xref: /petsc/src/ksp/pc/impls/fieldsplit/fieldsplit.c (revision d8a51d2aac522cef49bfbd84fd4cf473dc3fa6ee)
1 #include <petsc/private/pcimpl.h>  /*I "petscpc.h" I*/
2 #include <petsc/private/kspimpl.h> /*  This is needed to provide the appropriate PETSC_EXTERN for KSP_Solve_FS ....*/
3 #include <petscdm.h>
4 
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};
7 
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;
9 
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;
21 
22   /* Used only when setting coordinates with PCSetCoordinates */
23   PetscInt   dim;
24   PetscInt   ndofs;
25   PetscReal *coords;
26 };
27 
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;
39 
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 */
51 
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       */
62 
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;
72 
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 */
79 
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 }
97 
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;
105 
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   }
136 
137   if (isdraw) {
138     PetscDraw draw;
139     PetscReal x, y, w, wd;
140 
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 }
156 
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;
164 
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];
245 
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);
251 
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;
263 
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 }
280 
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;
287 
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"));
300 
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));
304 
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));
318 
319     PetscCall(PetscViewerASCIIPopTab(viewer));
320   }
321 
322   if (isdraw) {
323     PetscDraw draw;
324     PetscReal x, y, w, wd;
325 
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 }
341 
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];
349 
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 }
381 
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;
388 
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;
403 
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;
411 
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;
455 
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       }
470 
471       if (jac->detect) {
472         IS       zerodiags, rest;
473         PetscInt nmin, nmax;
474 
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;
489 
490         PetscCall(MatGetOwnershipRange(pc->mat, &nmin, &nmax));
491         if (jac->offdiag_use_amat) {
492           PetscCall(MatFindOffBlockDiagonalEntries(pc->mat, &coupling));
493         } else {
494           PetscCall(MatFindOffBlockDiagonalEntries(pc->pmat, &coupling));
495         }
496         PetscCall(ISCreateStride(PetscObjectComm((PetscObject)pc->mat), nmax - nmin, nmin, 1, &rest));
497         PetscCall(ISSetIdentity(rest));
498         PetscCall(PCFieldSplitSetIS(pc, "0", rest));
499         PetscCall(PCFieldSplitSetIS(pc, "1", coupling));
500         PetscCall(ISDestroy(&coupling));
501         PetscCall(ISDestroy(&rest));
502       } else {
503         PetscCall(PetscOptionsGetBool(((PetscObject)pc)->options, ((PetscObject)pc)->prefix, "-pc_fieldsplit_default", &fieldsplit_default, NULL));
504         if (!fieldsplit_default) {
505           /* Allow user to set fields from command line,  if bs was known at the time of PCSetFromOptions_FieldSplit()
506            then it is set there. This is not ideal because we should only have options set in XXSetFromOptions(). */
507           PetscCall(PCFieldSplitSetRuntimeSplits_Private(pc));
508           if (jac->splitdefined) PetscCall(PetscInfo(pc, "Splits defined using the options database\n"));
509         }
510         if ((fieldsplit_default || !jac->splitdefined) && !jac->isrestrict) {
511           Mat       M = pc->pmat;
512           PetscBool isnest;
513 
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;
523 
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;
543 
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   }
550 
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 }
554 
555 static PetscErrorCode MatGolubKahanComputeExplicitOperator(Mat A, Mat B, Mat C, Mat *H, PetscReal gkbnu)
556 {
557   Mat       BT, T;
558   PetscReal nrmT, nrmB;
559 
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.");
566 
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' */
572 
573   PetscCall(MatDestroy(&BT));
574   PetscCall(MatDestroy(&T));
575   PetscFunctionReturn(PETSC_SUCCESS);
576 }
577 
578 PETSC_EXTERN PetscErrorCode PetscOptionsFindPairPrefix_Private(PetscOptions, const char pre[], const char name[], const char *option[], const char *value[], PetscBool *flg);
579 
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;
586 
587   PetscFunctionBegin;
588   pc->failedreason = PC_NOERROR;
589   PetscCall(PCFieldSplitSetDefaults(pc));
590   nsplit = jac->nsplits;
591   ilink  = jac->head;
592 
593   /* get the matrices for each split */
594   if (!jac->issetup) {
595     PetscInt rstart, rend, nslots, bs;
596 
597     jac->issetup = PETSC_TRUE;
598 
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     }
603 
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;
608 
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     }
612 
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   }
646 
647   ilink = jac->head;
648   if (!jac->pmat) {
649     Vec xtmp;
650 
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;
656 
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];
663 
664           PetscCall(PetscObjectReference((PetscObject)jac->schur_user));
665         }
666       } else {
667         const char *prefix;
668         PetscCall(MatCreateSubMatrix(pc->pmat, ilink->is, ilink->is_col, MAT_INITIAL_MATRIX, &jac->pmat[i]));
669         PetscCall(MatGetOptionsPrefix(jac->pmat[i], &prefix));
670         if (!prefix) {
671           PetscCall(KSPGetOptionsPrefix(ilink->ksp, &prefix));
672           PetscCall(MatSetOptionsPrefix(jac->pmat[i], prefix));
673         }
674         PetscCall(MatSetFromOptions(jac->pmat[i]));
675         PetscCall(MatViewFromOptions(jac->pmat[i], NULL, "-mat_view"));
676       }
677       /* create work vectors for each split */
678       PetscCall(MatCreateVecs(jac->pmat[i], &jac->x[i], &jac->y[i]));
679       ilink->x = jac->x[i];
680       ilink->y = jac->y[i];
681       ilink->z = NULL;
682       /* compute scatter contexts needed by multiplicative versions and non-default splits */
683       PetscCall(VecScatterCreate(xtmp, ilink->is, jac->x[i], NULL, &ilink->sctx));
684       PetscCall(PetscObjectQuery((PetscObject)ilink->is, "nearnullspace", (PetscObject *)&sp));
685       if (sp) PetscCall(MatSetNearNullSpace(jac->pmat[i], sp));
686       ilink = ilink->next;
687     }
688     PetscCall(VecDestroy(&xtmp));
689   } else {
690     MatReuse      scall;
691     MatNullSpace *nullsp = NULL;
692 
693     if (pc->flag == DIFFERENT_NONZERO_PATTERN) {
694       PetscCall(MatGetNullSpaces(nsplit, jac->pmat, &nullsp));
695       for (i = 0; i < nsplit; i++) PetscCall(MatDestroy(&jac->pmat[i]));
696       scall = MAT_INITIAL_MATRIX;
697     } else scall = MAT_REUSE_MATRIX;
698 
699     for (i = 0; i < nsplit; i++) {
700       Mat pmat;
701 
702       /* Check for preconditioning matrix attached to IS */
703       PetscCall(PetscObjectQuery((PetscObject)ilink->is, "pmat", (PetscObject *)&pmat));
704       if (!pmat) PetscCall(MatCreateSubMatrix(pc->pmat, ilink->is, ilink->is_col, scall, &jac->pmat[i]));
705       ilink = ilink->next;
706     }
707     if (nullsp) PetscCall(MatRestoreNullSpaces(nsplit, jac->pmat, &nullsp));
708   }
709   if (jac->diag_use_amat) {
710     ilink = jac->head;
711     if (!jac->mat) {
712       PetscCall(PetscMalloc1(nsplit, &jac->mat));
713       for (i = 0; i < nsplit; i++) {
714         PetscCall(MatCreateSubMatrix(pc->mat, ilink->is, ilink->is_col, MAT_INITIAL_MATRIX, &jac->mat[i]));
715         ilink = ilink->next;
716       }
717     } else {
718       MatReuse      scall;
719       MatNullSpace *nullsp = NULL;
720 
721       if (pc->flag == DIFFERENT_NONZERO_PATTERN) {
722         PetscCall(MatGetNullSpaces(nsplit, jac->mat, &nullsp));
723         for (i = 0; i < nsplit; i++) PetscCall(MatDestroy(&jac->mat[i]));
724         scall = MAT_INITIAL_MATRIX;
725       } else scall = MAT_REUSE_MATRIX;
726 
727       for (i = 0; i < nsplit; i++) {
728         PetscCall(MatCreateSubMatrix(pc->mat, ilink->is, ilink->is_col, scall, &jac->mat[i]));
729         ilink = ilink->next;
730       }
731       if (nullsp) PetscCall(MatRestoreNullSpaces(nsplit, jac->mat, &nullsp));
732     }
733   } else {
734     jac->mat = jac->pmat;
735   }
736 
737   /* Check for null space attached to IS */
738   ilink = jac->head;
739   for (i = 0; i < nsplit; i++) {
740     MatNullSpace sp;
741 
742     PetscCall(PetscObjectQuery((PetscObject)ilink->is, "nullspace", (PetscObject *)&sp));
743     if (sp) PetscCall(MatSetNullSpace(jac->mat[i], sp));
744     ilink = ilink->next;
745   }
746 
747   if (jac->type != PC_COMPOSITE_ADDITIVE && jac->type != PC_COMPOSITE_SCHUR && jac->type != PC_COMPOSITE_GKB) {
748     /* extract the rows of the matrix associated with each field: used for efficient computation of residual inside algorithm */
749     /* FIXME: Can/should we reuse jac->mat whenever (jac->diag_use_amat) is true? */
750     ilink = jac->head;
751     if (nsplit == 2 && jac->type == PC_COMPOSITE_MULTIPLICATIVE) {
752       /* special case need where Afield[0] is not needed and only certain columns of Afield[1] are needed since update is only on those rows of the solution */
753       if (!jac->Afield) {
754         PetscCall(PetscCalloc1(nsplit, &jac->Afield));
755         if (jac->offdiag_use_amat) {
756           PetscCall(MatCreateSubMatrix(pc->mat, ilink->next->is, ilink->is, MAT_INITIAL_MATRIX, &jac->Afield[1]));
757         } else {
758           PetscCall(MatCreateSubMatrix(pc->pmat, ilink->next->is, ilink->is, MAT_INITIAL_MATRIX, &jac->Afield[1]));
759         }
760       } else {
761         MatReuse scall;
762 
763         if (pc->flag == DIFFERENT_NONZERO_PATTERN) {
764           PetscCall(MatDestroy(&jac->Afield[1]));
765           scall = MAT_INITIAL_MATRIX;
766         } else scall = MAT_REUSE_MATRIX;
767 
768         if (jac->offdiag_use_amat) {
769           PetscCall(MatCreateSubMatrix(pc->mat, ilink->next->is, ilink->is, scall, &jac->Afield[1]));
770         } else {
771           PetscCall(MatCreateSubMatrix(pc->pmat, ilink->next->is, ilink->is, scall, &jac->Afield[1]));
772         }
773       }
774     } else {
775       if (!jac->Afield) {
776         PetscCall(PetscMalloc1(nsplit, &jac->Afield));
777         for (i = 0; i < nsplit; i++) {
778           if (jac->offdiag_use_amat) {
779             PetscCall(MatCreateSubMatrix(pc->mat, ilink->is, NULL, MAT_INITIAL_MATRIX, &jac->Afield[i]));
780           } else {
781             PetscCall(MatCreateSubMatrix(pc->pmat, ilink->is, NULL, MAT_INITIAL_MATRIX, &jac->Afield[i]));
782           }
783           ilink = ilink->next;
784         }
785       } else {
786         MatReuse scall;
787         if (pc->flag == DIFFERENT_NONZERO_PATTERN) {
788           for (i = 0; i < nsplit; i++) PetscCall(MatDestroy(&jac->Afield[i]));
789           scall = MAT_INITIAL_MATRIX;
790         } else scall = MAT_REUSE_MATRIX;
791 
792         for (i = 0; i < nsplit; i++) {
793           if (jac->offdiag_use_amat) {
794             PetscCall(MatCreateSubMatrix(pc->mat, ilink->is, NULL, scall, &jac->Afield[i]));
795           } else {
796             PetscCall(MatCreateSubMatrix(pc->pmat, ilink->is, NULL, scall, &jac->Afield[i]));
797           }
798           ilink = ilink->next;
799         }
800       }
801     }
802   }
803 
804   if (jac->type == PC_COMPOSITE_SCHUR) {
805     IS          ccis;
806     PetscBool   isset, isspd;
807     PetscInt    rstart, rend;
808     char        lscname[256];
809     PetscObject LSC_L;
810     PetscBool   set, flg;
811 
812     PetscCheck(nsplit == 2, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_INCOMP, "To use Schur complement preconditioner you must have exactly 2 fields");
813 
814     /* If pc->mat is SPD, don't scale by -1 the Schur complement */
815     if (jac->schurscale == (PetscScalar)-1.0) {
816       PetscCall(MatIsSPDKnown(pc->pmat, &isset, &isspd));
817       jac->schurscale = (isset && isspd) ? 1.0 : -1.0;
818     }
819 
820     /* When extracting off-diagonal submatrices, we take complements from this range */
821     PetscCall(MatGetOwnershipRangeColumn(pc->mat, &rstart, &rend));
822     PetscCall(PetscObjectTypeCompareAny(jac->offdiag_use_amat ? (PetscObject)pc->mat : (PetscObject)pc->pmat, &flg, MATSEQSBAIJ, MATMPISBAIJ, ""));
823 
824     if (jac->schur) {
825       KSP      kspA = jac->head->ksp, kspInner = NULL, kspUpper = jac->kspupper;
826       MatReuse scall;
827 
828       if (pc->flag == DIFFERENT_NONZERO_PATTERN) {
829         scall = MAT_INITIAL_MATRIX;
830         PetscCall(MatDestroy(&jac->B));
831         PetscCall(MatDestroy(&jac->C));
832       } else scall = MAT_REUSE_MATRIX;
833 
834       PetscCall(MatSchurComplementGetKSP(jac->schur, &kspInner));
835       ilink = jac->head;
836       PetscCall(ISComplement(ilink->is_col, rstart, rend, &ccis));
837       if (jac->offdiag_use_amat) {
838         PetscCall(MatCreateSubMatrix(pc->mat, ilink->is, ccis, scall, &jac->B));
839       } else {
840         PetscCall(MatCreateSubMatrix(pc->pmat, ilink->is, ccis, scall, &jac->B));
841       }
842       PetscCall(ISDestroy(&ccis));
843       if (!flg) {
844         ilink = ilink->next;
845         PetscCall(ISComplement(ilink->is_col, rstart, rend, &ccis));
846         if (jac->offdiag_use_amat) {
847           PetscCall(MatCreateSubMatrix(pc->mat, ilink->is, ccis, scall, &jac->C));
848         } else {
849           PetscCall(MatCreateSubMatrix(pc->pmat, ilink->is, ccis, scall, &jac->C));
850         }
851         PetscCall(ISDestroy(&ccis));
852       } else {
853         PetscCall(MatIsHermitianKnown(jac->offdiag_use_amat ? pc->mat : pc->pmat, &set, &flg));
854         if (set && flg) PetscCall(MatCreateHermitianTranspose(jac->B, &jac->C));
855         else PetscCall(MatCreateTranspose(jac->B, &jac->C));
856       }
857       PetscCall(MatSchurComplementUpdateSubMatrices(jac->schur, jac->mat[0], jac->pmat[0], jac->B, jac->C, jac->mat[1]));
858       if (jac->schurpre == PC_FIELDSPLIT_SCHUR_PRE_SELFP) {
859         PetscCall(MatDestroy(&jac->schurp));
860         PetscCall(MatSchurComplementGetPmat(jac->schur, MAT_INITIAL_MATRIX, &jac->schurp));
861       }
862       if (kspA != kspInner) PetscCall(KSPSetOperators(kspA, jac->mat[0], jac->pmat[0]));
863       if (kspUpper != kspA) PetscCall(KSPSetOperators(kspUpper, jac->mat[0], jac->pmat[0]));
864       PetscCall(KSPSetOperators(jac->kspschur, jac->schur, FieldSplitSchurPre(jac)));
865     } else {
866       const char  *Dprefix;
867       char         schurprefix[256], schurmatprefix[256];
868       char         schurtestoption[256];
869       MatNullSpace sp;
870       KSP          kspt;
871 
872       /* extract the A01 and A10 matrices */
873       ilink = jac->head;
874       PetscCall(ISComplement(ilink->is_col, rstart, rend, &ccis));
875       if (jac->offdiag_use_amat) {
876         PetscCall(MatCreateSubMatrix(pc->mat, ilink->is, ccis, MAT_INITIAL_MATRIX, &jac->B));
877       } else {
878         PetscCall(MatCreateSubMatrix(pc->pmat, ilink->is, ccis, MAT_INITIAL_MATRIX, &jac->B));
879       }
880       PetscCall(ISDestroy(&ccis));
881       ilink = ilink->next;
882       if (!flg) {
883         PetscCall(ISComplement(ilink->is_col, rstart, rend, &ccis));
884         if (jac->offdiag_use_amat) {
885           PetscCall(MatCreateSubMatrix(pc->mat, ilink->is, ccis, MAT_INITIAL_MATRIX, &jac->C));
886         } else {
887           PetscCall(MatCreateSubMatrix(pc->pmat, ilink->is, ccis, MAT_INITIAL_MATRIX, &jac->C));
888         }
889         PetscCall(ISDestroy(&ccis));
890       } else {
891         PetscCall(MatIsHermitianKnown(jac->offdiag_use_amat ? pc->mat : pc->pmat, &set, &flg));
892         if (set && flg) PetscCall(MatCreateHermitianTranspose(jac->B, &jac->C));
893         else PetscCall(MatCreateTranspose(jac->B, &jac->C));
894       }
895       /* Use mat[0] (diagonal block of Amat) preconditioned by pmat[0] to define Schur complement */
896       PetscCall(MatCreate(((PetscObject)jac->mat[0])->comm, &jac->schur));
897       PetscCall(MatSetType(jac->schur, MATSCHURCOMPLEMENT));
898       PetscCall(MatSchurComplementSetSubMatrices(jac->schur, jac->mat[0], jac->pmat[0], jac->B, jac->C, jac->mat[1]));
899       PetscCall(PetscSNPrintf(schurmatprefix, sizeof(schurmatprefix), "%sfieldsplit_%s_", ((PetscObject)pc)->prefix ? ((PetscObject)pc)->prefix : "", ilink->splitname));
900       PetscCall(MatSetOptionsPrefix(jac->schur, schurmatprefix));
901       PetscCall(MatSchurComplementGetKSP(jac->schur, &kspt));
902       PetscCall(KSPSetOptionsPrefix(kspt, schurmatprefix));
903 
904       /* Note: this is not true in general */
905       PetscCall(MatGetNullSpace(jac->mat[1], &sp));
906       if (sp) PetscCall(MatSetNullSpace(jac->schur, sp));
907 
908       PetscCall(PetscSNPrintf(schurtestoption, sizeof(schurtestoption), "-fieldsplit_%s_inner_", ilink->splitname));
909       PetscCall(PetscOptionsFindPairPrefix_Private(((PetscObject)pc)->options, ((PetscObject)pc)->prefix, schurtestoption, NULL, NULL, &flg));
910       if (flg) {
911         DM  dmInner;
912         KSP kspInner;
913         PC  pcInner;
914 
915         PetscCall(MatSchurComplementGetKSP(jac->schur, &kspInner));
916         PetscCall(KSPReset(kspInner));
917         PetscCall(KSPSetOperators(kspInner, jac->mat[0], jac->pmat[0]));
918         PetscCall(PetscSNPrintf(schurprefix, sizeof(schurprefix), "%sfieldsplit_%s_inner_", ((PetscObject)pc)->prefix ? ((PetscObject)pc)->prefix : "", ilink->splitname));
919         /* Indent this deeper to emphasize the "inner" nature of this solver. */
920         PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspInner, (PetscObject)pc, 2));
921         PetscCall(PetscObjectIncrementTabLevel((PetscObject)kspInner->pc, (PetscObject)pc, 2));
922         PetscCall(KSPSetOptionsPrefix(kspInner, schurprefix));
923 
924         /* Set DM for new solver */
925         PetscCall(KSPGetDM(jac->head->ksp, &dmInner));
926         PetscCall(KSPSetDM(kspInner, dmInner));
927         PetscCall(KSPSetDMActive(kspInner, PETSC_FALSE));
928 
929         /* Defaults to PCKSP as preconditioner */
930         PetscCall(KSPGetPC(kspInner, &pcInner));
931         PetscCall(PCSetType(pcInner, PCKSP));
932         PetscCall(PCKSPSetKSP(pcInner, jac->head->ksp));
933       } else {
934         /* Use the outer solver for the inner solve, but revert the KSPPREONLY from PCFieldSplitSetFields_FieldSplit or
935           * PCFieldSplitSetIS_FieldSplit. We don't want KSPPREONLY because it makes the Schur complement inexact,
936           * preventing Schur complement reduction to be an accurate solve. Usually when an iterative solver is used for
937           * S = D - C A_inner^{-1} B, we expect S to be defined using an accurate definition of A_inner^{-1}, so we make
938           * GMRES the default. Note that it is also common to use PREONLY for S, in which case S may not be used
939           * directly, and the user is responsible for setting an inexact method for fieldsplit's A^{-1}. */
940         PetscCall(KSPSetType(jac->head->ksp, KSPGMRES));
941         PetscCall(MatSchurComplementSetKSP(jac->schur, jac->head->ksp));
942       }
943       PetscCall(KSPSetOperators(jac->head->ksp, jac->mat[0], jac->pmat[0]));
944       PetscCall(KSPSetFromOptions(jac->head->ksp));
945       PetscCall(MatSetFromOptions(jac->schur));
946 
947       PetscCall(PetscObjectTypeCompare((PetscObject)jac->schur, MATSCHURCOMPLEMENT, &flg));
948       if (flg) { /* Need to do this otherwise PCSetUp_KSP will overwrite the amat of jac->head->ksp */
949         KSP kspInner;
950         PC  pcInner;
951 
952         PetscCall(MatSchurComplementGetKSP(jac->schur, &kspInner));
953         PetscCall(KSPGetPC(kspInner, &pcInner));
954         PetscCall(PetscObjectTypeCompare((PetscObject)pcInner, PCKSP, &flg));
955         if (flg) {
956           KSP ksp;
957 
958           PetscCall(PCKSPGetKSP(pcInner, &ksp));
959           if (ksp == jac->head->ksp) PetscCall(PCSetUseAmat(pcInner, PETSC_TRUE));
960         }
961       }
962       PetscCall(PetscSNPrintf(schurtestoption, sizeof(schurtestoption), "-fieldsplit_%s_upper_", ilink->splitname));
963       PetscCall(PetscOptionsFindPairPrefix_Private(((PetscObject)pc)->options, ((PetscObject)pc)->prefix, schurtestoption, NULL, NULL, &flg));
964       if (flg) {
965         DM dmInner;
966 
967         PetscCall(PetscSNPrintf(schurprefix, sizeof(schurprefix), "%sfieldsplit_%s_upper_", ((PetscObject)pc)->prefix ? ((PetscObject)pc)->prefix : "", ilink->splitname));
968         PetscCall(KSPCreate(PetscObjectComm((PetscObject)pc), &jac->kspupper));
969         PetscCall(KSPSetNestLevel(jac->kspupper, pc->kspnestlevel));
970         PetscCall(KSPSetErrorIfNotConverged(jac->kspupper, pc->erroriffailure));
971         PetscCall(KSPSetOptionsPrefix(jac->kspupper, schurprefix));
972         PetscCall(PetscObjectIncrementTabLevel((PetscObject)jac->kspupper, (PetscObject)pc, 1));
973         PetscCall(PetscObjectIncrementTabLevel((PetscObject)jac->kspupper->pc, (PetscObject)pc, 1));
974         PetscCall(KSPGetDM(jac->head->ksp, &dmInner));
975         PetscCall(KSPSetDM(jac->kspupper, dmInner));
976         PetscCall(KSPSetDMActive(jac->kspupper, PETSC_FALSE));
977         PetscCall(KSPSetFromOptions(jac->kspupper));
978         PetscCall(KSPSetOperators(jac->kspupper, jac->mat[0], jac->pmat[0]));
979         PetscCall(VecDuplicate(jac->head->x, &jac->head->z));
980       } else {
981         jac->kspupper = jac->head->ksp;
982         PetscCall(PetscObjectReference((PetscObject)jac->head->ksp));
983       }
984 
985       if (jac->schurpre == PC_FIELDSPLIT_SCHUR_PRE_SELFP) PetscCall(MatSchurComplementGetPmat(jac->schur, MAT_INITIAL_MATRIX, &jac->schurp));
986       PetscCall(KSPCreate(PetscObjectComm((PetscObject)pc), &jac->kspschur));
987       PetscCall(KSPSetNestLevel(jac->kspschur, pc->kspnestlevel));
988       PetscCall(KSPSetErrorIfNotConverged(jac->kspschur, pc->erroriffailure));
989       PetscCall(PetscObjectIncrementTabLevel((PetscObject)jac->kspschur, (PetscObject)pc, 1));
990       if (jac->schurpre == PC_FIELDSPLIT_SCHUR_PRE_SELF) {
991         PC pcschur;
992         PetscCall(KSPGetPC(jac->kspschur, &pcschur));
993         PetscCall(PCSetType(pcschur, PCNONE));
994         /* Note: This is bad if there exist preconditioners for MATSCHURCOMPLEMENT */
995       } else if (jac->schurpre == PC_FIELDSPLIT_SCHUR_PRE_FULL) {
996         PetscCall(MatSchurComplementComputeExplicitOperator(jac->schur, &jac->schur_user));
997       }
998       PetscCall(KSPSetOperators(jac->kspschur, jac->schur, FieldSplitSchurPre(jac)));
999       PetscCall(KSPGetOptionsPrefix(jac->head->next->ksp, &Dprefix));
1000       PetscCall(KSPSetOptionsPrefix(jac->kspschur, Dprefix));
1001       /* propagate DM */
1002       {
1003         DM sdm;
1004         PetscCall(KSPGetDM(jac->head->next->ksp, &sdm));
1005         if (sdm) {
1006           PetscCall(KSPSetDM(jac->kspschur, sdm));
1007           PetscCall(KSPSetDMActive(jac->kspschur, PETSC_FALSE));
1008         }
1009       }
1010       /* really want setfromoptions called in PCSetFromOptions_FieldSplit(), but it is not ready yet */
1011       /* need to call this every time, since the jac->kspschur is freshly created, otherwise its options never get set */
1012       PetscCall(KSPSetFromOptions(jac->kspschur));
1013     }
1014     PetscCall(MatAssemblyBegin(jac->schur, MAT_FINAL_ASSEMBLY));
1015     PetscCall(MatAssemblyEnd(jac->schur, MAT_FINAL_ASSEMBLY));
1016 
1017     /* HACK: special support to forward L and Lp matrices that might be used by PCLSC */
1018     PetscCall(PetscSNPrintf(lscname, sizeof(lscname), "%s_LSC_L", ilink->splitname));
1019     PetscCall(PetscObjectQuery((PetscObject)pc->mat, lscname, (PetscObject *)&LSC_L));
1020     if (!LSC_L) PetscCall(PetscObjectQuery((PetscObject)pc->pmat, lscname, (PetscObject *)&LSC_L));
1021     if (LSC_L) PetscCall(PetscObjectCompose((PetscObject)jac->schur, "LSC_L", (PetscObject)LSC_L));
1022     PetscCall(PetscSNPrintf(lscname, sizeof(lscname), "%s_LSC_Lp", ilink->splitname));
1023     PetscCall(PetscObjectQuery((PetscObject)pc->pmat, lscname, (PetscObject *)&LSC_L));
1024     if (!LSC_L) PetscCall(PetscObjectQuery((PetscObject)pc->mat, lscname, (PetscObject *)&LSC_L));
1025     if (LSC_L) PetscCall(PetscObjectCompose((PetscObject)jac->schur, "LSC_Lp", (PetscObject)LSC_L));
1026   } else if (jac->type == PC_COMPOSITE_GKB) {
1027     IS       ccis;
1028     PetscInt rstart, rend;
1029 
1030     PetscCheck(nsplit == 2, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_INCOMP, "To use GKB preconditioner you must have exactly 2 fields");
1031 
1032     ilink = jac->head;
1033 
1034     /* When extracting off-diagonal submatrices, we take complements from this range */
1035     PetscCall(MatGetOwnershipRangeColumn(pc->mat, &rstart, &rend));
1036 
1037     PetscCall(ISComplement(ilink->is_col, rstart, rend, &ccis));
1038     if (jac->offdiag_use_amat) {
1039       PetscCall(MatCreateSubMatrix(pc->mat, ilink->is, ccis, MAT_INITIAL_MATRIX, &jac->B));
1040     } else {
1041       PetscCall(MatCreateSubMatrix(pc->pmat, ilink->is, ccis, MAT_INITIAL_MATRIX, &jac->B));
1042     }
1043     PetscCall(ISDestroy(&ccis));
1044     /* Create work vectors for GKB algorithm */
1045     PetscCall(VecDuplicate(ilink->x, &jac->u));
1046     PetscCall(VecDuplicate(ilink->x, &jac->Hu));
1047     PetscCall(VecDuplicate(ilink->x, &jac->w2));
1048     ilink = ilink->next;
1049     PetscCall(ISComplement(ilink->is_col, rstart, rend, &ccis));
1050     if (jac->offdiag_use_amat) {
1051       PetscCall(MatCreateSubMatrix(pc->mat, ilink->is, ccis, MAT_INITIAL_MATRIX, &jac->C));
1052     } else {
1053       PetscCall(MatCreateSubMatrix(pc->pmat, ilink->is, ccis, MAT_INITIAL_MATRIX, &jac->C));
1054     }
1055     PetscCall(ISDestroy(&ccis));
1056     /* Create work vectors for GKB algorithm */
1057     PetscCall(VecDuplicate(ilink->x, &jac->v));
1058     PetscCall(VecDuplicate(ilink->x, &jac->d));
1059     PetscCall(VecDuplicate(ilink->x, &jac->w1));
1060     PetscCall(MatGolubKahanComputeExplicitOperator(jac->mat[0], jac->B, jac->C, &jac->H, jac->gkbnu));
1061     PetscCall(PetscCalloc1(jac->gkbdelay, &jac->vecz));
1062 
1063     ilink = jac->head;
1064     PetscCall(KSPSetOperators(ilink->ksp, jac->H, jac->H));
1065     if (!jac->suboptionsset) PetscCall(KSPSetFromOptions(ilink->ksp));
1066     /* Create gkb_monitor context */
1067     if (jac->gkbmonitor) {
1068       PetscInt tablevel;
1069       PetscCall(PetscViewerCreate(PETSC_COMM_WORLD, &jac->gkbviewer));
1070       PetscCall(PetscViewerSetType(jac->gkbviewer, PETSCVIEWERASCII));
1071       PetscCall(PetscObjectGetTabLevel((PetscObject)ilink->ksp, &tablevel));
1072       PetscCall(PetscViewerASCIISetTab(jac->gkbviewer, tablevel));
1073       PetscCall(PetscObjectIncrementTabLevel((PetscObject)ilink->ksp, (PetscObject)ilink->ksp, 1));
1074     }
1075   } else {
1076     /* set up the individual splits' PCs */
1077     i     = 0;
1078     ilink = jac->head;
1079     while (ilink) {
1080       PetscCall(KSPSetOperators(ilink->ksp, jac->mat[i], jac->pmat[i]));
1081       /* really want setfromoptions called in PCSetFromOptions_FieldSplit(), but it is not ready yet */
1082       if (!jac->suboptionsset) PetscCall(KSPSetFromOptions(ilink->ksp));
1083       i++;
1084       ilink = ilink->next;
1085     }
1086   }
1087 
1088   /* Set coordinates to the sub PC objects whenever these are set */
1089   if (jac->coordinates_set) {
1090     PC pc_coords;
1091     if (jac->type == PC_COMPOSITE_SCHUR) {
1092       // Head is first block.
1093       PetscCall(KSPGetPC(jac->head->ksp, &pc_coords));
1094       PetscCall(PCSetCoordinates(pc_coords, jac->head->dim, jac->head->ndofs, jac->head->coords));
1095       // Second one is Schur block, but its KSP object is in kspschur.
1096       PetscCall(KSPGetPC(jac->kspschur, &pc_coords));
1097       PetscCall(PCSetCoordinates(pc_coords, jac->head->next->dim, jac->head->next->ndofs, jac->head->next->coords));
1098     } else if (jac->type == PC_COMPOSITE_GKB) {
1099       PetscCall(PetscInfo(pc, "Warning: Setting coordinates does nothing for the GKB Fieldpslit preconditioner\n"));
1100     } else {
1101       ilink = jac->head;
1102       while (ilink) {
1103         PetscCall(KSPGetPC(ilink->ksp, &pc_coords));
1104         PetscCall(PCSetCoordinates(pc_coords, ilink->dim, ilink->ndofs, ilink->coords));
1105         ilink = ilink->next;
1106       }
1107     }
1108   }
1109 
1110   jac->suboptionsset = PETSC_TRUE;
1111   PetscFunctionReturn(PETSC_SUCCESS);
1112 }
1113 
1114 #define FieldSplitSplitSolveAdd(ilink, xx, yy) \
1115   ((PetscErrorCode)(VecScatterBegin(ilink->sctx, xx, ilink->x, INSERT_VALUES, SCATTER_FORWARD) || VecScatterEnd(ilink->sctx, xx, ilink->x, INSERT_VALUES, SCATTER_FORWARD) || PetscLogEventBegin(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL) || \
1116                     KSPSolve(ilink->ksp, ilink->x, ilink->y) || KSPCheckSolve(ilink->ksp, pc, ilink->y) || PetscLogEventEnd(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL) || VecScatterBegin(ilink->sctx, ilink->y, yy, ADD_VALUES, SCATTER_REVERSE) || \
1117                     VecScatterEnd(ilink->sctx, ilink->y, yy, ADD_VALUES, SCATTER_REVERSE)))
1118 
1119 static PetscErrorCode PCApply_FieldSplit_Schur(PC pc, Vec x, Vec y)
1120 {
1121   PC_FieldSplit    *jac    = (PC_FieldSplit *)pc->data;
1122   PC_FieldSplitLink ilinkA = jac->head, ilinkD = ilinkA->next;
1123   KSP               kspA = ilinkA->ksp, kspLower = kspA, kspUpper = jac->kspupper;
1124 
1125   PetscFunctionBegin;
1126   switch (jac->schurfactorization) {
1127   case PC_FIELDSPLIT_SCHUR_FACT_DIAG:
1128     /* [A00 0; 0 -S], positive definite, suitable for MINRES */
1129     PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1130     PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1131     PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1132     PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1133     PetscCall(KSPSolve(kspA, ilinkA->x, ilinkA->y));
1134     PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1135     PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1136     PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1137     PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1138     PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1139     PetscCall(KSPSolve(jac->kspschur, ilinkD->x, ilinkD->y));
1140     PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y));
1141     PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1142     PetscCall(VecScale(ilinkD->y, jac->schurscale));
1143     PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1144     PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1145     PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1146     break;
1147   case PC_FIELDSPLIT_SCHUR_FACT_LOWER:
1148     /* [A00 0; A10 S], suitable for left preconditioning */
1149     PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1150     PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1151     PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1152     PetscCall(KSPSolve(kspA, ilinkA->x, ilinkA->y));
1153     PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1154     PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1155     PetscCall(MatMult(jac->C, ilinkA->y, ilinkD->x));
1156     PetscCall(VecScale(ilinkD->x, -1.));
1157     PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD));
1158     PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1159     PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD));
1160     PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1161     PetscCall(KSPSolve(jac->kspschur, ilinkD->x, ilinkD->y));
1162     PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y));
1163     PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1164     PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1165     PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1166     PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1167     break;
1168   case PC_FIELDSPLIT_SCHUR_FACT_UPPER:
1169     /* [A00 A01; 0 S], suitable for right preconditioning */
1170     PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1171     PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1172     PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1173     PetscCall(KSPSolve(jac->kspschur, ilinkD->x, ilinkD->y));
1174     PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y));
1175     PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1176     PetscCall(MatMult(jac->B, ilinkD->y, ilinkA->x));
1177     PetscCall(VecScale(ilinkA->x, -1.));
1178     PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, ADD_VALUES, SCATTER_FORWARD));
1179     PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1180     PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, ADD_VALUES, SCATTER_FORWARD));
1181     PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1182     PetscCall(KSPSolve(kspA, ilinkA->x, ilinkA->y));
1183     PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1184     PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1185     PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1186     PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1187     PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1188     break;
1189   case PC_FIELDSPLIT_SCHUR_FACT_FULL:
1190     /* [1 0; A10 A00^{-1} 1] [A00 0; 0 S] [1 A00^{-1}A01; 0 1] */
1191     PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1192     PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1193     PetscCall(PetscLogEventBegin(KSP_Solve_FS_L, kspLower, ilinkA->x, ilinkA->y, NULL));
1194     PetscCall(KSPSolve(kspLower, ilinkA->x, ilinkA->y));
1195     PetscCall(KSPCheckSolve(kspLower, pc, ilinkA->y));
1196     PetscCall(PetscLogEventEnd(KSP_Solve_FS_L, kspLower, ilinkA->x, ilinkA->y, NULL));
1197     PetscCall(MatMult(jac->C, ilinkA->y, ilinkD->x));
1198     PetscCall(VecScale(ilinkD->x, -1.0));
1199     PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD));
1200     PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD));
1201 
1202     PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1203     PetscCall(KSPSolve(jac->kspschur, ilinkD->x, ilinkD->y));
1204     PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y));
1205     PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1206     PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1207 
1208     if (kspUpper == kspA) {
1209       PetscCall(MatMult(jac->B, ilinkD->y, ilinkA->y));
1210       PetscCall(VecAXPY(ilinkA->x, -1.0, ilinkA->y));
1211       PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1212       PetscCall(KSPSolve(kspA, ilinkA->x, ilinkA->y));
1213       PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1214       PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1215     } else {
1216       PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1217       PetscCall(KSPSolve(kspA, ilinkA->x, ilinkA->y));
1218       PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1219       PetscCall(MatMult(jac->B, ilinkD->y, ilinkA->x));
1220       PetscCall(PetscLogEventBegin(KSP_Solve_FS_U, kspUpper, ilinkA->x, ilinkA->z, NULL));
1221       PetscCall(KSPSolve(kspUpper, ilinkA->x, ilinkA->z));
1222       PetscCall(KSPCheckSolve(kspUpper, pc, ilinkA->z));
1223       PetscCall(PetscLogEventEnd(KSP_Solve_FS_U, kspUpper, ilinkA->x, ilinkA->z, NULL));
1224       PetscCall(VecAXPY(ilinkA->y, -1.0, ilinkA->z));
1225     }
1226     PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1227     PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1228     PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1229   }
1230   PetscFunctionReturn(PETSC_SUCCESS);
1231 }
1232 
1233 static PetscErrorCode PCApplyTranspose_FieldSplit_Schur(PC pc, Vec x, Vec y)
1234 {
1235   PC_FieldSplit    *jac    = (PC_FieldSplit *)pc->data;
1236   PC_FieldSplitLink ilinkA = jac->head, ilinkD = ilinkA->next;
1237   KSP               kspA = ilinkA->ksp, kspLower = kspA, kspUpper = jac->kspupper;
1238 
1239   PetscFunctionBegin;
1240   switch (jac->schurfactorization) {
1241   case PC_FIELDSPLIT_SCHUR_FACT_DIAG:
1242     /* [A00 0; 0 -S], positive definite, suitable for MINRES */
1243     PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1244     PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1245     PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1246     PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1247     PetscCall(KSPSolveTranspose(kspA, ilinkA->x, ilinkA->y));
1248     PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1249     PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1250     PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1251     PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1252     PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1253     PetscCall(KSPSolveTranspose(jac->kspschur, ilinkD->x, ilinkD->y));
1254     PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y));
1255     PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1256     PetscCall(VecScale(ilinkD->y, jac->schurscale));
1257     PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1258     PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1259     PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1260     break;
1261   case PC_FIELDSPLIT_SCHUR_FACT_UPPER:
1262     PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1263     PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1264     PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1265     PetscCall(KSPSolveTranspose(kspA, ilinkA->x, ilinkA->y));
1266     PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1267     PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1268     PetscCall(MatMultTranspose(jac->B, ilinkA->y, ilinkD->x));
1269     PetscCall(VecScale(ilinkD->x, -1.));
1270     PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD));
1271     PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1272     PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD));
1273     PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1274     PetscCall(KSPSolveTranspose(jac->kspschur, ilinkD->x, ilinkD->y));
1275     PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y));
1276     PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1277     PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1278     PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1279     PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1280     break;
1281   case PC_FIELDSPLIT_SCHUR_FACT_LOWER:
1282     PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1283     PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1284     PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1285     PetscCall(KSPSolveTranspose(jac->kspschur, ilinkD->x, ilinkD->y));
1286     PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y));
1287     PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1288     PetscCall(MatMultTranspose(jac->C, ilinkD->y, ilinkA->x));
1289     PetscCall(VecScale(ilinkA->x, -1.));
1290     PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, ADD_VALUES, SCATTER_FORWARD));
1291     PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1292     PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, ADD_VALUES, SCATTER_FORWARD));
1293     PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1294     PetscCall(KSPSolveTranspose(kspA, ilinkA->x, ilinkA->y));
1295     PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1296     PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1297     PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1298     PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1299     PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1300     break;
1301   case PC_FIELDSPLIT_SCHUR_FACT_FULL:
1302     PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1303     PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1304     PetscCall(PetscLogEventBegin(KSP_Solve_FS_U, kspUpper, ilinkA->x, ilinkA->y, NULL));
1305     PetscCall(KSPSolveTranspose(kspUpper, ilinkA->x, ilinkA->y));
1306     PetscCall(KSPCheckSolve(kspUpper, pc, ilinkA->y));
1307     PetscCall(PetscLogEventEnd(KSP_Solve_FS_U, kspUpper, ilinkA->x, ilinkA->y, NULL));
1308     PetscCall(MatMultTranspose(jac->B, ilinkA->y, ilinkD->x));
1309     PetscCall(VecScale(ilinkD->x, -1.0));
1310     PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD));
1311     PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, ADD_VALUES, SCATTER_FORWARD));
1312 
1313     PetscCall(PetscLogEventBegin(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1314     PetscCall(KSPSolveTranspose(jac->kspschur, ilinkD->x, ilinkD->y));
1315     PetscCall(KSPCheckSolve(jac->kspschur, pc, ilinkD->y));
1316     PetscCall(PetscLogEventEnd(KSP_Solve_FS_S, jac->kspschur, ilinkD->x, ilinkD->y, NULL));
1317     PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1318 
1319     if (kspLower == kspA) {
1320       PetscCall(MatMultTranspose(jac->C, ilinkD->y, ilinkA->y));
1321       PetscCall(VecAXPY(ilinkA->x, -1.0, ilinkA->y));
1322       PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1323       PetscCall(KSPSolveTranspose(kspA, ilinkA->x, ilinkA->y));
1324       PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1325       PetscCall(PetscLogEventEnd(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1326     } else {
1327       PetscCall(PetscLogEventBegin(ilinkA->event, kspA, ilinkA->x, ilinkA->y, NULL));
1328       PetscCall(KSPSolveTranspose(kspA, ilinkA->x, ilinkA->y));
1329       PetscCall(KSPCheckSolve(kspA, pc, ilinkA->y));
1330       PetscCall(MatMultTranspose(jac->C, ilinkD->y, ilinkA->x));
1331       PetscCall(PetscLogEventBegin(KSP_Solve_FS_L, kspLower, ilinkA->x, ilinkA->z, NULL));
1332       PetscCall(KSPSolveTranspose(kspLower, ilinkA->x, ilinkA->z));
1333       PetscCall(KSPCheckSolve(kspLower, pc, ilinkA->z));
1334       PetscCall(PetscLogEventEnd(KSP_Solve_FS_L, kspLower, ilinkA->x, ilinkA->z, NULL));
1335       PetscCall(VecAXPY(ilinkA->y, -1.0, ilinkA->z));
1336     }
1337     PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1338     PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1339     PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1340   }
1341   PetscFunctionReturn(PETSC_SUCCESS);
1342 }
1343 
1344 static PetscErrorCode PCApply_FieldSplit(PC pc, Vec x, Vec y)
1345 {
1346   PC_FieldSplit    *jac   = (PC_FieldSplit *)pc->data;
1347   PC_FieldSplitLink ilink = jac->head;
1348   PetscInt          cnt, bs;
1349 
1350   PetscFunctionBegin;
1351   if (jac->type == PC_COMPOSITE_ADDITIVE) {
1352     if (jac->defaultsplit) {
1353       PetscCall(VecGetBlockSize(x, &bs));
1354       PetscCheck(jac->bs <= 0 || bs == jac->bs, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONGSTATE, "Blocksize of x vector %" PetscInt_FMT " does not match fieldsplit blocksize %" PetscInt_FMT, bs, jac->bs);
1355       PetscCall(VecGetBlockSize(y, &bs));
1356       PetscCheck(jac->bs <= 0 || bs == jac->bs, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONGSTATE, "Blocksize of y vector %" PetscInt_FMT " does not match fieldsplit blocksize %" PetscInt_FMT, bs, jac->bs);
1357       PetscCall(VecStrideGatherAll(x, jac->x, INSERT_VALUES));
1358       while (ilink) {
1359         PetscCall(PetscLogEventBegin(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1360         PetscCall(KSPSolve(ilink->ksp, ilink->x, ilink->y));
1361         PetscCall(KSPCheckSolve(ilink->ksp, pc, ilink->y));
1362         PetscCall(PetscLogEventEnd(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1363         ilink = ilink->next;
1364       }
1365       PetscCall(VecStrideScatterAll(jac->y, y, INSERT_VALUES));
1366     } else {
1367       PetscCall(VecSet(y, 0.0));
1368       while (ilink) {
1369         PetscCall(FieldSplitSplitSolveAdd(ilink, x, y));
1370         ilink = ilink->next;
1371       }
1372     }
1373   } else if (jac->type == PC_COMPOSITE_MULTIPLICATIVE && jac->nsplits == 2) {
1374     PetscCall(VecSet(y, 0.0));
1375     /* solve on first block for first block variables */
1376     PetscCall(VecScatterBegin(ilink->sctx, x, ilink->x, INSERT_VALUES, SCATTER_FORWARD));
1377     PetscCall(VecScatterEnd(ilink->sctx, x, ilink->x, INSERT_VALUES, SCATTER_FORWARD));
1378     PetscCall(PetscLogEventBegin(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1379     PetscCall(KSPSolve(ilink->ksp, ilink->x, ilink->y));
1380     PetscCall(KSPCheckSolve(ilink->ksp, pc, ilink->y));
1381     PetscCall(PetscLogEventEnd(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1382     PetscCall(VecScatterBegin(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE));
1383     PetscCall(VecScatterEnd(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE));
1384 
1385     /* compute the residual only onto second block variables using first block variables */
1386     PetscCall(MatMult(jac->Afield[1], ilink->y, ilink->next->x));
1387     ilink = ilink->next;
1388     PetscCall(VecScale(ilink->x, -1.0));
1389     PetscCall(VecScatterBegin(ilink->sctx, x, ilink->x, ADD_VALUES, SCATTER_FORWARD));
1390     PetscCall(VecScatterEnd(ilink->sctx, x, ilink->x, ADD_VALUES, SCATTER_FORWARD));
1391 
1392     /* solve on second block variables */
1393     PetscCall(PetscLogEventBegin(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1394     PetscCall(KSPSolve(ilink->ksp, ilink->x, ilink->y));
1395     PetscCall(KSPCheckSolve(ilink->ksp, pc, ilink->y));
1396     PetscCall(PetscLogEventEnd(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1397     PetscCall(VecScatterBegin(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE));
1398     PetscCall(VecScatterEnd(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE));
1399   } else if (jac->type == PC_COMPOSITE_MULTIPLICATIVE || jac->type == PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE) {
1400     if (!jac->w1) {
1401       PetscCall(VecDuplicate(x, &jac->w1));
1402       PetscCall(VecDuplicate(x, &jac->w2));
1403     }
1404     PetscCall(VecSet(y, 0.0));
1405     PetscCall(FieldSplitSplitSolveAdd(ilink, x, y));
1406     cnt = 1;
1407     while (ilink->next) {
1408       ilink = ilink->next;
1409       /* compute the residual only over the part of the vector needed */
1410       PetscCall(MatMult(jac->Afield[cnt++], y, ilink->x));
1411       PetscCall(VecScale(ilink->x, -1.0));
1412       PetscCall(VecScatterBegin(ilink->sctx, x, ilink->x, ADD_VALUES, SCATTER_FORWARD));
1413       PetscCall(VecScatterEnd(ilink->sctx, x, ilink->x, ADD_VALUES, SCATTER_FORWARD));
1414       PetscCall(PetscLogEventBegin(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1415       PetscCall(KSPSolve(ilink->ksp, ilink->x, ilink->y));
1416       PetscCall(KSPCheckSolve(ilink->ksp, pc, ilink->y));
1417       PetscCall(PetscLogEventEnd(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1418       PetscCall(VecScatterBegin(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE));
1419       PetscCall(VecScatterEnd(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE));
1420     }
1421     if (jac->type == PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE) {
1422       cnt -= 2;
1423       while (ilink->previous) {
1424         ilink = ilink->previous;
1425         /* compute the residual only over the part of the vector needed */
1426         PetscCall(MatMult(jac->Afield[cnt--], y, ilink->x));
1427         PetscCall(VecScale(ilink->x, -1.0));
1428         PetscCall(VecScatterBegin(ilink->sctx, x, ilink->x, ADD_VALUES, SCATTER_FORWARD));
1429         PetscCall(VecScatterEnd(ilink->sctx, x, ilink->x, ADD_VALUES, SCATTER_FORWARD));
1430         PetscCall(PetscLogEventBegin(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1431         PetscCall(KSPSolve(ilink->ksp, ilink->x, ilink->y));
1432         PetscCall(KSPCheckSolve(ilink->ksp, pc, ilink->y));
1433         PetscCall(PetscLogEventEnd(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1434         PetscCall(VecScatterBegin(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE));
1435         PetscCall(VecScatterEnd(ilink->sctx, ilink->y, y, ADD_VALUES, SCATTER_REVERSE));
1436       }
1437     }
1438   } else SETERRQ(PetscObjectComm((PetscObject)pc), PETSC_ERR_SUP, "Unsupported or unknown composition %d", (int)jac->type);
1439   PetscFunctionReturn(PETSC_SUCCESS);
1440 }
1441 
1442 static PetscErrorCode PCApply_FieldSplit_GKB(PC pc, Vec x, Vec y)
1443 {
1444   PC_FieldSplit    *jac    = (PC_FieldSplit *)pc->data;
1445   PC_FieldSplitLink ilinkA = jac->head, ilinkD = ilinkA->next;
1446   KSP               ksp = ilinkA->ksp;
1447   Vec               u, v, Hu, d, work1, work2;
1448   PetscScalar       alpha, z, nrmz2, *vecz;
1449   PetscReal         lowbnd, nu, beta;
1450   PetscInt          j, iterGKB;
1451 
1452   PetscFunctionBegin;
1453   PetscCall(VecScatterBegin(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1454   PetscCall(VecScatterBegin(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1455   PetscCall(VecScatterEnd(ilinkA->sctx, x, ilinkA->x, INSERT_VALUES, SCATTER_FORWARD));
1456   PetscCall(VecScatterEnd(ilinkD->sctx, x, ilinkD->x, INSERT_VALUES, SCATTER_FORWARD));
1457 
1458   u     = jac->u;
1459   v     = jac->v;
1460   Hu    = jac->Hu;
1461   d     = jac->d;
1462   work1 = jac->w1;
1463   work2 = jac->w2;
1464   vecz  = jac->vecz;
1465 
1466   /* Change RHS to comply with matrix regularization H = A + nu*B*B' */
1467   /* Add q = q + nu*B*b */
1468   if (jac->gkbnu) {
1469     nu = jac->gkbnu;
1470     PetscCall(VecScale(ilinkD->x, jac->gkbnu));
1471     PetscCall(MatMultAdd(jac->B, ilinkD->x, ilinkA->x, ilinkA->x)); /* q = q + nu*B*b */
1472   } else {
1473     /* Situation when no augmented Lagrangian is used. Then we set inner  */
1474     /* matrix N = I in [Ar13], and thus nu = 1.                           */
1475     nu = 1;
1476   }
1477 
1478   /* Transform rhs from [q,tilde{b}] to [0,b] */
1479   PetscCall(PetscLogEventBegin(ilinkA->event, ksp, ilinkA->x, ilinkA->y, NULL));
1480   PetscCall(KSPSolve(ksp, ilinkA->x, ilinkA->y));
1481   PetscCall(KSPCheckSolve(ksp, pc, ilinkA->y));
1482   PetscCall(PetscLogEventEnd(ilinkA->event, ksp, ilinkA->x, ilinkA->y, NULL));
1483   PetscCall(MatMultHermitianTranspose(jac->B, ilinkA->y, work1));
1484   PetscCall(VecAXPBY(work1, 1.0 / nu, -1.0, ilinkD->x)); /* c = b - B'*x        */
1485 
1486   /* First step of algorithm */
1487   PetscCall(VecNorm(work1, NORM_2, &beta)); /* beta = sqrt(nu*c'*c)*/
1488   KSPCheckDot(ksp, beta);
1489   beta = PetscSqrtReal(nu) * beta;
1490   PetscCall(VecAXPBY(v, nu / beta, 0.0, work1)); /* v = nu/beta *c      */
1491   PetscCall(MatMult(jac->B, v, work2));          /* u = H^{-1}*B*v      */
1492   PetscCall(PetscLogEventBegin(ilinkA->event, ksp, work2, u, NULL));
1493   PetscCall(KSPSolve(ksp, work2, u));
1494   PetscCall(KSPCheckSolve(ksp, pc, u));
1495   PetscCall(PetscLogEventEnd(ilinkA->event, ksp, work2, u, NULL));
1496   PetscCall(MatMult(jac->H, u, Hu)); /* alpha = u'*H*u      */
1497   PetscCall(VecDot(Hu, u, &alpha));
1498   KSPCheckDot(ksp, alpha);
1499   PetscCheck(PetscRealPart(alpha) > 0.0, PETSC_COMM_SELF, PETSC_ERR_NOT_CONVERGED, "GKB preconditioner diverged, H is not positive definite");
1500   alpha = PetscSqrtReal(PetscAbsScalar(alpha));
1501   PetscCall(VecScale(u, 1.0 / alpha));
1502   PetscCall(VecAXPBY(d, 1.0 / alpha, 0.0, v)); /* v = nu/beta *c      */
1503 
1504   z       = beta / alpha;
1505   vecz[1] = z;
1506 
1507   /* Computation of first iterate x(1) and p(1) */
1508   PetscCall(VecAXPY(ilinkA->y, z, u));
1509   PetscCall(VecCopy(d, ilinkD->y));
1510   PetscCall(VecScale(ilinkD->y, -z));
1511 
1512   iterGKB = 1;
1513   lowbnd  = 2 * jac->gkbtol;
1514   if (jac->gkbmonitor) PetscCall(PetscViewerASCIIPrintf(jac->gkbviewer, "%3" PetscInt_FMT " GKB Lower bound estimate %14.12e\n", iterGKB, (double)lowbnd));
1515 
1516   while (iterGKB < jac->gkbmaxit && lowbnd > jac->gkbtol) {
1517     iterGKB += 1;
1518     PetscCall(MatMultHermitianTranspose(jac->B, u, work1)); /* v <- nu*(B'*u-alpha/nu*v) */
1519     PetscCall(VecAXPBY(v, nu, -alpha, work1));
1520     PetscCall(VecNorm(v, NORM_2, &beta)); /* beta = sqrt(nu)*v'*v      */
1521     beta = beta / PetscSqrtReal(nu);
1522     PetscCall(VecScale(v, 1.0 / beta));
1523     PetscCall(MatMult(jac->B, v, work2)); /* u <- H^{-1}*(B*v-beta*H*u) */
1524     PetscCall(MatMult(jac->H, u, Hu));
1525     PetscCall(VecAXPY(work2, -beta, Hu));
1526     PetscCall(PetscLogEventBegin(ilinkA->event, ksp, work2, u, NULL));
1527     PetscCall(KSPSolve(ksp, work2, u));
1528     PetscCall(KSPCheckSolve(ksp, pc, u));
1529     PetscCall(PetscLogEventEnd(ilinkA->event, ksp, work2, u, NULL));
1530     PetscCall(MatMult(jac->H, u, Hu)); /* alpha = u'*H*u            */
1531     PetscCall(VecDot(Hu, u, &alpha));
1532     KSPCheckDot(ksp, alpha);
1533     PetscCheck(PetscRealPart(alpha) > 0.0, PETSC_COMM_SELF, PETSC_ERR_NOT_CONVERGED, "GKB preconditioner diverged, H is not positive definite");
1534     alpha = PetscSqrtReal(PetscAbsScalar(alpha));
1535     PetscCall(VecScale(u, 1.0 / alpha));
1536 
1537     z       = -beta / alpha * z; /* z <- beta/alpha*z     */
1538     vecz[0] = z;
1539 
1540     /* Computation of new iterate x(i+1) and p(i+1) */
1541     PetscCall(VecAXPBY(d, 1.0 / alpha, -beta / alpha, v)); /* d = (v-beta*d)/alpha */
1542     PetscCall(VecAXPY(ilinkA->y, z, u));                   /* r = r + z*u          */
1543     PetscCall(VecAXPY(ilinkD->y, -z, d));                  /* p = p - z*d          */
1544     PetscCall(MatMult(jac->H, ilinkA->y, Hu));             /* ||u||_H = u'*H*u     */
1545     PetscCall(VecDot(Hu, ilinkA->y, &nrmz2));
1546 
1547     /* Compute Lower Bound estimate */
1548     if (iterGKB > jac->gkbdelay) {
1549       lowbnd = 0.0;
1550       for (j = 0; j < jac->gkbdelay; j++) lowbnd += PetscAbsScalar(vecz[j] * vecz[j]);
1551       lowbnd = PetscSqrtReal(lowbnd / PetscAbsScalar(nrmz2));
1552     }
1553 
1554     for (j = 0; j < jac->gkbdelay - 1; j++) vecz[jac->gkbdelay - j - 1] = vecz[jac->gkbdelay - j - 2];
1555     if (jac->gkbmonitor) PetscCall(PetscViewerASCIIPrintf(jac->gkbviewer, "%3" PetscInt_FMT " GKB Lower bound estimate %14.12e\n", iterGKB, (double)lowbnd));
1556   }
1557 
1558   PetscCall(VecScatterBegin(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1559   PetscCall(VecScatterEnd(ilinkA->sctx, ilinkA->y, y, INSERT_VALUES, SCATTER_REVERSE));
1560   PetscCall(VecScatterBegin(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1561   PetscCall(VecScatterEnd(ilinkD->sctx, ilinkD->y, y, INSERT_VALUES, SCATTER_REVERSE));
1562 
1563   PetscFunctionReturn(PETSC_SUCCESS);
1564 }
1565 
1566 #define FieldSplitSplitSolveAddTranspose(ilink, xx, yy) \
1567   ((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) || \
1568                     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) || \
1569                     VecScatterEnd(ilink->sctx, ilink->x, yy, ADD_VALUES, SCATTER_REVERSE)))
1570 
1571 static PetscErrorCode PCApplyTranspose_FieldSplit(PC pc, Vec x, Vec y)
1572 {
1573   PC_FieldSplit    *jac   = (PC_FieldSplit *)pc->data;
1574   PC_FieldSplitLink ilink = jac->head;
1575   PetscInt          bs;
1576 
1577   PetscFunctionBegin;
1578   if (jac->type == PC_COMPOSITE_ADDITIVE) {
1579     if (jac->defaultsplit) {
1580       PetscCall(VecGetBlockSize(x, &bs));
1581       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);
1582       PetscCall(VecGetBlockSize(y, &bs));
1583       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);
1584       PetscCall(VecStrideGatherAll(x, jac->x, INSERT_VALUES));
1585       while (ilink) {
1586         PetscCall(PetscLogEventBegin(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1587         PetscCall(KSPSolveTranspose(ilink->ksp, ilink->x, ilink->y));
1588         PetscCall(KSPCheckSolve(ilink->ksp, pc, ilink->y));
1589         PetscCall(PetscLogEventEnd(ilink->event, ilink->ksp, ilink->x, ilink->y, NULL));
1590         ilink = ilink->next;
1591       }
1592       PetscCall(VecStrideScatterAll(jac->y, y, INSERT_VALUES));
1593     } else {
1594       PetscCall(VecSet(y, 0.0));
1595       while (ilink) {
1596         PetscCall(FieldSplitSplitSolveAddTranspose(ilink, x, y));
1597         ilink = ilink->next;
1598       }
1599     }
1600   } else {
1601     if (!jac->w1) {
1602       PetscCall(VecDuplicate(x, &jac->w1));
1603       PetscCall(VecDuplicate(x, &jac->w2));
1604     }
1605     PetscCall(VecSet(y, 0.0));
1606     if (jac->type == PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE) {
1607       PetscCall(FieldSplitSplitSolveAddTranspose(ilink, x, y));
1608       while (ilink->next) {
1609         ilink = ilink->next;
1610         PetscCall(MatMultTranspose(pc->mat, y, jac->w1));
1611         PetscCall(VecWAXPY(jac->w2, -1.0, jac->w1, x));
1612         PetscCall(FieldSplitSplitSolveAddTranspose(ilink, jac->w2, y));
1613       }
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     } else {
1621       while (ilink->next) { /* get to last entry in linked list */
1622         ilink = ilink->next;
1623       }
1624       PetscCall(FieldSplitSplitSolveAddTranspose(ilink, x, y));
1625       while (ilink->previous) {
1626         ilink = ilink->previous;
1627         PetscCall(MatMultTranspose(pc->mat, y, jac->w1));
1628         PetscCall(VecWAXPY(jac->w2, -1.0, jac->w1, x));
1629         PetscCall(FieldSplitSplitSolveAddTranspose(ilink, jac->w2, y));
1630       }
1631     }
1632   }
1633   PetscFunctionReturn(PETSC_SUCCESS);
1634 }
1635 
1636 static PetscErrorCode PCReset_FieldSplit(PC pc)
1637 {
1638   PC_FieldSplit    *jac   = (PC_FieldSplit *)pc->data;
1639   PC_FieldSplitLink ilink = jac->head, next;
1640 
1641   PetscFunctionBegin;
1642   while (ilink) {
1643     PetscCall(KSPDestroy(&ilink->ksp));
1644     PetscCall(VecDestroy(&ilink->x));
1645     PetscCall(VecDestroy(&ilink->y));
1646     PetscCall(VecDestroy(&ilink->z));
1647     PetscCall(VecScatterDestroy(&ilink->sctx));
1648     PetscCall(ISDestroy(&ilink->is));
1649     PetscCall(ISDestroy(&ilink->is_col));
1650     PetscCall(PetscFree(ilink->splitname));
1651     PetscCall(PetscFree(ilink->fields));
1652     PetscCall(PetscFree(ilink->fields_col));
1653     next = ilink->next;
1654     PetscCall(PetscFree(ilink));
1655     ilink = next;
1656   }
1657   jac->head = NULL;
1658   PetscCall(PetscFree2(jac->x, jac->y));
1659   if (jac->mat && jac->mat != jac->pmat) {
1660     PetscCall(MatDestroyMatrices(jac->nsplits, &jac->mat));
1661   } else if (jac->mat) {
1662     jac->mat = NULL;
1663   }
1664   if (jac->pmat) PetscCall(MatDestroyMatrices(jac->nsplits, &jac->pmat));
1665   if (jac->Afield) PetscCall(MatDestroyMatrices(jac->nsplits, &jac->Afield));
1666   jac->nsplits = 0;
1667   PetscCall(VecDestroy(&jac->w1));
1668   PetscCall(VecDestroy(&jac->w2));
1669   PetscCall(MatDestroy(&jac->schur));
1670   PetscCall(MatDestroy(&jac->schurp));
1671   PetscCall(MatDestroy(&jac->schur_user));
1672   PetscCall(KSPDestroy(&jac->kspschur));
1673   PetscCall(KSPDestroy(&jac->kspupper));
1674   PetscCall(MatDestroy(&jac->B));
1675   PetscCall(MatDestroy(&jac->C));
1676   PetscCall(MatDestroy(&jac->H));
1677   PetscCall(VecDestroy(&jac->u));
1678   PetscCall(VecDestroy(&jac->v));
1679   PetscCall(VecDestroy(&jac->Hu));
1680   PetscCall(VecDestroy(&jac->d));
1681   PetscCall(PetscFree(jac->vecz));
1682   PetscCall(PetscViewerDestroy(&jac->gkbviewer));
1683   jac->isrestrict = PETSC_FALSE;
1684   PetscFunctionReturn(PETSC_SUCCESS);
1685 }
1686 
1687 static PetscErrorCode PCDestroy_FieldSplit(PC pc)
1688 {
1689   PetscFunctionBegin;
1690   PetscCall(PCReset_FieldSplit(pc));
1691   PetscCall(PetscFree(pc->data));
1692   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCSetCoordinates_C", NULL));
1693   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetFields_C", NULL));
1694   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetIS_C", NULL));
1695   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetType_C", NULL));
1696   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetBlockSize_C", NULL));
1697   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitRestrictIS_C", NULL));
1698   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSchurGetSubKSP_C", NULL));
1699   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSubKSP_C", NULL));
1700 
1701   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBTol_C", NULL));
1702   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBMaxit_C", NULL));
1703   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBNu_C", NULL));
1704   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBDelay_C", NULL));
1705   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSubKSP_C", NULL));
1706   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurPre_C", NULL));
1707   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSchurPre_C", NULL));
1708   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurFactType_C", NULL));
1709   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurScale_C", NULL));
1710   PetscFunctionReturn(PETSC_SUCCESS);
1711 }
1712 
1713 static PetscErrorCode PCSetFromOptions_FieldSplit(PC pc, PetscOptionItems *PetscOptionsObject)
1714 {
1715   PetscInt        bs;
1716   PetscBool       flg;
1717   PC_FieldSplit  *jac = (PC_FieldSplit *)pc->data;
1718   PCCompositeType ctype;
1719 
1720   PetscFunctionBegin;
1721   PetscOptionsHeadBegin(PetscOptionsObject, "FieldSplit options");
1722   PetscCall(PetscOptionsBool("-pc_fieldsplit_dm_splits", "Whether to use DMCreateFieldDecomposition() for splits", "PCFieldSplitSetDMSplits", jac->dm_splits, &jac->dm_splits, NULL));
1723   PetscCall(PetscOptionsInt("-pc_fieldsplit_block_size", "Blocksize that defines number of fields", "PCFieldSplitSetBlockSize", jac->bs, &bs, &flg));
1724   if (flg) PetscCall(PCFieldSplitSetBlockSize(pc, bs));
1725   jac->diag_use_amat = pc->useAmat;
1726   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));
1727   jac->offdiag_use_amat = pc->useAmat;
1728   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));
1729   PetscCall(PetscOptionsBool("-pc_fieldsplit_detect_saddle_point", "Form 2-way split by detecting zero diagonal entries", "PCFieldSplitSetDetectSaddlePoint", jac->detect, &jac->detect, NULL));
1730   PetscCall(PCFieldSplitSetDetectSaddlePoint(pc, jac->detect)); /* Sets split type and Schur PC type */
1731   PetscCall(PetscOptionsEnum("-pc_fieldsplit_type", "Type of composition", "PCFieldSplitSetType", PCCompositeTypes, (PetscEnum)jac->type, (PetscEnum *)&ctype, &flg));
1732   if (flg) PetscCall(PCFieldSplitSetType(pc, ctype));
1733   /* Only setup fields once */
1734   if ((jac->bs > 0) && (jac->nsplits == 0)) {
1735     /* only allow user to set fields from command line if bs is already known.
1736        otherwise user can set them in PCFieldSplitSetDefaults() */
1737     PetscCall(PCFieldSplitSetRuntimeSplits_Private(pc));
1738     if (jac->splitdefined) PetscCall(PetscInfo(pc, "Splits defined using the options database\n"));
1739   }
1740   if (jac->type == PC_COMPOSITE_SCHUR) {
1741     PetscCall(PetscOptionsGetEnum(((PetscObject)pc)->options, ((PetscObject)pc)->prefix, "-pc_fieldsplit_schur_factorization_type", PCFieldSplitSchurFactTypes, (PetscEnum *)&jac->schurfactorization, &flg));
1742     if (flg) PetscCall(PetscInfo(pc, "Deprecated use of -pc_fieldsplit_schur_factorization_type\n"));
1743     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));
1744     PetscCall(PetscOptionsEnum("-pc_fieldsplit_schur_precondition", "How to build preconditioner for Schur complement", "PCFieldSplitSetSchurPre", PCFieldSplitSchurPreTypes, (PetscEnum)jac->schurpre, (PetscEnum *)&jac->schurpre, NULL));
1745     PetscCall(PetscOptionsScalar("-pc_fieldsplit_schur_scale", "Scale Schur complement", "PCFieldSplitSetSchurScale", jac->schurscale, &jac->schurscale, NULL));
1746   } else if (jac->type == PC_COMPOSITE_GKB) {
1747     PetscCall(PetscOptionsReal("-pc_fieldsplit_gkb_tol", "The tolerance for the lower bound stopping criterion", "PCFieldSplitGKBTol", jac->gkbtol, &jac->gkbtol, NULL));
1748     PetscCall(PetscOptionsInt("-pc_fieldsplit_gkb_delay", "The delay value for lower bound criterion", "PCFieldSplitGKBDelay", jac->gkbdelay, &jac->gkbdelay, NULL));
1749     PetscCall(PetscOptionsBoundedReal("-pc_fieldsplit_gkb_nu", "Parameter in augmented Lagrangian approach", "PCFieldSplitGKBNu", jac->gkbnu, &jac->gkbnu, NULL, 0.0));
1750     PetscCall(PetscOptionsInt("-pc_fieldsplit_gkb_maxit", "Maximum allowed number of iterations", "PCFieldSplitGKBMaxit", jac->gkbmaxit, &jac->gkbmaxit, NULL));
1751     PetscCall(PetscOptionsBool("-pc_fieldsplit_gkb_monitor", "Prints number of GKB iterations and error", "PCFieldSplitGKB", jac->gkbmonitor, &jac->gkbmonitor, NULL));
1752   }
1753   /*
1754     In the initial call to this routine the sub-solver data structures do not exist so we cannot call KSPSetFromOptions() on them yet.
1755     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
1756     is called on the outer solver in case changes were made in the options database
1757 
1758     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()
1759     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.
1760     Without this extra check test p2p1fetidp_olof_full and others fail with incorrect matrix types.
1761 
1762     There could be a negative side effect of calling the KSPSetFromOptions() below.
1763 
1764     If one captured the PetscObjectState of the options database one could skip these calls if the database has not changed from the previous call
1765   */
1766   if (jac->issetup) {
1767     PC_FieldSplitLink ilink = jac->head;
1768     if (jac->type == PC_COMPOSITE_SCHUR) {
1769       if (jac->kspupper && jac->kspupper->totalits > 0) PetscCall(KSPSetFromOptions(jac->kspupper));
1770       if (jac->kspschur && jac->kspschur->totalits > 0) PetscCall(KSPSetFromOptions(jac->kspschur));
1771     }
1772     while (ilink) {
1773       if (ilink->ksp->totalits > 0) PetscCall(KSPSetFromOptions(ilink->ksp));
1774       ilink = ilink->next;
1775     }
1776   }
1777   PetscOptionsHeadEnd();
1778   PetscFunctionReturn(PETSC_SUCCESS);
1779 }
1780 
1781 static PetscErrorCode PCFieldSplitSetFields_FieldSplit(PC pc, const char splitname[], PetscInt n, const PetscInt *fields, const PetscInt *fields_col)
1782 {
1783   PC_FieldSplit    *jac = (PC_FieldSplit *)pc->data;
1784   PC_FieldSplitLink ilink, next = jac->head;
1785   char              prefix[128];
1786   PetscInt          i;
1787 
1788   PetscFunctionBegin;
1789   if (jac->splitdefined) {
1790     PetscCall(PetscInfo(pc, "Ignoring new split \"%s\" because the splits have already been defined\n", splitname));
1791     PetscFunctionReturn(PETSC_SUCCESS);
1792   }
1793   for (i = 0; i < n; i++) {
1794     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);
1795     PetscCheck(fields[i] >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Negative field %" PetscInt_FMT " requested", fields[i]);
1796   }
1797   PetscCall(PetscNew(&ilink));
1798   if (splitname) {
1799     PetscCall(PetscStrallocpy(splitname, &ilink->splitname));
1800   } else {
1801     PetscCall(PetscMalloc1(3, &ilink->splitname));
1802     PetscCall(PetscSNPrintf(ilink->splitname, 2, "%" PetscInt_FMT, jac->nsplits));
1803   }
1804   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 */
1805   PetscCall(PetscMalloc1(n, &ilink->fields));
1806   PetscCall(PetscArraycpy(ilink->fields, fields, n));
1807   PetscCall(PetscMalloc1(n, &ilink->fields_col));
1808   PetscCall(PetscArraycpy(ilink->fields_col, fields_col, n));
1809 
1810   ilink->nfields = n;
1811   ilink->next    = NULL;
1812   PetscCall(KSPCreate(PetscObjectComm((PetscObject)pc), &ilink->ksp));
1813   PetscCall(KSPSetNestLevel(ilink->ksp, pc->kspnestlevel));
1814   PetscCall(KSPSetErrorIfNotConverged(ilink->ksp, pc->erroriffailure));
1815   PetscCall(PetscObjectIncrementTabLevel((PetscObject)ilink->ksp, (PetscObject)pc, 1));
1816   PetscCall(KSPSetType(ilink->ksp, KSPPREONLY));
1817 
1818   PetscCall(PetscSNPrintf(prefix, sizeof(prefix), "%sfieldsplit_%s_", ((PetscObject)pc)->prefix ? ((PetscObject)pc)->prefix : "", ilink->splitname));
1819   PetscCall(KSPSetOptionsPrefix(ilink->ksp, prefix));
1820 
1821   if (!next) {
1822     jac->head       = ilink;
1823     ilink->previous = NULL;
1824   } else {
1825     while (next->next) next = next->next;
1826     next->next      = ilink;
1827     ilink->previous = next;
1828   }
1829   jac->nsplits++;
1830   PetscFunctionReturn(PETSC_SUCCESS);
1831 }
1832 
1833 static PetscErrorCode PCFieldSplitSchurGetSubKSP_FieldSplit(PC pc, PetscInt *n, KSP **subksp)
1834 {
1835   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
1836 
1837   PetscFunctionBegin;
1838   *subksp = NULL;
1839   if (n) *n = 0;
1840   if (jac->type == PC_COMPOSITE_SCHUR) {
1841     PetscInt nn;
1842 
1843     PetscCheck(jac->schur, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONGSTATE, "Must call KSPSetUp() or PCSetUp() before calling PCFieldSplitSchurGetSubKSP()");
1844     PetscCheck(jac->nsplits == 2, PetscObjectComm((PetscObject)pc), PETSC_ERR_PLIB, "Unexpected number of splits %" PetscInt_FMT " != 2", jac->nsplits);
1845     nn = jac->nsplits + (jac->kspupper != jac->head->ksp ? 1 : 0);
1846     PetscCall(PetscMalloc1(nn, subksp));
1847     (*subksp)[0] = jac->head->ksp;
1848     (*subksp)[1] = jac->kspschur;
1849     if (jac->kspupper != jac->head->ksp) (*subksp)[2] = jac->kspupper;
1850     if (n) *n = nn;
1851   }
1852   PetscFunctionReturn(PETSC_SUCCESS);
1853 }
1854 
1855 static PetscErrorCode PCFieldSplitGetSubKSP_FieldSplit_Schur(PC pc, PetscInt *n, KSP **subksp)
1856 {
1857   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
1858 
1859   PetscFunctionBegin;
1860   PetscCheck(jac->schur, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONGSTATE, "Must call KSPSetUp() or PCSetUp() before calling PCFieldSplitGetSubKSP()");
1861   PetscCall(PetscMalloc1(jac->nsplits, subksp));
1862   PetscCall(MatSchurComplementGetKSP(jac->schur, *subksp));
1863 
1864   (*subksp)[1] = jac->kspschur;
1865   if (n) *n = jac->nsplits;
1866   PetscFunctionReturn(PETSC_SUCCESS);
1867 }
1868 
1869 static PetscErrorCode PCFieldSplitGetSubKSP_FieldSplit(PC pc, PetscInt *n, KSP **subksp)
1870 {
1871   PC_FieldSplit    *jac   = (PC_FieldSplit *)pc->data;
1872   PetscInt          cnt   = 0;
1873   PC_FieldSplitLink ilink = jac->head;
1874 
1875   PetscFunctionBegin;
1876   PetscCall(PetscMalloc1(jac->nsplits, subksp));
1877   while (ilink) {
1878     (*subksp)[cnt++] = ilink->ksp;
1879     ilink            = ilink->next;
1880   }
1881   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);
1882   if (n) *n = jac->nsplits;
1883   PetscFunctionReturn(PETSC_SUCCESS);
1884 }
1885 
1886 /*@C
1887   PCFieldSplitRestrictIS - Restricts the fieldsplit `IS`s to be within a given `IS`.
1888 
1889   Input Parameters:
1890 + pc  - the preconditioner context
1891 - isy - the index set that defines the indices to which the fieldsplit is to be restricted
1892 
1893   Level: advanced
1894 
1895   Developer Notes:
1896   It seems the resulting `IS`s will not cover the entire space, so
1897   how can they define a convergent preconditioner? Needs explaining.
1898 
1899 .seealso: [](sec_block_matrices), `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSetIS()`
1900 @*/
1901 PetscErrorCode PCFieldSplitRestrictIS(PC pc, IS isy)
1902 {
1903   PetscFunctionBegin;
1904   PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
1905   PetscValidHeaderSpecific(isy, IS_CLASSID, 2);
1906   PetscTryMethod(pc, "PCFieldSplitRestrictIS_C", (PC, IS), (pc, isy));
1907   PetscFunctionReturn(PETSC_SUCCESS);
1908 }
1909 
1910 static PetscErrorCode PCFieldSplitRestrictIS_FieldSplit(PC pc, IS isy)
1911 {
1912   PC_FieldSplit    *jac   = (PC_FieldSplit *)pc->data;
1913   PC_FieldSplitLink ilink = jac->head, next;
1914   PetscInt          localsize, size, sizez, i;
1915   const PetscInt   *ind, *indz;
1916   PetscInt         *indc, *indcz;
1917   PetscBool         flg;
1918 
1919   PetscFunctionBegin;
1920   PetscCall(ISGetLocalSize(isy, &localsize));
1921   PetscCallMPI(MPI_Scan(&localsize, &size, 1, MPIU_INT, MPI_SUM, PetscObjectComm((PetscObject)isy)));
1922   size -= localsize;
1923   while (ilink) {
1924     IS isrl, isr;
1925     PC subpc;
1926     PetscCall(ISEmbed(ilink->is, isy, PETSC_TRUE, &isrl));
1927     PetscCall(ISGetLocalSize(isrl, &localsize));
1928     PetscCall(PetscMalloc1(localsize, &indc));
1929     PetscCall(ISGetIndices(isrl, &ind));
1930     PetscCall(PetscArraycpy(indc, ind, localsize));
1931     PetscCall(ISRestoreIndices(isrl, &ind));
1932     PetscCall(ISDestroy(&isrl));
1933     for (i = 0; i < localsize; i++) *(indc + i) += size;
1934     PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)isy), localsize, indc, PETSC_OWN_POINTER, &isr));
1935     PetscCall(PetscObjectReference((PetscObject)isr));
1936     PetscCall(ISDestroy(&ilink->is));
1937     ilink->is = isr;
1938     PetscCall(PetscObjectReference((PetscObject)isr));
1939     PetscCall(ISDestroy(&ilink->is_col));
1940     ilink->is_col = isr;
1941     PetscCall(ISDestroy(&isr));
1942     PetscCall(KSPGetPC(ilink->ksp, &subpc));
1943     PetscCall(PetscObjectTypeCompare((PetscObject)subpc, PCFIELDSPLIT, &flg));
1944     if (flg) {
1945       IS       iszl, isz;
1946       MPI_Comm comm;
1947       PetscCall(ISGetLocalSize(ilink->is, &localsize));
1948       comm = PetscObjectComm((PetscObject)ilink->is);
1949       PetscCall(ISEmbed(isy, ilink->is, PETSC_TRUE, &iszl));
1950       PetscCallMPI(MPI_Scan(&localsize, &sizez, 1, MPIU_INT, MPI_SUM, comm));
1951       sizez -= localsize;
1952       PetscCall(ISGetLocalSize(iszl, &localsize));
1953       PetscCall(PetscMalloc1(localsize, &indcz));
1954       PetscCall(ISGetIndices(iszl, &indz));
1955       PetscCall(PetscArraycpy(indcz, indz, localsize));
1956       PetscCall(ISRestoreIndices(iszl, &indz));
1957       PetscCall(ISDestroy(&iszl));
1958       for (i = 0; i < localsize; i++) *(indcz + i) += sizez;
1959       PetscCall(ISCreateGeneral(comm, localsize, indcz, PETSC_OWN_POINTER, &isz));
1960       PetscCall(PCFieldSplitRestrictIS(subpc, isz));
1961       PetscCall(ISDestroy(&isz));
1962     }
1963     next  = ilink->next;
1964     ilink = next;
1965   }
1966   jac->isrestrict = PETSC_TRUE;
1967   PetscFunctionReturn(PETSC_SUCCESS);
1968 }
1969 
1970 static PetscErrorCode PCFieldSplitSetIS_FieldSplit(PC pc, const char splitname[], IS is)
1971 {
1972   PC_FieldSplit    *jac = (PC_FieldSplit *)pc->data;
1973   PC_FieldSplitLink ilink, next = jac->head;
1974   char              prefix[128];
1975 
1976   PetscFunctionBegin;
1977   if (jac->splitdefined) {
1978     PetscCall(PetscInfo(pc, "Ignoring new split \"%s\" because the splits have already been defined\n", splitname));
1979     PetscFunctionReturn(PETSC_SUCCESS);
1980   }
1981   PetscCall(PetscNew(&ilink));
1982   if (splitname) {
1983     PetscCall(PetscStrallocpy(splitname, &ilink->splitname));
1984   } else {
1985     PetscCall(PetscMalloc1(8, &ilink->splitname));
1986     PetscCall(PetscSNPrintf(ilink->splitname, 7, "%" PetscInt_FMT, jac->nsplits));
1987   }
1988   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 */
1989   PetscCall(PetscObjectReference((PetscObject)is));
1990   PetscCall(ISDestroy(&ilink->is));
1991   ilink->is = is;
1992   PetscCall(PetscObjectReference((PetscObject)is));
1993   PetscCall(ISDestroy(&ilink->is_col));
1994   ilink->is_col = is;
1995   ilink->next   = NULL;
1996   PetscCall(KSPCreate(PetscObjectComm((PetscObject)pc), &ilink->ksp));
1997   PetscCall(KSPSetNestLevel(ilink->ksp, pc->kspnestlevel));
1998   PetscCall(KSPSetErrorIfNotConverged(ilink->ksp, pc->erroriffailure));
1999   PetscCall(PetscObjectIncrementTabLevel((PetscObject)ilink->ksp, (PetscObject)pc, 1));
2000   PetscCall(KSPSetType(ilink->ksp, KSPPREONLY));
2001 
2002   PetscCall(PetscSNPrintf(prefix, sizeof(prefix), "%sfieldsplit_%s_", ((PetscObject)pc)->prefix ? ((PetscObject)pc)->prefix : "", ilink->splitname));
2003   PetscCall(KSPSetOptionsPrefix(ilink->ksp, prefix));
2004 
2005   if (!next) {
2006     jac->head       = ilink;
2007     ilink->previous = NULL;
2008   } else {
2009     while (next->next) next = next->next;
2010     next->next      = ilink;
2011     ilink->previous = next;
2012   }
2013   jac->nsplits++;
2014   PetscFunctionReturn(PETSC_SUCCESS);
2015 }
2016 
2017 /*@C
2018   PCFieldSplitSetFields - Sets the fields that define one particular split in `PCFIELDSPLIT`
2019 
2020   Logically Collective
2021 
2022   Input Parameters:
2023 + pc         - the preconditioner context
2024 . splitname  - name of this split, if `NULL` the number of the split is used
2025 . n          - the number of fields in this split
2026 . fields     - the fields in this split
2027 - 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
2028                  of the matrix and fields_col provides the column indices for that block
2029 
2030   Level: intermediate
2031 
2032   Notes:
2033   Use `PCFieldSplitSetIS()` to set a  general set of indices as a split.
2034 
2035   `PCFieldSplitSetFields()` is for defining fields as strided blocks. For example, if the block
2036   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
2037   0xx3xx6xx9xx12 ... x1xx4xx7xx ... xx2xx5xx8xx.. 01x34x67x... 0x1x3x5x7.. x12x45x78x....
2038   where the numbered entries indicate what is in the split.
2039 
2040   This function is called once per split (it creates a new split each time).  Solve options
2041   for this split will be available under the prefix `-fieldsplit_SPLITNAME_`.
2042 
2043   `PCFieldSplitSetIS()` does not support having a fields_col different from fields
2044 
2045   Developer Notes:
2046   This routine does not actually create the `IS` representing the split, that is delayed
2047   until `PCSetUp_FieldSplit()`, because information about the vector/matrix layouts may not be
2048   available when this routine is called.
2049 
2050 .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSetBlockSize()`, `PCFieldSplitSetIS()`, `PCFieldSplitRestrictIS()`
2051 @*/
2052 PetscErrorCode PCFieldSplitSetFields(PC pc, const char splitname[], PetscInt n, const PetscInt *fields, const PetscInt *fields_col)
2053 {
2054   PetscFunctionBegin;
2055   PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
2056   PetscAssertPointer(splitname, 2);
2057   PetscCheck(n >= 1, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_OUTOFRANGE, "Provided number of fields %" PetscInt_FMT " in split \"%s\" not positive", n, splitname);
2058   PetscAssertPointer(fields, 4);
2059   PetscTryMethod(pc, "PCFieldSplitSetFields_C", (PC, const char[], PetscInt, const PetscInt *, const PetscInt *), (pc, splitname, n, fields, fields_col));
2060   PetscFunctionReturn(PETSC_SUCCESS);
2061 }
2062 
2063 /*@
2064   PCFieldSplitSetDiagUseAmat - set flag indicating whether to extract diagonal blocks from Amat (rather than Pmat) to build
2065   the sub-matrices associated with each split. Where `KSPSetOperators`(ksp,Amat,Pmat) was used to supply the operators.
2066 
2067   Logically Collective
2068 
2069   Input Parameters:
2070 + pc  - the preconditioner object
2071 - flg - boolean flag indicating whether or not to use Amat to extract the diagonal blocks from
2072 
2073   Options Database Key:
2074 . -pc_fieldsplit_diag_use_amat - use the Amat to provide the diagonal blocks
2075 
2076   Level: intermediate
2077 
2078 .seealso: [](sec_block_matrices), `PC`, `PCSetOperators()`, `KSPSetOperators()`, `PCFieldSplitGetDiagUseAmat()`, `PCFieldSplitSetOffDiagUseAmat()`, `PCFIELDSPLIT`
2079 @*/
2080 PetscErrorCode PCFieldSplitSetDiagUseAmat(PC pc, PetscBool flg)
2081 {
2082   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
2083   PetscBool      isfs;
2084 
2085   PetscFunctionBegin;
2086   PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
2087   PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCFIELDSPLIT, &isfs));
2088   PetscCheck(isfs, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "PC not of type %s", PCFIELDSPLIT);
2089   jac->diag_use_amat = flg;
2090   PetscFunctionReturn(PETSC_SUCCESS);
2091 }
2092 
2093 /*@
2094   PCFieldSplitGetDiagUseAmat - get the flag indicating whether to extract diagonal blocks from Amat (rather than Pmat) to build
2095   the sub-matrices associated with each split.  Where `KSPSetOperators`(ksp,Amat,Pmat) was used to supply the operators.
2096 
2097   Logically Collective
2098 
2099   Input Parameter:
2100 . pc - the preconditioner object
2101 
2102   Output Parameter:
2103 . flg - boolean flag indicating whether or not to use Amat to extract the diagonal blocks from
2104 
2105   Level: intermediate
2106 
2107 .seealso: [](sec_block_matrices), `PC`, `PCSetOperators()`, `KSPSetOperators()`, `PCFieldSplitSetDiagUseAmat()`, `PCFieldSplitGetOffDiagUseAmat()`, `PCFIELDSPLIT`
2108 @*/
2109 PetscErrorCode PCFieldSplitGetDiagUseAmat(PC pc, PetscBool *flg)
2110 {
2111   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
2112   PetscBool      isfs;
2113 
2114   PetscFunctionBegin;
2115   PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
2116   PetscAssertPointer(flg, 2);
2117   PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCFIELDSPLIT, &isfs));
2118   PetscCheck(isfs, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "PC not of type %s", PCFIELDSPLIT);
2119   *flg = jac->diag_use_amat;
2120   PetscFunctionReturn(PETSC_SUCCESS);
2121 }
2122 
2123 /*@
2124   PCFieldSplitSetOffDiagUseAmat - set flag indicating whether to extract off-diagonal blocks from Amat (rather than Pmat) to build
2125   the sub-matrices associated with each split.  Where `KSPSetOperators`(ksp,Amat,Pmat) was used to supply the operators.
2126 
2127   Logically Collective
2128 
2129   Input Parameters:
2130 + pc  - the preconditioner object
2131 - flg - boolean flag indicating whether or not to use Amat to extract the off-diagonal blocks from
2132 
2133   Options Database Key:
2134 . -pc_fieldsplit_off_diag_use_amat <bool> - use the Amat to extract the off-diagonal blocks
2135 
2136   Level: intermediate
2137 
2138 .seealso: [](sec_block_matrices), `PC`, `PCSetOperators()`, `KSPSetOperators()`, `PCFieldSplitGetOffDiagUseAmat()`, `PCFieldSplitSetDiagUseAmat()`, `PCFIELDSPLIT`
2139 @*/
2140 PetscErrorCode PCFieldSplitSetOffDiagUseAmat(PC pc, PetscBool flg)
2141 {
2142   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
2143   PetscBool      isfs;
2144 
2145   PetscFunctionBegin;
2146   PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
2147   PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCFIELDSPLIT, &isfs));
2148   PetscCheck(isfs, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "PC not of type %s", PCFIELDSPLIT);
2149   jac->offdiag_use_amat = flg;
2150   PetscFunctionReturn(PETSC_SUCCESS);
2151 }
2152 
2153 /*@
2154   PCFieldSplitGetOffDiagUseAmat - get the flag indicating whether to extract off-diagonal blocks from Amat (rather than Pmat) to build
2155   the sub-matrices associated with each split.  Where `KSPSetOperators`(ksp,Amat,Pmat) was used to supply the operators.
2156 
2157   Logically Collective
2158 
2159   Input Parameter:
2160 . pc - the preconditioner object
2161 
2162   Output Parameter:
2163 . flg - boolean flag indicating whether or not to use Amat to extract the off-diagonal blocks from
2164 
2165   Level: intermediate
2166 
2167 .seealso: [](sec_block_matrices), `PC`, `PCSetOperators()`, `KSPSetOperators()`, `PCFieldSplitSetOffDiagUseAmat()`, `PCFieldSplitGetDiagUseAmat()`, `PCFIELDSPLIT`
2168 @*/
2169 PetscErrorCode PCFieldSplitGetOffDiagUseAmat(PC pc, PetscBool *flg)
2170 {
2171   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
2172   PetscBool      isfs;
2173 
2174   PetscFunctionBegin;
2175   PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
2176   PetscAssertPointer(flg, 2);
2177   PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCFIELDSPLIT, &isfs));
2178   PetscCheck(isfs, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "PC not of type %s", PCFIELDSPLIT);
2179   *flg = jac->offdiag_use_amat;
2180   PetscFunctionReturn(PETSC_SUCCESS);
2181 }
2182 
2183 /*@C
2184   PCFieldSplitSetIS - Sets the exact elements for a split in a `PCFIELDSPLIT`
2185 
2186   Logically Collective
2187 
2188   Input Parameters:
2189 + pc        - the preconditioner context
2190 . splitname - name of this split, if `NULL` the number of the split is used
2191 - is        - the index set that defines the elements in this split
2192 
2193   Level: intermediate
2194 
2195   Notes:
2196   Use `PCFieldSplitSetFields()`, for splits defined by strided types.
2197 
2198   This function is called once per split (it creates a new split each time).  Solve options
2199   for this split will be available under the prefix -fieldsplit_SPLITNAME_.
2200 
2201 .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSetBlockSize()`
2202 @*/
2203 PetscErrorCode PCFieldSplitSetIS(PC pc, const char splitname[], IS is)
2204 {
2205   PetscFunctionBegin;
2206   PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
2207   if (splitname) PetscAssertPointer(splitname, 2);
2208   PetscValidHeaderSpecific(is, IS_CLASSID, 3);
2209   PetscTryMethod(pc, "PCFieldSplitSetIS_C", (PC, const char[], IS), (pc, splitname, is));
2210   PetscFunctionReturn(PETSC_SUCCESS);
2211 }
2212 
2213 /*@C
2214   PCFieldSplitGetIS - Retrieves the elements for a split as an `IS`
2215 
2216   Logically Collective
2217 
2218   Input Parameters:
2219 + pc        - the preconditioner context
2220 - splitname - name of this split
2221 
2222   Output Parameter:
2223 . is - the index set that defines the elements in this split, or `NULL` if the split is not found
2224 
2225   Level: intermediate
2226 
2227 .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSetIS()`
2228 @*/
2229 PetscErrorCode PCFieldSplitGetIS(PC pc, const char splitname[], IS *is)
2230 {
2231   PetscFunctionBegin;
2232   PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
2233   PetscAssertPointer(splitname, 2);
2234   PetscAssertPointer(is, 3);
2235   {
2236     PC_FieldSplit    *jac   = (PC_FieldSplit *)pc->data;
2237     PC_FieldSplitLink ilink = jac->head;
2238     PetscBool         found;
2239 
2240     *is = NULL;
2241     while (ilink) {
2242       PetscCall(PetscStrcmp(ilink->splitname, splitname, &found));
2243       if (found) {
2244         *is = ilink->is;
2245         break;
2246       }
2247       ilink = ilink->next;
2248     }
2249   }
2250   PetscFunctionReturn(PETSC_SUCCESS);
2251 }
2252 
2253 /*@C
2254   PCFieldSplitGetISByIndex - Retrieves the elements for a given split as an `IS`
2255 
2256   Logically Collective
2257 
2258   Input Parameters:
2259 + pc    - the preconditioner context
2260 - index - index of this split
2261 
2262   Output Parameter:
2263 . is - the index set that defines the elements in this split
2264 
2265   Level: intermediate
2266 
2267 .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitGetIS()`, `PCFieldSplitSetIS()`
2268 @*/
2269 PetscErrorCode PCFieldSplitGetISByIndex(PC pc, PetscInt index, IS *is)
2270 {
2271   PetscFunctionBegin;
2272   PetscCheck(index >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Negative field %" PetscInt_FMT " requested", index);
2273   PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
2274   PetscAssertPointer(is, 3);
2275   {
2276     PC_FieldSplit    *jac   = (PC_FieldSplit *)pc->data;
2277     PC_FieldSplitLink ilink = jac->head;
2278     PetscInt          i     = 0;
2279     PetscCheck(index < jac->nsplits, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Field %" PetscInt_FMT " requested but only %" PetscInt_FMT " exist", index, jac->nsplits);
2280 
2281     while (i < index) {
2282       ilink = ilink->next;
2283       ++i;
2284     }
2285     PetscCall(PCFieldSplitGetIS(pc, ilink->splitname, is));
2286   }
2287   PetscFunctionReturn(PETSC_SUCCESS);
2288 }
2289 
2290 /*@
2291   PCFieldSplitSetBlockSize - Sets the block size for defining where fields start in the
2292   fieldsplit preconditioner when calling `PCFieldSplitSetIS()`. If not set the matrix block size is used.
2293 
2294   Logically Collective
2295 
2296   Input Parameters:
2297 + pc - the preconditioner context
2298 - bs - the block size
2299 
2300   Level: intermediate
2301 
2302 .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSetIS()`
2303 @*/
2304 PetscErrorCode PCFieldSplitSetBlockSize(PC pc, PetscInt bs)
2305 {
2306   PetscFunctionBegin;
2307   PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
2308   PetscValidLogicalCollectiveInt(pc, bs, 2);
2309   PetscTryMethod(pc, "PCFieldSplitSetBlockSize_C", (PC, PetscInt), (pc, bs));
2310   PetscFunctionReturn(PETSC_SUCCESS);
2311 }
2312 
2313 /*@C
2314   PCFieldSplitGetSubKSP - Gets the `KSP` contexts for all splits
2315 
2316   Collective
2317 
2318   Input Parameter:
2319 . pc - the preconditioner context
2320 
2321   Output Parameters:
2322 + n      - the number of splits
2323 - subksp - the array of `KSP` contexts
2324 
2325   Level: advanced
2326 
2327   Notes:
2328   After `PCFieldSplitGetSubKSP()` the array of `KSP`s is to be freed by the user with `PetscFree()`
2329   (not the `KSP`, just the array that contains them).
2330 
2331   You must call `PCSetUp()` before calling `PCFieldSplitGetSubKSP()`.
2332 
2333   If the fieldsplit is of type `PC_COMPOSITE_SCHUR`, it returns the `KSP` object used inside the
2334   Schur complement and the `KSP` object used to iterate over the Schur complement.
2335   To access all the `KSP` objects used in `PC_COMPOSITE_SCHUR`, use `PCFieldSplitSchurGetSubKSP()`.
2336 
2337   If the fieldsplit is of type `PC_COMPOSITE_GKB`, it returns the `KSP` object used to solve the
2338   inner linear system defined by the matrix H in each loop.
2339 
2340   Fortran Notes:
2341   You must pass in a `KSP` array that is large enough to contain all the `KSP`s.
2342   You can call `PCFieldSplitGetSubKSP`(pc,n,`PETSC_NULL_KSP`,ierr) to determine how large the
2343   `KSP` array must be.
2344 
2345   Developer Notes:
2346   There should be a `PCFieldSplitRestoreSubKSP()` instead of requiring the user to call `PetscFree()`
2347 
2348   The Fortran interface should be modernized to return directly the array of values.
2349 
2350 .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSetIS()`, `PCFieldSplitSchurGetSubKSP()`
2351 @*/
2352 PetscErrorCode PCFieldSplitGetSubKSP(PC pc, PetscInt *n, KSP *subksp[])
2353 {
2354   PetscFunctionBegin;
2355   PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
2356   if (n) PetscAssertPointer(n, 2);
2357   PetscUseMethod(pc, "PCFieldSplitGetSubKSP_C", (PC, PetscInt *, KSP **), (pc, n, subksp));
2358   PetscFunctionReturn(PETSC_SUCCESS);
2359 }
2360 
2361 /*@C
2362   PCFieldSplitSchurGetSubKSP - Gets the `KSP` contexts used inside the Schur complement based `PCFIELDSPLIT`
2363 
2364   Collective
2365 
2366   Input Parameter:
2367 . pc - the preconditioner context
2368 
2369   Output Parameters:
2370 + n      - the number of splits
2371 - subksp - the array of `KSP` contexts
2372 
2373   Level: advanced
2374 
2375   Notes:
2376   After `PCFieldSplitSchurGetSubKSP()` the array of `KSP`s is to be freed by the user with `PetscFree()`
2377   (not the `KSP` just the array that contains them).
2378 
2379   You must call `PCSetUp()` before calling `PCFieldSplitSchurGetSubKSP()`.
2380 
2381   If the fieldsplit type is of type `PC_COMPOSITE_SCHUR`, it returns (in order)
2382 +  1  - the `KSP` used for the (1,1) block
2383 .  2  - the `KSP` used for the Schur complement (not the one used for the interior Schur solver)
2384 -  3  - the `KSP` used for the (1,1) block in the upper triangular factor (if different from that of the (1,1) block).
2385 
2386   It returns a null array if the fieldsplit is not of type `PC_COMPOSITE_SCHUR`; in this case, you should use `PCFieldSplitGetSubKSP()`.
2387 
2388   Fortran Notes:
2389   You must pass in a `KSP` array that is large enough to contain all the local `KSP`s.
2390   You can call `PCFieldSplitSchurGetSubKSP`(pc,n,`PETSC_NULL_KSP`,ierr) to determine how large the
2391   `KSP` array must be.
2392 
2393   Developer Notes:
2394   There should be a `PCFieldSplitRestoreSubKSP()` instead of requiring the user to call `PetscFree()`
2395 
2396   Should the functionality of `PCFieldSplitSchurGetSubKSP()` and `PCFieldSplitGetSubKSP()` be merged?
2397 
2398   The Fortran interface should be modernized to return directly the array of values.
2399 
2400 .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSetIS()`, `PCFieldSplitGetSubKSP()`
2401 @*/
2402 PetscErrorCode PCFieldSplitSchurGetSubKSP(PC pc, PetscInt *n, KSP *subksp[])
2403 {
2404   PetscFunctionBegin;
2405   PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
2406   if (n) PetscAssertPointer(n, 2);
2407   PetscUseMethod(pc, "PCFieldSplitSchurGetSubKSP_C", (PC, PetscInt *, KSP **), (pc, n, subksp));
2408   PetscFunctionReturn(PETSC_SUCCESS);
2409 }
2410 
2411 /*@
2412   PCFieldSplitSetSchurPre -  Indicates from what operator the preconditioner is constructed for the Schur complement.
2413   The default is the A11 matrix.
2414 
2415   Collective
2416 
2417   Input Parameters:
2418 + pc    - the preconditioner context
2419 . ptype - which matrix to use for preconditioning the Schur complement: `PC_FIELDSPLIT_SCHUR_PRE_A11` (default),
2420               `PC_FIELDSPLIT_SCHUR_PRE_SELF`, `PC_FIELDSPLIT_SCHUR_PRE_USER`,
2421               `PC_FIELDSPLIT_SCHUR_PRE_SELFP`, and `PC_FIELDSPLIT_SCHUR_PRE_FULL`
2422 - pre   - matrix to use for preconditioning, or `NULL`
2423 
2424   Options Database Keys:
2425 + -pc_fieldsplit_schur_precondition <self,selfp,user,a11,full> - default is `a11`. See notes for meaning of various arguments
2426 - -fieldsplit_1_pc_type <pctype>                               - the preconditioner algorithm that is used to construct the preconditioner from the operator
2427 
2428   Level: intermediate
2429 
2430   Notes:
2431   If ptype is
2432 +     a11 - the preconditioner for the Schur complement is generated from the block diagonal part of the preconditioner
2433   matrix associated with the Schur complement (i.e. A11), not the Schur complement matrix
2434 .     self - the preconditioner for the Schur complement is generated from the symbolic representation of the Schur complement matrix:
2435   The only preconditioner that currently works with this symbolic representation matrix object is the `PCLSC`
2436   preconditioner
2437 .     user - the preconditioner for the Schur complement is generated from the user provided matrix (pre argument
2438   to this function).
2439 .     selfp - the preconditioning for the Schur complement is generated from an explicitly-assembled approximation Sp = A11 - A10 inv(diag(A00)) A01
2440   This is only a good preconditioner when diag(A00) is a good preconditioner for A00. Optionally, A00 can be
2441   lumped before extracting the diagonal using the additional option `-fieldsplit_1_mat_schur_complement_ainv_type lump`
2442 -     full - the preconditioner for the Schur complement is generated from the exact Schur complement matrix representation
2443   computed internally by `PCFIELDSPLIT` (this is expensive)
2444   useful mostly as a test that the Schur complement approach can work for your problem
2445 
2446   When solving a saddle point problem, where the A11 block is identically zero, using `a11` as the ptype only makes sense
2447   with the additional option `-fieldsplit_1_pc_type none`. Usually for saddle point problems one would use a ptype of self and
2448   `-fieldsplit_1_pc_type lsc` which uses the least squares commutator to compute a preconditioner for the Schur complement.
2449 
2450 .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSchurPre()`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSchurPreType`,
2451           `MatSchurComplementSetAinvType()`, `PCLSC`,
2452 
2453 @*/
2454 PetscErrorCode PCFieldSplitSetSchurPre(PC pc, PCFieldSplitSchurPreType ptype, Mat pre)
2455 {
2456   PetscFunctionBegin;
2457   PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
2458   PetscTryMethod(pc, "PCFieldSplitSetSchurPre_C", (PC, PCFieldSplitSchurPreType, Mat), (pc, ptype, pre));
2459   PetscFunctionReturn(PETSC_SUCCESS);
2460 }
2461 
2462 PetscErrorCode PCFieldSplitSchurPrecondition(PC pc, PCFieldSplitSchurPreType ptype, Mat pre)
2463 {
2464   return PCFieldSplitSetSchurPre(pc, ptype, pre);
2465 } /* Deprecated name */
2466 
2467 /*@
2468   PCFieldSplitGetSchurPre - For Schur complement fieldsplit, determine how the Schur complement will be
2469   preconditioned.  See `PCFieldSplitSetSchurPre()` for details.
2470 
2471   Logically Collective
2472 
2473   Input Parameter:
2474 . pc - the preconditioner context
2475 
2476   Output Parameters:
2477 + 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`
2478 - pre   - matrix to use for preconditioning (with `PC_FIELDSPLIT_SCHUR_PRE_USER`), or `NULL`
2479 
2480   Level: intermediate
2481 
2482 .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitSetSchurPre()`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSchurPreType`, `PCLSC`
2483 
2484 @*/
2485 PetscErrorCode PCFieldSplitGetSchurPre(PC pc, PCFieldSplitSchurPreType *ptype, Mat *pre)
2486 {
2487   PetscFunctionBegin;
2488   PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
2489   PetscUseMethod(pc, "PCFieldSplitGetSchurPre_C", (PC, PCFieldSplitSchurPreType *, Mat *), (pc, ptype, pre));
2490   PetscFunctionReturn(PETSC_SUCCESS);
2491 }
2492 
2493 /*@
2494   PCFieldSplitSchurGetS -  extract the `MATSCHURCOMPLEMENT` object used by this `PCFIELDSPLIT` in case it needs to be configured separately
2495 
2496   Not Collective
2497 
2498   Input Parameter:
2499 . pc - the preconditioner context
2500 
2501   Output Parameter:
2502 . S - the Schur complement matrix
2503 
2504   Level: advanced
2505 
2506   Note:
2507   This matrix should not be destroyed using `MatDestroy()`; rather, use `PCFieldSplitSchurRestoreS()`.
2508 
2509 .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSchurPreType`, `PCFieldSplitSetSchurPre()`, `MATSCHURCOMPLEMENT`, `PCFieldSplitSchurRestoreS()`,
2510           `MatCreateSchurComplement()`, `MatSchurComplementGetKSP()`, `MatSchurComplementComputeExplicitOperator()`, `MatGetSchurComplement()`
2511 @*/
2512 PetscErrorCode PCFieldSplitSchurGetS(PC pc, Mat *S)
2513 {
2514   const char    *t;
2515   PetscBool      isfs;
2516   PC_FieldSplit *jac;
2517 
2518   PetscFunctionBegin;
2519   PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
2520   PetscCall(PetscObjectGetType((PetscObject)pc, &t));
2521   PetscCall(PetscStrcmp(t, PCFIELDSPLIT, &isfs));
2522   PetscCheck(isfs, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Expected PC of type PCFIELDSPLIT, got %s instead", t);
2523   jac = (PC_FieldSplit *)pc->data;
2524   PetscCheck(jac->type == PC_COMPOSITE_SCHUR, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Expected PCFIELDSPLIT of type SCHUR, got %d instead", jac->type);
2525   if (S) *S = jac->schur;
2526   PetscFunctionReturn(PETSC_SUCCESS);
2527 }
2528 
2529 /*@
2530   PCFieldSplitSchurRestoreS -  returns the `MATSCHURCOMPLEMENT` matrix used by this `PC`
2531 
2532   Not Collective
2533 
2534   Input Parameters:
2535 + pc - the preconditioner context
2536 - S  - the Schur complement matrix
2537 
2538   Level: advanced
2539 
2540 .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSchurPreType`, `PCFieldSplitSetSchurPre()`, `MatSchurComplement`, `PCFieldSplitSchurGetS()`
2541 @*/
2542 PetscErrorCode PCFieldSplitSchurRestoreS(PC pc, Mat *S)
2543 {
2544   const char    *t;
2545   PetscBool      isfs;
2546   PC_FieldSplit *jac;
2547 
2548   PetscFunctionBegin;
2549   PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
2550   PetscCall(PetscObjectGetType((PetscObject)pc, &t));
2551   PetscCall(PetscStrcmp(t, PCFIELDSPLIT, &isfs));
2552   PetscCheck(isfs, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Expected PC of type PCFIELDSPLIT, got %s instead", t);
2553   jac = (PC_FieldSplit *)pc->data;
2554   PetscCheck(jac->type == PC_COMPOSITE_SCHUR, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Expected PCFIELDSPLIT of type SCHUR, got %d instead", jac->type);
2555   PetscCheck(S && (*S == jac->schur), PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "MatSchurComplement restored is not the same as gotten");
2556   PetscFunctionReturn(PETSC_SUCCESS);
2557 }
2558 
2559 static PetscErrorCode PCFieldSplitSetSchurPre_FieldSplit(PC pc, PCFieldSplitSchurPreType ptype, Mat pre)
2560 {
2561   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
2562 
2563   PetscFunctionBegin;
2564   jac->schurpre = ptype;
2565   if (ptype == PC_FIELDSPLIT_SCHUR_PRE_USER && pre) {
2566     PetscCall(MatDestroy(&jac->schur_user));
2567     jac->schur_user = pre;
2568     PetscCall(PetscObjectReference((PetscObject)jac->schur_user));
2569   }
2570   PetscFunctionReturn(PETSC_SUCCESS);
2571 }
2572 
2573 static PetscErrorCode PCFieldSplitGetSchurPre_FieldSplit(PC pc, PCFieldSplitSchurPreType *ptype, Mat *pre)
2574 {
2575   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
2576 
2577   PetscFunctionBegin;
2578   if (ptype) *ptype = jac->schurpre;
2579   if (pre) *pre = jac->schur_user;
2580   PetscFunctionReturn(PETSC_SUCCESS);
2581 }
2582 
2583 /*@
2584   PCFieldSplitSetSchurFactType -  sets which blocks of the approximate block factorization to retain in the preconditioner {cite}`murphy2000note` and {cite}`ipsen2001note`
2585 
2586   Collective
2587 
2588   Input Parameters:
2589 + pc    - the preconditioner context
2590 - ftype - which blocks of factorization to retain, `PC_FIELDSPLIT_SCHUR_FACT_FULL` is default
2591 
2592   Options Database Key:
2593 . -pc_fieldsplit_schur_fact_type <diag,lower,upper,full> - default is `full`
2594 
2595   Level: intermediate
2596 
2597   Notes:
2598   The FULL factorization is
2599 .vb
2600   (A   B)  = (1       0) (A   0) (1  Ainv*B)  = L D U
2601   (C   E)    (C*Ainv  1) (0   S) (0       1)
2602 .vb
2603   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 $L*D$,
2604   and DIAG is the diagonal part with the sign of S flipped (because this makes the preconditioner positive definite for many formulations,
2605   thus allowing the use of `KSPMINRES)`. Sign flipping of S can be turned off with `PCFieldSplitSetSchurScale()`.
2606 
2607   If A and S are solved exactly
2608 .vb
2609   *) FULL factorization is a direct solver.
2610   *) 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.
2611   *) 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.
2612 .ve
2613 
2614   If the iteration count is very low, consider using `KSPFGMRES` or `KSPGCR` which can use one less preconditioner
2615   application in this case. Note that the preconditioned operator may be highly non-normal, so such fast convergence may not be observed in practice.
2616 
2617   For symmetric problems in which A is positive definite and S is negative definite, DIAG can be used with `KSPMINRES`.
2618 
2619   A flexible method like `KSPFGMRES` or `KSPGCR`, [](sec_flexibleksp), must be used if the fieldsplit preconditioner is nonlinear (e.g. a few iterations of a Krylov method is used to solve with A or S).
2620 
2621 .seealso: [](sec_block_matrices), `PC`, `PCFieldSplitGetSubKSP()`, `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSchurPreType`, `PCFieldSplitSetSchurScale()`,
2622           [](sec_flexibleksp)
2623 @*/
2624 PetscErrorCode PCFieldSplitSetSchurFactType(PC pc, PCFieldSplitSchurFactType ftype)
2625 {
2626   PetscFunctionBegin;
2627   PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
2628   PetscTryMethod(pc, "PCFieldSplitSetSchurFactType_C", (PC, PCFieldSplitSchurFactType), (pc, ftype));
2629   PetscFunctionReturn(PETSC_SUCCESS);
2630 }
2631 
2632 static PetscErrorCode PCFieldSplitSetSchurFactType_FieldSplit(PC pc, PCFieldSplitSchurFactType ftype)
2633 {
2634   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
2635 
2636   PetscFunctionBegin;
2637   jac->schurfactorization = ftype;
2638   PetscFunctionReturn(PETSC_SUCCESS);
2639 }
2640 
2641 /*@
2642   PCFieldSplitSetSchurScale -  Controls the sign flip of S for `PC_FIELDSPLIT_SCHUR_FACT_DIAG`.
2643 
2644   Collective
2645 
2646   Input Parameters:
2647 + pc    - the preconditioner context
2648 - scale - scaling factor for the Schur complement
2649 
2650   Options Database Key:
2651 . -pc_fieldsplit_schur_scale <scale> - default is -1.0
2652 
2653   Level: intermediate
2654 
2655 .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetFields()`, `PCFieldSplitSchurFactType`, `PCFieldSplitSetSchurFactType()`
2656 @*/
2657 PetscErrorCode PCFieldSplitSetSchurScale(PC pc, PetscScalar scale)
2658 {
2659   PetscFunctionBegin;
2660   PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
2661   PetscValidLogicalCollectiveScalar(pc, scale, 2);
2662   PetscTryMethod(pc, "PCFieldSplitSetSchurScale_C", (PC, PetscScalar), (pc, scale));
2663   PetscFunctionReturn(PETSC_SUCCESS);
2664 }
2665 
2666 static PetscErrorCode PCFieldSplitSetSchurScale_FieldSplit(PC pc, PetscScalar scale)
2667 {
2668   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
2669 
2670   PetscFunctionBegin;
2671   jac->schurscale = scale;
2672   PetscFunctionReturn(PETSC_SUCCESS);
2673 }
2674 
2675 /*@C
2676   PCFieldSplitGetSchurBlocks - Gets all matrix blocks for the Schur complement
2677 
2678   Collective
2679 
2680   Input Parameter:
2681 . pc - the preconditioner context
2682 
2683   Output Parameters:
2684 + A00 - the (0,0) block
2685 . A01 - the (0,1) block
2686 . A10 - the (1,0) block
2687 - A11 - the (1,1) block
2688 
2689   Level: advanced
2690 
2691 .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `MatSchurComplementGetSubMatrices()`, `MatSchurComplementSetSubMatrices()`
2692 @*/
2693 PetscErrorCode PCFieldSplitGetSchurBlocks(PC pc, Mat *A00, Mat *A01, Mat *A10, Mat *A11)
2694 {
2695   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
2696 
2697   PetscFunctionBegin;
2698   PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
2699   PetscCheck(jac->type == PC_COMPOSITE_SCHUR, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONG, "FieldSplit is not using a Schur complement approach.");
2700   if (A00) *A00 = jac->pmat[0];
2701   if (A01) *A01 = jac->B;
2702   if (A10) *A10 = jac->C;
2703   if (A11) *A11 = jac->pmat[1];
2704   PetscFunctionReturn(PETSC_SUCCESS);
2705 }
2706 
2707 /*@
2708   PCFieldSplitSetGKBTol -  Sets the solver tolerance for the generalized Golub-Kahan bidiagonalization preconditioner {cite}`arioli2013` in `PCFIELDSPLIT`
2709 
2710   Collective
2711 
2712   Input Parameters:
2713 + pc        - the preconditioner context
2714 - tolerance - the solver tolerance
2715 
2716   Options Database Key:
2717 . -pc_fieldsplit_gkb_tol <tolerance> - default is 1e-5
2718 
2719   Level: intermediate
2720 
2721   Note:
2722   The generalized GKB algorithm {cite}`arioli2013` uses a lower bound estimate of the error in energy norm as stopping criterion.
2723   It stops once the lower bound estimate undershoots the required solver tolerance. Although the actual error might be bigger than
2724   this estimate, the stopping criterion is satisfactory in practical cases.
2725 
2726 .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetGKBDelay()`, `PCFieldSplitSetGKBNu()`, `PCFieldSplitSetGKBMaxit()`
2727 @*/
2728 PetscErrorCode PCFieldSplitSetGKBTol(PC pc, PetscReal tolerance)
2729 {
2730   PetscFunctionBegin;
2731   PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
2732   PetscValidLogicalCollectiveReal(pc, tolerance, 2);
2733   PetscTryMethod(pc, "PCFieldSplitSetGKBTol_C", (PC, PetscReal), (pc, tolerance));
2734   PetscFunctionReturn(PETSC_SUCCESS);
2735 }
2736 
2737 static PetscErrorCode PCFieldSplitSetGKBTol_FieldSplit(PC pc, PetscReal tolerance)
2738 {
2739   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
2740 
2741   PetscFunctionBegin;
2742   jac->gkbtol = tolerance;
2743   PetscFunctionReturn(PETSC_SUCCESS);
2744 }
2745 
2746 /*@
2747   PCFieldSplitSetGKBMaxit -  Sets the maximum number of iterations for the generalized Golub-Kahan bidiagonalization preconditioner in `PCFIELDSPLIT`
2748 
2749   Collective
2750 
2751   Input Parameters:
2752 + pc    - the preconditioner context
2753 - maxit - the maximum number of iterations
2754 
2755   Options Database Key:
2756 . -pc_fieldsplit_gkb_maxit <maxit> - default is 100
2757 
2758   Level: intermediate
2759 
2760 .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetGKBDelay()`, `PCFieldSplitSetGKBTol()`, `PCFieldSplitSetGKBNu()`
2761 @*/
2762 PetscErrorCode PCFieldSplitSetGKBMaxit(PC pc, PetscInt maxit)
2763 {
2764   PetscFunctionBegin;
2765   PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
2766   PetscValidLogicalCollectiveInt(pc, maxit, 2);
2767   PetscTryMethod(pc, "PCFieldSplitSetGKBMaxit_C", (PC, PetscInt), (pc, maxit));
2768   PetscFunctionReturn(PETSC_SUCCESS);
2769 }
2770 
2771 static PetscErrorCode PCFieldSplitSetGKBMaxit_FieldSplit(PC pc, PetscInt maxit)
2772 {
2773   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
2774 
2775   PetscFunctionBegin;
2776   jac->gkbmaxit = maxit;
2777   PetscFunctionReturn(PETSC_SUCCESS);
2778 }
2779 
2780 /*@
2781   PCFieldSplitSetGKBDelay -  Sets the delay in the lower bound error estimate in the generalized Golub-Kahan bidiagonalization {cite}`arioli2013` in `PCFIELDSPLIT`
2782   preconditioner.
2783 
2784   Collective
2785 
2786   Input Parameters:
2787 + pc    - the preconditioner context
2788 - delay - the delay window in the lower bound estimate
2789 
2790   Options Database Key:
2791 . -pc_fieldsplit_gkb_delay <delay> - default is 5
2792 
2793   Level: intermediate
2794 
2795   Notes:
2796   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 $
2797   is expressed as a truncated sum. The error at iteration k can only be measured at iteration (k + `delay`), and thus the algorithm needs
2798   at least (`delay` + 1) iterations to stop.
2799 
2800   For more details on the generalized Golub-Kahan bidiagonalization method and its lower bound stopping criterion, please refer to {cite}`arioli2013`
2801 
2802 .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetGKBNu()`, `PCFieldSplitSetGKBTol()`, `PCFieldSplitSetGKBMaxit()`
2803 @*/
2804 PetscErrorCode PCFieldSplitSetGKBDelay(PC pc, PetscInt delay)
2805 {
2806   PetscFunctionBegin;
2807   PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
2808   PetscValidLogicalCollectiveInt(pc, delay, 2);
2809   PetscTryMethod(pc, "PCFieldSplitSetGKBDelay_C", (PC, PetscInt), (pc, delay));
2810   PetscFunctionReturn(PETSC_SUCCESS);
2811 }
2812 
2813 static PetscErrorCode PCFieldSplitSetGKBDelay_FieldSplit(PC pc, PetscInt delay)
2814 {
2815   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
2816 
2817   PetscFunctionBegin;
2818   jac->gkbdelay = delay;
2819   PetscFunctionReturn(PETSC_SUCCESS);
2820 }
2821 
2822 /*@
2823   PCFieldSplitSetGKBNu -  Sets the scalar value nu >= 0 in the transformation H = A00 + nu*A01*A01' of the (1,1) block in the
2824   Golub-Kahan bidiagonalization preconditioner {cite}`arioli2013` in `PCFIELDSPLIT`
2825 
2826   Collective
2827 
2828   Input Parameters:
2829 + pc - the preconditioner context
2830 - nu - the shift parameter
2831 
2832   Options Database Key:
2833 . -pc_fieldsplit_gkb_nu <nu> - default is 1
2834 
2835   Level: intermediate
2836 
2837   Notes:
2838   This shift is in general done to obtain better convergence properties for the outer loop of the algorithm. This is often achieved by choosing `nu` sufficiently large. However,
2839   if `nu` is chosen too large, the matrix H might be badly conditioned and the solution of the linear system $Hx = b$ in the inner loop becomes difficult. It is therefore
2840   necessary to find a good balance in between the convergence of the inner and outer loop.
2841 
2842   For `nu` = 0, no shift is done. In this case A00 has to be positive definite. The matrix N in {cite}`arioli2013` is then chosen as identity.
2843 
2844 .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetGKBDelay()`, `PCFieldSplitSetGKBTol()`, `PCFieldSplitSetGKBMaxit()`
2845 @*/
2846 PetscErrorCode PCFieldSplitSetGKBNu(PC pc, PetscReal nu)
2847 {
2848   PetscFunctionBegin;
2849   PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
2850   PetscValidLogicalCollectiveReal(pc, nu, 2);
2851   PetscTryMethod(pc, "PCFieldSplitSetGKBNu_C", (PC, PetscReal), (pc, nu));
2852   PetscFunctionReturn(PETSC_SUCCESS);
2853 }
2854 
2855 static PetscErrorCode PCFieldSplitSetGKBNu_FieldSplit(PC pc, PetscReal nu)
2856 {
2857   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
2858 
2859   PetscFunctionBegin;
2860   jac->gkbnu = nu;
2861   PetscFunctionReturn(PETSC_SUCCESS);
2862 }
2863 
2864 static PetscErrorCode PCFieldSplitSetType_FieldSplit(PC pc, PCCompositeType type)
2865 {
2866   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
2867 
2868   PetscFunctionBegin;
2869   jac->type = type;
2870   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSubKSP_C", NULL));
2871   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurPre_C", NULL));
2872   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSchurPre_C", NULL));
2873   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurFactType_C", NULL));
2874   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurScale_C", NULL));
2875   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBTol_C", NULL));
2876   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBMaxit_C", NULL));
2877   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBNu_C", NULL));
2878   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBDelay_C", NULL));
2879 
2880   if (type == PC_COMPOSITE_SCHUR) {
2881     pc->ops->apply          = PCApply_FieldSplit_Schur;
2882     pc->ops->applytranspose = PCApplyTranspose_FieldSplit_Schur;
2883     pc->ops->view           = PCView_FieldSplit_Schur;
2884 
2885     PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSubKSP_C", PCFieldSplitGetSubKSP_FieldSplit_Schur));
2886     PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurPre_C", PCFieldSplitSetSchurPre_FieldSplit));
2887     PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSchurPre_C", PCFieldSplitGetSchurPre_FieldSplit));
2888     PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurFactType_C", PCFieldSplitSetSchurFactType_FieldSplit));
2889     PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetSchurScale_C", PCFieldSplitSetSchurScale_FieldSplit));
2890   } else if (type == PC_COMPOSITE_GKB) {
2891     pc->ops->apply = PCApply_FieldSplit_GKB;
2892     pc->ops->view  = PCView_FieldSplit_GKB;
2893 
2894     PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSubKSP_C", PCFieldSplitGetSubKSP_FieldSplit));
2895     PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBTol_C", PCFieldSplitSetGKBTol_FieldSplit));
2896     PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBMaxit_C", PCFieldSplitSetGKBMaxit_FieldSplit));
2897     PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBNu_C", PCFieldSplitSetGKBNu_FieldSplit));
2898     PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitSetGKBDelay_C", PCFieldSplitSetGKBDelay_FieldSplit));
2899   } else {
2900     pc->ops->apply = PCApply_FieldSplit;
2901     pc->ops->view  = PCView_FieldSplit;
2902 
2903     PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCFieldSplitGetSubKSP_C", PCFieldSplitGetSubKSP_FieldSplit));
2904   }
2905   PetscFunctionReturn(PETSC_SUCCESS);
2906 }
2907 
2908 static PetscErrorCode PCFieldSplitSetBlockSize_FieldSplit(PC pc, PetscInt bs)
2909 {
2910   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
2911 
2912   PetscFunctionBegin;
2913   PetscCheck(bs >= 1, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_OUTOFRANGE, "Blocksize must be positive, you gave %" PetscInt_FMT, bs);
2914   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);
2915   jac->bs = bs;
2916   PetscFunctionReturn(PETSC_SUCCESS);
2917 }
2918 
2919 static PetscErrorCode PCSetCoordinates_FieldSplit(PC pc, PetscInt dim, PetscInt nloc, PetscReal coords[])
2920 {
2921   PC_FieldSplit    *jac           = (PC_FieldSplit *)pc->data;
2922   PC_FieldSplitLink ilink_current = jac->head;
2923   IS                is_owned;
2924 
2925   PetscFunctionBegin;
2926   jac->coordinates_set = PETSC_TRUE; // Internal flag
2927   PetscCall(MatGetOwnershipIS(pc->mat, &is_owned, NULL));
2928 
2929   while (ilink_current) {
2930     // For each IS, embed it to get local coords indces
2931     IS              is_coords;
2932     PetscInt        ndofs_block;
2933     const PetscInt *block_dofs_enumeration; // Numbering of the dofs relevant to the current block
2934 
2935     // Setting drop to true for safety. It should make no difference.
2936     PetscCall(ISEmbed(ilink_current->is, is_owned, PETSC_TRUE, &is_coords));
2937     PetscCall(ISGetLocalSize(is_coords, &ndofs_block));
2938     PetscCall(ISGetIndices(is_coords, &block_dofs_enumeration));
2939 
2940     // Allocate coordinates vector and set it directly
2941     PetscCall(PetscMalloc1(ndofs_block * dim, &(ilink_current->coords)));
2942     for (PetscInt dof = 0; dof < ndofs_block; ++dof) {
2943       for (PetscInt d = 0; d < dim; ++d) (ilink_current->coords)[dim * dof + d] = coords[dim * block_dofs_enumeration[dof] + d];
2944     }
2945     ilink_current->dim   = dim;
2946     ilink_current->ndofs = ndofs_block;
2947     PetscCall(ISRestoreIndices(is_coords, &block_dofs_enumeration));
2948     PetscCall(ISDestroy(&is_coords));
2949     ilink_current = ilink_current->next;
2950   }
2951   PetscCall(ISDestroy(&is_owned));
2952   PetscFunctionReturn(PETSC_SUCCESS);
2953 }
2954 
2955 /*@
2956   PCFieldSplitSetType - Sets the type, `PCCompositeType`, of a `PCFIELDSPLIT`
2957 
2958   Collective
2959 
2960   Input Parameters:
2961 + pc   - the preconditioner context
2962 - type - `PC_COMPOSITE_ADDITIVE`, `PC_COMPOSITE_MULTIPLICATIVE` (default), `PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE`, `PC_COMPOSITE_SPECIAL`, `PC_COMPOSITE_SCHUR`
2963 
2964   Options Database Key:
2965 . -pc_fieldsplit_type <one of multiplicative, additive, symmetric_multiplicative, special, schur> - Sets fieldsplit preconditioner type
2966 
2967   Level: intermediate
2968 
2969 .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCCompositeType`, `PCCompositeGetType()`, `PC_COMPOSITE_ADDITIVE`, `PC_COMPOSITE_MULTIPLICATIVE`,
2970           `PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE`, `PC_COMPOSITE_SPECIAL`, `PC_COMPOSITE_SCHUR`
2971 @*/
2972 PetscErrorCode PCFieldSplitSetType(PC pc, PCCompositeType type)
2973 {
2974   PetscFunctionBegin;
2975   PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
2976   PetscTryMethod(pc, "PCFieldSplitSetType_C", (PC, PCCompositeType), (pc, type));
2977   PetscFunctionReturn(PETSC_SUCCESS);
2978 }
2979 
2980 /*@
2981   PCFieldSplitGetType - Gets the type, `PCCompositeType`, of a `PCFIELDSPLIT`
2982 
2983   Not collective
2984 
2985   Input Parameter:
2986 . pc - the preconditioner context
2987 
2988   Output Parameter:
2989 . type - `PC_COMPOSITE_ADDITIVE`, `PC_COMPOSITE_MULTIPLICATIVE` (default), `PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE`, `PC_COMPOSITE_SPECIAL`, `PC_COMPOSITE_SCHUR`
2990 
2991   Level: intermediate
2992 
2993 .seealso: [](sec_block_matrices), `PC`, `PCCompositeSetType()`, `PCFIELDSPLIT`, `PCCompositeType`, `PC_COMPOSITE_ADDITIVE`, `PC_COMPOSITE_MULTIPLICATIVE`,
2994           `PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE`, `PC_COMPOSITE_SPECIAL`, `PC_COMPOSITE_SCHUR`
2995 @*/
2996 PetscErrorCode PCFieldSplitGetType(PC pc, PCCompositeType *type)
2997 {
2998   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
2999 
3000   PetscFunctionBegin;
3001   PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
3002   PetscAssertPointer(type, 2);
3003   *type = jac->type;
3004   PetscFunctionReturn(PETSC_SUCCESS);
3005 }
3006 
3007 /*@
3008   PCFieldSplitSetDMSplits - Flags whether `DMCreateFieldDecomposition()` should be used to define the splits in a `PCFIELDSPLIT`, whenever possible.
3009 
3010   Logically Collective
3011 
3012   Input Parameters:
3013 + pc  - the preconditioner context
3014 - flg - boolean indicating whether to use field splits defined by the `DM`
3015 
3016   Options Database Key:
3017 . -pc_fieldsplit_dm_splits <bool> - use the field splits defined by the `DM`
3018 
3019   Level: intermediate
3020 
3021 .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitGetDMSplits()`, `PCFieldSplitSetFields()`, `PCFieldsplitSetIS()`
3022 @*/
3023 PetscErrorCode PCFieldSplitSetDMSplits(PC pc, PetscBool flg)
3024 {
3025   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
3026   PetscBool      isfs;
3027 
3028   PetscFunctionBegin;
3029   PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
3030   PetscValidLogicalCollectiveBool(pc, flg, 2);
3031   PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCFIELDSPLIT, &isfs));
3032   if (isfs) jac->dm_splits = flg;
3033   PetscFunctionReturn(PETSC_SUCCESS);
3034 }
3035 
3036 /*@
3037   PCFieldSplitGetDMSplits - Returns flag indicating whether `DMCreateFieldDecomposition()` should be used to define the splits in a `PCFIELDSPLIT`, whenever possible.
3038 
3039   Logically Collective
3040 
3041   Input Parameter:
3042 . pc - the preconditioner context
3043 
3044   Output Parameter:
3045 . flg - boolean indicating whether to use field splits defined by the `DM`
3046 
3047   Level: intermediate
3048 
3049 .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetDMSplits()`, `PCFieldSplitSetFields()`, `PCFieldsplitSetIS()`
3050 @*/
3051 PetscErrorCode PCFieldSplitGetDMSplits(PC pc, PetscBool *flg)
3052 {
3053   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
3054   PetscBool      isfs;
3055 
3056   PetscFunctionBegin;
3057   PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
3058   PetscAssertPointer(flg, 2);
3059   PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCFIELDSPLIT, &isfs));
3060   if (isfs) {
3061     if (flg) *flg = jac->dm_splits;
3062   }
3063   PetscFunctionReturn(PETSC_SUCCESS);
3064 }
3065 
3066 /*@
3067   PCFieldSplitGetDetectSaddlePoint - Returns flag indicating whether `PCFIELDSPLIT` will attempt to automatically determine fields based on zero diagonal entries.
3068 
3069   Logically Collective
3070 
3071   Input Parameter:
3072 . pc - the preconditioner context
3073 
3074   Output Parameter:
3075 . flg - boolean indicating whether to detect fields or not
3076 
3077   Level: intermediate
3078 
3079 .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitSetDetectSaddlePoint()`
3080 @*/
3081 PetscErrorCode PCFieldSplitGetDetectSaddlePoint(PC pc, PetscBool *flg)
3082 {
3083   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
3084 
3085   PetscFunctionBegin;
3086   *flg = jac->detect;
3087   PetscFunctionReturn(PETSC_SUCCESS);
3088 }
3089 
3090 /*@
3091   PCFieldSplitSetDetectSaddlePoint - Sets flag indicating whether `PCFIELDSPLIT` will attempt to automatically determine fields based on zero diagonal entries.
3092 
3093   Logically Collective
3094 
3095   Input Parameter:
3096 . pc - the preconditioner context
3097 
3098   Output Parameter:
3099 . flg - boolean indicating whether to detect fields or not
3100 
3101   Options Database Key:
3102 . -pc_fieldsplit_detect_saddle_point <bool> - detect and use the saddle point
3103 
3104   Level: intermediate
3105 
3106   Note:
3107   Also sets the split type to `PC_COMPOSITE_SCHUR` (see `PCFieldSplitSetType()`) and the Schur preconditioner type to `PC_FIELDSPLIT_SCHUR_PRE_SELF` (see `PCFieldSplitSetSchurPre()`).
3108 
3109 .seealso: [](sec_block_matrices), `PC`, `PCFIELDSPLIT`, `PCFieldSplitGetDetectSaddlePoint()`, `PCFieldSplitSetType()`, `PCFieldSplitSetSchurPre()`, `PC_FIELDSPLIT_SCHUR_PRE_SELF`
3110 @*/
3111 PetscErrorCode PCFieldSplitSetDetectSaddlePoint(PC pc, PetscBool flg)
3112 {
3113   PC_FieldSplit *jac = (PC_FieldSplit *)pc->data;
3114 
3115   PetscFunctionBegin;
3116   jac->detect = flg;
3117   if (jac->detect) {
3118     PetscCall(PCFieldSplitSetType(pc, PC_COMPOSITE_SCHUR));
3119     PetscCall(PCFieldSplitSetSchurPre(pc, PC_FIELDSPLIT_SCHUR_PRE_SELF, NULL));
3120   }
3121   PetscFunctionReturn(PETSC_SUCCESS);
3122 }
3123 
3124 /*MC
3125    PCFIELDSPLIT - Preconditioner created by combining separate preconditioners for individual
3126    collections of variables (that may overlap) called splits. See [the users manual section on "Solving Block Matrices"](sec_block_matrices) for more details.
3127 
3128    Options Database Keys:
3129 +   -pc_fieldsplit_%d_fields <a,b,..>                                                - indicates the fields to be used in the `%d`'th split
3130 .   -pc_fieldsplit_default                                                           - automatically add any fields to additional splits that have not
3131                                                                                      been supplied explicitly by `-pc_fieldsplit_%d_fields`
3132 .   -pc_fieldsplit_block_size <bs>                                                   - size of block that defines fields (i.e. there are bs fields)
3133 .   -pc_fieldsplit_type <additive,multiplicative,symmetric_multiplicative,schur,gkb> - type of relaxation or factorization splitting
3134 .   -pc_fieldsplit_schur_precondition <self,selfp,user,a11,full>                     - default is `a11`; see `PCFieldSplitSetSchurPre()`
3135 .   -pc_fieldsplit_schur_fact_type <diag,lower,upper,full>                           - set factorization type when using `-pc_fieldsplit_type schur`;
3136                                                                                      see `PCFieldSplitSetSchurFactType()`
3137 -   -pc_fieldsplit_detect_saddle_point                                               - automatically finds rows with zero diagonal and uses Schur complement with no preconditioner as the solver
3138 
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.
3142 
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`
3145 
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
3148 
3149     Level: intermediate
3150 
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.
3154 
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()`.
3159 
3160       For the Schur complement preconditioner if
3161 
3162       ```{math}
3163       J = \left[\begin{array}{cc} A_{00} & A_{01} \\ A_{10} & A_{11} \end{array}\right]
3164       ```
3165 
3166       the preconditioner using `full` factorization is logically
3167       ```{math}
3168       \left[\begin{array}{cc} I & -\text{ksp}(A_{00}) A_{01} \\ 0 & I \end{array}\right] \left[\begin{array}{cc} \text{inv}(A_{00}) & 0 \\ 0 & \text{ksp}(S) \end{array}\right] \left[\begin{array}{cc} I & 0 \\ -A_{10} \text{ksp}(A_{00}) & I \end{array}\right]
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 $S$.
3178 
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.
3194 
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.
3197 
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.
3200 
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".
3205 
3206      See "A taxonomy and comparison of parallel block multi-level preconditioners for the incompressible Navier-Stokes equations" {cite}`elman2008tcp`.
3207 
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.
3210 
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_`.
3217 
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.
3221 
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*/
3227 
3228 PETSC_EXTERN PetscErrorCode PCCreate_FieldSplit(PC pc)
3229 {
3230   PC_FieldSplit *jac;
3231 
3232   PetscFunctionBegin;
3233   PetscCall(PetscNew(&jac));
3234 
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;
3249 
3250   pc->data = (void *)jac;
3251 
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;
3260 
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 }
3271