Actual source code: fieldsplit.c

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

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

  8: PetscLogEvent KSP_Solve_FS_0, KSP_Solve_FS_1, KSP_Solve_FS_S, KSP_Solve_FS_U, KSP_Solve_FS_L, KSP_Solve_FS_2, KSP_Solve_FS_3, KSP_Solve_FS_4;

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

597:     jac->issetup = PETSC_TRUE;

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

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

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

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

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

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

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

664:           PetscCall(PetscObjectReference((PetscObject)jac->schur_user));
665:         }
666:       } else {
667:         const char *prefix;
668:         PetscCall(MatCreateSubMatrix(pc->pmat, ilink->is, ilink->is_col, MAT_INITIAL_MATRIX, &jac->pmat[i]));
669:         PetscCall(KSPGetOptionsPrefix(ilink->ksp, &prefix));
670:         PetscCall(MatSetOptionsPrefix(jac->pmat[i], prefix));
671:         PetscCall(MatSetFromOptions(jac->pmat[i]));
672:         PetscCall(MatViewFromOptions(jac->pmat[i], NULL, "-mat_view"));
673:       }
674:       /* create work vectors for each split */
675:       PetscCall(MatCreateVecs(jac->pmat[i], &jac->x[i], &jac->y[i]));
676:       ilink->x = jac->x[i];
677:       ilink->y = jac->y[i];
678:       ilink->z = NULL;
679:       /* compute scatter contexts needed by multiplicative versions and non-default splits */
680:       PetscCall(VecScatterCreate(xtmp, ilink->is, jac->x[i], NULL, &ilink->sctx));
681:       PetscCall(PetscObjectQuery((PetscObject)ilink->is, "nearnullspace", (PetscObject *)&sp));
682:       if (sp) PetscCall(MatSetNearNullSpace(jac->pmat[i], sp));
683:       ilink = ilink->next;
684:     }
685:     PetscCall(VecDestroy(&xtmp));
686:   } else {
687:     MatReuse scall;
688:     if (pc->flag == DIFFERENT_NONZERO_PATTERN) {
689:       for (i = 0; i < nsplit; i++) PetscCall(MatDestroy(&jac->pmat[i]));
690:       scall = MAT_INITIAL_MATRIX;
691:     } else scall = MAT_REUSE_MATRIX;

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

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

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

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

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

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

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

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

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

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

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

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

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

813:     if (jac->schur) {
814:       KSP      kspA = jac->head->ksp, kspInner = NULL, kspUpper = jac->kspupper;
815:       MatReuse scall;

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

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

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

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

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

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

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

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

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

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

947:           PetscCall(PCKSPGetKSP(pcInner, &ksp));
948:           if (ksp == jac->head->ksp) PetscCall(PCSetUseAmat(pcInner, PETSC_TRUE));
949:         }
950:       }
951:       PetscCall(PetscSNPrintf(schurtestoption, sizeof(schurtestoption), "-fieldsplit_%s_upper_", ilink->splitname));
952:       PetscCall(PetscOptionsFindPairPrefix_Private(((PetscObject)pc)->options, ((PetscObject)pc)->prefix, schurtestoption, NULL, &flg));
953:       if (flg) {
954:         DM dmInner;

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

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

1006:     /* HACK: special support to forward L and Lp matrices that might be used by PCLSC */
1007:     PetscCall(PetscSNPrintf(lscname, sizeof(lscname), "%s_LSC_L", ilink->splitname));
1008:     PetscCall(PetscObjectQuery((PetscObject)pc->mat, lscname, (PetscObject *)&LSC_L));
1009:     if (!LSC_L) PetscCall(PetscObjectQuery((PetscObject)pc->pmat, lscname, (PetscObject *)&LSC_L));
1010:     if (LSC_L) PetscCall(PetscObjectCompose((PetscObject)jac->schur, "LSC_L", (PetscObject)LSC_L));
1011:     PetscCall(PetscSNPrintf(lscname, sizeof(lscname), "%s_LSC_Lp", ilink->splitname));
1012:     PetscCall(PetscObjectQuery((PetscObject)pc->pmat, lscname, (PetscObject *)&LSC_L));
1013:     if (!LSC_L) PetscCall(PetscObjectQuery((PetscObject)pc->mat, lscname, (PetscObject *)&LSC_L));
1014:     if (LSC_L) PetscCall(PetscObjectCompose((PetscObject)jac->schur, "LSC_Lp", (PetscObject)LSC_L));
1015:   } else if (jac->type == PC_COMPOSITE_GKB) {
1016:     IS       ccis;
1017:     PetscInt rstart, rend;

1019:     PetscCheck(nsplit == 2, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_INCOMP, "To use GKB preconditioner you must have exactly 2 fields");

1021:     ilink = jac->head;

1023:     /* When extracting off-diagonal submatrices, we take complements from this range */
1024:     PetscCall(MatGetOwnershipRangeColumn(pc->mat, &rstart, &rend));

1026:     PetscCall(ISComplement(ilink->is_col, rstart, rend, &ccis));
1027:     if (jac->offdiag_use_amat) {
1028:       PetscCall(MatCreateSubMatrix(pc->mat, ilink->is, ccis, MAT_INITIAL_MATRIX, &jac->B));
1029:     } else {
1030:       PetscCall(MatCreateSubMatrix(pc->pmat, ilink->is, ccis, MAT_INITIAL_MATRIX, &jac->B));
1031:     }
1032:     PetscCall(ISDestroy(&ccis));
1033:     /* Create work vectors for GKB algorithm */
1034:     PetscCall(VecDuplicate(ilink->x, &jac->u));
1035:     PetscCall(VecDuplicate(ilink->x, &jac->Hu));
1036:     PetscCall(VecDuplicate(ilink->x, &jac->w2));
1037:     ilink = ilink->next;
1038:     PetscCall(ISComplement(ilink->is_col, rstart, rend, &ccis));
1039:     if (jac->offdiag_use_amat) {
1040:       PetscCall(MatCreateSubMatrix(pc->mat, ilink->is, ccis, MAT_INITIAL_MATRIX, &jac->C));
1041:     } else {
1042:       PetscCall(MatCreateSubMatrix(pc->pmat, ilink->is, ccis, MAT_INITIAL_MATRIX, &jac->C));
1043:     }
1044:     PetscCall(ISDestroy(&ccis));
1045:     /* Create work vectors for GKB algorithm */
1046:     PetscCall(VecDuplicate(ilink->x, &jac->v));
1047:     PetscCall(VecDuplicate(ilink->x, &jac->d));
1048:     PetscCall(VecDuplicate(ilink->x, &jac->w1));
1049:     PetscCall(MatGolubKahanComputeExplicitOperator(jac->mat[0], jac->B, jac->C, &jac->H, jac->gkbnu));
1050:     PetscCall(PetscCalloc1(jac->gkbdelay, &jac->vecz));

1052:     ilink = jac->head;
1053:     PetscCall(KSPSetOperators(ilink->ksp, jac->H, jac->H));
1054:     if (!jac->suboptionsset) PetscCall(KSPSetFromOptions(ilink->ksp));
1055:     /* Create gkb_monitor context */
1056:     if (jac->gkbmonitor) {
1057:       PetscInt tablevel;
1058:       PetscCall(PetscViewerCreate(PETSC_COMM_WORLD, &jac->gkbviewer));
1059:       PetscCall(PetscViewerSetType(jac->gkbviewer, PETSCVIEWERASCII));
1060:       PetscCall(PetscObjectGetTabLevel((PetscObject)ilink->ksp, &tablevel));
1061:       PetscCall(PetscViewerASCIISetTab(jac->gkbviewer, tablevel));
1062:       PetscCall(PetscObjectIncrementTabLevel((PetscObject)ilink->ksp, (PetscObject)ilink->ksp, 1));
1063:     }
1064:   } else {
1065:     /* set up the individual splits' PCs */
1066:     i     = 0;
1067:     ilink = jac->head;
1068:     while (ilink) {
1069:       PetscCall(KSPSetOperators(ilink->ksp, jac->mat[i], jac->pmat[i]));
1070:       /* really want setfromoptions called in PCSetFromOptions_FieldSplit(), but it is not ready yet */
1071:       if (!jac->suboptionsset) PetscCall(KSPSetFromOptions(ilink->ksp));
1072:       i++;
1073:       ilink = ilink->next;
1074:     }
1075:   }

1077:   /* Set coordinates to the sub PC objects whenever these are set */
1078:   if (jac->coordinates_set) {
1079:     PC pc_coords;
1080:     if (jac->type == PC_COMPOSITE_SCHUR) {
1081:       // Head is first block.
1082:       PetscCall(KSPGetPC(jac->head->ksp, &pc_coords));
1083:       PetscCall(PCSetCoordinates(pc_coords, jac->head->dim, jac->head->ndofs, jac->head->coords));
1084:       // Second one is Schur block, but its KSP object is in kspschur.
1085:       PetscCall(KSPGetPC(jac->kspschur, &pc_coords));
1086:       PetscCall(PCSetCoordinates(pc_coords, jac->head->next->dim, jac->head->next->ndofs, jac->head->next->coords));
1087:     } else if (jac->type == PC_COMPOSITE_GKB) {
1088:       PetscCall(PetscInfo(pc, "Warning: Setting coordinates does nothing for the GKB Fieldpslit preconditioner\n"));
1089:     } else {
1090:       ilink = jac->head;
1091:       while (ilink) {
1092:         PetscCall(KSPGetPC(ilink->ksp, &pc_coords));
1093:         PetscCall(PCSetCoordinates(pc_coords, ilink->dim, ilink->ndofs, ilink->coords));
1094:         ilink = ilink->next;
1095:       }
1096:     }
1097:   }

1099:   jac->suboptionsset = PETSC_TRUE;
1100:   PetscFunctionReturn(PETSC_SUCCESS);
1101: }

1103: #define FieldSplitSplitSolveAdd(ilink, xx, yy) \
1104:   ((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) || \
1105:                     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) || \
1106:                     VecScatterEnd(ilink->sctx, ilink->y, yy, ADD_VALUES, SCATTER_REVERSE)))

1108: static PetscErrorCode PCApply_FieldSplit_Schur(PC pc, Vec x, Vec y)
1109: {
1110:   PC_FieldSplit    *jac    = (PC_FieldSplit *)pc->data;
1111:   PC_FieldSplitLink ilinkA = jac->head, ilinkD = ilinkA->next;
1112:   KSP               kspA = ilinkA->ksp, kspLower = kspA, kspUpper = jac->kspupper;

1114:   PetscFunctionBegin;
1115:   switch (jac->schurfactorization) {
1116:   case PC_FIELDSPLIT_SCHUR_FACT_DIAG:
1117:     /* [A00 0; 0 -S], positive definite, suitable for MINRES */
1118:     PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1119:     PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1120:     PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1121:     PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1122:     PetscCall(KSPSolve(kspA, ilinkA->x, ilinkA->y));
1123:     PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1124:     PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1125:     PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1126:     PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1127:     PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1128:     PetscCall(KSPSolve(jac->kspschur, ilinkD->x, ilinkD->y));
1129:     PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y));
1130:     PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1131:     PetscCall(VecScale(ilinkD->y, jac->schurscale));
1132:     PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1133:     PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1134:     PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1135:     break;
1136:   case PC_FIELDSPLIT_SCHUR_FACT_LOWER:
1137:     /* [A00 0; A10 S], suitable for left preconditioning */
1138:     PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1139:     PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1140:     PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1141:     PetscCall(KSPSolve(kspA, ilinkA->x, ilinkA->y));
1142:     PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1143:     PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1144:     PetscCall(MatMult(jac->C, ilinkA->y, ilinkD->x));
1145:     PetscCall(VecScale(ilinkD->x, -1.));
1146:     PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD));
1147:     PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1148:     PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD));
1149:     PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1150:     PetscCall(KSPSolve(jac->kspschur, ilinkD->x, ilinkD->y));
1151:     PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y));
1152:     PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1153:     PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1154:     PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1155:     PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1156:     break;
1157:   case PC_FIELDSPLIT_SCHUR_FACT_UPPER:
1158:     /* [A00 A01; 0 S], suitable for right preconditioning */
1159:     PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1160:     PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1161:     PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1162:     PetscCall(KSPSolve(jac->kspschur, ilinkD->x, ilinkD->y));
1163:     PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y));
1164:     PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1165:     PetscCall(MatMult(jac->B, ilinkD->y, ilinkA->x));
1166:     PetscCall(VecScale(ilinkA->x, -1.));
1167:     PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, ADD_VALUES, SCATTER_FORWARD));
1168:     PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1169:     PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, ADD_VALUES, SCATTER_FORWARD));
1170:     PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1171:     PetscCall(KSPSolve(kspA, ilinkA->x, ilinkA->y));
1172:     PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1173:     PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1174:     PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1175:     PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1176:     PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1177:     break;
1178:   case PC_FIELDSPLIT_SCHUR_FACT_FULL:
1179:     /* [1 0; A10 A00^{-1} 1] [A00 0; 0 S] [1 A00^{-1}A01; 0 1] */
1180:     PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1181:     PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1182:     PetscCall(PetscLogEventBegin(KSP_Solve_FS_L, kspLower, ilinkA->x, ilinkA->y, NULL));
1183:     PetscCall(KSPSolve(kspLower, ilinkA->x, ilinkA->y));
1184:     PetscCall(KSPCheckSolve(kspLower, pc, ilinkA->y));
1185:     PetscCall(PetscLogEventEnd(KSP_Solve_FS_L, kspLower, ilinkA->x, ilinkA->y, NULL));
1186:     PetscCall(MatMult(jac->C, ilinkA->y, ilinkD->x));
1187:     PetscCall(VecScale(ilinkD->x, -1.0));
1188:     PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD));
1189:     PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD));

1191:     PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1192:     PetscCall(KSPSolve(jac->kspschur, ilinkD->x, ilinkD->y));
1193:     PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y));
1194:     PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1195:     PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));

1197:     if (kspUpper == kspA) {
1198:       PetscCall(MatMult(jac->B, ilinkD->y, ilinkA->y));
1199:       PetscCall(VecAXPY(ilinkA->x, -1.0, ilinkA->y));
1200:       PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1201:       PetscCall(KSPSolve(kspA, ilinkA->x, ilinkA->y));
1202:       PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1203:       PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1204:     } else {
1205:       PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1206:       PetscCall(KSPSolve(kspA, ilinkA->x, ilinkA->y));
1207:       PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1208:       PetscCall(MatMult(jac->B, ilinkD->y, ilinkA->x));
1209:       PetscCall(PetscLogEventBegin(KSP_Solve_FS_U, kspUpper, ilinkA->x, ilinkA->z, NULL));
1210:       PetscCall(KSPSolve(kspUpper, ilinkA->x, ilinkA->z));
1211:       PetscCall(KSPCheckSolve(kspUpper, pc, ilinkA->z));
1212:       PetscCall(PetscLogEventEnd(KSP_Solve_FS_U, kspUpper, ilinkA->x, ilinkA->z, NULL));
1213:       PetscCall(VecAXPY(ilinkA->y, -1.0, ilinkA->z));
1214:     }
1215:     PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1216:     PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1217:     PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1218:   }
1219:   PetscFunctionReturn(PETSC_SUCCESS);
1220: }

1222: static PetscErrorCode PCApplyTranspose_FieldSplit_Schur(PC pc, Vec x, Vec y)
1223: {
1224:   PC_FieldSplit    *jac    = (PC_FieldSplit *)pc->data;
1225:   PC_FieldSplitLink ilinkA = jac->head, ilinkD = ilinkA->next;
1226:   KSP               kspA = ilinkA->ksp, kspLower = kspA, kspUpper = jac->kspupper;

1228:   PetscFunctionBegin;
1229:   switch (jac->schurfactorization) {
1230:   case PC_FIELDSPLIT_SCHUR_FACT_DIAG:
1231:     /* [A00 0; 0 -S], positive definite, suitable for MINRES */
1232:     PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1233:     PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1234:     PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1235:     PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1236:     PetscCall(KSPSolveTranspose(kspA, ilinkA->x, ilinkA->y));
1237:     PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1238:     PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1239:     PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1240:     PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1241:     PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1242:     PetscCall(KSPSolveTranspose(jac->kspschur, ilinkD->x, ilinkD->y));
1243:     PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y));
1244:     PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1245:     PetscCall(VecScale(ilinkD->y, jac->schurscale));
1246:     PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1247:     PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1248:     PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1249:     break;
1250:   case PC_FIELDSPLIT_SCHUR_FACT_UPPER:
1251:     PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1252:     PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1253:     PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1254:     PetscCall(KSPSolveTranspose(kspA, ilinkA->x, ilinkA->y));
1255:     PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1256:     PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1257:     PetscCall(MatMultTranspose(jac->B, ilinkA->y, ilinkD->x));
1258:     PetscCall(VecScale(ilinkD->x, -1.));
1259:     PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD));
1260:     PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1261:     PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD));
1262:     PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1263:     PetscCall(KSPSolveTranspose(jac->kspschur, ilinkD->x, ilinkD->y));
1264:     PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y));
1265:     PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1266:     PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1267:     PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1268:     PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1269:     break;
1270:   case PC_FIELDSPLIT_SCHUR_FACT_LOWER:
1271:     PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1272:     PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1273:     PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1274:     PetscCall(KSPSolveTranspose(jac->kspschur, ilinkD->x, ilinkD->y));
1275:     PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y));
1276:     PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1277:     PetscCall(MatMultTranspose(jac->C, ilinkD->y, ilinkA->x));
1278:     PetscCall(VecScale(ilinkA->x, -1.));
1279:     PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, ADD_VALUES, SCATTER_FORWARD));
1280:     PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1281:     PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, ADD_VALUES, SCATTER_FORWARD));
1282:     PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1283:     PetscCall(KSPSolveTranspose(kspA, ilinkA->x, ilinkA->y));
1284:     PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1285:     PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1286:     PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1287:     PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1288:     PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1289:     break;
1290:   case PC_FIELDSPLIT_SCHUR_FACT_FULL:
1291:     PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1292:     PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1293:     PetscCall(PetscLogEventBegin(KSP_Solve_FS_U, kspUpper, ilinkA->x, ilinkA->y, NULL));
1294:     PetscCall(KSPSolveTranspose(kspUpper, ilinkA->x, ilinkA->y));
1295:     PetscCall(KSPCheckSolve(kspUpper, pc, ilinkA->y));
1296:     PetscCall(PetscLogEventEnd(KSP_Solve_FS_U, kspUpper, ilinkA->x, ilinkA->y, NULL));
1297:     PetscCall(MatMultTranspose(jac->B, ilinkA->y, ilinkD->x));
1298:     PetscCall(VecScale(ilinkD->x, -1.0));
1299:     PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD));
1300:     PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD));

1302:     PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1303:     PetscCall(KSPSolveTranspose(jac->kspschur, ilinkD->x, ilinkD->y));
1304:     PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y));
1305:     PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1306:     PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));

1308:     if (kspLower == kspA) {
1309:       PetscCall(MatMultTranspose(jac->C, ilinkD->y, ilinkA->y));
1310:       PetscCall(VecAXPY(ilinkA->x, -1.0, ilinkA->y));
1311:       PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1312:       PetscCall(KSPSolveTranspose(kspA, ilinkA->x, ilinkA->y));
1313:       PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1314:       PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1315:     } else {
1316:       PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1317:       PetscCall(KSPSolveTranspose(kspA, ilinkA->x, ilinkA->y));
1318:       PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1319:       PetscCall(MatMultTranspose(jac->C, ilinkD->y, ilinkA->x));
1320:       PetscCall(PetscLogEventBegin(KSP_Solve_FS_L, kspLower, ilinkA->x, ilinkA->z, NULL));
1321:       PetscCall(KSPSolveTranspose(kspLower, ilinkA->x, ilinkA->z));
1322:       PetscCall(KSPCheckSolve(kspLower, pc, ilinkA->z));
1323:       PetscCall(PetscLogEventEnd(KSP_Solve_FS_L, kspLower, ilinkA->x, ilinkA->z, NULL));
1324:       PetscCall(VecAXPY(ilinkA->y, -1.0, ilinkA->z));
1325:     }
1326:     PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1327:     PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1328:     PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1329:   }
1330:   PetscFunctionReturn(PETSC_SUCCESS);
1331: }

1333: static PetscErrorCode PCApply_FieldSplit(PC pc, Vec x, Vec y)
1334: {
1335:   PC_FieldSplit    *jac   = (PC_FieldSplit *)pc->data;
1336:   PC_FieldSplitLink ilink = jac->head;
1337:   PetscInt          cnt, bs;

1339:   PetscFunctionBegin;
1340:   if (jac->type == PC_COMPOSITE_ADDITIVE) {
1341:     if (jac->defaultsplit) {
1342:       PetscCall(VecGetBlockSize(x, &bs));
1343:       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);
1344:       PetscCall(VecGetBlockSize(y, &bs));
1345:       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);
1346:       PetscCall(VecStrideGatherAll(x, jac->x, INSERT_VALUES));
1347:       while (ilink) {
1348:         PetscCall(PetscLogEventBegin(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1349:         PetscCall(KSPSolve(ilink->ksp, ilink->x, ilink->y));
1350:         PetscCall(KSPCheckSolve(ilink->ksp, pc, ilink->y));
1351:         PetscCall(PetscLogEventEnd(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1352:         ilink = ilink->next;
1353:       }
1354:       PetscCall(VecStrideScatterAll(jac->y, y, INSERT_VALUES));
1355:     } else {
1356:       PetscCall(VecSet(y, 0.0));
1357:       while (ilink) {
1358:         PetscCall(FieldSplitSplitSolveAdd(ilink, x, y));
1359:         ilink = ilink->next;
1360:       }
1361:     }
1362:   } else if (jac->type == PC_COMPOSITE_MULTIPLICATIVE && jac->nsplits == 2) {
1363:     PetscCall(VecSet(y, 0.0));
1364:     /* solve on first block for first block variables */
1365:     PetscCall(VecScatterBegin(ilink->sctx, x, ilink->x, INSERT_VALUES, SCATTER_FORWARD));
1366:     PetscCall(VecScatterEnd(ilink->sctx, x, ilink->x, INSERT_VALUES, SCATTER_FORWARD));
1367:     PetscCall(PetscLogEventBegin(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1368:     PetscCall(KSPSolve(ilink->ksp, ilink->x, ilink->y));
1369:     PetscCall(KSPCheckSolve(ilink->ksp, pc, ilink->y));
1370:     PetscCall(PetscLogEventEnd(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1371:     PetscCall(VecScatterBegin(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE));
1372:     PetscCall(VecScatterEnd(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE));

1374:     /* compute the residual only onto second block variables using first block variables */
1375:     PetscCall(MatMult(jac->Afield[1], ilink->y, ilink->next->x));
1376:     ilink = ilink->next;
1377:     PetscCall(VecScale(ilink->x, -1.0));
1378:     PetscCall(VecScatterBegin(ilink->sctx, x, ilink->x, ADD_VALUES, SCATTER_FORWARD));
1379:     PetscCall(VecScatterEnd(ilink->sctx, x, ilink->x, ADD_VALUES, SCATTER_FORWARD));

1381:     /* solve on second block variables */
1382:     PetscCall(PetscLogEventBegin(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1383:     PetscCall(KSPSolve(ilink->ksp, ilink->x, ilink->y));
1384:     PetscCall(KSPCheckSolve(ilink->ksp, pc, ilink->y));
1385:     PetscCall(PetscLogEventEnd(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1386:     PetscCall(VecScatterBegin(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE));
1387:     PetscCall(VecScatterEnd(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE));
1388:   } else if (jac->type == PC_COMPOSITE_MULTIPLICATIVE || jac->type == PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE) {
1389:     if (!jac->w1) {
1390:       PetscCall(VecDuplicate(x, &jac->w1));
1391:       PetscCall(VecDuplicate(x, &jac->w2));
1392:     }
1393:     PetscCall(VecSet(y, 0.0));
1394:     PetscCall(FieldSplitSplitSolveAdd(ilink, x, y));
1395:     cnt = 1;
1396:     while (ilink->next) {
1397:       ilink = ilink->next;
1398:       /* compute the residual only over the part of the vector needed */
1399:       PetscCall(MatMult(jac->Afield[cnt++], y, ilink->x));
1400:       PetscCall(VecScale(ilink->x, -1.0));
1401:       PetscCall(VecScatterBegin(ilink->sctx, x, ilink->x, ADD_VALUES, SCATTER_FORWARD));
1402:       PetscCall(VecScatterEnd(ilink->sctx, x, ilink->x, ADD_VALUES, SCATTER_FORWARD));
1403:       PetscCall(PetscLogEventBegin(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1404:       PetscCall(KSPSolve(ilink->ksp, ilink->x, ilink->y));
1405:       PetscCall(KSPCheckSolve(ilink->ksp, pc, ilink->y));
1406:       PetscCall(PetscLogEventEnd(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1407:       PetscCall(VecScatterBegin(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE));
1408:       PetscCall(VecScatterEnd(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE));
1409:     }
1410:     if (jac->type == PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE) {
1411:       cnt -= 2;
1412:       while (ilink->previous) {
1413:         ilink = ilink->previous;
1414:         /* compute the residual only over the part of the vector needed */
1415:         PetscCall(MatMult(jac->Afield[cnt--], y, ilink->x));
1416:         PetscCall(VecScale(ilink->x, -1.0));
1417:         PetscCall(VecScatterBegin(ilink->sctx, x, ilink->x, ADD_VALUES, SCATTER_FORWARD));
1418:         PetscCall(VecScatterEnd(ilink->sctx, x, ilink->x, ADD_VALUES, SCATTER_FORWARD));
1419:         PetscCall(PetscLogEventBegin(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1420:         PetscCall(KSPSolve(ilink->ksp, ilink->x, ilink->y));
1421:         PetscCall(KSPCheckSolve(ilink->ksp, pc, ilink->y));
1422:         PetscCall(PetscLogEventEnd(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1423:         PetscCall(VecScatterBegin(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE));
1424:         PetscCall(VecScatterEnd(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE));
1425:       }
1426:     }
1427:   } else SETERRQ(PetscObjectComm((PetscObject)pc), PETSC_ERR_SUP, "Unsupported or unknown composition %d", (int)jac->type);
1428:   PetscFunctionReturn(PETSC_SUCCESS);
1429: }

1431: static PetscErrorCode PCApply_FieldSplit_GKB(PC pc, Vec x, Vec y)
1432: {
1433:   PC_FieldSplit    *jac    = (PC_FieldSplit *)pc->data;
1434:   PC_FieldSplitLink ilinkA = jac->head, ilinkD = ilinkA->next;
1435:   KSP               ksp = ilinkA->ksp;
1436:   Vec               u, v, Hu, d, work1, work2;
1437:   PetscScalar       alpha, z, nrmz2, *vecz;
1438:   PetscReal         lowbnd, nu, beta;
1439:   PetscInt          j, iterGKB;

1441:   PetscFunctionBegin;
1442:   PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1443:   PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1444:   PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1445:   PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));

1447:   u     = jac->u;
1448:   v     = jac->v;
1449:   Hu    = jac->Hu;
1450:   d     = jac->d;
1451:   work1 = jac->w1;
1452:   work2 = jac->w2;
1453:   vecz  = jac->vecz;

1455:   /* Change RHS to comply with matrix regularization H = A + nu*B*B' */
1456:   /* Add q = q + nu*B*b */
1457:   if (jac->gkbnu) {
1458:     nu = jac->gkbnu;
1459:     PetscCall(VecScale(ilinkD->x, jac->gkbnu));
1460:     PetscCall(MatMultAdd(jac->B, ilinkD->x, ilinkA->x, ilinkA->x)); /* q = q + nu*B*b */
1461:   } else {
1462:     /* Situation when no augmented Lagrangian is used. Then we set inner  */
1463:     /* matrix N = I in [Ar13], and thus nu = 1.                           */
1464:     nu = 1;
1465:   }

1467:   /* Transform rhs from [q,tilde{b}] to [0,b] */
1468:   PetscCall(PetscLogEventBegin(ilinkA->event, ksp, ilinkA->x, ilinkA->y, NULL));
1469:   PetscCall(KSPSolve(ksp, ilinkA->x, ilinkA->y));
1470:   PetscCall(KSPCheckSolve(ksp, pc, ilinkA->y));
1471:   PetscCall(PetscLogEventEnd(ilinkA->event, ksp, ilinkA->x, ilinkA->y, NULL));
1472:   PetscCall(MatMultHermitianTranspose(jac->B, ilinkA->y, work1));
1473:   PetscCall(VecAXPBY(work1, 1.0 / nu, -1.0, ilinkD->x)); /* c = b - B'*x        */

1475:   /* First step of algorithm */
1476:   PetscCall(VecNorm(work1, NORM_2, &beta)); /* beta = sqrt(nu*c'*c)*/
1477:   KSPCheckDot(ksp, beta);
1478:   beta = PetscSqrtReal(nu) * beta;
1479:   PetscCall(VecAXPBY(v, nu / beta, 0.0, work1)); /* v = nu/beta *c      */
1480:   PetscCall(MatMult(jac->B, v, work2));          /* u = H^{-1}*B*v      */
1481:   PetscCall(PetscLogEventBegin(ilinkA->event, ksp, work2, u, NULL));
1482:   PetscCall(KSPSolve(ksp, work2, u));
1483:   PetscCall(KSPCheckSolve(ksp, pc, u));
1484:   PetscCall(PetscLogEventEnd(ilinkA->event, ksp, work2, u, NULL));
1485:   PetscCall(MatMult(jac->H, u, Hu)); /* alpha = u'*H*u      */
1486:   PetscCall(VecDot(Hu, u, &alpha));
1487:   KSPCheckDot(ksp, alpha);
1488:   PetscCheck(PetscRealPart(alpha) > 0.0, PETSC_COMM_SELF, PETSC_ERR_NOT_CONVERGED, "GKB preconditioner diverged, H is not positive definite");
1489:   alpha = PetscSqrtReal(PetscAbsScalar(alpha));
1490:   PetscCall(VecScale(u, 1.0 / alpha));
1491:   PetscCall(VecAXPBY(d, 1.0 / alpha, 0.0, v)); /* v = nu/beta *c      */

1493:   z       = beta / alpha;
1494:   vecz[1] = z;

1496:   /* Computation of first iterate x(1) and p(1) */
1497:   PetscCall(VecAXPY(ilinkA->y, z, u));
1498:   PetscCall(VecCopy(d, ilinkD->y));
1499:   PetscCall(VecScale(ilinkD->y, -z));

1501:   iterGKB = 1;
1502:   lowbnd  = 2 * jac->gkbtol;
1503:   if (jac->gkbmonitor) PetscCall(PetscViewerASCIIPrintf(jac->gkbviewer, "%3" PetscInt_FMT " GKB Lower bound estimate %14.12e\n", iterGKB, (double)lowbnd));

1505:   while (iterGKB < jac->gkbmaxit && lowbnd > jac->gkbtol) {
1506:     iterGKB += 1;
1507:     PetscCall(MatMultHermitianTranspose(jac->B, u, work1)); /* v <- nu*(B'*u-alpha/nu*v) */
1508:     PetscCall(VecAXPBY(v, nu, -alpha, work1));
1509:     PetscCall(VecNorm(v, NORM_2, &beta)); /* beta = sqrt(nu)*v'*v      */
1510:     beta = beta / PetscSqrtReal(nu);
1511:     PetscCall(VecScale(v, 1.0 / beta));
1512:     PetscCall(MatMult(jac->B, v, work2)); /* u <- H^{-1}*(B*v-beta*H*u) */
1513:     PetscCall(MatMult(jac->H, u, Hu));
1514:     PetscCall(VecAXPY(work2, -beta, Hu));
1515:     PetscCall(PetscLogEventBegin(ilinkA->event, ksp, work2, u, NULL));
1516:     PetscCall(KSPSolve(ksp, work2, u));
1517:     PetscCall(KSPCheckSolve(ksp, pc, u));
1518:     PetscCall(PetscLogEventEnd(ilinkA->event, ksp, work2, u, NULL));
1519:     PetscCall(MatMult(jac->H, u, Hu)); /* alpha = u'*H*u            */
1520:     PetscCall(VecDot(Hu, u, &alpha));
1521:     KSPCheckDot(ksp, alpha);
1522:     PetscCheck(PetscRealPart(alpha) > 0.0, PETSC_COMM_SELF, PETSC_ERR_NOT_CONVERGED, "GKB preconditioner diverged, H is not positive definite");
1523:     alpha = PetscSqrtReal(PetscAbsScalar(alpha));
1524:     PetscCall(VecScale(u, 1.0 / alpha));

1526:     z       = -beta / alpha * z; /* z <- beta/alpha*z     */
1527:     vecz[0] = z;

1529:     /* Computation of new iterate x(i+1) and p(i+1) */
1530:     PetscCall(VecAXPBY(d, 1.0 / alpha, -beta / alpha, v)); /* d = (v-beta*d)/alpha */
1531:     PetscCall(VecAXPY(ilinkA->y, z, u));                   /* r = r + z*u          */
1532:     PetscCall(VecAXPY(ilinkD->y, -z, d));                  /* p = p - z*d          */
1533:     PetscCall(MatMult(jac->H, ilinkA->y, Hu));             /* ||u||_H = u'*H*u     */
1534:     PetscCall(VecDot(Hu, ilinkA->y, &nrmz2));

1536:     /* Compute Lower Bound estimate */
1537:     if (iterGKB > jac->gkbdelay) {
1538:       lowbnd = 0.0;
1539:       for (j = 0; j < jac->gkbdelay; j++) lowbnd += PetscAbsScalar(vecz[j] * vecz[j]);
1540:       lowbnd = PetscSqrtReal(lowbnd / PetscAbsScalar(nrmz2));
1541:     }

1543:     for (j = 0; j < jac->gkbdelay - 1; j++) vecz[jac->gkbdelay - j - 1] = vecz[jac->gkbdelay - j - 2];
1544:     if (jac->gkbmonitor) PetscCall(PetscViewerASCIIPrintf(jac->gkbviewer, "%3" PetscInt_FMT " GKB Lower bound estimate %14.12e\n", iterGKB, (double)lowbnd));
1545:   }

1547:   PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1548:   PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1549:   PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1550:   PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));

1552:   PetscFunctionReturn(PETSC_SUCCESS);
1553: }

1555: #define FieldSplitSplitSolveAddTranspose(ilink, xx, yy) \
1556:   ((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) || \
1557:                     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) || \
1558:                     VecScatterEnd(ilink->sctx, ilink->x, yy, ADD_VALUES, SCATTER_REVERSE)))

1560: static PetscErrorCode PCApplyTranspose_FieldSplit(PC pc, Vec x, Vec y)
1561: {
1562:   PC_FieldSplit    *jac   = (PC_FieldSplit *)pc->data;
1563:   PC_FieldSplitLink ilink = jac->head;
1564:   PetscInt          bs;

1566:   PetscFunctionBegin;
1567:   if (jac->type == PC_COMPOSITE_ADDITIVE) {
1568:     if (jac->defaultsplit) {
1569:       PetscCall(VecGetBlockSize(x, &bs));
1570:       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);
1571:       PetscCall(VecGetBlockSize(y, &bs));
1572:       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);
1573:       PetscCall(VecStrideGatherAll(x, jac->x, INSERT_VALUES));
1574:       while (ilink) {
1575:         PetscCall(PetscLogEventBegin(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1576:         PetscCall(KSPSolveTranspose(ilink->ksp, ilink->x, ilink->y));
1577:         PetscCall(KSPCheckSolve(ilink->ksp, pc, ilink->y));
1578:         PetscCall(PetscLogEventEnd(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1579:         ilink = ilink->next;
1580:       }
1581:       PetscCall(VecStrideScatterAll(jac->y, y, INSERT_VALUES));
1582:     } else {
1583:       PetscCall(VecSet(y, 0.0));
1584:       while (ilink) {
1585:         PetscCall(FieldSplitSplitSolveAddTranspose(ilink, x, y));
1586:         ilink = ilink->next;
1587:       }
1588:     }
1589:   } else {
1590:     if (!jac->w1) {
1591:       PetscCall(VecDuplicate(x, &jac->w1));
1592:       PetscCall(VecDuplicate(x, &jac->w2));
1593:     }
1594:     PetscCall(VecSet(y, 0.0));
1595:     if (jac->type == PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE) {
1596:       PetscCall(FieldSplitSplitSolveAddTranspose(ilink, x, y));
1597:       while (ilink->next) {
1598:         ilink = ilink->next;
1599:         PetscCall(MatMultTranspose(pc->mat, y, jac->w1));
1600:         PetscCall(VecWAXPY(jac->w2, -1.0, jac->w1, x));
1601:         PetscCall(FieldSplitSplitSolveAddTranspose(ilink, jac->w2, y));
1602:       }
1603:       while (ilink->previous) {
1604:         ilink = ilink->previous;
1605:         PetscCall(MatMultTranspose(pc->mat, y, jac->w1));
1606:         PetscCall(VecWAXPY(jac->w2, -1.0, jac->w1, x));
1607:         PetscCall(FieldSplitSplitSolveAddTranspose(ilink, jac->w2, y));
1608:       }
1609:     } else {
1610:       while (ilink->next) { /* get to last entry in linked list */
1611:         ilink = ilink->next;
1612:       }
1613:       PetscCall(FieldSplitSplitSolveAddTranspose(ilink, x, y));
1614:       while (ilink->previous) {
1615:         ilink = ilink->previous;
1616:         PetscCall(MatMultTranspose(pc->mat, y, jac->w1));
1617:         PetscCall(VecWAXPY(jac->w2, -1.0, jac->w1, x));
1618:         PetscCall(FieldSplitSplitSolveAddTranspose(ilink, jac->w2, y));
1619:       }
1620:     }
1621:   }
1622:   PetscFunctionReturn(PETSC_SUCCESS);
1623: }

1625: static PetscErrorCode PCReset_FieldSplit(PC pc)
1626: {
1627:   PC_FieldSplit    *jac   = (PC_FieldSplit *)pc->data;
1628:   PC_FieldSplitLink ilink = jac->head, next;

1630:   PetscFunctionBegin;
1631:   while (ilink) {
1632:     PetscCall(KSPDestroy(&ilink->ksp));
1633:     PetscCall(VecDestroy(&ilink->x));
1634:     PetscCall(VecDestroy(&ilink->y));
1635:     PetscCall(VecDestroy(&ilink->z));
1636:     PetscCall(VecScatterDestroy(&ilink->sctx));
1637:     PetscCall(ISDestroy(&ilink->is));
1638:     PetscCall(ISDestroy(&ilink->is_col));
1639:     PetscCall(PetscFree(ilink->splitname));
1640:     PetscCall(PetscFree(ilink->fields));
1641:     PetscCall(PetscFree(ilink->fields_col));
1642:     next = ilink->next;
1643:     PetscCall(PetscFree(ilink));
1644:     ilink = next;
1645:   }
1646:   jac->head = NULL;
1647:   PetscCall(PetscFree2(jac->x, jac->y));
1648:   if (jac->mat && jac->mat != jac->pmat) {
1649:     PetscCall(MatDestroyMatrices(jac->nsplits, &jac->mat));
1650:   } else if (jac->mat) {
1651:     jac->mat = NULL;
1652:   }
1653:   if (jac->pmat) PetscCall(MatDestroyMatrices(jac->nsplits, &jac->pmat));
1654:   if (jac->Afield) PetscCall(MatDestroyMatrices(jac->nsplits, &jac->Afield));
1655:   jac->nsplits = 0;
1656:   PetscCall(VecDestroy(&jac->w1));
1657:   PetscCall(VecDestroy(&jac->w2));
1658:   PetscCall(MatDestroy(&jac->schur));
1659:   PetscCall(MatDestroy(&jac->schurp));
1660:   PetscCall(MatDestroy(&jac->schur_user));
1661:   PetscCall(KSPDestroy(&jac->kspschur));
1662:   PetscCall(KSPDestroy(&jac->kspupper));
1663:   PetscCall(MatDestroy(&jac->B));
1664:   PetscCall(MatDestroy(&jac->C));
1665:   PetscCall(MatDestroy(&jac->H));
1666:   PetscCall(VecDestroy(&jac->u));
1667:   PetscCall(VecDestroy(&jac->v));
1668:   PetscCall(VecDestroy(&jac->Hu));
1669:   PetscCall(VecDestroy(&jac->d));
1670:   PetscCall(PetscFree(jac->vecz));
1671:   PetscCall(PetscViewerDestroy(&jac->gkbviewer));
1672:   jac->isrestrict = PETSC_FALSE;
1673:   PetscFunctionReturn(PETSC_SUCCESS);
1674: }

1676: static PetscErrorCode PCDestroy_FieldSplit(PC pc)
1677: {
1678:   PetscFunctionBegin;
1679:   PetscCall(PCReset_FieldSplit(pc));
1680:   PetscCall(PetscFree(pc->data));
1681:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCSetCoordinates_C", NULL));
1682:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetFields_C", NULL));
1683:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetIS_C", NULL));
1684:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetType_C", NULL));
1685:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetBlockSize_C", NULL));
1686:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitRestrictIS_C", NULL));
1687:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSchurGetSubKSP_C", NULL));
1688:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSubKSP_C", NULL));

1690:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBTol_C", NULL));
1691:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBMaxit_C", NULL));
1692:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBNu_C", NULL));
1693:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBDelay_C", NULL));
1694:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSubKSP_C", NULL));
1695:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurPre_C", NULL));
1696:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSchurPre_C", NULL));
1697:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurFactType_C", NULL));
1698:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurScale_C", NULL));
1699:   PetscFunctionReturn(PETSC_SUCCESS);
1700: }

1702: static PetscErrorCode PCSetFromOptions_FieldSplit(PC pc, PetscOptionItems *PetscOptionsObject)
1703: {
1704:   PetscInt        bs;
1705:   PetscBool       flg;
1706:   PC_FieldSplit  *jac = (PC_FieldSplit *)pc->data;
1707:   PCCompositeType ctype;

1709:   PetscFunctionBegin;
1710:   PetscOptionsHeadBegin(PetscOptionsObject, "FieldSplit options");
1711:   PetscCall(PetscOptionsBool("-pc_fieldsplit_dm_splits", "Whether to use DMCreateFieldDecomposition() for splits", "PCFieldSplitSetDMSplits", jac->dm_splits, &jac->dm_splits, NULL));
1712:   PetscCall(PetscOptionsInt("-pc_fieldsplit_block_size", "Blocksize that defines number of fields", "PCFieldSplitSetBlockSize", jac->bs, &bs, &flg));
1713:   if (flg) PetscCall(PCFieldSplitSetBlockSize(pc, bs));
1714:   jac->diag_use_amat = pc->useAmat;
1715:   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));
1716:   jac->offdiag_use_amat = pc->useAmat;
1717:   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));
1718:   PetscCall(PetscOptionsBool("-pc_fieldsplit_detect_saddle_point", "Form 2-way split by detecting zero diagonal entries", "PCFieldSplitSetDetectSaddlePoint", jac->detect, &jac->detect, NULL));
1719:   PetscCall(PCFieldSplitSetDetectSaddlePoint(pc, jac->detect)); /* Sets split type and Schur PC type */
1720:   PetscCall(PetscOptionsEnum("-pc_fieldsplit_type", "Type of composition", "PCFieldSplitSetType", PCCompositeTypes, (PetscEnum)jac->type, (PetscEnum *)&ctype, &flg));
1721:   if (flg) PetscCall(PCFieldSplitSetType(pc, ctype));
1722:   /* Only setup fields once */
1723:   if ((jac->bs > 0) && (jac->nsplits == 0)) {
1724:     /* only allow user to set fields from command line if bs is already known.
1725:        otherwise user can set them in PCFieldSplitSetDefaults() */
1726:     PetscCall(PCFieldSplitSetRuntimeSplits_Private(pc));
1727:     if (jac->splitdefined) PetscCall(PetscInfo(pc, "Splits defined using the options database\n"));
1728:   }
1729:   if (jac->type == PC_COMPOSITE_SCHUR) {
1730:     PetscCall(PetscOptionsGetEnum(((PetscObject)pc)->options, ((PetscObject)pc)->prefix, "-pc_fieldsplit_schur_factorization_type", PCFieldSplitSchurFactTypes, (PetscEnum *)&jac->schurfactorization, &flg));
1731:     if (flg) PetscCall(PetscInfo(pc, "Deprecated use of -pc_fieldsplit_schur_factorization_type\n"));
1732:     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));
1733:     PetscCall(PetscOptionsEnum("-pc_fieldsplit_schur_precondition", "How to build preconditioner for Schur complement", "PCFieldSplitSetSchurPre", PCFieldSplitSchurPreTypes, (PetscEnum)jac->schurpre, (PetscEnum *)&jac->schurpre, NULL));
1734:     PetscCall(PetscOptionsScalar("-pc_fieldsplit_schur_scale", "Scale Schur complement", "PCFieldSplitSetSchurScale", jac->schurscale, &jac->schurscale, NULL));
1735:   } else if (jac->type == PC_COMPOSITE_GKB) {
1736:     PetscCall(PetscOptionsReal("-pc_fieldsplit_gkb_tol", "The tolerance for the lower bound stopping criterion", "PCFieldSplitGKBTol", jac->gkbtol, &jac->gkbtol, NULL));
1737:     PetscCall(PetscOptionsInt("-pc_fieldsplit_gkb_delay", "The delay value for lower bound criterion", "PCFieldSplitGKBDelay", jac->gkbdelay, &jac->gkbdelay, NULL));
1738:     PetscCall(PetscOptionsReal("-pc_fieldsplit_gkb_nu", "Parameter in augmented Lagrangian approach", "PCFieldSplitGKBNu", jac->gkbnu, &jac->gkbnu, NULL));
1739:     PetscCheck(jac->gkbnu >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "nu cannot be less than 0: value %g", (double)jac->gkbnu);
1740:     PetscCall(PetscOptionsInt("-pc_fieldsplit_gkb_maxit", "Maximum allowed number of iterations", "PCFieldSplitGKBMaxit", jac->gkbmaxit, &jac->gkbmaxit, NULL));
1741:     PetscCall(PetscOptionsBool("-pc_fieldsplit_gkb_monitor", "Prints number of GKB iterations and error", "PCFieldSplitGKB", jac->gkbmonitor, &jac->gkbmonitor, NULL));
1742:   }
1743:   /*
1744:     In the initial call to this routine the sub-solver data structures do not exist so we cannot call KSPSetFromOptions() on them yet.
1745:     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
1746:     is called on the outer solver in case changes were made in the options database

1748:     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()
1749:     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.
1750:     Without this extra check test p2p1fetidp_olof_full and others fail with incorrect matrix types.

1752:     There could be a negative side effect of calling the KSPSetFromOptions() below.

1754:     If one captured the PetscObjectState of the options database one could skip these calls if the database has not changed from the previous call
1755:   */
1756:   if (jac->issetup) {
1757:     PC_FieldSplitLink ilink = jac->head;
1758:     if (jac->type == PC_COMPOSITE_SCHUR) {
1759:       if (jac->kspupper && jac->kspupper->totalits > 0) PetscCall(KSPSetFromOptions(jac->kspupper));
1760:       if (jac->kspschur && jac->kspschur->totalits > 0) PetscCall(KSPSetFromOptions(jac->kspschur));
1761:     }
1762:     while (ilink) {
1763:       if (ilink->ksp->totalits > 0) PetscCall(KSPSetFromOptions(ilink->ksp));
1764:       ilink = ilink->next;
1765:     }
1766:   }
1767:   PetscOptionsHeadEnd();
1768:   PetscFunctionReturn(PETSC_SUCCESS);
1769: }

1771: static PetscErrorCode PCFieldSplitSetFields_FieldSplit(PC pc, const char splitname[], PetscInt n, const PetscInt *fields, const PetscInt *fields_col)
1772: {
1773:   PC_FieldSplit    *jac = (PC_FieldSplit *)pc->data;
1774:   PC_FieldSplitLink ilink, next = jac->head;
1775:   char              prefix[128];
1776:   PetscInt          i;

1778:   PetscFunctionBegin;
1779:   if (jac->splitdefined) {
1780:     PetscCall(PetscInfo(pc, "Ignoring new split \"%s\" because the splits have already been defined\n", splitname));
1781:     PetscFunctionReturn(PETSC_SUCCESS);
1782:   }
1783:   for (i = 0; i < n; i++) {
1784:     PetscCheck(fields[i] < jac->bs, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Field %" PetscInt_FMT " requested but only %" PetscInt_FMT " exist", fields[i], jac->bs);
1785:     PetscCheck(fields[i] >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Negative field %" PetscInt_FMT " requested", fields[i]);
1786:   }
1787:   PetscCall(PetscNew(&ilink));
1788:   if (splitname) {
1789:     PetscCall(PetscStrallocpy(splitname, &ilink->splitname));
1790:   } else {
1791:     PetscCall(PetscMalloc1(3, &ilink->splitname));
1792:     PetscCall(PetscSNPrintf(ilink->splitname, 2, "%" PetscInt_FMT, jac->nsplits));
1793:   }
1794:   ilink->event = jac->nsplits < 5 ? KSP_Solve_FS_0 + jac->nsplits : KSP_Solve_FS_0 + 4; /* Any split great than 4 gets logged in the 4th split */
1795:   PetscCall(PetscMalloc1(n, &ilink->fields));
1796:   PetscCall(PetscArraycpy(ilink->fields, fields, n));
1797:   PetscCall(PetscMalloc1(n, &ilink->fields_col));
1798:   PetscCall(PetscArraycpy(ilink->fields_col, fields_col, n));

1800:   ilink->nfields = n;
1801:   ilink->next    = NULL;
1802:   PetscCall(KSPCreate(PetscObjectComm((PetscObject)pc), &ilink->ksp));
1803:   PetscCall(KSPSetNestLevel(ilink->ksp, pc->kspnestlevel));
1804:   PetscCall(KSPSetErrorIfNotConverged(ilink->ksp, pc->erroriffailure));
1805:   PetscCall(PetscObjectIncrementTabLevel((PetscObject)ilink->ksp, (PetscObject)pc, 1));
1806:   PetscCall(KSPSetType(ilink->ksp, KSPPREONLY));

1808:   PetscCall(PetscSNPrintf(prefix, sizeof(prefix), "%sfieldsplit_%s_", ((PetscObject)pc)->prefix ? ((PetscObject)pc)->prefix : "", ilink->splitname));
1809:   PetscCall(KSPSetOptionsPrefix(ilink->ksp, prefix));

1811:   if (!next) {
1812:     jac->head       = ilink;
1813:     ilink->previous = NULL;
1814:   } else {
1815:     while (next->next) next = next->next;
1816:     next->next      = ilink;
1817:     ilink->previous = next;
1818:   }
1819:   jac->nsplits++;
1820:   PetscFunctionReturn(PETSC_SUCCESS);
1821: }

1823: static PetscErrorCode PCFieldSplitSchurGetSubKSP_FieldSplit(PC pc, PetscInt *n, KSP **subksp)
1824: {
1825:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

1827:   PetscFunctionBegin;
1828:   *subksp = NULL;
1829:   if (n) *n = 0;
1830:   if (jac->type == PC_COMPOSITE_SCHUR) {
1831:     PetscInt nn;

1833:     PetscCheck(jac->schur, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONGSTATE, "Must call KSPSetUp() or PCSetUp() before calling PCFieldSplitSchurGetSubKSP()");
1834:     PetscCheck(jac->nsplits == 2, PetscObjectComm((PetscObject)pc), PETSC_ERR_PLIB, "Unexpected number of splits %" PetscInt_FMT " != 2", jac->nsplits);
1835:     nn = jac->nsplits + (jac->kspupper != jac->head->ksp ? 1 : 0);
1836:     PetscCall(PetscMalloc1(nn, subksp));
1837:     (*subksp)[0] = jac->head->ksp;
1838:     (*subksp)[1] = jac->kspschur;
1839:     if (jac->kspupper != jac->head->ksp) (*subksp)[2] = jac->kspupper;
1840:     if (n) *n = nn;
1841:   }
1842:   PetscFunctionReturn(PETSC_SUCCESS);
1843: }

1845: static PetscErrorCode PCFieldSplitGetSubKSP_FieldSplit_Schur(PC pc, PetscInt *n, KSP **subksp)
1846: {
1847:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

1849:   PetscFunctionBegin;
1850:   PetscCheck(jac->schur, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONGSTATE, "Must call KSPSetUp() or PCSetUp() before calling PCFieldSplitGetSubKSP()");
1851:   PetscCall(PetscMalloc1(jac->nsplits, subksp));
1852:   PetscCall(MatSchurComplementGetKSP(jac->schur, *subksp));

1854:   (*subksp)[1] = jac->kspschur;
1855:   if (n) *n = jac->nsplits;
1856:   PetscFunctionReturn(PETSC_SUCCESS);
1857: }

1859: static PetscErrorCode PCFieldSplitGetSubKSP_FieldSplit(PC pc, PetscInt *n, KSP **subksp)
1860: {
1861:   PC_FieldSplit    *jac   = (PC_FieldSplit *)pc->data;
1862:   PetscInt          cnt   = 0;
1863:   PC_FieldSplitLink ilink = jac->head;

1865:   PetscFunctionBegin;
1866:   PetscCall(PetscMalloc1(jac->nsplits, subksp));
1867:   while (ilink) {
1868:     (*subksp)[cnt++] = ilink->ksp;
1869:     ilink            = ilink->next;
1870:   }
1871:   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);
1872:   if (n) *n = jac->nsplits;
1873:   PetscFunctionReturn(PETSC_SUCCESS);
1874: }

1876: /*@C
1877:   PCFieldSplitRestrictIS - Restricts the fieldsplit `IS`s to be within a given `IS`.

1879:   Input Parameters:
1880: + pc  - the preconditioner context
1881: - isy - the index set that defines the indices to which the fieldsplit is to be restricted

1883:   Level: advanced

1885:   Developer Notes:
1886:   It seems the resulting `IS`s will not cover the entire space, so
1887:   how can they define a convergent preconditioner? Needs explaining.

1889: .seealso: [](sec_block_matrices), `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSetIS()`
1890: @*/
1891: PetscErrorCode PCFieldSplitRestrictIS(PC pc, IS isy)
1892: {
1893:   PetscFunctionBegin;
1896:   PetscTryMethod(pc, "PCFieldSplitRestrictIS_C", (PC, IS), (pc, isy));
1897:   PetscFunctionReturn(PETSC_SUCCESS);
1898: }

1900: static PetscErrorCode PCFieldSplitRestrictIS_FieldSplit(PC pc, IS isy)
1901: {
1902:   PC_FieldSplit    *jac   = (PC_FieldSplit *)pc->data;
1903:   PC_FieldSplitLink ilink = jac->head, next;
1904:   PetscInt          localsize, size, sizez, i;
1905:   const PetscInt   *ind, *indz;
1906:   PetscInt         *indc, *indcz;
1907:   PetscBool         flg;

1909:   PetscFunctionBegin;
1910:   PetscCall(ISGetLocalSize(isy, &localsize));
1911:   PetscCallMPI(MPI_Scan(&localsize, &size, 1, MPIU_INT, MPI_SUM, PetscObjectComm((PetscObject)isy)));
1912:   size -= localsize;
1913:   while (ilink) {
1914:     IS isrl, isr;
1915:     PC subpc;
1916:     PetscCall(ISEmbed(ilink->is, isy, PETSC_TRUE, &isrl));
1917:     PetscCall(ISGetLocalSize(isrl, &localsize));
1918:     PetscCall(PetscMalloc1(localsize, &indc));
1919:     PetscCall(ISGetIndices(isrl, &ind));
1920:     PetscCall(PetscArraycpy(indc, ind, localsize));
1921:     PetscCall(ISRestoreIndices(isrl, &ind));
1922:     PetscCall(ISDestroy(&isrl));
1923:     for (i = 0; i < localsize; i++) *(indc + i) += size;
1924:     PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)isy), localsize, indc, PETSC_OWN_POINTER, &isr));
1925:     PetscCall(PetscObjectReference((PetscObject)isr));
1926:     PetscCall(ISDestroy(&ilink->is));
1927:     ilink->is = isr;
1928:     PetscCall(PetscObjectReference((PetscObject)isr));
1929:     PetscCall(ISDestroy(&ilink->is_col));
1930:     ilink->is_col = isr;
1931:     PetscCall(ISDestroy(&isr));
1932:     PetscCall(KSPGetPC(ilink->ksp, &subpc));
1933:     PetscCall(PetscObjectTypeCompare((PetscObject)subpc, PCFIELDSPLIT, &flg));
1934:     if (flg) {
1935:       IS       iszl, isz;
1936:       MPI_Comm comm;
1937:       PetscCall(ISGetLocalSize(ilink->is, &localsize));
1938:       comm = PetscObjectComm((PetscObject)ilink->is);
1939:       PetscCall(ISEmbed(isy, ilink->is, PETSC_TRUE, &iszl));
1940:       PetscCallMPI(MPI_Scan(&localsize, &sizez, 1, MPIU_INT, MPI_SUM, comm));
1941:       sizez -= localsize;
1942:       PetscCall(ISGetLocalSize(iszl, &localsize));
1943:       PetscCall(PetscMalloc1(localsize, &indcz));
1944:       PetscCall(ISGetIndices(iszl, &indz));
1945:       PetscCall(PetscArraycpy(indcz, indz, localsize));
1946:       PetscCall(ISRestoreIndices(iszl, &indz));
1947:       PetscCall(ISDestroy(&iszl));
1948:       for (i = 0; i < localsize; i++) *(indcz + i) += sizez;
1949:       PetscCall(ISCreateGeneral(comm, localsize, indcz, PETSC_OWN_POINTER, &isz));
1950:       PetscCall(PCFieldSplitRestrictIS(subpc, isz));
1951:       PetscCall(ISDestroy(&isz));
1952:     }
1953:     next  = ilink->next;
1954:     ilink = next;
1955:   }
1956:   jac->isrestrict = PETSC_TRUE;
1957:   PetscFunctionReturn(PETSC_SUCCESS);
1958: }

1960: static PetscErrorCode PCFieldSplitSetIS_FieldSplit(PC pc, const char splitname[], IS is)
1961: {
1962:   PC_FieldSplit    *jac = (PC_FieldSplit *)pc->data;
1963:   PC_FieldSplitLink ilink, next = jac->head;
1964:   char              prefix[128];

1966:   PetscFunctionBegin;
1967:   if (jac->splitdefined) {
1968:     PetscCall(PetscInfo(pc, "Ignoring new split \"%s\" because the splits have already been defined\n", splitname));
1969:     PetscFunctionReturn(PETSC_SUCCESS);
1970:   }
1971:   PetscCall(PetscNew(&ilink));
1972:   if (splitname) {
1973:     PetscCall(PetscStrallocpy(splitname, &ilink->splitname));
1974:   } else {
1975:     PetscCall(PetscMalloc1(8, &ilink->splitname));
1976:     PetscCall(PetscSNPrintf(ilink->splitname, 7, "%" PetscInt_FMT, jac->nsplits));
1977:   }
1978:   ilink->event = jac->nsplits < 5 ? KSP_Solve_FS_0 + jac->nsplits : KSP_Solve_FS_0 + 4; /* Any split great than 4 gets logged in the 4th split */
1979:   PetscCall(PetscObjectReference((PetscObject)is));
1980:   PetscCall(ISDestroy(&ilink->is));
1981:   ilink->is = is;
1982:   PetscCall(PetscObjectReference((PetscObject)is));
1983:   PetscCall(ISDestroy(&ilink->is_col));
1984:   ilink->is_col = is;
1985:   ilink->next   = NULL;
1986:   PetscCall(KSPCreate(PetscObjectComm((PetscObject)pc), &ilink->ksp));
1987:   PetscCall(KSPSetNestLevel(ilink->ksp, pc->kspnestlevel));
1988:   PetscCall(KSPSetErrorIfNotConverged(ilink->ksp, pc->erroriffailure));
1989:   PetscCall(PetscObjectIncrementTabLevel((PetscObject)ilink->ksp, (PetscObject)pc, 1));
1990:   PetscCall(KSPSetType(ilink->ksp, KSPPREONLY));

1992:   PetscCall(PetscSNPrintf(prefix, sizeof(prefix), "%sfieldsplit_%s_", ((PetscObject)pc)->prefix ? ((PetscObject)pc)->prefix : "", ilink->splitname));
1993:   PetscCall(KSPSetOptionsPrefix(ilink->ksp, prefix));

1995:   if (!next) {
1996:     jac->head       = ilink;
1997:     ilink->previous = NULL;
1998:   } else {
1999:     while (next->next) next = next->next;
2000:     next->next      = ilink;
2001:     ilink->previous = next;
2002:   }
2003:   jac->nsplits++;
2004:   PetscFunctionReturn(PETSC_SUCCESS);
2005: }

2007: /*@C
2008:   PCFieldSplitSetFields - Sets the fields that define one particular split in `PCFIELDSPLIT`

2010:   Logically Collective

2012:   Input Parameters:
2013: + pc         - the preconditioner context
2014: . splitname  - name of this split, if `NULL` the number of the split is used
2015: . n          - the number of fields in this split
2016: . fields     - the fields in this split
2017: - fields_col - generally the same as fields, if it does not match fields then the matrix block that is solved for this set of fields comes from an off-diagonal block
2018:                  of the matrix and fields_col provides the column indices for that block

2020:   Level: intermediate

2022:   Notes:
2023:   Use `PCFieldSplitSetIS()` to set a  general set of indices as a split.

2025:   `PCFieldSplitSetFields()` is for defining fields as strided blocks. For example, if the block
2026:   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
2027:   0xx3xx6xx9xx12 ... x1xx4xx7xx ... xx2xx5xx8xx.. 01x34x67x... 0x1x3x5x7.. x12x45x78x....
2028:   where the numbered entries indicate what is in the split.

2030:   This function is called once per split (it creates a new split each time).  Solve options
2031:   for this split will be available under the prefix `-fieldsplit_SPLITNAME_`.

2033:   `PCFieldSplitSetIS()` does not support having a fields_col different from fields

2035:   Developer Notes:
2036:   This routine does not actually create the `IS` representing the split, that is delayed
2037:   until `PCSetUp_FieldSplit()`, because information about the vector/matrix layouts may not be
2038:   available when this routine is called.

2040: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSetBlockSize()`, `PCFieldSplitSetIS()`, `PCFieldSplitRestrictIS()`
2041: @*/
2042: PetscErrorCode PCFieldSplitSetFields(PC pc, const char splitname[], PetscInt n, const PetscInt *fields, const PetscInt *fields_col)
2043: {
2044:   PetscFunctionBegin;
2046:   PetscAssertPointer(splitname, 2);
2047:   PetscCheck(n >= 1, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_OUTOFRANGE, "Provided number of fields %" PetscInt_FMT " in split \"%s\" not positive", n, splitname);
2048:   PetscAssertPointer(fields, 4);
2049:   PetscTryMethod(pc, "PCFieldSplitSetFields_C", (PC, const char[], PetscInt, const PetscInt *, const PetscInt *), (pc, splitname, n, fields, fields_col));
2050:   PetscFunctionReturn(PETSC_SUCCESS);
2051: }

2053: /*@
2054:   PCFieldSplitSetDiagUseAmat - set flag indicating whether to extract diagonal blocks from Amat (rather than Pmat) to build
2055:   the sub-matrices associated with each split. Where `KSPSetOperators`(ksp,Amat,Pmat)) was used to supply the operators.

2057:   Logically Collective

2059:   Input Parameters:
2060: + pc  - the preconditioner object
2061: - flg - boolean flag indicating whether or not to use Amat to extract the diagonal blocks from

2063:   Options Database Key:
2064: . -pc_fieldsplit_diag_use_amat - use the Amat to provide the diagonal blocks

2066:   Level: intermediate

2068: .seealso: [](sec_block_matrices), `PC`, `PCSetOperators()`, `KSPSetOperators()`, `PCFieldSplitGetDiagUseAmat()`, `PCFieldSplitSetOffDiagUseAmat()`, `PCFIELDSPLIT`
2069: @*/
2070: PetscErrorCode PCFieldSplitSetDiagUseAmat(PC pc, PetscBool flg)
2071: {
2072:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
2073:   PetscBool      isfs;

2075:   PetscFunctionBegin;
2077:   PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCFIELDSPLIT, &isfs));
2078:   PetscCheck(isfs, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "PC not of type %s", PCFIELDSPLIT);
2079:   jac->diag_use_amat = flg;
2080:   PetscFunctionReturn(PETSC_SUCCESS);
2081: }

2083: /*@
2084:   PCFieldSplitGetDiagUseAmat - get the flag indicating whether to extract diagonal blocks from Amat (rather than Pmat) to build
2085:   the sub-matrices associated with each split.  Where `KSPSetOperators`(ksp,Amat,Pmat)) was used to supply the operators.

2087:   Logically Collective

2089:   Input Parameter:
2090: . pc - the preconditioner object

2092:   Output Parameter:
2093: . flg - boolean flag indicating whether or not to use Amat to extract the diagonal blocks from

2095:   Level: intermediate

2097: .seealso: [](sec_block_matrices), `PC`, `PCSetOperators()`, `KSPSetOperators()`, `PCFieldSplitSetDiagUseAmat()`, `PCFieldSplitGetOffDiagUseAmat()`, `PCFIELDSPLIT`
2098: @*/
2099: PetscErrorCode PCFieldSplitGetDiagUseAmat(PC pc, PetscBool *flg)
2100: {
2101:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
2102:   PetscBool      isfs;

2104:   PetscFunctionBegin;
2106:   PetscAssertPointer(flg, 2);
2107:   PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCFIELDSPLIT, &isfs));
2108:   PetscCheck(isfs, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "PC not of type %s", PCFIELDSPLIT);
2109:   *flg = jac->diag_use_amat;
2110:   PetscFunctionReturn(PETSC_SUCCESS);
2111: }

2113: /*@
2114:   PCFieldSplitSetOffDiagUseAmat - set flag indicating whether to extract off-diagonal blocks from Amat (rather than Pmat) to build
2115:   the sub-matrices associated with each split.  Where `KSPSetOperators`(ksp,Amat,Pmat)) was used to supply the operators.

2117:   Logically Collective

2119:   Input Parameters:
2120: + pc  - the preconditioner object
2121: - flg - boolean flag indicating whether or not to use Amat to extract the off-diagonal blocks from

2123:   Options Database Key:
2124: . -pc_fieldsplit_off_diag_use_amat <bool> - use the Amat to extract the off-diagonal blocks

2126:   Level: intermediate

2128: .seealso: [](sec_block_matrices), `PC`, `PCSetOperators()`, `KSPSetOperators()`, `PCFieldSplitGetOffDiagUseAmat()`, `PCFieldSplitSetDiagUseAmat()`, `PCFIELDSPLIT`
2129: @*/
2130: PetscErrorCode PCFieldSplitSetOffDiagUseAmat(PC pc, PetscBool flg)
2131: {
2132:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
2133:   PetscBool      isfs;

2135:   PetscFunctionBegin;
2137:   PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCFIELDSPLIT, &isfs));
2138:   PetscCheck(isfs, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "PC not of type %s", PCFIELDSPLIT);
2139:   jac->offdiag_use_amat = flg;
2140:   PetscFunctionReturn(PETSC_SUCCESS);
2141: }

2143: /*@
2144:   PCFieldSplitGetOffDiagUseAmat - get the flag indicating whether to extract off-diagonal blocks from Amat (rather than Pmat) to build
2145:   the sub-matrices associated with each split.  Where `KSPSetOperators`(ksp,Amat,Pmat)) was used to supply the operators.

2147:   Logically Collective

2149:   Input Parameter:
2150: . pc - the preconditioner object

2152:   Output Parameter:
2153: . flg - boolean flag indicating whether or not to use Amat to extract the off-diagonal blocks from

2155:   Level: intermediate

2157: .seealso: [](sec_block_matrices), `PC`, `PCSetOperators()`, `KSPSetOperators()`, `PCFieldSplitSetOffDiagUseAmat()`, `PCFieldSplitGetDiagUseAmat()`, `PCFIELDSPLIT`
2158: @*/
2159: PetscErrorCode PCFieldSplitGetOffDiagUseAmat(PC pc, PetscBool *flg)
2160: {
2161:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
2162:   PetscBool      isfs;

2164:   PetscFunctionBegin;
2166:   PetscAssertPointer(flg, 2);
2167:   PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCFIELDSPLIT, &isfs));
2168:   PetscCheck(isfs, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "PC not of type %s", PCFIELDSPLIT);
2169:   *flg = jac->offdiag_use_amat;
2170:   PetscFunctionReturn(PETSC_SUCCESS);
2171: }

2173: /*@C
2174:   PCFieldSplitSetIS - Sets the exact elements for a split in a `PCFIELDSPLIT`

2176:   Logically Collective

2178:   Input Parameters:
2179: + pc        - the preconditioner context
2180: . splitname - name of this split, if `NULL` the number of the split is used
2181: - is        - the index set that defines the elements in this split

2183:   Level: intermediate

2185:   Notes:
2186:   Use `PCFieldSplitSetFields()`, for splits defined by strided types.

2188:   This function is called once per split (it creates a new split each time).  Solve options
2189:   for this split will be available under the prefix -fieldsplit_SPLITNAME_.

2191: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSetBlockSize()`
2192: @*/
2193: PetscErrorCode PCFieldSplitSetIS(PC pc, const char splitname[], IS is)
2194: {
2195:   PetscFunctionBegin;
2197:   if (splitname) PetscAssertPointer(splitname, 2);
2199:   PetscTryMethod(pc, "PCFieldSplitSetIS_C", (PC, const char[], IS), (pc, splitname, is));
2200:   PetscFunctionReturn(PETSC_SUCCESS);
2201: }

2203: /*@C
2204:   PCFieldSplitGetIS - Retrieves the elements for a split as an `IS`

2206:   Logically Collective

2208:   Input Parameters:
2209: + pc        - the preconditioner context
2210: - splitname - name of this split

2212:   Output Parameter:
2213: . is - the index set that defines the elements in this split, or `NULL` if the split is not found

2215:   Level: intermediate

2217: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSetIS()`
2218: @*/
2219: PetscErrorCode PCFieldSplitGetIS(PC pc, const char splitname[], IS *is)
2220: {
2221:   PetscFunctionBegin;
2223:   PetscAssertPointer(splitname, 2);
2224:   PetscAssertPointer(is, 3);
2225:   {
2226:     PC_FieldSplit    *jac   = (PC_FieldSplit *)pc->data;
2227:     PC_FieldSplitLink ilink = jac->head;
2228:     PetscBool         found;

2230:     *is = NULL;
2231:     while (ilink) {
2232:       PetscCall(PetscStrcmp(ilink->splitname, splitname, &found));
2233:       if (found) {
2234:         *is = ilink->is;
2235:         break;
2236:       }
2237:       ilink = ilink->next;
2238:     }
2239:   }
2240:   PetscFunctionReturn(PETSC_SUCCESS);
2241: }

2243: /*@C
2244:   PCFieldSplitGetISByIndex - Retrieves the elements for a given split as an `IS`

2246:   Logically Collective

2248:   Input Parameters:
2249: + pc    - the preconditioner context
2250: - index - index of this split

2252:   Output Parameter:
2253: . is - the index set that defines the elements in this split

2255:   Level: intermediate

2257: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitGetIS()`, `PCFieldSplitSetIS()`
2258: @*/
2259: PetscErrorCode PCFieldSplitGetISByIndex(PC pc, PetscInt index, IS *is)
2260: {
2261:   PetscFunctionBegin;
2262:   PetscCheck(index >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Negative field %" PetscInt_FMT " requested", index);
2264:   PetscAssertPointer(is, 3);
2265:   {
2266:     PC_FieldSplit    *jac   = (PC_FieldSplit *)pc->data;
2267:     PC_FieldSplitLink ilink = jac->head;
2268:     PetscInt          i     = 0;
2269:     PetscCheck(index < jac->nsplits, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Field %" PetscInt_FMT " requested but only %" PetscInt_FMT " exist", index, jac->nsplits);

2271:     while (i < index) {
2272:       ilink = ilink->next;
2273:       ++i;
2274:     }
2275:     PetscCall(PCFieldSplitGetIS(pc, ilink->splitname, is));
2276:   }
2277:   PetscFunctionReturn(PETSC_SUCCESS);
2278: }

2280: /*@
2281:   PCFieldSplitSetBlockSize - Sets the block size for defining where fields start in the
2282:   fieldsplit preconditioner when calling `PCFieldSplitSetIS()`. If not set the matrix block size is used.

2284:   Logically Collective

2286:   Input Parameters:
2287: + pc - the preconditioner context
2288: - bs - the block size

2290:   Level: intermediate

2292: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSetIS()`
2293: @*/
2294: PetscErrorCode PCFieldSplitSetBlockSize(PC pc, PetscInt bs)
2295: {
2296:   PetscFunctionBegin;
2299:   PetscTryMethod(pc, "PCFieldSplitSetBlockSize_C", (PC, PetscInt), (pc, bs));
2300:   PetscFunctionReturn(PETSC_SUCCESS);
2301: }

2303: /*@C
2304:   PCFieldSplitGetSubKSP - Gets the `KSP` contexts for all splits

2306:   Collective

2308:   Input Parameter:
2309: . pc - the preconditioner context

2311:   Output Parameters:
2312: + n      - the number of splits
2313: - subksp - the array of `KSP` contexts

2315:   Level: advanced

2317:   Notes:
2318:   After `PCFieldSplitGetSubKSP()` the array of `KSP`s is to be freed by the user with `PetscFree()`
2319:   (not the `KSP`, just the array that contains them).

2321:   You must call `PCSetUp()` before calling `PCFieldSplitGetSubKSP()`.

2323:   If the fieldsplit is of type `PC_COMPOSITE_SCHUR`, it returns the `KSP` object used inside the
2324:   Schur complement and the `KSP` object used to iterate over the Schur complement.
2325:   To access all the `KSP` objects used in `PC_COMPOSITE_SCHUR`, use `PCFieldSplitSchurGetSubKSP()`.

2327:   If the fieldsplit is of type `PC_COMPOSITE_GKB`, it returns the `KSP` object used to solve the
2328:   inner linear system defined by the matrix H in each loop.

2330:   Fortran Notes:
2331:   You must pass in a `KSP` array that is large enough to contain all the `KSP`s.
2332:   You can call `PCFieldSplitGetSubKSP`(pc,n,`PETSC_NULL_KSP`,ierr) to determine how large the
2333:   `KSP` array must be.

2335:   Developer Notes:
2336:   There should be a `PCFieldSplitRestoreSubKSP()` instead of requiring the user to call `PetscFree()`

2338:   The Fortran interface should be modernized to return directly the array of values.

2340: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSetIS()`, `PCFieldSplitSchurGetSubKSP()`
2341: @*/
2342: PetscErrorCode PCFieldSplitGetSubKSP(PC pc, PetscInt *n, KSP *subksp[])
2343: {
2344:   PetscFunctionBegin;
2346:   if (n) PetscAssertPointer(n, 2);
2347:   PetscUseMethod(pc, "PCFieldSplitGetSubKSP_C", (PC, PetscInt *, KSP **), (pc, n, subksp));
2348:   PetscFunctionReturn(PETSC_SUCCESS);
2349: }

2351: /*@C
2352:   PCFieldSplitSchurGetSubKSP - Gets the `KSP` contexts used inside the Schur complement based `PCFIELDSPLIT`

2354:   Collective

2356:   Input Parameter:
2357: . pc - the preconditioner context

2359:   Output Parameters:
2360: + n      - the number of splits
2361: - subksp - the array of `KSP` contexts

2363:   Level: advanced

2365:   Notes:
2366:   After `PCFieldSplitSchurGetSubKSP()` the array of `KSP`s is to be freed by the user with `PetscFree()`
2367:   (not the `KSP` just the array that contains them).

2369:   You must call `PCSetUp()` before calling `PCFieldSplitSchurGetSubKSP()`.

2371:   If the fieldsplit type is of type `PC_COMPOSITE_SCHUR`, it returns (in order)
2372: +  1  - the `KSP` used for the (1,1) block
2373: .  2  - the `KSP` used for the Schur complement (not the one used for the interior Schur solver)
2374: -  3  - the `KSP` used for the (1,1) block in the upper triangular factor (if different from that of the (1,1) block).

2376:   It returns a null array if the fieldsplit is not of type `PC_COMPOSITE_SCHUR`; in this case, you should use `PCFieldSplitGetSubKSP()`.

2378:   Fortran Notes:
2379:   You must pass in a `KSP` array that is large enough to contain all the local `KSP`s.
2380:   You can call `PCFieldSplitSchurGetSubKSP`(pc,n,`PETSC_NULL_KSP`,ierr) to determine how large the
2381:   `KSP` array must be.

2383:   Developer Notes:
2384:   There should be a `PCFieldSplitRestoreSubKSP()` instead of requiring the user to call `PetscFree()`

2386:   Should the functionality of `PCFieldSplitSchurGetSubKSP()` and `PCFieldSplitGetSubKSP()` be merged?

2388:   The Fortran interface should be modernized to return directly the array of values.

2390: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSetIS()`, `PCFieldSplitGetSubKSP()`
2391: @*/
2392: PetscErrorCode PCFieldSplitSchurGetSubKSP(PC pc, PetscInt *n, KSP *subksp[])
2393: {
2394:   PetscFunctionBegin;
2396:   if (n) PetscAssertPointer(n, 2);
2397:   PetscUseMethod(pc, "PCFieldSplitSchurGetSubKSP_C", (PC, PetscInt *, KSP **), (pc, n, subksp));
2398:   PetscFunctionReturn(PETSC_SUCCESS);
2399: }

2401: /*@
2402:   PCFieldSplitSetSchurPre -  Indicates from what operator the preconditioner is constructucted for the Schur complement.
2403:   The default is the A11 matrix.

2405:   Collective

2407:   Input Parameters:
2408: + pc    - the preconditioner context
2409: . ptype - which matrix to use for preconditioning the Schur complement: `PC_FIELDSPLIT_SCHUR_PRE_A11` (default),
2410:               `PC_FIELDSPLIT_SCHUR_PRE_SELF`, `PC_FIELDSPLIT_SCHUR_PRE_USER`,
2411:               `PC_FIELDSPLIT_SCHUR_PRE_SELFP`, and `PC_FIELDSPLIT_SCHUR_PRE_FULL`
2412: - pre   - matrix to use for preconditioning, or `NULL`

2414:   Options Database Keys:
2415: + -pc_fieldsplit_schur_precondition <self,selfp,user,a11,full> - default is `a11`. See notes for meaning of various arguments
2416: - -fieldsplit_1_pc_type <pctype>                               - the preconditioner algorithm that is used to construct the preconditioner from the operator

2418:   Level: intermediate

2420:   Notes:
2421:   If ptype is
2422: +     a11 - the preconditioner for the Schur complement is generated from the block diagonal part of the preconditioner
2423:   matrix associated with the Schur complement (i.e. A11), not the Schur complement matrix
2424: .     self - the preconditioner for the Schur complement is generated from the symbolic representation of the Schur complement matrix:
2425:   The only preconditioner that currently works with this symbolic representation matrix object is the `PCLSC`
2426:   preconditioner
2427: .     user - the preconditioner for the Schur complement is generated from the user provided matrix (pre argument
2428:   to this function).
2429: .     selfp - the preconditioning for the Schur complement is generated from an explicitly-assembled approximation Sp = A11 - A10 inv(diag(A00)) A01
2430:   This is only a good preconditioner when diag(A00) is a good preconditioner for A00. Optionally, A00 can be
2431:   lumped before extracting the diagonal using the additional option `-fieldsplit_1_mat_schur_complement_ainv_type lump`
2432: -     full - the preconditioner for the Schur complement is generated from the exact Schur complement matrix representation
2433:   computed internally by `PCFIELDSPLIT` (this is expensive)
2434:   useful mostly as a test that the Schur complement approach can work for your problem

2436:   When solving a saddle point problem, where the A11 block is identically zero, using `a11` as the ptype only makes sense
2437:   with the additional option `-fieldsplit_1_pc_type none`. Usually for saddle point problems one would use a ptype of self and
2438:   `-fieldsplit_1_pc_type lsc` which uses the least squares commutator to compute a preconditioner for the Schur complement.

2440: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSchurPre()`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSchurPreType`,
2441:           `MatSchurComplementSetAinvType()`, `PCLSC`,

2443: @*/
2444: PetscErrorCode PCFieldSplitSetSchurPre(PC pc, PCFieldSplitSchurPreType ptype, Mat pre)
2445: {
2446:   PetscFunctionBegin;
2448:   PetscTryMethod(pc, "PCFieldSplitSetSchurPre_C", (PC, PCFieldSplitSchurPreType, Mat), (pc, ptype, pre));
2449:   PetscFunctionReturn(PETSC_SUCCESS);
2450: }

2452: PetscErrorCode PCFieldSplitSchurPrecondition(PC pc, PCFieldSplitSchurPreType ptype, Mat pre)
2453: {
2454:   return PCFieldSplitSetSchurPre(pc, ptype, pre);
2455: } /* Deprecated name */

2457: /*@
2458:   PCFieldSplitGetSchurPre - For Schur complement fieldsplit, determine how the Schur complement will be
2459:   preconditioned.  See `PCFieldSplitSetSchurPre()` for details.

2461:   Logically Collective

2463:   Input Parameter:
2464: . pc - the preconditioner context

2466:   Output Parameters:
2467: + 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`
2468: - pre   - matrix to use for preconditioning (with `PC_FIELDSPLIT_SCHUR_PRE_USER`), or `NULL`

2470:   Level: intermediate

2472: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitSetSchurPre()`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSchurPreType`, `PCLSC`

2474: @*/
2475: PetscErrorCode PCFieldSplitGetSchurPre(PC pc, PCFieldSplitSchurPreType *ptype, Mat *pre)
2476: {
2477:   PetscFunctionBegin;
2479:   PetscUseMethod(pc, "PCFieldSplitGetSchurPre_C", (PC, PCFieldSplitSchurPreType *, Mat *), (pc, ptype, pre));
2480:   PetscFunctionReturn(PETSC_SUCCESS);
2481: }

2483: /*@
2484:   PCFieldSplitSchurGetS -  extract the `MATSCHURCOMPLEMENT` object used by this `PCFIELDSPLIT` in case it needs to be configured separately

2486:   Not Collective

2488:   Input Parameter:
2489: . pc - the preconditioner context

2491:   Output Parameter:
2492: . S - the Schur complement matrix

2494:   Level: advanced

2496:   Note:
2497:   This matrix should not be destroyed using `MatDestroy()`; rather, use `PCFieldSplitSchurRestoreS()`.

2499: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSchurPreType`, `PCFieldSplitSetSchurPre()`, `MATSCHURCOMPLEMENT`, `PCFieldSplitSchurRestoreS()`,
2500:           `MatCreateSchurComplement()`, `MatSchurComplementGetKSP()`, `MatSchurComplementComputeExplicitOperator()`, `MatGetSchurComplement()`
2501: @*/
2502: PetscErrorCode PCFieldSplitSchurGetS(PC pc, Mat *S)
2503: {
2504:   const char    *t;
2505:   PetscBool      isfs;
2506:   PC_FieldSplit *jac;

2508:   PetscFunctionBegin;
2510:   PetscCall(PetscObjectGetType((PetscObject)pc, &t));
2511:   PetscCall(PetscStrcmp(t, PCFIELDSPLIT, &isfs));
2512:   PetscCheck(isfs, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Expected PC of type PCFIELDSPLIT, got %s instead", t);
2513:   jac = (PC_FieldSplit *)pc->data;
2514:   PetscCheck(jac->type == PC_COMPOSITE_SCHUR, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Expected PCFIELDSPLIT of type SCHUR, got %d instead", jac->type);
2515:   if (S) *S = jac->schur;
2516:   PetscFunctionReturn(PETSC_SUCCESS);
2517: }

2519: /*@
2520:   PCFieldSplitSchurRestoreS -  returns the `MATSCHURCOMPLEMENT` matrix used by this `PC`

2522:   Not Collective

2524:   Input Parameters:
2525: + pc - the preconditioner context
2526: - S  - the Schur complement matrix

2528:   Level: advanced

2530: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSchurPreType`, `PCFieldSplitSetSchurPre()`, `MatSchurComplement`, `PCFieldSplitSchurGetS()`
2531: @*/
2532: PetscErrorCode PCFieldSplitSchurRestoreS(PC pc, Mat *S)
2533: {
2534:   const char    *t;
2535:   PetscBool      isfs;
2536:   PC_FieldSplit *jac;

2538:   PetscFunctionBegin;
2540:   PetscCall(PetscObjectGetType((PetscObject)pc, &t));
2541:   PetscCall(PetscStrcmp(t, PCFIELDSPLIT, &isfs));
2542:   PetscCheck(isfs, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Expected PC of type PCFIELDSPLIT, got %s instead", t);
2543:   jac = (PC_FieldSplit *)pc->data;
2544:   PetscCheck(jac->type == PC_COMPOSITE_SCHUR, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Expected PCFIELDSPLIT of type SCHUR, got %d instead", jac->type);
2545:   PetscCheck(S && (*S == jac->schur), PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "MatSchurComplement restored is not the same as gotten");
2546:   PetscFunctionReturn(PETSC_SUCCESS);
2547: }

2549: static PetscErrorCode PCFieldSplitSetSchurPre_FieldSplit(PC pc, PCFieldSplitSchurPreType ptype, Mat pre)
2550: {
2551:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

2553:   PetscFunctionBegin;
2554:   jac->schurpre = ptype;
2555:   if (ptype == PC_FIELDSPLIT_SCHUR_PRE_USER && pre) {
2556:     PetscCall(MatDestroy(&jac->schur_user));
2557:     jac->schur_user = pre;
2558:     PetscCall(PetscObjectReference((PetscObject)jac->schur_user));
2559:   }
2560:   PetscFunctionReturn(PETSC_SUCCESS);
2561: }

2563: static PetscErrorCode PCFieldSplitGetSchurPre_FieldSplit(PC pc, PCFieldSplitSchurPreType *ptype, Mat *pre)
2564: {
2565:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

2567:   PetscFunctionBegin;
2568:   if (ptype) *ptype = jac->schurpre;
2569:   if (pre) *pre = jac->schur_user;
2570:   PetscFunctionReturn(PETSC_SUCCESS);
2571: }

2573: /*@
2574:   PCFieldSplitSetSchurFactType -  sets which blocks of the approximate block factorization to retain in the preconditioner

2576:   Collective

2578:   Input Parameters:
2579: + pc    - the preconditioner context
2580: - ftype - which blocks of factorization to retain, `PC_FIELDSPLIT_SCHUR_FACT_FULL` is default

2582:   Options Database Key:
2583: . -pc_fieldsplit_schur_fact_type <diag,lower,upper,full> - default is `full`

2585:   Level: intermediate

2587:   Notes:
2588:   The FULL factorization is

2590: .vb
2591:    (A   B)  = (1       0) (A   0) (1  Ainv*B)  = L D U
2592:    (C   E)    (C*Ainv  1) (0   S) (0       1)
2593: .vb
2594:     where S = E - C*Ainv*B. In practice, the full factorization is applied via block triangular solves with the grouping L*(D*U). UPPER uses D*U, LOWER uses L*D,
2595:     and DIAG is the diagonal part with the sign of S flipped (because this makes the preconditioner positive definite for many formulations, thus allowing the use of `KSPMINRES)`.
2596:     Sign flipping of S can be turned off with `PCFieldSplitSetSchurScale()`.

2598:     If A and S are solved exactly
2599: .vb
2600:       *) FULL factorization is a direct solver.
2601:       *) 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.
2602:       *) 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.
2603: .ve

2605:   If the iteration count is very low, consider using `KSPFGMRES` or `KSPGCR` which can use one less preconditioner
2606:   application in this case. Note that the preconditioned operator may be highly non-normal, so such fast convergence may not be observed in practice.

2608:   For symmetric problems in which A is positive definite and S is negative definite, DIAG can be used with `KSPMINRES`.

2610:   A flexible method like `KSPFGMRES` or `KSPGCR` 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).

2612:   References:
2613: +   * - Murphy, Golub, and Wathen, A note on preconditioning indefinite linear systems, SIAM J. Sci. Comput., 21 (2000).
2614: -   * - Ipsen, A note on preconditioning nonsymmetric matrices, SIAM J. Sci. Comput., 23 (2001).

2616: .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSchurPreType`, `PCFieldSplitSetSchurScale()`
2617: @*/
2618: PetscErrorCode PCFieldSplitSetSchurFactType(PC pc, PCFieldSplitSchurFactType ftype)
2619: {
2620:   PetscFunctionBegin;
2622:   PetscTryMethod(pc, "PCFieldSplitSetSchurFactType_C", (PC, PCFieldSplitSchurFactType), (pc, ftype));
2623:   PetscFunctionReturn(PETSC_SUCCESS);
2624: }

2626: static PetscErrorCode PCFieldSplitSetSchurFactType_FieldSplit(PC pc, PCFieldSplitSchurFactType ftype)
2627: {
2628:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

2630:   PetscFunctionBegin;
2631:   jac->schurfactorization = ftype;
2632:   PetscFunctionReturn(PETSC_SUCCESS);
2633: }

2635: /*@
2636:   PCFieldSplitSetSchurScale -  Controls the sign flip of S for `PC_FIELDSPLIT_SCHUR_FACT_DIAG`.

2638:   Collective

2640:   Input Parameters:
2641: + pc    - the preconditioner context
2642: - scale - scaling factor for the Schur complement

2644:   Options Database Key:
2645: . -pc_fieldsplit_schur_scale - default is -1.0

2647:   Level: intermediate

2649: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSchurFactType`, `PCFieldSplitSetSchurFactType()`
2650: @*/
2651: PetscErrorCode PCFieldSplitSetSchurScale(PC pc, PetscScalar scale)
2652: {
2653:   PetscFunctionBegin;
2656:   PetscTryMethod(pc, "PCFieldSplitSetSchurScale_C", (PC, PetscScalar), (pc, scale));
2657:   PetscFunctionReturn(PETSC_SUCCESS);
2658: }

2660: static PetscErrorCode PCFieldSplitSetSchurScale_FieldSplit(PC pc, PetscScalar scale)
2661: {
2662:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

2664:   PetscFunctionBegin;
2665:   jac->schurscale = scale;
2666:   PetscFunctionReturn(PETSC_SUCCESS);
2667: }

2669: /*@C
2670:   PCFieldSplitGetSchurBlocks - Gets all matrix blocks for the Schur complement

2672:   Collective

2674:   Input Parameter:
2675: . pc - the preconditioner context

2677:   Output Parameters:
2678: + A00 - the (0,0) block
2679: . A01 - the (0,1) block
2680: . A10 - the (1,0) block
2681: - A11 - the (1,1) block

2683:   Level: advanced

2685: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `MatSchurComplementGetSubMatrices()`, `MatSchurComplementSetSubMatrices()`
2686: @*/
2687: PetscErrorCode PCFieldSplitGetSchurBlocks(PC pc, Mat *A00, Mat *A01, Mat *A10, Mat *A11)
2688: {
2689:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

2691:   PetscFunctionBegin;
2693:   PetscCheck(jac->type == PC_COMPOSITE_SCHUR, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONG, "FieldSplit is not using a Schur complement approach.");
2694:   if (A00) *A00 = jac->pmat[0];
2695:   if (A01) *A01 = jac->B;
2696:   if (A10) *A10 = jac->C;
2697:   if (A11) *A11 = jac->pmat[1];
2698:   PetscFunctionReturn(PETSC_SUCCESS);
2699: }

2701: /*@
2702:   PCFieldSplitSetGKBTol -  Sets the solver tolerance for the generalized Golub-Kahan bidiagonalization preconditioner in `PCFIELDSPLIT`

2704:   Collective

2706:   Input Parameters:
2707: + pc        - the preconditioner context
2708: - tolerance - the solver tolerance

2710:   Options Database Key:
2711: . -pc_fieldsplit_gkb_tol - default is 1e-5

2713:   Level: intermediate

2715:   Note:
2716:   The generalized GKB algorithm uses a lower bound estimate of the error in energy norm as stopping criterion.
2717:   It stops once the lower bound estimate undershoots the required solver tolerance. Although the actual error might be bigger than
2718:   this estimate, the stopping criterion is satisfactory in practical cases [A13].

2720:   References:
2721:   [Ar13] Generalized Golub-Kahan bidiagonalization and stopping criteria, SIAM J. Matrix Anal. Appl., Vol. 34, No. 2, pp. 571-592, 2013.

2723: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetGKBDelay()`, `PCFieldSplitSetGKBNu()`, `PCFieldSplitSetGKBMaxit()`
2724: @*/
2725: PetscErrorCode PCFieldSplitSetGKBTol(PC pc, PetscReal tolerance)
2726: {
2727:   PetscFunctionBegin;
2730:   PetscTryMethod(pc, "PCFieldSplitSetGKBTol_C", (PC, PetscReal), (pc, tolerance));
2731:   PetscFunctionReturn(PETSC_SUCCESS);
2732: }

2734: static PetscErrorCode PCFieldSplitSetGKBTol_FieldSplit(PC pc, PetscReal tolerance)
2735: {
2736:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

2738:   PetscFunctionBegin;
2739:   jac->gkbtol = tolerance;
2740:   PetscFunctionReturn(PETSC_SUCCESS);
2741: }

2743: /*@
2744:   PCFieldSplitSetGKBMaxit -  Sets the maximum number of iterations for the generalized Golub-Kahan bidiagonalization preconditioner in `PCFIELDSPLIT`

2746:   Collective

2748:   Input Parameters:
2749: + pc    - the preconditioner context
2750: - maxit - the maximum number of iterations

2752:   Options Database Key:
2753: . -pc_fieldsplit_gkb_maxit - default is 100

2755:   Level: intermediate

2757: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetGKBDelay()`, `PCFieldSplitSetGKBTol()`, `PCFieldSplitSetGKBNu()`
2758: @*/
2759: PetscErrorCode PCFieldSplitSetGKBMaxit(PC pc, PetscInt maxit)
2760: {
2761:   PetscFunctionBegin;
2764:   PetscTryMethod(pc, "PCFieldSplitSetGKBMaxit_C", (PC, PetscInt), (pc, maxit));
2765:   PetscFunctionReturn(PETSC_SUCCESS);
2766: }

2768: static PetscErrorCode PCFieldSplitSetGKBMaxit_FieldSplit(PC pc, PetscInt maxit)
2769: {
2770:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

2772:   PetscFunctionBegin;
2773:   jac->gkbmaxit = maxit;
2774:   PetscFunctionReturn(PETSC_SUCCESS);
2775: }

2777: /*@
2778:   PCFieldSplitSetGKBDelay -  Sets the delay in the lower bound error estimate in the generalized Golub-Kahan bidiagonalization in `PCFIELDSPLIT`
2779:   preconditioner.

2781:   Collective

2783:   Input Parameters:
2784: + pc    - the preconditioner context
2785: - delay - the delay window in the lower bound estimate

2787:   Options Database Key:
2788: . -pc_fieldsplit_gkb_delay - default is 5

2790:   Level: intermediate

2792:   Note:
2793:   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
2794:   is expressed as a truncated sum. The error at iteration k can only be measured at iteration (k + delay), and thus the algorithm needs
2795:   at least (delay + 1) iterations to stop. For more details on the generalized Golub-Kahan bidiagonalization method and its lower bound stopping criterion, please refer to

2797:   References:
2798:   [Ar13] Generalized Golub-Kahan bidiagonalization and stopping criteria, SIAM J. Matrix Anal. Appl., Vol. 34, No. 2, pp. 571-592, 2013.

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

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

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

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

2824:   Collective

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

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

2833:   Level: intermediate

2835:   Notes:
2836:   This shift is in general done to obtain better convergence properties for the outer loop of the algorithm. This is often achieved by choosing nu sufficiently big. However,
2837:   if nu is chosen too big, the matrix H might be badly conditioned and the solution of the linear system Hx = b in the inner loop becomes difficult. It is therefore
2838:   necessary to find a good balance in between the convergence of the inner and outer loop.

2840:   For nu = 0, no shift is done. In this case A00 has to be positive definite. The matrix N in [Ar13] is then chosen as identity.

2842:   References:
2843:   [Ar13] Generalized Golub-Kahan bidiagonalization and stopping criteria, SIAM J. Matrix Anal. Appl., Vol. 34, No. 2, pp. 571-592, 2013.

2845: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetGKBDelay()`, `PCFieldSplitSetGKBTol()`, `PCFieldSplitSetGKBMaxit()`
2846: @*/
2847: PetscErrorCode PCFieldSplitSetGKBNu(PC pc, PetscReal nu)
2848: {
2849:   PetscFunctionBegin;
2852:   PetscTryMethod(pc, "PCFieldSplitSetGKBNu_C", (PC, PetscReal), (pc, nu));
2853:   PetscFunctionReturn(PETSC_SUCCESS);
2854: }

2856: static PetscErrorCode PCFieldSplitSetGKBNu_FieldSplit(PC pc, PetscReal nu)
2857: {
2858:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

2860:   PetscFunctionBegin;
2861:   jac->gkbnu = nu;
2862:   PetscFunctionReturn(PETSC_SUCCESS);
2863: }

2865: static PetscErrorCode PCFieldSplitSetType_FieldSplit(PC pc, PCCompositeType type)
2866: {
2867:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

2869:   PetscFunctionBegin;
2870:   jac->type = type;
2871:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSubKSP_C", NULL));
2872:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurPre_C", NULL));
2873:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSchurPre_C", NULL));
2874:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurFactType_C", NULL));
2875:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurScale_C", NULL));
2876:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBTol_C", NULL));
2877:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBMaxit_C", NULL));
2878:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBNu_C", NULL));
2879:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBDelay_C", NULL));

2881:   if (type == PC_COMPOSITE_SCHUR) {
2882:     pc->ops->apply          = PCApply_FieldSplit_Schur;
2883:     pc->ops->applytranspose = PCApplyTranspose_FieldSplit_Schur;
2884:     pc->ops->view           = PCView_FieldSplit_Schur;

2886:     PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSubKSP_C", PCFieldSplitGetSubKSP_FieldSplit_Schur));
2887:     PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurPre_C", PCFieldSplitSetSchurPre_FieldSplit));
2888:     PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSchurPre_C", PCFieldSplitGetSchurPre_FieldSplit));
2889:     PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurFactType_C", PCFieldSplitSetSchurFactType_FieldSplit));
2890:     PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurScale_C", PCFieldSplitSetSchurScale_FieldSplit));
2891:   } else if (type == PC_COMPOSITE_GKB) {
2892:     pc->ops->apply = PCApply_FieldSplit_GKB;
2893:     pc->ops->view  = PCView_FieldSplit_GKB;

2895:     PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSubKSP_C", PCFieldSplitGetSubKSP_FieldSplit));
2896:     PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBTol_C", PCFieldSplitSetGKBTol_FieldSplit));
2897:     PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBMaxit_C", PCFieldSplitSetGKBMaxit_FieldSplit));
2898:     PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBNu_C", PCFieldSplitSetGKBNu_FieldSplit));
2899:     PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBDelay_C", PCFieldSplitSetGKBDelay_FieldSplit));
2900:   } else {
2901:     pc->ops->apply = PCApply_FieldSplit;
2902:     pc->ops->view  = PCView_FieldSplit;

2904:     PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSubKSP_C", PCFieldSplitGetSubKSP_FieldSplit));
2905:   }
2906:   PetscFunctionReturn(PETSC_SUCCESS);
2907: }

2909: static PetscErrorCode PCFieldSplitSetBlockSize_FieldSplit(PC pc, PetscInt bs)
2910: {
2911:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

2913:   PetscFunctionBegin;
2914:   PetscCheck(bs >= 1, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_OUTOFRANGE, "Blocksize must be positive, you gave %" PetscInt_FMT, bs);
2915:   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);
2916:   jac->bs = bs;
2917:   PetscFunctionReturn(PETSC_SUCCESS);
2918: }

2920: static PetscErrorCode PCSetCoordinates_FieldSplit(PC pc, PetscInt dim, PetscInt nloc, PetscReal coords[])
2921: {
2922:   PC_FieldSplit    *jac           = (PC_FieldSplit *)pc->data;
2923:   PC_FieldSplitLink ilink_current = jac->head;
2924:   IS                is_owned;

2926:   PetscFunctionBegin;
2927:   jac->coordinates_set = PETSC_TRUE; // Internal flag
2928:   PetscCall(MatGetOwnershipIS(pc->mat, &is_owned, NULL));

2930:   while (ilink_current) {
2931:     // For each IS, embed it to get local coords indces
2932:     IS              is_coords;
2933:     PetscInt        ndofs_block;
2934:     const PetscInt *block_dofs_enumeration; // Numbering of the dofs relevant to the current block

2936:     // Setting drop to true for safety. It should make no difference.
2937:     PetscCall(ISEmbed(ilink_current->is, is_owned, PETSC_TRUE, &is_coords));
2938:     PetscCall(ISGetLocalSize(is_coords, &ndofs_block));
2939:     PetscCall(ISGetIndices(is_coords, &block_dofs_enumeration));

2941:     // Allocate coordinates vector and set it directly
2942:     PetscCall(PetscMalloc1(ndofs_block * dim, &(ilink_current->coords)));
2943:     for (PetscInt dof = 0; dof < ndofs_block; ++dof) {
2944:       for (PetscInt d = 0; d < dim; ++d) (ilink_current->coords)[dim * dof + d] = coords[dim * block_dofs_enumeration[dof] + d];
2945:     }
2946:     ilink_current->dim   = dim;
2947:     ilink_current->ndofs = ndofs_block;
2948:     PetscCall(ISRestoreIndices(is_coords, &block_dofs_enumeration));
2949:     PetscCall(ISDestroy(&is_coords));
2950:     ilink_current = ilink_current->next;
2951:   }
2952:   PetscCall(ISDestroy(&is_owned));
2953:   PetscFunctionReturn(PETSC_SUCCESS);
2954: }

2956: /*@
2957:   PCFieldSplitSetType - Sets the type, `PCCompositeType`, of a `PCFIELDSPLIT`

2959:   Collective

2961:   Input Parameters:
2962: + pc   - the preconditioner context
2963: - type - `PC_COMPOSITE_ADDITIVE`, `PC_COMPOSITE_MULTIPLICATIVE` (default), `PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE`, `PC_COMPOSITE_SPECIAL`, `PC_COMPOSITE_SCHUR`

2965:   Options Database Key:
2966: . -pc_fieldsplit_type <type: one of multiplicative, additive, symmetric_multiplicative, special, schur> - Sets fieldsplit preconditioner type

2968:   Level: intermediate

2970: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCCompositeType`, `PCCompositeGetType()`, `PC_COMPOSITE_ADDITIVE`, `PC_COMPOSITE_MULTIPLICATIVE`,
2971:           `PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE`, `PC_COMPOSITE_SPECIAL`, `PC_COMPOSITE_SCHUR`
2972: @*/
2973: PetscErrorCode PCFieldSplitSetType(PC pc, PCCompositeType type)
2974: {
2975:   PetscFunctionBegin;
2977:   PetscTryMethod(pc, "PCFieldSplitSetType_C", (PC, PCCompositeType), (pc, type));
2978:   PetscFunctionReturn(PETSC_SUCCESS);
2979: }

2981: /*@
2982:   PCFieldSplitGetType - Gets the type, `PCCompositeType`, of a `PCFIELDSPLIT`

2984:   Not collective

2986:   Input Parameter:
2987: . pc - the preconditioner context

2989:   Output Parameter:
2990: . type - `PC_COMPOSITE_ADDITIVE`, `PC_COMPOSITE_MULTIPLICATIVE` (default), `PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE`, `PC_COMPOSITE_SPECIAL`, `PC_COMPOSITE_SCHUR`

2992:   Level: intermediate

2994: .seealso: [](sec_block_matrices), `PC`, `PCCompositeSetType()`, `PCFIELDSPLIT`, `PCCompositeType`, `PC_COMPOSITE_ADDITIVE`, `PC_COMPOSITE_MULTIPLICATIVE`,
2995:           `PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE`, `PC_COMPOSITE_SPECIAL`, `PC_COMPOSITE_SCHUR`
2996: @*/
2997: PetscErrorCode PCFieldSplitGetType(PC pc, PCCompositeType *type)
2998: {
2999:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

3001:   PetscFunctionBegin;
3003:   PetscAssertPointer(type, 2);
3004:   *type = jac->type;
3005:   PetscFunctionReturn(PETSC_SUCCESS);
3006: }

3008: /*@
3009:   PCFieldSplitSetDMSplits - Flags whether `DMCreateFieldDecomposition()` should be used to define the splits in a `PCFIELDSPLIT`, whenever possible.

3011:   Logically Collective

3013:   Input Parameters:
3014: + pc  - the preconditioner context
3015: - flg - boolean indicating whether to use field splits defined by the `DM`

3017:   Options Database Key:
3018: . -pc_fieldsplit_dm_splits <bool> - use the field splits defined by the `DM`

3020:   Level: intermediate

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

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

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

3040:   Logically Collective

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

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

3048:   Level: intermediate

3050: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetDMSplits()`, `PCFieldSplitSetFields()`, `PCFieldsplitSetIS()`
3051: @*/
3052: PetscErrorCode PCFieldSplitGetDMSplits(PC pc, PetscBool *flg)
3053: {
3054:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
3055:   PetscBool      isfs;

3057:   PetscFunctionBegin;
3059:   PetscAssertPointer(flg, 2);
3060:   PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCFIELDSPLIT, &isfs));
3061:   if (isfs) {
3062:     if (flg) *flg = jac->dm_splits;
3063:   }
3064:   PetscFunctionReturn(PETSC_SUCCESS);
3065: }

3067: /*@
3068:   PCFieldSplitGetDetectSaddlePoint - Returns flag indicating whether `PCFIELDSPLIT` will attempt to automatically determine fields based on zero diagonal entries.

3070:   Logically Collective

3072:   Input Parameter:
3073: . pc - the preconditioner context

3075:   Output Parameter:
3076: . flg - boolean indicating whether to detect fields or not

3078:   Level: intermediate

3080: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetDetectSaddlePoint()`
3081: @*/
3082: PetscErrorCode PCFieldSplitGetDetectSaddlePoint(PC pc, PetscBool *flg)
3083: {
3084:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

3086:   PetscFunctionBegin;
3087:   *flg = jac->detect;
3088:   PetscFunctionReturn(PETSC_SUCCESS);
3089: }

3091: /*@
3092:   PCFieldSplitSetDetectSaddlePoint - Sets flag indicating whether `PCFIELDSPLIT` will attempt to automatically determine fields based on zero diagonal entries.

3094:   Logically Collective

3096:   Input Parameter:
3097: . pc - the preconditioner context

3099:   Output Parameter:
3100: . flg - boolean indicating whether to detect fields or not

3102:   Options Database Key:
3103: . -pc_fieldsplit_detect_saddle_point <bool> - detect and use the saddle point

3105:   Level: intermediate

3107:   Note:
3108:   Also sets the split type to `PC_COMPOSITE_SCHUR` (see `PCFieldSplitSetType()`) and the Schur preconditioner type to `PC_FIELDSPLIT_SCHUR_PRE_SELF` (see `PCFieldSplitSetSchurPre()`).

3110: .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitGetDetectSaddlePoint()`, `PCFieldSplitSetType()`, `PCFieldSplitSetSchurPre()`, `PC_FIELDSPLIT_SCHUR_PRE_SELF`
3111: @*/
3112: PetscErrorCode PCFieldSplitSetDetectSaddlePoint(PC pc, PetscBool flg)
3113: {
3114:   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;

3116:   PetscFunctionBegin;
3117:   jac->detect = flg;
3118:   if (jac->detect) {
3119:     PetscCall(PCFieldSplitSetType(pc, PC_COMPOSITE_SCHUR));
3120:     PetscCall(PCFieldSplitSetSchurPre(pc, PC_FIELDSPLIT_SCHUR_PRE_SELF, NULL));
3121:   }
3122:   PetscFunctionReturn(PETSC_SUCCESS);
3123: }

3125: /*MC
3126:    PCFIELDSPLIT - Preconditioner created by combining separate preconditioners for individual
3127:    collections of variables (that may overlap) called splits. See [the users manual section on "Solving Block Matrices"](sec_block_matrices) for more details.

3129:    Options Database Keys:
3130: +   -pc_fieldsplit_%d_fields <a,b,..> - indicates the fields to be used in the `%d`'th split
3131: .   -pc_fieldsplit_default - automatically add any fields to additional splits that have not
3132:                               been supplied explicitly by `-pc_fieldsplit_%d_fields`
3133: .   -pc_fieldsplit_block_size <bs> - size of block that defines fields (i.e. there are bs fields)
3134: .   -pc_fieldsplit_type <additive,multiplicative,symmetric_multiplicative,schur,gkb> - type of relaxation or factorization splitting
3135: .   -pc_fieldsplit_schur_precondition <self,selfp,user,a11,full> - default is `a11`; see `PCFieldSplitSetSchurPre()`
3136: .   -pc_fieldsplit_schur_fact_type <diag,lower,upper,full> - set factorization type when using `-pc_fieldsplit_type schur`; see `PCFieldSplitSetSchurFactType()`
3137: -   -pc_fieldsplit_detect_saddle_point - automatically finds rows with zero diagonal and uses Schur complement with no preconditioner as the solver

3139:      Options prefixes for inner solvers when using the Schur complement preconditioner are `-fieldsplit_0_` and `-fieldsplit_1_` .
3140:      The options prefix for the inner solver when using the Golub-Kahan biadiagonalization preconditioner is `-fieldsplit_0_`
3141:      For all other solvers they are `-fieldsplit_%d_` for the `%d`'th field; use `-fieldsplit_` for all fields.

3143:      To set options on the solvers for each block append `-fieldsplit_` to all the `PC`
3144:      options database keys. For example, `-fieldsplit_pc_type ilu` `-fieldsplit_pc_factor_levels 1`

3146:      To set the options on the solvers separate for each block call `PCFieldSplitGetSubKSP()`
3147:       and set the options directly on the resulting `KSP` object

3149:     Level: intermediate

3151:    Notes:
3152:     Use `PCFieldSplitSetFields()` to set splits defined by "strided" entries and `PCFieldSplitSetIS()`
3153:      to define a split by an arbitrary collection of entries.

3155:       If no splits are set the default is used. The splits are defined by entries strided by bs,
3156:       beginning at 0 then 1, etc to bs-1. The block size can be set with `PCFieldSplitSetBlockSize()`,
3157:       if this is not called the block size defaults to the blocksize of the second matrix passed
3158:       to `KSPSetOperators()`/`PCSetOperators()`.

3160:       For the Schur complement preconditioner if

3162:       ```{math}
3163:       J = \left[\begin{array}{cc} A_{00} & A_{01} \\ A_{10} & A_{11} \end{array}\right]
3164:       ```

3166:       the preconditioner using `full` factorization is logically
3167:       ```{math}
3168:       \left[\begin{array}{cc} I & -\text{ksp}(A_{00}) \\ 0 & I \end{array}\right] \left[\begin{array}{cc} \text{inv}(A_{00}) & 0 \\ 0 & \text{ksp}(S) \end{array}\right] \left[\begin{array}{cc} I & 0 \\ -A_{10} \text{ksp}(A_{00}) & I \end{array}\right]
3169:       ```
3170:      where the action of $\text{inv}(A_{00})$ is applied using the KSP solver with prefix `-fieldsplit_0_`.  $S$ is the Schur complement
3171:      ```{math}
3172:      S = A_{11} - A_{10} \text{ksp}(A_{00}) A_{01}
3173:      ```
3174:      which is usually dense and not stored explicitly.  The action of $\text{ksp}(S)$ is computed using the KSP solver with prefix `-fieldsplit_splitname_` (where `splitname` was given
3175:      in providing the SECOND split or 1 if not given). For `PCFieldSplitGetSubKSP()` when field number is 0,
3176:      it returns the KSP associated with `-fieldsplit_0_` while field number 1 gives `-fieldsplit_1_` KSP. By default
3177:      $A_{11}$ is used to construct a preconditioner for $S$, use `PCFieldSplitSetSchurPre()` for all the possible ways to construct the preconditioner for $S$.

3179:      The factorization type is set using `-pc_fieldsplit_schur_fact_type <diag, lower, upper, full>`. `full` is shown above,
3180:      `diag` gives
3181:       ```{math}
3182:       \left[\begin{array}{cc} \text{inv}(A_{00}) & 0 \\  0 & -\text{ksp}(S) \end{array}\right]
3183:       ```
3184:      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
3185:      can be turned off with `PCFieldSplitSetSchurScale()` or by command line `-pc_fieldsplit_schur_scale 1.0`. The `lower` factorization is the inverse of
3186:       ```{math}
3187:       \left[\begin{array}{cc} A_{00} & 0 \\  A_{10} & S \end{array}\right]
3188:       ```
3189:      where the inverses of A_{00} and S are applied using KSPs. The upper factorization is the inverse of
3190:       ```{math}
3191:       \left[\begin{array}{cc} A_{00} & A_{01} \\  0 & S \end{array}\right]
3192:       ```
3193:      where again the inverses of $A_{00}$ and $S$ are applied using `KSP`s.

3195:      If only one set of indices (one `IS`) is provided with `PCFieldSplitSetIS()` then the complement of that `IS`
3196:      is used automatically for a second block.

3198:      The fieldsplit preconditioner cannot currently be used with the `MATBAIJ` or `MATSBAIJ` data formats if the blocksize is larger than 1.
3199:      Generally it should be used with the `MATAIJ` format.

3201:      The forms of these preconditioners are closely related if not identical to forms derived as "Distributive Iterations", see,
3202:      for example, page 294 in "Principles of Computational Fluid Dynamics" by Pieter Wesseling {cite}`wesseling2009`.
3203:      One can also use `PCFIELDSPLIT`
3204:      inside a smoother resulting in "Distributive Smoothers".

3206:      See "A taxonomy and comparison of parallel block multi-level preconditioners for the incompressible Navier-Stokes equations" {cite}`elman2008tcp`.

3208:      The Constrained Pressure Preconditioner (CPR) can be implemented using `PCCOMPOSITE` with `PCGALERKIN`. CPR first solves an $R A P$ subsystem, updates the
3209:      residual on all variables (`PCCompositeSetType(pc,PC_COMPOSITE_MULTIPLICATIVE)`), and then applies a simple ILU like preconditioner on all the variables.

3211:      The generalized Golub-Kahan bidiagonalization preconditioner (GKB) can be applied to symmetric $2 \times 2$ block matrices of the shape
3212:      ```{math}
3213:      \left[\begin{array}{cc} A_{00} & A_{01} \\ A_{01}' & 0 \end{array}\right]
3214:      ```
3215:      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 $H = _{A00} + \nu*A_{01}*A_{01}'$.
3216:      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_`.

3218:    Developer Note:
3219:    The Schur complement functionality of `PCFIELDSPLIT` should likely be factored into its own `PC` thus simplifying the implementation of the preconditioners and their
3220:    user API.

3222: .seealso: [](sec_block_matrices), `PC`, `PCCreate()`, `PCSetType()`, `PCType`, `PC`, `PCLSC`,
3223:           `PCFieldSplitGetSubKSP()`, `PCFieldSplitSchurGetSubKSP()`, `PCFieldSplitSetFields()`,
3224:           `PCFieldSplitSetType()`, `PCFieldSplitSetIS()`, `PCFieldSplitSetSchurPre()`, `PCFieldSplitSetSchurFactType()`,
3225:           `MatSchurComplementSetAinvType()`, `PCFieldSplitSetSchurScale()`, `PCFieldSplitSetDetectSaddlePoint()`
3226: M*/

3228: PETSC_EXTERN PetscErrorCode PCCreate_FieldSplit(PC pc)
3229: {
3230:   PC_FieldSplit *jac;

3232:   PetscFunctionBegin;
3233:   PetscCall(PetscNew(&jac));

3235:   jac->bs                 = -1;
3236:   jac->nsplits            = 0;
3237:   jac->type               = PC_COMPOSITE_MULTIPLICATIVE;
3238:   jac->schurpre           = PC_FIELDSPLIT_SCHUR_PRE_USER; /* Try user preconditioner first, fall back on diagonal */
3239:   jac->schurfactorization = PC_FIELDSPLIT_SCHUR_FACT_FULL;
3240:   jac->schurscale         = -1.0;
3241:   jac->dm_splits          = PETSC_TRUE;
3242:   jac->detect             = PETSC_FALSE;
3243:   jac->gkbtol             = 1e-5;
3244:   jac->gkbdelay           = 5;
3245:   jac->gkbnu              = 1;
3246:   jac->gkbmaxit           = 100;
3247:   jac->gkbmonitor         = PETSC_FALSE;
3248:   jac->coordinates_set    = PETSC_FALSE;

3250:   pc->data = (void *)jac;

3252:   pc->ops->apply           = PCApply_FieldSplit;
3253:   pc->ops->applytranspose  = PCApplyTranspose_FieldSplit;
3254:   pc->ops->setup           = PCSetUp_FieldSplit;
3255:   pc->ops->reset           = PCReset_FieldSplit;
3256:   pc->ops->destroy         = PCDestroy_FieldSplit;
3257:   pc->ops->setfromoptions  = PCSetFromOptions_FieldSplit;
3258:   pc->ops->view            = PCView_FieldSplit;
3259:   pc->ops->applyrichardson = NULL;

3261:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSchurGetSubKSP_C", PCFieldSplitSchurGetSubKSP_FieldSplit));
3262:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSubKSP_C", PCFieldSplitGetSubKSP_FieldSplit));
3263:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetFields_C", PCFieldSplitSetFields_FieldSplit));
3264:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetIS_C", PCFieldSplitSetIS_FieldSplit));
3265:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetType_C", PCFieldSplitSetType_FieldSplit));
3266:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetBlockSize_C", PCFieldSplitSetBlockSize_FieldSplit));
3267:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitRestrictIS_C", PCFieldSplitRestrictIS_FieldSplit));
3268:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCSetCoordinates_C", PCSetCoordinates_FieldSplit));
3269:   PetscFunctionReturn(PETSC_SUCCESS);
3270: }