xref: /petsc/src/ksp/pc/impls/fieldsplit/fieldsplit.c (revision be95d8f1844f2f8de343ad9c31bb253bac1e0696) !
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","SELFP","A11","USER","FULL","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   PetscInt        bs;                              /* Block size for IS and Mat structures */
33   PetscInt        nsplits;                         /* Number of field divisions defined */
34   Vec             *x,*y,w1,w2;
35   Mat             *mat;                            /* The diagonal block for each split */
36   Mat             *pmat;                           /* The preconditioning diagonal block for each split */
37   Mat             *Afield;                         /* The rows of the matrix associated with each split */
38   PetscBool       issetup;
39 
40   /* Only used when Schur complement preconditioning is used */
41   Mat                       B;                     /* The (0,1) block */
42   Mat                       C;                     /* The (1,0) block */
43   Mat                       schur;                 /* The Schur complement S = A11 - A10 A00^{-1} A01, the KSP here, kspinner, is H_1 in [El08] */
44   Mat                       schurp;                /* Assembled approximation to S built by MatSchurComplement to be used as a preconditioning matrix when solving with S */
45   Mat                       schur_user;            /* User-provided preconditioning matrix for the Schur complement */
46   PCFieldSplitSchurPreType  schurpre;              /* Determines which preconditioning matrix is used for the Schur complement */
47   PCFieldSplitSchurFactType schurfactorization;
48   KSP                       kspschur;              /* The solver for S */
49   KSP                       kspupper;              /* The solver for A in the upper diagonal part of the factorization (H_2 in [El08]) */
50   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_SELFP: return jac->schurp;
69   case PC_FIELDSPLIT_SCHUR_PRE_A11: return jac->pmat[1];
70   case PC_FIELDSPLIT_SCHUR_PRE_FULL: /* We calculate this and store it in schur_user */
71   case PC_FIELDSPLIT_SCHUR_PRE_USER: /* Use a user-provided matrix if it is given, otherwise diagonal block */
72   default:
73     return jac->schur_user ? jac->schur_user : jac->pmat[1];
74   }
75 }
76 
77 
78 #include <petscdraw.h>
79 #undef __FUNCT__
80 #define __FUNCT__ "PCView_FieldSplit"
81 static PetscErrorCode PCView_FieldSplit(PC pc,PetscViewer viewer)
82 {
83   PC_FieldSplit     *jac = (PC_FieldSplit*)pc->data;
84   PetscErrorCode    ierr;
85   PetscBool         iascii,isdraw;
86   PetscInt          i,j;
87   PC_FieldSplitLink ilink = jac->head;
88 
89   PetscFunctionBegin;
90   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);CHKERRQ(ierr);
91   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERDRAW,&isdraw);CHKERRQ(ierr);
92   if (iascii) {
93     if (jac->bs > 0) {
94       ierr = PetscViewerASCIIPrintf(viewer,"  FieldSplit with %s composition: total splits = %D, blocksize = %D\n",PCCompositeTypes[jac->type],jac->nsplits,jac->bs);CHKERRQ(ierr);
95     } else {
96       ierr = PetscViewerASCIIPrintf(viewer,"  FieldSplit with %s composition: total splits = %D\n",PCCompositeTypes[jac->type],jac->nsplits);CHKERRQ(ierr);
97     }
98     if (pc->useAmat) {
99       ierr = PetscViewerASCIIPrintf(viewer,"  using Amat (not Pmat) as operator for blocks\n");CHKERRQ(ierr);
100     }
101     ierr = PetscViewerASCIIPrintf(viewer,"  Solver info for each split is in the following KSP objects:\n");CHKERRQ(ierr);
102     ierr = PetscViewerASCIIPushTab(viewer);CHKERRQ(ierr);
103     for (i=0; i<jac->nsplits; i++) {
104       if (ilink->fields) {
105         ierr = PetscViewerASCIIPrintf(viewer,"Split number %D Fields ",i);CHKERRQ(ierr);
106         ierr = PetscViewerASCIIUseTabs(viewer,PETSC_FALSE);CHKERRQ(ierr);
107         for (j=0; j<ilink->nfields; j++) {
108           if (j > 0) {
109             ierr = PetscViewerASCIIPrintf(viewer,",");CHKERRQ(ierr);
110           }
111           ierr = PetscViewerASCIIPrintf(viewer," %D",ilink->fields[j]);CHKERRQ(ierr);
112         }
113         ierr = PetscViewerASCIIPrintf(viewer,"\n");CHKERRQ(ierr);
114         ierr = PetscViewerASCIIUseTabs(viewer,PETSC_TRUE);CHKERRQ(ierr);
115       } else {
116         ierr = PetscViewerASCIIPrintf(viewer,"Split number %D Defined by IS\n",i);CHKERRQ(ierr);
117       }
118       ierr  = KSPView(ilink->ksp,viewer);CHKERRQ(ierr);
119       ilink = ilink->next;
120     }
121     ierr = PetscViewerASCIIPopTab(viewer);CHKERRQ(ierr);
122   }
123 
124  if (isdraw) {
125     PetscDraw draw;
126     PetscReal x,y,w,wd;
127 
128     ierr = PetscViewerDrawGetDraw(viewer,0,&draw);CHKERRQ(ierr);
129     ierr = PetscDrawGetCurrentPoint(draw,&x,&y);CHKERRQ(ierr);
130     w    = 2*PetscMin(1.0 - x,x);
131     wd   = w/(jac->nsplits + 1);
132     x    = x - wd*(jac->nsplits-1)/2.0;
133     for (i=0; i<jac->nsplits; i++) {
134       ierr  = PetscDrawPushCurrentPoint(draw,x,y);CHKERRQ(ierr);
135       ierr  = KSPView(ilink->ksp,viewer);CHKERRQ(ierr);
136       ierr  = PetscDrawPopCurrentPoint(draw);CHKERRQ(ierr);
137       x    += wd;
138       ilink = ilink->next;
139     }
140   }
141   PetscFunctionReturn(0);
142 }
143 
144 #undef __FUNCT__
145 #define __FUNCT__ "PCView_FieldSplit_Schur"
146 static PetscErrorCode PCView_FieldSplit_Schur(PC pc,PetscViewer viewer)
147 {
148   PC_FieldSplit     *jac = (PC_FieldSplit*)pc->data;
149   PetscErrorCode    ierr;
150   PetscBool         iascii,isdraw;
151   PetscInt          i,j;
152   PC_FieldSplitLink ilink = jac->head;
153 
154   PetscFunctionBegin;
155   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);CHKERRQ(ierr);
156   ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERDRAW,&isdraw);CHKERRQ(ierr);
157   if (iascii) {
158     if (jac->bs > 0) {
159       ierr = PetscViewerASCIIPrintf(viewer,"  FieldSplit with Schur preconditioner, blocksize = %D, factorization %s\n",jac->bs,PCFieldSplitSchurFactTypes[jac->schurfactorization]);CHKERRQ(ierr);
160     } else {
161       ierr = PetscViewerASCIIPrintf(viewer,"  FieldSplit with Schur preconditioner, factorization %s\n",PCFieldSplitSchurFactTypes[jac->schurfactorization]);CHKERRQ(ierr);
162     }
163     if (pc->useAmat) {
164       ierr = PetscViewerASCIIPrintf(viewer,"  using Amat (not Pmat) as operator for blocks\n");CHKERRQ(ierr);
165     }
166     switch (jac->schurpre) {
167     case PC_FIELDSPLIT_SCHUR_PRE_SELF:
168       ierr = PetscViewerASCIIPrintf(viewer,"  Preconditioner for the Schur complement formed from S itself\n");CHKERRQ(ierr);break;
169     case PC_FIELDSPLIT_SCHUR_PRE_SELFP:
170       ierr = PetscViewerASCIIPrintf(viewer,"  Preconditioner for the Schur complement formed from Sp, an assembled approximation to S, which uses A00's diagonal's inverse\n");CHKERRQ(ierr);break;
171     case PC_FIELDSPLIT_SCHUR_PRE_A11:
172       ierr = PetscViewerASCIIPrintf(viewer,"  Preconditioner for the Schur complement formed from A11\n");CHKERRQ(ierr);break;
173     case PC_FIELDSPLIT_SCHUR_PRE_FULL:
174       ierr = PetscViewerASCIIPrintf(viewer,"  Preconditioner for the Schur complement formed from the exact Schur complement\n");CHKERRQ(ierr);break;
175     case PC_FIELDSPLIT_SCHUR_PRE_USER:
176       if (jac->schur_user) {
177         ierr = PetscViewerASCIIPrintf(viewer,"  Preconditioner for the Schur complement formed from user provided matrix\n");CHKERRQ(ierr);
178       } else {
179         ierr = PetscViewerASCIIPrintf(viewer,"  Preconditioner for the Schur complement formed from A11\n");CHKERRQ(ierr);
180       }
181       break;
182     default:
183       SETERRQ1(PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_OUTOFRANGE, "Invalid Schur preconditioning type: %d", jac->schurpre);
184     }
185     ierr = PetscViewerASCIIPrintf(viewer,"  Split info:\n");CHKERRQ(ierr);
186     ierr = PetscViewerASCIIPushTab(viewer);CHKERRQ(ierr);
187     for (i=0; i<jac->nsplits; i++) {
188       if (ilink->fields) {
189         ierr = PetscViewerASCIIPrintf(viewer,"Split number %D Fields ",i);CHKERRQ(ierr);
190         ierr = PetscViewerASCIIUseTabs(viewer,PETSC_FALSE);CHKERRQ(ierr);
191         for (j=0; j<ilink->nfields; j++) {
192           if (j > 0) {
193             ierr = PetscViewerASCIIPrintf(viewer,",");CHKERRQ(ierr);
194           }
195           ierr = PetscViewerASCIIPrintf(viewer," %D",ilink->fields[j]);CHKERRQ(ierr);
196         }
197         ierr = PetscViewerASCIIPrintf(viewer,"\n");CHKERRQ(ierr);
198         ierr = PetscViewerASCIIUseTabs(viewer,PETSC_TRUE);CHKERRQ(ierr);
199       } else {
200         ierr = PetscViewerASCIIPrintf(viewer,"Split number %D Defined by IS\n",i);CHKERRQ(ierr);
201       }
202       ilink = ilink->next;
203     }
204     ierr = PetscViewerASCIIPrintf(viewer,"KSP solver for A00 block\n");CHKERRQ(ierr);
205     ierr = PetscViewerASCIIPushTab(viewer);CHKERRQ(ierr);
206     if (jac->head) {
207       ierr = KSPView(jac->head->ksp,viewer);CHKERRQ(ierr);
208     } else  {ierr = PetscViewerASCIIPrintf(viewer,"  not yet available\n");CHKERRQ(ierr);}
209     ierr = PetscViewerASCIIPopTab(viewer);CHKERRQ(ierr);
210     if (jac->head && jac->kspupper != jac->head->ksp) {
211       ierr = PetscViewerASCIIPrintf(viewer,"KSP solver for upper A00 in upper triangular factor \n");CHKERRQ(ierr);
212       ierr = PetscViewerASCIIPushTab(viewer);CHKERRQ(ierr);
213       if (jac->kspupper) {ierr = KSPView(jac->kspupper,viewer);CHKERRQ(ierr);}
214       else {ierr = PetscViewerASCIIPrintf(viewer,"  not yet available\n");CHKERRQ(ierr);}
215       ierr = PetscViewerASCIIPopTab(viewer);CHKERRQ(ierr);
216     }
217     ierr = PetscViewerASCIIPrintf(viewer,"KSP solver for S = A11 - A10 inv(A00) A01 \n");CHKERRQ(ierr);
218     ierr = PetscViewerASCIIPushTab(viewer);CHKERRQ(ierr);
219     if (jac->kspschur) {
220       ierr = KSPView(jac->kspschur,viewer);CHKERRQ(ierr);
221     } else {
222       ierr = PetscViewerASCIIPrintf(viewer,"  not yet available\n");CHKERRQ(ierr);
223     }
224     ierr = PetscViewerASCIIPopTab(viewer);CHKERRQ(ierr);
225     ierr = PetscViewerASCIIPopTab(viewer);CHKERRQ(ierr);
226   } else if (isdraw && jac->head) {
227     PetscDraw draw;
228     PetscReal x,y,w,wd,h;
229     PetscInt  cnt = 2;
230     char      str[32];
231 
232     ierr = PetscViewerDrawGetDraw(viewer,0,&draw);CHKERRQ(ierr);
233     ierr = PetscDrawGetCurrentPoint(draw,&x,&y);CHKERRQ(ierr);
234     if (jac->kspupper != jac->head->ksp) cnt++;
235     w  = 2*PetscMin(1.0 - x,x);
236     wd = w/(cnt + 1);
237 
238     ierr = PetscSNPrintf(str,32,"Schur fact. %s",PCFieldSplitSchurFactTypes[jac->schurfactorization]);CHKERRQ(ierr);
239     ierr = PetscDrawBoxedString(draw,x,y,PETSC_DRAW_RED,PETSC_DRAW_BLACK,str,NULL,&h);CHKERRQ(ierr);
240     y   -= h;
241     if (jac->schurpre == PC_FIELDSPLIT_SCHUR_PRE_USER &&  !jac->schur_user) {
242       ierr = PetscSNPrintf(str,32,"Prec. for Schur from %s",PCFieldSplitSchurPreTypes[PC_FIELDSPLIT_SCHUR_PRE_A11]);CHKERRQ(ierr);
243     } else {
244       ierr = PetscSNPrintf(str,32,"Prec. for Schur from %s",PCFieldSplitSchurPreTypes[jac->schurpre]);CHKERRQ(ierr);
245     }
246     ierr = PetscDrawBoxedString(draw,x+wd*(cnt-1)/2.0,y,PETSC_DRAW_RED,PETSC_DRAW_BLACK,str,NULL,&h);CHKERRQ(ierr);
247     y   -= h;
248     x    = x - wd*(cnt-1)/2.0;
249 
250     ierr = PetscDrawPushCurrentPoint(draw,x,y);CHKERRQ(ierr);
251     ierr = KSPView(jac->head->ksp,viewer);CHKERRQ(ierr);
252     ierr = PetscDrawPopCurrentPoint(draw);CHKERRQ(ierr);
253     if (jac->kspupper != jac->head->ksp) {
254       x   += wd;
255       ierr = PetscDrawPushCurrentPoint(draw,x,y);CHKERRQ(ierr);
256       ierr = KSPView(jac->kspupper,viewer);CHKERRQ(ierr);
257       ierr = PetscDrawPopCurrentPoint(draw);CHKERRQ(ierr);
258     }
259     x   += wd;
260     ierr = PetscDrawPushCurrentPoint(draw,x,y);CHKERRQ(ierr);
261     ierr = KSPView(jac->kspschur,viewer);CHKERRQ(ierr);
262     ierr = PetscDrawPopCurrentPoint(draw);CHKERRQ(ierr);
263   }
264   PetscFunctionReturn(0);
265 }
266 
267 #undef __FUNCT__
268 #define __FUNCT__ "PCFieldSplitSetRuntimeSplits_Private"
269 /* Precondition: jac->bs is set to a meaningful value */
270 static PetscErrorCode PCFieldSplitSetRuntimeSplits_Private(PC pc)
271 {
272   PetscErrorCode ierr;
273   PC_FieldSplit  *jac = (PC_FieldSplit*)pc->data;
274   PetscInt       i,nfields,*ifields,nfields_col,*ifields_col;
275   PetscBool      flg,flg_col;
276   char           optionname[128],splitname[8],optionname_col[128];
277 
278   PetscFunctionBegin;
279   ierr = PetscMalloc1(jac->bs,&ifields);CHKERRQ(ierr);
280   ierr = PetscMalloc1(jac->bs,&ifields_col);CHKERRQ(ierr);
281   for (i=0,flg=PETSC_TRUE;; i++) {
282     ierr        = PetscSNPrintf(splitname,sizeof(splitname),"%D",i);CHKERRQ(ierr);
283     ierr        = PetscSNPrintf(optionname,sizeof(optionname),"-pc_fieldsplit_%D_fields",i);CHKERRQ(ierr);
284     ierr        = PetscSNPrintf(optionname_col,sizeof(optionname_col),"-pc_fieldsplit_%D_fields_col",i);CHKERRQ(ierr);
285     nfields     = jac->bs;
286     nfields_col = jac->bs;
287     ierr        = PetscOptionsGetIntArray(((PetscObject)pc)->prefix,optionname,ifields,&nfields,&flg);CHKERRQ(ierr);
288     ierr        = PetscOptionsGetIntArray(((PetscObject)pc)->prefix,optionname_col,ifields_col,&nfields_col,&flg_col);CHKERRQ(ierr);
289     if (!flg) break;
290     else if (flg && !flg_col) {
291       if (!nfields) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_USER,"Cannot list zero fields");
292       ierr = PCFieldSplitSetFields(pc,splitname,nfields,ifields,ifields);CHKERRQ(ierr);
293     } else {
294       if (!nfields || !nfields_col) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_USER,"Cannot list zero fields");
295       if (nfields != nfields_col) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_USER,"Number of row and column fields must match");
296       ierr = PCFieldSplitSetFields(pc,splitname,nfields,ifields,ifields_col);CHKERRQ(ierr);
297     }
298   }
299   if (i > 0) {
300     /* Makes command-line setting of splits take precedence over setting them in code.
301        Otherwise subsequent calls to PCFieldSplitSetIS() or PCFieldSplitSetFields() would
302        create new splits, which would probably not be what the user wanted. */
303     jac->splitdefined = PETSC_TRUE;
304   }
305   ierr = PetscFree(ifields);CHKERRQ(ierr);
306   ierr = PetscFree(ifields_col);CHKERRQ(ierr);
307   PetscFunctionReturn(0);
308 }
309 
310 #undef __FUNCT__
311 #define __FUNCT__ "PCFieldSplitSetDefaults"
312 static PetscErrorCode PCFieldSplitSetDefaults(PC pc)
313 {
314   PC_FieldSplit     *jac = (PC_FieldSplit*)pc->data;
315   PetscErrorCode    ierr;
316   PC_FieldSplitLink ilink              = jac->head;
317   PetscBool         fieldsplit_default = PETSC_FALSE,stokes = PETSC_FALSE,coupling = PETSC_FALSE;
318   PetscInt          i;
319 
320   PetscFunctionBegin;
321   /*
322    Kinda messy, but at least this now uses DMCreateFieldDecomposition() even with jac->reset.
323    Should probably be rewritten.
324    */
325   if (!ilink || jac->reset) {
326     ierr = PetscOptionsGetBool(((PetscObject)pc)->prefix,"-pc_fieldsplit_detect_saddle_point",&stokes,NULL);CHKERRQ(ierr);
327     ierr = PetscOptionsGetBool(((PetscObject)pc)->prefix,"-pc_fieldsplit_detect_coupling",&coupling,NULL);CHKERRQ(ierr);
328     if (pc->dm && jac->dm_splits && !stokes && !coupling) {
329       PetscInt  numFields, f, i, j;
330       char      **fieldNames;
331       IS        *fields;
332       DM        *dms;
333       DM        subdm[128];
334       PetscBool flg;
335 
336       ierr = DMCreateFieldDecomposition(pc->dm, &numFields, &fieldNames, &fields, &dms);CHKERRQ(ierr);
337       /* Allow the user to prescribe the splits */
338       for (i = 0, flg = PETSC_TRUE;; i++) {
339         PetscInt ifields[128];
340         IS       compField;
341         char     optionname[128], splitname[8];
342         PetscInt nfields = numFields;
343 
344         ierr = PetscSNPrintf(optionname, sizeof(optionname), "-pc_fieldsplit_%D_fields", i);CHKERRQ(ierr);
345         ierr = PetscOptionsGetIntArray(((PetscObject) pc)->prefix, optionname, ifields, &nfields, &flg);CHKERRQ(ierr);
346         if (!flg) break;
347         if (numFields > 128) SETERRQ1(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"Cannot currently support %d > 128 fields", numFields);
348         ierr = DMCreateSubDM(pc->dm, nfields, ifields, &compField, &subdm[i]);CHKERRQ(ierr);
349         if (nfields == 1) {
350           ierr = PCFieldSplitSetIS(pc, fieldNames[ifields[0]], compField);CHKERRQ(ierr);
351           /* ierr = PetscPrintf(PetscObjectComm((PetscObject)pc), "%s Field Indices:", fieldNames[ifields[0]]);CHKERRQ(ierr);
352              ierr = ISView(compField, NULL);CHKERRQ(ierr); */
353         } else {
354           ierr = PetscSNPrintf(splitname, sizeof(splitname), "%D", i);CHKERRQ(ierr);
355           ierr = PCFieldSplitSetIS(pc, splitname, compField);CHKERRQ(ierr);
356           /* ierr = PetscPrintf(PetscObjectComm((PetscObject)pc), "%s Field Indices:", splitname);CHKERRQ(ierr);
357              ierr = ISView(compField, NULL);CHKERRQ(ierr); */
358         }
359         ierr = ISDestroy(&compField);CHKERRQ(ierr);
360         for (j = 0; j < nfields; ++j) {
361           f    = ifields[j];
362           ierr = PetscFree(fieldNames[f]);CHKERRQ(ierr);
363           ierr = ISDestroy(&fields[f]);CHKERRQ(ierr);
364         }
365       }
366       if (i == 0) {
367         for (f = 0; f < numFields; ++f) {
368           ierr = PCFieldSplitSetIS(pc, fieldNames[f], fields[f]);CHKERRQ(ierr);
369           ierr = PetscFree(fieldNames[f]);CHKERRQ(ierr);
370           ierr = ISDestroy(&fields[f]);CHKERRQ(ierr);
371         }
372       } else {
373         for (j=0; j<numFields; j++) {
374           ierr = DMDestroy(dms+j);CHKERRQ(ierr);
375         }
376         ierr = PetscFree(dms);CHKERRQ(ierr);
377         ierr = PetscMalloc1(i, &dms);CHKERRQ(ierr);
378         for (j = 0; j < i; ++j) dms[j] = subdm[j];
379       }
380       ierr = PetscFree(fieldNames);CHKERRQ(ierr);
381       ierr = PetscFree(fields);CHKERRQ(ierr);
382       if (dms) {
383         ierr = PetscInfo(pc, "Setting up physics based fieldsplit preconditioner using the embedded DM\n");CHKERRQ(ierr);
384         for (ilink = jac->head, i = 0; ilink; ilink = ilink->next, ++i) {
385           const char *prefix;
386           ierr = PetscObjectGetOptionsPrefix((PetscObject)(ilink->ksp),&prefix);CHKERRQ(ierr);
387           ierr = PetscObjectSetOptionsPrefix((PetscObject)(dms[i]), prefix);CHKERRQ(ierr);
388           ierr = KSPSetDM(ilink->ksp, dms[i]);CHKERRQ(ierr);
389           ierr = KSPSetDMActive(ilink->ksp, PETSC_FALSE);CHKERRQ(ierr);
390           ierr = PetscObjectIncrementTabLevel((PetscObject)dms[i],(PetscObject)ilink->ksp,0);CHKERRQ(ierr);
391           ierr = DMDestroy(&dms[i]);CHKERRQ(ierr);
392         }
393         ierr = PetscFree(dms);CHKERRQ(ierr);
394       }
395     } else {
396       if (jac->bs <= 0) {
397         if (pc->pmat) {
398           ierr = MatGetBlockSize(pc->pmat,&jac->bs);CHKERRQ(ierr);
399         } else jac->bs = 1;
400       }
401 
402       if (stokes) {
403         IS       zerodiags,rest;
404         PetscInt nmin,nmax;
405 
406         ierr = MatGetOwnershipRange(pc->mat,&nmin,&nmax);CHKERRQ(ierr);
407         ierr = MatFindZeroDiagonals(pc->mat,&zerodiags);CHKERRQ(ierr);
408         ierr = ISComplement(zerodiags,nmin,nmax,&rest);CHKERRQ(ierr);
409         if (jac->reset) {
410           jac->head->is       = rest;
411           jac->head->next->is = zerodiags;
412         } else {
413           ierr = PCFieldSplitSetIS(pc,"0",rest);CHKERRQ(ierr);
414           ierr = PCFieldSplitSetIS(pc,"1",zerodiags);CHKERRQ(ierr);
415         }
416         ierr = ISDestroy(&zerodiags);CHKERRQ(ierr);
417         ierr = ISDestroy(&rest);CHKERRQ(ierr);
418       } else if (coupling) {
419         IS       coupling,rest;
420         PetscInt nmin,nmax;
421 
422         ierr = MatGetOwnershipRange(pc->mat,&nmin,&nmax);CHKERRQ(ierr);
423         ierr = MatFindOffBlockDiagonalEntries(pc->mat,&coupling);CHKERRQ(ierr);
424         ierr = ISCreateStride(PetscObjectComm((PetscObject)pc->mat),nmax-nmin,nmin,1,&rest);CHKERRQ(ierr);
425         if (jac->reset) {
426           jac->head->is       = coupling;
427           jac->head->next->is = rest;
428         } else {
429           ierr = PCFieldSplitSetIS(pc,"0",coupling);CHKERRQ(ierr);
430           ierr = PCFieldSplitSetIS(pc,"1",rest);CHKERRQ(ierr);
431         }
432         ierr = ISDestroy(&coupling);CHKERRQ(ierr);
433         ierr = ISDestroy(&rest);CHKERRQ(ierr);
434       } else {
435         if (jac->reset) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"Cases not yet handled when PCReset() was used");
436         ierr = PetscOptionsGetBool(((PetscObject)pc)->prefix,"-pc_fieldsplit_default",&fieldsplit_default,NULL);CHKERRQ(ierr);
437         if (!fieldsplit_default) {
438           /* Allow user to set fields from command line,  if bs was known at the time of PCSetFromOptions_FieldSplit()
439            then it is set there. This is not ideal because we should only have options set in XXSetFromOptions(). */
440           ierr = PCFieldSplitSetRuntimeSplits_Private(pc);CHKERRQ(ierr);
441           if (jac->splitdefined) {ierr = PetscInfo(pc,"Splits defined using the options database\n");CHKERRQ(ierr);}
442         }
443         if (fieldsplit_default || !jac->splitdefined) {
444           ierr = PetscInfo(pc,"Using default splitting of fields\n");CHKERRQ(ierr);
445           for (i=0; i<jac->bs; i++) {
446             char splitname[8];
447             ierr = PetscSNPrintf(splitname,sizeof(splitname),"%D",i);CHKERRQ(ierr);
448             ierr = PCFieldSplitSetFields(pc,splitname,1,&i,&i);CHKERRQ(ierr);
449           }
450           jac->defaultsplit = PETSC_TRUE;
451         }
452       }
453     }
454   } else if (jac->nsplits == 1) {
455     if (ilink->is) {
456       IS       is2;
457       PetscInt nmin,nmax;
458 
459       ierr = MatGetOwnershipRange(pc->mat,&nmin,&nmax);CHKERRQ(ierr);
460       ierr = ISComplement(ilink->is,nmin,nmax,&is2);CHKERRQ(ierr);
461       ierr = PCFieldSplitSetIS(pc,"1",is2);CHKERRQ(ierr);
462       ierr = ISDestroy(&is2);CHKERRQ(ierr);
463     } else SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"Must provide at least two sets of fields to PCFieldSplit()");
464   }
465 
466 
467   if (jac->nsplits < 2) SETERRQ1(PetscObjectComm((PetscObject)pc),PETSC_ERR_PLIB,"Unhandled case, must have at least two fields, not %d", jac->nsplits);
468   PetscFunctionReturn(0);
469 }
470 
471 PETSC_EXTERN PetscErrorCode PetscOptionsFindPairPrefix_Private(const char pre[], const char name[], char *value[], PetscBool *flg);
472 
473 #undef __FUNCT__
474 #define __FUNCT__ "PCSetUp_FieldSplit"
475 static PetscErrorCode PCSetUp_FieldSplit(PC pc)
476 {
477   PC_FieldSplit     *jac = (PC_FieldSplit*)pc->data;
478   PetscErrorCode    ierr;
479   PC_FieldSplitLink ilink;
480   PetscInt          i,nsplit;
481   MatStructure      flag = pc->flag;
482   PetscBool         sorted, sorted_col;
483 
484   PetscFunctionBegin;
485   ierr   = PCFieldSplitSetDefaults(pc);CHKERRQ(ierr);
486   nsplit = jac->nsplits;
487   ilink  = jac->head;
488 
489   /* get the matrices for each split */
490   if (!jac->issetup) {
491     PetscInt rstart,rend,nslots,bs;
492 
493     jac->issetup = PETSC_TRUE;
494 
495     /* This is done here instead of in PCFieldSplitSetFields() because may not have matrix at that point */
496     if (jac->defaultsplit || !ilink->is) {
497       if (jac->bs <= 0) jac->bs = nsplit;
498     }
499     bs     = jac->bs;
500     ierr   = MatGetOwnershipRange(pc->pmat,&rstart,&rend);CHKERRQ(ierr);
501     nslots = (rend - rstart)/bs;
502     for (i=0; i<nsplit; i++) {
503       if (jac->defaultsplit) {
504         ierr = ISCreateStride(PetscObjectComm((PetscObject)pc),nslots,rstart+i,nsplit,&ilink->is);CHKERRQ(ierr);
505         ierr = ISDuplicate(ilink->is,&ilink->is_col);CHKERRQ(ierr);
506       } else if (!ilink->is) {
507         if (ilink->nfields > 1) {
508           PetscInt *ii,*jj,j,k,nfields = ilink->nfields,*fields = ilink->fields,*fields_col = ilink->fields_col;
509           ierr = PetscMalloc1(ilink->nfields*nslots,&ii);CHKERRQ(ierr);
510           ierr = PetscMalloc1(ilink->nfields*nslots,&jj);CHKERRQ(ierr);
511           for (j=0; j<nslots; j++) {
512             for (k=0; k<nfields; k++) {
513               ii[nfields*j + k] = rstart + bs*j + fields[k];
514               jj[nfields*j + k] = rstart + bs*j + fields_col[k];
515             }
516           }
517           ierr = ISCreateGeneral(PetscObjectComm((PetscObject)pc),nslots*nfields,ii,PETSC_OWN_POINTER,&ilink->is);CHKERRQ(ierr);
518           ierr = ISCreateGeneral(PetscObjectComm((PetscObject)pc),nslots*nfields,jj,PETSC_OWN_POINTER,&ilink->is_col);CHKERRQ(ierr);
519         } else {
520           ierr = ISCreateStride(PetscObjectComm((PetscObject)pc),nslots,rstart+ilink->fields[0],bs,&ilink->is);CHKERRQ(ierr);
521           ierr = ISCreateStride(PetscObjectComm((PetscObject)pc),nslots,rstart+ilink->fields_col[0],bs,&ilink->is_col);CHKERRQ(ierr);
522        }
523       }
524       ierr = ISSorted(ilink->is,&sorted);CHKERRQ(ierr);
525       if (ilink->is_col) { ierr = ISSorted(ilink->is_col,&sorted_col);CHKERRQ(ierr); }
526       if (!sorted || !sorted_col) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_USER,"Fields must be sorted when creating split");
527       ilink = ilink->next;
528     }
529   }
530 
531   ilink = jac->head;
532   if (!jac->pmat) {
533     Vec xtmp;
534 
535     ierr = MatGetVecs(pc->pmat,&xtmp,NULL);CHKERRQ(ierr);
536     ierr = PetscMalloc1(nsplit,&jac->pmat);CHKERRQ(ierr);
537     ierr = PetscMalloc2(nsplit,&jac->x,nsplit,&jac->y);CHKERRQ(ierr);
538     for (i=0; i<nsplit; i++) {
539       MatNullSpace sp;
540 
541       /* Check for preconditioning matrix attached to IS */
542       ierr = PetscObjectQuery((PetscObject) ilink->is, "pmat", (PetscObject*) &jac->pmat[i]);CHKERRQ(ierr);
543       if (jac->pmat[i]) {
544         ierr = PetscObjectReference((PetscObject) jac->pmat[i]);CHKERRQ(ierr);
545         if (jac->type == PC_COMPOSITE_SCHUR) {
546           jac->schur_user = jac->pmat[i];
547 
548           ierr = PetscObjectReference((PetscObject) jac->schur_user);CHKERRQ(ierr);
549         }
550       } else {
551         const char *prefix;
552         ierr = MatGetSubMatrix(pc->pmat,ilink->is,ilink->is_col,MAT_INITIAL_MATRIX,&jac->pmat[i]);CHKERRQ(ierr);
553         ierr = KSPGetOptionsPrefix(ilink->ksp,&prefix);CHKERRQ(ierr);
554         ierr = MatSetOptionsPrefix(jac->pmat[i],prefix);CHKERRQ(ierr);
555         ierr = MatViewFromOptions(jac->pmat[i],NULL,"-mat_view");CHKERRQ(ierr);
556       }
557       /* create work vectors for each split */
558       ierr     = MatGetVecs(jac->pmat[i],&jac->x[i],&jac->y[i]);CHKERRQ(ierr);
559       ilink->x = jac->x[i]; ilink->y = jac->y[i]; ilink->z = NULL;
560       /* compute scatter contexts needed by multiplicative versions and non-default splits */
561       ierr = VecScatterCreate(xtmp,ilink->is,jac->x[i],NULL,&ilink->sctx);CHKERRQ(ierr);
562       /* Check for null space attached to IS */
563       ierr = PetscObjectQuery((PetscObject) ilink->is, "nullspace", (PetscObject*) &sp);CHKERRQ(ierr);
564       if (sp) {
565         ierr = MatSetNullSpace(jac->pmat[i], sp);CHKERRQ(ierr);
566       }
567       ierr = PetscObjectQuery((PetscObject) ilink->is, "nearnullspace", (PetscObject*) &sp);CHKERRQ(ierr);
568       if (sp) {
569         ierr = MatSetNearNullSpace(jac->pmat[i], sp);CHKERRQ(ierr);
570       }
571       ilink = ilink->next;
572     }
573     ierr = VecDestroy(&xtmp);CHKERRQ(ierr);
574   } else {
575     for (i=0; i<nsplit; i++) {
576       Mat pmat;
577 
578       /* Check for preconditioning matrix attached to IS */
579       ierr = PetscObjectQuery((PetscObject) ilink->is, "pmat", (PetscObject*) &pmat);CHKERRQ(ierr);
580       if (!pmat) {
581         ierr = MatGetSubMatrix(pc->pmat,ilink->is,ilink->is_col,MAT_REUSE_MATRIX,&jac->pmat[i]);CHKERRQ(ierr);
582       }
583       ilink = ilink->next;
584     }
585   }
586   if (pc->useAmat) {
587     ilink = jac->head;
588     if (!jac->mat) {
589       ierr = PetscMalloc1(nsplit,&jac->mat);CHKERRQ(ierr);
590       for (i=0; i<nsplit; i++) {
591         ierr  = MatGetSubMatrix(pc->mat,ilink->is,ilink->is_col,MAT_INITIAL_MATRIX,&jac->mat[i]);CHKERRQ(ierr);
592         ilink = ilink->next;
593       }
594     } else {
595       for (i=0; i<nsplit; i++) {
596         if (jac->mat[i]) {ierr = MatGetSubMatrix(pc->mat,ilink->is,ilink->is_col,MAT_REUSE_MATRIX,&jac->mat[i]);CHKERRQ(ierr);}
597         ilink = ilink->next;
598       }
599     }
600   } else {
601     jac->mat = jac->pmat;
602   }
603 
604   if (jac->type != PC_COMPOSITE_ADDITIVE  && jac->type != PC_COMPOSITE_SCHUR) {
605     /* extract the rows of the matrix associated with each field: used for efficient computation of residual inside algorithm */
606     ilink = jac->head;
607     if (!jac->Afield) {
608       ierr = PetscMalloc1(nsplit,&jac->Afield);CHKERRQ(ierr);
609       for (i=0; i<nsplit; i++) {
610         ierr  = MatGetSubMatrix(pc->mat,ilink->is,NULL,MAT_INITIAL_MATRIX,&jac->Afield[i]);CHKERRQ(ierr);
611         ilink = ilink->next;
612       }
613     } else {
614       for (i=0; i<nsplit; i++) {
615         ierr  = MatGetSubMatrix(pc->mat,ilink->is,NULL,MAT_REUSE_MATRIX,&jac->Afield[i]);CHKERRQ(ierr);
616         ilink = ilink->next;
617       }
618     }
619   }
620 
621   if (jac->type == PC_COMPOSITE_SCHUR) {
622     IS          ccis;
623     PetscInt    rstart,rend;
624     char        lscname[256];
625     PetscObject LSC_L;
626 
627     if (nsplit != 2) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_ARG_INCOMP,"To use Schur complement preconditioner you must have exactly 2 fields");
628 
629     /* When extracting off-diagonal submatrices, we take complements from this range */
630     ierr = MatGetOwnershipRangeColumn(pc->mat,&rstart,&rend);CHKERRQ(ierr);
631 
632     /* need to handle case when one is resetting up the preconditioner */
633     if (jac->schur) {
634       KSP kspA = jac->head->ksp, kspInner = NULL, kspUpper = jac->kspupper;
635 
636       ierr  = MatSchurComplementGetKSP(jac->schur, &kspInner);CHKERRQ(ierr);
637       ilink = jac->head;
638       ierr  = ISComplement(ilink->is_col,rstart,rend,&ccis);CHKERRQ(ierr);
639       ierr  = MatGetSubMatrix(pc->mat,ilink->is,ccis,MAT_REUSE_MATRIX,&jac->B);CHKERRQ(ierr);
640       ierr  = ISDestroy(&ccis);CHKERRQ(ierr);
641       ilink = ilink->next;
642       ierr  = ISComplement(ilink->is_col,rstart,rend,&ccis);CHKERRQ(ierr);
643       ierr  = MatGetSubMatrix(pc->mat,ilink->is,ccis,MAT_REUSE_MATRIX,&jac->C);CHKERRQ(ierr);
644       ierr  = ISDestroy(&ccis);CHKERRQ(ierr);
645       ierr  = MatSchurComplementUpdateSubMatrices(jac->schur,jac->mat[0],jac->pmat[0],jac->B,jac->C,jac->mat[1],pc->flag);CHKERRQ(ierr);
646       if (jac->schurpre == PC_FIELDSPLIT_SCHUR_PRE_SELFP) {
647 	ierr = MatDestroy(&jac->schurp);CHKERRQ(ierr);
648 	ierr = MatSchurComplementGetPmat(jac->schur,MAT_INITIAL_MATRIX,&jac->schurp);CHKERRQ(ierr);
649       }
650       if (kspA != kspInner) {
651         ierr = KSPSetOperators(kspA,jac->mat[0],jac->pmat[0],pc->flag);CHKERRQ(ierr);
652       }
653       if (kspUpper != kspA) {
654         ierr = KSPSetOperators(kspUpper,jac->mat[0],jac->pmat[0],pc->flag);CHKERRQ(ierr);
655       }
656       ierr = KSPSetOperators(jac->kspschur,jac->schur,FieldSplitSchurPre(jac),pc->flag);CHKERRQ(ierr);
657     } else {
658       const char   *Dprefix;
659       char         schurprefix[256], schurmatprefix[256];
660       char         schurtestoption[256];
661       MatNullSpace sp;
662       PetscBool    flg;
663 
664       /* extract the A01 and A10 matrices */
665       ilink = jac->head;
666       ierr  = ISComplement(ilink->is_col,rstart,rend,&ccis);CHKERRQ(ierr);
667       ierr  = MatGetSubMatrix(pc->mat,ilink->is,ccis,MAT_INITIAL_MATRIX,&jac->B);CHKERRQ(ierr);
668       ierr  = ISDestroy(&ccis);CHKERRQ(ierr);
669       ilink = ilink->next;
670       ierr  = ISComplement(ilink->is_col,rstart,rend,&ccis);CHKERRQ(ierr);
671       ierr  = MatGetSubMatrix(pc->mat,ilink->is,ccis,MAT_INITIAL_MATRIX,&jac->C);CHKERRQ(ierr);
672       ierr  = ISDestroy(&ccis);CHKERRQ(ierr);
673 
674       /* Use mat[0] (diagonal block of Amat) preconditioned by pmat[0] to define Schur complement */
675       ierr = MatCreate(((PetscObject)jac->mat[0])->comm,&jac->schur);CHKERRQ(ierr);
676       ierr = MatSetType(jac->schur,MATSCHURCOMPLEMENT);CHKERRQ(ierr);
677       ierr = MatSchurComplementSetSubMatrices(jac->schur,jac->mat[0],jac->pmat[0],jac->B,jac->C,jac->mat[1]);CHKERRQ(ierr);
678       ierr = PetscSNPrintf(schurmatprefix, sizeof(schurmatprefix), "%sfieldsplit_%s_", ((PetscObject)pc)->prefix ? ((PetscObject)pc)->prefix : "", ilink->splitname);CHKERRQ(ierr);
679       /* Note that the inner KSP is NOT going to inherit this prefix, and if it did, it would be reset just below.  Is that what we want? */
680       ierr = MatSetOptionsPrefix(jac->schur,schurmatprefix);CHKERRQ(ierr);
681       ierr = MatSetFromOptions(jac->schur);CHKERRQ(ierr);
682       ierr = MatGetNullSpace(jac->pmat[1], &sp);CHKERRQ(ierr);
683       if (sp) {
684         ierr = MatSetNullSpace(jac->schur, sp);CHKERRQ(ierr);
685       }
686 
687       ierr = PetscSNPrintf(schurtestoption, sizeof(schurtestoption), "-fieldsplit_%s_inner_", ilink->splitname);CHKERRQ(ierr);
688       ierr = PetscOptionsFindPairPrefix_Private(((PetscObject)pc)->prefix, schurtestoption, NULL, &flg);CHKERRQ(ierr);
689       if (flg) {
690         DM  dmInner;
691         KSP kspInner;
692 
693         ierr = MatSchurComplementGetKSP(jac->schur, &kspInner);CHKERRQ(ierr);
694         ierr = PetscSNPrintf(schurprefix, sizeof(schurprefix), "%sfieldsplit_%s_inner_", ((PetscObject)pc)->prefix ? ((PetscObject)pc)->prefix : "", ilink->splitname);CHKERRQ(ierr);
695         /* Indent this deeper to emphasize the "inner" nature of this solver. */
696         ierr = PetscObjectIncrementTabLevel((PetscObject)kspInner, (PetscObject) pc, 2);CHKERRQ(ierr);
697         ierr = KSPSetOptionsPrefix(kspInner, schurprefix);CHKERRQ(ierr);
698 
699         /* Set DM for new solver */
700         ierr = KSPGetDM(jac->head->ksp, &dmInner);CHKERRQ(ierr);
701         ierr = KSPSetDM(kspInner, dmInner);CHKERRQ(ierr);
702         ierr = KSPSetDMActive(kspInner, PETSC_FALSE);CHKERRQ(ierr);
703       } else {
704          /* Use the outer solver for the inner solve, but revert the KSPPREONLY from PCFieldSplitSetFields_FieldSplit or
705           * PCFieldSplitSetIS_FieldSplit. We don't want KSPPREONLY because it makes the Schur complement inexact,
706           * preventing Schur complement reduction to be an accurate solve. Usually when an iterative solver is used for
707           * S = D - C A_inner^{-1} B, we expect S to be defined using an accurate definition of A_inner^{-1}, so we make
708           * GMRES the default. Note that it is also common to use PREONLY for S, in which case S may not be used
709           * directly, and the user is responsible for setting an inexact method for fieldsplit's A^{-1}. */
710         ierr = KSPSetType(jac->head->ksp,KSPGMRES);CHKERRQ(ierr);
711         ierr = MatSchurComplementSetKSP(jac->schur,jac->head->ksp);CHKERRQ(ierr);
712       }
713       ierr = KSPSetOperators(jac->head->ksp,jac->mat[0],jac->pmat[0],flag);CHKERRQ(ierr);
714       ierr = KSPSetFromOptions(jac->head->ksp);CHKERRQ(ierr);
715       ierr = MatSetFromOptions(jac->schur);CHKERRQ(ierr);
716 
717       ierr = PetscSNPrintf(schurtestoption, sizeof(schurtestoption), "-fieldsplit_%s_upper_", ilink->splitname);CHKERRQ(ierr);
718       ierr = PetscOptionsFindPairPrefix_Private(((PetscObject)pc)->prefix, schurtestoption, NULL, &flg);CHKERRQ(ierr);
719       if (flg) {
720         DM dmInner;
721 
722         ierr = PetscSNPrintf(schurprefix, sizeof(schurprefix), "%sfieldsplit_%s_upper_", ((PetscObject)pc)->prefix ? ((PetscObject)pc)->prefix : "", ilink->splitname);CHKERRQ(ierr);
723         ierr = KSPCreate(PetscObjectComm((PetscObject)pc), &jac->kspupper);CHKERRQ(ierr);
724         ierr = KSPSetOptionsPrefix(jac->kspupper, schurprefix);CHKERRQ(ierr);
725         ierr = KSPGetDM(jac->head->ksp, &dmInner);CHKERRQ(ierr);
726         ierr = KSPSetDM(jac->kspupper, dmInner);CHKERRQ(ierr);
727         ierr = KSPSetDMActive(jac->kspupper, PETSC_FALSE);CHKERRQ(ierr);
728         ierr = KSPSetFromOptions(jac->kspupper);CHKERRQ(ierr);
729         ierr = KSPSetOperators(jac->kspupper,jac->mat[0],jac->pmat[0],flag);CHKERRQ(ierr);
730         ierr = VecDuplicate(jac->head->x, &jac->head->z);CHKERRQ(ierr);
731       } else {
732         jac->kspupper = jac->head->ksp;
733         ierr          = PetscObjectReference((PetscObject) jac->head->ksp);CHKERRQ(ierr);
734       }
735 
736       if (jac->schurpre == PC_FIELDSPLIT_SCHUR_PRE_SELFP) {
737 	ierr = MatSchurComplementGetPmat(jac->schur,MAT_INITIAL_MATRIX,&jac->schurp);CHKERRQ(ierr);
738       }
739       ierr = KSPCreate(PetscObjectComm((PetscObject)pc),&jac->kspschur);CHKERRQ(ierr);
740       ierr = PetscLogObjectParent((PetscObject)pc,(PetscObject)jac->kspschur);CHKERRQ(ierr);
741       ierr = PetscObjectIncrementTabLevel((PetscObject)jac->kspschur,(PetscObject)pc,1);CHKERRQ(ierr);
742       if (jac->schurpre == PC_FIELDSPLIT_SCHUR_PRE_SELF) {
743         PC pcschur;
744         ierr = KSPGetPC(jac->kspschur,&pcschur);CHKERRQ(ierr);
745         ierr = PCSetType(pcschur,PCNONE);CHKERRQ(ierr);
746         /* Note: This is bad if there exist preconditioners for MATSCHURCOMPLEMENT */
747       } else if (jac->schurpre == PC_FIELDSPLIT_SCHUR_PRE_FULL) {
748         ierr = MatSchurComplementComputeExplicitOperator(jac->schur, &jac->schur_user);CHKERRQ(ierr);
749       }
750       ierr = KSPSetOperators(jac->kspschur,jac->schur,FieldSplitSchurPre(jac),DIFFERENT_NONZERO_PATTERN);CHKERRQ(ierr);
751       ierr = KSPGetOptionsPrefix(jac->head->next->ksp, &Dprefix);CHKERRQ(ierr);
752       ierr = KSPSetOptionsPrefix(jac->kspschur,         Dprefix);CHKERRQ(ierr);
753       /* propogate DM */
754       {
755         DM sdm;
756         ierr = KSPGetDM(jac->head->next->ksp, &sdm);CHKERRQ(ierr);
757         if (sdm) {
758           ierr = KSPSetDM(jac->kspschur, sdm);CHKERRQ(ierr);
759           ierr = KSPSetDMActive(jac->kspschur, PETSC_FALSE);CHKERRQ(ierr);
760         }
761       }
762       /* really want setfromoptions called in PCSetFromOptions_FieldSplit(), but it is not ready yet */
763       /* need to call this every time, since the jac->kspschur is freshly created, otherwise its options never get set */
764       ierr = KSPSetFromOptions(jac->kspschur);CHKERRQ(ierr);
765     }
766 
767     /* HACK: special support to forward L and Lp matrices that might be used by PCLSC */
768     ierr = PetscSNPrintf(lscname,sizeof(lscname),"%s_LSC_L",ilink->splitname);CHKERRQ(ierr);
769     ierr = PetscObjectQuery((PetscObject)pc->mat,lscname,(PetscObject*)&LSC_L);CHKERRQ(ierr);
770     if (!LSC_L) {ierr = PetscObjectQuery((PetscObject)pc->pmat,lscname,(PetscObject*)&LSC_L);CHKERRQ(ierr);}
771     if (LSC_L) {ierr = PetscObjectCompose((PetscObject)jac->schur,"LSC_L",(PetscObject)LSC_L);CHKERRQ(ierr);}
772     ierr = PetscSNPrintf(lscname,sizeof(lscname),"%s_LSC_Lp",ilink->splitname);CHKERRQ(ierr);
773     ierr = PetscObjectQuery((PetscObject)pc->pmat,lscname,(PetscObject*)&LSC_L);CHKERRQ(ierr);
774     if (!LSC_L) {ierr = PetscObjectQuery((PetscObject)pc->mat,lscname,(PetscObject*)&LSC_L);CHKERRQ(ierr);}
775     if (LSC_L) {ierr = PetscObjectCompose((PetscObject)jac->schur,"LSC_Lp",(PetscObject)LSC_L);CHKERRQ(ierr);}
776   } else {
777     /* set up the individual splits' PCs */
778     i     = 0;
779     ilink = jac->head;
780     while (ilink) {
781       ierr = KSPSetOperators(ilink->ksp,jac->mat[i],jac->pmat[i],flag);CHKERRQ(ierr);
782       /* really want setfromoptions called in PCSetFromOptions_FieldSplit(), but it is not ready yet */
783       if (!jac->suboptionsset) {ierr = KSPSetFromOptions(ilink->ksp);CHKERRQ(ierr);}
784       i++;
785       ilink = ilink->next;
786     }
787   }
788 
789   jac->suboptionsset = PETSC_TRUE;
790   PetscFunctionReturn(0);
791 }
792 
793 #define FieldSplitSplitSolveAdd(ilink,xx,yy) \
794   (VecScatterBegin(ilink->sctx,xx,ilink->x,INSERT_VALUES,SCATTER_FORWARD) || \
795    VecScatterEnd(ilink->sctx,xx,ilink->x,INSERT_VALUES,SCATTER_FORWARD) || \
796    KSPSolve(ilink->ksp,ilink->x,ilink->y) || \
797    VecScatterBegin(ilink->sctx,ilink->y,yy,ADD_VALUES,SCATTER_REVERSE) || \
798    VecScatterEnd(ilink->sctx,ilink->y,yy,ADD_VALUES,SCATTER_REVERSE))
799 
800 #undef __FUNCT__
801 #define __FUNCT__ "PCApply_FieldSplit_Schur"
802 static PetscErrorCode PCApply_FieldSplit_Schur(PC pc,Vec x,Vec y)
803 {
804   PC_FieldSplit     *jac = (PC_FieldSplit*)pc->data;
805   PetscErrorCode    ierr;
806   PC_FieldSplitLink ilinkA = jac->head, ilinkD = ilinkA->next;
807   KSP               kspA   = ilinkA->ksp, kspLower = kspA, kspUpper = jac->kspupper;
808 
809   PetscFunctionBegin;
810   switch (jac->schurfactorization) {
811   case PC_FIELDSPLIT_SCHUR_FACT_DIAG:
812     /* [A00 0; 0 -S], positive definite, suitable for MINRES */
813     ierr = VecScatterBegin(ilinkA->sctx,x,ilinkA->x,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
814     ierr = VecScatterBegin(ilinkD->sctx,x,ilinkD->x,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
815     ierr = VecScatterEnd(ilinkA->sctx,x,ilinkA->x,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
816     ierr = KSPSolve(kspA,ilinkA->x,ilinkA->y);CHKERRQ(ierr);
817     ierr = VecScatterBegin(ilinkA->sctx,ilinkA->y,y,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
818     ierr = VecScatterEnd(ilinkD->sctx,x,ilinkD->x,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
819     ierr = KSPSolve(jac->kspschur,ilinkD->x,ilinkD->y);CHKERRQ(ierr);
820     ierr = VecScale(ilinkD->y,-1.);CHKERRQ(ierr);
821     ierr = VecScatterBegin(ilinkD->sctx,ilinkD->y,y,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
822     ierr = VecScatterEnd(ilinkA->sctx,ilinkA->y,y,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
823     ierr = VecScatterEnd(ilinkD->sctx,ilinkD->y,y,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
824     break;
825   case PC_FIELDSPLIT_SCHUR_FACT_LOWER:
826     /* [A00 0; A10 S], suitable for left preconditioning */
827     ierr = VecScatterBegin(ilinkA->sctx,x,ilinkA->x,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
828     ierr = VecScatterEnd(ilinkA->sctx,x,ilinkA->x,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
829     ierr = KSPSolve(kspA,ilinkA->x,ilinkA->y);CHKERRQ(ierr);
830     ierr = MatMult(jac->C,ilinkA->y,ilinkD->x);CHKERRQ(ierr);
831     ierr = VecScale(ilinkD->x,-1.);CHKERRQ(ierr);
832     ierr = VecScatterBegin(ilinkD->sctx,x,ilinkD->x,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
833     ierr = VecScatterBegin(ilinkA->sctx,ilinkA->y,y,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
834     ierr = VecScatterEnd(ilinkD->sctx,x,ilinkD->x,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
835     ierr = KSPSolve(jac->kspschur,ilinkD->x,ilinkD->y);CHKERRQ(ierr);
836     ierr = VecScatterBegin(ilinkD->sctx,ilinkD->y,y,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
837     ierr = VecScatterEnd(ilinkA->sctx,ilinkA->y,y,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
838     ierr = VecScatterEnd(ilinkD->sctx,ilinkD->y,y,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
839     break;
840   case PC_FIELDSPLIT_SCHUR_FACT_UPPER:
841     /* [A00 A01; 0 S], suitable for right preconditioning */
842     ierr = VecScatterBegin(ilinkD->sctx,x,ilinkD->x,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
843     ierr = VecScatterEnd(ilinkD->sctx,x,ilinkD->x,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
844     ierr = KSPSolve(jac->kspschur,ilinkD->x,ilinkD->y);CHKERRQ(ierr);
845     ierr = MatMult(jac->B,ilinkD->y,ilinkA->x);CHKERRQ(ierr);
846     ierr = VecScale(ilinkA->x,-1.);CHKERRQ(ierr);
847     ierr = VecScatterBegin(ilinkA->sctx,x,ilinkA->x,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
848     ierr = VecScatterBegin(ilinkD->sctx,ilinkD->y,y,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
849     ierr = VecScatterEnd(ilinkA->sctx,x,ilinkA->x,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
850     ierr = KSPSolve(kspA,ilinkA->x,ilinkA->y);CHKERRQ(ierr);
851     ierr = VecScatterBegin(ilinkA->sctx,ilinkA->y,y,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
852     ierr = VecScatterEnd(ilinkD->sctx,ilinkD->y,y,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
853     ierr = VecScatterEnd(ilinkA->sctx,ilinkA->y,y,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
854     break;
855   case PC_FIELDSPLIT_SCHUR_FACT_FULL:
856     /* [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 */
857     ierr = VecScatterBegin(ilinkA->sctx,x,ilinkA->x,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
858     ierr = VecScatterEnd(ilinkA->sctx,x,ilinkA->x,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
859     ierr = KSPSolve(kspLower,ilinkA->x,ilinkA->y);CHKERRQ(ierr);
860     ierr = MatMult(jac->C,ilinkA->y,ilinkD->x);CHKERRQ(ierr);
861     ierr = VecScale(ilinkD->x,-1.0);CHKERRQ(ierr);
862     ierr = VecScatterBegin(ilinkD->sctx,x,ilinkD->x,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
863     ierr = VecScatterEnd(ilinkD->sctx,x,ilinkD->x,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
864 
865     ierr = KSPSolve(jac->kspschur,ilinkD->x,ilinkD->y);CHKERRQ(ierr);
866     ierr = VecScatterBegin(ilinkD->sctx,ilinkD->y,y,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
867     ierr = VecScatterEnd(ilinkD->sctx,ilinkD->y,y,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
868 
869     if (kspUpper == kspA) {
870       ierr = MatMult(jac->B,ilinkD->y,ilinkA->y);CHKERRQ(ierr);
871       ierr = VecAXPY(ilinkA->x,-1.0,ilinkA->y);CHKERRQ(ierr);
872       ierr = KSPSolve(kspA,ilinkA->x,ilinkA->y);CHKERRQ(ierr);
873     } else {
874       ierr = KSPSolve(kspA,ilinkA->x,ilinkA->y);CHKERRQ(ierr);
875       ierr = MatMult(jac->B,ilinkD->y,ilinkA->x);CHKERRQ(ierr);
876       ierr = KSPSolve(kspUpper,ilinkA->x,ilinkA->z);CHKERRQ(ierr);
877       ierr = VecAXPY(ilinkA->y,-1.0,ilinkA->z);CHKERRQ(ierr);
878     }
879     ierr = VecScatterBegin(ilinkA->sctx,ilinkA->y,y,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
880     ierr = VecScatterEnd(ilinkA->sctx,ilinkA->y,y,INSERT_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
881   }
882   PetscFunctionReturn(0);
883 }
884 
885 #undef __FUNCT__
886 #define __FUNCT__ "PCApply_FieldSplit"
887 static PetscErrorCode PCApply_FieldSplit(PC pc,Vec x,Vec y)
888 {
889   PC_FieldSplit     *jac = (PC_FieldSplit*)pc->data;
890   PetscErrorCode    ierr;
891   PC_FieldSplitLink ilink = jac->head;
892   PetscInt          cnt,bs;
893 
894   PetscFunctionBegin;
895   if (jac->type == PC_COMPOSITE_ADDITIVE) {
896     if (jac->defaultsplit) {
897       ierr = VecGetBlockSize(x,&bs);CHKERRQ(ierr);
898       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);
899       ierr = VecGetBlockSize(y,&bs);CHKERRQ(ierr);
900       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);
901       ierr = VecStrideGatherAll(x,jac->x,INSERT_VALUES);CHKERRQ(ierr);
902       while (ilink) {
903         ierr  = KSPSolve(ilink->ksp,ilink->x,ilink->y);CHKERRQ(ierr);
904         ilink = ilink->next;
905       }
906       ierr = VecStrideScatterAll(jac->y,y,INSERT_VALUES);CHKERRQ(ierr);
907     } else {
908       ierr = VecSet(y,0.0);CHKERRQ(ierr);
909       while (ilink) {
910         ierr  = FieldSplitSplitSolveAdd(ilink,x,y);CHKERRQ(ierr);
911         ilink = ilink->next;
912       }
913     }
914   } else if (jac->type == PC_COMPOSITE_MULTIPLICATIVE || jac->type == PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE) {
915     if (!jac->w1) {
916       ierr = VecDuplicate(x,&jac->w1);CHKERRQ(ierr);
917       ierr = VecDuplicate(x,&jac->w2);CHKERRQ(ierr);
918     }
919     ierr = VecSet(y,0.0);CHKERRQ(ierr);
920     ierr = FieldSplitSplitSolveAdd(ilink,x,y);CHKERRQ(ierr);
921     cnt  = 1;
922     while (ilink->next) {
923       ilink = ilink->next;
924       /* compute the residual only over the part of the vector needed */
925       ierr = MatMult(jac->Afield[cnt++],y,ilink->x);CHKERRQ(ierr);
926       ierr = VecScale(ilink->x,-1.0);CHKERRQ(ierr);
927       ierr = VecScatterBegin(ilink->sctx,x,ilink->x,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
928       ierr = VecScatterEnd(ilink->sctx,x,ilink->x,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
929       ierr = KSPSolve(ilink->ksp,ilink->x,ilink->y);CHKERRQ(ierr);
930       ierr = VecScatterBegin(ilink->sctx,ilink->y,y,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
931       ierr = VecScatterEnd(ilink->sctx,ilink->y,y,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
932     }
933     if (jac->type == PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE) {
934       cnt -= 2;
935       while (ilink->previous) {
936         ilink = ilink->previous;
937         /* compute the residual only over the part of the vector needed */
938         ierr = MatMult(jac->Afield[cnt--],y,ilink->x);CHKERRQ(ierr);
939         ierr = VecScale(ilink->x,-1.0);CHKERRQ(ierr);
940         ierr = VecScatterBegin(ilink->sctx,x,ilink->x,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
941         ierr = VecScatterEnd(ilink->sctx,x,ilink->x,ADD_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
942         ierr = KSPSolve(ilink->ksp,ilink->x,ilink->y);CHKERRQ(ierr);
943         ierr = VecScatterBegin(ilink->sctx,ilink->y,y,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
944         ierr = VecScatterEnd(ilink->sctx,ilink->y,y,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
945       }
946     }
947   } else SETERRQ1(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"Unsupported or unknown composition",(int) jac->type);
948   PetscFunctionReturn(0);
949 }
950 
951 #define FieldSplitSplitSolveAddTranspose(ilink,xx,yy) \
952   (VecScatterBegin(ilink->sctx,xx,ilink->y,INSERT_VALUES,SCATTER_FORWARD) || \
953    VecScatterEnd(ilink->sctx,xx,ilink->y,INSERT_VALUES,SCATTER_FORWARD) || \
954    KSPSolveTranspose(ilink->ksp,ilink->y,ilink->x) || \
955    VecScatterBegin(ilink->sctx,ilink->x,yy,ADD_VALUES,SCATTER_REVERSE) || \
956    VecScatterEnd(ilink->sctx,ilink->x,yy,ADD_VALUES,SCATTER_REVERSE))
957 
958 #undef __FUNCT__
959 #define __FUNCT__ "PCApplyTranspose_FieldSplit"
960 static PetscErrorCode PCApplyTranspose_FieldSplit(PC pc,Vec x,Vec y)
961 {
962   PC_FieldSplit     *jac = (PC_FieldSplit*)pc->data;
963   PetscErrorCode    ierr;
964   PC_FieldSplitLink ilink = jac->head;
965   PetscInt          bs;
966 
967   PetscFunctionBegin;
968   if (jac->type == PC_COMPOSITE_ADDITIVE) {
969     if (jac->defaultsplit) {
970       ierr = VecGetBlockSize(x,&bs);CHKERRQ(ierr);
971       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);
972       ierr = VecGetBlockSize(y,&bs);CHKERRQ(ierr);
973       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);
974       ierr = VecStrideGatherAll(x,jac->x,INSERT_VALUES);CHKERRQ(ierr);
975       while (ilink) {
976         ierr  = KSPSolveTranspose(ilink->ksp,ilink->x,ilink->y);CHKERRQ(ierr);
977         ilink = ilink->next;
978       }
979       ierr = VecStrideScatterAll(jac->y,y,INSERT_VALUES);CHKERRQ(ierr);
980     } else {
981       ierr = VecSet(y,0.0);CHKERRQ(ierr);
982       while (ilink) {
983         ierr  = FieldSplitSplitSolveAddTranspose(ilink,x,y);CHKERRQ(ierr);
984         ilink = ilink->next;
985       }
986     }
987   } else {
988     if (!jac->w1) {
989       ierr = VecDuplicate(x,&jac->w1);CHKERRQ(ierr);
990       ierr = VecDuplicate(x,&jac->w2);CHKERRQ(ierr);
991     }
992     ierr = VecSet(y,0.0);CHKERRQ(ierr);
993     if (jac->type == PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE) {
994       ierr = FieldSplitSplitSolveAddTranspose(ilink,x,y);CHKERRQ(ierr);
995       while (ilink->next) {
996         ilink = ilink->next;
997         ierr  = MatMultTranspose(pc->mat,y,jac->w1);CHKERRQ(ierr);
998         ierr  = VecWAXPY(jac->w2,-1.0,jac->w1,x);CHKERRQ(ierr);
999         ierr  = FieldSplitSplitSolveAddTranspose(ilink,jac->w2,y);CHKERRQ(ierr);
1000       }
1001       while (ilink->previous) {
1002         ilink = ilink->previous;
1003         ierr  = MatMultTranspose(pc->mat,y,jac->w1);CHKERRQ(ierr);
1004         ierr  = VecWAXPY(jac->w2,-1.0,jac->w1,x);CHKERRQ(ierr);
1005         ierr  = FieldSplitSplitSolveAddTranspose(ilink,jac->w2,y);CHKERRQ(ierr);
1006       }
1007     } else {
1008       while (ilink->next) {   /* get to last entry in linked list */
1009         ilink = ilink->next;
1010       }
1011       ierr = FieldSplitSplitSolveAddTranspose(ilink,x,y);CHKERRQ(ierr);
1012       while (ilink->previous) {
1013         ilink = ilink->previous;
1014         ierr  = MatMultTranspose(pc->mat,y,jac->w1);CHKERRQ(ierr);
1015         ierr  = VecWAXPY(jac->w2,-1.0,jac->w1,x);CHKERRQ(ierr);
1016         ierr  = FieldSplitSplitSolveAddTranspose(ilink,jac->w2,y);CHKERRQ(ierr);
1017       }
1018     }
1019   }
1020   PetscFunctionReturn(0);
1021 }
1022 
1023 #undef __FUNCT__
1024 #define __FUNCT__ "PCReset_FieldSplit"
1025 static PetscErrorCode PCReset_FieldSplit(PC pc)
1026 {
1027   PC_FieldSplit     *jac = (PC_FieldSplit*)pc->data;
1028   PetscErrorCode    ierr;
1029   PC_FieldSplitLink ilink = jac->head,next;
1030 
1031   PetscFunctionBegin;
1032   while (ilink) {
1033     ierr  = KSPReset(ilink->ksp);CHKERRQ(ierr);
1034     ierr  = VecDestroy(&ilink->x);CHKERRQ(ierr);
1035     ierr  = VecDestroy(&ilink->y);CHKERRQ(ierr);
1036     ierr  = VecDestroy(&ilink->z);CHKERRQ(ierr);
1037     ierr  = VecScatterDestroy(&ilink->sctx);CHKERRQ(ierr);
1038     ierr  = ISDestroy(&ilink->is);CHKERRQ(ierr);
1039     ierr  = ISDestroy(&ilink->is_col);CHKERRQ(ierr);
1040     next  = ilink->next;
1041     ilink = next;
1042   }
1043   ierr = PetscFree2(jac->x,jac->y);CHKERRQ(ierr);
1044   if (jac->mat && jac->mat != jac->pmat) {
1045     ierr = MatDestroyMatrices(jac->nsplits,&jac->mat);CHKERRQ(ierr);
1046   } else if (jac->mat) {
1047     jac->mat = NULL;
1048   }
1049   if (jac->pmat) {ierr = MatDestroyMatrices(jac->nsplits,&jac->pmat);CHKERRQ(ierr);}
1050   if (jac->Afield) {ierr = MatDestroyMatrices(jac->nsplits,&jac->Afield);CHKERRQ(ierr);}
1051   ierr       = VecDestroy(&jac->w1);CHKERRQ(ierr);
1052   ierr       = VecDestroy(&jac->w2);CHKERRQ(ierr);
1053   ierr       = MatDestroy(&jac->schur);CHKERRQ(ierr);
1054   ierr       = MatDestroy(&jac->schurp);CHKERRQ(ierr);
1055   ierr       = MatDestroy(&jac->schur_user);CHKERRQ(ierr);
1056   ierr       = KSPDestroy(&jac->kspschur);CHKERRQ(ierr);
1057   ierr       = KSPDestroy(&jac->kspupper);CHKERRQ(ierr);
1058   ierr       = MatDestroy(&jac->B);CHKERRQ(ierr);
1059   ierr       = MatDestroy(&jac->C);CHKERRQ(ierr);
1060   jac->reset = PETSC_TRUE;
1061   PetscFunctionReturn(0);
1062 }
1063 
1064 #undef __FUNCT__
1065 #define __FUNCT__ "PCDestroy_FieldSplit"
1066 static PetscErrorCode PCDestroy_FieldSplit(PC pc)
1067 {
1068   PC_FieldSplit     *jac = (PC_FieldSplit*)pc->data;
1069   PetscErrorCode    ierr;
1070   PC_FieldSplitLink ilink = jac->head,next;
1071 
1072   PetscFunctionBegin;
1073   ierr = PCReset_FieldSplit(pc);CHKERRQ(ierr);
1074   while (ilink) {
1075     ierr  = KSPDestroy(&ilink->ksp);CHKERRQ(ierr);
1076     next  = ilink->next;
1077     ierr  = PetscFree(ilink->splitname);CHKERRQ(ierr);
1078     ierr  = PetscFree(ilink->fields);CHKERRQ(ierr);
1079     ierr  = PetscFree(ilink->fields_col);CHKERRQ(ierr);
1080     ierr  = PetscFree(ilink);CHKERRQ(ierr);
1081     ilink = next;
1082   }
1083   ierr = PetscFree2(jac->x,jac->y);CHKERRQ(ierr);
1084   ierr = PetscFree(pc->data);CHKERRQ(ierr);
1085   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCFieldSplitGetSubKSP_C",NULL);CHKERRQ(ierr);
1086   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCFieldSplitSetFields_C",NULL);CHKERRQ(ierr);
1087   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCFieldSplitSetIS_C",NULL);CHKERRQ(ierr);
1088   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCFieldSplitSetType_C",NULL);CHKERRQ(ierr);
1089   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCFieldSplitSetBlockSize_C",NULL);CHKERRQ(ierr);
1090   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCFieldSplitSchurPrecondition_C",NULL);CHKERRQ(ierr);
1091   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCFieldSplitSetSchurFactType_C",NULL);CHKERRQ(ierr);
1092   PetscFunctionReturn(0);
1093 }
1094 
1095 #undef __FUNCT__
1096 #define __FUNCT__ "PCSetFromOptions_FieldSplit"
1097 static PetscErrorCode PCSetFromOptions_FieldSplit(PC pc)
1098 {
1099   PetscErrorCode  ierr;
1100   PetscInt        bs;
1101   PetscBool       flg,stokes = PETSC_FALSE;
1102   PC_FieldSplit   *jac = (PC_FieldSplit*)pc->data;
1103   PCCompositeType ctype;
1104 
1105   PetscFunctionBegin;
1106   ierr = PetscOptionsHead("FieldSplit options");CHKERRQ(ierr);
1107   ierr = PetscOptionsBool("-pc_fieldsplit_dm_splits","Whether to use DMCreateFieldDecomposition() for splits","PCFieldSplitSetDMSplits",jac->dm_splits,&jac->dm_splits,NULL);CHKERRQ(ierr);
1108   ierr = PetscOptionsInt("-pc_fieldsplit_block_size","Blocksize that defines number of fields","PCFieldSplitSetBlockSize",jac->bs,&bs,&flg);CHKERRQ(ierr);
1109   if (flg) {
1110     ierr = PCFieldSplitSetBlockSize(pc,bs);CHKERRQ(ierr);
1111   }
1112 
1113   ierr = PetscOptionsGetBool(((PetscObject)pc)->prefix,"-pc_fieldsplit_detect_saddle_point",&stokes,NULL);CHKERRQ(ierr);
1114   if (stokes) {
1115     ierr          = PCFieldSplitSetType(pc,PC_COMPOSITE_SCHUR);CHKERRQ(ierr);
1116     jac->schurpre = PC_FIELDSPLIT_SCHUR_PRE_SELF;
1117   }
1118 
1119   ierr = PetscOptionsEnum("-pc_fieldsplit_type","Type of composition","PCFieldSplitSetType",PCCompositeTypes,(PetscEnum)jac->type,(PetscEnum*)&ctype,&flg);CHKERRQ(ierr);
1120   if (flg) {
1121     ierr = PCFieldSplitSetType(pc,ctype);CHKERRQ(ierr);
1122   }
1123   /* Only setup fields once */
1124   if ((jac->bs > 0) && (jac->nsplits == 0)) {
1125     /* only allow user to set fields from command line if bs is already known.
1126        otherwise user can set them in PCFieldSplitSetDefaults() */
1127     ierr = PCFieldSplitSetRuntimeSplits_Private(pc);CHKERRQ(ierr);
1128     if (jac->splitdefined) {ierr = PetscInfo(pc,"Splits defined using the options database\n");CHKERRQ(ierr);}
1129   }
1130   if (jac->type == PC_COMPOSITE_SCHUR) {
1131     ierr = PetscOptionsGetEnum(((PetscObject)pc)->prefix,"-pc_fieldsplit_schur_factorization_type",PCFieldSplitSchurFactTypes,(PetscEnum*)&jac->schurfactorization,&flg);CHKERRQ(ierr);
1132     if (flg) {ierr = PetscInfo(pc,"Deprecated use of -pc_fieldsplit_schur_factorization_type\n");CHKERRQ(ierr);}
1133     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);
1134     ierr = PetscOptionsEnum("-pc_fieldsplit_schur_precondition","How to build preconditioner for Schur complement","PCFieldSplitSchurPrecondition",PCFieldSplitSchurPreTypes,(PetscEnum)jac->schurpre,(PetscEnum*)&jac->schurpre,NULL);CHKERRQ(ierr);
1135   }
1136   ierr = PetscOptionsTail();CHKERRQ(ierr);
1137   PetscFunctionReturn(0);
1138 }
1139 
1140 /*------------------------------------------------------------------------------------*/
1141 
1142 #undef __FUNCT__
1143 #define __FUNCT__ "PCFieldSplitSetFields_FieldSplit"
1144 static PetscErrorCode  PCFieldSplitSetFields_FieldSplit(PC pc,const char splitname[],PetscInt n,const PetscInt *fields,const PetscInt *fields_col)
1145 {
1146   PC_FieldSplit     *jac = (PC_FieldSplit*)pc->data;
1147   PetscErrorCode    ierr;
1148   PC_FieldSplitLink ilink,next = jac->head;
1149   char              prefix[128];
1150   PetscInt          i;
1151 
1152   PetscFunctionBegin;
1153   if (jac->splitdefined) {
1154     ierr = PetscInfo1(pc,"Ignoring new split \"%s\" because the splits have already been defined\n",splitname);CHKERRQ(ierr);
1155     PetscFunctionReturn(0);
1156   }
1157   for (i=0; i<n; i++) {
1158     if (fields[i] >= jac->bs) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Field %D requested but only %D exist",fields[i],jac->bs);
1159     if (fields[i] < 0) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Negative field %D requested",fields[i]);
1160   }
1161   ierr = PetscNew(&ilink);CHKERRQ(ierr);
1162   if (splitname) {
1163     ierr = PetscStrallocpy(splitname,&ilink->splitname);CHKERRQ(ierr);
1164   } else {
1165     ierr = PetscMalloc1(3,&ilink->splitname);CHKERRQ(ierr);
1166     ierr = PetscSNPrintf(ilink->splitname,2,"%s",jac->nsplits);CHKERRQ(ierr);
1167   }
1168   ierr = PetscMalloc1(n,&ilink->fields);CHKERRQ(ierr);
1169   ierr = PetscMemcpy(ilink->fields,fields,n*sizeof(PetscInt));CHKERRQ(ierr);
1170   ierr = PetscMalloc1(n,&ilink->fields_col);CHKERRQ(ierr);
1171   ierr = PetscMemcpy(ilink->fields_col,fields_col,n*sizeof(PetscInt));CHKERRQ(ierr);
1172 
1173   ilink->nfields = n;
1174   ilink->next    = NULL;
1175   ierr           = KSPCreate(PetscObjectComm((PetscObject)pc),&ilink->ksp);CHKERRQ(ierr);
1176   ierr           = PetscObjectIncrementTabLevel((PetscObject)ilink->ksp,(PetscObject)pc,1);CHKERRQ(ierr);
1177   ierr           = KSPSetType(ilink->ksp,KSPPREONLY);CHKERRQ(ierr);
1178   ierr           = PetscLogObjectParent((PetscObject)pc,(PetscObject)ilink->ksp);CHKERRQ(ierr);
1179 
1180   ierr = PetscSNPrintf(prefix,sizeof(prefix),"%sfieldsplit_%s_",((PetscObject)pc)->prefix ? ((PetscObject)pc)->prefix : "",ilink->splitname);CHKERRQ(ierr);
1181   ierr = KSPSetOptionsPrefix(ilink->ksp,prefix);CHKERRQ(ierr);
1182 
1183   if (!next) {
1184     jac->head       = ilink;
1185     ilink->previous = NULL;
1186   } else {
1187     while (next->next) {
1188       next = next->next;
1189     }
1190     next->next      = ilink;
1191     ilink->previous = next;
1192   }
1193   jac->nsplits++;
1194   PetscFunctionReturn(0);
1195 }
1196 
1197 #undef __FUNCT__
1198 #define __FUNCT__ "PCFieldSplitGetSubKSP_FieldSplit_Schur"
1199 static PetscErrorCode  PCFieldSplitGetSubKSP_FieldSplit_Schur(PC pc,PetscInt *n,KSP **subksp)
1200 {
1201   PC_FieldSplit  *jac = (PC_FieldSplit*)pc->data;
1202   PetscErrorCode ierr;
1203 
1204   PetscFunctionBegin;
1205   ierr = PetscMalloc1(jac->nsplits,subksp);CHKERRQ(ierr);
1206   ierr = MatSchurComplementGetKSP(jac->schur,*subksp);CHKERRQ(ierr);
1207 
1208   (*subksp)[1] = jac->kspschur;
1209   if (n) *n = jac->nsplits;
1210   PetscFunctionReturn(0);
1211 }
1212 
1213 #undef __FUNCT__
1214 #define __FUNCT__ "PCFieldSplitGetSubKSP_FieldSplit"
1215 static PetscErrorCode  PCFieldSplitGetSubKSP_FieldSplit(PC pc,PetscInt *n,KSP **subksp)
1216 {
1217   PC_FieldSplit     *jac = (PC_FieldSplit*)pc->data;
1218   PetscErrorCode    ierr;
1219   PetscInt          cnt   = 0;
1220   PC_FieldSplitLink ilink = jac->head;
1221 
1222   PetscFunctionBegin;
1223   ierr = PetscMalloc1(jac->nsplits,subksp);CHKERRQ(ierr);
1224   while (ilink) {
1225     (*subksp)[cnt++] = ilink->ksp;
1226     ilink            = ilink->next;
1227   }
1228   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);
1229   if (n) *n = jac->nsplits;
1230   PetscFunctionReturn(0);
1231 }
1232 
1233 #undef __FUNCT__
1234 #define __FUNCT__ "PCFieldSplitSetIS_FieldSplit"
1235 static PetscErrorCode  PCFieldSplitSetIS_FieldSplit(PC pc,const char splitname[],IS is)
1236 {
1237   PC_FieldSplit     *jac = (PC_FieldSplit*)pc->data;
1238   PetscErrorCode    ierr;
1239   PC_FieldSplitLink ilink, next = jac->head;
1240   char              prefix[128];
1241 
1242   PetscFunctionBegin;
1243   if (jac->splitdefined) {
1244     ierr = PetscInfo1(pc,"Ignoring new split \"%s\" because the splits have already been defined\n",splitname);CHKERRQ(ierr);
1245     PetscFunctionReturn(0);
1246   }
1247   ierr = PetscNew(&ilink);CHKERRQ(ierr);
1248   if (splitname) {
1249     ierr = PetscStrallocpy(splitname,&ilink->splitname);CHKERRQ(ierr);
1250   } else {
1251     ierr = PetscMalloc1(8,&ilink->splitname);CHKERRQ(ierr);
1252     ierr = PetscSNPrintf(ilink->splitname,7,"%D",jac->nsplits);CHKERRQ(ierr);
1253   }
1254   ierr          = PetscObjectReference((PetscObject)is);CHKERRQ(ierr);
1255   ierr          = ISDestroy(&ilink->is);CHKERRQ(ierr);
1256   ilink->is     = is;
1257   ierr          = PetscObjectReference((PetscObject)is);CHKERRQ(ierr);
1258   ierr          = ISDestroy(&ilink->is_col);CHKERRQ(ierr);
1259   ilink->is_col = is;
1260   ilink->next   = NULL;
1261   ierr          = KSPCreate(PetscObjectComm((PetscObject)pc),&ilink->ksp);CHKERRQ(ierr);
1262   ierr          = PetscObjectIncrementTabLevel((PetscObject)ilink->ksp,(PetscObject)pc,1);CHKERRQ(ierr);
1263   ierr          = KSPSetType(ilink->ksp,KSPPREONLY);CHKERRQ(ierr);
1264   ierr          = PetscLogObjectParent((PetscObject)pc,(PetscObject)ilink->ksp);CHKERRQ(ierr);
1265 
1266   ierr = PetscSNPrintf(prefix,sizeof(prefix),"%sfieldsplit_%s_",((PetscObject)pc)->prefix ? ((PetscObject)pc)->prefix : "",ilink->splitname);CHKERRQ(ierr);
1267   ierr = KSPSetOptionsPrefix(ilink->ksp,prefix);CHKERRQ(ierr);
1268 
1269   if (!next) {
1270     jac->head       = ilink;
1271     ilink->previous = NULL;
1272   } else {
1273     while (next->next) {
1274       next = next->next;
1275     }
1276     next->next      = ilink;
1277     ilink->previous = next;
1278   }
1279   jac->nsplits++;
1280   PetscFunctionReturn(0);
1281 }
1282 
1283 #undef __FUNCT__
1284 #define __FUNCT__ "PCFieldSplitSetFields"
1285 /*@
1286     PCFieldSplitSetFields - Sets the fields for one particular split in the field split preconditioner
1287 
1288     Logically Collective on PC
1289 
1290     Input Parameters:
1291 +   pc  - the preconditioner context
1292 .   splitname - name of this split, if NULL the number of the split is used
1293 .   n - the number of fields in this split
1294 -   fields - the fields in this split
1295 
1296     Level: intermediate
1297 
1298     Notes: Use PCFieldSplitSetIS() to set a completely general set of indices as a field.
1299 
1300      The PCFieldSplitSetFields() is for defining fields as strided blocks. For example, if the block
1301      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
1302      0xx3xx6xx9xx12 ... x1xx4xx7xx ... xx2xx5xx8xx.. 01x34x67x... 0x1x3x5x7.. x12x45x78x....
1303      where the numbered entries indicate what is in the field.
1304 
1305      This function is called once per split (it creates a new split each time).  Solve options
1306      for this split will be available under the prefix -fieldsplit_SPLITNAME_.
1307 
1308      Developer Note: This routine does not actually create the IS representing the split, that is delayed
1309      until PCSetUp_FieldSplit(), because information about the vector/matrix layouts may not be
1310      available when this routine is called.
1311 
1312 .seealso: PCFieldSplitGetSubKSP(), PCFIELDSPLIT, PCFieldSplitSetBlockSize(), PCFieldSplitSetIS()
1313 
1314 @*/
1315 PetscErrorCode  PCFieldSplitSetFields(PC pc,const char splitname[],PetscInt n,const PetscInt *fields,const PetscInt *fields_col)
1316 {
1317   PetscErrorCode ierr;
1318 
1319   PetscFunctionBegin;
1320   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
1321   PetscValidCharPointer(splitname,2);
1322   if (n < 1) SETERRQ2(PetscObjectComm((PetscObject)pc),PETSC_ERR_ARG_OUTOFRANGE,"Provided number of fields %D in split \"%s\" not positive",n,splitname);
1323   PetscValidIntPointer(fields,3);
1324   ierr = PetscTryMethod(pc,"PCFieldSplitSetFields_C",(PC,const char[],PetscInt,const PetscInt*,const PetscInt*),(pc,splitname,n,fields,fields_col));CHKERRQ(ierr);
1325   PetscFunctionReturn(0);
1326 }
1327 
1328 #undef __FUNCT__
1329 #define __FUNCT__ "PCFieldSplitSetIS"
1330 /*@
1331     PCFieldSplitSetIS - Sets the exact elements for field
1332 
1333     Logically Collective on PC
1334 
1335     Input Parameters:
1336 +   pc  - the preconditioner context
1337 .   splitname - name of this split, if NULL the number of the split is used
1338 -   is - the index set that defines the vector elements in this field
1339 
1340 
1341     Notes:
1342     Use PCFieldSplitSetFields(), for fields defined by strided types.
1343 
1344     This function is called once per split (it creates a new split each time).  Solve options
1345     for this split will be available under the prefix -fieldsplit_SPLITNAME_.
1346 
1347     Level: intermediate
1348 
1349 .seealso: PCFieldSplitGetSubKSP(), PCFIELDSPLIT, PCFieldSplitSetBlockSize()
1350 
1351 @*/
1352 PetscErrorCode  PCFieldSplitSetIS(PC pc,const char splitname[],IS is)
1353 {
1354   PetscErrorCode ierr;
1355 
1356   PetscFunctionBegin;
1357   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
1358   if (splitname) PetscValidCharPointer(splitname,2);
1359   PetscValidHeaderSpecific(is,IS_CLASSID,3);
1360   ierr = PetscTryMethod(pc,"PCFieldSplitSetIS_C",(PC,const char[],IS),(pc,splitname,is));CHKERRQ(ierr);
1361   PetscFunctionReturn(0);
1362 }
1363 
1364 #undef __FUNCT__
1365 #define __FUNCT__ "PCFieldSplitGetIS"
1366 /*@
1367     PCFieldSplitGetIS - Retrieves the elements for a field as an IS
1368 
1369     Logically Collective on PC
1370 
1371     Input Parameters:
1372 +   pc  - the preconditioner context
1373 -   splitname - name of this split
1374 
1375     Output Parameter:
1376 -   is - the index set that defines the vector elements in this field, or NULL if the field is not found
1377 
1378     Level: intermediate
1379 
1380 .seealso: PCFieldSplitGetSubKSP(), PCFIELDSPLIT, PCFieldSplitSetIS()
1381 
1382 @*/
1383 PetscErrorCode PCFieldSplitGetIS(PC pc,const char splitname[],IS *is)
1384 {
1385   PetscErrorCode ierr;
1386 
1387   PetscFunctionBegin;
1388   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
1389   PetscValidCharPointer(splitname,2);
1390   PetscValidPointer(is,3);
1391   {
1392     PC_FieldSplit     *jac  = (PC_FieldSplit*) pc->data;
1393     PC_FieldSplitLink ilink = jac->head;
1394     PetscBool         found;
1395 
1396     *is = NULL;
1397     while (ilink) {
1398       ierr = PetscStrcmp(ilink->splitname, splitname, &found);CHKERRQ(ierr);
1399       if (found) {
1400         *is = ilink->is;
1401         break;
1402       }
1403       ilink = ilink->next;
1404     }
1405   }
1406   PetscFunctionReturn(0);
1407 }
1408 
1409 #undef __FUNCT__
1410 #define __FUNCT__ "PCFieldSplitSetBlockSize"
1411 /*@
1412     PCFieldSplitSetBlockSize - Sets the block size for defining where fields start in the
1413       fieldsplit preconditioner. If not set the matrix block size is used.
1414 
1415     Logically Collective on PC
1416 
1417     Input Parameters:
1418 +   pc  - the preconditioner context
1419 -   bs - the block size
1420 
1421     Level: intermediate
1422 
1423 .seealso: PCFieldSplitGetSubKSP(), PCFIELDSPLIT, PCFieldSplitSetFields()
1424 
1425 @*/
1426 PetscErrorCode  PCFieldSplitSetBlockSize(PC pc,PetscInt bs)
1427 {
1428   PetscErrorCode ierr;
1429 
1430   PetscFunctionBegin;
1431   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
1432   PetscValidLogicalCollectiveInt(pc,bs,2);
1433   ierr = PetscTryMethod(pc,"PCFieldSplitSetBlockSize_C",(PC,PetscInt),(pc,bs));CHKERRQ(ierr);
1434   PetscFunctionReturn(0);
1435 }
1436 
1437 #undef __FUNCT__
1438 #define __FUNCT__ "PCFieldSplitGetSubKSP"
1439 /*@C
1440    PCFieldSplitGetSubKSP - Gets the KSP contexts for all splits
1441 
1442    Collective on KSP
1443 
1444    Input Parameter:
1445 .  pc - the preconditioner context
1446 
1447    Output Parameters:
1448 +  n - the number of splits
1449 -  pc - the array of KSP contexts
1450 
1451    Note:
1452    After PCFieldSplitGetSubKSP() the array of KSPs IS to be freed by the user
1453    (not the KSP just the array that contains them).
1454 
1455    You must call KSPSetUp() before calling PCFieldSplitGetSubKSP().
1456 
1457    Fortran Usage: You must pass in a KSP array that is large enough to contain all the local KSPs.
1458       You can call PCFieldSplitGetSubKSP(pc,n,NULL_OBJECT,ierr) to determine how large the
1459       KSP array must be.
1460 
1461 
1462    Level: advanced
1463 
1464 .seealso: PCFIELDSPLIT
1465 @*/
1466 PetscErrorCode  PCFieldSplitGetSubKSP(PC pc,PetscInt *n,KSP *subksp[])
1467 {
1468   PetscErrorCode ierr;
1469 
1470   PetscFunctionBegin;
1471   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
1472   if (n) PetscValidIntPointer(n,2);
1473   ierr = PetscUseMethod(pc,"PCFieldSplitGetSubKSP_C",(PC,PetscInt*,KSP **),(pc,n,subksp));CHKERRQ(ierr);
1474   PetscFunctionReturn(0);
1475 }
1476 
1477 #undef __FUNCT__
1478 #define __FUNCT__ "PCFieldSplitSchurPrecondition"
1479 /*@
1480     PCFieldSplitSchurPrecondition -  Indicates if the Schur complement is preconditioned by a preconditioner constructed by the
1481       A11 matrix. Otherwise no preconditioner is used.
1482 
1483     Collective on PC
1484 
1485     Input Parameters:
1486 +   pc      - the preconditioner context
1487 .   ptype   - which matrix to use for preconditioning the Schur complement: PC_FIELDSPLIT_SCHUR_PRE_A11 (default), PC_FIELDSPLIT_SCHUR_PRE_SELF, PC_FIELDSPLIT_PRE_USER
1488 -   userpre - matrix to use for preconditioning, or NULL
1489 
1490     Options Database:
1491 .     -pc_fieldsplit_schur_precondition <self,selfp,user,a11,full> default is a11
1492 
1493     Notes:
1494 $    If ptype is
1495 $        user then the preconditioner for the Schur complement is generated by the provided matrix (pre argument
1496 $             to this function).
1497 $        a11 then the preconditioner for the Schur complement is generated by the block diagonal part of the original
1498 $             matrix associated with the Schur complement (i.e. A11)
1499 $        full then the preconditioner uses the exact Schur complement (this is expensive)
1500 $        self the preconditioner for the Schur complement is generated from the Schur complement matrix itself:
1501 $             The only preconditioner that currently works directly with the Schur complement matrix object is the PCLSC
1502 $             preconditioner
1503 $        selfp then the preconditioning matrix is an explicitly-assembled approximation Sp = A11 - A10 inv(diag(A00)) A01
1504 $             This is only a good preconditioner when diag(A00) is a good preconditioner for A00.
1505 
1506      When solving a saddle point problem, where the A11 block is identically zero, using a11 as the ptype only makes sense
1507     with the additional option -fieldsplit_1_pc_type none. Usually for saddle point problems one would use a ptype of self and
1508     -fieldsplit_1_pc_type lsc which uses the least squares commutator to compute a preconditioner for the Schur complement.
1509 
1510     Developer Notes: This is a terrible name, which gives no good indication of what the function does.
1511                      Among other things, it should have 'Set' in the name, since it sets the type of matrix to use.
1512 
1513     Level: intermediate
1514 
1515 .seealso: PCFieldSplitGetSubKSP(), PCFIELDSPLIT, PCFieldSplitSetFields(), PCFieldSplitSchurPreType, PCLSC
1516 
1517 @*/
1518 PetscErrorCode  PCFieldSplitSchurPrecondition(PC pc,PCFieldSplitSchurPreType ptype,Mat pre)
1519 {
1520   PetscErrorCode ierr;
1521 
1522   PetscFunctionBegin;
1523   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
1524   ierr = PetscTryMethod(pc,"PCFieldSplitSchurPrecondition_C",(PC,PCFieldSplitSchurPreType,Mat),(pc,ptype,pre));CHKERRQ(ierr);
1525   PetscFunctionReturn(0);
1526 }
1527 
1528 #undef __FUNCT__
1529 #define __FUNCT__ "PCFieldSplitSchurGetS"
1530 /*@
1531     PCFieldSplitSchurGetS -  extract the MatSchurComplement object used by this PC in case it needs to be configured separately
1532 
1533     Not collective
1534 
1535     Input Parameter:
1536 .   pc      - the preconditioner context
1537 
1538     Output Parameter:
1539 .   S       - the Schur complement matrix
1540 
1541     Notes:
1542     This matrix should not be destroyed using MatDestroy(); rather, use PCFieldSplitSchurRestoreS().
1543 
1544     Level: advanced
1545 
1546 .seealso: PCFieldSplitGetSubKSP(), PCFIELDSPLIT, PCFieldSplitSchurPreType, PCFieldSplitSchurPrecondition(), MatSchurComplement, PCFieldSplitSchurRestoreS()
1547 
1548 @*/
1549 PetscErrorCode  PCFieldSplitSchurGetS(PC pc,Mat *S)
1550 {
1551   PetscErrorCode ierr;
1552   const char*    t;
1553   PetscBool      isfs;
1554   PC_FieldSplit  *jac;
1555 
1556   PetscFunctionBegin;
1557   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
1558   ierr = PetscObjectGetType((PetscObject)pc,&t);CHKERRQ(ierr);
1559   ierr = PetscStrcmp(t,PCFIELDSPLIT,&isfs);CHKERRQ(ierr);
1560   if (!isfs) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Expected PC of type PCFIELDSPLIT, got %s instead",t);
1561   jac = (PC_FieldSplit*)pc->data;
1562   if (jac->type != PC_COMPOSITE_SCHUR) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Expected PCFIELDSPLIT of type SCHUR, got %D instead",jac->type);
1563   if (S) *S = jac->schur;
1564   PetscFunctionReturn(0);
1565 }
1566 
1567 #undef __FUNCT__
1568 #define __FUNCT__ "PCFieldSplitSchurRestoreS"
1569 /*@
1570     PCFieldSplitSchurRestoreS -  restores the MatSchurComplement object used by this PC
1571 
1572     Not collective
1573 
1574     Input Parameters:
1575 +   pc      - the preconditioner context
1576 .   S       - the Schur complement matrix
1577 
1578     Level: advanced
1579 
1580 .seealso: PCFieldSplitGetSubKSP(), PCFIELDSPLIT, PCFieldSplitSchurPreType, PCFieldSplitSchurPrecondition(), MatSchurComplement, PCFieldSplitSchurGetS()
1581 
1582 @*/
1583 PetscErrorCode  PCFieldSplitSchurRestoreS(PC pc,Mat *S)
1584 {
1585   PetscErrorCode ierr;
1586   const char*    t;
1587   PetscBool      isfs;
1588   PC_FieldSplit  *jac;
1589 
1590   PetscFunctionBegin;
1591   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
1592   ierr = PetscObjectGetType((PetscObject)pc,&t);CHKERRQ(ierr);
1593   ierr = PetscStrcmp(t,PCFIELDSPLIT,&isfs);CHKERRQ(ierr);
1594   if (!isfs) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Expected PC of type PCFIELDSPLIT, got %s instead",t);
1595   jac = (PC_FieldSplit*)pc->data;
1596   if (jac->type != PC_COMPOSITE_SCHUR) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Expected PCFIELDSPLIT of type SCHUR, got %D instead",jac->type);
1597   if (!S || *S != jac->schur) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"MatSchurComplement restored is not the same as gotten");
1598   PetscFunctionReturn(0);
1599 }
1600 
1601 
1602 #undef __FUNCT__
1603 #define __FUNCT__ "PCFieldSplitSchurPrecondition_FieldSplit"
1604 static PetscErrorCode  PCFieldSplitSchurPrecondition_FieldSplit(PC pc,PCFieldSplitSchurPreType ptype,Mat pre)
1605 {
1606   PC_FieldSplit  *jac = (PC_FieldSplit*)pc->data;
1607   PetscErrorCode ierr;
1608 
1609   PetscFunctionBegin;
1610   jac->schurpre = ptype;
1611   if (ptype == PC_FIELDSPLIT_SCHUR_PRE_USER && pre) {
1612     ierr            = MatDestroy(&jac->schur_user);CHKERRQ(ierr);
1613     jac->schur_user = pre;
1614     ierr            = PetscObjectReference((PetscObject)jac->schur_user);CHKERRQ(ierr);
1615   }
1616   PetscFunctionReturn(0);
1617 }
1618 
1619 #undef __FUNCT__
1620 #define __FUNCT__ "PCFieldSplitSetSchurFactType"
1621 /*@
1622     PCFieldSplitSetSchurFactType -  sets which blocks of the approximate block factorization to retain
1623 
1624     Collective on PC
1625 
1626     Input Parameters:
1627 +   pc  - the preconditioner context
1628 -   ftype - which blocks of factorization to retain, PC_FIELDSPLIT_SCHUR_FACT_FULL is default
1629 
1630     Options Database:
1631 .     -pc_fieldsplit_schur_fact_type <diag,lower,upper,full> default is full
1632 
1633 
1634     Level: intermediate
1635 
1636     Notes:
1637     The FULL factorization is
1638 
1639 $   (A   B)  = (1       0) (A   0) (1  Ainv*B)
1640 $   (C   D)    (C*Ainv  1) (0   S) (0     1  )
1641 
1642     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,
1643     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).
1644 
1645     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
1646     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
1647     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,
1648     the preconditioned operator has three distinct nonzero eigenvalues and minimal polynomial of degree at most 4, so KSPGMRES converges in at most 4 iterations.
1649 
1650     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
1651     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).
1652 
1653     References:
1654     Murphy, Golub, and Wathen, A note on preconditioning indefinite linear systems, SIAM J. Sci. Comput., 21 (2000) pp. 1969-1972.
1655 
1656     Ipsen, A note on preconditioning nonsymmetric matrices, SIAM J. Sci. Comput., 23 (2001), pp. 1050-1051.
1657 
1658 .seealso: PCFieldSplitGetSubKSP(), PCFIELDSPLIT, PCFieldSplitSetFields(), PCFieldSplitSchurPreType
1659 @*/
1660 PetscErrorCode  PCFieldSplitSetSchurFactType(PC pc,PCFieldSplitSchurFactType ftype)
1661 {
1662   PetscErrorCode ierr;
1663 
1664   PetscFunctionBegin;
1665   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
1666   ierr = PetscTryMethod(pc,"PCFieldSplitSetSchurFactType_C",(PC,PCFieldSplitSchurFactType),(pc,ftype));CHKERRQ(ierr);
1667   PetscFunctionReturn(0);
1668 }
1669 
1670 #undef __FUNCT__
1671 #define __FUNCT__ "PCFieldSplitSetSchurFactType_FieldSplit"
1672 static PetscErrorCode PCFieldSplitSetSchurFactType_FieldSplit(PC pc,PCFieldSplitSchurFactType ftype)
1673 {
1674   PC_FieldSplit *jac = (PC_FieldSplit*)pc->data;
1675 
1676   PetscFunctionBegin;
1677   jac->schurfactorization = ftype;
1678   PetscFunctionReturn(0);
1679 }
1680 
1681 #undef __FUNCT__
1682 #define __FUNCT__ "PCFieldSplitGetSchurBlocks"
1683 /*@C
1684    PCFieldSplitGetSchurBlocks - Gets all matrix blocks for the Schur complement
1685 
1686    Collective on KSP
1687 
1688    Input Parameter:
1689 .  pc - the preconditioner context
1690 
1691    Output Parameters:
1692 +  A00 - the (0,0) block
1693 .  A01 - the (0,1) block
1694 .  A10 - the (1,0) block
1695 -  A11 - the (1,1) block
1696 
1697    Level: advanced
1698 
1699 .seealso: PCFIELDSPLIT
1700 @*/
1701 PetscErrorCode  PCFieldSplitGetSchurBlocks(PC pc,Mat *A00,Mat *A01,Mat *A10, Mat *A11)
1702 {
1703   PC_FieldSplit *jac = (PC_FieldSplit*) pc->data;
1704 
1705   PetscFunctionBegin;
1706   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
1707   if (jac->type != PC_COMPOSITE_SCHUR) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_ARG_WRONG, "FieldSplit is not using a Schur complement approach.");
1708   if (A00) *A00 = jac->pmat[0];
1709   if (A01) *A01 = jac->B;
1710   if (A10) *A10 = jac->C;
1711   if (A11) *A11 = jac->pmat[1];
1712   PetscFunctionReturn(0);
1713 }
1714 
1715 #undef __FUNCT__
1716 #define __FUNCT__ "PCFieldSplitSetType_FieldSplit"
1717 static PetscErrorCode  PCFieldSplitSetType_FieldSplit(PC pc,PCCompositeType type)
1718 {
1719   PC_FieldSplit  *jac = (PC_FieldSplit*)pc->data;
1720   PetscErrorCode ierr;
1721 
1722   PetscFunctionBegin;
1723   jac->type = type;
1724   if (type == PC_COMPOSITE_SCHUR) {
1725     pc->ops->apply = PCApply_FieldSplit_Schur;
1726     pc->ops->view  = PCView_FieldSplit_Schur;
1727 
1728     ierr = PetscObjectComposeFunction((PetscObject)pc,"PCFieldSplitGetSubKSP_C",PCFieldSplitGetSubKSP_FieldSplit_Schur);CHKERRQ(ierr);
1729     ierr = PetscObjectComposeFunction((PetscObject)pc,"PCFieldSplitSchurPrecondition_C",PCFieldSplitSchurPrecondition_FieldSplit);CHKERRQ(ierr);
1730     ierr = PetscObjectComposeFunction((PetscObject)pc,"PCFieldSplitSetSchurFactType_C",PCFieldSplitSetSchurFactType_FieldSplit);CHKERRQ(ierr);
1731 
1732   } else {
1733     pc->ops->apply = PCApply_FieldSplit;
1734     pc->ops->view  = PCView_FieldSplit;
1735 
1736     ierr = PetscObjectComposeFunction((PetscObject)pc,"PCFieldSplitGetSubKSP_C",PCFieldSplitGetSubKSP_FieldSplit);CHKERRQ(ierr);
1737     ierr = PetscObjectComposeFunction((PetscObject)pc,"PCFieldSplitSchurPrecondition_C",0);CHKERRQ(ierr);
1738     ierr = PetscObjectComposeFunction((PetscObject)pc,"PCFieldSplitSetSchurFactType_C",0);CHKERRQ(ierr);
1739   }
1740   PetscFunctionReturn(0);
1741 }
1742 
1743 #undef __FUNCT__
1744 #define __FUNCT__ "PCFieldSplitSetBlockSize_FieldSplit"
1745 static PetscErrorCode  PCFieldSplitSetBlockSize_FieldSplit(PC pc,PetscInt bs)
1746 {
1747   PC_FieldSplit *jac = (PC_FieldSplit*)pc->data;
1748 
1749   PetscFunctionBegin;
1750   if (bs < 1) SETERRQ1(PetscObjectComm((PetscObject)pc),PETSC_ERR_ARG_OUTOFRANGE,"Blocksize must be positive, you gave %D",bs);
1751   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);
1752   jac->bs = bs;
1753   PetscFunctionReturn(0);
1754 }
1755 
1756 #undef __FUNCT__
1757 #define __FUNCT__ "PCFieldSplitSetType"
1758 /*@
1759    PCFieldSplitSetType - Sets the type of fieldsplit preconditioner.
1760 
1761    Collective on PC
1762 
1763    Input Parameter:
1764 .  pc - the preconditioner context
1765 .  type - PC_COMPOSITE_ADDITIVE, PC_COMPOSITE_MULTIPLICATIVE (default), PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE, PC_COMPOSITE_SPECIAL, PC_COMPOSITE_SCHUR
1766 
1767    Options Database Key:
1768 .  -pc_fieldsplit_type <type: one of multiplicative, additive, symmetric_multiplicative, special, schur> - Sets fieldsplit preconditioner type
1769 
1770    Level: Intermediate
1771 
1772 .keywords: PC, set, type, composite preconditioner, additive, multiplicative
1773 
1774 .seealso: PCCompositeSetType()
1775 
1776 @*/
1777 PetscErrorCode  PCFieldSplitSetType(PC pc,PCCompositeType type)
1778 {
1779   PetscErrorCode ierr;
1780 
1781   PetscFunctionBegin;
1782   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
1783   ierr = PetscTryMethod(pc,"PCFieldSplitSetType_C",(PC,PCCompositeType),(pc,type));CHKERRQ(ierr);
1784   PetscFunctionReturn(0);
1785 }
1786 
1787 #undef __FUNCT__
1788 #define __FUNCT__ "PCFieldSplitGetType"
1789 /*@
1790   PCFieldSplitGetType - Gets the type of fieldsplit preconditioner.
1791 
1792   Not collective
1793 
1794   Input Parameter:
1795 . pc - the preconditioner context
1796 
1797   Output Parameter:
1798 . type - PC_COMPOSITE_ADDITIVE, PC_COMPOSITE_MULTIPLICATIVE (default), PC_COMPOSITE_SYMMETRIC_MULTIPLICATIVE, PC_COMPOSITE_SPECIAL, PC_COMPOSITE_SCHUR
1799 
1800   Level: Intermediate
1801 
1802 .keywords: PC, set, type, composite preconditioner, additive, multiplicative
1803 .seealso: PCCompositeSetType()
1804 @*/
1805 PetscErrorCode PCFieldSplitGetType(PC pc, PCCompositeType *type)
1806 {
1807   PC_FieldSplit *jac = (PC_FieldSplit*) pc->data;
1808 
1809   PetscFunctionBegin;
1810   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
1811   PetscValidIntPointer(type,2);
1812   *type = jac->type;
1813   PetscFunctionReturn(0);
1814 }
1815 
1816 #undef __FUNCT__
1817 #define __FUNCT__ "PCFieldSplitSetDMSplits"
1818 /*@
1819    PCFieldSplitSetDMSplits - Flags whether DMCreateFieldDecomposition() should be used to define the splits, whenever possible.
1820 
1821    Logically Collective
1822 
1823    Input Parameters:
1824 +  pc   - the preconditioner context
1825 -  flg  - boolean indicating whether to use field splits defined by the DM
1826 
1827    Options Database Key:
1828 .  -pc_fieldsplit_dm_splits
1829 
1830    Level: Intermediate
1831 
1832 .keywords: PC, DM, composite preconditioner, additive, multiplicative
1833 
1834 .seealso: PCFieldSplitGetDMSplits()
1835 
1836 @*/
1837 PetscErrorCode  PCFieldSplitSetDMSplits(PC pc,PetscBool flg)
1838 {
1839   PC_FieldSplit  *jac = (PC_FieldSplit*)pc->data;
1840   PetscBool      isfs;
1841   PetscErrorCode ierr;
1842 
1843   PetscFunctionBegin;
1844   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
1845   PetscValidLogicalCollectiveBool(pc,flg,2);
1846   ierr = PetscObjectTypeCompare((PetscObject)pc,PCFIELDSPLIT,&isfs);CHKERRQ(ierr);
1847   if (isfs) {
1848     jac->dm_splits = flg;
1849   }
1850   PetscFunctionReturn(0);
1851 }
1852 
1853 
1854 #undef __FUNCT__
1855 #define __FUNCT__ "PCFieldSplitGetDMSplits"
1856 /*@
1857    PCFieldSplitGetDMSplits - Returns flag indicating whether DMCreateFieldDecomposition() should be used to define the splits, whenever possible.
1858 
1859    Logically Collective
1860 
1861    Input Parameter:
1862 .  pc   - the preconditioner context
1863 
1864    Output Parameter:
1865 .  flg  - boolean indicating whether to use field splits defined by the DM
1866 
1867    Level: Intermediate
1868 
1869 .keywords: PC, DM, composite preconditioner, additive, multiplicative
1870 
1871 .seealso: PCFieldSplitSetDMSplits()
1872 
1873 @*/
1874 PetscErrorCode  PCFieldSplitGetDMSplits(PC pc,PetscBool* flg)
1875 {
1876   PC_FieldSplit  *jac = (PC_FieldSplit*)pc->data;
1877   PetscBool      isfs;
1878   PetscErrorCode ierr;
1879 
1880   PetscFunctionBegin;
1881   PetscValidHeaderSpecific(pc,PC_CLASSID,1);
1882   PetscValidPointer(flg,2);
1883   ierr = PetscObjectTypeCompare((PetscObject)pc,PCFIELDSPLIT,&isfs);CHKERRQ(ierr);
1884   if (isfs) {
1885     if(flg) *flg = jac->dm_splits;
1886   }
1887   PetscFunctionReturn(0);
1888 }
1889 
1890 /* -------------------------------------------------------------------------------------*/
1891 /*MC
1892    PCFIELDSPLIT - Preconditioner created by combining separate preconditioners for individual
1893                   fields or groups of fields. See the users manual section "Solving Block Matrices" for more details.
1894 
1895      To set options on the solvers for each block append -fieldsplit_ to all the PC
1896         options database keys. For example, -fieldsplit_pc_type ilu -fieldsplit_pc_factor_levels 1
1897 
1898      To set the options on the solvers separate for each block call PCFieldSplitGetSubKSP()
1899          and set the options directly on the resulting KSP object
1900 
1901    Level: intermediate
1902 
1903    Options Database Keys:
1904 +   -pc_fieldsplit_%d_fields <a,b,..> - indicates the fields to be used in the %d'th split
1905 .   -pc_fieldsplit_default - automatically add any fields to additional splits that have not
1906                               been supplied explicitly by -pc_fieldsplit_%d_fields
1907 .   -pc_fieldsplit_block_size <bs> - size of block that defines fields (i.e. there are bs fields)
1908 .   -pc_fieldsplit_type <additive,multiplicative,symmetric_multiplicative,schur> - type of relaxation or factorization splitting
1909 .   -pc_fieldsplit_schur_precondition <self,selfp,user,a11,full> - default is a11
1910 .   -pc_fieldsplit_detect_saddle_point - automatically finds rows with zero or negative diagonal and uses Schur complement with no preconditioner as the solver
1911 
1912 -    Options prefix for inner solvers when using Schur complement preconditioner are -fieldsplit_0_ and -fieldsplit_1_
1913      for all other solvers they are -fieldsplit_%d_ for the dth field, use -fieldsplit_ for all fields
1914 
1915    Notes:
1916     Use PCFieldSplitSetFields() to set fields defined by "strided" entries and PCFieldSplitSetIS()
1917      to define a field by an arbitrary collection of entries.
1918 
1919       If no fields are set the default is used. The fields are defined by entries strided by bs,
1920       beginning at 0 then 1, etc to bs-1. The block size can be set with PCFieldSplitSetBlockSize(),
1921       if this is not called the block size defaults to the blocksize of the second matrix passed
1922       to KSPSetOperators()/PCSetOperators().
1923 
1924 $     For the Schur complement preconditioner if J = ( A00 A01 )
1925 $                                                    ( A10 A11 )
1926 $     the preconditioner using full factorization is
1927 $              ( I   -ksp(A00) A01 ) ( inv(A00)     0  ) (     I          0  )
1928 $              ( 0         I       ) (   0      ksp(S) ) ( -A10 ksp(A00)  I  )
1929      where the action of inv(A00) is applied using the KSP solver with prefix -fieldsplit_0_.  S is the Schur complement
1930 $              S = A11 - A10 ksp(A00) A01
1931      which is usually dense and not stored explicitly.  The action of ksp(S) is computed using the KSP solver with prefix -fieldsplit_splitname_ (where splitname was given
1932      in providing the SECOND split or 1 if not give). For PCFieldSplitGetKSP() when field number is 0,
1933      it returns the KSP associated with -fieldsplit_0_ while field number 1 gives -fieldsplit_1_ KSP. By default
1934      A11 is used to construct a preconditioner for S, use PCFieldSplitSchurPrecondition() to turn on or off this
1935      option. You can use the preconditioner PCLSC to precondition the Schur complement with -fieldsplit_1_pc_type lsc.
1936      When option -fieldsplit_schur_precondition selfp is given, an approximation to S is assembled --
1937      Sp = A11 - A10 inv(diag(A00)) A01, which has type AIJ and can be used with a variety of preconditioners
1938      (e.g., -fieldsplit_1_pc_type asm).
1939      The factorization type is set using -pc_fieldsplit_schur_fact_type <diag, lower, upper, full>. The full is shown above,
1940      diag gives
1941 $              ( inv(A00)     0   )
1942 $              (   0      -ksp(S) )
1943      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
1944 $              (  A00   0 )
1945 $              (  A10   S )
1946      where the inverses of A00 and S are applied using KSPs. The upper factorization is the inverse of
1947 $              ( A00 A01 )
1948 $              (  0   S  )
1949      where again the inverses of A00 and S are applied using KSPs.
1950 
1951      If only one set of indices (one IS) is provided with PCFieldSplitSetIS() then the complement of that IS
1952      is used automatically for a second block.
1953 
1954      The fieldsplit preconditioner cannot currently be used with the BAIJ or SBAIJ data formats if the blocksize is larger than 1.
1955      Generally it should be used with the AIJ format.
1956 
1957      The forms of these preconditioners are closely related if not identical to forms derived as "Distributive Iterations", see,
1958      for example, page 294 in "Principles of Computational Fluid Dynamics" by Pieter Wesseling. Note that one can also use PCFIELDSPLIT
1959      inside a smoother resulting in "Distributive Smoothers".
1960 
1961    Concepts: physics based preconditioners, block preconditioners
1962 
1963 .seealso:  PCCreate(), PCSetType(), PCType (for list of available types), PC, Block_Preconditioners, PCLSC,
1964            PCFieldSplitGetSubKSP(), PCFieldSplitSetFields(), PCFieldSplitSetType(), PCFieldSplitSetIS(), PCFieldSplitSchurPrecondition()
1965 M*/
1966 
1967 #undef __FUNCT__
1968 #define __FUNCT__ "PCCreate_FieldSplit"
1969 PETSC_EXTERN PetscErrorCode PCCreate_FieldSplit(PC pc)
1970 {
1971   PetscErrorCode ierr;
1972   PC_FieldSplit  *jac;
1973 
1974   PetscFunctionBegin;
1975   ierr = PetscNewLog(pc,&jac);CHKERRQ(ierr);
1976 
1977   jac->bs                 = -1;
1978   jac->nsplits            = 0;
1979   jac->type               = PC_COMPOSITE_MULTIPLICATIVE;
1980   jac->schurpre           = PC_FIELDSPLIT_SCHUR_PRE_USER; /* Try user preconditioner first, fall back on diagonal */
1981   jac->schurfactorization = PC_FIELDSPLIT_SCHUR_FACT_FULL;
1982   jac->dm_splits          = PETSC_TRUE;
1983 
1984   pc->data = (void*)jac;
1985 
1986   pc->ops->apply           = PCApply_FieldSplit;
1987   pc->ops->applytranspose  = PCApplyTranspose_FieldSplit;
1988   pc->ops->setup           = PCSetUp_FieldSplit;
1989   pc->ops->reset           = PCReset_FieldSplit;
1990   pc->ops->destroy         = PCDestroy_FieldSplit;
1991   pc->ops->setfromoptions  = PCSetFromOptions_FieldSplit;
1992   pc->ops->view            = PCView_FieldSplit;
1993   pc->ops->applyrichardson = 0;
1994 
1995   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCFieldSplitGetSubKSP_C",PCFieldSplitGetSubKSP_FieldSplit);CHKERRQ(ierr);
1996   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCFieldSplitSetFields_C",PCFieldSplitSetFields_FieldSplit);CHKERRQ(ierr);
1997   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCFieldSplitSetIS_C",PCFieldSplitSetIS_FieldSplit);CHKERRQ(ierr);
1998   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCFieldSplitSetType_C",PCFieldSplitSetType_FieldSplit);CHKERRQ(ierr);
1999   ierr = PetscObjectComposeFunction((PetscObject)pc,"PCFieldSplitSetBlockSize_C",PCFieldSplitSetBlockSize_FieldSplit);CHKERRQ(ierr);
2000   PetscFunctionReturn(0);
2001 }
2002 
2003 
2004 
2005