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

391: static PetscErrorCode PCFieldSplitSetDefaults(PC pc)
392: {
393:   PC_FieldSplit    *jac                = (PC_FieldSplit *)pc->data;
394:   PC_FieldSplitLink ilink              = jac->head;
395:   PetscBool         fieldsplit_default = PETSC_FALSE, coupling = PETSC_FALSE;
396:   PetscInt          i;

398:   PetscFunctionBegin;
399:   /*
400:    Kinda messy, but at least this now uses DMCreateFieldDecomposition().
401:    Should probably be rewritten.
402:    */
403:   if (!ilink) {
404:     PetscCall(PetscOptionsGetBool(((PetscObject)pc)->options, ((PetscObject)pc)->prefix, "-pc_fieldsplit_detect_coupling", &coupling, NULL));
405:     if (pc->dm && jac->dm_splits && !jac->detect && !coupling) {
406:       PetscInt  numFields, f, i, j;
407:       char    **fieldNames;
408:       IS       *fields;
409:       DM       *dms;
410:       DM        subdm[128];
411:       PetscBool flg;

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

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

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

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

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

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

526:             PetscCall(PetscSNPrintf(splitname, sizeof(splitname), "%" PetscInt_FMT, i));
527:             PetscCall(PCFieldSplitSetFields(pc, splitname, 1, &i, &i));
528:           }
529:           jac->defaultsplit = PETSC_TRUE;
530:         }
531:       }
532:     }
533:   } else if (jac->nsplits == 1) {
534:     IS       is2;
535:     PetscInt nmin, nmax;

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

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

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

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

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

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

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

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

580:   PetscFunctionBegin;
581:   pc->failedreason = PC_NOERROR;
582:   PetscCall(PCFieldSplitSetDefaults(pc));
583:   nsplit = jac->nsplits;
584:   ilink  = jac->head;
585:   if (pc->pmat) PetscCall(PetscObjectTypeCompare((PetscObject)pc->pmat, MATNEST, &matnest));

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

591:     jac->issetup = PETSC_TRUE;

593:     /* This is done here instead of in PCFieldSplitSetFields() because may not have matrix at that point */
594:     if (jac->defaultsplit || !ilink->is) {
595:       if (jac->bs <= 0) jac->bs = nsplit;
596:     }

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

603:       PetscCall(PetscObjectTypeCompareAny((PetscObject)pc->pmat, &blk, MATBAIJ, MATSBAIJ, MATSEQBAIJ, MATSEQSBAIJ, MATMPIBAIJ, MATMPISBAIJ, NULL));
604:       PetscCheck(!blk, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONG, "Cannot use MATBAIJ with PCFIELDSPLIT and currently set matrix and PC blocksizes");
605:     }

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

619:           for (PetscInt k = 0; k < ilink->nfields; k++) {
620:             if (ilink->fields[k] != ilink->fields_col[k]) same_fields = PETSC_FALSE;
621:           }

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

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

657:       PetscCall(MatNestGetSize(pc->pmat, &mis, &nis));
658:       PetscCall(PetscMalloc2(mis, &rowis, nis, &colis));
659:       PetscCall(MatNestGetISs(pc->pmat, rowis, colis));
660:       if (!jac->defaultsplit) PetscCall(PetscMalloc1(mis, &ises));

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

684:   ilink = jac->head;
685:   if (!jac->pmat) {
686:     Vec xtmp;

688:     PetscCall(MatCreateVecs(pc->pmat, &xtmp, NULL));
689:     PetscCall(PetscMalloc1(nsplit, &jac->pmat));
690:     PetscCall(PetscMalloc2(nsplit, &jac->x, nsplit, &jac->y));
691:     for (i = 0; i < nsplit; i++) {
692:       MatNullSpace sp;

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

701:           PetscCall(PetscObjectReference((PetscObject)jac->schur_user));
702:         }
703:       } else {
704:         const char *prefix;
705:         PetscCall(MatCreateSubMatrix(pc->pmat, ilink->is, ilink->is_col, MAT_INITIAL_MATRIX, &jac->pmat[i]));
706:         PetscCall(MatGetOptionsPrefix(jac->pmat[i], &prefix));
707:         if (!prefix) {
708:           PetscCall(KSPGetOptionsPrefix(ilink->ksp, &prefix));
709:           PetscCall(MatSetOptionsPrefix(jac->pmat[i], prefix));
710:         }
711:         PetscCall(MatSetFromOptions(jac->pmat[i]));
712:         PetscCall(MatViewFromOptions(jac->pmat[i], NULL, "-mat_view"));
713:       }
714:       /* create work vectors for each split */
715:       PetscCall(MatCreateVecs(jac->pmat[i], &jac->x[i], &jac->y[i]));
716:       ilink->x = jac->x[i];
717:       ilink->y = jac->y[i];
718:       ilink->z = NULL;
719:       /* compute scatter contexts needed by multiplicative versions and non-default splits */
720:       PetscCall(VecScatterCreate(xtmp, ilink->is, jac->x[i], NULL, &ilink->sctx));
721:       PetscCall(PetscObjectQuery((PetscObject)ilink->is, "nearnullspace", (PetscObject *)&sp));
722:       if (sp) PetscCall(MatSetNearNullSpace(jac->pmat[i], sp));
723:       ilink = ilink->next;
724:     }
725:     PetscCall(VecDestroy(&xtmp));
726:   } else {
727:     MatReuse      scall;
728:     MatNullSpace *nullsp = NULL;

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

736:     for (i = 0; i < nsplit; i++) {
737:       Mat pmat;

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

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

764:       for (i = 0; i < nsplit; i++) {
765:         PetscCall(MatCreateSubMatrix(pc->mat, ilink->is, ilink->is_col, scall, &jac->mat[i]));
766:         ilink = ilink->next;
767:       }
768:       if (nullsp) PetscCall(MatRestoreNullSpaces(nsplit, jac->mat, &nullsp));
769:     }
770:   } else {
771:     jac->mat = jac->pmat;
772:   }

774:   /* Check for null space attached to IS */
775:   ilink = jac->head;
776:   for (i = 0; i < nsplit; i++) {
777:     MatNullSpace sp;

779:     PetscCall(PetscObjectQuery((PetscObject)ilink->is, "nullspace", (PetscObject *)&sp));
780:     if (sp) PetscCall(MatSetNullSpace(jac->mat[i], sp));
781:     ilink = ilink->next;
782:   }

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

800:         if (pc->flag == DIFFERENT_NONZERO_PATTERN) {
801:           PetscCall(MatDestroy(&jac->Afield[1]));
802:           scall = MAT_INITIAL_MATRIX;
803:         } else scall = MAT_REUSE_MATRIX;

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

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

841:   if (jac->type == PC_COMPOSITE_SCHUR) {
842:     PetscBool   isset, isspd = PETSC_FALSE, issym = PETSC_FALSE, flg;
843:     char        lscname[256];
844:     PetscObject LSC_L;

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

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

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

855:     if (jac->schur) {
856:       KSP      kspA = jac->head->ksp, kspInner = NULL, kspUpper = jac->kspupper;
857:       MatReuse scall;

859:       if (pc->flag == DIFFERENT_NONZERO_PATTERN) {
860:         scall = MAT_INITIAL_MATRIX;
861:         PetscCall(MatDestroy(&jac->B));
862:         PetscCall(MatDestroy(&jac->C));
863:       } else scall = MAT_REUSE_MATRIX;

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

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

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

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

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

932:         /* Set DM for new solver */
933:         PetscCall(KSPGetDM(jac->head->ksp, &dmInner));
934:         PetscCall(KSPSetDM(kspInner, dmInner));
935:         PetscCall(KSPSetDMActive(kspInner, KSP_DMACTIVE_ALL, PETSC_FALSE));

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

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

960:         PetscCall(MatSchurComplementGetKSP(jac->schur, &kspInner));
961:         PetscCall(KSPGetPC(kspInner, &pcInner));
962:         PetscCall(PetscObjectTypeCompare((PetscObject)pcInner, PCKSP, &flg));
963:         if (flg) {
964:           KSP ksp;

966:           PetscCall(PCKSPGetKSP(pcInner, &ksp));
967:           if (ksp == jac->head->ksp) PetscCall(PCSetUseAmat(pcInner, PETSC_TRUE));
968:         }
969:       }
970:       PetscCall(PetscSNPrintf(schurtestoption, sizeof(schurtestoption), "-fieldsplit_%s_upper_", ilink->splitname));
971:       PetscCall(PetscOptionsFindPairPrefix_Private(((PetscObject)pc)->options, ((PetscObject)pc)->prefix, schurtestoption, NULL, NULL, &flg));
972:       if (flg) {
973:         DM dmInner;

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

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

1027:     /* HACK: special support to forward L and Lp matrices that might be used by PCLSC */
1028:     PetscCall(PetscSNPrintf(lscname, sizeof(lscname), "%s_LSC_L", ilink->splitname));
1029:     PetscCall(PetscObjectQuery((PetscObject)pc->mat, lscname, &LSC_L));
1030:     if (!LSC_L) PetscCall(PetscObjectQuery((PetscObject)pc->pmat, lscname, &LSC_L));
1031:     if (LSC_L) PetscCall(PetscObjectCompose((PetscObject)jac->schur, "LSC_L", LSC_L));
1032:     PetscCall(PetscSNPrintf(lscname, sizeof(lscname), "%s_LSC_Lp", ilink->splitname));
1033:     PetscCall(PetscObjectQuery((PetscObject)pc->pmat, lscname, &LSC_L));
1034:     if (!LSC_L) PetscCall(PetscObjectQuery((PetscObject)pc->mat, lscname, &LSC_L));
1035:     if (LSC_L) PetscCall(PetscObjectCompose((PetscObject)jac->schur, "LSC_Lp", LSC_L));
1036:   } else if (jac->type == PC_COMPOSITE_GKB) {
1037:     PetscCheck(nsplit == 2, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_INCOMP, "To use GKB preconditioner you must have exactly 2 fields");
1038:     ilink = jac->head;
1039:     PetscCall(MatCreateSubMatrix(jac->offdiag_use_amat ? pc->mat : pc->pmat, ilink->is, ilink->next->is, MAT_INITIAL_MATRIX, &jac->B));
1040:     /* Create work vectors for GKB algorithm */
1041:     PetscCall(VecDuplicate(ilink->x, &jac->u));
1042:     PetscCall(VecDuplicate(ilink->x, &jac->Hu));
1043:     PetscCall(VecDuplicate(ilink->x, &jac->w2));
1044:     PetscCall(MatCreateSubMatrix(jac->offdiag_use_amat ? pc->mat : pc->pmat, ilink->next->is, ilink->is, MAT_INITIAL_MATRIX, &jac->C));
1045:     ilink = ilink->next;
1046:     /* Create work vectors for GKB algorithm */
1047:     PetscCall(VecDuplicate(ilink->x, &jac->v));
1048:     PetscCall(VecDuplicate(ilink->x, &jac->d));
1049:     PetscCall(VecDuplicate(ilink->x, &jac->w1));
1050:     PetscCall(MatGolubKahanComputeExplicitOperator(jac->mat[0], jac->B, jac->C, &jac->H, jac->gkbnu));
1051:     PetscCall(PetscCalloc1(jac->gkbdelay, &jac->vecz));

1053:     ilink = jac->head;
1054:     PetscCall(KSPSetOperators(ilink->ksp, jac->H, jac->H));
1055:     if (!jac->suboptionsset) PetscCall(KSPSetFromOptions(ilink->ksp));
1056:     /* Create gkb_monitor context */
1057:     if (jac->gkbmonitor) {
1058:       PetscInt tablevel;
1059:       PetscCall(PetscViewerCreate(PETSC_COMM_WORLD, &jac->gkbviewer));
1060:       PetscCall(PetscViewerSetType(jac->gkbviewer, PETSCVIEWERASCII));
1061:       PetscCall(PetscObjectGetTabLevel((PetscObject)ilink->ksp, &tablevel));
1062:       PetscCall(PetscViewerASCIISetTab(jac->gkbviewer, tablevel));
1063:       PetscCall(PetscObjectIncrementTabLevel((PetscObject)ilink->ksp, (PetscObject)ilink->ksp, 1));
1064:     }
1065:   } else {
1066:     /* set up the individual splits' PCs */
1067:     i     = 0;
1068:     ilink = jac->head;
1069:     while (ilink) {
1070:       PetscCall(KSPSetOperators(ilink->ksp, jac->mat[i], jac->pmat[i]));
1071:       /* really want setfromoptions called in PCSetFromOptions_FieldSplit(), but it is not ready yet */
1072:       if (!jac->suboptionsset) PetscCall(KSPSetFromOptions(ilink->ksp));
1073:       i++;
1074:       ilink = ilink->next;
1075:     }
1076:   }

1078:   /* Set coordinates to the sub PC objects whenever these are set */
1079:   if (jac->coordinates_set) {
1080:     PC pc_coords;
1081:     if (jac->type == PC_COMPOSITE_SCHUR) {
1082:       // Head is first block.
1083:       PetscCall(KSPGetPC(jac->head->ksp, &pc_coords));
1084:       PetscCall(PCSetCoordinates(pc_coords, jac->head->dim, jac->head->ndofs, jac->head->coords));
1085:       // Second one is Schur block, but its KSP object is in kspschur.
1086:       PetscCall(KSPGetPC(jac->kspschur, &pc_coords));
1087:       PetscCall(PCSetCoordinates(pc_coords, jac->head->next->dim, jac->head->next->ndofs, jac->head->next->coords));
1088:     } else if (jac->type == PC_COMPOSITE_GKB) {
1089:       PetscCall(PetscInfo(pc, "Warning: Setting coordinates does nothing for the GKB Fieldpslit preconditioner\n"));
1090:     } else {
1091:       ilink = jac->head;
1092:       while (ilink) {
1093:         PetscCall(KSPGetPC(ilink->ksp, &pc_coords));
1094:         PetscCall(PCSetCoordinates(pc_coords, ilink->dim, ilink->ndofs, ilink->coords));
1095:         ilink = ilink->next;
1096:       }
1097:     }
1098:   }

1100:   jac->suboptionsset = PETSC_TRUE;
1101:   PetscFunctionReturn(PETSC_SUCCESS);
1102: }

1104: static PetscErrorCode PCSetUpOnBlocks_FieldSplit_Schur(PC pc)
1105: {
1106:   PC_FieldSplit    *jac    = (PC_FieldSplit *)pc->data;
1107:   PC_FieldSplitLink ilinkA = jac->head;
1108:   KSP               kspA = ilinkA->ksp, kspUpper = jac->kspupper;

1110:   PetscFunctionBegin;
1111:   if (jac->schurfactorization == PC_FIELDSPLIT_SCHUR_FACT_FULL && kspUpper != kspA) {
1112:     PetscCall(KSPSetUp(kspUpper));
1113:     PetscCall(KSPSetUpOnBlocks(kspUpper));
1114:   }
1115:   PetscCall(KSPSetUp(kspA));
1116:   PetscCall(KSPSetUpOnBlocks(kspA));
1117:   if (jac->schurpre != PC_FIELDSPLIT_SCHUR_PRE_FULL) {
1118:     PetscCall(KSPSetUp(jac->kspschur));
1119:     PetscCall(KSPSetUpOnBlocks(jac->kspschur));
1120:   } else if (kspUpper == kspA && jac->schurfactorization == PC_FIELDSPLIT_SCHUR_FACT_FULL) {
1121:     Mat          A;
1122:     PetscInt     m, M, N;
1123:     VecType      vtype;
1124:     PetscMemType mtype;
1125:     PetscScalar *array;

1127:     PetscCall(MatGetSize(jac->B, &M, &N));
1128:     PetscCall(MatGetLocalSize(jac->B, &m, NULL));
1129:     PetscCall(MatGetVecType(jac->B, &vtype));
1130:     PetscCall(VecGetArrayAndMemType(ilinkA->x, &array, &mtype));
1131:     PetscCall(VecRestoreArrayAndMemType(ilinkA->x, &array));
1132:     PetscCall(PetscObjectQuery((PetscObject)jac->schur, "AinvB", (PetscObject *)&A));
1133:     if (A) {
1134:       PetscInt P;

1136:       PetscCall(MatGetSize(A, NULL, &P));
1137:       if (P < N + 1) { // need to recreate AinvB, otherwise, the Schur complement won't be updated
1138:         PetscCall(PetscObjectCompose((PetscObject)jac->schur, "AinvB", NULL));
1139:         A = NULL;
1140:       }
1141:     }
1142:     if (!A) {
1143:       if (PetscMemTypeHost(mtype) || (!PetscDefined(HAVE_CUDA) && !PetscDefined(HAVE_HIP))) PetscCall(PetscMalloc1(m * (N + 1), &array));
1144: #if PetscDefined(HAVE_CUDA)
1145:       else if (PetscMemTypeCUDA(mtype)) PetscCallCUDA(cudaMalloc((void **)&array, sizeof(PetscScalar) * m * (N + 1)));
1146: #endif
1147: #if PetscDefined(HAVE_HIP)
1148:       else if (PetscMemTypeHIP(mtype)) PetscCallHIP(hipMalloc((void **)&array, sizeof(PetscScalar) * m * (N + 1)));
1149: #endif
1150:       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
1151:       PetscCall(PetscObjectCompose((PetscObject)jac->schur, "AinvB", (PetscObject)A));
1152:       PetscCall(MatDestroy(&A));
1153:     }
1154:   }
1155:   PetscFunctionReturn(PETSC_SUCCESS);
1156: }

1158: static PetscErrorCode PCSetUpOnBlocks_FieldSplit(PC pc)
1159: {
1160:   PC_FieldSplit    *jac   = (PC_FieldSplit *)pc->data;
1161:   PC_FieldSplitLink ilink = jac->head;

1163:   PetscFunctionBegin;
1164:   while (ilink) {
1165:     PetscCall(KSPSetUp(ilink->ksp));
1166:     PetscCall(KSPSetUpOnBlocks(ilink->ksp));
1167:     ilink = ilink->next;
1168:   }
1169:   PetscFunctionReturn(PETSC_SUCCESS);
1170: }

1172: static PetscErrorCode PCSetUpOnBlocks_FieldSplit_GKB(PC pc)
1173: {
1174:   PC_FieldSplit    *jac    = (PC_FieldSplit *)pc->data;
1175:   PC_FieldSplitLink ilinkA = jac->head;
1176:   KSP               ksp    = ilinkA->ksp;

1178:   PetscFunctionBegin;
1179:   PetscCall(KSPSetUp(ksp));
1180:   PetscCall(KSPSetUpOnBlocks(ksp));
1181:   PetscFunctionReturn(PETSC_SUCCESS);
1182: }

1184: static PetscErrorCode PCApply_FieldSplit_Schur(PC pc, Vec x, Vec y)
1185: {
1186:   PC_FieldSplit    *jac    = (PC_FieldSplit *)pc->data;
1187:   PC_FieldSplitLink ilinkA = jac->head, ilinkD = ilinkA->next;
1188:   KSP               kspA = ilinkA->ksp, kspLower = kspA, kspUpper = jac->kspupper;
1189:   Mat               AinvB = NULL;
1190:   PetscInt          N, P;

1192:   PetscFunctionBegin;
1193:   switch (jac->schurfactorization) {
1194:   case PC_FIELDSPLIT_SCHUR_FACT_DIAG:
1195:     /* [A00 0; 0 -S], positive definite, suitable for MINRES */
1196:     PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1197:     PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1198:     PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1199:     PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1200:     PetscCall(KSPSolve(kspA, ilinkA->x, ilinkA->y));
1201:     PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1202:     PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1203:     PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1204:     PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1205:     PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1206:     PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, 1));
1207:     PetscCall(KSPSolve(jac->kspschur, ilinkD->x, ilinkD->y));
1208:     PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y));
1209:     PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, -1));
1210:     PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1211:     PetscCall(VecScale(ilinkD->y, jac->schurscale));
1212:     PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1213:     PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1214:     PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1215:     break;
1216:   case PC_FIELDSPLIT_SCHUR_FACT_LOWER:
1217:     /* [A00 0; A10 S], suitable for left preconditioning */
1218:     PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1219:     PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1220:     PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1221:     PetscCall(KSPSolve(kspA, ilinkA->x, ilinkA->y));
1222:     PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1223:     PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1224:     PetscCall(MatMult(jac->C, ilinkA->y, ilinkD->x));
1225:     PetscCall(VecScale(ilinkD->x, -1.));
1226:     PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD));
1227:     PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1228:     PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD));
1229:     PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1230:     PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, 1));
1231:     PetscCall(KSPSolve(jac->kspschur, ilinkD->x, ilinkD->y));
1232:     PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, -1));
1233:     PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y));
1234:     PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1235:     PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1236:     PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1237:     PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1238:     break;
1239:   case PC_FIELDSPLIT_SCHUR_FACT_UPPER:
1240:     /* [A00 A01; 0 S], suitable for right preconditioning */
1241:     PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1242:     PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1243:     PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1244:     PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, 1));
1245:     PetscCall(KSPSolve(jac->kspschur, ilinkD->x, ilinkD->y));
1246:     PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, -1));
1247:     PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y));
1248:     PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1249:     PetscCall(MatMult(jac->B, ilinkD->y, ilinkA->x));
1250:     PetscCall(VecScale(ilinkA->x, -1.));
1251:     PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, ADD_VALUES, SCATTER_FORWARD));
1252:     PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1253:     PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, ADD_VALUES, SCATTER_FORWARD));
1254:     PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1255:     PetscCall(KSPSolve(kspA, ilinkA->x, ilinkA->y));
1256:     PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1257:     PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1258:     PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1259:     PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1260:     PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1261:     break;
1262:   case PC_FIELDSPLIT_SCHUR_FACT_FULL:
1263:     /* [1 0; A10 A00^{-1} 1] [A00 0; 0 S] [1 A00^{-1}A01; 0 1] */
1264:     PetscCall(MatGetSize(jac->B, NULL, &P));
1265:     N = P;
1266:     PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1267:     PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1268:     PetscCall(PetscLogEventBegin(KSP_Solve_FS_L, kspLower, ilinkA->x, ilinkA->y, NULL));
1269:     if (kspUpper == kspA) {
1270:       PetscCall(PetscObjectQuery((PetscObject)jac->schur, "AinvB", (PetscObject *)&AinvB));
1271:       if (AinvB) {
1272:         PetscCall(MatGetSize(AinvB, NULL, &N));
1273:         if (N > P) { // first time PCApply_FieldSplit_Schur() is called
1274:           PetscMemType mtype;
1275:           Vec          c = NULL;
1276:           PetscScalar *array;
1277:           PetscInt     m, M;

1279:           PetscCall(MatGetSize(jac->B, &M, NULL));
1280:           PetscCall(MatGetLocalSize(jac->B, &m, NULL));
1281:           PetscCall(MatDenseGetArrayAndMemType(AinvB, &array, &mtype));
1282:           if (PetscMemTypeHost(mtype) || (!PetscDefined(HAVE_CUDA) && !PetscDefined(HAVE_HIP))) PetscCall(VecCreateMPIWithArray(PetscObjectComm((PetscObject)jac->schur), 1, m, M, array + m * P, &c));
1283: #if PetscDefined(HAVE_CUDA)
1284:           else if (PetscMemTypeCUDA(mtype)) PetscCall(VecCreateMPICUDAWithArray(PetscObjectComm((PetscObject)jac->schur), 1, m, M, array + m * P, &c));
1285: #endif
1286: #if PetscDefined(HAVE_HIP)
1287:           else if (PetscMemTypeHIP(mtype)) PetscCall(VecCreateMPIHIPWithArray(PetscObjectComm((PetscObject)jac->schur), 1, m, M, array + m * P, &c));
1288: #endif
1289:           PetscCall(MatDenseRestoreArrayAndMemType(AinvB, &array));
1290:           PetscCall(VecCopy(ilinkA->x, c));
1291:           PetscCall(MatSchurComplementComputeExplicitOperator(jac->schur, &jac->schur_user));
1292:           PetscCall(KSPSetOperators(jac->kspschur, jac->schur, jac->schur_user));
1293:           PetscCall(VecCopy(c, ilinkA->y)); // retrieve the solution as the last column of the composed Mat
1294:           PetscCall(VecDestroy(&c));
1295:         }
1296:       }
1297:     }
1298:     if (N == P) PetscCall(KSPSolve(kspLower, ilinkA->x, ilinkA->y));
1299:     PetscCall(KSPCheckSolve(kspLower, pc, ilinkA->y));
1300:     PetscCall(PetscLogEventEnd(KSP_Solve_FS_L, kspLower, ilinkA->x, ilinkA->y, NULL));
1301:     PetscCall(MatMult(jac->C, ilinkA->y, ilinkD->x));
1302:     PetscCall(VecScale(ilinkD->x, -1.0));
1303:     PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD));
1304:     PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD));

1306:     PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1307:     PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, 1));
1308:     PetscCall(KSPSolve(jac->kspschur, ilinkD->x, ilinkD->y));
1309:     PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, -1));
1310:     PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y));
1311:     PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1312:     PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));

1314:     if (kspUpper == kspA) {
1315:       if (!AinvB) {
1316:         PetscCall(MatMult(jac->B, ilinkD->y, ilinkA->y));
1317:         PetscCall(VecAXPY(ilinkA->x, -1.0, ilinkA->y));
1318:         PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1319:         PetscCall(KSPSolve(kspA, ilinkA->x, ilinkA->y));
1320:         PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1321:         PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1322:       } else PetscCall(MatMultAdd(AinvB, ilinkD->y, ilinkA->y, ilinkA->y));
1323:     } else {
1324:       PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1325:       PetscCall(KSPSolve(kspA, ilinkA->x, ilinkA->y));
1326:       PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1327:       PetscCall(MatMult(jac->B, ilinkD->y, ilinkA->x));
1328:       PetscCall(PetscLogEventBegin(KSP_Solve_FS_U, kspUpper, ilinkA->x, ilinkA->z, NULL));
1329:       PetscCall(KSPSolve(kspUpper, ilinkA->x, ilinkA->z));
1330:       PetscCall(KSPCheckSolve(kspUpper, pc, ilinkA->z));
1331:       PetscCall(PetscLogEventEnd(KSP_Solve_FS_U, kspUpper, ilinkA->x, ilinkA->z, NULL));
1332:       PetscCall(VecAXPY(ilinkA->y, -1.0, ilinkA->z));
1333:     }
1334:     PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1335:     PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1336:     PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1337:   }
1338:   PetscFunctionReturn(PETSC_SUCCESS);
1339: }

1341: /*
1342:   PCFieldSplitCreateWorkMats_Private - Allocate per-field dense work matrices for multi-RHS

1344:   Input Parameters:
1345: + pc - the PC context
1346: - X  - matrix to copy column-layout from

1348:   Notes:
1349:   If matrices already exist with correct column count, they are reused.
1350:   If column count changed, old matrices are destroyed and new ones created.
1351: */
1352: static PetscErrorCode PCFieldSplitCreateWorkMats_Private(PC pc, Mat X)
1353: {
1354:   PC_FieldSplit    *jac   = (PC_FieldSplit *)pc->data;
1355:   PC_FieldSplitLink ilink = jac->head;
1356:   PetscInt          mx, Mx, my, My, N;

1358:   PetscFunctionBegin;
1359:   while (ilink) {
1360:     /* check if reallocation needed (previous allocation with wrong column count) */
1361:     if (ilink->X) {
1362:       PetscCall(MatGetSize(ilink->X, NULL, &N));
1363:       if (N != X->cmap->N) {
1364:         PetscCall(MatDestroy(&ilink->X));
1365:         PetscCall(MatDestroy(&ilink->Y));
1366:         PetscCall(MatDestroy(&ilink->Z));
1367:       }
1368:     }
1369:     /* create if needed */
1370:     if (!ilink->X) {
1371:       VecType xtype, ytype;

1373:       PetscCall(VecGetType(ilink->x, &xtype));
1374:       PetscCall(VecGetType(ilink->y, &ytype));
1375:       PetscCall(VecGetLocalSize(ilink->x, &mx));
1376:       PetscCall(VecGetSize(ilink->x, &Mx));
1377:       PetscCall(VecGetLocalSize(ilink->y, &my));
1378:       PetscCall(VecGetSize(ilink->y, &My));
1379:       /* use default lda */
1380:       PetscCall(MatCreateDenseFromVecType(PetscObjectComm((PetscObject)pc), xtype, mx, X->cmap->n, Mx, X->cmap->N, PETSC_DECIDE, NULL, &ilink->X));
1381:       PetscCall(MatCreateDenseFromVecType(PetscObjectComm((PetscObject)pc), ytype, my, X->cmap->n, My, X->cmap->N, PETSC_DECIDE, NULL, &ilink->Y));
1382:     }
1383:     ilink = ilink->next;
1384:   }
1385:   PetscFunctionReturn(PETSC_SUCCESS);
1386: }

1388: static PetscErrorCode PCMatApply_FieldSplit_Schur(PC pc, Mat X, Mat Y)
1389: {
1390:   PC_FieldSplit    *jac    = (PC_FieldSplit *)pc->data;
1391:   PC_FieldSplitLink ilinkA = jac->head, ilinkD = ilinkA->next;
1392:   KSP               kspA = ilinkA->ksp, kspLower = kspA, kspUpper = jac->kspupper;
1393:   Mat               AinvB = NULL;
1394:   PetscInt          N, P;

1396:   PetscFunctionBegin;
1397:   /* create working matrices with the correct number of columns */
1398:   PetscCall(PCFieldSplitCreateWorkMats_Private(pc, X));
1399:   switch (jac->schurfactorization) {
1400:   case PC_FIELDSPLIT_SCHUR_FACT_DIAG:
1401:     /* [A00 0; 0 -S], positive definite, suitable for MINRES */
1402:     PetscCall(MatDenseScatter_Private(ilinkA->sctx, X, ilinkA->X, INSERT_VALUES, SCATTER_FORWARD));
1403:     PetscCall(MatDenseScatter_Private(ilinkD->sctx, X, ilinkD->X, INSERT_VALUES, SCATTER_FORWARD));
1404:     PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->X, ilinkA->Y, NULL));
1405:     PetscCall(KSPMatSolve(kspA, ilinkA->X, ilinkA->Y));
1406:     PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->X, ilinkA->Y, NULL));
1407:     PetscCall(MatDenseScatter_Private(ilinkA->sctx, ilinkA->Y, Y, INSERT_VALUES, SCATTER_REVERSE));
1408:     PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->X, ilinkD->Y, NULL));
1409:     PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, 1));
1410:     PetscCall(KSPMatSolve(jac->kspschur, ilinkD->X, ilinkD->Y));
1411:     PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, -1));
1412:     PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->X, ilinkD->Y, NULL));
1413:     PetscCall(MatScale(ilinkD->Y, jac->schurscale));
1414:     PetscCall(MatDenseScatter_Private(ilinkD->sctx, ilinkD->Y, Y, INSERT_VALUES, SCATTER_REVERSE));
1415:     break;
1416:   case PC_FIELDSPLIT_SCHUR_FACT_LOWER:
1417:     /* [A00 0; A10 S], suitable for left preconditioning */
1418:     PetscCall(MatDenseScatter_Private(ilinkA->sctx, X, ilinkA->X, INSERT_VALUES, SCATTER_FORWARD));
1419:     PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->X, ilinkA->Y, NULL));
1420:     PetscCall(KSPMatSolve(kspA, ilinkA->X, ilinkA->Y));
1421:     PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->X, ilinkA->Y, NULL));
1422:     PetscCall(MatMatMult(jac->C, ilinkA->Y, MAT_REUSE_MATRIX, PETSC_DETERMINE, &ilinkD->X));
1423:     PetscCall(MatScale(ilinkD->X, -1.0));
1424:     PetscCall(MatDenseScatter_Private(ilinkD->sctx, X, ilinkD->X, ADD_VALUES, SCATTER_FORWARD));
1425:     PetscCall(MatDenseScatter_Private(ilinkA->sctx, ilinkA->Y, Y, INSERT_VALUES, SCATTER_REVERSE));
1426:     PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->X, ilinkD->Y, NULL));
1427:     PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, 1));
1428:     PetscCall(KSPMatSolve(jac->kspschur, ilinkD->X, ilinkD->Y));
1429:     PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, -1));
1430:     PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->X, ilinkD->Y, NULL));
1431:     PetscCall(MatDenseScatter_Private(ilinkD->sctx, ilinkD->Y, Y, INSERT_VALUES, SCATTER_REVERSE));
1432:     break;
1433:   case PC_FIELDSPLIT_SCHUR_FACT_UPPER:
1434:     /* [A00 A01; 0 S], suitable for right preconditioning */
1435:     PetscCall(MatDenseScatter_Private(ilinkD->sctx, X, ilinkD->X, INSERT_VALUES, SCATTER_FORWARD));
1436:     PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->X, ilinkD->Y, NULL));
1437:     PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, 1));
1438:     PetscCall(KSPMatSolve(jac->kspschur, ilinkD->X, ilinkD->Y));
1439:     PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, -1));
1440:     PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->X, ilinkD->Y, NULL));
1441:     PetscCall(MatMatMult(jac->B, ilinkD->Y, MAT_REUSE_MATRIX, PETSC_DETERMINE, &ilinkA->X));
1442:     PetscCall(MatScale(ilinkA->X, -1.0));
1443:     PetscCall(MatDenseScatter_Private(ilinkA->sctx, X, ilinkA->X, ADD_VALUES, SCATTER_FORWARD));
1444:     PetscCall(MatDenseScatter_Private(ilinkD->sctx, ilinkD->Y, Y, INSERT_VALUES, SCATTER_REVERSE));
1445:     PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->X, ilinkA->Y, NULL));
1446:     PetscCall(KSPMatSolve(kspA, ilinkA->X, ilinkA->Y));
1447:     PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->X, ilinkA->Y, NULL));
1448:     PetscCall(MatDenseScatter_Private(ilinkA->sctx, ilinkA->Y, Y, INSERT_VALUES, SCATTER_REVERSE));
1449:     break;
1450:   case PC_FIELDSPLIT_SCHUR_FACT_FULL:
1451:     /* [1 0; A10 A00^{-1} 1] [A00 0; 0 S] [1 A00^{-1}A01; 0 1] */
1452:     PetscCall(MatGetSize(jac->B, NULL, &P));
1453:     N = P;
1454:     PetscCall(MatDenseScatter_Private(ilinkA->sctx, X, ilinkA->X, INSERT_VALUES, SCATTER_FORWARD));
1455:     PetscCall(PetscLogEventBegin(KSP_Solve_FS_L, kspLower, ilinkA->X, ilinkA->Y, NULL));
1456:     if (kspUpper == kspA) {
1457:       PetscCall(PetscObjectQuery((PetscObject)jac->schur, "AinvB", (PetscObject *)&AinvB));
1458:       if (AinvB) {
1459:         PetscCall(MatGetSize(AinvB, NULL, &N));
1460:         if (N > P) { // first time PCApply_FieldSplit_Schur() is called
1461:           PetscMemType mtype;
1462:           Mat          C = NULL;
1463:           PetscScalar *array;
1464:           PetscInt     m, M, q, Q, p;

1466:           PetscCall(MatGetSize(jac->B, &M, NULL));
1467:           PetscCall(MatGetLocalSize(jac->B, &m, NULL));
1468:           PetscCall(MatGetSize(X, NULL, &Q));
1469:           PetscCall(MatGetLocalSize(X, NULL, &q));
1470:           PetscCall(MatDenseGetArrayAndMemType(AinvB, &array, &mtype));
1471:           if (N != P + Q) {
1472:             Mat replace;

1474:             PetscCall(MatGetLocalSize(jac->B, NULL, &p));
1475:             if (PetscMemTypeCUDA(mtype)) {
1476: #if PetscDefined(HAVE_CUDA)
1477:               PetscCallCUDA(cudaFree(array));
1478:               PetscCallCUDA(cudaMalloc((void **)&array, sizeof(PetscScalar) * m * (P + Q)));
1479: #endif
1480:             } else if (PetscMemTypeHIP(mtype)) {
1481: #if PetscDefined(HAVE_HIP)
1482:               PetscCallHIP(hipFree(array));
1483:               PetscCallHIP(hipMalloc((void **)&array, sizeof(PetscScalar) * m * (P + Q)));
1484: #endif
1485:             } else {
1486:               PetscCheck(PetscMemTypeHost(mtype), PetscObjectComm((PetscObject)jac->schur), PETSC_ERR_SUP, "PetscMemType should be either PETSC_MEMTYPE_HOST, PETSC_MEMTYPE_CUDA, or PETSC_MEMTYPE_HIP");
1487:               PetscCall(PetscFree(array));
1488:               PetscCall(PetscMalloc1(m * (P + Q), &array));
1489:             }
1490:             PetscCall(MatCreateDenseWithMemType(PetscObjectComm((PetscObject)jac->schur), mtype, m, PETSC_DECIDE, M, P + Q, PETSC_DECIDE, array, &replace));
1491:             PetscCall(MatHeaderReplace(AinvB, &replace));
1492:           }
1493:           PetscCall(MatCreateDenseWithMemType(PetscObjectComm((PetscObject)jac->schur), mtype, m, q, M, Q, PETSC_DECIDE, array + m * P, &C));
1494:           PetscCall(MatDenseRestoreArrayAndMemType(AinvB, &array));
1495:           PetscCall(MatCopy(ilinkA->X, C, SAME_NONZERO_PATTERN));
1496:           PetscCall(MatSchurComplementComputeExplicitOperator(jac->schur, &jac->schur_user));
1497:           PetscCall(KSPSetOperators(jac->kspschur, jac->schur, jac->schur_user));
1498:           PetscCall(MatCopy(C, ilinkA->Y, SAME_NONZERO_PATTERN)); // retrieve solutions as last columns of the composed Mat
1499:           PetscCall(MatDestroy(&C));
1500:         }
1501:       }
1502:     }
1503:     if (N == P) PetscCall(KSPMatSolve(kspLower, ilinkA->X, ilinkA->Y));
1504:     PetscCall(PetscLogEventEnd(KSP_Solve_FS_L, kspLower, ilinkA->X, ilinkA->Y, NULL));
1505:     PetscCall(MatMatMult(jac->C, ilinkA->Y, MAT_REUSE_MATRIX, PETSC_DETERMINE, &ilinkD->X));
1506:     PetscCall(MatScale(ilinkD->X, -1.0));
1507:     PetscCall(MatDenseScatter_Private(ilinkD->sctx, X, ilinkD->X, ADD_VALUES, SCATTER_FORWARD));

1509:     PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->X, ilinkD->Y, NULL));
1510:     PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, 1));
1511:     PetscCall(KSPMatSolve(jac->kspschur, ilinkD->X, ilinkD->Y));
1512:     PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, -1));
1513:     PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->X, ilinkD->Y, NULL));
1514:     PetscCall(MatDenseScatter_Private(ilinkD->sctx, ilinkD->Y, Y, INSERT_VALUES, SCATTER_REVERSE));

1516:     if (kspUpper == kspA) {
1517:       if (!AinvB) {
1518:         PetscCall(MatMatMult(jac->B, ilinkD->Y, MAT_REUSE_MATRIX, PETSC_DETERMINE, &ilinkA->Y));
1519:         PetscCall(MatAXPY(ilinkA->X, -1.0, ilinkA->Y, SAME_NONZERO_PATTERN));
1520:         PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->X, ilinkA->Y, NULL));
1521:         PetscCall(KSPMatSolve(kspA, ilinkA->X, ilinkA->Y));
1522:         PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->X, ilinkA->Y, NULL));
1523:       } else {
1524:         PetscCall(MatMatMult(AinvB, ilinkD->Y, MAT_REUSE_MATRIX, PETSC_DETERMINE, &ilinkA->X));
1525:         PetscCall(MatAXPY(ilinkA->Y, 1.0, ilinkA->X, SAME_NONZERO_PATTERN));
1526:       }
1527:     } else {
1528:       PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->X, ilinkA->Y, NULL));
1529:       PetscCall(KSPMatSolve(kspA, ilinkA->X, ilinkA->Y));
1530:       PetscCall(MatMatMult(jac->B, ilinkD->Y, MAT_REUSE_MATRIX, PETSC_DETERMINE, &ilinkA->X));
1531:       if (!ilinkA->Z) PetscCall(MatDuplicate(ilinkA->X, MAT_DO_NOT_COPY_VALUES, &ilinkA->Z));
1532:       PetscCall(PetscLogEventBegin(KSP_Solve_FS_U, kspUpper, ilinkA->X, ilinkA->Z, NULL));
1533:       PetscCall(KSPMatSolve(kspUpper, ilinkA->X, ilinkA->Z));
1534:       PetscCall(PetscLogEventEnd(KSP_Solve_FS_U, kspUpper, ilinkA->X, ilinkA->Z, NULL));
1535:       PetscCall(MatAXPY(ilinkA->Y, -1.0, ilinkA->Z, SAME_NONZERO_PATTERN));
1536:     }
1537:     PetscCall(MatDenseScatter_Private(ilinkA->sctx, ilinkA->Y, Y, INSERT_VALUES, SCATTER_REVERSE));
1538:   }
1539:   PetscFunctionReturn(PETSC_SUCCESS);
1540: }

1542: static PetscErrorCode PCApplyTranspose_FieldSplit_Schur(PC pc, Vec x, Vec y)
1543: {
1544:   PC_FieldSplit    *jac    = (PC_FieldSplit *)pc->data;
1545:   PC_FieldSplitLink ilinkA = jac->head, ilinkD = ilinkA->next;
1546:   KSP               kspA = ilinkA->ksp, kspLower = kspA, kspUpper = jac->kspupper;

1548:   PetscFunctionBegin;
1549:   switch (jac->schurfactorization) {
1550:   case PC_FIELDSPLIT_SCHUR_FACT_DIAG:
1551:     /* [A00 0; 0 -S], positive definite, suitable for MINRES */
1552:     PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1553:     PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1554:     PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1555:     PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1556:     PetscCall(KSPSolveTranspose(kspA, ilinkA->x, ilinkA->y));
1557:     PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1558:     PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1559:     PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1560:     PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1561:     PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1562:     PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, 1));
1563:     PetscCall(KSPSolveTranspose(jac->kspschur, ilinkD->x, ilinkD->y));
1564:     PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, -1));
1565:     PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y));
1566:     PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1567:     PetscCall(VecScale(ilinkD->y, jac->schurscale));
1568:     PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1569:     PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1570:     PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1571:     break;
1572:   case PC_FIELDSPLIT_SCHUR_FACT_UPPER:
1573:     PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1574:     PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1575:     PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1576:     PetscCall(KSPSolveTranspose(kspA, ilinkA->x, ilinkA->y));
1577:     PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1578:     PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1579:     PetscCall(MatMultTranspose(jac->B, ilinkA->y, ilinkD->x));
1580:     PetscCall(VecScale(ilinkD->x, -1.));
1581:     PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD));
1582:     PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1583:     PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD));
1584:     PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1585:     PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, 1));
1586:     PetscCall(KSPSolveTranspose(jac->kspschur, ilinkD->x, ilinkD->y));
1587:     PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, -1));
1588:     PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y));
1589:     PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1590:     PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1591:     PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1592:     PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1593:     break;
1594:   case PC_FIELDSPLIT_SCHUR_FACT_LOWER:
1595:     PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1596:     PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1597:     PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1598:     PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, 1));
1599:     PetscCall(KSPSolveTranspose(jac->kspschur, ilinkD->x, ilinkD->y));
1600:     PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, -1));
1601:     PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y));
1602:     PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1603:     PetscCall(MatMultTranspose(jac->C, ilinkD->y, ilinkA->x));
1604:     PetscCall(VecScale(ilinkA->x, -1.));
1605:     PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, ADD_VALUES, SCATTER_FORWARD));
1606:     PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1607:     PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, ADD_VALUES, SCATTER_FORWARD));
1608:     PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1609:     PetscCall(KSPSolveTranspose(kspA, ilinkA->x, ilinkA->y));
1610:     PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1611:     PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1612:     PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1613:     PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1614:     PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1615:     break;
1616:   case PC_FIELDSPLIT_SCHUR_FACT_FULL:
1617:     PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1618:     PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1619:     PetscCall(PetscLogEventBegin(KSP_Solve_FS_U, kspUpper, ilinkA->x, ilinkA->y, NULL));
1620:     PetscCall(KSPSolveTranspose(kspUpper, ilinkA->x, ilinkA->y));
1621:     PetscCall(KSPCheckSolve(kspUpper, pc, ilinkA->y));
1622:     PetscCall(PetscLogEventEnd(KSP_Solve_FS_U, kspUpper, ilinkA->x, ilinkA->y, NULL));
1623:     PetscCall(MatMultTranspose(jac->B, ilinkA->y, ilinkD->x));
1624:     PetscCall(VecScale(ilinkD->x, -1.0));
1625:     PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD));
1626:     PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD));

1628:     PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1629:     PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, 1));
1630:     PetscCall(KSPSolveTranspose(jac->kspschur, ilinkD->x, ilinkD->y));
1631:     PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspA, (PetscObject)kspA, -1));
1632:     PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y));
1633:     PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1634:     PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));

1636:     if (kspLower == kspA) {
1637:       PetscCall(MatMultTranspose(jac->C, ilinkD->y, ilinkA->y));
1638:       PetscCall(VecAXPY(ilinkA->x, -1.0, ilinkA->y));
1639:       PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1640:       PetscCall(KSPSolveTranspose(kspA, ilinkA->x, ilinkA->y));
1641:       PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1642:       PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1643:     } else {
1644:       PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1645:       PetscCall(KSPSolveTranspose(kspA, ilinkA->x, ilinkA->y));
1646:       PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1647:       PetscCall(MatMultTranspose(jac->C, ilinkD->y, ilinkA->x));
1648:       PetscCall(PetscLogEventBegin(KSP_Solve_FS_L, kspLower, ilinkA->x, ilinkA->z, NULL));
1649:       PetscCall(KSPSolveTranspose(kspLower, ilinkA->x, ilinkA->z));
1650:       PetscCall(KSPCheckSolve(kspLower, pc, ilinkA->z));
1651:       PetscCall(PetscLogEventEnd(KSP_Solve_FS_L, kspLower, ilinkA->x, ilinkA->z, NULL));
1652:       PetscCall(VecAXPY(ilinkA->y, -1.0, ilinkA->z));
1653:     }
1654:     PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1655:     PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1656:     PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1657:   }
1658:   PetscFunctionReturn(PETSC_SUCCESS);
1659: }

1661: #define FieldSplitSplitSolveAdd(ilink, xx, yy) \
1662:   ((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) || \
1663:                     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) || \
1664:                     VecScatterEnd(ilink->sctx, ilink->y, yy, ADD_VALUES, SCATTER_REVERSE)))

1666: static PetscErrorCode PCApply_FieldSplit(PC pc, Vec x, Vec y)
1667: {
1668:   PC_FieldSplit    *jac   = (PC_FieldSplit *)pc->data;
1669:   PC_FieldSplitLink ilink = jac->head;
1670:   PetscInt          cnt, bs;

1672:   PetscFunctionBegin;
1673:   if (jac->type == PC_COMPOSITE_ADDITIVE) {
1674:     PetscBool matnest;

1676:     PetscCall(PetscObjectTypeCompare((PetscObject)pc->pmat, MATNEST, &matnest));
1677:     if (jac->defaultsplit && !matnest) {
1678:       PetscCall(VecGetBlockSize(x, &bs));
1679:       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);
1680:       PetscCall(VecGetBlockSize(y, &bs));
1681:       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);
1682:       PetscCall(VecStrideGatherAll(x, jac->x, INSERT_VALUES));
1683:       while (ilink) {
1684:         PetscCall(PetscLogEventBegin(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1685:         PetscCall(KSPSolve(ilink->ksp, ilink->x, ilink->y));
1686:         PetscCall(KSPCheckSolve(ilink->ksp, pc, ilink->y));
1687:         PetscCall(PetscLogEventEnd(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1688:         ilink = ilink->next;
1689:       }
1690:       PetscCall(VecStrideScatterAll(jac->y, y, INSERT_VALUES));
1691:     } else {
1692:       PetscCall(VecSet(y, 0.0));
1693:       while (ilink) {
1694:         PetscCall(FieldSplitSplitSolveAdd(ilink, x, y));
1695:         ilink = ilink->next;
1696:       }
1697:     }
1698:   } else if (jac->type == PC_COMPOSITE_MULTIPLICATIVE && jac->nsplits == 2) {
1699:     PetscCall(VecSet(y, 0.0));
1700:     /* solve on first block for first block variables */
1701:     PetscCall(VecScatterBegin(ilink->sctx, x, ilink->x, INSERT_VALUES, SCATTER_FORWARD));
1702:     PetscCall(VecScatterEnd(ilink->sctx, x, ilink->x, INSERT_VALUES, SCATTER_FORWARD));
1703:     PetscCall(PetscLogEventBegin(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1704:     PetscCall(KSPSolve(ilink->ksp, ilink->x, ilink->y));
1705:     PetscCall(KSPCheckSolve(ilink->ksp, pc, ilink->y));
1706:     PetscCall(PetscLogEventEnd(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1707:     PetscCall(VecScatterBegin(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE));
1708:     PetscCall(VecScatterEnd(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE));

1710:     /* compute the residual only onto second block variables using first block variables */
1711:     PetscCall(MatMult(jac->Afield[1], ilink->y, ilink->next->x));
1712:     ilink = ilink->next;
1713:     PetscCall(VecScale(ilink->x, -1.0));
1714:     PetscCall(VecScatterBegin(ilink->sctx, x, ilink->x, ADD_VALUES, SCATTER_FORWARD));
1715:     PetscCall(VecScatterEnd(ilink->sctx, x, ilink->x, ADD_VALUES, SCATTER_FORWARD));

1717:     /* solve on second block variables */
1718:     PetscCall(PetscLogEventBegin(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1719:     PetscCall(KSPSolve(ilink->ksp, ilink->x, ilink->y));
1720:     PetscCall(KSPCheckSolve(ilink->ksp, pc, ilink->y));
1721:     PetscCall(PetscLogEventEnd(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1722:     PetscCall(VecScatterBegin(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE));
1723:     PetscCall(VecScatterEnd(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE));
1724:   } else if (jac->type == PC_COMPOSITE_MULTIPLICATIVE || jac->type == PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE) {
1725:     if (!jac->w1) {
1726:       PetscCall(VecDuplicate(x, &jac->w1));
1727:       PetscCall(VecDuplicate(x, &jac->w2));
1728:     }
1729:     PetscCall(VecSet(y, 0.0));
1730:     PetscCall(FieldSplitSplitSolveAdd(ilink, x, y));
1731:     cnt = 1;
1732:     while (ilink->next) {
1733:       ilink = ilink->next;
1734:       /* compute the residual only over the part of the vector needed */
1735:       PetscCall(MatMult(jac->Afield[cnt++], y, ilink->x));
1736:       PetscCall(VecScale(ilink->x, -1.0));
1737:       PetscCall(VecScatterBegin(ilink->sctx, x, ilink->x, ADD_VALUES, SCATTER_FORWARD));
1738:       PetscCall(VecScatterEnd(ilink->sctx, x, ilink->x, ADD_VALUES, SCATTER_FORWARD));
1739:       PetscCall(PetscLogEventBegin(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1740:       PetscCall(KSPSolve(ilink->ksp, ilink->x, ilink->y));
1741:       PetscCall(KSPCheckSolve(ilink->ksp, pc, ilink->y));
1742:       PetscCall(PetscLogEventEnd(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1743:       PetscCall(VecScatterBegin(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE));
1744:       PetscCall(VecScatterEnd(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE));
1745:     }
1746:     if (jac->type == PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE) {
1747:       cnt -= 2;
1748:       while (ilink->previous) {
1749:         ilink = ilink->previous;
1750:         /* compute the residual only over the part of the vector needed */
1751:         PetscCall(MatMult(jac->Afield[cnt--], y, ilink->x));
1752:         PetscCall(VecScale(ilink->x, -1.0));
1753:         PetscCall(VecScatterBegin(ilink->sctx, x, ilink->x, ADD_VALUES, SCATTER_FORWARD));
1754:         PetscCall(VecScatterEnd(ilink->sctx, x, ilink->x, ADD_VALUES, SCATTER_FORWARD));
1755:         PetscCall(PetscLogEventBegin(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1756:         PetscCall(KSPSolve(ilink->ksp, ilink->x, ilink->y));
1757:         PetscCall(KSPCheckSolve(ilink->ksp, pc, ilink->y));
1758:         PetscCall(PetscLogEventEnd(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1759:         PetscCall(VecScatterBegin(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE));
1760:         PetscCall(VecScatterEnd(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE));
1761:       }
1762:     }
1763:   } else SETERRQ(PetscObjectComm((PetscObject)pc), PETSC_ERR_SUP, "Unsupported or unknown composition %d", (int)jac->type);
1764:   PetscFunctionReturn(PETSC_SUCCESS);
1765: }

1767: static PetscErrorCode PCMatApply_FieldSplit(PC pc, Mat X, Mat Y)
1768: {
1769:   PC_FieldSplit    *jac   = (PC_FieldSplit *)pc->data;
1770:   PC_FieldSplitLink ilink = jac->head;
1771:   PetscInt          cnt;

1773:   PetscFunctionBegin;
1774:   /* create working matrices with the correct number of columns */
1775:   PetscCall(PCFieldSplitCreateWorkMats_Private(pc, X));
1776:   if (jac->type == PC_COMPOSITE_ADDITIVE) {
1777:     PetscCall(MatZeroEntries(Y));
1778:     while (ilink) {
1779:       PetscCall(MatDenseScatter_Private(ilink->sctx, X, ilink->X, INSERT_VALUES, SCATTER_FORWARD));
1780:       PetscCall(PetscLogEventBegin(ilink->event, ilink->ksp, ilink->X, ilink->Y, NULL));
1781:       PetscCall(KSPMatSolve(ilink->ksp, ilink->X, ilink->Y));
1782:       PetscCall(PetscLogEventEnd(ilink->event, ilink->ksp, ilink->X, ilink->Y, NULL));
1783:       PetscCall(MatDenseScatter_Private(ilink->sctx, ilink->Y, Y, ADD_VALUES, SCATTER_REVERSE));
1784:       ilink = ilink->next;
1785:     }
1786:   } else if (jac->type == PC_COMPOSITE_MULTIPLICATIVE && jac->nsplits == 2) {
1787:     PetscCall(MatZeroEntries(Y));
1788:     PetscCall(MatDenseScatter_Private(ilink->sctx, X, ilink->X, INSERT_VALUES, SCATTER_FORWARD));
1789:     PetscCall(PetscLogEventBegin(ilink->event, ilink->ksp, ilink->X, ilink->Y, NULL));
1790:     PetscCall(KSPMatSolve(ilink->ksp, ilink->X, ilink->Y));
1791:     PetscCall(PetscLogEventEnd(ilink->event, ilink->ksp, ilink->X, ilink->Y, NULL));
1792:     PetscCall(MatDenseScatter_Private(ilink->sctx, ilink->Y, Y, ADD_VALUES, SCATTER_REVERSE));

1794:     /* compute the residual only onto second block variables using first block variables */
1795:     PetscCall(MatMatMult(jac->Afield[1], ilink->Y, MAT_REUSE_MATRIX, PETSC_DETERMINE, &ilink->next->X));
1796:     ilink = ilink->next;
1797:     PetscCall(MatScale(ilink->X, -1.0));
1798:     PetscCall(MatDenseScatter_Private(ilink->sctx, X, ilink->X, ADD_VALUES, SCATTER_FORWARD));

1800:     /* solve on second block variables */
1801:     PetscCall(PetscLogEventBegin(ilink->event, ilink->ksp, ilink->X, ilink->Y, NULL));
1802:     PetscCall(KSPMatSolve(ilink->ksp, ilink->X, ilink->Y));
1803:     PetscCall(PetscLogEventEnd(ilink->event, ilink->ksp, ilink->X, ilink->Y, NULL));
1804:     PetscCall(MatDenseScatter_Private(ilink->sctx, ilink->Y, Y, ADD_VALUES, SCATTER_REVERSE));
1805:   } else if (jac->type == PC_COMPOSITE_MULTIPLICATIVE || jac->type == PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE) {
1806:     /* general multiplicative with any number of splits */
1807:     PetscCall(MatZeroEntries(Y));
1808:     /* first split */
1809:     PetscCall(MatDenseScatter_Private(ilink->sctx, X, ilink->X, INSERT_VALUES, SCATTER_FORWARD));
1810:     PetscCall(PetscLogEventBegin(ilink->event, ilink->ksp, ilink->X, ilink->Y, NULL));
1811:     PetscCall(KSPMatSolve(ilink->ksp, ilink->X, ilink->Y));
1812:     PetscCall(PetscLogEventEnd(ilink->event, ilink->ksp, ilink->X, ilink->Y, NULL));
1813:     PetscCall(MatDenseScatter_Private(ilink->sctx, ilink->Y, Y, ADD_VALUES, SCATTER_REVERSE));
1814:     cnt = 1;
1815:     /* forward sweep */
1816:     while (ilink->next) {
1817:       ilink = ilink->next;
1818:       /* compute the residual only over the part of the vector needed */
1819:       PetscCall(MatMatMult(jac->Afield[cnt++], Y, MAT_REUSE_MATRIX, PETSC_DETERMINE, &ilink->X));
1820:       PetscCall(MatScale(ilink->X, -1.0));
1821:       PetscCall(MatDenseScatter_Private(ilink->sctx, X, ilink->X, ADD_VALUES, SCATTER_FORWARD));
1822:       PetscCall(PetscLogEventBegin(ilink->event, ilink->ksp, ilink->X, ilink->Y, NULL));
1823:       PetscCall(KSPMatSolve(ilink->ksp, ilink->X, ilink->Y));
1824:       PetscCall(PetscLogEventEnd(ilink->event, ilink->ksp, ilink->X, ilink->Y, NULL));
1825:       PetscCall(MatDenseScatter_Private(ilink->sctx, ilink->Y, Y, ADD_VALUES, SCATTER_REVERSE));
1826:     }
1827:     /* backward sweep for symmetric multiplicative */
1828:     if (jac->type == PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE) {
1829:       cnt -= 2;
1830:       while (ilink->previous) {
1831:         ilink = ilink->previous;
1832:         /* compute the residual only over the part of the vector needed */
1833:         PetscCall(MatMatMult(jac->Afield[cnt--], Y, MAT_REUSE_MATRIX, PETSC_DETERMINE, &ilink->X));
1834:         PetscCall(MatScale(ilink->X, -1.0));
1835:         PetscCall(MatDenseScatter_Private(ilink->sctx, X, ilink->X, ADD_VALUES, SCATTER_FORWARD));
1836:         PetscCall(PetscLogEventBegin(ilink->event, ilink->ksp, ilink->X, ilink->Y, NULL));
1837:         PetscCall(KSPMatSolve(ilink->ksp, ilink->X, ilink->Y));
1838:         PetscCall(PetscLogEventEnd(ilink->event, ilink->ksp, ilink->X, ilink->Y, NULL));
1839:         PetscCall(MatDenseScatter_Private(ilink->sctx, ilink->Y, Y, ADD_VALUES, SCATTER_REVERSE));
1840:       }
1841:     }
1842:   } else SETERRQ(PetscObjectComm((PetscObject)pc), PETSC_ERR_SUP, "PCMatApply() not implemented for this fieldsplit type");
1843:   PetscFunctionReturn(PETSC_SUCCESS);
1844: }

1846: static PetscErrorCode PCApply_FieldSplit_GKB(PC pc, Vec x, Vec y)
1847: {
1848:   PC_FieldSplit    *jac    = (PC_FieldSplit *)pc->data;
1849:   PC_FieldSplitLink ilinkA = jac->head, ilinkD = ilinkA->next;
1850:   KSP               ksp = ilinkA->ksp;
1851:   Vec               u, v, Hu, d, work1, work2;
1852:   PetscScalar       alpha, z, nrmz2, *vecz;
1853:   PetscReal         lowbnd, nu, beta;
1854:   PetscInt          j, iterGKB;

1856:   PetscFunctionBegin;
1857:   PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1858:   PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1859:   PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1860:   PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));

1862:   u     = jac->u;
1863:   v     = jac->v;
1864:   Hu    = jac->Hu;
1865:   d     = jac->d;
1866:   work1 = jac->w1;
1867:   work2 = jac->w2;
1868:   vecz  = jac->vecz;

1870:   /* Change RHS to comply with matrix regularization H = A + nu*B*B' */
1871:   /* Add q = q + nu*B*b */
1872:   if (jac->gkbnu) {
1873:     nu = jac->gkbnu;
1874:     PetscCall(VecScale(ilinkD->x, jac->gkbnu));
1875:     PetscCall(MatMultAdd(jac->B, ilinkD->x, ilinkA->x, ilinkA->x)); /* q = q + nu*B*b */
1876:   } else {
1877:     /* Situation when no augmented Lagrangian is used. Then we set inner  */
1878:     /* matrix N = I in [Ar13], and thus nu = 1.                           */
1879:     nu = 1;
1880:   }

1882:   /* Transform rhs from [q,tilde{b}] to [0,b] */
1883:   PetscCall(PetscLogEventBegin(ilinkA->event, ksp, ilinkA->x, ilinkA->y, NULL));
1884:   PetscCall(KSPSolve(ksp, ilinkA->x, ilinkA->y));
1885:   PetscCall(KSPCheckSolve(ksp, pc, ilinkA->y));
1886:   PetscCall(PetscLogEventEnd(ilinkA->event, ksp, ilinkA->x, ilinkA->y, NULL));
1887:   PetscCall(MatMultHermitianTranspose(jac->B, ilinkA->y, work1));
1888:   PetscCall(VecAXPBY(work1, 1.0 / nu, -1.0, ilinkD->x)); /* c = b - B'*x        */

1890:   /* First step of algorithm */
1891:   PetscCall(VecNorm(work1, NORM_2, &beta)); /* beta = sqrt(nu*c'*c)*/
1892:   KSPCheckDot(ksp, beta);
1893:   beta = PetscSqrtReal(nu) * beta;
1894:   PetscCall(VecAXPBY(v, nu / beta, 0.0, work1)); /* v = nu/beta *c      */
1895:   PetscCall(MatMult(jac->B, v, work2));          /* u = H^{-1}*B*v      */
1896:   PetscCall(PetscLogEventBegin(ilinkA->event, ksp, work2, u, NULL));
1897:   PetscCall(KSPSolve(ksp, work2, u));
1898:   PetscCall(KSPCheckSolve(ksp, pc, u));
1899:   PetscCall(PetscLogEventEnd(ilinkA->event, ksp, work2, u, NULL));
1900:   PetscCall(MatMult(jac->H, u, Hu)); /* alpha = u'*H*u      */
1901:   PetscCall(VecDot(Hu, u, &alpha));
1902:   KSPCheckDot(ksp, alpha);
1903:   PetscCheck(PetscRealPart(alpha) > 0.0, PETSC_COMM_SELF, PETSC_ERR_NOT_CONVERGED, "GKB preconditioner diverged, H is not positive definite");
1904:   alpha = PetscSqrtReal(PetscAbsScalar(alpha));
1905:   PetscCall(VecScale(u, 1.0 / alpha));
1906:   PetscCall(VecAXPBY(d, 1.0 / alpha, 0.0, v)); /* v = nu/beta *c      */

1908:   z       = beta / alpha;
1909:   vecz[1] = z;

1911:   /* Computation of first iterate x(1) and p(1) */
1912:   PetscCall(VecAXPY(ilinkA->y, z, u));
1913:   PetscCall(VecCopy(d, ilinkD->y));
1914:   PetscCall(VecScale(ilinkD->y, -z));

1916:   iterGKB = 1;
1917:   lowbnd  = 2 * jac->gkbtol;
1918:   if (jac->gkbmonitor) PetscCall(PetscViewerASCIIPrintf(jac->gkbviewer, "%3" PetscInt_FMT " GKB Lower bound estimate %14.12e\n", iterGKB, (double)lowbnd));

1920:   while (iterGKB < jac->gkbmaxit && lowbnd > jac->gkbtol) {
1921:     iterGKB += 1;
1922:     PetscCall(MatMultHermitianTranspose(jac->B, u, work1)); /* v <- nu*(B'*u-alpha/nu*v) */
1923:     PetscCall(VecAXPBY(v, nu, -alpha, work1));
1924:     PetscCall(VecNorm(v, NORM_2, &beta)); /* beta = sqrt(nu)*v'*v      */
1925:     beta = beta / PetscSqrtReal(nu);
1926:     PetscCall(VecScale(v, 1.0 / beta));
1927:     PetscCall(MatMult(jac->B, v, work2)); /* u <- H^{-1}*(B*v-beta*H*u) */
1928:     PetscCall(MatMult(jac->H, u, Hu));
1929:     PetscCall(VecAXPY(work2, -beta, Hu));
1930:     PetscCall(PetscLogEventBegin(ilinkA->event, ksp, work2, u, NULL));
1931:     PetscCall(KSPSolve(ksp, work2, u));
1932:     PetscCall(KSPCheckSolve(ksp, pc, u));
1933:     PetscCall(PetscLogEventEnd(ilinkA->event, ksp, work2, u, NULL));
1934:     PetscCall(MatMult(jac->H, u, Hu)); /* alpha = u'*H*u            */
1935:     PetscCall(VecDot(Hu, u, &alpha));
1936:     KSPCheckDot(ksp, alpha);
1937:     PetscCheck(PetscRealPart(alpha) > 0.0, PETSC_COMM_SELF, PETSC_ERR_NOT_CONVERGED, "GKB preconditioner diverged, H is not positive definite");
1938:     alpha = PetscSqrtReal(PetscAbsScalar(alpha));
1939:     PetscCall(VecScale(u, 1.0 / alpha));

1941:     z       = -beta / alpha * z; /* z <- beta/alpha*z     */
1942:     vecz[0] = z;

1944:     /* Computation of new iterate x(i+1) and p(i+1) */
1945:     PetscCall(VecAXPBY(d, 1.0 / alpha, -beta / alpha, v)); /* d = (v-beta*d)/alpha */
1946:     PetscCall(VecAXPY(ilinkA->y, z, u));                   /* r = r + z*u          */
1947:     PetscCall(VecAXPY(ilinkD->y, -z, d));                  /* p = p - z*d          */
1948:     PetscCall(MatMult(jac->H, ilinkA->y, Hu));             /* ||u||_H = u'*H*u     */
1949:     PetscCall(VecDot(Hu, ilinkA->y, &nrmz2));

1951:     /* Compute Lower Bound estimate */
1952:     if (iterGKB > jac->gkbdelay) {
1953:       lowbnd = 0.0;
1954:       for (j = 0; j < jac->gkbdelay; j++) lowbnd += PetscAbsScalar(vecz[j] * vecz[j]);
1955:       lowbnd = PetscSqrtReal(lowbnd / PetscAbsScalar(nrmz2));
1956:     }

1958:     for (j = 0; j < jac->gkbdelay - 1; j++) vecz[jac->gkbdelay - j - 1] = vecz[jac->gkbdelay - j - 2];
1959:     if (jac->gkbmonitor) PetscCall(PetscViewerASCIIPrintf(jac->gkbviewer, "%3" PetscInt_FMT " GKB Lower bound estimate %14.12e\n", iterGKB, (double)lowbnd));
1960:   }

1962:   PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1963:   PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1964:   PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1965:   PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1966:   PetscFunctionReturn(PETSC_SUCCESS);
1967: }

1969: #define FieldSplitSplitSolveAddTranspose(ilink, xx, yy) \
1970:   ((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) || \
1971:                     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) || \
1972:                     VecScatterEnd(ilink->sctx, ilink->x, yy, ADD_VALUES, SCATTER_REVERSE)))

1974: static PetscErrorCode PCApplyTranspose_FieldSplit(PC pc, Vec x, Vec y)
1975: {
1976:   PC_FieldSplit    *jac   = (PC_FieldSplit *)pc->data;
1977:   PC_FieldSplitLink ilink = jac->head;
1978:   PetscInt          bs;

1980:   PetscFunctionBegin;
1981:   if (jac->type == PC_COMPOSITE_ADDITIVE) {
1982:     PetscBool matnest;

1984:     PetscCall(PetscObjectTypeCompare((PetscObject)pc->pmat, MATNEST, &matnest));
1985:     if (jac->defaultsplit && !matnest) {
1986:       PetscCall(VecGetBlockSize(x, &bs));
1987:       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);
1988:       PetscCall(VecGetBlockSize(y, &bs));
1989:       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);
1990:       PetscCall(VecStrideGatherAll(x, jac->x, INSERT_VALUES));
1991:       while (ilink) {
1992:         PetscCall(PetscLogEventBegin(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1993:         PetscCall(KSPSolveTranspose(ilink->ksp, ilink->x, ilink->y));
1994:         PetscCall(KSPCheckSolve(ilink->ksp, pc, ilink->y));
1995:         PetscCall(PetscLogEventEnd(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1996:         ilink = ilink->next;
1997:       }
1998:       PetscCall(VecStrideScatterAll(jac->y, y, INSERT_VALUES));
1999:     } else {
2000:       PetscCall(VecSet(y, 0.0));
2001:       while (ilink) {
2002:         PetscCall(FieldSplitSplitSolveAddTranspose(ilink, x, y));
2003:         ilink = ilink->next;
2004:       }
2005:     }
2006:   } else {
2007:     if (!jac->w1) {
2008:       PetscCall(VecDuplicate(x, &jac->w1));
2009:       PetscCall(VecDuplicate(x, &jac->w2));
2010:     }
2011:     PetscCall(VecSet(y, 0.0));
2012:     if (jac->type == PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE) {
2013:       PetscCall(FieldSplitSplitSolveAddTranspose(ilink, x, y));
2014:       while (ilink->next) {
2015:         ilink = ilink->next;
2016:         PetscCall(MatMultTranspose(pc->mat, y, jac->w1));
2017:         PetscCall(VecWAXPY(jac->w2, -1.0, jac->w1, x));
2018:         PetscCall(FieldSplitSplitSolveAddTranspose(ilink, jac->w2, y));
2019:       }
2020:       while (ilink->previous) {
2021:         ilink = ilink->previous;
2022:         PetscCall(MatMultTranspose(pc->mat, y, jac->w1));
2023:         PetscCall(VecWAXPY(jac->w2, -1.0, jac->w1, x));
2024:         PetscCall(FieldSplitSplitSolveAddTranspose(ilink, jac->w2, y));
2025:       }
2026:     } else {
2027:       while (ilink->next) { /* get to last entry in linked list */
2028:         ilink = ilink->next;
2029:       }
2030:       PetscCall(FieldSplitSplitSolveAddTranspose(ilink, x, y));
2031:       while (ilink->previous) {
2032:         ilink = ilink->previous;
2033:         PetscCall(MatMultTranspose(pc->mat, y, jac->w1));
2034:         PetscCall(VecWAXPY(jac->w2, -1.0, jac->w1, x));
2035:         PetscCall(FieldSplitSplitSolveAddTranspose(ilink, jac->w2, y));
2036:       }
2037:     }
2038:   }
2039:   PetscFunctionReturn(PETSC_SUCCESS);
2040: }

2042: static PetscErrorCode PCReset_FieldSplit(PC pc)
2043: {
2044:   PC_FieldSplit    *jac   = (PC_FieldSplit *)pc->data;
2045:   PC_FieldSplitLink ilink = jac->head, next;

2047:   PetscFunctionBegin;
2048:   while (ilink) {
2049:     PetscCall(KSPDestroy(&ilink->ksp));
2050:     PetscCall(VecDestroy(&ilink->x));
2051:     PetscCall(VecDestroy(&ilink->y));
2052:     PetscCall(VecDestroy(&ilink->z));
2053:     PetscCall(MatDestroy(&ilink->X));
2054:     PetscCall(MatDestroy(&ilink->Y));
2055:     PetscCall(MatDestroy(&ilink->Z));
2056:     PetscCall(VecScatterDestroy(&ilink->sctx));
2057:     PetscCall(ISDestroy(&ilink->is));
2058:     PetscCall(ISDestroy(&ilink->is_col));
2059:     PetscCall(PetscFree(ilink->splitname));
2060:     PetscCall(PetscFree(ilink->fields));
2061:     PetscCall(PetscFree(ilink->fields_col));
2062:     next = ilink->next;
2063:     PetscCall(PetscFree(ilink));
2064:     ilink = next;
2065:   }
2066:   jac->head = NULL;
2067:   PetscCall(PetscFree2(jac->x, jac->y));
2068:   if (jac->mat && jac->mat != jac->pmat) {
2069:     PetscCall(MatDestroyMatrices(jac->nsplits, &jac->mat));
2070:   } else if (jac->mat) {
2071:     jac->mat = NULL;
2072:   }
2073:   if (jac->pmat) PetscCall(MatDestroyMatrices(jac->nsplits, &jac->pmat));
2074:   if (jac->Afield) PetscCall(MatDestroyMatrices(jac->nsplits, &jac->Afield));
2075:   jac->nsplits = 0;
2076:   PetscCall(VecDestroy(&jac->w1));
2077:   PetscCall(VecDestroy(&jac->w2));
2078:   if (jac->schur) PetscCall(PetscObjectCompose((PetscObject)jac->schur, "AinvB", NULL));
2079:   PetscCall(MatDestroy(&jac->schur));
2080:   PetscCall(MatDestroy(&jac->schurp));
2081:   PetscCall(MatDestroy(&jac->schur_user));
2082:   PetscCall(KSPDestroy(&jac->kspschur));
2083:   PetscCall(KSPDestroy(&jac->kspupper));
2084:   PetscCall(MatDestroy(&jac->B));
2085:   PetscCall(MatDestroy(&jac->C));
2086:   PetscCall(MatDestroy(&jac->H));
2087:   PetscCall(VecDestroy(&jac->u));
2088:   PetscCall(VecDestroy(&jac->v));
2089:   PetscCall(VecDestroy(&jac->Hu));
2090:   PetscCall(VecDestroy(&jac->d));
2091:   PetscCall(PetscFree(jac->vecz));
2092:   PetscCall(PetscViewerDestroy(&jac->gkbviewer));
2093:   jac->isrestrict = PETSC_FALSE;
2094:   PetscFunctionReturn(PETSC_SUCCESS);
2095: }

2097: static PetscErrorCode PCDestroy_FieldSplit(PC pc)
2098: {
2099:   PetscFunctionBegin;
2100:   PetscCall(PCReset_FieldSplit(pc));
2101:   PetscCall(PetscFree(pc->data));
2102:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCSetCoordinates_C", NULL));
2103:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetFields_C", NULL));
2104:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetIS_C", NULL));
2105:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetType_C", NULL));
2106:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetBlockSize_C", NULL));
2107:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitRestrictIS_C", NULL));
2108:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSchurGetSubKSP_C", NULL));
2109:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSubKSP_C", NULL));
2110:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBTol_C", NULL));
2111:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBMaxit_C", NULL));
2112:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBNu_C", NULL));
2113:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBDelay_C", NULL));
2114:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurPre_C", NULL));
2115:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSchurPre_C", NULL));
2116:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurFactType_C", NULL));
2117:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurScale_C", NULL));
2118:   PetscFunctionReturn(PETSC_SUCCESS);
2119: }

2121: static PetscErrorCode PCSetFromOptions_FieldSplit(PC pc, PetscOptionItems PetscOptionsObject)
2122: {
2123:   PetscInt        bs;
2124:   PetscBool       flg;
2125:   PC_FieldSplit  *jac = (PC_FieldSplit *)pc->data;
2126:   PCCompositeType ctype;

2128:   PetscFunctionBegin;
2129:   PetscOptionsHeadBegin(PetscOptionsObject, "FieldSplit options");
2130:   PetscCall(PetscOptionsBool("-pc_fieldsplit_dm_splits", "Whether to use DMCreateFieldDecomposition() for splits", "PCFieldSplitSetDMSplits", jac->dm_splits, &jac->dm_splits, NULL));
2131:   PetscCall(PetscOptionsInt("-pc_fieldsplit_block_size", "Blocksize that defines number of fields", "PCFieldSplitSetBlockSize", jac->bs, &bs, &flg));
2132:   if (flg) PetscCall(PCFieldSplitSetBlockSize(pc, bs));
2133:   jac->diag_use_amat = pc->useAmat;
2134:   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));
2135:   jac->offdiag_use_amat = pc->useAmat;
2136:   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));
2137:   PetscCall(PetscOptionsBool("-pc_fieldsplit_detect_saddle_point", "Form 2-way split by detecting zero diagonal entries", "PCFieldSplitSetDetectSaddlePoint", jac->detect, &jac->detect, NULL));
2138:   PetscCall(PCFieldSplitSetDetectSaddlePoint(pc, jac->detect)); /* Sets split type and Schur PC type */
2139:   PetscCall(PetscOptionsEnum("-pc_fieldsplit_type", "Type of composition", "PCFieldSplitSetType", PCCompositeTypes, (PetscEnum)jac->type, (PetscEnum *)&ctype, &flg));
2140:   if (flg) PetscCall(PCFieldSplitSetType(pc, ctype));
2141:   /* Only setup fields once */
2142:   if (jac->bs > 0 && jac->nsplits == 0) {
2143:     /* only allow user to set fields from command line.
2144:        otherwise user can set them in PCFieldSplitSetDefaults() */
2145:     PetscCall(PCFieldSplitSetRuntimeSplits_Private(pc));
2146:     if (jac->splitdefined) PetscCall(PetscInfo(pc, "Splits defined using the options database\n"));
2147:   }
2148:   if (jac->type == PC_COMPOSITE_SCHUR) {
2149:     PetscCall(PetscOptionsGetEnum(((PetscObject)pc)->options, ((PetscObject)pc)->prefix, "-pc_fieldsplit_schur_factorization_type", PCFieldSplitSchurFactTypes, (PetscEnum *)&jac->schurfactorization, &flg));
2150:     if (flg) PetscCall(PetscInfo(pc, "Deprecated use of -pc_fieldsplit_schur_factorization_type\n"));
2151:     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));
2152:     PetscCall(PetscOptionsEnum("-pc_fieldsplit_schur_precondition", "How to build preconditioner for Schur complement", "PCFieldSplitSetSchurPre", PCFieldSplitSchurPreTypes, (PetscEnum)jac->schurpre, (PetscEnum *)&jac->schurpre, NULL));
2153:     PetscCall(PetscOptionsScalar("-pc_fieldsplit_schur_scale", "Scale Schur complement", "PCFieldSplitSetSchurScale", jac->schurscale, &jac->schurscale, NULL));
2154:   } else if (jac->type == PC_COMPOSITE_GKB) {
2155:     PetscCall(PetscOptionsReal("-pc_fieldsplit_gkb_tol", "The tolerance for the lower bound stopping criterion", "PCFieldSplitSetGKBTol", jac->gkbtol, &jac->gkbtol, NULL));
2156:     PetscCall(PetscOptionsInt("-pc_fieldsplit_gkb_delay", "The delay value for lower bound criterion", "PCFieldSplitSetGKBDelay", jac->gkbdelay, &jac->gkbdelay, NULL));
2157:     PetscCall(PetscOptionsBoundedReal("-pc_fieldsplit_gkb_nu", "Parameter in augmented Lagrangian approach", "PCFieldSplitSetGKBNu", jac->gkbnu, &jac->gkbnu, NULL, 0.0));
2158:     PetscCall(PetscOptionsInt("-pc_fieldsplit_gkb_maxit", "Maximum allowed number of iterations", "PCFieldSplitSetGKBMaxit", jac->gkbmaxit, &jac->gkbmaxit, NULL));
2159:     PetscCall(PetscOptionsBool("-pc_fieldsplit_gkb_monitor", "Prints number of GKB iterations and error", "PCFieldSplitGKB", jac->gkbmonitor, &jac->gkbmonitor, NULL));
2160:   }
2161:   /*
2162:     In the initial call to this routine the sub-solver data structures do not exist so we cannot call KSPSetFromOptions() on them yet.
2163:     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
2164:     is called on the outer solver in case changes were made in the options database

2166:     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()
2167:     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.
2168:     Without this extra check test p2p1fetidp_olof_full and others fail with incorrect matrix types.

2170:     There could be a negative side effect of calling the KSPSetFromOptions() below.

2172:     If one captured the PetscObjectState of the options database one could skip these calls if the database has not changed from the previous call
2173:   */
2174:   if (jac->issetup) {
2175:     PC_FieldSplitLink ilink = jac->head;
2176:     if (jac->type == PC_COMPOSITE_SCHUR) {
2177:       if (jac->kspupper && jac->kspupper->totalits > 0) PetscCall(KSPSetFromOptions(jac->kspupper));
2178:       if (jac->kspschur && jac->kspschur->totalits > 0) PetscCall(KSPSetFromOptions(jac->kspschur));
2179:     }
2180:     while (ilink) {
2181:       if (ilink->ksp->totalits > 0) PetscCall(KSPSetFromOptions(ilink->ksp));
2182:       ilink = ilink->next;
2183:     }
2184:   }
2185:   PetscOptionsHeadEnd();
2186:   PetscFunctionReturn(PETSC_SUCCESS);
2187: }

2189: static PetscErrorCode PCFieldSplitSetFields_FieldSplit(PC pc, const char splitname[], PetscInt n, const PetscInt *fields, const PetscInt *fields_col)
2190: {
2191:   PC_FieldSplit    *jac = (PC_FieldSplit *)pc->data;
2192:   PC_FieldSplitLink ilink, next = jac->head;
2193:   char              prefix[128];
2194:   PetscInt          i;
2195:   PetscLogEvent     nse;

2197:   PetscFunctionBegin;
2198:   if (jac->splitdefined) {
2199:     PetscCall(PetscInfo(pc, "Ignoring new split \"%s\" because the splits have already been defined\n", splitname));
2200:     PetscFunctionReturn(PETSC_SUCCESS);
2201:   }
2202:   for (i = 0; i < n; i++) PetscCheck(fields[i] >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Negative field %" PetscInt_FMT " requested", fields[i]);
2203:   PetscCall(PetscNew(&ilink));
2204:   if (splitname) {
2205:     PetscCall(PetscStrallocpy(splitname, &ilink->splitname));
2206:   } else {
2207:     PetscCall(PetscMalloc1(3, &ilink->splitname));
2208:     PetscCall(PetscSNPrintf(ilink->splitname, 2, "%" PetscInt_FMT, jac->nsplits));
2209:   }
2210:   PetscCall(PetscMPIIntCast(jac->nsplits, &nse));
2211:   ilink->event = jac->nsplits < 5 ? KSP_Solve_FS_0 + nse : KSP_Solve_FS_0 + 4; /* Splits greater than 4 logged in 4th split */
2212:   PetscCall(PetscMalloc1(n, &ilink->fields));
2213:   PetscCall(PetscArraycpy(ilink->fields, fields, n));
2214:   PetscCall(PetscMalloc1(n, &ilink->fields_col));
2215:   PetscCall(PetscArraycpy(ilink->fields_col, fields_col, n));

2217:   ilink->nfields = n;
2218:   ilink->next    = NULL;
2219:   PetscCall(KSPCreate(PetscObjectComm((PetscObject)pc), &ilink->ksp));
2220:   PetscCall(KSPSetNestLevel(ilink->ksp, pc->kspnestlevel));
2221:   PetscCall(KSPSetErrorIfNotConverged(ilink->ksp, pc->erroriffailure));
2222:   PetscCall(PetscObjectIncrementTabLevel((PetscObject)ilink->ksp, (PetscObject)pc, 1));
2223:   PetscCall(KSPSetType(ilink->ksp, KSPPREONLY));

2225:   PetscCall(PetscSNPrintf(prefix, sizeof(prefix), "%sfieldsplit_%s_", ((PetscObject)pc)->prefix ? ((PetscObject)pc)->prefix : "", ilink->splitname));
2226:   PetscCall(KSPSetOptionsPrefix(ilink->ksp, prefix));

2228:   if (!next) {
2229:     jac->head       = ilink;
2230:     ilink->previous = NULL;
2231:   } else {
2232:     while (next->next) next = next->next;
2233:     next->next      = ilink;
2234:     ilink->previous = next;
2235:   }
2236:   jac->nsplits++;
2237:   PetscFunctionReturn(PETSC_SUCCESS);
2238: }

2240: static PetscErrorCode PCFieldSplitSchurGetSubKSP_FieldSplit(PC pc, PetscInt *n, KSP **subksp)
2241: {
2242:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

2244:   PetscFunctionBegin;
2245:   *subksp = NULL;
2246:   if (n) *n = 0;
2247:   if (jac->type == PC_COMPOSITE_SCHUR) {
2248:     PetscInt nn;

2250:     PetscCheck(jac->schur, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONGSTATE, "Must call KSPSetUp() or PCSetUp() before calling PCFieldSplitSchurGetSubKSP()");
2251:     PetscCheck(jac->nsplits == 2, PetscObjectComm((PetscObject)pc), PETSC_ERR_PLIB, "Unexpected number of splits %" PetscInt_FMT " != 2", jac->nsplits);
2252:     nn = jac->nsplits + (jac->kspupper != jac->head->ksp ? 1 : 0);
2253:     PetscCall(PetscMalloc1(nn, subksp));
2254:     (*subksp)[0] = jac->head->ksp;
2255:     (*subksp)[1] = jac->kspschur;
2256:     if (jac->kspupper != jac->head->ksp) (*subksp)[2] = jac->kspupper;
2257:     if (n) *n = nn;
2258:   }
2259:   PetscFunctionReturn(PETSC_SUCCESS);
2260: }

2262: static PetscErrorCode PCFieldSplitGetSubKSP_FieldSplit_Schur(PC pc, PetscInt *n, KSP **subksp)
2263: {
2264:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

2266:   PetscFunctionBegin;
2267:   PetscCheck(jac->schur, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONGSTATE, "Must call KSPSetUp() or PCSetUp() before calling PCFieldSplitGetSubKSP()");
2268:   PetscCall(PetscMalloc1(jac->nsplits, subksp));
2269:   PetscCall(MatSchurComplementGetKSP(jac->schur, *subksp));

2271:   (*subksp)[1] = jac->kspschur;
2272:   if (n) *n = jac->nsplits;
2273:   PetscFunctionReturn(PETSC_SUCCESS);
2274: }

2276: static PetscErrorCode PCFieldSplitGetSubKSP_FieldSplit(PC pc, PetscInt *n, KSP **subksp)
2277: {
2278:   PC_FieldSplit    *jac   = (PC_FieldSplit *)pc->data;
2279:   PetscInt          cnt   = 0;
2280:   PC_FieldSplitLink ilink = jac->head;

2282:   PetscFunctionBegin;
2283:   PetscCall(PetscMalloc1(jac->nsplits, subksp));
2284:   while (ilink) {
2285:     (*subksp)[cnt++] = ilink->ksp;
2286:     ilink            = ilink->next;
2287:   }
2288:   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);
2289:   if (n) *n = jac->nsplits;
2290:   PetscFunctionReturn(PETSC_SUCCESS);
2291: }

2293: /*@
2294:   PCFieldSplitRestrictIS - Restricts the fieldsplit `IS`s to be within a given `IS`.

2296:   Input Parameters:
2297: + pc  - the preconditioner context
2298: - isy - the index set that defines the indices to which the fieldsplit is to be restricted

2300:   Level: advanced

2302:   Developer Notes:
2303:   It seems the resulting `IS`s will not cover the entire space, so
2304:   how can they define a convergent preconditioner? Needs explaining.

2306: .seealso: [](sec_block_matrices), `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSetIS()`
2307: @*/
2308: PetscErrorCode PCFieldSplitRestrictIS(PC pc, IS isy)
2309: {
2310:   PetscFunctionBegin;
2313:   PetscTryMethod(pc, "PCFieldSplitRestrictIS_C", (PC, IS), (pc, isy));
2314:   PetscFunctionReturn(PETSC_SUCCESS);
2315: }

2317: static PetscErrorCode PCFieldSplitRestrictIS_FieldSplit(PC pc, IS isy)
2318: {
2319:   PC_FieldSplit    *jac   = (PC_FieldSplit *)pc->data;
2320:   PC_FieldSplitLink ilink = jac->head, next;
2321:   PetscInt          localsize, size, sizez, i;
2322:   const PetscInt   *ind, *indz;
2323:   PetscInt         *indc, *indcz;
2324:   PetscBool         flg;

2326:   PetscFunctionBegin;
2327:   PetscCall(ISGetLocalSize(isy, &localsize));
2328:   PetscCallMPI(MPI_Scan(&localsize, &size, 1, MPIU_INT, MPI_SUM, PetscObjectComm((PetscObject)isy)));
2329:   size -= localsize;
2330:   while (ilink) {
2331:     IS isrl, isr;
2332:     PC subpc;
2333:     PetscCall(ISEmbed(ilink->is, isy, PETSC_TRUE, &isrl));
2334:     PetscCall(ISGetLocalSize(isrl, &localsize));
2335:     PetscCall(PetscMalloc1(localsize, &indc));
2336:     PetscCall(ISGetIndices(isrl, &ind));
2337:     PetscCall(PetscArraycpy(indc, ind, localsize));
2338:     PetscCall(ISRestoreIndices(isrl, &ind));
2339:     PetscCall(ISDestroy(&isrl));
2340:     for (i = 0; i < localsize; i++) *(indc + i) += size;
2341:     PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)isy), localsize, indc, PETSC_OWN_POINTER, &isr));
2342:     PetscCall(PetscObjectReference((PetscObject)isr));
2343:     PetscCall(ISDestroy(&ilink->is));
2344:     ilink->is = isr;
2345:     PetscCall(PetscObjectReference((PetscObject)isr));
2346:     PetscCall(ISDestroy(&ilink->is_col));
2347:     ilink->is_col = isr;
2348:     PetscCall(ISDestroy(&isr));
2349:     PetscCall(KSPGetPC(ilink->ksp, &subpc));
2350:     PetscCall(PetscObjectTypeCompare((PetscObject)subpc, PCFIELDSPLIT, &flg));
2351:     if (flg) {
2352:       IS       iszl, isz;
2353:       MPI_Comm comm;
2354:       PetscCall(ISGetLocalSize(ilink->is, &localsize));
2355:       comm = PetscObjectComm((PetscObject)ilink->is);
2356:       PetscCall(ISEmbed(isy, ilink->is, PETSC_TRUE, &iszl));
2357:       PetscCallMPI(MPI_Scan(&localsize, &sizez, 1, MPIU_INT, MPI_SUM, comm));
2358:       sizez -= localsize;
2359:       PetscCall(ISGetLocalSize(iszl, &localsize));
2360:       PetscCall(PetscMalloc1(localsize, &indcz));
2361:       PetscCall(ISGetIndices(iszl, &indz));
2362:       PetscCall(PetscArraycpy(indcz, indz, localsize));
2363:       PetscCall(ISRestoreIndices(iszl, &indz));
2364:       PetscCall(ISDestroy(&iszl));
2365:       for (i = 0; i < localsize; i++) *(indcz + i) += sizez;
2366:       PetscCall(ISCreateGeneral(comm, localsize, indcz, PETSC_OWN_POINTER, &isz));
2367:       PetscCall(PCFieldSplitRestrictIS(subpc, isz));
2368:       PetscCall(ISDestroy(&isz));
2369:     }
2370:     next  = ilink->next;
2371:     ilink = next;
2372:   }
2373:   jac->isrestrict = PETSC_TRUE;
2374:   PetscFunctionReturn(PETSC_SUCCESS);
2375: }

2377: static PetscErrorCode PCFieldSplitSetIS_FieldSplit(PC pc, const char splitname[], IS is)
2378: {
2379:   PC_FieldSplit    *jac = (PC_FieldSplit *)pc->data;
2380:   PC_FieldSplitLink ilink, next = jac->head;
2381:   char              prefix[128];
2382:   PetscLogEvent     nse;

2384:   PetscFunctionBegin;
2385:   if (jac->splitdefined) {
2386:     PetscCall(PetscInfo(pc, "Ignoring new split \"%s\" because the splits have already been defined\n", splitname));
2387:     PetscFunctionReturn(PETSC_SUCCESS);
2388:   }
2389:   PetscCall(PetscNew(&ilink));
2390:   if (splitname) {
2391:     PetscCall(PetscStrallocpy(splitname, &ilink->splitname));
2392:   } else {
2393:     PetscCall(PetscMalloc1(8, &ilink->splitname));
2394:     PetscCall(PetscSNPrintf(ilink->splitname, 7, "%" PetscInt_FMT, jac->nsplits));
2395:   }
2396:   PetscCall(PetscMPIIntCast(jac->nsplits, &nse));
2397:   ilink->event = jac->nsplits < 5 ? KSP_Solve_FS_0 + nse : KSP_Solve_FS_0 + 4; /* Splits greater than 4 logged in 4th split */
2398:   PetscCall(PetscObjectReference((PetscObject)is));
2399:   PetscCall(ISDestroy(&ilink->is));
2400:   ilink->is = is;
2401:   PetscCall(PetscObjectReference((PetscObject)is));
2402:   PetscCall(ISDestroy(&ilink->is_col));
2403:   ilink->is_col = is;
2404:   ilink->next   = NULL;
2405:   PetscCall(KSPCreate(PetscObjectComm((PetscObject)pc), &ilink->ksp));
2406:   PetscCall(KSPSetNestLevel(ilink->ksp, pc->kspnestlevel));
2407:   PetscCall(KSPSetErrorIfNotConverged(ilink->ksp, pc->erroriffailure));
2408:   PetscCall(PetscObjectIncrementTabLevel((PetscObject)ilink->ksp, (PetscObject)pc, 1));
2409:   PetscCall(KSPSetType(ilink->ksp, KSPPREONLY));

2411:   PetscCall(PetscSNPrintf(prefix, sizeof(prefix), "%sfieldsplit_%s_", ((PetscObject)pc)->prefix ? ((PetscObject)pc)->prefix : "", ilink->splitname));
2412:   PetscCall(KSPSetOptionsPrefix(ilink->ksp, prefix));

2414:   if (!next) {
2415:     jac->head       = ilink;
2416:     ilink->previous = NULL;
2417:   } else {
2418:     while (next->next) next = next->next;
2419:     next->next      = ilink;
2420:     ilink->previous = next;
2421:   }
2422:   jac->nsplits++;
2423:   PetscFunctionReturn(PETSC_SUCCESS);
2424: }

2426: /*@
2427:   PCFieldSplitSetFields - Sets the fields that define one particular split in `PCFIELDSPLIT`

2429:   Logically Collective

2431:   Input Parameters:
2432: + pc         - the preconditioner context
2433: . splitname  - name of this split, if `NULL` the number of the split is used
2434: . n          - the number of fields in this split
2435: . fields     - the fields in this split
2436: - 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
2437:                of the matrix and `fields_col` provides the column indices for that block

2439:   Options Database Key:
2440: . -pc_fieldsplit_%d_fields a,b,... - indicates the fields to be used in the `%d`'th split

2442:   Level: intermediate

2444:   Notes:
2445:   Use `PCFieldSplitSetIS()` to set a  general set of indices as a split.

2447:   If the matrix used to construct the preconditioner is `MATNEST` then field i refers to the `is_row[i]` `IS` passed to `MatCreateNest()`.

2449:   If the matrix used to construct the preconditioner is not `MATNEST` then
2450:   `PCFieldSplitSetFields()` is for defining fields as strided blocks (based on the block size provided to the matrix with `MatSetBlockSize()` or
2451:   to the `PC` with `PCFieldSplitSetBlockSize()`). For example, if the block
2452:   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
2453:   0xx3xx6xx9xx12 ... x1xx4xx7xx ... xx2xx5xx8xx.. 01x34x67x... 0x23x56x8.. x12x45x78x....
2454:   where the numbered entries indicate what is in the split.

2456:   This function is called once per split (it creates a new split each time).  Solve options
2457:   for this split will be available under the prefix `-fieldsplit_SPLITNAME_`.

2459:   `PCFieldSplitSetIS()` does not support having a `fields_col` different from `fields`

2461:   Developer Notes:
2462:   This routine does not actually create the `IS` representing the split, that is delayed
2463:   until `PCSetUp_FieldSplit()`, because information about the vector/matrix layouts may not be
2464:   available when this routine is called.

2466: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSetBlockSize()`, `PCFieldSplitSetIS()`, `PCFieldSplitRestrictIS()`,
2467:           `MatSetBlockSize()`, `MatCreateNest()`
2468: @*/
2469: PetscErrorCode PCFieldSplitSetFields(PC pc, const char splitname[], PetscInt n, const PetscInt fields[], const PetscInt fields_col[])
2470: {
2471:   PetscFunctionBegin;
2473:   PetscAssertPointer(splitname, 2);
2474:   PetscCheck(n >= 1, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_OUTOFRANGE, "Provided number of fields %" PetscInt_FMT " in split \"%s\" not positive", n, splitname);
2475:   PetscAssertPointer(fields, 4);
2476:   PetscTryMethod(pc, "PCFieldSplitSetFields_C", (PC, const char[], PetscInt, const PetscInt *, const PetscInt *), (pc, splitname, n, fields, fields_col));
2477:   PetscFunctionReturn(PETSC_SUCCESS);
2478: }

2480: /*@
2481:   PCFieldSplitSetDiagUseAmat - set flag indicating whether to extract diagonal blocks from Amat (rather than Pmat) to build
2482:   the sub-matrices associated with each split. Where `KSPSetOperators`(ksp,Amat,Pmat) was used to supply the operators.

2484:   Logically Collective

2486:   Input Parameters:
2487: + pc  - the preconditioner object
2488: - flg - boolean flag indicating whether or not to use Amat to extract the diagonal blocks from

2490:   Options Database Key:
2491: . -pc_fieldsplit_diag_use_amat - use the Amat to provide the diagonal blocks

2493:   Level: intermediate

2495: .seealso: [](sec_block_matrices), `PC`, `PCSetOperators()`, `KSPSetOperators()`, `PCFieldSplitGetDiagUseAmat()`, `PCFieldSplitSetOffDiagUseAmat()`, `PCFIELDSPLIT`
2496: @*/
2497: PetscErrorCode PCFieldSplitSetDiagUseAmat(PC pc, PetscBool flg)
2498: {
2499:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
2500:   PetscBool      isfs;

2502:   PetscFunctionBegin;
2504:   PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCFIELDSPLIT, &isfs));
2505:   PetscCheck(isfs, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "PC not of type %s", PCFIELDSPLIT);
2506:   jac->diag_use_amat = flg;
2507:   PetscFunctionReturn(PETSC_SUCCESS);
2508: }

2510: /*@
2511:   PCFieldSplitGetDiagUseAmat - get the flag indicating whether to extract diagonal blocks from Amat (rather than Pmat) to build
2512:   the sub-matrices associated with each split.  Where `KSPSetOperators`(ksp,Amat,Pmat) was used to supply the operators.

2514:   Logically Collective

2516:   Input Parameter:
2517: . pc - the preconditioner object

2519:   Output Parameter:
2520: . flg - boolean flag indicating whether or not to use Amat to extract the diagonal blocks from

2522:   Level: intermediate

2524: .seealso: [](sec_block_matrices), `PC`, `PCSetOperators()`, `KSPSetOperators()`, `PCFieldSplitSetDiagUseAmat()`, `PCFieldSplitGetOffDiagUseAmat()`, `PCFIELDSPLIT`
2525: @*/
2526: PetscErrorCode PCFieldSplitGetDiagUseAmat(PC pc, PetscBool *flg)
2527: {
2528:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
2529:   PetscBool      isfs;

2531:   PetscFunctionBegin;
2533:   PetscAssertPointer(flg, 2);
2534:   PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCFIELDSPLIT, &isfs));
2535:   PetscCheck(isfs, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "PC not of type %s", PCFIELDSPLIT);
2536:   *flg = jac->diag_use_amat;
2537:   PetscFunctionReturn(PETSC_SUCCESS);
2538: }

2540: /*@
2541:   PCFieldSplitSetOffDiagUseAmat - set flag indicating whether to extract off-diagonal blocks from Amat (rather than Pmat) to build
2542:   the sub-matrices associated with each split.  Where `KSPSetOperators`(ksp,Amat,Pmat) was used to supply the operators.

2544:   Logically Collective

2546:   Input Parameters:
2547: + pc  - the preconditioner object
2548: - flg - boolean flag indicating whether or not to use Amat to extract the off-diagonal blocks from

2550:   Options Database Key:
2551: . -pc_fieldsplit_off_diag_use_amat (true|false) - use the Amat to extract the off-diagonal blocks

2553:   Level: intermediate

2555: .seealso: [](sec_block_matrices), `PC`, `PCSetOperators()`, `KSPSetOperators()`, `PCFieldSplitGetOffDiagUseAmat()`, `PCFieldSplitSetDiagUseAmat()`, `PCFIELDSPLIT`
2556: @*/
2557: PetscErrorCode PCFieldSplitSetOffDiagUseAmat(PC pc, PetscBool flg)
2558: {
2559:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
2560:   PetscBool      isfs;

2562:   PetscFunctionBegin;
2564:   PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCFIELDSPLIT, &isfs));
2565:   PetscCheck(isfs, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "PC not of type %s", PCFIELDSPLIT);
2566:   jac->offdiag_use_amat = flg;
2567:   PetscFunctionReturn(PETSC_SUCCESS);
2568: }

2570: /*@
2571:   PCFieldSplitGetOffDiagUseAmat - get the flag indicating whether to extract off-diagonal blocks from Amat (rather than Pmat) to build
2572:   the sub-matrices associated with each split.  Where `KSPSetOperators`(ksp,Amat,Pmat) was used to supply the operators.

2574:   Logically Collective

2576:   Input Parameter:
2577: . pc - the preconditioner object

2579:   Output Parameter:
2580: . flg - boolean flag indicating whether or not to use Amat to extract the off-diagonal blocks from

2582:   Level: intermediate

2584: .seealso: [](sec_block_matrices), `PC`, `PCSetOperators()`, `KSPSetOperators()`, `PCFieldSplitSetOffDiagUseAmat()`, `PCFieldSplitGetDiagUseAmat()`, `PCFIELDSPLIT`
2585: @*/
2586: PetscErrorCode PCFieldSplitGetOffDiagUseAmat(PC pc, PetscBool *flg)
2587: {
2588:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
2589:   PetscBool      isfs;

2591:   PetscFunctionBegin;
2593:   PetscAssertPointer(flg, 2);
2594:   PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCFIELDSPLIT, &isfs));
2595:   PetscCheck(isfs, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "PC not of type %s", PCFIELDSPLIT);
2596:   *flg = jac->offdiag_use_amat;
2597:   PetscFunctionReturn(PETSC_SUCCESS);
2598: }

2600: /*@
2601:   PCFieldSplitSetIS - Sets the exact elements for a split in a `PCFIELDSPLIT`

2603:   Logically Collective

2605:   Input Parameters:
2606: + pc        - the preconditioner context
2607: . splitname - name of this split, if `NULL` the number of the split is used
2608: - is        - the index set that defines the elements in this split

2610:   Level: intermediate

2612:   Notes:
2613:   Use `PCFieldSplitSetFields()`, for splits defined by strided `IS` based on the matrix block size or the `is_rows[]` passed into `MATNEST`

2615:   This function is called once per split (it creates a new split each time).  Solve options
2616:   for this split will be available under the prefix -fieldsplit_SPLITNAME_.

2618: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSetBlockSize()`, `PCFieldSplitSetFields()`
2619: @*/
2620: PetscErrorCode PCFieldSplitSetIS(PC pc, const char splitname[], IS is)
2621: {
2622:   PetscFunctionBegin;
2624:   if (splitname) PetscAssertPointer(splitname, 2);
2626:   PetscTryMethod(pc, "PCFieldSplitSetIS_C", (PC, const char[], IS), (pc, splitname, is));
2627:   PetscFunctionReturn(PETSC_SUCCESS);
2628: }

2630: /*@
2631:   PCFieldSplitGetIS - Retrieves the elements for a split as an `IS`

2633:   Logically Collective

2635:   Input Parameters:
2636: + pc        - the preconditioner context
2637: - splitname - name of this split

2639:   Output Parameter:
2640: . is - the index set that defines the elements in this split, or `NULL` if the split is not found

2642:   Level: intermediate

2644: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSetIS()`, `PCFieldSplitGetISByIndex()`
2645: @*/
2646: PetscErrorCode PCFieldSplitGetIS(PC pc, const char splitname[], IS *is)
2647: {
2648:   PetscFunctionBegin;
2650:   PetscAssertPointer(splitname, 2);
2651:   PetscAssertPointer(is, 3);
2652:   {
2653:     PC_FieldSplit    *jac   = (PC_FieldSplit *)pc->data;
2654:     PC_FieldSplitLink ilink = jac->head;
2655:     PetscBool         found;

2657:     *is = NULL;
2658:     while (ilink) {
2659:       PetscCall(PetscStrcmp(ilink->splitname, splitname, &found));
2660:       if (found) {
2661:         *is = ilink->is;
2662:         break;
2663:       }
2664:       ilink = ilink->next;
2665:     }
2666:   }
2667:   PetscFunctionReturn(PETSC_SUCCESS);
2668: }

2670: /*@
2671:   PCFieldSplitGetISByIndex - Retrieves the elements for a given split as an `IS`

2673:   Logically Collective

2675:   Input Parameters:
2676: + pc    - the preconditioner context
2677: - index - index of this split

2679:   Output Parameter:
2680: . is - the index set that defines the elements in this split

2682:   Level: intermediate

2684: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitGetIS()`, `PCFieldSplitSetIS()`
2685: @*/
2686: PetscErrorCode PCFieldSplitGetISByIndex(PC pc, PetscInt index, IS *is)
2687: {
2688:   PetscFunctionBegin;
2689:   PetscCheck(index >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Negative field %" PetscInt_FMT " requested", index);
2691:   PetscAssertPointer(is, 3);
2692:   {
2693:     PC_FieldSplit    *jac   = (PC_FieldSplit *)pc->data;
2694:     PC_FieldSplitLink ilink = jac->head;
2695:     PetscInt          i     = 0;
2696:     PetscCheck(index < jac->nsplits, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Field %" PetscInt_FMT " requested but only %" PetscInt_FMT " exist", index, jac->nsplits);

2698:     while (i < index) {
2699:       ilink = ilink->next;
2700:       ++i;
2701:     }
2702:     PetscCall(PCFieldSplitGetIS(pc, ilink->splitname, is));
2703:   }
2704:   PetscFunctionReturn(PETSC_SUCCESS);
2705: }

2707: /*@
2708:   PCFieldSplitSetBlockSize - Sets the block size for defining where fields start in the
2709:   fieldsplit preconditioner when calling `PCFieldSplitSetFields()`. If not set the matrix block size is used.

2711:   Logically Collective

2713:   Input Parameters:
2714: + pc - the preconditioner context
2715: - bs - the block size

2717:   Level: intermediate

2719:   Note:
2720:   If the matrix is a `MATNEST` then the `is_rows[]` passed to `MatCreateNest()` determines the fields.

2722: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSetIS()`
2723: @*/
2724: PetscErrorCode PCFieldSplitSetBlockSize(PC pc, PetscInt bs)
2725: {
2726:   PetscFunctionBegin;
2729:   PetscTryMethod(pc, "PCFieldSplitSetBlockSize_C", (PC, PetscInt), (pc, bs));
2730:   PetscFunctionReturn(PETSC_SUCCESS);
2731: }

2733: /*@C
2734:   PCFieldSplitGetSubKSP - Gets the `KSP` contexts for all splits

2736:   Collective

2738:   Input Parameter:
2739: . pc - the preconditioner context

2741:   Output Parameters:
2742: + n      - the number of splits
2743: - subksp - the array of `KSP` contexts

2745:   Level: advanced

2747:   Notes:
2748:   After `PCFieldSplitGetSubKSP()` the array of `KSP`s is to be freed by the user with `PetscFree()`
2749:   (not the `KSP`, just the array that contains them).

2751:   You must call `PCSetUp()` before calling `PCFieldSplitGetSubKSP()`.

2753:   If the fieldsplit is of type `PC_COMPOSITE_SCHUR`, it returns the `KSP` object used inside the
2754:   Schur complement and the `KSP` object used to iterate over the Schur complement.
2755:   To access all the `KSP` objects used in `PC_COMPOSITE_SCHUR`, use `PCFieldSplitSchurGetSubKSP()`.

2757:   If the fieldsplit is of type `PC_COMPOSITE_GKB`, it returns the `KSP` object used to solve the
2758:   inner linear system defined by the matrix H in each loop.

2760:   Fortran Note:
2761:   Call `PCFieldSplitRestoreSubKSP()` when the array of `KSP` is no longer needed

2763:   Developer Notes:
2764:   There should be a `PCFieldSplitRestoreSubKSP()` instead of requiring the user to call `PetscFree()`

2766: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSetIS()`, `PCFieldSplitSchurGetSubKSP()`
2767: @*/
2768: PetscErrorCode PCFieldSplitGetSubKSP(PC pc, PetscInt *n, KSP *subksp[])
2769: {
2770:   PetscFunctionBegin;
2772:   if (n) PetscAssertPointer(n, 2);
2773:   PetscUseMethod(pc, "PCFieldSplitGetSubKSP_C", (PC, PetscInt *, KSP **), (pc, n, subksp));
2774:   PetscFunctionReturn(PETSC_SUCCESS);
2775: }

2777: /*@C
2778:   PCFieldSplitSchurGetSubKSP - Gets the `KSP` contexts used inside the Schur complement based `PCFIELDSPLIT`

2780:   Collective

2782:   Input Parameter:
2783: . pc - the preconditioner context

2785:   Output Parameters:
2786: + n      - the number of splits
2787: - subksp - the array of `KSP` contexts

2789:   Level: advanced

2791:   Notes:
2792:   After `PCFieldSplitSchurGetSubKSP()` the array of `KSP`s is to be freed by the user with `PetscFree()`
2793:   (not the `KSP` just the array that contains them).

2795:   You must call `PCSetUp()` before calling `PCFieldSplitSchurGetSubKSP()`.

2797:   If the fieldsplit type is of type `PC_COMPOSITE_SCHUR`, it returns (in order)
2798: +  1  - the `KSP` used for the (1,1) block
2799: .  2  - the `KSP` used for the Schur complement (not the one used for the interior Schur solver)
2800: -  3  - the `KSP` used for the (1,1) block in the upper triangular factor (if different from that of the (1,1) block).

2802:   It returns a null array if the fieldsplit is not of type `PC_COMPOSITE_SCHUR`; in this case, you should use `PCFieldSplitGetSubKSP()`.

2804:   Fortran Note:
2805:   Call `PCFieldSplitSchurRestoreSubKSP()` when the array of `KSP` is no longer needed

2807:   Developer Notes:
2808:   There should be a `PCFieldSplitRestoreSubKSP()` instead of requiring the user to call `PetscFree()`

2810:   Should the functionality of `PCFieldSplitSchurGetSubKSP()` and `PCFieldSplitGetSubKSP()` be merged?

2812: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSetIS()`, `PCFieldSplitGetSubKSP()`
2813: @*/
2814: PetscErrorCode PCFieldSplitSchurGetSubKSP(PC pc, PetscInt *n, KSP *subksp[])
2815: {
2816:   PetscFunctionBegin;
2818:   if (n) PetscAssertPointer(n, 2);
2819:   PetscUseMethod(pc, "PCFieldSplitSchurGetSubKSP_C", (PC, PetscInt *, KSP **), (pc, n, subksp));
2820:   PetscFunctionReturn(PETSC_SUCCESS);
2821: }

2823: /*@
2824:   PCFieldSplitSetSchurPre -  Indicates from what operator the preconditioner is constructed for the Schur complement.
2825:   The default is the A11 matrix.

2827:   Collective

2829:   Input Parameters:
2830: + pc    - the preconditioner context
2831: . ptype - which matrix to use for preconditioning the Schur complement: `PC_FIELDSPLIT_SCHUR_PRE_A11` (default),
2832:               `PC_FIELDSPLIT_SCHUR_PRE_SELF`, `PC_FIELDSPLIT_SCHUR_PRE_USER`,
2833:               `PC_FIELDSPLIT_SCHUR_PRE_SELFP`, and `PC_FIELDSPLIT_SCHUR_PRE_FULL`
2834: - pre   - matrix to use for preconditioning, or `NULL`

2836:   Options Database Keys:
2837: + -pc_fieldsplit_schur_precondition (self|selfp|user|a11|full) - default is `a11`. See notes for meaning of various arguments
2838: - -fieldsplit_1_pc_type pctype                                 - the preconditioner algorithm that is used to construct the preconditioner from the operator

2840:   Level: intermediate

2842:   Notes:
2843:   If ptype is
2844: +     a11 - the preconditioner for the Schur complement is generated from the block diagonal part of the preconditioner
2845:   matrix associated with the Schur complement (i.e. A11), not the Schur complement matrix
2846: .     self - the preconditioner for the Schur complement is generated from the symbolic representation of the Schur complement matrix:
2847:   The only preconditioners that currently work with this symbolic representation matrix object are `PCLSC` and `PCHPDDM`
2848: .     user - the preconditioner for the Schur complement is generated from the user provided matrix (pre argument
2849:   to this function).
2850: .     selfp - the preconditioning for the Schur complement is generated from an explicitly-assembled approximation $ Sp = A11 - A10 inv(diag(A00)) A01 $
2851:   This is only a good preconditioner when diag(A00) is a good preconditioner for A00. Optionally, A00 can be
2852:   lumped before extracting the diagonal using the additional option `-fieldsplit_1_mat_schur_complement_ainv_type lump`
2853: -     full - the preconditioner for the Schur complement is generated from the exact Schur complement matrix representation
2854:   computed internally by `PCFIELDSPLIT` (this is expensive)
2855:   useful mostly as a test that the Schur complement approach can work for your problem

2857:   When solving a saddle point problem, where the A11 block is identically zero, using `a11` as the ptype only makes sense
2858:   with the additional option `-fieldsplit_1_pc_type none`. Usually for saddle point problems one would use a `ptype` of `self` and
2859:   `-fieldsplit_1_pc_type lsc` which uses the least squares commutator to compute a preconditioner for the Schur complement.

2861:   Developer Note:
2862:   The name of this function and the option `-pc_fieldsplit_schur_precondition` are inconsistent; precondition should be used everywhere.

2864: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSchurPre()`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSchurPreType`,
2865:           `MatSchurComplementSetAinvType()`, `PCLSC`, `PCFieldSplitSetSchurFactType()`
2866: @*/
2867: PetscErrorCode PCFieldSplitSetSchurPre(PC pc, PCFieldSplitSchurPreType ptype, Mat pre)
2868: {
2869:   PetscFunctionBegin;
2871:   PetscTryMethod(pc, "PCFieldSplitSetSchurPre_C", (PC, PCFieldSplitSchurPreType, Mat), (pc, ptype, pre));
2872:   PetscFunctionReturn(PETSC_SUCCESS);
2873: }

2875: PetscErrorCode PCFieldSplitSchurPrecondition(PC pc, PCFieldSplitSchurPreType ptype, Mat pre)
2876: {
2877:   return PCFieldSplitSetSchurPre(pc, ptype, pre);
2878: } /* Deprecated name */

2880: /*@
2881:   PCFieldSplitGetSchurPre - For Schur complement fieldsplit, determine how the Schur complement will be
2882:   preconditioned.  See `PCFieldSplitSetSchurPre()` for details.

2884:   Logically Collective

2886:   Input Parameter:
2887: . pc - the preconditioner context

2889:   Output Parameters:
2890: + 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`
2891: - pre   - matrix to use for preconditioning (with `PC_FIELDSPLIT_SCHUR_PRE_USER`), or `NULL`

2893:   Level: intermediate

2895: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitSetSchurPre()`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSchurPreType`, `PCLSC`
2896: @*/
2897: PetscErrorCode PCFieldSplitGetSchurPre(PC pc, PCFieldSplitSchurPreType *ptype, Mat *pre)
2898: {
2899:   PetscFunctionBegin;
2901:   PetscUseMethod(pc, "PCFieldSplitGetSchurPre_C", (PC, PCFieldSplitSchurPreType *, Mat *), (pc, ptype, pre));
2902:   PetscFunctionReturn(PETSC_SUCCESS);
2903: }

2905: /*@
2906:   PCFieldSplitSchurGetS -  extract the `MATSCHURCOMPLEMENT` object used by this `PCFIELDSPLIT` in case it needs to be configured separately

2908:   Not Collective

2910:   Input Parameter:
2911: . pc - the preconditioner context

2913:   Output Parameter:
2914: . S - the Schur complement matrix

2916:   Level: advanced

2918:   Note:
2919:   This matrix should not be destroyed using `MatDestroy()`; rather, use `PCFieldSplitSchurRestoreS()`.

2921: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSchurPreType`, `PCFieldSplitSetSchurPre()`, `MATSCHURCOMPLEMENT`, `PCFieldSplitSchurRestoreS()`,
2922:           `MatCreateSchurComplement()`, `MatSchurComplementGetKSP()`, `MatSchurComplementComputeExplicitOperator()`, `MatGetSchurComplement()`
2923: @*/
2924: PetscErrorCode PCFieldSplitSchurGetS(PC pc, Mat *S)
2925: {
2926:   const char    *t;
2927:   PetscBool      isfs;
2928:   PC_FieldSplit *jac;

2930:   PetscFunctionBegin;
2932:   PetscCall(PetscObjectGetType((PetscObject)pc, &t));
2933:   PetscCall(PetscStrcmp(t, PCFIELDSPLIT, &isfs));
2934:   PetscCheck(isfs, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Expected PC of type PCFIELDSPLIT, got %s instead", t);
2935:   jac = (PC_FieldSplit *)pc->data;
2936:   PetscCheck(jac->type == PC_COMPOSITE_SCHUR, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Expected PCFIELDSPLIT of type SCHUR, got %d instead", jac->type);
2937:   if (S) *S = jac->schur;
2938:   PetscFunctionReturn(PETSC_SUCCESS);
2939: }

2941: /*@
2942:   PCFieldSplitSchurRestoreS -  returns the `MATSCHURCOMPLEMENT` matrix used by this `PC`

2944:   Not Collective

2946:   Input Parameters:
2947: + pc - the preconditioner context
2948: - S  - the Schur complement matrix

2950:   Level: advanced

2952: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSchurPreType`, `PCFieldSplitSetSchurPre()`, `MatSchurComplement`, `PCFieldSplitSchurGetS()`
2953: @*/
2954: PetscErrorCode PCFieldSplitSchurRestoreS(PC pc, Mat *S)
2955: {
2956:   const char    *t;
2957:   PetscBool      isfs;
2958:   PC_FieldSplit *jac;

2960:   PetscFunctionBegin;
2962:   PetscCall(PetscObjectGetType((PetscObject)pc, &t));
2963:   PetscCall(PetscStrcmp(t, PCFIELDSPLIT, &isfs));
2964:   PetscCheck(isfs, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Expected PC of type PCFIELDSPLIT, got %s instead", t);
2965:   jac = (PC_FieldSplit *)pc->data;
2966:   PetscCheck(jac->type == PC_COMPOSITE_SCHUR, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Expected PCFIELDSPLIT of type SCHUR, got %d instead", jac->type);
2967:   PetscCheck(S && (*S == jac->schur), PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "MatSchurComplement restored is not the same as gotten");
2968:   PetscFunctionReturn(PETSC_SUCCESS);
2969: }

2971: static PetscErrorCode PCFieldSplitSetSchurPre_FieldSplit(PC pc, PCFieldSplitSchurPreType ptype, Mat pre)
2972: {
2973:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

2975:   PetscFunctionBegin;
2976:   jac->schurpre = ptype;
2977:   if (ptype == PC_FIELDSPLIT_SCHUR_PRE_USER && pre) {
2978:     PetscCall(MatDestroy(&jac->schur_user));
2979:     jac->schur_user = pre;
2980:     PetscCall(PetscObjectReference((PetscObject)jac->schur_user));
2981:   }
2982:   PetscFunctionReturn(PETSC_SUCCESS);
2983: }

2985: static PetscErrorCode PCFieldSplitGetSchurPre_FieldSplit(PC pc, PCFieldSplitSchurPreType *ptype, Mat *pre)
2986: {
2987:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

2989:   PetscFunctionBegin;
2990:   if (ptype) *ptype = jac->schurpre;
2991:   if (pre) *pre = jac->schur_user;
2992:   PetscFunctionReturn(PETSC_SUCCESS);
2993: }

2995: /*@
2996:   PCFieldSplitSetSchurFactType -  sets which blocks of the approximate block factorization to retain in the preconditioner {cite}`murphy2000note` and {cite}`ipsen2001note`

2998:   Collective

3000:   Input Parameters:
3001: + pc    - the preconditioner context
3002: - ftype - which blocks of factorization to retain, `PC_FIELDSPLIT_SCHUR_FACT_FULL` is default

3004:   Options Database Key:
3005: . -pc_fieldsplit_schur_fact_type (diag|lower|upper|full) - default is `full`

3007:   Level: intermediate

3009:   Notes:
3010:   The `full` factorization is

3012:   ```{math}
3013:   \left(\begin{array}{cc} A & B \\
3014:   C & E \\
3015:   \end{array}\right) =
3016:   \left(\begin{array}{cc} I & 0 \\
3017:   C A^{-1} & I \\
3018:   \end{array}\right)
3019:   \left(\begin{array}{cc} A & 0 \\
3020:   0 & S \\
3021:   \end{array}\right)
3022:   \left(\begin{array}{cc} I & A^{-1}B \\
3023:   0 & I \\
3024:   \end{array}\right) = L D U,
3025:   ```

3027:   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 $LD$,
3028:   and `diag` is the diagonal part with the sign of $S$ flipped (because this makes the preconditioner positive definite for many formulations,
3029:   thus allowing the use of `KSPMINRES)`. Sign flipping of $S$ can be turned off with `PCFieldSplitSetSchurScale()`.

3031:   If $A$ and $S$ are solved exactly
3032: +  1 - `full` factorization is a direct solver.
3033: .  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.
3034: -  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.

3036:   If the iteration count is very low, consider using `KSPFGMRES` or `KSPGCR` which can use one less preconditioner
3037:   application in this case. Note that the preconditioned operator may be highly non-normal, so such fast convergence may not be observed in practice.

3039:   For symmetric problems in which $A$ is positive definite and $S$ is negative definite, `diag` can be used with `KSPMINRES`.

3041:   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 $S$).

3043: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSchurPreType`, `PCFieldSplitSetSchurScale()`,
3044:           [](sec_flexibleksp), `PCFieldSplitSetSchurPre()`
3045: @*/
3046: PetscErrorCode PCFieldSplitSetSchurFactType(PC pc, PCFieldSplitSchurFactType ftype)
3047: {
3048:   PetscFunctionBegin;
3050:   PetscTryMethod(pc, "PCFieldSplitSetSchurFactType_C", (PC, PCFieldSplitSchurFactType), (pc, ftype));
3051:   PetscFunctionReturn(PETSC_SUCCESS);
3052: }

3054: static PetscErrorCode PCFieldSplitSetSchurFactType_FieldSplit(PC pc, PCFieldSplitSchurFactType ftype)
3055: {
3056:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

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

3063: /*@
3064:   PCFieldSplitSetSchurScale -  Controls the sign flip of S for `PC_FIELDSPLIT_SCHUR_FACT_DIAG`.

3066:   Collective

3068:   Input Parameters:
3069: + pc    - the preconditioner context
3070: - scale - scaling factor for the Schur complement

3072:   Options Database Key:
3073: . -pc_fieldsplit_schur_scale scale - default is -1.0

3075:   Level: intermediate

3077: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSchurFactType`, `PCFieldSplitSetSchurFactType()`
3078: @*/
3079: PetscErrorCode PCFieldSplitSetSchurScale(PC pc, PetscScalar scale)
3080: {
3081:   PetscFunctionBegin;
3084:   PetscTryMethod(pc, "PCFieldSplitSetSchurScale_C", (PC, PetscScalar), (pc, scale));
3085:   PetscFunctionReturn(PETSC_SUCCESS);
3086: }

3088: static PetscErrorCode PCFieldSplitSetSchurScale_FieldSplit(PC pc, PetscScalar scale)
3089: {
3090:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

3092:   PetscFunctionBegin;
3093:   jac->schurscale = scale;
3094:   PetscFunctionReturn(PETSC_SUCCESS);
3095: }

3097: /*@C
3098:   PCFieldSplitGetSchurBlocks - Gets all matrix blocks for the Schur complement

3100:   Collective

3102:   Input Parameter:
3103: . pc - the preconditioner context

3105:   Output Parameters:
3106: + A00 - the (0,0) block
3107: . A01 - the (0,1) block
3108: . A10 - the (1,0) block
3109: - A11 - the (1,1) block

3111:   Level: advanced

3113:   Note:
3114:   Use `NULL` for any unneeded output arguments

3116: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `MatSchurComplementGetSubMatrices()`, `MatSchurComplementSetSubMatrices()`
3117: @*/
3118: PetscErrorCode PCFieldSplitGetSchurBlocks(PC pc, Mat *A00, Mat *A01, Mat *A10, Mat *A11)
3119: {
3120:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

3122:   PetscFunctionBegin;
3124:   PetscCheck(jac->type == PC_COMPOSITE_SCHUR, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONG, "FieldSplit is not using a Schur complement approach.");
3125:   if (A00) *A00 = jac->pmat[0];
3126:   if (A01) *A01 = jac->B;
3127:   if (A10) *A10 = jac->C;
3128:   if (A11) *A11 = jac->pmat[1];
3129:   PetscFunctionReturn(PETSC_SUCCESS);
3130: }

3132: /*@
3133:   PCFieldSplitSetGKBTol -  Sets the solver tolerance for the generalized Golub-Kahan bidiagonalization preconditioner {cite}`arioli2013` in `PCFIELDSPLIT`

3135:   Collective

3137:   Input Parameters:
3138: + pc        - the preconditioner context
3139: - tolerance - the solver tolerance

3141:   Options Database Key:
3142: . -pc_fieldsplit_gkb_tol tolerance - default is 1e-5

3144:   Level: intermediate

3146:   Note:
3147:   The generalized GKB algorithm {cite}`arioli2013` uses a lower bound estimate of the error in energy norm as stopping criterion.
3148:   It stops once the lower bound estimate undershoots the required solver tolerance. Although the actual error might be bigger than
3149:   this estimate, the stopping criterion is satisfactory in practical cases.

3151: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetGKBDelay()`, `PCFieldSplitSetGKBNu()`, `PCFieldSplitSetGKBMaxit()`
3152: @*/
3153: PetscErrorCode PCFieldSplitSetGKBTol(PC pc, PetscReal tolerance)
3154: {
3155:   PetscFunctionBegin;
3158:   PetscTryMethod(pc, "PCFieldSplitSetGKBTol_C", (PC, PetscReal), (pc, tolerance));
3159:   PetscFunctionReturn(PETSC_SUCCESS);
3160: }

3162: static PetscErrorCode PCFieldSplitSetGKBTol_FieldSplit(PC pc, PetscReal tolerance)
3163: {
3164:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

3166:   PetscFunctionBegin;
3167:   jac->gkbtol = tolerance;
3168:   PetscFunctionReturn(PETSC_SUCCESS);
3169: }

3171: /*@
3172:   PCFieldSplitSetGKBMaxit -  Sets the maximum number of iterations for the generalized Golub-Kahan bidiagonalization preconditioner {cite}`arioli2013` in `PCFIELDSPLIT`

3174:   Collective

3176:   Input Parameters:
3177: + pc    - the preconditioner context
3178: - maxit - the maximum number of iterations

3180:   Options Database Key:
3181: . -pc_fieldsplit_gkb_maxit maxit - default is 100

3183:   Level: intermediate

3185: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetGKBDelay()`, `PCFieldSplitSetGKBTol()`, `PCFieldSplitSetGKBNu()`
3186: @*/
3187: PetscErrorCode PCFieldSplitSetGKBMaxit(PC pc, PetscInt maxit)
3188: {
3189:   PetscFunctionBegin;
3192:   PetscTryMethod(pc, "PCFieldSplitSetGKBMaxit_C", (PC, PetscInt), (pc, maxit));
3193:   PetscFunctionReturn(PETSC_SUCCESS);
3194: }

3196: static PetscErrorCode PCFieldSplitSetGKBMaxit_FieldSplit(PC pc, PetscInt maxit)
3197: {
3198:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

3200:   PetscFunctionBegin;
3201:   jac->gkbmaxit = maxit;
3202:   PetscFunctionReturn(PETSC_SUCCESS);
3203: }

3205: /*@
3206:   PCFieldSplitSetGKBDelay -  Sets the delay in the lower bound error estimate in the generalized Golub-Kahan bidiagonalization {cite}`arioli2013` in `PCFIELDSPLIT`
3207:   preconditioner.

3209:   Collective

3211:   Input Parameters:
3212: + pc    - the preconditioner context
3213: - delay - the delay window in the lower bound estimate

3215:   Options Database Key:
3216: . -pc_fieldsplit_gkb_delay delay - default is 5

3218:   Level: intermediate

3220:   Notes:
3221:   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 $
3222:   is expressed as a truncated sum. The error at iteration k can only be measured at iteration (k + `delay`), and thus the algorithm needs
3223:   at least (`delay` + 1) iterations to stop.

3225:   For more details on the generalized Golub-Kahan bidiagonalization method and its lower bound stopping criterion, please refer to {cite}`arioli2013`

3227: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetGKBNu()`, `PCFieldSplitSetGKBTol()`, `PCFieldSplitSetGKBMaxit()`
3228: @*/
3229: PetscErrorCode PCFieldSplitSetGKBDelay(PC pc, PetscInt delay)
3230: {
3231:   PetscFunctionBegin;
3234:   PetscTryMethod(pc, "PCFieldSplitSetGKBDelay_C", (PC, PetscInt), (pc, delay));
3235:   PetscFunctionReturn(PETSC_SUCCESS);
3236: }

3238: static PetscErrorCode PCFieldSplitSetGKBDelay_FieldSplit(PC pc, PetscInt delay)
3239: {
3240:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

3242:   PetscFunctionBegin;
3243:   jac->gkbdelay = delay;
3244:   PetscFunctionReturn(PETSC_SUCCESS);
3245: }

3247: /*@
3248:   PCFieldSplitSetGKBNu -  Sets the scalar value nu >= 0 in the transformation H = A00 + nu*A01*A01' of the (1,1) block in the
3249:   Golub-Kahan bidiagonalization preconditioner {cite}`arioli2013` in `PCFIELDSPLIT`

3251:   Collective

3253:   Input Parameters:
3254: + pc - the preconditioner context
3255: - nu - the shift parameter

3257:   Options Database Key:
3258: . -pc_fieldsplit_gkb_nu nu - default is 1

3260:   Level: intermediate

3262:   Notes:
3263:   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,
3264:   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
3265:   necessary to find a good balance in between the convergence of the inner and outer loop.

3267:   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.

3269: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetGKBDelay()`, `PCFieldSplitSetGKBTol()`, `PCFieldSplitSetGKBMaxit()`
3270: @*/
3271: PetscErrorCode PCFieldSplitSetGKBNu(PC pc, PetscReal nu)
3272: {
3273:   PetscFunctionBegin;
3276:   PetscTryMethod(pc, "PCFieldSplitSetGKBNu_C", (PC, PetscReal), (pc, nu));
3277:   PetscFunctionReturn(PETSC_SUCCESS);
3278: }

3280: static PetscErrorCode PCFieldSplitSetGKBNu_FieldSplit(PC pc, PetscReal nu)
3281: {
3282:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

3284:   PetscFunctionBegin;
3285:   jac->gkbnu = nu;
3286:   PetscFunctionReturn(PETSC_SUCCESS);
3287: }

3289: static PetscErrorCode PCFieldSplitSetType_FieldSplit(PC pc, PCCompositeType type)
3290: {
3291:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

3293:   PetscFunctionBegin;
3294:   jac->type = type;
3295:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSubKSP_C", NULL));
3296:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurPre_C", NULL));
3297:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSchurPre_C", NULL));
3298:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurFactType_C", NULL));
3299:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurScale_C", NULL));
3300:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBTol_C", NULL));
3301:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBMaxit_C", NULL));
3302:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBNu_C", NULL));
3303:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBDelay_C", NULL));

3305:   if (type == PC_COMPOSITE_SCHUR) {
3306:     pc->ops->apply          = PCApply_FieldSplit_Schur;
3307:     pc->ops->applytranspose = PCApplyTranspose_FieldSplit_Schur;
3308:     pc->ops->matapply       = PCMatApply_FieldSplit_Schur;
3309:     pc->ops->view           = PCView_FieldSplit_Schur;
3310:     pc->ops->setuponblocks  = PCSetUpOnBlocks_FieldSplit_Schur;

3312:     PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSubKSP_C", PCFieldSplitGetSubKSP_FieldSplit_Schur));
3313:     PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurPre_C", PCFieldSplitSetSchurPre_FieldSplit));
3314:     PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSchurPre_C", PCFieldSplitGetSchurPre_FieldSplit));
3315:     PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurFactType_C", PCFieldSplitSetSchurFactType_FieldSplit));
3316:     PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurScale_C", PCFieldSplitSetSchurScale_FieldSplit));
3317:   } else if (type == PC_COMPOSITE_GKB) {
3318:     pc->ops->apply          = PCApply_FieldSplit_GKB;
3319:     pc->ops->applytranspose = NULL;
3320:     pc->ops->matapply       = NULL;
3321:     pc->ops->view           = PCView_FieldSplit_GKB;
3322:     pc->ops->setuponblocks  = PCSetUpOnBlocks_FieldSplit_GKB;

3324:     PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSubKSP_C", PCFieldSplitGetSubKSP_FieldSplit));
3325:     PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBTol_C", PCFieldSplitSetGKBTol_FieldSplit));
3326:     PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBMaxit_C", PCFieldSplitSetGKBMaxit_FieldSplit));
3327:     PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBNu_C", PCFieldSplitSetGKBNu_FieldSplit));
3328:     PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBDelay_C", PCFieldSplitSetGKBDelay_FieldSplit));
3329:   } else {
3330:     pc->ops->apply          = PCApply_FieldSplit;
3331:     pc->ops->applytranspose = PCApplyTranspose_FieldSplit;
3332:     pc->ops->matapply       = PCMatApply_FieldSplit;
3333:     pc->ops->view           = PCView_FieldSplit;
3334:     pc->ops->setuponblocks  = PCSetUpOnBlocks_FieldSplit;

3336:     PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSubKSP_C", PCFieldSplitGetSubKSP_FieldSplit));
3337:   }
3338:   PetscFunctionReturn(PETSC_SUCCESS);
3339: }

3341: static PetscErrorCode PCFieldSplitSetBlockSize_FieldSplit(PC pc, PetscInt bs)
3342: {
3343:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

3345:   PetscFunctionBegin;
3346:   PetscCheck(bs >= 1, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_OUTOFRANGE, "Blocksize must be positive, you gave %" PetscInt_FMT, bs);
3347:   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);
3348:   jac->bs = bs;
3349:   PetscFunctionReturn(PETSC_SUCCESS);
3350: }

3352: static PetscErrorCode PCSetCoordinates_FieldSplit(PC pc, PetscInt dim, PetscInt nloc, PetscReal coords[])
3353: {
3354:   PC_FieldSplit    *jac           = (PC_FieldSplit *)pc->data;
3355:   PC_FieldSplitLink ilink_current = jac->head;
3356:   IS                is_owned;

3358:   PetscFunctionBegin;
3359:   jac->coordinates_set = PETSC_TRUE; // Internal flag
3360:   PetscCall(MatGetOwnershipIS(pc->mat, &is_owned, NULL));

3362:   while (ilink_current) {
3363:     // For each IS, embed it to get local coords indces
3364:     IS              is_coords;
3365:     PetscInt        ndofs_block;
3366:     const PetscInt *block_dofs_enumeration; // Numbering of the dofs relevant to the current block

3368:     // Setting drop to true for safety. It should make no difference.
3369:     PetscCall(ISEmbed(ilink_current->is, is_owned, PETSC_TRUE, &is_coords));
3370:     PetscCall(ISGetLocalSize(is_coords, &ndofs_block));
3371:     PetscCall(ISGetIndices(is_coords, &block_dofs_enumeration));

3373:     // Allocate coordinates vector and set it directly
3374:     PetscCall(PetscMalloc1(ndofs_block * dim, &ilink_current->coords));
3375:     for (PetscInt dof = 0; dof < ndofs_block; ++dof) {
3376:       for (PetscInt d = 0; d < dim; ++d) (ilink_current->coords)[dim * dof + d] = coords[dim * block_dofs_enumeration[dof] + d];
3377:     }
3378:     ilink_current->dim   = dim;
3379:     ilink_current->ndofs = ndofs_block;
3380:     PetscCall(ISRestoreIndices(is_coords, &block_dofs_enumeration));
3381:     PetscCall(ISDestroy(&is_coords));
3382:     ilink_current = ilink_current->next;
3383:   }
3384:   PetscCall(ISDestroy(&is_owned));
3385:   PetscFunctionReturn(PETSC_SUCCESS);
3386: }

3388: /*@
3389:   PCFieldSplitSetType - Sets the type, `PCCompositeType`, of a `PCFIELDSPLIT`

3391:   Collective

3393:   Input Parameters:
3394: + pc   - the preconditioner context
3395: - type - `PC_COMPOSITE_ADDITIVE`, `PC_COMPOSITE_MULTIPLICATIVE` (default), `PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE`, `PC_COMPOSITE_SPECIAL`, `PC_COMPOSITE_SCHUR`,
3396:          `PC_COMPOSITE_GKB`

3398:   Options Database Key:
3399: . -pc_fieldsplit_type (multiplicative|additive|symmetric_multiplicative|special|schur) - Sets fieldsplit preconditioner type

3401:   Level: intermediate

3403: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCCompositeType`, `PCCompositeGetType()`, `PC_COMPOSITE_ADDITIVE`, `PC_COMPOSITE_MULTIPLICATIVE`,
3404:           `PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE`, `PC_COMPOSITE_SPECIAL`, `PC_COMPOSITE_SCHUR`, `PCFieldSplitSetSchurFactType()`
3405: @*/
3406: PetscErrorCode PCFieldSplitSetType(PC pc, PCCompositeType type)
3407: {
3408:   PetscFunctionBegin;
3410:   PetscTryMethod(pc, "PCFieldSplitSetType_C", (PC, PCCompositeType), (pc, type));
3411:   PetscFunctionReturn(PETSC_SUCCESS);
3412: }

3414: /*@
3415:   PCFieldSplitGetType - Gets the type, `PCCompositeType`, of a `PCFIELDSPLIT`

3417:   Not collective

3419:   Input Parameter:
3420: . pc - the preconditioner context

3422:   Output Parameter:
3423: . type - `PC_COMPOSITE_ADDITIVE`, `PC_COMPOSITE_MULTIPLICATIVE` (default), `PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE`, `PC_COMPOSITE_SPECIAL`, `PC_COMPOSITE_SCHUR`

3425:   Level: intermediate

3427: .seealso: [](sec_block_matrices), `PC`, `PCCompositeSetType()`, `PCFIELDSPLIT`, `PCCompositeType`, `PC_COMPOSITE_ADDITIVE`, `PC_COMPOSITE_MULTIPLICATIVE`,
3428:           `PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE`, `PC_COMPOSITE_SPECIAL`, `PC_COMPOSITE_SCHUR`
3429: @*/
3430: PetscErrorCode PCFieldSplitGetType(PC pc, PCCompositeType *type)
3431: {
3432:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

3434:   PetscFunctionBegin;
3436:   PetscAssertPointer(type, 2);
3437:   *type = jac->type;
3438:   PetscFunctionReturn(PETSC_SUCCESS);
3439: }

3441: /*@
3442:   PCFieldSplitSetDMSplits - Flags whether `DMCreateFieldDecomposition()` should be used to define the splits in a `PCFIELDSPLIT`, whenever possible.

3444:   Logically Collective

3446:   Input Parameters:
3447: + pc  - the preconditioner context
3448: - flg - boolean indicating whether to use field splits defined by the `DM`

3450:   Options Database Key:
3451: . -pc_fieldsplit_dm_splits (true|false) - use the field splits defined by the `DM`

3453:   Level: intermediate

3455:   Developer Note:
3456:   The name should be `PCFieldSplitSetUseDMSplits()`, similar change to options database

3458: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitGetDMSplits()`, `DMCreateFieldDecomposition()`, `PCFieldSplitSetFields()`, `PCFieldSplitSetIS()`
3459: @*/
3460: PetscErrorCode PCFieldSplitSetDMSplits(PC pc, PetscBool flg)
3461: {
3462:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
3463:   PetscBool      isfs;

3465:   PetscFunctionBegin;
3468:   PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCFIELDSPLIT, &isfs));
3469:   if (isfs) jac->dm_splits = flg;
3470:   PetscFunctionReturn(PETSC_SUCCESS);
3471: }

3473: /*@
3474:   PCFieldSplitGetDMSplits - Returns flag indicating whether `DMCreateFieldDecomposition()` should be used to define the splits in a `PCFIELDSPLIT`, whenever possible.

3476:   Logically Collective

3478:   Input Parameter:
3479: . pc - the preconditioner context

3481:   Output Parameter:
3482: . flg - boolean indicating whether to use field splits defined by the `DM`

3484:   Level: intermediate

3486:   Developer Note:
3487:   The name should be `PCFieldSplitGetUseDMSplits()`

3489: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetDMSplits()`, `DMCreateFieldDecomposition()`, `PCFieldSplitSetFields()`, `PCFieldSplitSetIS()`
3490: @*/
3491: PetscErrorCode PCFieldSplitGetDMSplits(PC pc, PetscBool *flg)
3492: {
3493:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
3494:   PetscBool      isfs;

3496:   PetscFunctionBegin;
3498:   PetscAssertPointer(flg, 2);
3499:   PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCFIELDSPLIT, &isfs));
3500:   if (isfs) {
3501:     if (flg) *flg = jac->dm_splits;
3502:   }
3503:   PetscFunctionReturn(PETSC_SUCCESS);
3504: }

3506: /*@
3507:   PCFieldSplitGetDetectSaddlePoint - Returns flag indicating whether `PCFIELDSPLIT` will attempt to automatically determine fields based on zero diagonal entries.

3509:   Logically Collective

3511:   Input Parameter:
3512: . pc - the preconditioner context

3514:   Output Parameter:
3515: . flg - boolean indicating whether to detect fields or not

3517:   Level: intermediate

3519: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetDetectSaddlePoint()`
3520: @*/
3521: PetscErrorCode PCFieldSplitGetDetectSaddlePoint(PC pc, PetscBool *flg)
3522: {
3523:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

3525:   PetscFunctionBegin;
3526:   *flg = jac->detect;
3527:   PetscFunctionReturn(PETSC_SUCCESS);
3528: }

3530: /*@
3531:   PCFieldSplitSetDetectSaddlePoint - Sets flag indicating whether `PCFIELDSPLIT` will attempt to automatically determine fields based on zero diagonal entries.

3533:   Logically Collective

3535:   Input Parameter:
3536: . pc - the preconditioner context

3538:   Output Parameter:
3539: . flg - boolean indicating whether to detect fields or not

3541:   Options Database Key:
3542: . -pc_fieldsplit_detect_saddle_point (true|false) - detect and use the saddle point

3544:   Level: intermediate

3546:   Note:
3547:   Also sets the split type to `PC_COMPOSITE_SCHUR` (see `PCFieldSplitSetType()`) and the Schur preconditioner type to `PC_FIELDSPLIT_SCHUR_PRE_SELF` (see `PCFieldSplitSetSchurPre()`).

3549: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitGetDetectSaddlePoint()`, `PCFieldSplitSetType()`, `PCFieldSplitSetSchurPre()`, `PC_FIELDSPLIT_SCHUR_PRE_SELF`
3550: @*/
3551: PetscErrorCode PCFieldSplitSetDetectSaddlePoint(PC pc, PetscBool flg)
3552: {
3553:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

3555:   PetscFunctionBegin;
3556:   jac->detect = flg;
3557:   if (jac->detect) {
3558:     PetscCall(PCFieldSplitSetType(pc, PC_COMPOSITE_SCHUR));
3559:     PetscCall(PCFieldSplitSetSchurPre(pc, PC_FIELDSPLIT_SCHUR_PRE_SELF, NULL));
3560:   }
3561:   PetscFunctionReturn(PETSC_SUCCESS);
3562: }

3564: /*MC
3565:   PCFIELDSPLIT - Preconditioner created by combining separate preconditioners for individual
3566:   collections of variables (that may overlap) called fields or splits. Each field often represents a different continuum variable
3567:   represented on a grid, such as velocity, pressure, or temperature.
3568:   In the literature these are sometimes called block preconditioners; but should not be confused with `PCBJACOBI`.
3569:   See [the users manual section on "Solving Block Matrices"](sec_block_matrices) for more details.

3571:   Options Database Keys:
3572: +   -pc_fieldsplit_%d_fields a,b,...                                                 - indicates the fields to be used in the `%d`'th split
3573: .   -pc_fieldsplit_default                                                           - automatically add any fields to additional splits that have not
3574:                                                                                        been supplied explicitly by `-pc_fieldsplit_%d_fields`
3575: .   -pc_fieldsplit_block_size bs                                                     - size of block that defines fields (i.e. there are bs fields)
3576:                                                                                        when the matrix is not of `MatType` `MATNEST`
3577: .   -pc_fieldsplit_type (additive|multiplicative|symmetric_multiplicative|schur|gkb) - type of relaxation or factorization splitting
3578: .   -pc_fieldsplit_schur_precondition (self|selfp|user|a11|full)                     - default is `a11`; see `PCFieldSplitSetSchurPre()`
3579: .   -pc_fieldsplit_schur_fact_type (diag|lower|upper|full)                           - set factorization type when using `-pc_fieldsplit_type schur`;
3580:                                                                                        see `PCFieldSplitSetSchurFactType()`
3581: .   -pc_fieldsplit_dm_splits (true|false) (default is true)                          - Whether to use `DMCreateFieldDecomposition()` for splits
3582: -   -pc_fieldsplit_detect_saddle_point (true|false)                                  - automatically finds rows with zero diagonal and uses Schur complement with no preconditioner as the solver

3584:   Options prefixes for inner solvers when using the Schur complement preconditioner are `-fieldsplit_0_` and `-fieldsplit_1_` .
3585:   The options prefix for the inner solver when using the Golub-Kahan biadiagonalization preconditioner is `-fieldsplit_0_`
3586:   For all other solvers they are `-fieldsplit_%d_` for the `%d`'th field; use `-fieldsplit_` for all fields.

3588:   To set options on the solvers for all blocks, prepend `-fieldsplit_` to all the `PC`
3589:   options database keys. For example, `-fieldsplit_pc_type ilu` `-fieldsplit_pc_factor_levels 1`.

3591:   To set the options on the solvers separate for each block call `PCFieldSplitGetSubKSP()`
3592:   and set the options directly on the resulting `KSP` object

3594:   Level: intermediate

3596:   Notes:
3597:   Use `PCFieldSplitSetFields()` to set splits defined by "strided" entries or with a `MATNEST` and `PCFieldSplitSetIS()`
3598:   to define a split by an arbitrary collection of entries.

3600:   If no splits are set, the default is used. If a `DM` is associated with the `PC` and it supports
3601:   `DMCreateFieldDecomposition()`, then that is used for the default. Otherwise if the matrix is not `MATNEST`, the splits are defined by entries strided by bs,
3602:   beginning at 0 then 1, etc to bs-1. The block size can be set with `PCFieldSplitSetBlockSize()`,
3603:   if this is not called the block size defaults to the blocksize of the second matrix passed
3604:   to `KSPSetOperators()`/`PCSetOperators()`.

3606:   For the Schur complement preconditioner if
3607:   ```{math}
3608:     J = \left[\begin{array}{cc} A_{00} & A_{01} \\ A_{10} & A_{11} \end{array}\right]
3609:   ```

3611:   the preconditioner using `full` factorization is logically
3612:   ```{math}
3613:     \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]
3614:       ```
3615:   where the action of $\text{ksp}(A_{00})$ is applied using the `KSP` solver with prefix `-fieldsplit_0_`.  $S$ is the Schur complement
3616:   ```{math}
3617:      S = A_{11} - A_{10} \text{ksp}(A_{00}) A_{01}
3618:   ```
3619:   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`
3620:   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
3621:   0th index, the `KSP` associated with `-fieldsplit_0_`, and at its 1st index, the `KSP` corresponding to `-fieldsplit_1_`.
3622:   By default, $A_{11}$ is used to construct a preconditioner for $S$, use `PCFieldSplitSetSchurPre()` for all the possible ways to construct the preconditioner for $S$.

3624:   The factorization type is set using `-pc_fieldsplit_schur_fact_type <diag, lower, upper, full>`. `full` is shown above,
3625:   `diag` gives
3626:   ```{math}
3627:     \left[\begin{array}{cc} \text{ksp}(A_{00}) & 0 \\  0 & -\text{ksp}(S) \end{array}\right]
3628:   ```
3629:   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
3630:   can be turned off with `PCFieldSplitSetSchurScale()` or by command line `-pc_fieldsplit_schur_scale 1.0`. The `lower` factorization is the inverse of
3631:   ```{math}
3632:     \left[\begin{array}{cc} A_{00} & 0 \\  A_{10} & S \end{array}\right]
3633:   ```
3634:   where the inverses of $A_{00}$ and $S$ are applied using `KSP`s. The upper factorization is the inverse of
3635:   ```{math}
3636:     \left[\begin{array}{cc} A_{00} & A_{01} \\  0 & S \end{array}\right]
3637:   ```
3638:   where again the inverses of $A_{00}$ and $S$ are applied using `KSP`s.

3640:   If only one set of indices (one `IS`) is provided with `PCFieldSplitSetIS()` then the complement of that `IS`
3641:   is used automatically for a second submatrix.

3643:   The fieldsplit preconditioner cannot currently be used with the `MATBAIJ` or `MATSBAIJ` data formats if the blocksize is larger than 1.
3644:   Generally it should be used with the `MATAIJ` or `MATNEST` `MatType`

3646:   The forms of these preconditioners are closely related, if not identical, to forms derived as "Distributive Iterations", see,
3647:   for example, page 294 in "Principles of Computational Fluid Dynamics" by Pieter Wesseling {cite}`wesseling2009`.
3648:   One can also use `PCFIELDSPLIT` inside a smoother resulting in "Distributive Smoothers".

3650:   See "A taxonomy and comparison of parallel block multi-level preconditioners for the incompressible Navier-Stokes equations" {cite}`elman2008tcp`.

3652:   The Constrained Pressure Preconditioner (CPR) can be implemented using `PCCOMPOSITE` with `PCGALERKIN`. CPR first solves an $R A P$ subsystem, updates the
3653:   residual on all variables (`PCCompositeSetType(pc,PC_COMPOSITE_MULTIPLICATIVE)`), and then applies a simple ILU like preconditioner on all the variables.

3655:   The generalized Golub-Kahan bidiagonalization preconditioner (GKB) can be applied to symmetric $2 \times 2$ block matrices of the shape
3656:   ```{math}
3657:     \left[\begin{array}{cc} A_{00} & A_{01} \\ A_{01}' & 0 \end{array}\right]
3658:   ```
3659:   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 $H = _{A00} + \nu*A_{01}*A_{01}'$.
3660:   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_`.

3662:   Some `PCFIELDSPLIT` variants are called physics-based preconditioners, since the preconditioner takes into account the underlying physics of the
3663:   problem. But this nomenclature is not well-defined.

3665:   Developer Note:
3666:   The Schur complement functionality of `PCFIELDSPLIT` should likely be factored into its own `PC` thus simplifying the implementation of the preconditioners and their
3667:   user API.

3669: .seealso: [](sec_block_matrices), `PC`, `PCCreate()`, `PCSetType()`, `PCType`, `PCLSC`,
3670:           `PCFieldSplitGetSubKSP()`, `PCFieldSplitSchurGetSubKSP()`, `PCFieldSplitSetFields()`,
3671:           `PCFieldSplitSetType()`, `PCFieldSplitSetIS()`, `PCFieldSplitSetSchurPre()`, `PCFieldSplitSetSchurFactType()`,
3672:           `MatSchurComplementSetAinvType()`, `PCFieldSplitSetSchurScale()`, `PCFieldSplitSetDetectSaddlePoint()`
3673: M*/

3675: PETSC_EXTERN PetscErrorCode PCCreate_FieldSplit(PC pc)
3676: {
3677:   PC_FieldSplit *jac;

3679:   PetscFunctionBegin;
3680:   PetscCall(PetscNew(&jac));

3682:   jac->bs                 = -1;
3683:   jac->type               = PC_COMPOSITE_MULTIPLICATIVE;
3684:   jac->schurpre           = PC_FIELDSPLIT_SCHUR_PRE_USER; /* Try user preconditioner first, fall back on diagonal */
3685:   jac->schurfactorization = PC_FIELDSPLIT_SCHUR_FACT_FULL;
3686:   jac->schurscale         = -1.0;
3687:   jac->dm_splits          = PETSC_TRUE;
3688:   jac->gkbtol             = 1e-5;
3689:   jac->gkbdelay           = 5;
3690:   jac->gkbnu              = 1;
3691:   jac->gkbmaxit           = 100;

3693:   pc->data = (void *)jac;

3695:   pc->ops->setup           = PCSetUp_FieldSplit;
3696:   pc->ops->reset           = PCReset_FieldSplit;
3697:   pc->ops->destroy         = PCDestroy_FieldSplit;
3698:   pc->ops->setfromoptions  = PCSetFromOptions_FieldSplit;
3699:   pc->ops->applyrichardson = NULL;

3701:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSchurGetSubKSP_C", PCFieldSplitSchurGetSubKSP_FieldSplit));
3702:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetFields_C", PCFieldSplitSetFields_FieldSplit));
3703:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetIS_C", PCFieldSplitSetIS_FieldSplit));
3704:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetType_C", PCFieldSplitSetType_FieldSplit));
3705:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetBlockSize_C", PCFieldSplitSetBlockSize_FieldSplit));
3706:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitRestrictIS_C", PCFieldSplitRestrictIS_FieldSplit));
3707:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCSetCoordinates_C", PCSetCoordinates_FieldSplit));

3709:   /* Initialize function pointers */
3710:   PetscCall(PCFieldSplitSetType(pc, jac->type));
3711:   PetscFunctionReturn(PETSC_SUCCESS);
3712: }