xref: /petsc/src/ksp/pc/impls/fieldsplit/fieldsplit.c (revision 665c2ded495bb9782a7454dcfef3abf1536c3670)
1 
2 #include <petsc-private/pcimpl.h>     /*I "petscpc.h" I*/
3 #include <petscdm.h>
4 
5 /*
6   There is a nice discussion of block preconditioners in
7 
8 [El08] A taxonomy and comparison of parallel block multi-level preconditioners for the incompressible Navier–Stokes equations
9        Howard Elman, V.E. Howle, John Shadid, Robert Shuttleworth, Ray Tuminaro, Journal of Computational Physics 227 (2008) 1790--1808
10        http://chess.cs.umd.edu/~elman/papers/tax.pdf
11 */
12 
13 const char *const PCFieldSplitSchurPreTypes[] = {"SELF","A11","USER","PCFieldSplitSchurPreType","PC_FIELDSPLIT_SCHUR_PRE_",0};
14 const char *const PCFieldSplitSchurFactTypes[] = {"DIAG","LOWER","UPPER","FULL","PCFieldSplitSchurFactType","PC_FIELDSPLIT_SCHUR_FACT_",0};
15 
16 typedef struct _PC_FieldSplitLink *PC_FieldSplitLink;
17 struct _PC_FieldSplitLink {
18   KSP               ksp;
19   Vec               x,y,z;
20   char              *splitname;
21   PetscInt          nfields;
22   PetscInt          *fields,*fields_col;
23   VecScatter        sctx;
24   IS                is,is_col;
25   PC_FieldSplitLink next,previous;
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   PetscBool       realdiagonal;                    /* Flag to use the diagonal blocks of mat preconditioned by pmat, instead of just pmat */
33   PetscInt        bs;                              /* Block size for IS and Mat structures */
34   PetscInt        nsplits;                         /* Number of field divisions defined */
35   Vec             *x,*y,w1,w2;
36   Mat             *mat;                            /* The diagonal block for each split */
37   Mat             *pmat;                           /* The preconditioning diagonal block for each split */
38   Mat             *Afield;                         /* The rows of the matrix associated with each split */
39   PetscBool       issetup;
40 
41   /* Only used when Schur complement preconditioning is used */
42   Mat                       B;                     /* The (0,1) block */
43   Mat                       C;                     /* The (1,0) block */
44   Mat                       schur;                 /* The Schur complement S = A11 - A10 A00^{-1} A01, the KSP here, kspinner, is H_1 in [El08] */
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   PC_FieldSplitLink         head;
51   PetscBool                 reset;                  /* indicates PCReset() has been last called on this object, hack */
52   PetscBool                 suboptionsset;          /* Indicates that the KSPSetFromOptions() has been called on the sub-KSPs */
53   PetscBool                 dm_splits;              /* Whether to use DMCreateFieldDecomposition() whenever possible */
54 } PC_FieldSplit;
55 
56 /*
57     Notes: there is no particular reason that pmat, x, and y are stored as arrays in PC_FieldSplit instead of
58    inside PC_FieldSplitLink, just historical. If you want to be able to add new fields after already using the
59    PC you could change this.
60 */
61 
62 /* This helper is so that setting a user-provided preconditioning matrix is orthogonal to choosing to use it.  This way the
63 * application-provided FormJacobian can provide this matrix without interfering with the user's (command-line) choices. */
64 static Mat FieldSplitSchurPre(PC_FieldSplit *jac)
65 {
66   switch (jac->schurpre) {
67   case PC_FIELDSPLIT_SCHUR_PRE_SELF: return jac->schur;
68   case PC_FIELDSPLIT_SCHUR_PRE_A11: return jac->pmat[1];
69   case PC_FIELDSPLIT_SCHUR_PRE_USER:   /* Use a user-provided matrix if it is given, otherwise diagonal block */
70   default:
71     return jac->schur_user ? jac->schur_user : jac->pmat[1];
72   }
73 }
74 
75 
76 #include <petscdraw.h>
77 #undef __FUNCT__
78 #define __FUNCT__ "PCView_FieldSplit"
79 static PetscErrorCode PCView_FieldSplit(PC pc,PetscViewer viewer)
80 {
81   PC_FieldSplit     *jac = (PC_FieldSplit*)pc->data;
82   PetscErrorCode    ierr;
83   PetscBool         iascii,isdraw;
84   PetscInt          i,j;
85   PC_FieldSplitLink ilink = jac->head;
86 
87   PetscFunctionBegin;
88   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);CHKERRQ(ierr);
89   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERDRAW,&isdraw);CHKERRQ(ierr);
90   if (iascii) {
91     if (jac->bs > 0) {
92       ierr = PetscViewerASCIIPrintf(viewer,"  FieldSplit with %s composition: total splits = %D, blocksize = %D\n",PCCompositeTypes[jac->type],jac->nsplits,jac->bs);CHKERRQ(ierr);
93     } else {
94       ierr = PetscViewerASCIIPrintf(viewer,"  FieldSplit with %s composition: total splits = %D\n",PCCompositeTypes[jac->type],jac->nsplits);CHKERRQ(ierr);
95     }
96     if (jac->realdiagonal) {
97       ierr = PetscViewerASCIIPrintf(viewer,"  using actual matrix for blocks rather than preconditioner matrix\n");CHKERRQ(ierr);
98     }
99     ierr = PetscViewerASCIIPrintf(viewer,"  Solver info for each split is in the following KSP objects:\n");CHKERRQ(ierr);
100     ierr = PetscViewerASCIIPushTab(viewer);CHKERRQ(ierr);
101     for (i=0; i<jac->nsplits; i++) {
102       if (ilink->fields) {
103         ierr = PetscViewerASCIIPrintf(viewer,"Split number %D Fields ",i);CHKERRQ(ierr);
104         ierr = PetscViewerASCIIUseTabs(viewer,PETSC_FALSE);CHKERRQ(ierr);
105         for (j=0; j<ilink->nfields; j++) {
106           if (j > 0) {
107             ierr = PetscViewerASCIIPrintf(viewer,",");CHKERRQ(ierr);
108           }
109           ierr = PetscViewerASCIIPrintf(viewer," %D",ilink->fields[j]);CHKERRQ(ierr);
110         }
111         ierr = PetscViewerASCIIPrintf(viewer,"\n");CHKERRQ(ierr);
112         ierr = PetscViewerASCIIUseTabs(viewer,PETSC_TRUE);CHKERRQ(ierr);
113       } else {
114         ierr = PetscViewerASCIIPrintf(viewer,"Split number %D Defined by IS\n",i);CHKERRQ(ierr);
115       }
116       ierr  = KSPView(ilink->ksp,viewer);CHKERRQ(ierr);
117       ilink = ilink->next;
118     }
119     ierr = PetscViewerASCIIPopTab(viewer);CHKERRQ(ierr);
120   }
121 
122  if (isdraw) {
123     PetscDraw draw;
124     PetscReal x,y,w,wd;
125 
126     ierr = PetscViewerDrawGetDraw(viewer,0,&draw);CHKERRQ(ierr);
127     ierr = PetscDrawGetCurrentPoint(draw,&x,&y);CHKERRQ(ierr);
128     w    = 2*PetscMin(1.0 - x,x);
129     wd   = w/(jac->nsplits + 1);
130     x    = x - wd*(jac->nsplits-1)/2.0;
131     for (i=0; i<jac->nsplits; i++) {
132       ierr  = PetscDrawPushCurrentPoint(draw,x,y);CHKERRQ(ierr);
133       ierr  = KSPView(ilink->ksp,viewer);CHKERRQ(ierr);
134       ierr  = PetscDrawPopCurrentPoint(draw);CHKERRQ(ierr);
135       x    += wd;
136       ilink = ilink->next;
137     }
138   }
139   PetscFunctionReturn(0);
140 }
141 
142 #undef __FUNCT__
143 #define __FUNCT__ "PCView_FieldSplit_Schur"
144 static PetscErrorCode PCView_FieldSplit_Schur(PC pc,PetscViewer viewer)
145 {
146   PC_FieldSplit     *jac = (PC_FieldSplit*)pc->data;
147   PetscErrorCode    ierr;
148   PetscBool         iascii,isdraw;
149   PetscInt          i,j;
150   PC_FieldSplitLink ilink = jac->head;
151 
152   PetscFunctionBegin;
153   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);CHKERRQ(ierr);
154   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERDRAW,&isdraw);CHKERRQ(ierr);
155   if (iascii) {
156     if (jac->bs > 0) {
157       ierr = PetscViewerASCIIPrintf(viewer,"  FieldSplit with Schur preconditioner, blocksize = %D, factorization %s\n",jac->bs,PCFieldSplitSchurFactTypes[jac->schurfactorization]);CHKERRQ(ierr);
158     } else {
159       ierr = PetscViewerASCIIPrintf(viewer,"  FieldSplit with Schur preconditioner, factorization %s\n",PCFieldSplitSchurFactTypes[jac->schurfactorization]);CHKERRQ(ierr);
160     }
161     if (jac->realdiagonal) {
162       ierr = PetscViewerASCIIPrintf(viewer,"  using actual matrix for blocks rather than preconditioner matrix\n");CHKERRQ(ierr);
163     }
164     switch (jac->schurpre) {
165     case PC_FIELDSPLIT_SCHUR_PRE_SELF:
166       ierr = PetscViewerASCIIPrintf(viewer,"  Preconditioner for the Schur complement formed from S itself\n");CHKERRQ(ierr);break;
167     case PC_FIELDSPLIT_SCHUR_PRE_A11:
168       ierr = PetscViewerASCIIPrintf(viewer,"  Preconditioner for the Schur complement formed from A11\n");CHKERRQ(ierr);break;
169     case PC_FIELDSPLIT_SCHUR_PRE_USER:
170       if (jac->schur_user) {
171         ierr = PetscViewerASCIIPrintf(viewer,"  Preconditioner for the Schur complement formed from user provided matrix\n");CHKERRQ(ierr);
172       } else {
173         ierr = PetscViewerASCIIPrintf(viewer,"  Preconditioner for the Schur complement formed from A11\n");CHKERRQ(ierr);
174       }
175       break;
176     default:
177       SETERRQ1(PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_OUTOFRANGE, "Invalid Schur preconditioning type: %d", jac->schurpre);
178     }
179     ierr = PetscViewerASCIIPrintf(viewer,"  Split info:\n");CHKERRQ(ierr);
180     ierr = PetscViewerASCIIPushTab(viewer);CHKERRQ(ierr);
181     for (i=0; i<jac->nsplits; i++) {
182       if (ilink->fields) {
183         ierr = PetscViewerASCIIPrintf(viewer,"Split number %D Fields ",i);CHKERRQ(ierr);
184         ierr = PetscViewerASCIIUseTabs(viewer,PETSC_FALSE);CHKERRQ(ierr);
185         for (j=0; j<ilink->nfields; j++) {
186           if (j > 0) {
187             ierr = PetscViewerASCIIPrintf(viewer,",");CHKERRQ(ierr);
188           }
189           ierr = PetscViewerASCIIPrintf(viewer," %D",ilink->fields[j]);CHKERRQ(ierr);
190         }
191         ierr = PetscViewerASCIIPrintf(viewer,"\n");CHKERRQ(ierr);
192         ierr = PetscViewerASCIIUseTabs(viewer,PETSC_TRUE);CHKERRQ(ierr);
193       } else {
194         ierr = PetscViewerASCIIPrintf(viewer,"Split number %D Defined by IS\n",i);CHKERRQ(ierr);
195       }
196       ilink = ilink->next;
197     }
198     ierr = PetscViewerASCIIPrintf(viewer,"KSP solver for A00 block \n");CHKERRQ(ierr);
199     ierr = PetscViewerASCIIPushTab(viewer);CHKERRQ(ierr);
200     ierr = KSPView(jac->head->ksp,viewer);CHKERRQ(ierr);
201     ierr = PetscViewerASCIIPopTab(viewer);CHKERRQ(ierr);
202     if (jac->kspupper != jac->head->ksp) {
203       ierr = PetscViewerASCIIPrintf(viewer,"KSP solver for upper A00 in upper triangular factor \n");CHKERRQ(ierr);
204       ierr = PetscViewerASCIIPushTab(viewer);CHKERRQ(ierr);
205       ierr = KSPView(jac->kspupper,viewer);CHKERRQ(ierr);
206       ierr = PetscViewerASCIIPopTab(viewer);CHKERRQ(ierr);
207     }
208     ierr = PetscViewerASCIIPrintf(viewer,"KSP solver for S = A11 - A10 inv(A00) A01 \n");CHKERRQ(ierr);
209     ierr = PetscViewerASCIIPushTab(viewer);CHKERRQ(ierr);
210     if (jac->kspschur) {
211       ierr = KSPView(jac->kspschur,viewer);CHKERRQ(ierr);
212     } else {
213       ierr = PetscViewerASCIIPrintf(viewer,"  not yet available\n");CHKERRQ(ierr);
214     }
215     ierr = PetscViewerASCIIPopTab(viewer);CHKERRQ(ierr);
216     ierr = PetscViewerASCIIPopTab(viewer);CHKERRQ(ierr);
217   } else if (isdraw) {
218     PetscDraw draw;
219     PetscReal x,y,w,wd,h;
220     PetscInt  cnt = 2;
221     char      str[32];
222 
223     ierr = PetscViewerDrawGetDraw(viewer,0,&draw);CHKERRQ(ierr);
224     ierr = PetscDrawGetCurrentPoint(draw,&x,&y);CHKERRQ(ierr);
225     if (jac->kspupper != jac->head->ksp) cnt++;
226     w  = 2*PetscMin(1.0 - x,x);
227     wd = w/(cnt + 1);
228 
229     ierr = PetscSNPrintf(str,32,"Schur fact. %s",PCFieldSplitSchurFactTypes[jac->schurfactorization]);CHKERRQ(ierr);
230     ierr = PetscDrawBoxedString(draw,x,y,PETSC_DRAW_RED,PETSC_DRAW_BLACK,str,NULL,&h);CHKERRQ(ierr);
231     y   -= h;
232     if (jac->schurpre == PC_FIELDSPLIT_SCHUR_PRE_USER &&  !jac->schur_user) {
233       ierr = PetscSNPrintf(str,32,"Prec. for Schur from %s",PCFieldSplitSchurPreTypes[PC_FIELDSPLIT_SCHUR_PRE_A11]);CHKERRQ(ierr);
234     } else {
235       ierr = PetscSNPrintf(str,32,"Prec. for Schur from %s",PCFieldSplitSchurPreTypes[jac->schurpre]);CHKERRQ(ierr);
236     }
237     ierr = PetscDrawBoxedString(draw,x+wd*(cnt-1)/2.0,y,PETSC_DRAW_RED,PETSC_DRAW_BLACK,str,NULL,&h);CHKERRQ(ierr);
238     y   -= h;
239     x    = x - wd*(cnt-1)/2.0;
240 
241     ierr = PetscDrawPushCurrentPoint(draw,x,y);CHKERRQ(ierr);
242     ierr = KSPView(jac->head->ksp,viewer);CHKERRQ(ierr);
243     ierr = PetscDrawPopCurrentPoint(draw);CHKERRQ(ierr);
244     if (jac->kspupper != jac->head->ksp) {
245       x   += wd;
246       ierr = PetscDrawPushCurrentPoint(draw,x,y);CHKERRQ(ierr);
247       ierr = KSPView(jac->kspupper,viewer);CHKERRQ(ierr);
248       ierr = PetscDrawPopCurrentPoint(draw);CHKERRQ(ierr);
249     }
250     x   += wd;
251     ierr = PetscDrawPushCurrentPoint(draw,x,y);CHKERRQ(ierr);
252     ierr = KSPView(jac->kspschur,viewer);CHKERRQ(ierr);
253     ierr = PetscDrawPopCurrentPoint(draw);CHKERRQ(ierr);
254   }
255   PetscFunctionReturn(0);
256 }
257 
258 #undef __FUNCT__
259 #define __FUNCT__ "PCFieldSplitSetRuntimeSplits_Private"
260 /* Precondition: jac->bs is set to a meaningful value */
261 static PetscErrorCode PCFieldSplitSetRuntimeSplits_Private(PC pc)
262 {
263   PetscErrorCode ierr;
264   PC_FieldSplit  *jac = (PC_FieldSplit*)pc->data;
265   PetscInt       i,nfields,*ifields,nfields_col,*ifields_col;
266   PetscBool      flg,flg_col;
267   char           optionname[128],splitname[8],optionname_col[128];
268 
269   PetscFunctionBegin;
270   ierr = PetscMalloc(jac->bs*sizeof(PetscInt),&ifields);CHKERRQ(ierr);
271   ierr = PetscMalloc(jac->bs*sizeof(PetscInt),&ifields_col);CHKERRQ(ierr);
272   for (i=0,flg=PETSC_TRUE;; i++) {
273     ierr        = PetscSNPrintf(splitname,sizeof(splitname),"%D",i);CHKERRQ(ierr);
274     ierr        = PetscSNPrintf(optionname,sizeof(optionname),"-pc_fieldsplit_%D_fields",i);CHKERRQ(ierr);
275     ierr        = PetscSNPrintf(optionname_col,sizeof(optionname_col),"-pc_fieldsplit_%D_fields_col",i);CHKERRQ(ierr);
276     nfields     = jac->bs;
277     nfields_col = jac->bs;
278     ierr        = PetscOptionsGetIntArray(((PetscObject)pc)->prefix,optionname,ifields,&nfields,&flg);CHKERRQ(ierr);
279     ierr        = PetscOptionsGetIntArray(((PetscObject)pc)->prefix,optionname_col,ifields_col,&nfields_col,&flg_col);CHKERRQ(ierr);
280     if (!flg) break;
281     else if (flg && !flg_col) {
282       if (!nfields) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_USER,"Cannot list zero fields");
283       ierr = PCFieldSplitSetFields(pc,splitname,nfields,ifields,ifields);CHKERRQ(ierr);
284     } else {
285       if (!nfields || !nfields_col) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_USER,"Cannot list zero fields");
286       if (nfields != nfields_col) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_USER,"Number of row and column fields must match");
287       ierr = PCFieldSplitSetFields(pc,splitname,nfields,ifields,ifields_col);CHKERRQ(ierr);
288     }
289   }
290   if (i > 0) {
291     /* Makes command-line setting of splits take precedence over setting them in code.
292        Otherwise subsequent calls to PCFieldSplitSetIS() or PCFieldSplitSetFields() would
293        create new splits, which would probably not be what the user wanted. */
294     jac->splitdefined = PETSC_TRUE;
295   }
296   ierr = PetscFree(ifields);CHKERRQ(ierr);
297   ierr = PetscFree(ifields_col);CHKERRQ(ierr);
298   PetscFunctionReturn(0);
299 }
300 
301 #undef __FUNCT__
302 #define __FUNCT__ "PCFieldSplitSetDefaults"
303 static PetscErrorCode PCFieldSplitSetDefaults(PC pc)
304 {
305   PC_FieldSplit     *jac = (PC_FieldSplit*)pc->data;
306   PetscErrorCode    ierr;
307   PC_FieldSplitLink ilink              = jac->head;
308   PetscBool         fieldsplit_default = PETSC_FALSE,stokes = PETSC_FALSE;
309   PetscInt          i;
310 
311   PetscFunctionBegin;
312   /*
313    Kinda messy, but at least this now uses DMCreateFieldDecomposition() even with jac->reset.
314    Should probably be rewritten.
315    */
316   if (!ilink || jac->reset) {
317     ierr = PetscOptionsGetBool(((PetscObject)pc)->prefix,"-pc_fieldsplit_detect_saddle_point",&stokes,NULL);CHKERRQ(ierr);
318     if (pc->dm && jac->dm_splits && !stokes) {
319       PetscInt  numFields, f, i, j;
320       char      **fieldNames;
321       IS        *fields;
322       DM        *dms;
323       DM        subdm[128];
324       PetscBool flg;
325 
326       ierr = DMCreateFieldDecomposition(pc->dm, &numFields, &fieldNames, &fields, &dms);CHKERRQ(ierr);
327       /* Allow the user to prescribe the splits */
328       for (i = 0, flg = PETSC_TRUE;; i++) {
329         PetscInt ifields[128];
330         IS       compField;
331         char     optionname[128], splitname[8];
332         PetscInt nfields = numFields;
333 
334         ierr = PetscSNPrintf(optionname, sizeof(optionname), "-pc_fieldsplit_%D_fields", i);CHKERRQ(ierr);
335         ierr = PetscOptionsGetIntArray(((PetscObject) pc)->prefix, optionname, ifields, &nfields, &flg);CHKERRQ(ierr);
336         if (!flg) break;
337         if (numFields > 128) SETERRQ1(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"Cannot currently support %d > 128 fields", numFields);
338         ierr = DMCreateSubDM(pc->dm, nfields, ifields, &compField, &subdm[i]);CHKERRQ(ierr);
339         if (nfields == 1) {
340           ierr = PCFieldSplitSetIS(pc, fieldNames[ifields[0]], compField);CHKERRQ(ierr);
341           /* ierr = PetscPrintf(PetscObjectComm((PetscObject)pc), "%s Field Indices:", fieldNames[ifields[0]]);CHKERRQ(ierr);
342              ierr = ISView(compField, NULL);CHKERRQ(ierr); */
343         } else {
344           ierr = PetscSNPrintf(splitname, sizeof(splitname), "%D", i);CHKERRQ(ierr);
345           ierr = PCFieldSplitSetIS(pc, splitname, compField);CHKERRQ(ierr);
346           /* ierr = PetscPrintf(PetscObjectComm((PetscObject)pc), "%s Field Indices:", splitname);CHKERRQ(ierr);
347              ierr = ISView(compField, NULL);CHKERRQ(ierr); */
348         }
349         ierr = ISDestroy(&compField);CHKERRQ(ierr);
350         for (j = 0; j < nfields; ++j) {
351           f    = ifields[j];
352           ierr = PetscFree(fieldNames[f]);CHKERRQ(ierr);
353           ierr = ISDestroy(&fields[f]);CHKERRQ(ierr);
354         }
355       }
356       if (i == 0) {
357         for (f = 0; f < numFields; ++f) {
358           ierr = PCFieldSplitSetIS(pc, fieldNames[f], fields[f]);CHKERRQ(ierr);
359           ierr = PetscFree(fieldNames[f]);CHKERRQ(ierr);
360           ierr = ISDestroy(&fields[f]);CHKERRQ(ierr);
361         }
362       } else {
363         for (j=0; j<numFields; j++) {
364           ierr = DMDestroy(dms+j);CHKERRQ(ierr);
365         }
366         ierr = PetscFree(dms);CHKERRQ(ierr);
367         ierr = PetscMalloc(i * sizeof(DM), &dms);CHKERRQ(ierr);
368         for (j = 0; j < i; ++j) dms[j] = subdm[j];
369       }
370       ierr = PetscFree(fieldNames);CHKERRQ(ierr);
371       ierr = PetscFree(fields);CHKERRQ(ierr);
372       if (dms) {
373         ierr = PetscInfo(pc, "Setting up physics based fieldsplit preconditioner using the embedded DM\n");CHKERRQ(ierr);
374         for (ilink = jac->head, i = 0; ilink; ilink = ilink->next, ++i) {
375           const char *prefix;
376           ierr = PetscObjectGetOptionsPrefix((PetscObject)(ilink->ksp),&prefix);CHKERRQ(ierr);
377           ierr = PetscObjectSetOptionsPrefix((PetscObject)(dms[i]), prefix);CHKERRQ(ierr);
378           ierr = KSPSetDM(ilink->ksp, dms[i]);CHKERRQ(ierr);
379           ierr = KSPSetDMActive(ilink->ksp, PETSC_FALSE);CHKERRQ(ierr);
380           ierr = PetscObjectIncrementTabLevel((PetscObject)dms[i],(PetscObject)ilink->ksp,0);CHKERRQ(ierr);
381           ierr = DMDestroy(&dms[i]);CHKERRQ(ierr);
382         }
383         ierr = PetscFree(dms);CHKERRQ(ierr);
384       }
385     } else {
386       if (jac->bs <= 0) {
387         if (pc->pmat) {
388           ierr = MatGetBlockSize(pc->pmat,&jac->bs);CHKERRQ(ierr);
389         } else jac->bs = 1;
390       }
391 
392       if (stokes) {
393         IS       zerodiags,rest;
394         PetscInt nmin,nmax;
395 
396         ierr = MatGetOwnershipRange(pc->mat,&nmin,&nmax);CHKERRQ(ierr);
397         ierr = MatFindZeroDiagonals(pc->mat,&zerodiags);CHKERRQ(ierr);
398         ierr = ISComplement(zerodiags,nmin,nmax,&rest);CHKERRQ(ierr);
399         if (jac->reset) {
400           jac->head->is       = rest;
401           jac->head->next->is = zerodiags;
402         } else {
403           ierr = PCFieldSplitSetIS(pc,"0",rest);CHKERRQ(ierr);
404           ierr = PCFieldSplitSetIS(pc,"1",zerodiags);CHKERRQ(ierr);
405         }
406         ierr = ISDestroy(&zerodiags);CHKERRQ(ierr);
407         ierr = ISDestroy(&rest);CHKERRQ(ierr);
408       } else {
409         if (jac->reset) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"Cases not yet handled when PCReset() was used");
410         ierr = PetscOptionsGetBool(((PetscObject)pc)->prefix,"-pc_fieldsplit_default",&fieldsplit_default,NULL);CHKERRQ(ierr);
411         if (!fieldsplit_default) {
412           /* Allow user to set fields from command line,  if bs was known at the time of PCSetFromOptions_FieldSplit()
413            then it is set there. This is not ideal because we should only have options set in XXSetFromOptions(). */
414           ierr = PCFieldSplitSetRuntimeSplits_Private(pc);CHKERRQ(ierr);
415           if (jac->splitdefined) {ierr = PetscInfo(pc,"Splits defined using the options database\n");CHKERRQ(ierr);}
416         }
417         if (fieldsplit_default || !jac->splitdefined) {
418           ierr = PetscInfo(pc,"Using default splitting of fields\n");CHKERRQ(ierr);
419           for (i=0; i<jac->bs; i++) {
420             char splitname[8];
421             ierr = PetscSNPrintf(splitname,sizeof(splitname),"%D",i);CHKERRQ(ierr);
422             ierr = PCFieldSplitSetFields(pc,splitname,1,&i,&i);CHKERRQ(ierr);
423           }
424           jac->defaultsplit = PETSC_TRUE;
425         }
426       }
427     }
428   } else if (jac->nsplits == 1) {
429     if (ilink->is) {
430       IS       is2;
431       PetscInt nmin,nmax;
432 
433       ierr = MatGetOwnershipRange(pc->mat,&nmin,&nmax);CHKERRQ(ierr);
434       ierr = ISComplement(ilink->is,nmin,nmax,&is2);CHKERRQ(ierr);
435       ierr = PCFieldSplitSetIS(pc,"1",is2);CHKERRQ(ierr);
436       ierr = ISDestroy(&is2);CHKERRQ(ierr);
437     } else SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"Must provide at least two sets of fields to PCFieldSplit()");
438   }
439 
440 
441   if (jac->nsplits < 2) SETERRQ1(PetscObjectComm((PetscObject)pc),PETSC_ERR_PLIB,"Unhandled case, must have at least two fields, not %d", jac->nsplits);
442   PetscFunctionReturn(0);
443 }
444 
445 PetscErrorCode PetscOptionsFindPairPrefix_Private(const char pre[], const char name[], char *value[], PetscBool *flg);
446 
447 #undef __FUNCT__
448 #define __FUNCT__ "PCSetUp_FieldSplit"
449 static PetscErrorCode PCSetUp_FieldSplit(PC pc)
450 {
451   PC_FieldSplit     *jac = (PC_FieldSplit*)pc->data;
452   PetscErrorCode    ierr;
453   PC_FieldSplitLink ilink;
454   PetscInt          i,nsplit;
455   MatStructure      flag = pc->flag;
456   PetscBool         sorted, sorted_col;
457 
458   PetscFunctionBegin;
459   ierr   = PCFieldSplitSetDefaults(pc);CHKERRQ(ierr);
460   nsplit = jac->nsplits;
461   ilink  = jac->head;
462 
463   /* get the matrices for each split */
464   if (!jac->issetup) {
465     PetscInt rstart,rend,nslots,bs;
466 
467     jac->issetup = PETSC_TRUE;
468 
469     /* This is done here instead of in PCFieldSplitSetFields() because may not have matrix at that point */
470     if (jac->defaultsplit || !ilink->is) {
471       if (jac->bs <= 0) jac->bs = nsplit;
472     }
473     bs     = jac->bs;
474     ierr   = MatGetOwnershipRange(pc->pmat,&rstart,&rend);CHKERRQ(ierr);
475     nslots = (rend - rstart)/bs;
476     for (i=0; i<nsplit; i++) {
477       if (jac->defaultsplit) {
478         ierr = ISCreateStride(PetscObjectComm((PetscObject)pc),nslots,rstart+i,nsplit,&ilink->is);CHKERRQ(ierr);
479         ierr = ISDuplicate(ilink->is,&ilink->is_col);CHKERRQ(ierr);
480       } else if (!ilink->is) {
481         if (ilink->nfields > 1) {
482           PetscInt *ii,*jj,j,k,nfields = ilink->nfields,*fields = ilink->fields,*fields_col = ilink->fields_col;
483           ierr = PetscMalloc(ilink->nfields*nslots*sizeof(PetscInt),&ii);CHKERRQ(ierr);
484           ierr = PetscMalloc(ilink->nfields*nslots*sizeof(PetscInt),&jj);CHKERRQ(ierr);
485           for (j=0; j<nslots; j++) {
486             for (k=0; k<nfields; k++) {
487               ii[nfields*j + k] = rstart + bs*j + fields[k];
488               jj[nfields*j + k] = rstart + bs*j + fields_col[k];
489             }
490           }
491           ierr = ISCreateGeneral(PetscObjectComm((PetscObject)pc),nslots*nfields,ii,PETSC_OWN_POINTER,&ilink->is);CHKERRQ(ierr);
492           ierr = ISCreateGeneral(PetscObjectComm((PetscObject)pc),nslots*nfields,jj,PETSC_OWN_POINTER,&ilink->is_col);CHKERRQ(ierr);
493         } else {
494           ierr = ISCreateStride(PetscObjectComm((PetscObject)pc),nslots,rstart+ilink->fields[0],bs,&ilink->is);CHKERRQ(ierr);
495           ierr = ISCreateStride(PetscObjectComm((PetscObject)pc),nslots,rstart+ilink->fields_col[0],bs,&ilink->is_col);CHKERRQ(ierr);
496        }
497       }
498       ierr = ISSorted(ilink->is,&sorted);CHKERRQ(ierr);
499       if (ilink->is_col) { ierr = ISSorted(ilink->is_col,&sorted_col);CHKERRQ(ierr); }
500       if (!sorted || !sorted_col) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_USER,"Fields must be sorted when creating split");
501       ilink = ilink->next;
502     }
503   }
504 
505   ilink = jac->head;
506   if (!jac->pmat) {
507     Vec xtmp;
508 
509     ierr = MatGetVecs(pc->pmat,&xtmp,NULL);CHKERRQ(ierr);
510     ierr = PetscMalloc(nsplit*sizeof(Mat),&jac->pmat);CHKERRQ(ierr);
511     ierr = PetscMalloc2(nsplit,Vec,&jac->x,nsplit,Vec,&jac->y);CHKERRQ(ierr);
512     for (i=0; i<nsplit; i++) {
513       MatNullSpace sp;
514 
515       /* Check for preconditioning matrix attached to IS */
516       ierr = PetscObjectQuery((PetscObject) ilink->is, "pmat", (PetscObject*) &jac->pmat[i]);CHKERRQ(ierr);
517       if (jac->pmat[i]) {
518         ierr = PetscObjectReference((PetscObject) jac->pmat[i]);CHKERRQ(ierr);
519         if (jac->type == PC_COMPOSITE_SCHUR) {
520           jac->schur_user = jac->pmat[i];
521 
522           ierr = PetscObjectReference((PetscObject) jac->schur_user);CHKERRQ(ierr);
523         }
524       } else {
525         ierr = MatGetSubMatrix(pc->pmat,ilink->is,ilink->is_col,MAT_INITIAL_MATRIX,&jac->pmat[i]);CHKERRQ(ierr);
526       }
527       /* create work vectors for each split */
528       ierr     = MatGetVecs(jac->pmat[i],&jac->x[i],&jac->y[i]);CHKERRQ(ierr);
529       ilink->x = jac->x[i]; ilink->y = jac->y[i]; ilink->z = NULL;
530       /* compute scatter contexts needed by multiplicative versions and non-default splits */
531       ierr = VecScatterCreate(xtmp,ilink->is,jac->x[i],NULL,&ilink->sctx);CHKERRQ(ierr);
532       /* Check for null space attached to IS */
533       ierr = PetscObjectQuery((PetscObject) ilink->is, "nullspace", (PetscObject*) &sp);CHKERRQ(ierr);
534       if (sp) {
535         ierr = MatSetNullSpace(jac->pmat[i], sp);CHKERRQ(ierr);
536       }
537       ierr = PetscObjectQuery((PetscObject) ilink->is, "nearnullspace", (PetscObject*) &sp);CHKERRQ(ierr);
538       if (sp) {
539         ierr = MatSetNearNullSpace(jac->pmat[i], sp);CHKERRQ(ierr);
540       }
541       ilink = ilink->next;
542     }
543     ierr = VecDestroy(&xtmp);CHKERRQ(ierr);
544   } else {
545     for (i=0; i<nsplit; i++) {
546       Mat pmat;
547 
548       /* Check for preconditioning matrix attached to IS */
549       ierr = PetscObjectQuery((PetscObject) ilink->is, "pmat", (PetscObject*) &pmat);CHKERRQ(ierr);
550       if (!pmat) {
551         ierr = MatGetSubMatrix(pc->pmat,ilink->is,ilink->is_col,MAT_REUSE_MATRIX,&jac->pmat[i]);CHKERRQ(ierr);
552       }
553       ilink = ilink->next;
554     }
555   }
556   if (jac->realdiagonal) {
557     ilink = jac->head;
558     if (!jac->mat) {
559       ierr = PetscMalloc(nsplit*sizeof(Mat),&jac->mat);CHKERRQ(ierr);
560       for (i=0; i<nsplit; i++) {
561         ierr  = MatGetSubMatrix(pc->mat,ilink->is,ilink->is_col,MAT_INITIAL_MATRIX,&jac->mat[i]);CHKERRQ(ierr);
562         ilink = ilink->next;
563       }
564     } else {
565       for (i=0; i<nsplit; i++) {
566         if (jac->mat[i]) {ierr = MatGetSubMatrix(pc->mat,ilink->is,ilink->is_col,MAT_REUSE_MATRIX,&jac->mat[i]);CHKERRQ(ierr);}
567         ilink = ilink->next;
568       }
569     }
570   } else {
571     jac->mat = jac->pmat;
572   }
573 
574   if (jac->type != PC_COMPOSITE_ADDITIVE  && jac->type != PC_COMPOSITE_SCHUR) {
575     /* extract the rows of the matrix associated with each field: used for efficient computation of residual inside algorithm */
576     ilink = jac->head;
577     if (!jac->Afield) {
578       ierr = PetscMalloc(nsplit*sizeof(Mat),&jac->Afield);CHKERRQ(ierr);
579       for (i=0; i<nsplit; i++) {
580         ierr  = MatGetSubMatrix(pc->mat,ilink->is,NULL,MAT_INITIAL_MATRIX,&jac->Afield[i]);CHKERRQ(ierr);
581         ilink = ilink->next;
582       }
583     } else {
584       for (i=0; i<nsplit; i++) {
585         ierr  = MatGetSubMatrix(pc->mat,ilink->is,NULL,MAT_REUSE_MATRIX,&jac->Afield[i]);CHKERRQ(ierr);
586         ilink = ilink->next;
587       }
588     }
589   }
590 
591   if (jac->type == PC_COMPOSITE_SCHUR) {
592     IS          ccis;
593     PetscInt    rstart,rend;
594     char        lscname[256];
595     PetscObject LSC_L;
596 
597     if (nsplit != 2) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_ARG_INCOMP,"To use Schur complement preconditioner you must have exactly 2 fields");
598 
599     /* When extracting off-diagonal submatrices, we take complements from this range */
600     ierr = MatGetOwnershipRangeColumn(pc->mat,&rstart,&rend);CHKERRQ(ierr);
601 
602     /* need to handle case when one is resetting up the preconditioner */
603     if (jac->schur) {
604       KSP kspA = jac->head->ksp, kspInner = NULL, kspUpper = jac->kspupper;
605 
606       ierr  = MatSchurComplementGetKSP(jac->schur, &kspInner);CHKERRQ(ierr);
607       ilink = jac->head;
608       ierr  = ISComplement(ilink->is_col,rstart,rend,&ccis);CHKERRQ(ierr);
609       ierr  = MatGetSubMatrix(pc->mat,ilink->is,ccis,MAT_REUSE_MATRIX,&jac->B);CHKERRQ(ierr);
610       ierr  = ISDestroy(&ccis);CHKERRQ(ierr);
611       ilink = ilink->next;
612       ierr  = ISComplement(ilink->is_col,rstart,rend,&ccis);CHKERRQ(ierr);
613       ierr  = MatGetSubMatrix(pc->mat,ilink->is,ccis,MAT_REUSE_MATRIX,&jac->C);CHKERRQ(ierr);
614       ierr  = ISDestroy(&ccis);CHKERRQ(ierr);
615       ierr  = MatSchurComplementUpdate(jac->schur,jac->mat[0],jac->pmat[0],jac->B,jac->C,jac->mat[1],pc->flag);CHKERRQ(ierr);
616       if (kspA != kspInner) {
617         ierr = KSPSetOperators(kspA,jac->mat[0],jac->pmat[0],pc->flag);CHKERRQ(ierr);
618       }
619       if (kspUpper != kspA) {
620         ierr = KSPSetOperators(kspUpper,jac->mat[0],jac->pmat[0],pc->flag);CHKERRQ(ierr);
621       }
622       ierr = KSPSetOperators(jac->kspschur,jac->schur,FieldSplitSchurPre(jac),pc->flag);CHKERRQ(ierr);
623     } else {
624       KSP          ksp;
625       const char   *Dprefix;
626       char         schurprefix[256];
627       char         schurtestoption[256];
628       MatNullSpace sp;
629       PetscBool    flg;
630 
631       /* extract the A01 and A10 matrices */
632       ilink = jac->head;
633       ierr  = ISComplement(ilink->is_col,rstart,rend,&ccis);CHKERRQ(ierr);
634       ierr  = MatGetSubMatrix(pc->mat,ilink->is,ccis,MAT_INITIAL_MATRIX,&jac->B);CHKERRQ(ierr);
635       ierr  = ISDestroy(&ccis);CHKERRQ(ierr);
636       ilink = ilink->next;
637       ierr  = ISComplement(ilink->is_col,rstart,rend,&ccis);CHKERRQ(ierr);
638       ierr  = MatGetSubMatrix(pc->mat,ilink->is,ccis,MAT_INITIAL_MATRIX,&jac->C);CHKERRQ(ierr);
639       ierr  = ISDestroy(&ccis);CHKERRQ(ierr);
640 
641       /* Use mat[0] (diagonal block of the real matrix) preconditioned by pmat[0] to define Schur complement */
642       ierr = MatCreate(((PetscObject)jac->mat[0])->comm,&jac->schur);CHKERRQ(ierr);
643       ierr = MatSetType(jac->schur,MATSCHURCOMPLEMENT);CHKERRQ(ierr);
644       ierr = MatSchurComplementGetKSP(jac->schur, &ksp);CHKERRQ(ierr);
645       ierr = PetscSNPrintf(schurprefix, sizeof(schurprefix), "%sfieldsplit_%s_inner_", ((PetscObject)pc)->prefix ? ((PetscObject)pc)->prefix : "", ilink->splitname);CHKERRQ(ierr);
646       /* Indent this deeper to emphasize the "inner" nature of this solver. */
647       ierr = PetscObjectIncrementTabLevel((PetscObject)ksp, (PetscObject) pc, 2);CHKERRQ(ierr);
648       ierr = KSPSetOptionsPrefix(ksp, schurprefix);CHKERRQ(ierr);
649       ierr = MatSchurComplementSet(jac->schur,jac->mat[0],jac->pmat[0],jac->B,jac->C,jac->mat[1]);CHKERRQ(ierr);
650 
651       ierr = MatGetNullSpace(jac->pmat[1], &sp);CHKERRQ(ierr);
652       if (sp) {
653         ierr = MatSetNullSpace(jac->schur, sp);CHKERRQ(ierr);
654       }
655 
656       ierr = PetscSNPrintf(schurtestoption, sizeof(schurtestoption), "-fieldsplit_%s_inner_", ilink->splitname);CHKERRQ(ierr);
657       ierr = PetscOptionsFindPairPrefix_Private(((PetscObject)pc)->prefix, schurtestoption, NULL, &flg);CHKERRQ(ierr);
658       if (flg) {
659         DM dmInner;
660 
661         /* Set DM for new solver */
662         ierr = KSPGetDM(jac->head->ksp, &dmInner);CHKERRQ(ierr);
663         ierr = KSPSetDM(ksp, dmInner);CHKERRQ(ierr);
664         ierr = KSPSetDMActive(ksp, PETSC_FALSE);CHKERRQ(ierr);
665         ierr = KSPSetOperators(jac->head->ksp,jac->mat[0],jac->pmat[0],flag);CHKERRQ(ierr);
666         ierr = KSPSetFromOptions(jac->head->ksp);CHKERRQ(ierr);
667       } else {
668         ierr = MatSchurComplementSetKSP(jac->schur, jac->head->ksp);CHKERRQ(ierr);
669         ierr = PetscObjectReference((PetscObject) jac->head->ksp);CHKERRQ(ierr);
670       }
671       ierr = MatSetFromOptions(jac->schur);CHKERRQ(ierr);
672 
673       ierr = PetscSNPrintf(schurtestoption, sizeof(schurtestoption), "-fieldsplit_%s_upper_", ilink->splitname);CHKERRQ(ierr);
674       ierr = PetscOptionsFindPairPrefix_Private(((PetscObject)pc)->prefix, schurtestoption, NULL, &flg);CHKERRQ(ierr);
675       if (flg) {
676         DM dmInner;
677 
678         ierr = PetscSNPrintf(schurprefix, sizeof(schurprefix), "%sfieldsplit_%s_upper_", ((PetscObject)pc)->prefix ? ((PetscObject)pc)->prefix : "", ilink->splitname);CHKERRQ(ierr);
679         ierr = KSPCreate(PetscObjectComm((PetscObject)pc), &jac->kspupper);CHKERRQ(ierr);
680         ierr = KSPSetOptionsPrefix(jac->kspupper, schurprefix);CHKERRQ(ierr);
681         ierr = KSPGetDM(jac->head->ksp, &dmInner);CHKERRQ(ierr);
682         ierr = KSPSetDM(jac->kspupper, dmInner);CHKERRQ(ierr);
683         ierr = KSPSetDMActive(jac->kspupper, PETSC_FALSE);CHKERRQ(ierr);
684         ierr = KSPSetFromOptions(jac->kspupper);CHKERRQ(ierr);
685         ierr = KSPSetOperators(jac->kspupper,jac->mat[0],jac->pmat[0],flag);CHKERRQ(ierr);
686         ierr = VecDuplicate(jac->head->x, &jac->head->z);CHKERRQ(ierr);
687       } else {
688         jac->kspupper = jac->head->ksp;
689         ierr          = PetscObjectReference((PetscObject) jac->head->ksp);CHKERRQ(ierr);
690       }
691 
692       ierr = KSPCreate(PetscObjectComm((PetscObject)pc),&jac->kspschur);CHKERRQ(ierr);
693       ierr = PetscLogObjectParent((PetscObject)pc,(PetscObject)jac->kspschur);CHKERRQ(ierr);
694       ierr = PetscObjectIncrementTabLevel((PetscObject)jac->kspschur,(PetscObject)pc,1);CHKERRQ(ierr);
695       ierr = KSPSetOperators(jac->kspschur,jac->schur,FieldSplitSchurPre(jac),DIFFERENT_NONZERO_PATTERN);CHKERRQ(ierr);
696       if (jac->schurpre == PC_FIELDSPLIT_SCHUR_PRE_SELF) {
697         PC pcschur;
698         ierr = KSPGetPC(jac->kspschur,&pcschur);CHKERRQ(ierr);
699         ierr = PCSetType(pcschur,PCNONE);CHKERRQ(ierr);
700         /* Note: This is bad if there exist preconditioners for MATSCHURCOMPLEMENT */
701       }
702       ierr = KSPGetOptionsPrefix(jac->head->next->ksp, &Dprefix);CHKERRQ(ierr);
703       ierr = KSPSetOptionsPrefix(jac->kspschur,         Dprefix);CHKERRQ(ierr);
704       /* really want setfromoptions called in PCSetFromOptions_FieldSplit(), but it is not ready yet */
705       /* need to call this every time, since the jac->kspschur is freshly created, otherwise its options never get set */
706       ierr = KSPSetFromOptions(jac->kspschur);CHKERRQ(ierr);
707     }
708 
709     /* HACK: special support to forward L and Lp matrices that might be used by PCLSC */
710     ierr = PetscSNPrintf(lscname,sizeof(lscname),"%s_LSC_L",ilink->splitname);CHKERRQ(ierr);
711     ierr = PetscObjectQuery((PetscObject)pc->mat,lscname,(PetscObject*)&LSC_L);CHKERRQ(ierr);
712     if (!LSC_L) {ierr = PetscObjectQuery((PetscObject)pc->pmat,lscname,(PetscObject*)&LSC_L);CHKERRQ(ierr);}
713     if (LSC_L) {ierr = PetscObjectCompose((PetscObject)jac->schur,"LSC_L",(PetscObject)LSC_L);CHKERRQ(ierr);}
714     ierr = PetscSNPrintf(lscname,sizeof(lscname),"%s_LSC_Lp",ilink->splitname);CHKERRQ(ierr);
715     ierr = PetscObjectQuery((PetscObject)pc->pmat,lscname,(PetscObject*)&LSC_L);CHKERRQ(ierr);
716     if (!LSC_L) {ierr = PetscObjectQuery((PetscObject)pc->mat,lscname,(PetscObject*)&LSC_L);CHKERRQ(ierr);}
717     if (LSC_L) {ierr = PetscObjectCompose((PetscObject)jac->schur,"LSC_Lp",(PetscObject)LSC_L);CHKERRQ(ierr);}
718   } else {
719     /* set up the individual splits' PCs */
720     i     = 0;
721     ilink = jac->head;
722     while (ilink) {
723       ierr = KSPSetOperators(ilink->ksp,jac->mat[i],jac->pmat[i],flag);CHKERRQ(ierr);
724       /* really want setfromoptions called in PCSetFromOptions_FieldSplit(), but it is not ready yet */
725       if (!jac->suboptionsset) {ierr = KSPSetFromOptions(ilink->ksp);CHKERRQ(ierr);}
726       i++;
727       ilink = ilink->next;
728     }
729   }
730 
731   jac->suboptionsset = PETSC_TRUE;
732   PetscFunctionReturn(0);
733 }
734 
735 #define FieldSplitSplitSolveAdd(ilink,xx,yy) \
736   (VecScatterBegin(ilink->sctx,xx,ilink->x,INSERT_VALUES,SCATTER_FORWARD) || \
737    VecScatterEnd(ilink->sctx,xx,ilink->x,INSERT_VALUES,SCATTER_FORWARD) || \
738    KSPSolve(ilink->ksp,ilink->x,ilink->y) || \
739    VecScatterBegin(ilink->sctx,ilink->y,yy,ADD_VALUES,SCATTER_REVERSE) || \
740    VecScatterEnd(ilink->sctx,ilink->y,yy,ADD_VALUES,SCATTER_REVERSE))
741 
742 #undef __FUNCT__
743 #define __FUNCT__ "PCApply_FieldSplit_Schur"
744 static PetscErrorCode PCApply_FieldSplit_Schur(PC pc,Vec x,Vec y)
745 {
746   PC_FieldSplit     *jac = (PC_FieldSplit*)pc->data;
747   PetscErrorCode    ierr;
748   PC_FieldSplitLink ilinkA = jac->head, ilinkD = ilinkA->next;
749   KSP               kspA   = ilinkA->ksp, kspLower = kspA, kspUpper = jac->kspupper;
750 
751   PetscFunctionBegin;
752   switch (jac->schurfactorization) {
753   case PC_FIELDSPLIT_SCHUR_FACT_DIAG:
754     /* [A00 0; 0 -S], positive definite, suitable for MINRES */
755     ierr = VecScatterBegin(ilinkA->sctx,x,ilinkA->x,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
756     ierr = VecScatterBegin(ilinkD->sctx,x,ilinkD->x,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
757     ierr = VecScatterEnd(ilinkA->sctx,x,ilinkA->x,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
758     ierr = KSPSolve(kspA,ilinkA->x,ilinkA->y);CHKERRQ(ierr);
759     ierr = VecScatterBegin(ilinkA->sctx,ilinkA->y,y,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
760     ierr = VecScatterEnd(ilinkD->sctx,x,ilinkD->x,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
761     ierr = KSPSolve(jac->kspschur,ilinkD->x,ilinkD->y);CHKERRQ(ierr);
762     ierr = VecScale(ilinkD->y,-1.);CHKERRQ(ierr);
763     ierr = VecScatterBegin(ilinkD->sctx,ilinkD->y,y,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
764     ierr = VecScatterEnd(ilinkA->sctx,ilinkA->y,y,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
765     ierr = VecScatterEnd(ilinkD->sctx,ilinkD->y,y,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
766     break;
767   case PC_FIELDSPLIT_SCHUR_FACT_LOWER:
768     /* [A00 0; A10 S], suitable for left preconditioning */
769     ierr = VecScatterBegin(ilinkA->sctx,x,ilinkA->x,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
770     ierr = VecScatterEnd(ilinkA->sctx,x,ilinkA->x,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
771     ierr = KSPSolve(kspA,ilinkA->x,ilinkA->y);CHKERRQ(ierr);
772     ierr = MatMult(jac->C,ilinkA->y,ilinkD->x);CHKERRQ(ierr);
773     ierr = VecScale(ilinkD->x,-1.);CHKERRQ(ierr);
774     ierr = VecScatterBegin(ilinkD->sctx,x,ilinkD->x,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
775     ierr = VecScatterBegin(ilinkA->sctx,ilinkA->y,y,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
776     ierr = VecScatterEnd(ilinkD->sctx,x,ilinkD->x,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
777     ierr = KSPSolve(jac->kspschur,ilinkD->x,ilinkD->y);CHKERRQ(ierr);
778     ierr = VecScatterBegin(ilinkD->sctx,ilinkD->y,y,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
779     ierr = VecScatterEnd(ilinkA->sctx,ilinkA->y,y,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
780     ierr = VecScatterEnd(ilinkD->sctx,ilinkD->y,y,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
781     break;
782   case PC_FIELDSPLIT_SCHUR_FACT_UPPER:
783     /* [A00 A01; 0 S], suitable for right preconditioning */
784     ierr = VecScatterBegin(ilinkD->sctx,x,ilinkD->x,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
785     ierr = VecScatterEnd(ilinkD->sctx,x,ilinkD->x,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
786     ierr = KSPSolve(jac->kspschur,ilinkD->x,ilinkD->y);CHKERRQ(ierr);
787     ierr = MatMult(jac->B,ilinkD->y,ilinkA->x);CHKERRQ(ierr);
788     ierr = VecScale(ilinkA->x,-1.);CHKERRQ(ierr);
789     ierr = VecScatterBegin(ilinkA->sctx,x,ilinkA->x,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
790     ierr = VecScatterBegin(ilinkD->sctx,ilinkD->y,y,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
791     ierr = VecScatterEnd(ilinkA->sctx,x,ilinkA->x,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
792     ierr = KSPSolve(kspA,ilinkA->x,ilinkA->y);CHKERRQ(ierr);
793     ierr = VecScatterBegin(ilinkA->sctx,ilinkA->y,y,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
794     ierr = VecScatterEnd(ilinkD->sctx,ilinkD->y,y,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
795     ierr = VecScatterEnd(ilinkA->sctx,ilinkA->y,y,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
796     break;
797   case PC_FIELDSPLIT_SCHUR_FACT_FULL:
798     /* [1 0; A10 A00^{-1} 1] [A00 0; 0 S] [1 A00^{-1}A01; 0 1], an exact solve if applied exactly, needs one extra solve with A */
799     ierr = VecScatterBegin(ilinkA->sctx,x,ilinkA->x,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
800     ierr = VecScatterEnd(ilinkA->sctx,x,ilinkA->x,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
801     ierr = KSPSolve(kspLower,ilinkA->x,ilinkA->y);CHKERRQ(ierr);
802     ierr = MatMult(jac->C,ilinkA->y,ilinkD->x);CHKERRQ(ierr);
803     ierr = VecScale(ilinkD->x,-1.0);CHKERRQ(ierr);
804     ierr = VecScatterBegin(ilinkD->sctx,x,ilinkD->x,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
805     ierr = VecScatterEnd(ilinkD->sctx,x,ilinkD->x,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
806 
807     ierr = KSPSolve(jac->kspschur,ilinkD->x,ilinkD->y);CHKERRQ(ierr);
808     ierr = VecScatterBegin(ilinkD->sctx,ilinkD->y,y,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
809     ierr = VecScatterEnd(ilinkD->sctx,ilinkD->y,y,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
810 
811     if (kspUpper == kspA) {
812       ierr = MatMult(jac->B,ilinkD->y,ilinkA->y);CHKERRQ(ierr);
813       ierr = VecAXPY(ilinkA->x,-1.0,ilinkA->y);CHKERRQ(ierr);
814       ierr = KSPSolve(kspA,ilinkA->x,ilinkA->y);CHKERRQ(ierr);
815     } else {
816       ierr = KSPSolve(kspA,ilinkA->x,ilinkA->y);CHKERRQ(ierr);
817       ierr = MatMult(jac->B,ilinkD->y,ilinkA->x);CHKERRQ(ierr);
818       ierr = KSPSolve(kspUpper,ilinkA->x,ilinkA->z);CHKERRQ(ierr);
819       ierr = VecAXPY(ilinkA->y,-1.0,ilinkA->z);CHKERRQ(ierr);
820     }
821     ierr = VecScatterBegin(ilinkA->sctx,ilinkA->y,y,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
822     ierr = VecScatterEnd(ilinkA->sctx,ilinkA->y,y,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
823   }
824   PetscFunctionReturn(0);
825 }
826 
827 #undef __FUNCT__
828 #define __FUNCT__ "PCApply_FieldSplit"
829 static PetscErrorCode PCApply_FieldSplit(PC pc,Vec x,Vec y)
830 {
831   PC_FieldSplit     *jac = (PC_FieldSplit*)pc->data;
832   PetscErrorCode    ierr;
833   PC_FieldSplitLink ilink = jac->head;
834   PetscInt          cnt,bs;
835 
836   PetscFunctionBegin;
837   CHKMEMQ;
838   if (jac->type == PC_COMPOSITE_ADDITIVE) {
839     if (jac->defaultsplit) {
840       ierr = VecGetBlockSize(x,&bs);CHKERRQ(ierr);
841       if (jac->bs > 0 && bs != jac->bs) SETERRQ2(PetscObjectComm((PetscObject)pc),PETSC_ERR_ARG_WRONGSTATE,"Blocksize of x vector %D does not match fieldsplit blocksize %D",bs,jac->bs);
842       ierr = VecGetBlockSize(y,&bs);CHKERRQ(ierr);
843       if (jac->bs > 0 && bs != jac->bs) SETERRQ2(PetscObjectComm((PetscObject)pc),PETSC_ERR_ARG_WRONGSTATE,"Blocksize of y vector %D does not match fieldsplit blocksize %D",bs,jac->bs);
844       ierr = VecStrideGatherAll(x,jac->x,INSERT_VALUES);CHKERRQ(ierr);
845       while (ilink) {
846         ierr  = KSPSolve(ilink->ksp,ilink->x,ilink->y);CHKERRQ(ierr);
847         ilink = ilink->next;
848       }
849       ierr = VecStrideScatterAll(jac->y,y,INSERT_VALUES);CHKERRQ(ierr);
850     } else {
851       ierr = VecSet(y,0.0);CHKERRQ(ierr);
852       while (ilink) {
853         ierr  = FieldSplitSplitSolveAdd(ilink,x,y);CHKERRQ(ierr);
854         ilink = ilink->next;
855       }
856     }
857   } else if (jac->type == PC_COMPOSITE_MULTIPLICATIVE || jac->type == PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE) {
858     if (!jac->w1) {
859       ierr = VecDuplicate(x,&jac->w1);CHKERRQ(ierr);
860       ierr = VecDuplicate(x,&jac->w2);CHKERRQ(ierr);
861     }
862     ierr = VecSet(y,0.0);CHKERRQ(ierr);
863     ierr = FieldSplitSplitSolveAdd(ilink,x,y);CHKERRQ(ierr);
864     cnt  = 1;
865     while (ilink->next) {
866       ilink = ilink->next;
867       /* compute the residual only over the part of the vector needed */
868       ierr = MatMult(jac->Afield[cnt++],y,ilink->x);CHKERRQ(ierr);
869       ierr = VecScale(ilink->x,-1.0);CHKERRQ(ierr);
870       ierr = VecScatterBegin(ilink->sctx,x,ilink->x,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
871       ierr = VecScatterEnd(ilink->sctx,x,ilink->x,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
872       ierr = KSPSolve(ilink->ksp,ilink->x,ilink->y);CHKERRQ(ierr);
873       ierr = VecScatterBegin(ilink->sctx,ilink->y,y,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
874       ierr = VecScatterEnd(ilink->sctx,ilink->y,y,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
875     }
876     if (jac->type == PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE) {
877       cnt -= 2;
878       while (ilink->previous) {
879         ilink = ilink->previous;
880         /* compute the residual only over the part of the vector needed */
881         ierr = MatMult(jac->Afield[cnt--],y,ilink->x);CHKERRQ(ierr);
882         ierr = VecScale(ilink->x,-1.0);CHKERRQ(ierr);
883         ierr = VecScatterBegin(ilink->sctx,x,ilink->x,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
884         ierr = VecScatterEnd(ilink->sctx,x,ilink->x,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
885         ierr = KSPSolve(ilink->ksp,ilink->x,ilink->y);CHKERRQ(ierr);
886         ierr = VecScatterBegin(ilink->sctx,ilink->y,y,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
887         ierr = VecScatterEnd(ilink->sctx,ilink->y,y,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
888       }
889     }
890   } else SETERRQ1(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"Unsupported or unknown composition",(int) jac->type);
891   CHKMEMQ;
892   PetscFunctionReturn(0);
893 }
894 
895 #define FieldSplitSplitSolveAddTranspose(ilink,xx,yy) \
896   (VecScatterBegin(ilink->sctx,xx,ilink->y,INSERT_VALUES,SCATTER_FORWARD) || \
897    VecScatterEnd(ilink->sctx,xx,ilink->y,INSERT_VALUES,SCATTER_FORWARD) || \
898    KSPSolveTranspose(ilink->ksp,ilink->y,ilink->x) || \
899    VecScatterBegin(ilink->sctx,ilink->x,yy,ADD_VALUES,SCATTER_REVERSE) || \
900    VecScatterEnd(ilink->sctx,ilink->x,yy,ADD_VALUES,SCATTER_REVERSE))
901 
902 #undef __FUNCT__
903 #define __FUNCT__ "PCApplyTranspose_FieldSplit"
904 static PetscErrorCode PCApplyTranspose_FieldSplit(PC pc,Vec x,Vec y)
905 {
906   PC_FieldSplit     *jac = (PC_FieldSplit*)pc->data;
907   PetscErrorCode    ierr;
908   PC_FieldSplitLink ilink = jac->head;
909   PetscInt          bs;
910 
911   PetscFunctionBegin;
912   CHKMEMQ;
913   if (jac->type == PC_COMPOSITE_ADDITIVE) {
914     if (jac->defaultsplit) {
915       ierr = VecGetBlockSize(x,&bs);CHKERRQ(ierr);
916       if (jac->bs > 0 && bs != jac->bs) SETERRQ2(PetscObjectComm((PetscObject)pc),PETSC_ERR_ARG_WRONGSTATE,"Blocksize of x vector %D does not match fieldsplit blocksize %D",bs,jac->bs);
917       ierr = VecGetBlockSize(y,&bs);CHKERRQ(ierr);
918       if (jac->bs > 0 && bs != jac->bs) SETERRQ2(PetscObjectComm((PetscObject)pc),PETSC_ERR_ARG_WRONGSTATE,"Blocksize of y vector %D does not match fieldsplit blocksize %D",bs,jac->bs);
919       ierr = VecStrideGatherAll(x,jac->x,INSERT_VALUES);CHKERRQ(ierr);
920       while (ilink) {
921         ierr  = KSPSolveTranspose(ilink->ksp,ilink->x,ilink->y);CHKERRQ(ierr);
922         ilink = ilink->next;
923       }
924       ierr = VecStrideScatterAll(jac->y,y,INSERT_VALUES);CHKERRQ(ierr);
925     } else {
926       ierr = VecSet(y,0.0);CHKERRQ(ierr);
927       while (ilink) {
928         ierr  = FieldSplitSplitSolveAddTranspose(ilink,x,y);CHKERRQ(ierr);
929         ilink = ilink->next;
930       }
931     }
932   } else {
933     if (!jac->w1) {
934       ierr = VecDuplicate(x,&jac->w1);CHKERRQ(ierr);
935       ierr = VecDuplicate(x,&jac->w2);CHKERRQ(ierr);
936     }
937     ierr = VecSet(y,0.0);CHKERRQ(ierr);
938     if (jac->type == PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE) {
939       ierr = FieldSplitSplitSolveAddTranspose(ilink,x,y);CHKERRQ(ierr);
940       while (ilink->next) {
941         ilink = ilink->next;
942         ierr  = MatMultTranspose(pc->mat,y,jac->w1);CHKERRQ(ierr);
943         ierr  = VecWAXPY(jac->w2,-1.0,jac->w1,x);CHKERRQ(ierr);
944         ierr  = FieldSplitSplitSolveAddTranspose(ilink,jac->w2,y);CHKERRQ(ierr);
945       }
946       while (ilink->previous) {
947         ilink = ilink->previous;
948         ierr  = MatMultTranspose(pc->mat,y,jac->w1);CHKERRQ(ierr);
949         ierr  = VecWAXPY(jac->w2,-1.0,jac->w1,x);CHKERRQ(ierr);
950         ierr  = FieldSplitSplitSolveAddTranspose(ilink,jac->w2,y);CHKERRQ(ierr);
951       }
952     } else {
953       while (ilink->next) {   /* get to last entry in linked list */
954         ilink = ilink->next;
955       }
956       ierr = FieldSplitSplitSolveAddTranspose(ilink,x,y);CHKERRQ(ierr);
957       while (ilink->previous) {
958         ilink = ilink->previous;
959         ierr  = MatMultTranspose(pc->mat,y,jac->w1);CHKERRQ(ierr);
960         ierr  = VecWAXPY(jac->w2,-1.0,jac->w1,x);CHKERRQ(ierr);
961         ierr  = FieldSplitSplitSolveAddTranspose(ilink,jac->w2,y);CHKERRQ(ierr);
962       }
963     }
964   }
965   CHKMEMQ;
966   PetscFunctionReturn(0);
967 }
968 
969 #undef __FUNCT__
970 #define __FUNCT__ "PCReset_FieldSplit"
971 static PetscErrorCode PCReset_FieldSplit(PC pc)
972 {
973   PC_FieldSplit     *jac = (PC_FieldSplit*)pc->data;
974   PetscErrorCode    ierr;
975   PC_FieldSplitLink ilink = jac->head,next;
976 
977   PetscFunctionBegin;
978   while (ilink) {
979     ierr  = KSPReset(ilink->ksp);CHKERRQ(ierr);
980     ierr  = VecDestroy(&ilink->x);CHKERRQ(ierr);
981     ierr  = VecDestroy(&ilink->y);CHKERRQ(ierr);
982     ierr  = VecDestroy(&ilink->z);CHKERRQ(ierr);
983     ierr  = VecScatterDestroy(&ilink->sctx);CHKERRQ(ierr);
984     ierr  = ISDestroy(&ilink->is);CHKERRQ(ierr);
985     ierr  = ISDestroy(&ilink->is_col);CHKERRQ(ierr);
986     next  = ilink->next;
987     ilink = next;
988   }
989   ierr = PetscFree2(jac->x,jac->y);CHKERRQ(ierr);
990   if (jac->mat && jac->mat != jac->pmat) {
991     ierr = MatDestroyMatrices(jac->nsplits,&jac->mat);CHKERRQ(ierr);
992   } else if (jac->mat) {
993     jac->mat = NULL;
994   }
995   if (jac->pmat) {ierr = MatDestroyMatrices(jac->nsplits,&jac->pmat);CHKERRQ(ierr);}
996   if (jac->Afield) {ierr = MatDestroyMatrices(jac->nsplits,&jac->Afield);CHKERRQ(ierr);}
997   ierr       = VecDestroy(&jac->w1);CHKERRQ(ierr);
998   ierr       = VecDestroy(&jac->w2);CHKERRQ(ierr);
999   ierr       = MatDestroy(&jac->schur);CHKERRQ(ierr);
1000   ierr       = MatDestroy(&jac->schur_user);CHKERRQ(ierr);
1001   ierr       = KSPDestroy(&jac->kspschur);CHKERRQ(ierr);
1002   ierr       = KSPDestroy(&jac->kspupper);CHKERRQ(ierr);
1003   ierr       = MatDestroy(&jac->B);CHKERRQ(ierr);
1004   ierr       = MatDestroy(&jac->C);CHKERRQ(ierr);
1005   jac->reset = PETSC_TRUE;
1006   PetscFunctionReturn(0);
1007 }
1008 
1009 #undef __FUNCT__
1010 #define __FUNCT__ "PCDestroy_FieldSplit"
1011 static PetscErrorCode PCDestroy_FieldSplit(PC pc)
1012 {
1013   PC_FieldSplit     *jac = (PC_FieldSplit*)pc->data;
1014   PetscErrorCode    ierr;
1015   PC_FieldSplitLink ilink = jac->head,next;
1016 
1017   PetscFunctionBegin;
1018   ierr = PCReset_FieldSplit(pc);CHKERRQ(ierr);
1019   while (ilink) {
1020     ierr  = KSPDestroy(&ilink->ksp);CHKERRQ(ierr);
1021     next  = ilink->next;
1022     ierr  = PetscFree(ilink->splitname);CHKERRQ(ierr);
1023     ierr  = PetscFree(ilink->fields);CHKERRQ(ierr);
1024     ierr  = PetscFree(ilink->fields_col);CHKERRQ(ierr);
1025     ierr  = PetscFree(ilink);CHKERRQ(ierr);
1026     ilink = next;
1027   }
1028   ierr = PetscFree2(jac->x,jac->y);CHKERRQ(ierr);
1029   ierr = PetscFree(pc->data);CHKERRQ(ierr);
1030   ierr = PetscObjectComposeFunctionDynamic((PetscObject)pc,"PCFieldSplitGetSubKSP_C","",NULL);CHKERRQ(ierr);
1031   ierr = PetscObjectComposeFunctionDynamic((PetscObject)pc,"PCFieldSplitSetFields_C","",NULL);CHKERRQ(ierr);
1032   ierr = PetscObjectComposeFunctionDynamic((PetscObject)pc,"PCFieldSplitSetIS_C","",NULL);CHKERRQ(ierr);
1033   ierr = PetscObjectComposeFunctionDynamic((PetscObject)pc,"PCFieldSplitSetType_C","",NULL);CHKERRQ(ierr);
1034   ierr = PetscObjectComposeFunctionDynamic((PetscObject)pc,"PCFieldSplitSetBlockSize_C","",NULL);CHKERRQ(ierr);
1035   ierr = PetscObjectComposeFunctionDynamic((PetscObject)pc,"PCFieldSplitSchurPrecondition_C","",NULL);CHKERRQ(ierr);
1036   ierr = PetscObjectComposeFunctionDynamic((PetscObject)pc,"PCFieldSplitSetSchurFactType_C","",NULL);CHKERRQ(ierr);
1037   PetscFunctionReturn(0);
1038 }
1039 
1040 #undef __FUNCT__
1041 #define __FUNCT__ "PCSetFromOptions_FieldSplit"
1042 static PetscErrorCode PCSetFromOptions_FieldSplit(PC pc)
1043 {
1044   PetscErrorCode  ierr;
1045   PetscInt        bs;
1046   PetscBool       flg,stokes = PETSC_FALSE;
1047   PC_FieldSplit   *jac = (PC_FieldSplit*)pc->data;
1048   PCCompositeType ctype;
1049 
1050   PetscFunctionBegin;
1051   ierr = PetscOptionsHead("FieldSplit options");CHKERRQ(ierr);
1052   ierr = PetscOptionsBool("-pc_fieldsplit_real_diagonal","Use diagonal blocks of the operator","PCFieldSplitSetRealDiagonal",jac->realdiagonal,&jac->realdiagonal,NULL);CHKERRQ(ierr);
1053   ierr = PetscOptionsBool("-pc_fieldsplit_dm_splits","Whether to use DMCreateFieldDecomposition() for splits","PCFieldSplitSetDMSplits",jac->dm_splits,&jac->dm_splits,NULL);CHKERRQ(ierr);
1054   ierr = PetscOptionsInt("-pc_fieldsplit_block_size","Blocksize that defines number of fields","PCFieldSplitSetBlockSize",jac->bs,&bs,&flg);CHKERRQ(ierr);
1055   if (flg) {
1056     ierr = PCFieldSplitSetBlockSize(pc,bs);CHKERRQ(ierr);
1057   }
1058 
1059   ierr = PetscOptionsGetBool(((PetscObject)pc)->prefix,"-pc_fieldsplit_detect_saddle_point",&stokes,NULL);CHKERRQ(ierr);
1060   if (stokes) {
1061     ierr          = PCFieldSplitSetType(pc,PC_COMPOSITE_SCHUR);CHKERRQ(ierr);
1062     jac->schurpre = PC_FIELDSPLIT_SCHUR_PRE_SELF;
1063   }
1064 
1065   ierr = PetscOptionsEnum("-pc_fieldsplit_type","Type of composition","PCFieldSplitSetType",PCCompositeTypes,(PetscEnum)jac->type,(PetscEnum*)&ctype,&flg);CHKERRQ(ierr);
1066   if (flg) {
1067     ierr = PCFieldSplitSetType(pc,ctype);CHKERRQ(ierr);
1068   }
1069   /* Only setup fields once */
1070   if ((jac->bs > 0) && (jac->nsplits == 0)) {
1071     /* only allow user to set fields from command line if bs is already known.
1072        otherwise user can set them in PCFieldSplitSetDefaults() */
1073     ierr = PCFieldSplitSetRuntimeSplits_Private(pc);CHKERRQ(ierr);
1074     if (jac->splitdefined) {ierr = PetscInfo(pc,"Splits defined using the options database\n");CHKERRQ(ierr);}
1075   }
1076   if (jac->type == PC_COMPOSITE_SCHUR) {
1077     ierr = PetscOptionsGetEnum(((PetscObject)pc)->prefix,"-pc_fieldsplit_schur_factorization_type",PCFieldSplitSchurFactTypes,(PetscEnum*)&jac->schurfactorization,&flg);CHKERRQ(ierr);
1078     if (flg) {ierr = PetscInfo(pc,"Deprecated use of -pc_fieldsplit_schur_factorization_type\n");CHKERRQ(ierr);}
1079     ierr = 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);CHKERRQ(ierr);
1080     ierr = PetscOptionsEnum("-pc_fieldsplit_schur_precondition","How to build preconditioner for Schur complement","PCFieldSplitSchurPrecondition",PCFieldSplitSchurPreTypes,(PetscEnum)jac->schurpre,(PetscEnum*)&jac->schurpre,NULL);CHKERRQ(ierr);
1081   }
1082   ierr = PetscOptionsTail();CHKERRQ(ierr);
1083   PetscFunctionReturn(0);
1084 }
1085 
1086 /*------------------------------------------------------------------------------------*/
1087 
1088 EXTERN_C_BEGIN
1089 #undef __FUNCT__
1090 #define __FUNCT__ "PCFieldSplitSetFields_FieldSplit"
1091 PetscErrorCode  PCFieldSplitSetFields_FieldSplit(PC pc,const char splitname[],PetscInt n,const PetscInt *fields,const PetscInt *fields_col)
1092 {
1093   PC_FieldSplit     *jac = (PC_FieldSplit*)pc->data;
1094   PetscErrorCode    ierr;
1095   PC_FieldSplitLink ilink,next = jac->head;
1096   char              prefix[128];
1097   PetscInt          i;
1098 
1099   PetscFunctionBegin;
1100   if (jac->splitdefined) {
1101     ierr = PetscInfo1(pc,"Ignoring new split \"%s\" because the splits have already been defined\n",splitname);CHKERRQ(ierr);
1102     PetscFunctionReturn(0);
1103   }
1104   for (i=0; i<n; i++) {
1105     if (fields[i] >= jac->bs) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Field %D requested but only %D exist",fields[i],jac->bs);
1106     if (fields[i] < 0) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Negative field %D requested",fields[i]);
1107   }
1108   ierr = PetscNew(struct _PC_FieldSplitLink,&ilink);CHKERRQ(ierr);
1109   if (splitname) {
1110     ierr = PetscStrallocpy(splitname,&ilink->splitname);CHKERRQ(ierr);
1111   } else {
1112     ierr = PetscMalloc(3*sizeof(char),&ilink->splitname);CHKERRQ(ierr);
1113     ierr = PetscSNPrintf(ilink->splitname,2,"%s",jac->nsplits);CHKERRQ(ierr);
1114   }
1115   ierr = PetscMalloc(n*sizeof(PetscInt),&ilink->fields);CHKERRQ(ierr);
1116   ierr = PetscMemcpy(ilink->fields,fields,n*sizeof(PetscInt));CHKERRQ(ierr);
1117   ierr = PetscMalloc(n*sizeof(PetscInt),&ilink->fields_col);CHKERRQ(ierr);
1118   ierr = PetscMemcpy(ilink->fields_col,fields_col,n*sizeof(PetscInt));CHKERRQ(ierr);
1119 
1120   ilink->nfields = n;
1121   ilink->next    = NULL;
1122   ierr           = KSPCreate(PetscObjectComm((PetscObject)pc),&ilink->ksp);CHKERRQ(ierr);
1123   ierr           = PetscObjectIncrementTabLevel((PetscObject)ilink->ksp,(PetscObject)pc,1);CHKERRQ(ierr);
1124   ierr           = KSPSetType(ilink->ksp,KSPPREONLY);CHKERRQ(ierr);
1125   ierr           = PetscLogObjectParent((PetscObject)pc,(PetscObject)ilink->ksp);CHKERRQ(ierr);
1126 
1127   ierr = PetscSNPrintf(prefix,sizeof(prefix),"%sfieldsplit_%s_",((PetscObject)pc)->prefix ? ((PetscObject)pc)->prefix : "",ilink->splitname);CHKERRQ(ierr);
1128   ierr = KSPSetOptionsPrefix(ilink->ksp,prefix);CHKERRQ(ierr);
1129 
1130   if (!next) {
1131     jac->head       = ilink;
1132     ilink->previous = NULL;
1133   } else {
1134     while (next->next) {
1135       next = next->next;
1136     }
1137     next->next      = ilink;
1138     ilink->previous = next;
1139   }
1140   jac->nsplits++;
1141   PetscFunctionReturn(0);
1142 }
1143 EXTERN_C_END
1144 
1145 EXTERN_C_BEGIN
1146 #undef __FUNCT__
1147 #define __FUNCT__ "PCFieldSplitGetSubKSP_FieldSplit_Schur"
1148 PetscErrorCode  PCFieldSplitGetSubKSP_FieldSplit_Schur(PC pc,PetscInt *n,KSP **subksp)
1149 {
1150   PC_FieldSplit  *jac = (PC_FieldSplit*)pc->data;
1151   PetscErrorCode ierr;
1152 
1153   PetscFunctionBegin;
1154   ierr = PetscMalloc(jac->nsplits*sizeof(KSP),subksp);CHKERRQ(ierr);
1155   ierr = MatSchurComplementGetKSP(jac->schur,*subksp);CHKERRQ(ierr);
1156 
1157   (*subksp)[1] = jac->kspschur;
1158   if (n) *n = jac->nsplits;
1159   PetscFunctionReturn(0);
1160 }
1161 EXTERN_C_END
1162 
1163 EXTERN_C_BEGIN
1164 #undef __FUNCT__
1165 #define __FUNCT__ "PCFieldSplitGetSubKSP_FieldSplit"
1166 PetscErrorCode  PCFieldSplitGetSubKSP_FieldSplit(PC pc,PetscInt *n,KSP **subksp)
1167 {
1168   PC_FieldSplit     *jac = (PC_FieldSplit*)pc->data;
1169   PetscErrorCode    ierr;
1170   PetscInt          cnt   = 0;
1171   PC_FieldSplitLink ilink = jac->head;
1172 
1173   PetscFunctionBegin;
1174   ierr = PetscMalloc(jac->nsplits*sizeof(KSP),subksp);CHKERRQ(ierr);
1175   while (ilink) {
1176     (*subksp)[cnt++] = ilink->ksp;
1177     ilink            = ilink->next;
1178   }
1179   if (cnt != jac->nsplits) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Corrupt PCFIELDSPLIT object: number of splits in linked list %D does not match number in object %D",cnt,jac->nsplits);
1180   if (n) *n = jac->nsplits;
1181   PetscFunctionReturn(0);
1182 }
1183 EXTERN_C_END
1184 
1185 EXTERN_C_BEGIN
1186 #undef __FUNCT__
1187 #define __FUNCT__ "PCFieldSplitSetIS_FieldSplit"
1188 PetscErrorCode  PCFieldSplitSetIS_FieldSplit(PC pc,const char splitname[],IS is)
1189 {
1190   PC_FieldSplit     *jac = (PC_FieldSplit*)pc->data;
1191   PetscErrorCode    ierr;
1192   PC_FieldSplitLink ilink, next = jac->head;
1193   char              prefix[128];
1194 
1195   PetscFunctionBegin;
1196   if (jac->splitdefined) {
1197     ierr = PetscInfo1(pc,"Ignoring new split \"%s\" because the splits have already been defined\n",splitname);CHKERRQ(ierr);
1198     PetscFunctionReturn(0);
1199   }
1200   ierr = PetscNew(struct _PC_FieldSplitLink,&ilink);CHKERRQ(ierr);
1201   if (splitname) {
1202     ierr = PetscStrallocpy(splitname,&ilink->splitname);CHKERRQ(ierr);
1203   } else {
1204     ierr = PetscMalloc(8*sizeof(char),&ilink->splitname);CHKERRQ(ierr);
1205     ierr = PetscSNPrintf(ilink->splitname,7,"%D",jac->nsplits);CHKERRQ(ierr);
1206   }
1207   ierr          = PetscObjectReference((PetscObject)is);CHKERRQ(ierr);
1208   ierr          = ISDestroy(&ilink->is);CHKERRQ(ierr);
1209   ilink->is     = is;
1210   ierr          = PetscObjectReference((PetscObject)is);CHKERRQ(ierr);
1211   ierr          = ISDestroy(&ilink->is_col);CHKERRQ(ierr);
1212   ilink->is_col = is;
1213   ilink->next   = NULL;
1214   ierr          = KSPCreate(PetscObjectComm((PetscObject)pc),&ilink->ksp);CHKERRQ(ierr);
1215   ierr          = PetscObjectIncrementTabLevel((PetscObject)ilink->ksp,(PetscObject)pc,1);CHKERRQ(ierr);
1216   ierr          = KSPSetType(ilink->ksp,KSPPREONLY);CHKERRQ(ierr);
1217   ierr          = PetscLogObjectParent((PetscObject)pc,(PetscObject)ilink->ksp);CHKERRQ(ierr);
1218 
1219   ierr = PetscSNPrintf(prefix,sizeof(prefix),"%sfieldsplit_%s_",((PetscObject)pc)->prefix ? ((PetscObject)pc)->prefix : "",ilink->splitname);CHKERRQ(ierr);
1220   ierr = KSPSetOptionsPrefix(ilink->ksp,prefix);CHKERRQ(ierr);
1221 
1222   if (!next) {
1223     jac->head       = ilink;
1224     ilink->previous = NULL;
1225   } else {
1226     while (next->next) {
1227       next = next->next;
1228     }
1229     next->next      = ilink;
1230     ilink->previous = next;
1231   }
1232   jac->nsplits++;
1233   PetscFunctionReturn(0);
1234 }
1235 EXTERN_C_END
1236 
1237 #undef __FUNCT__
1238 #define __FUNCT__ "PCFieldSplitSetFields"
1239 /*@
1240     PCFieldSplitSetFields - Sets the fields for one particular split in the field split preconditioner
1241 
1242     Logically Collective on PC
1243 
1244     Input Parameters:
1245 +   pc  - the preconditioner context
1246 .   splitname - name of this split, if NULL the number of the split is used
1247 .   n - the number of fields in this split
1248 -   fields - the fields in this split
1249 
1250     Level: intermediate
1251 
1252     Notes: Use PCFieldSplitSetIS() to set a completely general set of indices as a field.
1253 
1254      The PCFieldSplitSetFields() is for defining fields as strided blocks. For example, if the block
1255      size is three then one can define a field as 0, or 1 or 2 or 0,1 or 0,2 or 1,2 which mean
1256      0xx3xx6xx9xx12 ... x1xx4xx7xx ... xx2xx5xx8xx.. 01x34x67x... 0x1x3x5x7.. x12x45x78x....
1257      where the numbered entries indicate what is in the field.
1258 
1259      This function is called once per split (it creates a new split each time).  Solve options
1260      for this split will be available under the prefix -fieldsplit_SPLITNAME_.
1261 
1262      Developer Note: This routine does not actually create the IS representing the split, that is delayed
1263      until PCSetUp_FieldSplit(), because information about the vector/matrix layouts may not be
1264      available when this routine is called.
1265 
1266 .seealso: PCFieldSplitGetSubKSP(), PCFIELDSPLIT, PCFieldSplitSetBlockSize(), PCFieldSplitSetIS()
1267 
1268 @*/
1269 PetscErrorCode  PCFieldSplitSetFields(PC pc,const char splitname[],PetscInt n,const PetscInt *fields,const PetscInt *fields_col)
1270 {
1271   PetscErrorCode ierr;
1272 
1273   PetscFunctionBegin;
1274   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
1275   PetscValidCharPointer(splitname,2);
1276   if (n < 1) SETERRQ2(PetscObjectComm((PetscObject)pc),PETSC_ERR_ARG_OUTOFRANGE,"Provided number of fields %D in split \"%s\" not positive",n,splitname);
1277   PetscValidIntPointer(fields,3);
1278   ierr = PetscTryMethod(pc,"PCFieldSplitSetFields_C",(PC,const char[],PetscInt,const PetscInt*,const PetscInt*),(pc,splitname,n,fields,fields_col));CHKERRQ(ierr);
1279   PetscFunctionReturn(0);
1280 }
1281 
1282 #undef __FUNCT__
1283 #define __FUNCT__ "PCFieldSplitSetIS"
1284 /*@
1285     PCFieldSplitSetIS - Sets the exact elements for field
1286 
1287     Logically Collective on PC
1288 
1289     Input Parameters:
1290 +   pc  - the preconditioner context
1291 .   splitname - name of this split, if NULL the number of the split is used
1292 -   is - the index set that defines the vector elements in this field
1293 
1294 
1295     Notes:
1296     Use PCFieldSplitSetFields(), for fields defined by strided types.
1297 
1298     This function is called once per split (it creates a new split each time).  Solve options
1299     for this split will be available under the prefix -fieldsplit_SPLITNAME_.
1300 
1301     Level: intermediate
1302 
1303 .seealso: PCFieldSplitGetSubKSP(), PCFIELDSPLIT, PCFieldSplitSetBlockSize()
1304 
1305 @*/
1306 PetscErrorCode  PCFieldSplitSetIS(PC pc,const char splitname[],IS is)
1307 {
1308   PetscErrorCode ierr;
1309 
1310   PetscFunctionBegin;
1311   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
1312   if (splitname) PetscValidCharPointer(splitname,2);
1313   PetscValidHeaderSpecific(is,IS_CLASSID,3);
1314   ierr = PetscTryMethod(pc,"PCFieldSplitSetIS_C",(PC,const char[],IS),(pc,splitname,is));CHKERRQ(ierr);
1315   PetscFunctionReturn(0);
1316 }
1317 
1318 #undef __FUNCT__
1319 #define __FUNCT__ "PCFieldSplitGetIS"
1320 /*@
1321     PCFieldSplitGetIS - Retrieves the elements for a field as an IS
1322 
1323     Logically Collective on PC
1324 
1325     Input Parameters:
1326 +   pc  - the preconditioner context
1327 -   splitname - name of this split
1328 
1329     Output Parameter:
1330 -   is - the index set that defines the vector elements in this field, or NULL if the field is not found
1331 
1332     Level: intermediate
1333 
1334 .seealso: PCFieldSplitGetSubKSP(), PCFIELDSPLIT, PCFieldSplitSetIS()
1335 
1336 @*/
1337 PetscErrorCode PCFieldSplitGetIS(PC pc,const char splitname[],IS *is)
1338 {
1339   PetscErrorCode ierr;
1340 
1341   PetscFunctionBegin;
1342   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
1343   PetscValidCharPointer(splitname,2);
1344   PetscValidPointer(is,3);
1345   {
1346     PC_FieldSplit     *jac  = (PC_FieldSplit*) pc->data;
1347     PC_FieldSplitLink ilink = jac->head;
1348     PetscBool         found;
1349 
1350     *is = NULL;
1351     while (ilink) {
1352       ierr = PetscStrcmp(ilink->splitname, splitname, &found);CHKERRQ(ierr);
1353       if (found) {
1354         *is = ilink->is;
1355         break;
1356       }
1357       ilink = ilink->next;
1358     }
1359   }
1360   PetscFunctionReturn(0);
1361 }
1362 
1363 #undef __FUNCT__
1364 #define __FUNCT__ "PCFieldSplitSetBlockSize"
1365 /*@
1366     PCFieldSplitSetBlockSize - Sets the block size for defining where fields start in the
1367       fieldsplit preconditioner. If not set the matrix block size is used.
1368 
1369     Logically Collective on PC
1370 
1371     Input Parameters:
1372 +   pc  - the preconditioner context
1373 -   bs - the block size
1374 
1375     Level: intermediate
1376 
1377 .seealso: PCFieldSplitGetSubKSP(), PCFIELDSPLIT, PCFieldSplitSetFields()
1378 
1379 @*/
1380 PetscErrorCode  PCFieldSplitSetBlockSize(PC pc,PetscInt bs)
1381 {
1382   PetscErrorCode ierr;
1383 
1384   PetscFunctionBegin;
1385   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
1386   PetscValidLogicalCollectiveInt(pc,bs,2);
1387   ierr = PetscTryMethod(pc,"PCFieldSplitSetBlockSize_C",(PC,PetscInt),(pc,bs));CHKERRQ(ierr);
1388   PetscFunctionReturn(0);
1389 }
1390 
1391 #undef __FUNCT__
1392 #define __FUNCT__ "PCFieldSplitGetSubKSP"
1393 /*@C
1394    PCFieldSplitGetSubKSP - Gets the KSP contexts for all splits
1395 
1396    Collective on KSP
1397 
1398    Input Parameter:
1399 .  pc - the preconditioner context
1400 
1401    Output Parameters:
1402 +  n - the number of splits
1403 -  pc - the array of KSP contexts
1404 
1405    Note:
1406    After PCFieldSplitGetSubKSP() the array of KSPs IS to be freed by the user
1407    (not the KSP just the array that contains them).
1408 
1409    You must call KSPSetUp() before calling PCFieldSplitGetSubKSP().
1410 
1411    Fortran Usage: You must pass in a KSP array that is large enough to contain all the local KSPs.
1412       You can call PCFieldSplitGetSubKSP(pc,n,NULL_OBJECT,ierr) to determine how large the
1413       KSP array must be.
1414 
1415 
1416    Level: advanced
1417 
1418 .seealso: PCFIELDSPLIT
1419 @*/
1420 PetscErrorCode  PCFieldSplitGetSubKSP(PC pc,PetscInt *n,KSP *subksp[])
1421 {
1422   PetscErrorCode ierr;
1423 
1424   PetscFunctionBegin;
1425   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
1426   if (n) PetscValidIntPointer(n,2);
1427   ierr = PetscUseMethod(pc,"PCFieldSplitGetSubKSP_C",(PC,PetscInt*,KSP **),(pc,n,subksp));CHKERRQ(ierr);
1428   PetscFunctionReturn(0);
1429 }
1430 
1431 #undef __FUNCT__
1432 #define __FUNCT__ "PCFieldSplitSchurPrecondition"
1433 /*@
1434     PCFieldSplitSchurPrecondition -  Indicates if the Schur complement is preconditioned by a preconditioner constructed by the
1435       A11 matrix. Otherwise no preconditioner is used.
1436 
1437     Collective on PC
1438 
1439     Input Parameters:
1440 +   pc  - the preconditioner context
1441 .   ptype - which matrix to use for preconditioning the Schur complement, PC_FIELDSPLIT_SCHUR_PRE_A11 (diag) is default
1442 -   userpre - matrix to use for preconditioning, or NULL
1443 
1444     Options Database:
1445 .     -pc_fieldsplit_schur_precondition <self,user,a11> default is a11
1446 
1447     Notes:
1448 $    If ptype is
1449 $        user then the preconditioner for the Schur complement is generated by the provided matrix (pre argument
1450 $             to this function).
1451 $        a11 then the preconditioner for the Schur complement is generated by the block diagonal part of the original
1452 $             matrix associated with the Schur complement (i.e. A11)
1453 $        self the preconditioner for the Schur complement is generated from the Schur complement matrix itself:
1454 $             The only preconditioner that currently works directly with the Schur complement matrix object is the PCLSC
1455 $             preconditioner
1456 
1457      When solving a saddle point problem, where the A11 block is identically zero, using a11 as the ptype only makes sense
1458     with the additional option -fieldsplit_1_pc_type none. Usually for saddle point problems one would use a ptype of self and
1459     -fieldsplit_1_pc_type lsc which uses the least squares commutator compute a preconditioner for the Schur complement.
1460 
1461     Developer Notes: This is a terrible name, gives no good indication of what the function does and should also have Set in
1462      the name since it sets a proceedure to use.
1463 
1464     Level: intermediate
1465 
1466 .seealso: PCFieldSplitGetSubKSP(), PCFIELDSPLIT, PCFieldSplitSetFields(), PCFieldSplitSchurPreType, PCLSC
1467 
1468 @*/
1469 PetscErrorCode  PCFieldSplitSchurPrecondition(PC pc,PCFieldSplitSchurPreType ptype,Mat pre)
1470 {
1471   PetscErrorCode ierr;
1472 
1473   PetscFunctionBegin;
1474   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
1475   ierr = PetscTryMethod(pc,"PCFieldSplitSchurPrecondition_C",(PC,PCFieldSplitSchurPreType,Mat),(pc,ptype,pre));CHKERRQ(ierr);
1476   PetscFunctionReturn(0);
1477 }
1478 
1479 EXTERN_C_BEGIN
1480 #undef __FUNCT__
1481 #define __FUNCT__ "PCFieldSplitSchurPrecondition_FieldSplit"
1482 PetscErrorCode  PCFieldSplitSchurPrecondition_FieldSplit(PC pc,PCFieldSplitSchurPreType ptype,Mat pre)
1483 {
1484   PC_FieldSplit  *jac = (PC_FieldSplit*)pc->data;
1485   PetscErrorCode ierr;
1486 
1487   PetscFunctionBegin;
1488   jac->schurpre = ptype;
1489   if (pre) {
1490     ierr            = MatDestroy(&jac->schur_user);CHKERRQ(ierr);
1491     jac->schur_user = pre;
1492     ierr            = PetscObjectReference((PetscObject)jac->schur_user);CHKERRQ(ierr);
1493   }
1494   PetscFunctionReturn(0);
1495 }
1496 EXTERN_C_END
1497 
1498 #undef __FUNCT__
1499 #define __FUNCT__ "PCFieldSplitSetSchurFactType"
1500 /*@
1501     PCFieldSplitSetSchurFactType -  sets which blocks of the approximate block factorization to retain
1502 
1503     Collective on PC
1504 
1505     Input Parameters:
1506 +   pc  - the preconditioner context
1507 -   ftype - which blocks of factorization to retain, PC_FIELDSPLIT_SCHUR_FACT_FULL is default
1508 
1509     Options Database:
1510 .     -pc_fieldsplit_schur_fact_type <diag,lower,upper,full> default is full
1511 
1512 
1513     Level: intermediate
1514 
1515     Notes:
1516     The FULL factorization is
1517 
1518 $   (A   B)  = (1       0) (A   0) (1  Ainv*B)
1519 $   (C   D)    (C*Ainv  1) (0   S) (0     1  )
1520 
1521     where S = D - 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,
1522     and DIAG is the diagonal part with the sign of S flipped (because this makes the preconditioner positive definite for many formulations, thus allowing the use of KSPMINRES).
1523 
1524     If applied exactly, FULL factorization is a direct solver. The preconditioned operator with LOWER or UPPER has all eigenvalues equal to 1 and minimal polynomial
1525     of degree 2, so KSPGMRES converges in 2 iterations. If the iteration count is very low, consider using KSPFGMRES or KSPGCR which can use one less preconditioner
1526     application in this case. Note that the preconditioned operator may be highly non-normal, so such fast convergence may not be observed in practice. With DIAG,
1527     the preconditioned operator has three distinct nonzero eigenvalues and minimal polynomial of degree at most 4, so KSPGMRES converges in at most 4 iterations.
1528 
1529     For symmetric problems in which A is positive definite and S is negative definite, DIAG can be used with KSPMINRES. Note that a flexible method like KSPFGMRES
1530     or KSPGCR must be used if the fieldsplit preconditioner is nonlinear (e.g. a few iterations of a Krylov method is used inside a split).
1531 
1532     References:
1533     Murphy, Golub, and Wathen, A note on preconditioning indefinite linear systems, SIAM J. Sci. Comput., 21 (2000) pp. 1969-1972.
1534 
1535     Ipsen, A note on preconditioning nonsymmetric matrices, SIAM J. Sci. Comput., 23 (2001), pp. 1050-1051.
1536 
1537 .seealso: PCFieldSplitGetSubKSP(), PCFIELDSPLIT, PCFieldSplitSetFields(), PCFieldSplitSchurPreType
1538 @*/
1539 PetscErrorCode  PCFieldSplitSetSchurFactType(PC pc,PCFieldSplitSchurFactType ftype)
1540 {
1541   PetscErrorCode ierr;
1542 
1543   PetscFunctionBegin;
1544   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
1545   ierr = PetscTryMethod(pc,"PCFieldSplitSetSchurFactType_C",(PC,PCFieldSplitSchurFactType),(pc,ftype));CHKERRQ(ierr);
1546   PetscFunctionReturn(0);
1547 }
1548 
1549 #undef __FUNCT__
1550 #define __FUNCT__ "PCFieldSplitSetSchurFactType_FieldSplit"
1551 PETSC_EXTERN_C PetscErrorCode PCFieldSplitSetSchurFactType_FieldSplit(PC pc,PCFieldSplitSchurFactType ftype)
1552 {
1553   PC_FieldSplit *jac = (PC_FieldSplit*)pc->data;
1554 
1555   PetscFunctionBegin;
1556   jac->schurfactorization = ftype;
1557   PetscFunctionReturn(0);
1558 }
1559 
1560 #undef __FUNCT__
1561 #define __FUNCT__ "PCFieldSplitGetSchurBlocks"
1562 /*@C
1563    PCFieldSplitGetSchurBlocks - Gets all matrix blocks for the Schur complement
1564 
1565    Collective on KSP
1566 
1567    Input Parameter:
1568 .  pc - the preconditioner context
1569 
1570    Output Parameters:
1571 +  A00 - the (0,0) block
1572 .  A01 - the (0,1) block
1573 .  A10 - the (1,0) block
1574 -  A11 - the (1,1) block
1575 
1576    Level: advanced
1577 
1578 .seealso: PCFIELDSPLIT
1579 @*/
1580 PetscErrorCode  PCFieldSplitGetSchurBlocks(PC pc,Mat *A00,Mat *A01,Mat *A10, Mat *A11)
1581 {
1582   PC_FieldSplit *jac = (PC_FieldSplit*) pc->data;
1583 
1584   PetscFunctionBegin;
1585   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
1586   if (jac->type != PC_COMPOSITE_SCHUR) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_ARG_WRONG, "FieldSplit is not using a Schur complement approach.");
1587   if (A00) *A00 = jac->pmat[0];
1588   if (A01) *A01 = jac->B;
1589   if (A10) *A10 = jac->C;
1590   if (A11) *A11 = jac->pmat[1];
1591   PetscFunctionReturn(0);
1592 }
1593 
1594 EXTERN_C_BEGIN
1595 #undef __FUNCT__
1596 #define __FUNCT__ "PCFieldSplitSetType_FieldSplit"
1597 PetscErrorCode  PCFieldSplitSetType_FieldSplit(PC pc,PCCompositeType type)
1598 {
1599   PC_FieldSplit  *jac = (PC_FieldSplit*)pc->data;
1600   PetscErrorCode ierr;
1601 
1602   PetscFunctionBegin;
1603   jac->type = type;
1604   if (type == PC_COMPOSITE_SCHUR) {
1605     pc->ops->apply = PCApply_FieldSplit_Schur;
1606     pc->ops->view  = PCView_FieldSplit_Schur;
1607 
1608     ierr = PetscObjectComposeFunctionDynamic((PetscObject)pc,"PCFieldSplitGetSubKSP_C","PCFieldSplitGetSubKSP_FieldSplit_Schur",PCFieldSplitGetSubKSP_FieldSplit_Schur);CHKERRQ(ierr);
1609     ierr = PetscObjectComposeFunctionDynamic((PetscObject)pc,"PCFieldSplitSchurPrecondition_C","PCFieldSplitSchurPrecondition_FieldSplit",PCFieldSplitSchurPrecondition_FieldSplit);CHKERRQ(ierr);
1610     ierr = PetscObjectComposeFunctionDynamic((PetscObject)pc,"PCFieldSplitSetSchurFactType_C","PCFieldSplitSetSchurFactType_FieldSplit",PCFieldSplitSetSchurFactType_FieldSplit);CHKERRQ(ierr);
1611 
1612   } else {
1613     pc->ops->apply = PCApply_FieldSplit;
1614     pc->ops->view  = PCView_FieldSplit;
1615 
1616     ierr = PetscObjectComposeFunctionDynamic((PetscObject)pc,"PCFieldSplitGetSubKSP_C","PCFieldSplitGetSubKSP_FieldSplit",PCFieldSplitGetSubKSP_FieldSplit);CHKERRQ(ierr);
1617     ierr = PetscObjectComposeFunctionDynamic((PetscObject)pc,"PCFieldSplitSchurPrecondition_C","",0);CHKERRQ(ierr);
1618     ierr = PetscObjectComposeFunctionDynamic((PetscObject)pc,"PCFieldSplitSetSchurFactType_C","",0);CHKERRQ(ierr);
1619   }
1620   PetscFunctionReturn(0);
1621 }
1622 EXTERN_C_END
1623 
1624 EXTERN_C_BEGIN
1625 #undef __FUNCT__
1626 #define __FUNCT__ "PCFieldSplitSetBlockSize_FieldSplit"
1627 PetscErrorCode  PCFieldSplitSetBlockSize_FieldSplit(PC pc,PetscInt bs)
1628 {
1629   PC_FieldSplit *jac = (PC_FieldSplit*)pc->data;
1630 
1631   PetscFunctionBegin;
1632   if (bs < 1) SETERRQ1(PetscObjectComm((PetscObject)pc),PETSC_ERR_ARG_OUTOFRANGE,"Blocksize must be positive, you gave %D",bs);
1633   if (jac->bs > 0 && jac->bs != bs) SETERRQ2(PetscObjectComm((PetscObject)pc),PETSC_ERR_ARG_WRONGSTATE,"Cannot change fieldsplit blocksize from %D to %D after it has been set",jac->bs,bs);
1634   jac->bs = bs;
1635   PetscFunctionReturn(0);
1636 }
1637 EXTERN_C_END
1638 
1639 #undef __FUNCT__
1640 #define __FUNCT__ "PCFieldSplitSetType"
1641 /*@
1642    PCFieldSplitSetType - Sets the type of fieldsplit preconditioner.
1643 
1644    Collective on PC
1645 
1646    Input Parameter:
1647 .  pc - the preconditioner context
1648 .  type - PC_COMPOSITE_ADDITIVE, PC_COMPOSITE_MULTIPLICATIVE (default), PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE, PC_COMPOSITE_SPECIAL, PC_COMPOSITE_SCHUR
1649 
1650    Options Database Key:
1651 .  -pc_fieldsplit_type <type: one of multiplicative, additive, symmetric_multiplicative, special, schur> - Sets fieldsplit preconditioner type
1652 
1653    Level: Intermediate
1654 
1655 .keywords: PC, set, type, composite preconditioner, additive, multiplicative
1656 
1657 .seealso: PCCompositeSetType()
1658 
1659 @*/
1660 PetscErrorCode  PCFieldSplitSetType(PC pc,PCCompositeType type)
1661 {
1662   PetscErrorCode ierr;
1663 
1664   PetscFunctionBegin;
1665   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
1666   ierr = PetscTryMethod(pc,"PCFieldSplitSetType_C",(PC,PCCompositeType),(pc,type));CHKERRQ(ierr);
1667   PetscFunctionReturn(0);
1668 }
1669 
1670 #undef __FUNCT__
1671 #define __FUNCT__ "PCFieldSplitGetType"
1672 /*@
1673   PCFieldSplitGetType - Gets the type of fieldsplit preconditioner.
1674 
1675   Not collective
1676 
1677   Input Parameter:
1678 . pc - the preconditioner context
1679 
1680   Output Parameter:
1681 . type - PC_COMPOSITE_ADDITIVE, PC_COMPOSITE_MULTIPLICATIVE (default), PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE, PC_COMPOSITE_SPECIAL, PC_COMPOSITE_SCHUR
1682 
1683   Level: Intermediate
1684 
1685 .keywords: PC, set, type, composite preconditioner, additive, multiplicative
1686 .seealso: PCCompositeSetType()
1687 @*/
1688 PetscErrorCode PCFieldSplitGetType(PC pc, PCCompositeType *type)
1689 {
1690   PC_FieldSplit *jac = (PC_FieldSplit*) pc->data;
1691 
1692   PetscFunctionBegin;
1693   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
1694   PetscValidIntPointer(type,2);
1695   *type = jac->type;
1696   PetscFunctionReturn(0);
1697 }
1698 
1699 #undef __FUNCT__
1700 #define __FUNCT__ "PCFieldSplitSetDMSplits"
1701 /*@
1702    PCFieldSplitSetDMSplits - Flags whether DMCreateFieldDecomposition() should be used to define the splits, whenever possible.
1703 
1704    Logically Collective
1705 
1706    Input Parameters:
1707 +  pc   - the preconditioner context
1708 -  flg  - boolean indicating whether to use field splits defined by the DM
1709 
1710    Options Database Key:
1711 .  -pc_fieldsplit_dm_splits
1712 
1713    Level: Intermediate
1714 
1715 .keywords: PC, DM, composite preconditioner, additive, multiplicative
1716 
1717 .seealso: PCFieldSplitGetDMSplits()
1718 
1719 @*/
1720 PetscErrorCode  PCFieldSplitSetDMSplits(PC pc,PetscBool flg)
1721 {
1722   PC_FieldSplit  *jac = (PC_FieldSplit*)pc->data;
1723   PetscBool      isfs;
1724   PetscErrorCode ierr;
1725 
1726   PetscFunctionBegin;
1727   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
1728   PetscValidLogicalCollectiveBool(pc,flg,2);
1729   ierr = PetscObjectTypeCompare((PetscObject)pc,PCFIELDSPLIT,&isfs);CHKERRQ(ierr);
1730   if (isfs) {
1731     jac->dm_splits = flg;
1732   }
1733   PetscFunctionReturn(0);
1734 }
1735 
1736 
1737 #undef __FUNCT__
1738 #define __FUNCT__ "PCFieldSplitGetDMSplits"
1739 /*@
1740    PCFieldSplitGetDMSplits - Returns flag indicating whether DMCreateFieldDecomposition() should be used to define the splits, whenever possible.
1741 
1742    Logically Collective
1743 
1744    Input Parameter:
1745 .  pc   - the preconditioner context
1746 
1747    Output Parameter:
1748 .  flg  - boolean indicating whether to use field splits defined by the DM
1749 
1750    Level: Intermediate
1751 
1752 .keywords: PC, DM, composite preconditioner, additive, multiplicative
1753 
1754 .seealso: PCFieldSplitSetDMSplits()
1755 
1756 @*/
1757 PetscErrorCode  PCFieldSplitGetDMSplits(PC pc,PetscBool* flg)
1758 {
1759   PC_FieldSplit  *jac = (PC_FieldSplit*)pc->data;
1760   PetscBool      isfs;
1761   PetscErrorCode ierr;
1762 
1763   PetscFunctionBegin;
1764   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
1765   PetscValidPointer(flg,2);
1766   ierr = PetscObjectTypeCompare((PetscObject)pc,PCFIELDSPLIT,&isfs);CHKERRQ(ierr);
1767   if (isfs) {
1768     if(flg) *flg = jac->dm_splits;
1769   }
1770   PetscFunctionReturn(0);
1771 }
1772 
1773 /* -------------------------------------------------------------------------------------*/
1774 /*MC
1775    PCFIELDSPLIT - Preconditioner created by combining separate preconditioners for individual
1776                   fields or groups of fields. See the users manual section "Solving Block Matrices" for more details.
1777 
1778      To set options on the solvers for each block append -fieldsplit_ to all the PC
1779         options database keys. For example, -fieldsplit_pc_type ilu -fieldsplit_pc_factor_levels 1
1780 
1781      To set the options on the solvers separate for each block call PCFieldSplitGetSubKSP()
1782          and set the options directly on the resulting KSP object
1783 
1784    Level: intermediate
1785 
1786    Options Database Keys:
1787 +   -pc_fieldsplit_%d_fields <a,b,..> - indicates the fields to be used in the %d'th split
1788 .   -pc_fieldsplit_default - automatically add any fields to additional splits that have not
1789                               been supplied explicitly by -pc_fieldsplit_%d_fields
1790 .   -pc_fieldsplit_block_size <bs> - size of block that defines fields (i.e. there are bs fields)
1791 .   -pc_fieldsplit_type <additive,multiplicative,symmetric_multiplicative,schur> - type of relaxation or factorization splitting
1792 .   -pc_fieldsplit_schur_precondition <self,user,a11> - default is a11
1793 .   -pc_fieldsplit_detect_saddle_point - automatically finds rows with zero or negative diagonal and uses Schur complement with no preconditioner as the solver
1794 
1795 -    Options prefix for inner solvers when using Schur complement preconditioner are -fieldsplit_0_ and -fieldsplit_1_
1796      for all other solvers they are -fieldsplit_%d_ for the dth field, use -fieldsplit_ for all fields
1797 
1798    Notes:
1799     Use PCFieldSplitSetFields() to set fields defined by "strided" entries and PCFieldSplitSetIS()
1800      to define a field by an arbitrary collection of entries.
1801 
1802       If no fields are set the default is used. The fields are defined by entries strided by bs,
1803       beginning at 0 then 1, etc to bs-1. The block size can be set with PCFieldSplitSetBlockSize(),
1804       if this is not called the block size defaults to the blocksize of the second matrix passed
1805       to KSPSetOperators()/PCSetOperators().
1806 
1807 $     For the Schur complement preconditioner if J = ( A00 A01 )
1808 $                                                    ( A10 A11 )
1809 $     the preconditioner using full factorization is
1810 $              ( I   -A10 ksp(A00) ) ( inv(A00)     0  ) (     I          0  )
1811 $              ( 0         I       ) (   0      ksp(S) ) ( -A10 ksp(A00)  I  )
1812      where the action of inv(A00) is applied using the KSP solver with prefix -fieldsplit_0_. The action of
1813      ksp(S) is computed using the KSP solver with prefix -fieldsplit_splitname_ (where splitname was given
1814      in providing the SECOND split or 1 if not give). For PCFieldSplitGetKSP() when field number is 0,
1815      it returns the KSP associated with -fieldsplit_0_ while field number 1 gives -fieldsplit_1_ KSP. By default
1816      A11 is used to construct a preconditioner for S, use PCFieldSplitSchurPrecondition() to turn on or off this
1817      option. You can use the preconditioner PCLSC to precondition the Schur complement with -fieldsplit_1_pc_type lsc. The
1818      factorization type is set using -pc_fieldsplit_schur_fact_type <diag, lower, upper, full>. The full is shown above,
1819      diag gives
1820 $              ( inv(A00)     0   )
1821 $              (   0      -ksp(S) )
1822      note that slightly counter intuitively there is a negative in front of the ksp(S) so that the preconditioner is positive definite. The lower factorization is the inverse of
1823 $              (  A00   0 )
1824 $              (  A10   S )
1825      where the inverses of A00 and S are applied using KSPs. The upper factorization is the inverse of
1826 $              ( A00 A01 )
1827 $              (  0   S  )
1828      where again the inverses of A00 and S are applied using KSPs.
1829 
1830      If only one set of indices (one IS) is provided with PCFieldSplitSetIS() then the complement of that IS
1831      is used automatically for a second block.
1832 
1833      The fieldsplit preconditioner cannot currently be used with the BAIJ or SBAIJ data formats if the blocksize is larger than 1.
1834      Generally it should be used with the AIJ format.
1835 
1836      The forms of these preconditioners are closely related if not identical to forms derived as "Distributive Iterations", see,
1837      for example, page 294 in "Principles of Computational Fluid Dynamics" by Pieter Wesseling. Note that one can also use PCFIELDSPLIT
1838      inside a smoother resulting in "Distributive Smoothers".
1839 
1840    Concepts: physics based preconditioners, block preconditioners
1841 
1842 .seealso:  PCCreate(), PCSetType(), PCType (for list of available types), PC, Block_Preconditioners, PCLSC,
1843            PCFieldSplitGetSubKSP(), PCFieldSplitSetFields(), PCFieldSplitSetType(), PCFieldSplitSetIS(), PCFieldSplitSchurPrecondition()
1844 M*/
1845 
1846 EXTERN_C_BEGIN
1847 #undef __FUNCT__
1848 #define __FUNCT__ "PCCreate_FieldSplit"
1849 PetscErrorCode  PCCreate_FieldSplit(PC pc)
1850 {
1851   PetscErrorCode ierr;
1852   PC_FieldSplit  *jac;
1853 
1854   PetscFunctionBegin;
1855   ierr = PetscNewLog(pc,PC_FieldSplit,&jac);CHKERRQ(ierr);
1856 
1857   jac->bs                 = -1;
1858   jac->nsplits            = 0;
1859   jac->type               = PC_COMPOSITE_MULTIPLICATIVE;
1860   jac->schurpre           = PC_FIELDSPLIT_SCHUR_PRE_USER; /* Try user preconditioner first, fall back on diagonal */
1861   jac->schurfactorization = PC_FIELDSPLIT_SCHUR_FACT_FULL;
1862   jac->dm_splits          = PETSC_FALSE;
1863 
1864   pc->data = (void*)jac;
1865 
1866   pc->ops->apply           = PCApply_FieldSplit;
1867   pc->ops->applytranspose  = PCApplyTranspose_FieldSplit;
1868   pc->ops->setup           = PCSetUp_FieldSplit;
1869   pc->ops->reset           = PCReset_FieldSplit;
1870   pc->ops->destroy         = PCDestroy_FieldSplit;
1871   pc->ops->setfromoptions  = PCSetFromOptions_FieldSplit;
1872   pc->ops->view            = PCView_FieldSplit;
1873   pc->ops->applyrichardson = 0;
1874 
1875   ierr = PetscObjectComposeFunctionDynamic((PetscObject)pc,"PCFieldSplitGetSubKSP_C","PCFieldSplitGetSubKSP_FieldSplit",
1876                                            PCFieldSplitGetSubKSP_FieldSplit);CHKERRQ(ierr);
1877   ierr = PetscObjectComposeFunctionDynamic((PetscObject)pc,"PCFieldSplitSetFields_C","PCFieldSplitSetFields_FieldSplit",
1878                                            PCFieldSplitSetFields_FieldSplit);CHKERRQ(ierr);
1879   ierr = PetscObjectComposeFunctionDynamic((PetscObject)pc,"PCFieldSplitSetIS_C","PCFieldSplitSetIS_FieldSplit",
1880                                            PCFieldSplitSetIS_FieldSplit);CHKERRQ(ierr);
1881   ierr = PetscObjectComposeFunctionDynamic((PetscObject)pc,"PCFieldSplitSetType_C","PCFieldSplitSetType_FieldSplit",
1882                                            PCFieldSplitSetType_FieldSplit);CHKERRQ(ierr);
1883   ierr = PetscObjectComposeFunctionDynamic((PetscObject)pc,"PCFieldSplitSetBlockSize_C","PCFieldSplitSetBlockSize_FieldSplit",
1884                                            PCFieldSplitSetBlockSize_FieldSplit);CHKERRQ(ierr);
1885   PetscFunctionReturn(0);
1886 }
1887 EXTERN_C_END
1888 
1889 
1890 
1891