database\n"));
2151:   }
2152:   if (jac->type == PC_COMPOSITE_SCHUR) {
2153:     PetscCall(PetscOptionsGetEnum(((PetscObject)pc)->options, ((PetscObject)pc)->prefix, "-pc_fieldsplit_schur_factorization_type", PCFieldSplitSchurFactTypes, (PetscEnum *)&jac->schurfactorization, &flg));
2154:     if (flg) PetscCall(PetscInfo(pc, "Deprecated use of -pc_fieldsplit_schur_factorization_type\n"));
2155:     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));
2156:     PetscCall(PetscOptionsEnum("-pc_fieldsplit_schur_precondition", "How to build preconditioner for Schur complement", "PCFieldSplitSetSchurPre", PCFieldSplitSchurPreTypes, (PetscEnum)jac->schurpre, (PetscEnum *)&jac->schurpre, NULL));
2157:     PetscCall(PetscOptionsScalar("-pc_fieldsplit_schur_scale", "Scale Schur complement", "PCFieldSplitSetSchurScale", jac->schurscale, &jac->schurscale, NULL));
2158:   } else if (jac->type == PC_COMPOSITE_GKB) {
2159:     PetscCall(PetscOptionsReal("-pc_fieldsplit_gkb_tol", "The tolerance for the lower bound stopping criterion", "PCFieldSplitSetGKBTol", jac->gkbtol, &jac->gkbtol, NULL));
2160:     PetscCall(PetscOptionsInt("-pc_fieldsplit_gkb_delay", "The delay value for lower bound criterion", "PCFieldSplitSetGKBDelay", jac->gkbdelay, &jac->gkbdelay, NULL));
2161:     PetscCall(PetscOptionsBoundedReal("-pc_fieldsplit_gkb_nu", "Parameter in augmented Lagrangian approach", "PCFieldSplitSetGKBNu", jac->gkbnu, &jac->gkbnu, NULL, 0.0));
2162:     PetscCall(PetscOptionsInt("-pc_fieldsplit_gkb_maxit", "Maximum allowed number of iterations", "PCFieldSplitSetGKBMaxit", jac->gkbmaxit, &jac->gkbmaxit, NULL));
2163:     PetscCall(PetscOptionsBool("-pc_fieldsplit_gkb_monitor", "Prints number of GKB iterations and error", "PCFieldSplitGKB", jac->gkbmonitor, &jac->gkbmonitor, NULL));
2164:   }
2165:   /*
2166:     In the initial call to this routine the sub-solver data structures do not exist so we cannot call KSPSetFromOptions() on them yet.
2167:     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
2168:     is called on the outer solver in case changes were made in the options database

2170:     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()
2171:     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.
2172:     Without this extra check test p2p1fetidp_olof_full and others fail with incorrect matrix types.

2174:     There could be a negative side effect of calling the KSPSetFromOptions() below.

2176:     If one captured the PetscObjectState of the options database one could skip these calls if the database has not changed from the previous call
2177:   */
2178:   if (jac->issetup) {
2179:     PC_FieldSplitLink ilink = jac->head;
2180:     if (jac->type == PC_COMPOSITE_SCHUR) {
2181:       if (jac->kspupper && jac->kspupper->totalits > 0) PetscCall(KSPSetFromOptions(jac->kspupper));
2182:       if (jac->kspschur && jac->kspschur->totalits > 0) PetscCall(KSPSetFromOptions(jac->kspschur));
2183:     }
2184:     while (ilink) {
2185:       if (ilink->ksp->totalits > 0) PetscCall(KSPSetFromOptions(ilink->ksp));
2186:       ilink = ilink->next;
2187:     }
2188:   }
2189:   PetscOptionsHeadEnd();
2190:   PetscFunctionReturn(PETSC_SUCCESS);
2191: }

2193: static PetscErrorCode PCFieldSplitSetFields_FieldSplit(PC pc, const char splitname[], PetscInt n, const PetscInt *fields, const PetscInt *fields_col)
2194: {
2195:   PC_FieldSplit    *jac = (PC_FieldSplit *)pc->data;
2196:   PC_FieldSplitLink ilink, next = jac->head;
2197:   char              prefix[128];
2198:   PetscInt          i;
2199:   PetscLogEvent     nse;

2201:   PetscFunctionBegin;
2202:   if (jac->splitdefined) {
2203:     PetscCall(PetscInfo(pc, "Ignoring new split \"%s\" because the splits have already been defined\n", splitname));
2204:     PetscFunctionReturn(PETSC_SUCCESS);
2205:   }
2206:   for (i = 0; i < n; i++) PetscCheck(fields[i] >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Negative field %" PetscInt_FMT " requested", fields[i]);
2207:   PetscCall(PetscNew(&ilink));
2208:   if (splitname) {
2209:     PetscCall(PetscStrallocpy(splitname, &ilink->splitname));
2210:   } else {
2211:     PetscCall(PetscMalloc1(3, &ilink->splitname));
2212:     PetscCall(PetscSNPrintf(ilink->splitname, 2, "%" PetscInt_FMT, jac->nsplits));
2213:   }
2214:   PetscCall(PetscMPIIntCast(jac->nsplits, &nse));
2215:   ilink->event = jac->nsplits < 5 ? KSP_Solve_FS_0 + nse : KSP_Solve_FS_0 + 4; /* Splits greater than 4 logged in 4th split */
2216:   PetscCall(PetscMalloc1(n, &ilink->fields));
2217:   PetscCall(PetscArraycpy(ilink->fields, fields, n));
2218:   PetscCall(PetscMalloc1(n, &ilink->fields_col));
2219:   PetscCall(PetscArraycpy(ilink->fields_col, fields_col, n));

2221:   ilink->nfields = n;
2222:   ilink->next    = NULL;
2223:   PetscCall(KSPCreate(PetscObjectComm((PetscObject)pc), &ilink->ksp));
2224:   PetscCall(KSPSetNestLevel(ilink->ksp, pc->kspnestlevel));
2225:   PetscCall(KSPSetErrorIfNotConverged(ilink->ksp, pc->erroriffailure));
2226:   PetscCall(PetscObjectIncrementTabLevel((PetscObject)ilink->ksp, (PetscObject)pc, 1));
2227:   PetscCall(KSPSetType(ilink->ksp, KSPPREONLY));

2229:   PetscCall(PetscSNPrintf(prefix, sizeof(prefix), "%sfieldsplit_%s_", ((PetscObject)pc)->prefix ? ((PetscObject)pc)->prefix : "", ilink->splitname));
2230:   PetscCall(KSPSetOptionsPrefix(ilink->ksp, prefix));

2232:   if (!next) {
2233:     jac->head       = ilink;
2234:     ilink->previous = NULL;
2235:   } else {
2236:     while (next->next) next = next->next;
2237:     next->next      = ilink;
2238:     ilink->previous = next;
2239:   }
2240:   jac->nsplits++;
2241:   PetscFunctionReturn(PETSC_SUCCESS);
2242: }

2244: static PetscErrorCode PCFieldSplitSchurGetSubKSP_FieldSplit(PC pc, PetscInt *n, KSP **subksp)
2245: {
2246:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

2248:   PetscFunctionBegin;
2249:   *subksp = NULL;
2250:   if (n) *n = 0;
2251:   if (jac->type == PC_COMPOSITE_SCHUR) {
2252:     PetscInt nn;

2254:     PetscCheck(jac->schur, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONGSTATE, "Must call KSPSetUp() or PCSetUp() before calling PCFieldSplitSchurGetSubKSP()");
2255:     PetscCheck(jac->nsplits == 2, PetscObjectComm((PetscObject)pc), PETSC_ERR_PLIB, "Unexpected number of splits %" PetscInt_FMT " != 2", jac->nsplits);
2256:     nn = jac->nsplits + (jac->kspupper != jac->head->ksp ? 1 : 0);
2257:     PetscCall(PetscMalloc1(nn, subksp));
2258:     (*subksp)[0] = jac->head->ksp;
2259:     (*subksp)[1] = jac->kspschur;
2260:     if (jac->kspupper != jac->head->ksp) (*subksp)[2] = jac->kspupper;
2261:     if (n) *n = nn;
2262:   }
2263:   PetscFunctionReturn(PETSC_SUCCESS);
2264: }

2266: static PetscErrorCode PCFieldSplitGetSubKSP_FieldSplit_Schur(PC pc, PetscInt *n, KSP **subksp)
2267: {
2268:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

2270:   PetscFunctionBegin;
2271:   PetscCheck(jac->schur, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONGSTATE, "Must call KSPSetUp() or PCSetUp() before calling PCFieldSplitGetSubKSP()");
2272:   PetscCall(PetscMalloc1(jac->nsplits, subksp));
2273:   PetscCall(MatSchurComplementGetKSP(jac->schur, *subksp));

2275:   (*subksp)[1] = jac->kspschur;
2276:   if (n) *n = jac->nsplits;
2277:   PetscFunctionReturn(PETSC_SUCCESS);
2278: }

2280: static PetscErrorCode PCFieldSplitGetSubKSP_FieldSplit(PC pc, PetscInt *n, KSP **subksp)
2281: {
2282:   PC_FieldSplit    *jac   = (PC_FieldSplit *)pc->data;
2283:   PetscInt          cnt   = 0;
2284:   PC_FieldSplitLink ilink = jac->head;

2286:   PetscFunctionBegin;
2287:   PetscCall(PetscMalloc1(jac->nsplits, subksp));
2288:   while (ilink) {
2289:     (*subksp)[cnt++] = ilink->ksp;
2290:     ilink            = ilink->next;
2291:   }
2292:   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);
2293:   if (n) *n = jac->nsplits;
2294:   PetscFunctionReturn(PETSC_SUCCESS);
2295: }

2297: /*@
2298:   PCFieldSplitRestrictIS - Restricts the fieldsplit `IS`s to be within a given `IS`.

2300:   Input Parameters:
2301: + pc  - the preconditioner context
2302: - isy - the index set that defines the indices to which the fieldsplit is to be restricted

2304:   Level: advanced

2306:   Developer Notes:
2307:   It seems the resulting `IS`s will not cover the entire space, so
2308:   how can they define a convergent preconditioner? Needs explaining.

2310: .seealso: [](sec_block_matrices), `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSetIS()`
2311: @*/
2312: PetscErrorCode PCFieldSplitRestrictIS(PC pc, IS isy)
2313: {
2314:   PetscFunctionBegin;
2317:   PetscTryMethod(pc, "PCFieldSplitRestrictIS_C", (PC, IS), (pc, isy));
2318:   PetscFunctionReturn(PETSC_SUCCESS);
2319: }

2321: static PetscErrorCode PCFieldSplitRestrictIS_FieldSplit(PC pc, IS isy)
2322: {
2323:   PC_FieldSplit    *jac   = (PC_FieldSplit *)pc->data;
2324:   PC_FieldSplitLink ilink = jac->head, next;
2325:   PetscInt          localsize, size, sizez, i;
2326:   const PetscInt   *ind, *indz;
2327:   PetscInt         *indc, *indcz;
2328:   PetscBool         flg;

2330:   PetscFunctionBegin;
2331:   PetscCall(ISGetLocalSize(isy, &localsize));
2332:   PetscCallMPI(MPI_Scan(&localsize, &size, 1, MPIU_INT, MPI_SUM, PetscObjectComm((PetscObject)isy)));
2333:   size -= localsize;
2334:   while (ilink) {
2335:     IS isrl, isr;
2336:     PC subpc;
2337:     PetscCall(ISEmbed(ilink->is, isy, PETSC_TRUE, &isrl));
2338:     PetscCall(ISGetLocalSize(isrl, &localsize));
2339:     PetscCall(PetscMalloc1(localsize, &indc));
2340:     PetscCall(ISGetIndices(isrl, &ind));
2341:     PetscCall(PetscArraycpy(indc, ind, localsize));
2342:     PetscCall(ISRestoreIndices(isrl, &ind));
2343:     PetscCall(ISDestroy(&isrl));
2344:     for (i = 0; i < localsize; i++) *(indc + i) += size;
2345:     PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)isy), localsize, indc, PETSC_OWN_POINTER, &isr));
2346:     PetscCall(PetscObjectReference((PetscObject)isr));
2347:     PetscCall(ISDestroy(&ilink->is));
2348:     ilink->is = isr;
2349:     PetscCall(PetscObjectReference((PetscObject)isr));
2350:     PetscCall(ISDestroy(&ilink->is_col));
2351:     ilink->is_col = isr;
2352:     PetscCall(ISDestroy(&isr));
2353:     PetscCall(KSPGetPC(ilink->ksp, &subpc));
2354:     PetscCall(PetscObjectTypeCompare((PetscObject)subpc, PCFIELDSPLIT, &flg));
2355:     if (flg) {
2356:       IS       iszl, isz;
2357:       MPI_Comm comm;
2358:       PetscCall(ISGetLocalSize(ilink->is, &localsize));
2359:       comm = PetscObjectComm((PetscObject)ilink->is);
2360:       PetscCall(ISEmbed(isy, ilink->is, PETSC_TRUE, &iszl));
2361:       PetscCallMPI(MPI_Scan(&localsize, &sizez, 1, MPIU_INT, MPI_SUM, comm));
2362:       sizez -= localsize;
2363:       PetscCall(ISGetLocalSize(iszl, &localsize));
2364:       PetscCall(PetscMalloc1(localsize, &indcz));
2365:       PetscCall(ISGetIndices(iszl, &indz));
2366:       PetscCall(PetscArraycpy(indcz, indz, localsize));
2367:       PetscCall(ISRestoreIndices(iszl, &indz));
2368:       PetscCall(ISDestroy(&iszl));
2369:       for (i = 0; i < localsize; i++) *(indcz + i) += sizez;
2370:       PetscCall(ISCreateGeneral(comm, localsize, indcz, PETSC_OWN_POINTER, &isz));
2371:       PetscCall(PCFieldSplitRestrictIS(subpc, isz));
2372:       PetscCall(ISDestroy(&isz));
2373:     }
2374:     next  = ilink->next;
2375:     ilink = next;
2376:   }
2377:   jac->isrestrict = PETSC_TRUE;
2378:   PetscFunctionReturn(PETSC_SUCCESS);
2379: }

2381: static PetscErrorCode PCFieldSplitSetIS_FieldSplit(PC pc, const char splitname[], IS is)
2382: {
2383:   PC_FieldSplit    *jac = (PC_FieldSplit *)pc->data;
2384:   PC_FieldSplitLink ilink, next = jac->head;
2385:   char              prefix[128];
2386:   PetscLogEvent     nse;

2388:   PetscFunctionBegin;
2389:   if (jac->splitdefined) {
2390:     PetscCall(PetscInfo(pc, "Ignoring new split \"%s\" because the splits have already been defined\n", splitname));
2391:     PetscFunctionReturn(PETSC_SUCCESS);
2392:   }
2393:   PetscCall(PetscNew(&ilink));
2394:   if (splitname) {
2395:     PetscCall(PetscStrallocpy(splitname, &ilink->splitname));
2396:   } else {
2397:     PetscCall(PetscMalloc1(8, &ilink->splitname));
2398:     PetscCall(PetscSNPrintf(ilink->splitname, 7, "%" PetscInt_FMT, jac->nsplits));
2399:   }
2400:   PetscCall(PetscMPIIntCast(jac->nsplits, &nse));
2401:   ilink->event = jac->nsplits < 5 ? KSP_Solve_FS_0 + nse : KSP_Solve_FS_0 + 4; /* Splits greater than 4 logged in 4th split */
2402:   PetscCall(PetscObjectReference((PetscObject)is));
2403:   PetscCall(ISDestroy(&ilink->is));
2404:   ilink->is = is;
2405:   PetscCall(PetscObjectReference((PetscObject)is));
2406:   PetscCall(ISDestroy(&ilink->is_col));
2407:   ilink->is_col = is;
2408:   ilink->next   = NULL;
2409:   PetscCall(KSPCreate(PetscObjectComm((PetscObject)pc), &ilink->ksp));
2410:   PetscCall(KSPSetNestLevel(ilink->ksp, pc->kspnestlevel));
2411:   PetscCall(KSPSetErrorIfNotConverged(ilink->ksp, pc->erroriffailure));
2412:   PetscCall(PetscObjectIncrementTabLevel((PetscObject)ilink->ksp, (PetscObject)pc, 1));
2413:   PetscCall(KSPSetType(ilink->ksp, KSPPREONLY));

2415:   PetscCall(PetscSNPrintf(prefix, sizeof(prefix), "%sfieldsplit_%s_", ((PetscObject)pc)->prefix ? ((PetscObject)pc)->prefix : "", ilink->splitname));
2416:   PetscCall(KSPSetOptionsPrefix(ilink->ksp, prefix));

2418:   if (!next) {
2419:     jac->head       = ilink;
2420:     ilink->previous = NULL;
2421:   } else {
2422:     while (next->next) next = next->next;
2423:     next->next      = ilink;
2424:     ilink->previous = next;
2425:   }
2426:   jac->nsplits++;
2427:   PetscFunctionReturn(PETSC_SUCCESS);
2428: }

2430: /*@
2431:   PCFieldSplitSetFields - Sets the fields that define one particular split in `PCFIELDSPLIT`

2433:   Logically Collective

2435:   Input Parameters:
2436: + pc         - the preconditioner context
2437: . splitname  - name of this split, if `NULL` the number of the split is used
2438: . n          - the number of fields in this split
2439: . fields     - the fields in this split
2440: - fields_col - generally the same as `fields`, if it does not match `fields` then the submatrix that is solved for this set of fields comes from an off-diagonal block
2441:                of the matrix and `fields_col` provides the column indices for that block

2443:   Options Database Key:
2444: . -pc_fieldsplit_%d_fields a,b,... - indicates the fields to be used in the `%d`'th split

2446:   Level: intermediate

2448:   Notes:
2449:   Use `PCFieldSplitSetIS()` to set a  general set of indices as a split.

2451:   If the matrix used to construct the preconditioner is `MATNEST` then field i refers to the `is_row[i]` `IS` passed to `MatCreateNest()`.

2453:   If the matrix used to construct the preconditioner is not `MATNEST` then
2454:   `PCFieldSplitSetFields()` is for defining fields as strided blocks (based on the block size provided to the matrix with `MatSetBlockSize()` or
2455:   to the `PC` with `PCFieldSplitSetBlockSize()`). For example, if the block
2456:   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
2457:   0xx3xx6xx9xx12 ... x1xx4xx7xx ... xx2xx5xx8xx.. 01x34x67x... 0x23x56x8.. x12x45x78x....
2458:   where the numbered entries indicate what is in the split.

2460:   This function is called once per split (it creates a new split each time).  Solve options
2461:   for this split will be available under the prefix `-fieldsplit_SPLITNAME_`.

2463:   `PCFieldSplitSetIS()` does not support having a `fields_col` different from `fields`

2465:   Developer Notes:
2466:   This routine does not actually create the `IS` representing the split, that is delayed
2467:   until `PCSetUp_FieldSplit()`, because information about the vector/matrix layouts may not be
2468:   available when this routine is called.

2470: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSetBlockSize()`, `PCFieldSplitSetIS()`, `PCFieldSplitRestrictIS()`,
2471:           `MatSetBlockSize()`, `MatCreateNest()`
2472: @*/
2473: PetscErrorCode PCFieldSplitSetFields(PC pc, const char splitname[], PetscInt n, const PetscInt fields[], const PetscInt fields_col[])
2474: {
2475:   PetscFunctionBegin;
2477:   PetscAssertPointer(splitname, 2);
2478:   PetscCheck(n >= 1, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_OUTOFRANGE, "Provided number of fields %" PetscInt_FMT " in split \"%s\" not positive", n, splitname);
2479:   PetscAssertPointer(fields, 4);
2480:   PetscTryMethod(pc, "PCFieldSplitSetFields_C", (PC, const char[], PetscInt, const PetscInt *, const PetscInt *), (pc, splitname, n, fields, fields_col));
2481:   PetscFunctionReturn(PETSC_SUCCESS);
2482: }

2484: /*@
2485:   PCFieldSplitSetDiagUseAmat - set flag indicating whether to extract diagonal blocks from Amat (rather than Pmat) to build
2486:   the sub-matrices associated with each split. Where `KSPSetOperators`(ksp,Amat,Pmat) was used to supply the operators.

2488:   Logically Collective

2490:   Input Parameters:
2491: + pc  - the preconditioner object
2492: - flg - boolean flag indicating whether or not to use Amat to extract the diagonal blocks from

2494:   Options Database Key:
2495: . -pc_fieldsplit_diag_use_amat - use the Amat to provide the diagonal blocks

2497:   Level: intermediate

2499: .seealso: [](sec_block_matrices), `PC`, `PCSetOperators()`, `KSPSetOperators()`, `PCFieldSplitGetDiagUseAmat()`, `PCFieldSplitSetOffDiagUseAmat()`, `PCFIELDSPLIT`
2500: @*/
2501: PetscErrorCode PCFieldSplitSetDiagUseAmat(PC pc, PetscBool flg)
2502: {
2503:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
2504:   PetscBool      isfs;

2506:   PetscFunctionBegin;
2508:   PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCFIELDSPLIT, &isfs));
2509:   PetscCheck(isfs, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "PC not of type %s", PCFIELDSPLIT);
2510:   jac->diag_use_amat = flg;
2511:   PetscFunctionReturn(PETSC_SUCCESS);
2512: }

2514: /*@
2515:   PCFieldSplitGetDiagUseAmat - get the flag indicating whether to extract diagonal blocks from Amat (rather than Pmat) to build
2516:   the sub-matrices associated with each split.  Where `KSPSetOperators`(ksp,Amat,Pmat) was used to supply the operators.

2518:   Logically Collective

2520:   Input Parameter:
2521: . pc - the preconditioner object

2523:   Output Parameter:
2524: . flg - boolean flag indicating whether or not to use Amat to extract the diagonal blocks from

2526:   Level: intermediate

2528: .seealso: [](sec_block_matrices), `PC`, `PCSetOperators()`, `KSPSetOperators()`, `PCFieldSplitSetDiagUseAmat()`, `PCFieldSplitGetOffDiagUseAmat()`, `PCFIELDSPLIT`
2529: @*/
2530: PetscErrorCode PCFieldSplitGetDiagUseAmat(PC pc, PetscBool *flg)
2531: {
2532:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
2533:   PetscBool      isfs;

2535:   PetscFunctionBegin;
2537:   PetscAssertPointer(flg, 2);
2538:   PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCFIELDSPLIT, &isfs));
2539:   PetscCheck(isfs, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "PC not of type %s", PCFIELDSPLIT);
2540:   *flg = jac->diag_use_amat;
2541:   PetscFunctionReturn(PETSC_SUCCESS);
2542: }

2544: /*@
2545:   PCFieldSplitSetOffDiagUseAmat - set flag indicating whether to extract off-diagonal blocks from Amat (rather than Pmat) to build
2546:   the sub-matrices associated with each split.  Where `KSPSetOperators`(ksp,Amat,Pmat) was used to supply the operators.

2548:   Logically Collective

2550:   Input Parameters:
2551: + pc  - the preconditioner object
2552: - flg - boolean flag indicating whether or not to use Amat to extract the off-diagonal blocks from

2554:   Options Database Key:
2555: . -pc_fieldsplit_off_diag_use_amat (true|false) - use the Amat to extract the off-diagonal blocks

2557:   Level: intermediate

2559: .seealso: [](sec_block_matrices), `PC`, `PCSetOperators()`, `KSPSetOperators()`, `PCFieldSplitGetOffDiagUseAmat()`, `PCFieldSplitSetDiagUseAmat()`, `PCFIELDSPLIT`
2560: @*/
2561: PetscErrorCode PCFieldSplitSetOffDiagUseAmat(PC pc, PetscBool flg)
2562: {
2563:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
2564:   PetscBool      isfs;

2566:   PetscFunctionBegin;
2568:   PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCFIELDSPLIT, &isfs));
2569:   PetscCheck(isfs, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "PC not of type %s", PCFIELDSPLIT);
2570:   jac->offdiag_use_amat = flg;
2571:   PetscFunctionReturn(PETSC_SUCCESS);
2572: }

2574: /*@
2575:   PCFieldSplitGetOffDiagUseAmat - get the flag indicating whether to extract off-diagonal blocks from Amat (rather than Pmat) to build
2576:   the sub-matrices associated with each split.  Where `KSPSetOperators`(ksp,Amat,Pmat) was used to supply the operators.

2578:   Logically Collective

2580:   Input Parameter:
2581: . pc - the preconditioner object

2583:   Output Parameter:
2584: . flg - boolean flag indicating whether or not to use Amat to extract the off-diagonal blocks from

2586:   Level: intermediate

2588: .seealso: [](sec_block_matrices), `PC`, `PCSetOperators()`, `KSPSetOperators()`, `PCFieldSplitSetOffDiagUseAmat()`, `PCFieldSplitGetDiagUseAmat()`, `PCFIELDSPLIT`
2589: @*/
2590: PetscErrorCode PCFieldSplitGetOffDiagUseAmat(PC pc, PetscBool *flg)
2591: {
2592:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
2593:   PetscBool      isfs;

2595:   PetscFunctionBegin;
2597:   PetscAssertPointer(flg, 2);
2598:   PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCFIELDSPLIT, &isfs));
2599:   PetscCheck(isfs, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "PC not of type %s", PCFIELDSPLIT);
2600:   *flg = jac->offdiag_use_amat;
2601:   PetscFunctionReturn(PETSC_SUCCESS);
2602: }

2604: /*@
2605:   PCFieldSplitSetIS - Sets the exact elements for a split in a `PCFIELDSPLIT`

2607:   Logically Collective

2609:   Input Parameters:
2610: + pc        - the preconditioner context
2611: . splitname - name of this split, if `NULL` the number of the split is used
2612: - is        - the index set that defines the elements in this split

2614:   Level: intermediate

2616:   Notes:
2617:   Use `PCFieldSplitSetFields()`, for splits defined by strided `IS` based on the matrix block size or the `is_rows[]` passed into `MATNEST`

2619:   This function is called once per split (it creates a new split each time).  Solve options
2620:   for this split will be available under the prefix -fieldsplit_SPLITNAME_.

2622: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSetBlockSize()`, `PCFieldSplitSetFields()`
2623: @*/
2624: PetscErrorCode PCFieldSplitSetIS(PC pc, const char splitname[], IS is)
2625: {
2626:   PetscFunctionBegin;
2628:   if (splitname) PetscAssertPointer(splitname, 2);
2630:   PetscTryMethod(pc, "PCFieldSplitSetIS_C", (PC, const char[], IS), (pc, splitname, is));
2631:   PetscFunctionReturn(PETSC_SUCCESS);
2632: }

2634: /*@
2635:   PCFieldSplitGetIS - Retrieves the elements for a split as an `IS`

2637:   Logically Collective

2639:   Input Parameters:
2640: + pc        - the preconditioner context
2641: - splitname - name of this split

2643:   Output Parameter:
2644: . is - the index set that defines the elements in this split, or `NULL` if the split is not found

2646:   Level: intermediate

2648: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSetIS()`, `PCFieldSplitGetISByIndex()`
2649: @*/
2650: PetscErrorCode PCFieldSplitGetIS(PC pc, const char splitname[], IS *is)
2651: {
2652:   PetscFunctionBegin;
2654:   PetscAssertPointer(splitname, 2);
2655:   PetscAssertPointer(is, 3);
2656:   {
2657:     PC_FieldSplit    *jac   = (PC_FieldSplit *)pc->data;
2658:     PC_FieldSplitLink ilink = jac->head;
2659:     PetscBool         found;

2661:     *is = NULL;
2662:     while (ilink) {
2663:       PetscCall(PetscStrcmp(ilink->splitname, splitname, &found));
2664:       if (found) {
2665:         *is = ilink->is;
2666:         break;
2667:       }
2668:       ilink = ilink->next;
2669:     }
2670:   }
2671:   PetscFunctionReturn(PETSC_SUCCESS);
2672: }

2674: /*@
2675:   PCFieldSplitGetISByIndex - Retrieves the elements for a given split as an `IS`

2677:   Logically Collective

2679:   Input Parameters:
2680: + pc    - the preconditioner context
2681: - index - index of this split

2683:   Output Parameter:
2684: . is - the index set that defines the elements in this split

2686:   Level: intermediate

2688: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitGetIS()`, `PCFieldSplitSetIS()`
2689: @*/
2690: PetscErrorCode PCFieldSplitGetISByIndex(PC pc, PetscInt index, IS *is)
2691: {
2692:   PetscFunctionBegin;
2693:   PetscCheck(index >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Negative field %" PetscInt_FMT " requested", index);
2695:   PetscAssertPointer(is, 3);
2696:   {
2697:     PC_FieldSplit    *jac   = (PC_FieldSplit *)pc->data;
2698:     PC_FieldSplitLink ilink = jac->head;
2699:     PetscInt          i     = 0;
2700:     PetscCheck(index < jac->nsplits, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Field %" PetscInt_FMT " requested but only %" PetscInt_FMT " exist", index, jac->nsplits);

2702:     while (i < index) {
2703:       ilink = ilink->next;
2704:       ++i;
2705:     }
2706:     PetscCall(PCFieldSplitGetIS(pc, ilink->splitname, is));
2707:   }
2708:   PetscFunctionReturn(PETSC_SUCCESS);
2709: }

2711: /*@
2712:   PCFieldSplitSetBlockSize - Sets the block size for defining where fields start in the
2713:   fieldsplit preconditioner when calling `PCFieldSplitSetFields()`. If not set the matrix block size is used.

2715:   Logically Collective

2717:   Input Parameters:
2718: + pc - the preconditioner context
2719: - bs - the block size

2721:   Level: intermediate

2723:   Note:
2724:   If the matrix is a `MATNEST` then the `is_rows[]` passed to `MatCreateNest()` determines the fields.

2726: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSetIS()`
2727: @*/
2728: PetscErrorCode PCFieldSplitSetBlockSize(PC pc, PetscInt bs)
2729: {
2730:   PetscFunctionBegin;
2733:   PetscTryMethod(pc, "PCFieldSplitSetBlockSize_C", (PC, PetscInt), (pc, bs));
2734:   PetscFunctionReturn(PETSC_SUCCESS);
2735: }

2737: /*@C
2738:   PCFieldSplitGetSubKSP - Gets the `KSP` contexts for all splits

2740:   Collective

2742:   Input Parameter:
2743: . pc - the preconditioner context

2745:   Output Parameters:
2746: + n      - the number of splits
2747: - subksp - the array of `KSP` contexts

2749:   Level: advanced

2751:   Notes:
2752:   After `PCFieldSplitGetSubKSP()` the array of `KSP`s is to be freed by the user with `PetscFree()`
2753:   (not the `KSP`, just the array that contains them).

2755:   You must call `PCSetUp()` before calling `PCFieldSplitGetSubKSP()`.

2757:   If the fieldsplit is of type `PC_COMPOSITE_SCHUR`, it returns the `KSP` object used inside the
2758:   Schur complement and the `KSP` object used to iterate over the Schur complement.
2759:   To access all the `KSP` objects used in `PC_COMPOSITE_SCHUR`, use `PCFieldSplitSchurGetSubKSP()`.

2761:   If the fieldsplit is of type `PC_COMPOSITE_GKB`, it returns the `KSP` object used to solve the
2762:   inner linear system defined by the matrix H in each loop.

2764:   Fortran Note:
2765:   Call `PCFieldSplitRestoreSubKSP()` when the array of `KSP` is no longer needed

2767:   Developer Notes:
2768:   There should be a `PCFieldSplitRestoreSubKSP()` instead of requiring the user to call `PetscFree()`

2770: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSetIS()`, `PCFieldSplitSchurGetSubKSP()`
2771: @*/
2772: PetscErrorCode PCFieldSplitGetSubKSP(PC pc, PetscInt *n, KSP *subksp[])
2773: {
2774:   PetscFunctionBegin;
2776:   if (n) PetscAssertPointer(n, 2);
2777:   PetscUseMethod(pc, "PCFieldSplitGetSubKSP_C", (PC, PetscInt *, KSP **), (pc, n, subksp));
2778:   PetscFunctionReturn(PETSC_SUCCESS);
2779: }

2781: /*@C
2782:   PCFieldSplitSchurGetSubKSP - Gets the `KSP` contexts used inside the Schur complement based `PCFIELDSPLIT`

2784:   Collective

2786:   Input Parameter:
2787: . pc - the preconditioner context

2789:   Output Parameters:
2790: + n      - the number of splits
2791: - subksp - the array of `KSP` contexts

2793:   Level: advanced

2795:   Notes:
2796:   After `PCFieldSplitSchurGetSubKSP()` the array of `KSP`s is to be freed by the user with `PetscFree()`
2797:   (not the `KSP` just the array that contains them).

2799:   You must call `PCSetUp()` before calling `PCFieldSplitSchurGetSubKSP()`.

2801:   If the fieldsplit type is of type `PC_COMPOSITE_SCHUR`, it returns (in order)
2802: +  1  - the `KSP` used for the (1,1) block
2803: .  2  - the `KSP` used for the Schur complement (not the one used for the interior Schur solver)
2804: -  3  - the `KSP` used for the (1,1) block in the upper triangular factor (if different from that of the (1,1) block).

2806:   It returns a null array if the fieldsplit is not of type `PC_COMPOSITE_SCHUR`; in this case, you should use `PCFieldSplitGetSubKSP()`.

2808:   Fortran Note:
2809:   Call `PCFieldSplitSchurRestoreSubKSP()` when the array of `KSP` is no longer needed

2811:   Developer Notes:
2812:   There should be a `PCFieldSplitRestoreSubKSP()` instead of requiring the user to call `PetscFree()`

2814:   Should the functionality of `PCFieldSplitSchurGetSubKSP()` and `PCFieldSplitGetSubKSP()` be merged?

2816: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSetIS()`, `PCFieldSplitGetSubKSP()`
2817: @*/
2818: PetscErrorCode PCFieldSplitSchurGetSubKSP(PC pc, PetscInt *n, KSP *subksp[])
2819: {
2820:   PetscFunctionBegin;
2822:   if (n) PetscAssertPointer(n, 2);
2823:   PetscUseMethod(pc, "PCFieldSplitSchurGetSubKSP_C", (PC, PetscInt *, KSP **), (pc, n, subksp));
2824:   PetscFunctionReturn(PETSC_SUCCESS);
2825: }

2827: /*@
2828:   PCFieldSplitSetSchurPre -  Indicates from what operator the preconditioner is constructed for the Schur complement.
2829:   The default is the A11 matrix.

2831:   Collective

2833:   Input Parameters:
2834: + pc    - the preconditioner context
2835: . ptype - which matrix to use for preconditioning the Schur complement: `PC_FIELDSPLIT_SCHUR_PRE_A11` (default),
2836:               `PC_FIELDSPLIT_SCHUR_PRE_SELF`, `PC_FIELDSPLIT_SCHUR_PRE_USER`,
2837:               `PC_FIELDSPLIT_SCHUR_PRE_SELFP`, and `PC_FIELDSPLIT_SCHUR_PRE_FULL`
2838: - pre   - matrix to use for preconditioning, or `NULL`

2840:   Options Database Keys:
2841: + -pc_fieldsplit_schur_precondition (self|selfp|user|a11|full) - default is `a11`. See notes for meaning of various arguments
2842: - -fieldsplit_1_pc_type pctype                                 - the preconditioner algorithm that is used to construct the preconditioner from the operator

2844:   Level: intermediate

2846:   Notes:
2847:   If ptype is
2848: +     a11 - the preconditioner for the Schur complement is generated from the block diagonal part of the preconditioner
2849:   matrix associated with the Schur complement (i.e. A11), not the Schur complement matrix
2850: .     self - the preconditioner for the Schur complement is generated from the symbolic representation of the Schur complement matrix:
2851:   The only preconditioners that currently work with this symbolic representation matrix object are `PCLSC` and `PCHPDDM`
2852: .     user - the preconditioner for the Schur complement is generated from the user provided matrix (pre argument
2853:   to this function).
2854: .     selfp - the preconditioning for the Schur complement is generated from an explicitly-assembled approximation $ Sp = A11 - A10 inv(diag(A00)) A01 $
2855:   This is only a good preconditioner when diag(A00) is a good preconditioner for A00. Optionally, A00 can be
2856:   lumped before extracting the diagonal using the additional option `-fieldsplit_1_mat_schur_complement_ainv_type lump`
2857: -     full - the preconditioner for the Schur complement is generated from the exact Schur complement matrix representation
2858:   computed internally by `PCFIELDSPLIT` (this is expensive)
2859:   useful mostly as a test that the Schur complement approach can work for your problem

2861:   When solving a saddle point problem, where the A11 block is identically zero, using `a11` as the ptype only makes sense
2862:   with the additional option `-fieldsplit_1_pc_type none`. Usually for saddle point problems one would use a `ptype` of `self` and
2863:   `-fieldsplit_1_pc_type lsc` which uses the least squares commutator to compute a preconditioner for the Schur complement.

2865:   Developer Note:
2866:   The name of this function and the option `-pc_fieldsplit_schur_precondition` are inconsistent; precondition should be used everywhere.

2868: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSchurPre()`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSchurPreType`,
2869:           `MatSchurComplementSetAinvType()`, `PCLSC`, `PCFieldSplitSetSchurFactType()`
2870: @*/
2871: PetscErrorCode PCFieldSplitSetSchurPre(PC pc, PCFieldSplitSchurPreType ptype, Mat pre)
2872: {
2873:   PetscFunctionBegin;
2875:   PetscTryMethod(pc, "PCFieldSplitSetSchurPre_C", (PC, PCFieldSplitSchurPreType, Mat), (pc, ptype, pre));
2876:   PetscFunctionReturn(PETSC_SUCCESS);
2877: }

2879: PetscErrorCode PCFieldSplitSchurPrecondition(PC pc, PCFieldSplitSchurPreType ptype, Mat pre)
2880: {
2881:   return PCFieldSplitSetSchurPre(pc, ptype, pre);
2882: } /* Deprecated name */

2884: /*@
2885:   PCFieldSplitGetSchurPre - For Schur complement fieldsplit, determine how the Schur complement will be
2886:   preconditioned.  See `PCFieldSplitSetSchurPre()` for details.

2888:   Logically Collective

2890:   Input Parameter:
2891: . pc - the preconditioner context

2893:   Output Parameters:
2894: + 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`
2895: - pre   - matrix to use for preconditioning (with `PC_FIELDSPLIT_SCHUR_PRE_USER`), or `NULL`

2897:   Level: intermediate

2899: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitSetSchurPre()`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSchurPreType`, `PCLSC`
2900: @*/
2901: PetscErrorCode PCFieldSplitGetSchurPre(PC pc, PCFieldSplitSchurPreType *ptype, Mat *pre)
2902: {
2903:   PetscFunctionBegin;
2905:   PetscUseMethod(pc, "PCFieldSplitGetSchurPre_C", (PC, PCFieldSplitSchurPreType *, Mat *), (pc, ptype, pre));
2906:   PetscFunctionReturn(PETSC_SUCCESS);
2907: }

2909: /*@
2910:   PCFieldSplitSchurGetS -  extract the `MATSCHURCOMPLEMENT` object used by this `PCFIELDSPLIT` in case it needs to be configured separately

2912:   Not Collective

2914:   Input Parameter:
2915: . pc - the preconditioner context

2917:   Output Parameter:
2918: . S - the Schur complement matrix

2920:   Level: advanced

2922:   Note:
2923:   This matrix should not be destroyed using `MatDestroy()`; rather, use `PCFieldSplitSchurRestoreS()`.

2925: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSchurPreType`, `PCFieldSplitSetSchurPre()`, `MATSCHURCOMPLEMENT`, `PCFieldSplitSchurRestoreS()`,
2926:           `MatCreateSchurComplement()`, `MatSchurComplementGetKSP()`, `MatSchurComplementComputeExplicitOperator()`, `MatGetSchurComplement()`
2927: @*/
2928: PetscErrorCode PCFieldSplitSchurGetS(PC pc, Mat *S)
2929: {
2930:   const char    *t;
2931:   PetscBool      isfs;
2932:   PC_FieldSplit *jac;

2934:   PetscFunctionBegin;
2936:   PetscCall(PetscObjectGetType((PetscObject)pc, &t));
2937:   PetscCall(PetscStrcmp(t, PCFIELDSPLIT, &isfs));
2938:   PetscCheck(isfs, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Expected PC of type PCFIELDSPLIT, got %s instead", t);
2939:   jac = (PC_FieldSplit *)pc->data;
2940:   PetscCheck(jac->type == PC_COMPOSITE_SCHUR, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Expected PCFIELDSPLIT of type SCHUR, got %d instead", jac->type);
2941:   if (S) *S = jac->schur;
2942:   PetscFunctionReturn(PETSC_SUCCESS);
2943: }

2945: /*@
2946:   PCFieldSplitSchurRestoreS -  returns the `MATSCHURCOMPLEMENT` matrix used by this `PC`

2948:   Not Collective

2950:   Input Parameters:
2951: + pc - the preconditioner context
2952: - S  - the Schur complement matrix

2954:   Level: advanced

2956: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSchurPreType`, `PCFieldSplitSetSchurPre()`, `MatSchurComplement`, `PCFieldSplitSchurGetS()`
2957: @*/
2958: PetscErrorCode PCFieldSplitSchurRestoreS(PC pc, Mat *S)
2959: {
2960:   const char    *t;
2961:   PetscBool      isfs;
2962:   PC_FieldSplit *jac;

2964:   PetscFunctionBegin;
2966:   PetscCall(PetscObjectGetType((PetscObject)pc, &t));
2967:   PetscCall(PetscStrcmp(t, PCFIELDSPLIT, &isfs));
2968:   PetscCheck(isfs, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Expected PC of type PCFIELDSPLIT, got %s instead", t);
2969:   jac = (PC_FieldSplit *)pc->data;
2970:   PetscCheck(jac->type == PC_COMPOSITE_SCHUR, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Expected PCFIELDSPLIT of type SCHUR, got %d instead", jac->type);
2971:   PetscCheck(S && (*S == jac->schur), PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "MatSchurComplement restored is not the same as gotten");
2972:   PetscFunctionReturn(PETSC_SUCCESS);
2973: }

2975: static PetscErrorCode PCFieldSplitSetSchurPre_FieldSplit(PC pc, PCFieldSplitSchurPreType ptype, Mat pre)
2976: {
2977:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

2979:   PetscFunctionBegin;
2980:   jac->schurpre = ptype;
2981:   if (ptype == PC_FIELDSPLIT_SCHUR_PRE_USER && pre) {
2982:     PetscCall(MatDestroy(&jac->schur_user));
2983:     jac->schur_user = pre;
2984:     PetscCall(PetscObjectReference((PetscObject)jac->schur_user));
2985:   }
2986:   PetscFunctionReturn(PETSC_SUCCESS);
2987: }

2989: static PetscErrorCode PCFieldSplitGetSchurPre_FieldSplit(PC pc, PCFieldSplitSchurPreType *ptype, Mat *pre)
2990: {
2991:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

2993:   PetscFunctionBegin;
2994:   if (ptype) *ptype = jac->schurpre;
2995:   if (pre) *pre = jac->schur_user;
2996:   PetscFunctionReturn(PETSC_SUCCESS);
2997: }

2999: /*@
3000:   PCFieldSplitSetSchurFactType -  sets which blocks of the approximate block factorization to retain in the preconditioner {cite}`murphy2000note` and {cite}`ipsen2001note`

3002:   Collective

3004:   Input Parameters:
3005: + pc    - the preconditioner context
3006: - ftype - which blocks of factorization to retain, `PC_FIELDSPLIT_SCHUR_FACT_FULL` is default

3008:   Options Database Key:
3009: . -pc_fieldsplit_schur_fact_type (diag|lower|upper|full) - default is `full`

3011:   Level: intermediate

3013:   Notes:
3014:   The `full` factorization is

3016:   ```{math}
3017:   \left(\begin{array}{cc} A & B \\
3018:   C & E \\
3019:   \end{array}\right) =
3020:   \left(\begin{array}{cc} I & 0 \\
3021:   C A^{-1} & I \\
3022:   \end{array}\right)
3023:   \left(\begin{array}{cc} A & 0 \\
3024:   0 & S \\
3025:   \end{array}\right)
3026:   \left(\begin{array}{cc} I & A^{-1}B \\
3027:   0 & I \\
3028:   \end{array}\right) = L D U,
3029:   ```

3031:   where $ S = E - C A^{-1} B $. In practice, the full factorization is applied via block triangular solves with the grouping $L(DU)$. `upper` uses $DU$, `lower` uses $LD$,
3032:   and `diag` is the diagonal part with the sign of $S$ flipped (because this makes the preconditioner positive definite for many formulations,
3033:   thus allowing the use of `KSPMINRES)`. Sign flipping of $S$ can be turned off with `PCFieldSplitSetSchurScale()`.

3035:   If $A$ and $S$ are solved exactly
3036: +  1 - `full` factorization is a direct solver.
3037: .  2 - The preconditioned operator with `lower` or `upper` has all eigenvalues equal to 1 and minimal polynomial of degree 2, so `KSPGMRES` converges in 2 iterations.
3038: -  3 - With `diag`, the preconditioned operator has three distinct nonzero eigenvalues and minimal polynomial of degree at most 4, so `KSPGMRES` converges in at most 4 iterations.

3040:   If the iteration count is very low, consider using `KSPFGMRES` or `KSPGCR` which can use one less preconditioner
3041:   application in this case. Note that the preconditioned operator may be highly non-normal, so such fast convergence may not be observed in practice.

3043:   For symmetric problems in which $A$ is positive definite and $S$ is negative definite, `diag` can be used with `KSPMINRES`.

3045:   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 $S$).

3047: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSchurPreType`, `PCFieldSplitSetSchurScale()`,
3048:           [](sec_flexibleksp), `PCFieldSplitSetSchurPre()`
3049: @*/
3050: PetscErrorCode PCFieldSplitSetSchurFactType(PC pc, PCFieldSplitSchurFactType ftype)
3051: {
3052:   PetscFunctionBegin;
3054:   PetscTryMethod(pc, "PCFieldSplitSetSchurFactType_C", (PC, PCFieldSplitSchurFactType), (pc, ftype));
3055:   PetscFunctionReturn(PETSC_SUCCESS);
3056: }

3058: static PetscErrorCode PCFieldSplitSetSchurFactType_FieldSplit(PC pc, PCFieldSplitSchurFactType ftype)
3059: {
3060:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

3062:   PetscFunctionBegin;
3063:   jac->schurfactorization = ftype;
3064:   PetscFunctionReturn(PETSC_SUCCESS);
3065: }

3067: /*@
3068:   PCFieldSplitSetSchurScale -  Controls the sign flip of S for `PC_FIELDSPLIT_SCHUR_FACT_DIAG`.

3070:   Collective

3072:   Input Parameters:
3073: + pc    - the preconditioner context
3074: - scale - scaling factor for the Schur complement

3076:   Options Database Key:
3077: . -pc_fieldsplit_schur_scale scale - default is -1.0

3079:   Level: intermediate

3081: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSchurFactType`, `PCFieldSplitSetSchurFactType()`
3082: @*/
3083: PetscErrorCode PCFieldSplitSetSchurScale(PC pc, PetscScalar scale)
3084: {
3085:   PetscFunctionBegin;
3088:   PetscTryMethod(pc, "PCFieldSplitSetSchurScale_C", (PC, PetscScalar), (pc, scale));
3089:   PetscFunctionReturn(PETSC_SUCCESS);
3090: }

3092: static PetscErrorCode PCFieldSplitSetSchurScale_FieldSplit(PC pc, PetscScalar scale)
3093: {
3094:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

3096:   PetscFunctionBegin;
3097:   jac->schurscale = scale;
3098:   PetscFunctionReturn(PETSC_SUCCESS);
3099: }

3101: /*@C
3102:   PCFieldSplitGetSchurBlocks - Gets all matrix blocks for the Schur complement

3104:   Collective

3106:   Input Parameter:
3107: . pc - the preconditioner context

3109:   Output Parameters:
3110: + A00 - the (0,0) block
3111: . A01 - the (0,1) block
3112: . A10 - the (1,0) block
3113: - A11 - the (1,1) block

3115:   Level: advanced

3117:   Note:
3118:   Use `NULL` for any unneeded output arguments

3120: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `MatSchurComplementGetSubMatrices()`, `MatSchurComplementSetSubMatrices()`
3121: @*/
3122: PetscErrorCode PCFieldSplitGetSchurBlocks(PC pc, Mat *A00, Mat *A01, Mat *A10, Mat *A11)
3123: {
3124:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

3126:   PetscFunctionBegin;
3128:   PetscCheck(jac->type == PC_COMPOSITE_SCHUR, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONG, "FieldSplit is not using a Schur complement approach.");
3129:   if (A00) *A00 = jac->pmat[0];
3130:   if (A01) *A01 = jac->B;
3131:   if (A10) *A10 = jac->C;
3132:   if (A11) *A11 = jac->pmat[1];
3133:   PetscFunctionReturn(PETSC_SUCCESS);
3134: }

3136: /*@
3137:   PCFieldSplitSetGKBTol -  Sets the solver tolerance for the generalized Golub-Kahan bidiagonalization preconditioner {cite}`arioli2013` in `PCFIELDSPLIT`

3139:   Collective

3141:   Input Parameters:
3142: + pc        - the preconditioner context
3143: - tolerance - the solver tolerance

3145:   Options Database Key:
3146: . -pc_fieldsplit_gkb_tol tolerance - default is 1e-5

3148:   Level: intermediate

3150:   Note:
3151:   The generalized GKB algorithm {cite}`arioli2013` uses a lower bound estimate of the error in energy norm as stopping criterion.
3152:   It stops once the lower bound estimate undershoots the required solver tolerance. Although the actual error might be bigger than
3153:   this estimate, the stopping criterion is satisfactory in practical cases.

3155: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetGKBDelay()`, `PCFieldSplitSetGKBNu()`, `PCFieldSplitSetGKBMaxit()`
3156: @*/
3157: PetscErrorCode PCFieldSplitSetGKBTol(PC pc, PetscReal tolerance)
3158: {
3159:   PetscFunctionBegin;
3162:   PetscTryMethod(pc, "PCFieldSplitSetGKBTol_C", (PC, PetscReal), (pc, tolerance));
3163:   PetscFunctionReturn(PETSC_SUCCESS);
3164: }

3166: static PetscErrorCode PCFieldSplitSetGKBTol_FieldSplit(PC pc, PetscReal tolerance)
3167: {
3168:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

3170:   PetscFunctionBegin;
3171:   jac->gkbtol = tolerance;
3172:   PetscFunctionReturn(PETSC_SUCCESS);
3173: }

3175: /*@
3176:   PCFieldSplitSetGKBMaxit -  Sets the maximum number of iterations for the generalized Golub-Kahan bidiagonalization preconditioner {cite}`arioli2013` in `PCFIELDSPLIT`

3178:   Collective

3180:   Input Parameters:
3181: + pc    - the preconditioner context
3182: - maxit - the maximum number of iterations

3184:   Options Database Key:
3185: . -pc_fieldsplit_gkb_maxit maxit - default is 100

3187:   Level: intermediate

3189: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetGKBDelay()`, `PCFieldSplitSetGKBTol()`, `PCFieldSplitSetGKBNu()`
3190: @*/
3191: PetscErrorCode PCFieldSplitSetGKBMaxit(PC pc, PetscInt maxit)
3192: {
3193:   PetscFunctionBegin;
3196:   PetscTryMethod(pc, "PCFieldSplitSetGKBMaxit_C", (PC, PetscInt), (pc, maxit));
3197:   PetscFunctionReturn(PETSC_SUCCESS);
3198: }

3200: static PetscErrorCode PCFieldSplitSetGKBMaxit_FieldSplit(PC pc, PetscInt maxit)
3201: {
3202:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

3204:   PetscFunctionBegin;
3205:   jac->gkbmaxit = maxit;
3206:   PetscFunctionReturn(PETSC_SUCCESS);
3207: }

3209: /*@
3210:   PCFieldSplitSetGKBDelay -  Sets the delay in the lower bound error estimate in the generalized Golub-Kahan bidiagonalization {cite}`arioli2013` in `PCFIELDSPLIT`
3211:   preconditioner.

3213:   Collective

3215:   Input Parameters:
3216: + pc    - the preconditioner context
3217: - delay - the delay window in the lower bound estimate

3219:   Options Database Key:
3220: . -pc_fieldsplit_gkb_delay delay - default is 5

3222:   Level: intermediate

3224:   Notes:
3225:   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 $
3226:   is expressed as a truncated sum. The error at iteration k can only be measured at iteration (k + `delay`), and thus the algorithm needs
3227:   at least (`delay` + 1) iterations to stop.

3229:   For more details on the generalized Golub-Kahan bidiagonalization method and its lower bound stopping criterion, please refer to {cite}`arioli2013`

3231: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetGKBNu()`, `PCFieldSplitSetGKBTol()`, `PCFieldSplitSetGKBMaxit()`
3232: @*/
3233: PetscErrorCode PCFieldSplitSetGKBDelay(PC pc, PetscInt delay)
3234: {
3235:   PetscFunctionBegin;
3238:   PetscTryMethod(pc, "PCFieldSplitSetGKBDelay_C", (PC, PetscInt), (pc, delay));
3239:   PetscFunctionReturn(PETSC_SUCCESS);
3240: }

3242: static PetscErrorCode PCFieldSplitSetGKBDelay_FieldSplit(PC pc, PetscInt delay)
3243: {
3244:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

3246:   PetscFunctionBegin;
3247:   jac->gkbdelay = delay;
3248:   PetscFunctionReturn(PETSC_SUCCESS);
3249: }

3251: /*@
3252:   PCFieldSplitSetGKBNu -  Sets the scalar value nu >= 0 in the transformation H = A00 + nu*A01*A01' of the (1,1) block in the
3253:   Golub-Kahan bidiagonalization preconditioner {cite}`arioli2013` in `PCFIELDSPLIT`

3255:   Collective

3257:   Input Parameters:
3258: + pc - the preconditioner context
3259: - nu - the shift parameter

3261:   Options Database Key:
3262: . -pc_fieldsplit_gkb_nu nu - default is 1

3264:   Level: intermediate

3266:   Notes:
3267:   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,
3268:   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
3269:   necessary to find a good balance in between the convergence of the inner and outer loop.

3271:   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.

3273: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetGKBDelay()`, `PCFieldSplitSetGKBTol()`, `PCFieldSplitSetGKBMaxit()`
3274: @*/
3275: PetscErrorCode PCFieldSplitSetGKBNu(PC pc, PetscReal nu)
3276: {
3277:   PetscFunctionBegin;
3280:   PetscTryMethod(pc, "PCFieldSplitSetGKBNu_C", (PC, PetscReal), (pc, nu));
3281:   PetscFunctionReturn(PETSC_SUCCESS);
3282: }

3284: static PetscErrorCode PCFieldSplitSetGKBNu_FieldSplit(PC pc, PetscReal nu)
3285: {
3286:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

3288:   PetscFunctionBegin;
3289:   jac->gkbnu = nu;
3290:   PetscFunctionReturn(PETSC_SUCCESS);
3291: }

3293: static PetscErrorCode PCFieldSplitSetType_FieldSplit(PC pc, PCCompositeType type)
3294: {
3295:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

3297:   PetscFunctionBegin;
3298:   jac->type = type;
3299:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSubKSP_C", NULL));
3300:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurPre_C", NULL));
3301:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSchurPre_C", NULL));
3302:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurFactType_C", NULL));
3303:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurScale_C", NULL));
3304:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBTol_C", NULL));
3305:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBMaxit_C", NULL));
3306:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBNu_C", NULL));
3307:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBDelay_C", NULL));

3309:   if (type == PC_COMPOSITE_SCHUR) {
3310:     pc->ops->apply          = PCApply_FieldSplit_Schur;
3311:     pc->ops->applytranspose = PCApplyTranspose_FieldSplit_Schur;
3312:     pc->ops->matapply       = PCMatApply_FieldSplit_Schur;
3313:     pc->ops->view           = PCView_FieldSplit_Schur;
3314:     pc->ops->setuponblocks  = PCSetUpOnBlocks_FieldSplit_Schur;

3316:     PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSubKSP_C", PCFieldSplitGetSubKSP_FieldSplit_Schur));
3317:     PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurPre_C", PCFieldSplitSetSchurPre_FieldSplit));
3318:     PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSchurPre_C", PCFieldSplitGetSchurPre_FieldSplit));
3319:     PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurFactType_C", PCFieldSplitSetSchurFactType_FieldSplit));
3320:     PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurScale_C", PCFieldSplitSetSchurScale_FieldSplit));
3321:   } else if (type == PC_COMPOSITE_GKB) {
3322:     pc->ops->apply          = PCApply_FieldSplit_GKB;
3323:     pc->ops->applytranspose = NULL;
3324:     pc->ops->matapply       = NULL;
3325:     pc->ops->view           = PCView_FieldSplit_GKB;
3326:     pc->ops->setuponblocks  = PCSetUpOnBlocks_FieldSplit_GKB;

3328:     PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSubKSP_C", PCFieldSplitGetSubKSP_FieldSplit));
3329:     PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBTol_C", PCFieldSplitSetGKBTol_FieldSplit));
3330:     PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBMaxit_C", PCFieldSplitSetGKBMaxit_FieldSplit));
3331:     PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBNu_C", PCFieldSplitSetGKBNu_FieldSplit));
3332:     PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBDelay_C", PCFieldSplitSetGKBDelay_FieldSplit));
3333:   } else {
3334:     pc->ops->apply          = PCApply_FieldSplit;
3335:     pc->ops->applytranspose = PCApplyTranspose_FieldSplit;
3336:     pc->ops->matapply       = PCMatApply_FieldSplit;
3337:     pc->ops->view           = PCView_FieldSplit;
3338:     pc->ops->setuponblocks  = PCSetUpOnBlocks_FieldSplit;

3340:     PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSubKSP_C", PCFieldSplitGetSubKSP_FieldSplit));
3341:   }
3342:   PetscFunctionReturn(PETSC_SUCCESS);
3343: }

3345: static PetscErrorCode PCFieldSplitSetBlockSize_FieldSplit(PC pc, PetscInt bs)
3346: {
3347:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

3349:   PetscFunctionBegin;
3350:   PetscCheck(bs >= 1, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_OUTOFRANGE, "Blocksize must be positive, you gave %" PetscInt_FMT, bs);
3351:   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);
3352:   jac->bs = bs;
3353:   PetscFunctionReturn(PETSC_SUCCESS);
3354: }

3356: static PetscErrorCode PCSetCoordinates_FieldSplit(PC pc, PetscInt dim, PetscInt nloc, PetscReal coords[])
3357: {
3358:   PC_FieldSplit    *jac           = (PC_FieldSplit *)pc->data;
3359:   PC_FieldSplitLink ilink_current = jac->head;
3360:   IS                is_owned;

3362:   PetscFunctionBegin;
3363:   jac->coordinates_set = PETSC_TRUE; // Internal flag
3364:   PetscCall(MatGetOwnershipIS(pc->mat, &is_owned, NULL));

3366:   while (ilink_current) {
3367:     // For each IS, embed it to get local coords indces
3368:     IS              is_coords;
3369:     PetscInt        ndofs_block;
3370:     const PetscInt *block_dofs_enumeration; // Numbering of the dofs relevant to the current block

3372:     // Setting drop to true for safety. It should make no difference.
3373:     PetscCall(ISEmbed(ilink_current->is, is_owned, PETSC_TRUE, &is_coords));
3374:     PetscCall(ISGetLocalSize(is_coords, &ndofs_block));
3375:     PetscCall(ISGetIndices(is_coords, &block_dofs_enumeration));

3377:     // Allocate coordinates vector and set it directly
3378:     PetscCall(PetscMalloc1(ndofs_block * dim, &ilink_current->coords));
3379:     for (PetscInt dof = 0; dof < ndofs_block; ++dof) {
3380:       for (PetscInt d = 0; d < dim; ++d) (ilink_current->coords)[dim * dof + d] = coords[dim * block_dofs_enumeration[dof] + d];
3381:     }
3382:     ilink_current->dim   = dim;
3383:     ilink_current->ndofs = ndofs_block;
3384:     PetscCall(ISRestoreIndices(is_coords, &block_dofs_enumeration));
3385:     PetscCall(ISDestroy(&is_coords));
3386:     ilink_current = ilink_current->next;
3387:   }
3388:   PetscCall(ISDestroy(&is_owned));
3389:   PetscFunctionReturn(PETSC_SUCCESS);
3390: }

3392: /*@
3393:   PCFieldSplitSetType - Sets the type, `PCCompositeType`, of a `PCFIELDSPLIT`

3395:   Collective

3397:   Input Parameters:
3398: + pc   - the preconditioner context
3399: - type - `PC_COMPOSITE_ADDITIVE`, `PC_COMPOSITE_MULTIPLICATIVE` (default), `PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE`, `PC_COMPOSITE_SPECIAL`, `PC_COMPOSITE_SCHUR`,
3400:          `PC_COMPOSITE_GKB`

3402:   Options Database Key:
3403: . -pc_fieldsplit_type (multiplicative|additive|symmetric_multiplicative|special|schur) - Sets fieldsplit preconditioner type

3405:   Level: intermediate

3407: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCCompositeType`, `PCCompositeGetType()`, `PC_COMPOSITE_ADDITIVE`, `PC_COMPOSITE_MULTIPLICATIVE`,
3408:           `PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE`, `PC_COMPOSITE_SPECIAL`, `PC_COMPOSITE_SCHUR`, `PCFieldSplitSetSchurFactType()`
3409: @*/
3410: PetscErrorCode PCFieldSplitSetType(PC pc, PCCompositeType type)
3411: {
3412:   PetscFunctionBegin;
3414:   PetscTryMethod(pc, "PCFieldSplitSetType_C", (PC, PCCompositeType), (pc, type));
3415:   PetscFunctionReturn(PETSC_SUCCESS);
3416: }

3418: /*@
3419:   PCFieldSplitGetType - Gets the type, `PCCompositeType`, of a `PCFIELDSPLIT`

3421:   Not collective

3423:   Input Parameter:
3424: . pc - the preconditioner context

3426:   Output Parameter:
3427: . type - `PC_COMPOSITE_ADDITIVE`, `PC_COMPOSITE_MULTIPLICATIVE` (default), `PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE`, `PC_COMPOSITE_SPECIAL`, `PC_COMPOSITE_SCHUR`

3429:   Level: intermediate

3431: .seealso: [](sec_block_matrices), `PC`, `PCCompositeSetType()`, `PCFIELDSPLIT`, `PCCompositeType`, `PC_COMPOSITE_ADDITIVE`, `PC_COMPOSITE_MULTIPLICATIVE`,
3432:           `PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE`, `PC_COMPOSITE_SPECIAL`, `PC_COMPOSITE_SCHUR`
3433: @*/
3434: PetscErrorCode PCFieldSplitGetType(PC pc, PCCompositeType *type)
3435: {
3436:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

3438:   PetscFunctionBegin;
3440:   PetscAssertPointer(type, 2);
3441:   *type = jac->type;
3442:   PetscFunctionReturn(PETSC_SUCCESS);
3443: }

3445: /*@
3446:   PCFieldSplitSetDMSplits - Flags whether `DMCreateFieldDecomposition()` should be used to define the splits in a `PCFIELDSPLIT`, whenever possible.

3448:   Logically Collective

3450:   Input Parameters:
3451: + pc  - the preconditioner context
3452: - flg - boolean indicating whether to use field splits defined by the `DM`

3454:   Options Database Key:
3455: . -pc_fieldsplit_dm_splits (true|false) - use the field splits defined by the `DM`

3457:   Level: intermediate

3459:   Developer Note:
3460:   The name should be `PCFieldSplitSetUseDMSplits()`, similar change to options database

3462: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitGetDMSplits()`, `DMCreateFieldDecomposition()`, `PCFieldSplitSetFields()`, `PCFieldSplitSetIS()`
3463: @*/
3464: PetscErrorCode PCFieldSplitSetDMSplits(PC pc, PetscBool flg)
3465: {
3466:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
3467:   PetscBool      isfs;

3469:   PetscFunctionBegin;
3472:   PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCFIELDSPLIT, &isfs));
3473:   if (isfs) jac->dm_splits = flg;
3474:   PetscFunctionReturn(PETSC_SUCCESS);
3475: }

3477: /*@
3478:   PCFieldSplitGetDMSplits - Returns flag indicating whether `DMCreateFieldDecomposition()` should be used to define the splits in a `PCFIELDSPLIT`, whenever possible.

3480:   Logically Collective

3482:   Input Parameter:
3483: . pc - the preconditioner context

3485:   Output Parameter:
3486: . flg - boolean indicating whether to use field splits defined by the `DM`

3488:   Level: intermediate

3490:   Developer Note:
3491:   The name should be `PCFieldSplitGetUseDMSplits()`

3493: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetDMSplits()`, `DMCreateFieldDecomposition()`, `PCFieldSplitSetFields()`, `PCFieldSplitSetIS()`
3494: @*/
3495: PetscErrorCode PCFieldSplitGetDMSplits(PC pc, PetscBool *flg)
3496: {
3497:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
3498:   PetscBool      isfs;

3500:   PetscFunctionBegin;
3502:   PetscAssertPointer(flg, 2);
3503:   PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCFIELDSPLIT, &isfs));
3504:   if (isfs) {
3505:     if (flg) *flg = jac->dm_splits;
3506:   }
3507:   PetscFunctionReturn(PETSC_SUCCESS);
3508: }

3510: /*@
3511:   PCFieldSplitGetDetectSaddlePoint - Returns flag indicating whether `PCFIELDSPLIT` will attempt to automatically determine fields based on zero diagonal entries.

3513:   Logically Collective

3515:   Input Parameter:
3516: . pc - the preconditioner context

3518:   Output Parameter:
3519: . flg - boolean indicating whether to detect fields or not

3521:   Level: intermediate

3523: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetDetectSaddlePoint()`
3524: @*/
3525: PetscErrorCode PCFieldSplitGetDetectSaddlePoint(PC pc, PetscBool *flg)
3526: {
3527:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

3529:   PetscFunctionBegin;
3530:   *flg = jac->detect;
3531:   PetscFunctionReturn(PETSC_SUCCESS);
3532: }

3534: /*@
3535:   PCFieldSplitSetDetectSaddlePoint - Sets flag indicating whether `PCFIELDSPLIT` will attempt to automatically determine fields based on zero diagonal entries.

3537:   Logically Collective

3539:   Input Parameter:
3540: . pc - the preconditioner context

3542:   Output Parameter:
3543: . flg - boolean indicating whether to detect fields or not

3545:   Options Database Key:
3546: . -pc_fieldsplit_detect_saddle_point (true|false) - detect and use the saddle point

3548:   Level: intermediate

3550:   Note:
3551:   Also sets the split type to `PC_COMPOSITE_SCHUR` (see `PCFieldSplitSetType()`) and the Schur preconditioner type to `PC_FIELDSPLIT_SCHUR_PRE_SELF` (see `PCFieldSplitSetSchurPre()`).

3553: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitGetDetectSaddlePoint()`, `PCFieldSplitSetType()`, `PCFieldSplitSetSchurPre()`, `PC_FIELDSPLIT_SCHUR_PRE_SELF`
3554: @*/
3555: PetscErrorCode PCFieldSplitSetDetectSaddlePoint(PC pc, PetscBool flg)
3556: {
3557:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

3559:   PetscFunctionBegin;
3560:   jac->detect = flg;
3561:   if (jac->detect) {
3562:     PetscCall(PCFieldSplitSetType(pc, PC_COMPOSITE_SCHUR));
3563:     PetscCall(PCFieldSplitSetSchurPre(pc, PC_FIELDSPLIT_SCHUR_PRE_SELF, NULL));
3564:   }
3565:   PetscFunctionReturn(PETSC_SUCCESS);
3566: }

3568: /*MC
3569:   PCFIELDSPLIT - Preconditioner created by combining separate preconditioners for individual
3570:   collections of variables (that may overlap) called fields or splits. Each field often represents a different continuum variable
3571:   represented on a grid, such as velocity, pressure, or temperature.
3572:   In the literature these are sometimes called block preconditioners; but should not be confused with `PCBJACOBI`.
3573:   See [the users manual section on "Solving Block Matrices"](sec_block_matrices) for more details.

3575:   Options Database Keys:
3576: +   -pc_fieldsplit_%d_fields a,b,...                                                 - indicates the fields to be used in the `%d`'th split
3577: .   -pc_fieldsplit_default                                                           - automatically add any fields to additional splits that have not
3578:                                                                                        been supplied explicitly by `-pc_fieldsplit_%d_fields`
3579: .   -pc_fieldsplit_block_size bs                                                     - size of block that defines fields (i.e. there are bs fields)
3580:                                                                                        when the matrix is not of `MatType` `MATNEST`
3581: .   -pc_fieldsplit_type (additive|multiplicative|symmetric_multiplicative|schur|gkb) - type of relaxation or factorization splitting
3582: .   -pc_fieldsplit_schur_precondition (self|selfp|user|a11|full)                     - default is `a11`; see `PCFieldSplitSetSchurPre()`
3583: .   -pc_fieldsplit_schur_fact_type (diag|lower|upper|full)                           - set factorization type when using `-pc_fieldsplit_type schur`;
3584:                                                                                        see `PCFieldSplitSetSchurFactType()`
3585: .   -pc_fieldsplit_dm_splits (true|false) (default is true)                          - Whether to use `DMCreateFieldDecomposition()` for splits
3586: -   -pc_fieldsplit_detect_saddle_point (true|false)                                  - automatically finds rows with zero diagonal and uses Schur complement with no preconditioner as the solver

3588:   Options prefixes for inner solvers when using the Schur complement preconditioner are `-fieldsplit_0_` and `-fieldsplit_1_` .
3589:   The options prefix for the inner solver when using the Golub-Kahan biadiagonalization preconditioner is `-fieldsplit_0_`
3590:   For all other solvers they are `-fieldsplit_%d_` for the `%d`'th field; use `-fieldsplit_` for all fields.

3592:   To set options on the solvers for all blocks, prepend `-fieldsplit_` to all the `PC`
3593:   options database keys. For example, `-fieldsplit_pc_type ilu` `-fieldsplit_pc_factor_levels 1`.

3595:   To set the options on the solvers separate for each block call `PCFieldSplitGetSubKSP()`
3596:   and set the options directly on the resulting `KSP` object

3598:   Level: intermediate

3600:   Notes:
3601:   Use `PCFieldSplitSetFields()` to set splits defined by "strided" entries or with a `MATNEST` and `PCFieldSplitSetIS()`
3602:   to define a split by an arbitrary collection of entries.

3604:   If no splits are set, the default is used. If a `DM` is associated with the `PC` and it supports
3605:   `DMCreateFieldDecomposition()`, then that is used for the default. Otherwise if the matrix is not `MATNEST`, the splits are defined by entries strided by bs,
3606:   beginning at 0 then 1, etc to bs-1. The block size can be set with `PCFieldSplitSetBlockSize()`,
3607:   if this is not called the block size defaults to the blocksize of the second matrix passed
3608:   to `KSPSetOperators()`/`PCSetOperators()`.

3610:   For the Schur complement preconditioner if
3611:   ```{math}
3612:     J = \left[\begin{array}{cc} A_{00} & A_{01} \\ A_{10} & A_{11} \end{array}\right]
3613:   ```

3615:   the preconditioner using `full` factorization is logically
3616:   ```{math}
3617:     \left[\begin{array}{cc} I & -\text{ksp}(A_{00}) A_{01} \\ 0 & I \end{array}\right] \left[\begin{array}{cc} \text{ksp}(A_{00}) & 0 \\ 0 & \text{ksp}(S) \end{array}\right] \left[\begin{array}{cc} I & 0 \\ -A_{10} \text{ksp}(A_{00}) & I \end{array}\right]
3618:       ```
3619:   where the action of $\text{ksp}(A_{00})$ is applied using the `KSP` solver with prefix `-fieldsplit_0_`.  $S$ is the Schur complement
3620:   ```{math}
3621:      S = A_{11} - A_{10} \text{ksp}(A_{00}) A_{01}
3622:   ```
3623:   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`
3624:   was given in providing the SECOND split or 1 if not given). Accordingly, if using `PCFieldSplitGetSubKSP()`, the array of sub-`KSP` contexts will hold two `KSP`s: at its
3625:   0th index, the `KSP` associated with `-fieldsplit_0_`, and at its 1st index, the `KSP` corresponding to `-fieldsplit_1_`.
3626:   By default, $A_{11}$ is used to construct a preconditioner for $S$, use `PCFieldSplitSetSchurPre()` for all the possible ways to construct the preconditioner for $S$.

3628:   The factorization type is set using `-pc_fieldsplit_schur_fact_type <diag, lower, upper, full>`. `full` is shown above,
3629:   `diag` gives
3630:   ```{math}
3631:     \left[\begin{array}{cc} \text{ksp}(A_{00}) & 0 \\  0 & -\text{ksp}(S) \end{array}\right]
3632:   ```
3633:   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
3634:   can be turned off with `PCFieldSplitSetSchurScale()` or by command line `-pc_fieldsplit_schur_scale 1.0`. The `lower` factorization is the inverse of
3635:   ```{math}
3636:     \left[\begin{array}{cc} A_{00} & 0 \\  A_{10} & S \end{array}\right]
3637:   ```
3638:   where the inverses of $A_{00}$ and $S$ are applied using `KSP`s. The upper factorization is the inverse of
3639:   ```{math}
3640:     \left[\begin{array}{cc} A_{00} & A_{01} \\  0 & S \end{array}\right]
3641:   ```
3642:   where again the inverses of $A_{00}$ and $S$ are applied using `KSP`s.

3644:   If only one set of indices (one `IS`) is provided with `PCFieldSplitSetIS()` then the complement of that `IS`
3645:   is used automatically for a second submatrix.

3647:   The fieldsplit preconditioner cannot currently be used with the `MATBAIJ` or `MATSBAIJ` data formats if the blocksize is larger than 1.
3648:   Generally it should be used with the `MATAIJ` or `MATNEST` `MatType`

3650:   The forms of these preconditioners are closely related, if not identical, to forms derived as "Distributive Iterations", see,
3651:   for example, page 294 in "Principles of Computational Fluid Dynamics" by Pieter Wesseling {cite}`wesseling2009`.
3652:   One can also use `PCFIELDSPLIT` inside a smoother resulting in "Distributive Smoothers".

3654:   See "A taxonomy and comparison of parallel block multi-level preconditioners for the incompressible Navier-Stokes equations" {cite}`elman2008tcp`.

3656:   The Constrained Pressure Preconditioner (CPR) can be implemented using `PCCOMPOSITE` with `PCGALERKIN`. CPR first solves an $R A P$ subsystem, updates the
3657:   residual on all variables (`PCCompositeSetType(pc,PC_COMPOSITE_MULTIPLICATIVE)`), and then applies a simple ILU like preconditioner on all the variables.

3659:   The generalized Golub-Kahan bidiagonalization preconditioner (GKB) can be applied to symmetric $2 \times 2$ block matrices of the shape
3660:   ```{math}
3661:     \left[\begin{array}{cc} A_{00} & A_{01} \\ A_{01}' & 0 \end{array}\right]
3662:   ```
3663:   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 $H = _{A00} + \nu*A_{01}*A_{01}'$.
3664:   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_`.

3666:   Some `PCFIELDSPLIT` variants are called physics-based preconditioners, since the preconditioner takes into account the underlying physics of the
3667:   problem. But this nomenclature is not well-defined.

3669:   Developer Note:
3670:   The Schur complement functionality of `PCFIELDSPLIT` should likely be factored into its own `PC` thus simplifying the implementation of the preconditioners and their
3671:   user API.

3673: .seealso: [](sec_block_matrices), `PC`, `PCCreate()`, `PCSetType()`, `PCType`, `PCLSC`,
3674:           `PCFieldSplitGetSubKSP()`, `PCFieldSplitSchurGetSubKSP()`, `PCFieldSplitSetFields()`,
3675:           `PCFieldSplitSetType()`, `PCFieldSplitSetIS()`, `PCFieldSplitSetSchurPre()`, `PCFieldSplitSetSchurFactType()`,
3676:           `MatSchurComplementSetAinvType()`, `PCFieldSplitSetSchurScale()`, `PCFieldSplitSetDetectSaddlePoint()`
3677: M*/

3679: PETSC_EXTERN PetscErrorCode PCCreate_FieldSplit(PC pc)
3680: {
3681:   PC_FieldSplit *jac;

3683:   PetscFunctionBegin;
3684:   PetscCall(PetscNew(&jac));

3686:   jac->bs                 = -1;
3687:   jac->type               = PC_COMPOSITE_MULTIPLICATIVE;
3688:   jac->schurpre           = PC_FIELDSPLIT_SCHUR_PRE_USER; /* Try user preconditioner first, fall back on diagonal */
3689:   jac->schurfactorization = PC_FIELDSPLIT_SCHUR_FACT_FULL;
3690:   jac->schurscale         = -1.0;
3691:   jac->dm_splits          = PETSC_TRUE;
3692:   jac->gkbtol             = 1e-5;
3693:   jac->gkbdelay           = 5;
3694:   jac->gkbnu              = 1;
3695:   jac->gkbmaxit           = 100;

3697:   pc->data = (void *)jac;

3699:   pc->ops->setup           = PCSetUp_FieldSplit;
3700:   pc->ops->reset           = PCReset_FieldSplit;
3701:   pc->ops->destroy         = PCDestroy_FieldSplit;
3702:   pc->ops->setfromoptions  = PCSetFromOptions_FieldSplit;
3703:   pc->ops->applyrichardson = NULL;

3705:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSchurGetSubKSP_C", PCFieldSplitSchurGetSubKSP_FieldSplit));
3706:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetFields_C", PCFieldSplitSetFields_FieldSplit));
3707:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetIS_C", PCFieldSplitSetIS_FieldSplit));
3708:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetType_C", PCFieldSplitSetType_FieldSplit));
3709:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetBlockSize_C", PCFieldSplitSetBlockSize_FieldSplit));
3710:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitRestrictIS_C", PCFieldSplitRestrictIS_FieldSplit));
3711:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCSetCoordinates_C", PCSetCoordinates_FieldSplit));

3713:   /* Initialize function pointers */
3714:   PetscCall(PCFieldSplitSetType(pc, jac->type));
3715:   PetscFunctionReturn(PETSC_SUCCESS);
3716: }