xref: /petsc/src/snes/impls/fas/fas.c (revision c688d0420b4e513ff34944d1e1ad7d4e50aafa8d)
1 /* Defines the basic SNES object */
2 #include <../src/snes/impls/fas/fasimpls.h>    /*I  "petscsnes.h"  I*/
3 
4 const char *const SNESFASTypes[] = {"MULTIPLICATIVE","ADDITIVE","FULL","KASKADE","SNESFASType","SNES_FAS",0};
5 
6 extern PetscErrorCode SNESFASGalerkinDefaultFunction(SNES,Vec,Vec,void*);
7 
8 #undef __FUNCT__
9 #define __FUNCT__ "SNESReset_FAS"
10 static PetscErrorCode SNESReset_FAS(SNES snes)
11 {
12   PetscErrorCode ierr  = 0;
13   SNES_FAS       * fas = (SNES_FAS*)snes->data;
14 
15   PetscFunctionBegin;
16   ierr = SNESDestroy(&fas->smoothu);CHKERRQ(ierr);
17   ierr = SNESDestroy(&fas->smoothd);CHKERRQ(ierr);
18   ierr = MatDestroy(&fas->inject);CHKERRQ(ierr);
19   ierr = MatDestroy(&fas->interpolate);CHKERRQ(ierr);
20   ierr = MatDestroy(&fas->restrct);CHKERRQ(ierr);
21   ierr = VecDestroy(&fas->rscale);CHKERRQ(ierr);
22   if (fas->galerkin) {
23     ierr = VecDestroy(&fas->Xg);CHKERRQ(ierr);
24     ierr = VecDestroy(&fas->Fg);CHKERRQ(ierr);
25   }
26   if (fas->next) {ierr = SNESReset(fas->next);CHKERRQ(ierr);}
27   PetscFunctionReturn(0);
28 }
29 
30 #undef __FUNCT__
31 #define __FUNCT__ "SNESDestroy_FAS"
32 static PetscErrorCode SNESDestroy_FAS(SNES snes)
33 {
34   SNES_FAS       * fas = (SNES_FAS*)snes->data;
35   PetscErrorCode ierr  = 0;
36 
37   PetscFunctionBegin;
38   /* recursively resets and then destroys */
39   ierr = SNESReset(snes);CHKERRQ(ierr);
40   if (fas->next) {
41     ierr = SNESDestroy(&fas->next);CHKERRQ(ierr);
42   }
43   ierr = PetscFree(fas);CHKERRQ(ierr);
44   PetscFunctionReturn(0);
45 }
46 
47 #undef __FUNCT__
48 #define __FUNCT__ "SNESSetUp_FAS"
49 static PetscErrorCode SNESSetUp_FAS(SNES snes)
50 {
51   SNES_FAS       *fas = (SNES_FAS*) snes->data;
52   PetscErrorCode ierr;
53   PetscInt       dm_levels;
54   Vec            vec_sol, vec_func, vec_sol_update, vec_rhs; /* preserve these if they're set through the reset */
55   SNES           next;
56   PetscBool      isFine;
57   SNESLineSearch linesearch;
58   SNESLineSearch slinesearch;
59   void           *lsprectx,*lspostctx;
60   PetscErrorCode (*precheck)(SNESLineSearch,Vec,Vec,PetscBool*,void*);
61   PetscErrorCode (*postcheck)(SNESLineSearch,Vec,Vec,Vec,PetscBool*,PetscBool*,void*);
62 
63   PetscFunctionBegin;
64   ierr = SNESFASCycleIsFine(snes, &isFine);CHKERRQ(ierr);
65   if (fas->usedmfornumberoflevels && isFine) {
66     ierr = DMGetRefineLevel(snes->dm,&dm_levels);CHKERRQ(ierr);
67     dm_levels++;
68     if (dm_levels > fas->levels) {
69       /* we don't want the solution and func vectors to be destroyed in the SNESReset when it's called in SNESFASSetLevels_FAS*/
70       vec_sol              = snes->vec_sol;
71       vec_func             = snes->vec_func;
72       vec_sol_update       = snes->vec_sol_update;
73       vec_rhs              = snes->vec_rhs;
74       snes->vec_sol        = NULL;
75       snes->vec_func       = NULL;
76       snes->vec_sol_update = NULL;
77       snes->vec_rhs        = NULL;
78 
79       /* reset the number of levels */
80       ierr = SNESFASSetLevels(snes,dm_levels,NULL);CHKERRQ(ierr);
81       ierr = SNESSetFromOptions(snes);CHKERRQ(ierr);
82 
83       snes->vec_sol        = vec_sol;
84       snes->vec_func       = vec_func;
85       snes->vec_rhs        = vec_rhs;
86       snes->vec_sol_update = vec_sol_update;
87     }
88   }
89   ierr = SNESFASCycleGetCorrection(snes, &next);CHKERRQ(ierr);
90   if (!isFine) snes->gridsequence = 0; /* no grid sequencing inside the multigrid hierarchy! */
91 
92   ierr = SNESSetWorkVecs(snes, 2);CHKERRQ(ierr); /* work vectors used for intergrid transfers */
93 
94   /* set up the smoothers if they haven't already been set up */
95   if (!fas->smoothd) {
96     ierr = SNESFASCycleCreateSmoother_Private(snes, &fas->smoothd);CHKERRQ(ierr);
97   }
98 
99   if (snes->dm) {
100     /* set the smoother DMs properly */
101     if (fas->smoothu) ierr = SNESSetDM(fas->smoothu, snes->dm);CHKERRQ(ierr);
102     ierr = SNESSetDM(fas->smoothd, snes->dm);CHKERRQ(ierr);
103     /* construct EVERYTHING from the DM -- including the progressive set of smoothers */
104     if (next) {
105       /* for now -- assume the DM and the evaluation functions have been set externally */
106       if (!next->dm) {
107         ierr = DMCoarsen(snes->dm, PetscObjectComm((PetscObject)next), &next->dm);CHKERRQ(ierr);
108         ierr = SNESSetDM(next, next->dm);CHKERRQ(ierr);
109       }
110       /* set the interpolation and restriction from the DM */
111       if (!fas->interpolate) {
112         ierr = DMCreateInterpolation(next->dm, snes->dm, &fas->interpolate, &fas->rscale);CHKERRQ(ierr);
113         if (!fas->restrct) {
114           ierr         = PetscObjectReference((PetscObject)fas->interpolate);CHKERRQ(ierr);
115           fas->restrct = fas->interpolate;
116         }
117       }
118       /* set the injection from the DM */
119       if (!fas->inject) {
120         ierr = DMCreateInjection(next->dm, snes->dm, &fas->inject);CHKERRQ(ierr);
121       }
122     }
123   }
124   /*pass the smoother, function, and jacobian up to the next level if it's not user set already */
125   if (fas->galerkin) {
126     if (next) {
127       ierr = SNESSetFunction(next, NULL, SNESFASGalerkinDefaultFunction, next);CHKERRQ(ierr);
128     }
129     if (fas->smoothd && fas->level != fas->levels - 1) {
130       ierr = SNESSetFunction(fas->smoothd, NULL, SNESFASGalerkinDefaultFunction, snes);CHKERRQ(ierr);
131     }
132     if (fas->smoothu && fas->level != fas->levels - 1) {
133       ierr = SNESSetFunction(fas->smoothu, NULL, SNESFASGalerkinDefaultFunction, snes);CHKERRQ(ierr);
134     }
135   }
136 
137   /* sets the down (pre) smoother's default norm and sets it from options */
138   if (fas->smoothd) {
139     if (fas->level == 0 && fas->levels != 1) {
140       ierr = SNESSetNormSchedule(fas->smoothd, SNES_NORM_NONE);CHKERRQ(ierr);
141     } else {
142       ierr = SNESSetNormSchedule(fas->smoothd, SNES_NORM_FINAL_ONLY);CHKERRQ(ierr);
143     }
144     ierr = PetscObjectCopyFortranFunctionPointers((PetscObject)snes, (PetscObject)fas->smoothd);CHKERRQ(ierr);
145     ierr = SNESSetFromOptions(fas->smoothd);CHKERRQ(ierr);
146     ierr = SNESGetLineSearch(snes,&linesearch);CHKERRQ(ierr);
147     ierr = SNESGetLineSearch(fas->smoothd,&slinesearch);CHKERRQ(ierr);
148     ierr = SNESLineSearchGetPreCheck(linesearch,&precheck,&lsprectx);CHKERRQ(ierr);
149     ierr = SNESLineSearchGetPostCheck(linesearch,&postcheck,&lspostctx);CHKERRQ(ierr);
150     ierr = SNESLineSearchSetPreCheck(slinesearch,precheck,lsprectx);CHKERRQ(ierr);
151     ierr = SNESLineSearchSetPostCheck(slinesearch,postcheck,lspostctx);CHKERRQ(ierr);
152     ierr = PetscObjectCopyFortranFunctionPointers((PetscObject)linesearch, (PetscObject)slinesearch);CHKERRQ(ierr);
153 
154     fas->smoothd->vec_sol        = snes->vec_sol;
155     ierr                         = PetscObjectReference((PetscObject)snes->vec_sol);CHKERRQ(ierr);
156     fas->smoothd->vec_sol_update = snes->vec_sol_update;
157     ierr                         = PetscObjectReference((PetscObject)snes->vec_sol_update);CHKERRQ(ierr);
158     fas->smoothd->vec_func       = snes->vec_func;
159     ierr                         = PetscObjectReference((PetscObject)snes->vec_func);CHKERRQ(ierr);
160 
161     if (fas->eventsmoothsetup) {ierr = PetscLogEventBegin(fas->eventsmoothsetup,0,0,0,0);CHKERRQ(ierr);}
162     ierr = SNESSetUp(fas->smoothd);CHKERRQ(ierr);
163     if (fas->eventsmoothsetup) {ierr = PetscLogEventEnd(fas->eventsmoothsetup,0,0,0,0);CHKERRQ(ierr);}
164   }
165 
166   /* sets the up (post) smoother's default norm and sets it from options */
167   if (fas->smoothu) {
168     if (fas->level != fas->levels - 1) {
169       ierr = SNESSetNormSchedule(fas->smoothu, SNES_NORM_NONE);CHKERRQ(ierr);
170     } else {
171       ierr = SNESSetNormSchedule(fas->smoothu, SNES_NORM_FINAL_ONLY);CHKERRQ(ierr);
172     }
173     ierr = PetscObjectCopyFortranFunctionPointers((PetscObject)snes, (PetscObject)fas->smoothu);CHKERRQ(ierr);
174     ierr = SNESSetFromOptions(fas->smoothu);CHKERRQ(ierr);
175     ierr = SNESGetLineSearch(snes,&linesearch);CHKERRQ(ierr);
176     ierr = SNESGetLineSearch(fas->smoothu,&slinesearch);CHKERRQ(ierr);
177     ierr = SNESLineSearchGetPreCheck(linesearch,&precheck,&lsprectx);CHKERRQ(ierr);
178     ierr = SNESLineSearchGetPostCheck(linesearch,&postcheck,&lspostctx);CHKERRQ(ierr);
179     ierr = SNESLineSearchSetPreCheck(slinesearch,precheck,lsprectx);CHKERRQ(ierr);
180     ierr = SNESLineSearchSetPostCheck(slinesearch,postcheck,lspostctx);CHKERRQ(ierr);
181     ierr = PetscObjectCopyFortranFunctionPointers((PetscObject)linesearch, (PetscObject)slinesearch);CHKERRQ(ierr);
182 
183     fas->smoothu->vec_sol        = snes->vec_sol;
184     ierr                         = PetscObjectReference((PetscObject)snes->vec_sol);CHKERRQ(ierr);
185     fas->smoothu->vec_sol_update = snes->vec_sol_update;
186     ierr                         = PetscObjectReference((PetscObject)snes->vec_sol_update);CHKERRQ(ierr);
187     fas->smoothu->vec_func       = snes->vec_func;
188     ierr                         = PetscObjectReference((PetscObject)snes->vec_func);CHKERRQ(ierr);
189 
190     if (fas->eventsmoothsetup) {ierr = PetscLogEventBegin(fas->eventsmoothsetup,0,0,0,0);CHKERRQ(ierr);}
191     ierr = SNESSetUp(fas->smoothu);CHKERRQ(ierr);
192     if (fas->eventsmoothsetup) {ierr = PetscLogEventEnd(fas->eventsmoothsetup,0,0,0,0);CHKERRQ(ierr);}
193 
194   }
195 
196   if (next) {
197     /* gotta set up the solution vector for this to work */
198     if (!next->vec_sol) {ierr = SNESFASCreateCoarseVec(snes,&next->vec_sol);CHKERRQ(ierr);}
199     if (!next->vec_rhs) {ierr = SNESFASCreateCoarseVec(snes,&next->vec_rhs);CHKERRQ(ierr);}
200     ierr = PetscObjectCopyFortranFunctionPointers((PetscObject)snes, (PetscObject)next);CHKERRQ(ierr);
201     ierr = SNESGetLineSearch(snes,&linesearch);CHKERRQ(ierr);
202     ierr = SNESGetLineSearch(fas->next,&slinesearch);CHKERRQ(ierr);
203     ierr = SNESLineSearchGetPreCheck(linesearch,&precheck,&lsprectx);CHKERRQ(ierr);
204     ierr = SNESLineSearchGetPostCheck(linesearch,&postcheck,&lspostctx);CHKERRQ(ierr);
205     ierr = SNESLineSearchSetPreCheck(slinesearch,precheck,lsprectx);CHKERRQ(ierr);
206     ierr = SNESLineSearchSetPostCheck(slinesearch,postcheck,lspostctx);CHKERRQ(ierr);
207     ierr = PetscObjectCopyFortranFunctionPointers((PetscObject)linesearch, (PetscObject)slinesearch);CHKERRQ(ierr);
208     ierr = SNESSetUp(next);CHKERRQ(ierr);
209   }
210   /* setup FAS work vectors */
211   if (fas->galerkin) {
212     ierr = VecDuplicate(snes->vec_sol, &fas->Xg);CHKERRQ(ierr);
213     ierr = VecDuplicate(snes->vec_sol, &fas->Fg);CHKERRQ(ierr);
214   }
215   PetscFunctionReturn(0);
216 }
217 
218 #undef __FUNCT__
219 #define __FUNCT__ "SNESSetFromOptions_FAS"
220 static PetscErrorCode SNESSetFromOptions_FAS(PetscOptionItems *PetscOptionsObject,SNES snes)
221 {
222   SNES_FAS       *fas   = (SNES_FAS*) snes->data;
223   PetscInt       levels = 1;
224   PetscBool      flg    = PETSC_FALSE, upflg = PETSC_FALSE, downflg = PETSC_FALSE, monflg = PETSC_FALSE, galerkinflg = PETSC_FALSE,continuationflg = PETSC_FALSE;
225   PetscErrorCode ierr;
226   SNESFASType    fastype;
227   const char     *optionsprefix;
228   SNESLineSearch linesearch;
229   PetscInt       m, n_up, n_down;
230   SNES           next;
231   PetscBool      isFine;
232 
233   PetscFunctionBegin;
234   ierr = SNESFASCycleIsFine(snes, &isFine);CHKERRQ(ierr);
235   ierr = PetscOptionsHead(PetscOptionsObject,"SNESFAS Options-----------------------------------");CHKERRQ(ierr);
236 
237   /* number of levels -- only process most options on the finest level */
238   if (isFine) {
239     ierr = PetscOptionsInt("-snes_fas_levels", "Number of Levels", "SNESFASSetLevels", levels, &levels, &flg);CHKERRQ(ierr);
240     if (!flg && snes->dm) {
241       ierr = DMGetRefineLevel(snes->dm,&levels);CHKERRQ(ierr);
242       levels++;
243       fas->usedmfornumberoflevels = PETSC_TRUE;
244     }
245     ierr    = SNESFASSetLevels(snes, levels, NULL);CHKERRQ(ierr);
246     fastype = fas->fastype;
247     ierr    = PetscOptionsEnum("-snes_fas_type","FAS correction type","SNESFASSetType",SNESFASTypes,(PetscEnum)fastype,(PetscEnum*)&fastype,&flg);CHKERRQ(ierr);
248     if (flg) {
249       ierr = SNESFASSetType(snes, fastype);CHKERRQ(ierr);
250     }
251 
252     ierr = SNESGetOptionsPrefix(snes, &optionsprefix);CHKERRQ(ierr);
253     ierr = PetscOptionsInt("-snes_fas_cycles","Number of cycles","SNESFASSetCycles",fas->n_cycles,&m,&flg);CHKERRQ(ierr);
254     if (flg) {
255       ierr = SNESFASSetCycles(snes, m);CHKERRQ(ierr);
256     }
257     ierr = PetscOptionsBool("-snes_fas_continuation","Corrected grid-sequence continuation","SNESFASSetContinuation",fas->continuation,&continuationflg,&flg);CHKERRQ(ierr);
258     if (flg) {
259       ierr = SNESFASSetContinuation(snes,continuationflg);CHKERRQ(ierr);
260     }
261 
262     ierr = PetscOptionsBool("-snes_fas_galerkin", "Form coarse problems with Galerkin","SNESFASSetGalerkin",fas->galerkin,&galerkinflg,&flg);CHKERRQ(ierr);
263     if (flg) {
264       ierr = SNESFASSetGalerkin(snes, galerkinflg);CHKERRQ(ierr);
265     }
266 
267     if (fas->fastype == SNES_FAS_FULL) {
268       ierr   = PetscOptionsBool("-snes_fas_full_downsweep","Smooth on the initial upsweep for full FAS cycles","SNESFASFullSetDownSweep",fas->full_downsweep,&fas->full_downsweep,&flg);CHKERRQ(ierr);
269       if (flg) {SNESFASFullSetDownSweep(snes,fas->full_downsweep);CHKERRQ(ierr);}
270     }
271 
272     ierr = PetscOptionsInt("-snes_fas_smoothup","Number of post-smoothing steps","SNESFASSetNumberSmoothUp",fas->max_up_it,&n_up,&upflg);CHKERRQ(ierr);
273 
274     ierr = PetscOptionsInt("-snes_fas_smoothdown","Number of pre-smoothing steps","SNESFASSetNumberSmoothDown",fas->max_down_it,&n_down,&downflg);CHKERRQ(ierr);
275 
276     {
277       PetscViewer viewer;
278       PetscViewerFormat format;
279       ierr = PetscOptionsGetViewer(PetscObjectComm((PetscObject)snes),((PetscObject)snes)->prefix,
280                                    "-snes_fas_monitor",&viewer,&format,&monflg);CHKERRQ(ierr);
281       if (monflg) {
282         PetscViewerAndFormat *vf;
283         ierr = PetscViewerAndFormatCreate(viewer,format,&vf);CHKERRQ(ierr);
284         ierr = PetscObjectDereference((PetscObject)viewer);CHKERRQ(ierr);
285         ierr = SNESFASSetMonitor(snes,vf,PETSC_TRUE);CHKERRQ(ierr);
286       }
287     }
288     flg    = PETSC_FALSE;
289     monflg = PETSC_TRUE;
290     ierr   = PetscOptionsBool("-snes_fas_log","Log times for each FAS level","SNESFASSetLog",monflg,&monflg,&flg);CHKERRQ(ierr);
291     if (flg) {ierr = SNESFASSetLog(snes,monflg);CHKERRQ(ierr);}
292   }
293 
294   ierr = PetscOptionsTail();CHKERRQ(ierr);
295   /* setup from the determined types if there is no pointwise procedure or smoother defined */
296   if (upflg) {
297     ierr = SNESFASSetNumberSmoothUp(snes,n_up);CHKERRQ(ierr);
298   }
299   if (downflg) {
300     ierr = SNESFASSetNumberSmoothDown(snes,n_down);CHKERRQ(ierr);
301   }
302 
303   /* set up the default line search for coarse grid corrections */
304   if (fas->fastype == SNES_FAS_ADDITIVE) {
305     if (!snes->linesearch) {
306       ierr = SNESGetLineSearch(snes, &linesearch);CHKERRQ(ierr);
307       ierr = SNESLineSearchSetType(linesearch, SNESLINESEARCHL2);CHKERRQ(ierr);
308     }
309   }
310 
311   ierr = SNESFASCycleGetCorrection(snes, &next);CHKERRQ(ierr);
312   /* recursive option setting for the smoothers */
313   if (next) {ierr = SNESSetFromOptions(next);CHKERRQ(ierr);}
314   PetscFunctionReturn(0);
315 }
316 
317 #include <petscdraw.h>
318 #undef __FUNCT__
319 #define __FUNCT__ "SNESView_FAS"
320 static PetscErrorCode SNESView_FAS(SNES snes, PetscViewer viewer)
321 {
322   SNES_FAS       *fas = (SNES_FAS*) snes->data;
323   PetscBool      isFine,iascii,isdraw;
324   PetscInt       i;
325   PetscErrorCode ierr;
326   SNES           smoothu, smoothd, levelsnes;
327 
328   PetscFunctionBegin;
329   ierr = SNESFASCycleIsFine(snes, &isFine);CHKERRQ(ierr);
330   if (isFine) {
331     ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);CHKERRQ(ierr);
332     ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERDRAW,&isdraw);CHKERRQ(ierr);
333     if (iascii) {
334       ierr = PetscViewerASCIIPrintf(viewer, "FAS: type is %s, levels=%D, cycles=%D\n",  SNESFASTypes[fas->fastype], fas->levels, fas->n_cycles);CHKERRQ(ierr);
335       if (fas->galerkin) {
336         ierr = PetscViewerASCIIPrintf(viewer,"    Using Galerkin computed coarse grid function evaluation\n");CHKERRQ(ierr);
337       } else {
338         ierr = PetscViewerASCIIPrintf(viewer,"    Not using Galerkin computed coarse grid function evaluation\n");CHKERRQ(ierr);
339       }
340       for (i=0; i<fas->levels; i++) {
341         ierr = SNESFASGetCycleSNES(snes, i, &levelsnes);CHKERRQ(ierr);
342         ierr = SNESFASCycleGetSmootherUp(levelsnes, &smoothu);CHKERRQ(ierr);
343         ierr = SNESFASCycleGetSmootherDown(levelsnes, &smoothd);CHKERRQ(ierr);
344         if (!i) {
345           ierr = PetscViewerASCIIPrintf(viewer,"Coarse grid solver -- level %D -------------------------------\n",i);CHKERRQ(ierr);
346         } else {
347           ierr = PetscViewerASCIIPrintf(viewer,"Down solver (pre-smoother) on level %D -------------------------------\n",i);CHKERRQ(ierr);
348         }
349         ierr = PetscViewerASCIIPushTab(viewer);CHKERRQ(ierr);
350         if (smoothd) {
351           ierr = SNESView(smoothd,viewer);CHKERRQ(ierr);
352         } else {
353           ierr = PetscViewerASCIIPrintf(viewer,"Not yet available\n");CHKERRQ(ierr);
354         }
355         ierr = PetscViewerASCIIPopTab(viewer);CHKERRQ(ierr);
356         if (i && (smoothd == smoothu)) {
357           ierr = PetscViewerASCIIPrintf(viewer,"Up solver (post-smoother) same as down solver (pre-smoother)\n");CHKERRQ(ierr);
358         } else if (i) {
359           ierr = PetscViewerASCIIPrintf(viewer,"Up solver (post-smoother) on level %D -------------------------------\n",i);CHKERRQ(ierr);
360           ierr = PetscViewerASCIIPushTab(viewer);CHKERRQ(ierr);
361           if (smoothu) {
362             ierr = SNESView(smoothu,viewer);CHKERRQ(ierr);
363           } else {
364             ierr = PetscViewerASCIIPrintf(viewer,"Not yet available\n");CHKERRQ(ierr);
365           }
366           ierr = PetscViewerASCIIPopTab(viewer);CHKERRQ(ierr);
367         }
368       }
369     } else if (isdraw) {
370       PetscDraw draw;
371       PetscReal x,w,y,bottom,th,wth;
372       SNES_FAS  *curfas = fas;
373       ierr   = PetscViewerDrawGetDraw(viewer,0,&draw);CHKERRQ(ierr);
374       ierr   = PetscDrawGetCurrentPoint(draw,&x,&y);CHKERRQ(ierr);
375       ierr   = PetscDrawStringGetSize(draw,&wth,&th);CHKERRQ(ierr);
376       bottom = y - th;
377       while (curfas) {
378         if (!curfas->smoothu) {
379           ierr = PetscDrawPushCurrentPoint(draw,x,bottom);CHKERRQ(ierr);
380           if (curfas->smoothd) ierr = SNESView(curfas->smoothd,viewer);CHKERRQ(ierr);
381           ierr = PetscDrawPopCurrentPoint(draw);CHKERRQ(ierr);
382         } else {
383           w    = 0.5*PetscMin(1.0-x,x);
384           ierr = PetscDrawPushCurrentPoint(draw,x-w,bottom);CHKERRQ(ierr);
385           if (curfas->smoothd) ierr = SNESView(curfas->smoothd,viewer);CHKERRQ(ierr);
386           ierr = PetscDrawPopCurrentPoint(draw);CHKERRQ(ierr);
387           ierr = PetscDrawPushCurrentPoint(draw,x+w,bottom);CHKERRQ(ierr);
388           if (curfas->smoothu) ierr = SNESView(curfas->smoothu,viewer);CHKERRQ(ierr);
389           ierr = PetscDrawPopCurrentPoint(draw);CHKERRQ(ierr);
390         }
391         /* this is totally bogus but we have no way of knowing how low the previous one was draw to */
392         bottom -= 5*th;
393         if (curfas->next) curfas = (SNES_FAS*)curfas->next->data;
394         else curfas = NULL;
395       }
396     }
397   }
398   PetscFunctionReturn(0);
399 }
400 
401 #undef __FUNCT__
402 #define __FUNCT__ "SNESFASDownSmooth_Private"
403 /*
404 Defines the action of the downsmoother
405  */
406 static PetscErrorCode SNESFASDownSmooth_Private(SNES snes, Vec B, Vec X, Vec F, PetscReal *fnorm)
407 {
408   PetscErrorCode      ierr = 0;
409   SNESConvergedReason reason;
410   Vec                 FPC;
411   SNES                smoothd;
412   PetscBool           flg;
413   SNES_FAS            *fas = (SNES_FAS*) snes->data;
414 
415   PetscFunctionBegin;
416   ierr = SNESFASCycleGetSmootherDown(snes, &smoothd);CHKERRQ(ierr);
417   ierr = SNESSetInitialFunction(smoothd, F);CHKERRQ(ierr);
418   if (fas->eventsmoothsolve) {ierr = PetscLogEventBegin(fas->eventsmoothsolve,0,0,0,0);CHKERRQ(ierr);}
419   ierr = SNESSolve(smoothd, B, X);CHKERRQ(ierr);
420   if (fas->eventsmoothsolve) {ierr = PetscLogEventEnd(fas->eventsmoothsolve,0,0,0,0);CHKERRQ(ierr);}
421   /* check convergence reason for the smoother */
422   ierr = SNESGetConvergedReason(smoothd,&reason);CHKERRQ(ierr);
423   if (reason < 0 && !(reason == SNES_DIVERGED_MAX_IT || reason == SNES_DIVERGED_LOCAL_MIN || reason == SNES_DIVERGED_LINE_SEARCH)) {
424     snes->reason = SNES_DIVERGED_INNER;
425     PetscFunctionReturn(0);
426   }
427 
428   ierr = SNESGetFunction(smoothd, &FPC, NULL, NULL);CHKERRQ(ierr);
429   ierr = SNESGetAlwaysComputesFinalResidual(smoothd, &flg);CHKERRQ(ierr);
430   if (!flg) {
431     ierr = SNESComputeFunction(smoothd, X, FPC);CHKERRQ(ierr);
432   }
433   ierr = VecCopy(FPC, F);CHKERRQ(ierr);
434   if (fnorm) {ierr = VecNorm(F,NORM_2,fnorm);CHKERRQ(ierr);}
435   PetscFunctionReturn(0);
436 }
437 
438 
439 #undef __FUNCT__
440 #define __FUNCT__ "SNESFASUpSmooth_Private"
441 /*
442 Defines the action of the upsmoother
443  */
444 static PetscErrorCode SNESFASUpSmooth_Private(SNES snes, Vec B, Vec X, Vec F, PetscReal *fnorm)
445 {
446   PetscErrorCode      ierr = 0;
447   SNESConvergedReason reason;
448   Vec                 FPC;
449   SNES                smoothu;
450   PetscBool           flg;
451   SNES_FAS            *fas = (SNES_FAS*) snes->data;
452 
453   PetscFunctionBegin;
454   ierr = SNESFASCycleGetSmootherUp(snes, &smoothu);CHKERRQ(ierr);
455   if (fas->eventsmoothsolve) {ierr = PetscLogEventBegin(fas->eventsmoothsolve,0,0,0,0);CHKERRQ(ierr);}
456   ierr = SNESSolve(smoothu, B, X);CHKERRQ(ierr);
457   if (fas->eventsmoothsolve) {ierr = PetscLogEventEnd(fas->eventsmoothsolve,0,0,0,0);CHKERRQ(ierr);}
458   /* check convergence reason for the smoother */
459   ierr = SNESGetConvergedReason(smoothu,&reason);CHKERRQ(ierr);
460   if (reason < 0 && !(reason == SNES_DIVERGED_MAX_IT || reason == SNES_DIVERGED_LOCAL_MIN || reason == SNES_DIVERGED_LINE_SEARCH)) {
461     snes->reason = SNES_DIVERGED_INNER;
462     PetscFunctionReturn(0);
463   }
464   ierr = SNESGetFunction(smoothu, &FPC, NULL, NULL);CHKERRQ(ierr);
465   ierr = SNESGetAlwaysComputesFinalResidual(smoothu, &flg);CHKERRQ(ierr);
466   if (!flg) {
467     ierr = SNESComputeFunction(smoothu, X, FPC);CHKERRQ(ierr);
468   }
469   ierr = VecCopy(FPC, F);CHKERRQ(ierr);
470   if (fnorm) {ierr = VecNorm(F,NORM_2,fnorm);CHKERRQ(ierr);}
471   PetscFunctionReturn(0);
472 }
473 
474 #undef __FUNCT__
475 #define __FUNCT__ "SNESFASCreateCoarseVec"
476 /*@
477    SNESFASCreateCoarseVec - create Vec corresponding to a state vector on one level coarser than current level
478 
479    Collective
480 
481    Input Arguments:
482 .  snes - SNESFAS
483 
484    Output Arguments:
485 .  Xcoarse - vector on level one coarser than snes
486 
487    Level: developer
488 
489 .seealso: SNESFASSetRestriction(), SNESFASRestrict()
490 @*/
491 PetscErrorCode SNESFASCreateCoarseVec(SNES snes,Vec *Xcoarse)
492 {
493   PetscErrorCode ierr;
494   SNES_FAS       *fas = (SNES_FAS*)snes->data;
495 
496   PetscFunctionBegin;
497   if (fas->rscale) {
498     ierr = VecDuplicate(fas->rscale,Xcoarse);CHKERRQ(ierr);
499   } else if (fas->inject) {
500     ierr = MatCreateVecs(fas->inject,Xcoarse,NULL);CHKERRQ(ierr);
501   } else SETERRQ(PetscObjectComm((PetscObject)snes),PETSC_ERR_ARG_WRONGSTATE,"Must set restriction or injection");CHKERRQ(ierr);
502   PetscFunctionReturn(0);
503 }
504 
505 #undef __FUNCT__
506 #define __FUNCT__ "SNESFASRestrict"
507 /*@
508    SNESFASRestrict - restrict a Vec to the next coarser level
509 
510    Collective
511 
512    Input Arguments:
513 +  fine - SNES from which to restrict
514 -  Xfine - vector to restrict
515 
516    Output Arguments:
517 .  Xcoarse - result of restriction
518 
519    Level: developer
520 
521 .seealso: SNESFASSetRestriction(), SNESFASSetInjection()
522 @*/
523 PetscErrorCode SNESFASRestrict(SNES fine,Vec Xfine,Vec Xcoarse)
524 {
525   PetscErrorCode ierr;
526   SNES_FAS       *fas = (SNES_FAS*)fine->data;
527 
528   PetscFunctionBegin;
529   PetscValidHeaderSpecific(fine,SNES_CLASSID,1);
530   PetscValidHeaderSpecific(Xfine,VEC_CLASSID,2);
531   PetscValidHeaderSpecific(Xcoarse,VEC_CLASSID,3);
532   if (fas->inject) {
533     ierr = MatRestrict(fas->inject,Xfine,Xcoarse);CHKERRQ(ierr);
534   } else {
535     ierr = MatRestrict(fas->restrct,Xfine,Xcoarse);CHKERRQ(ierr);
536     ierr = VecPointwiseMult(Xcoarse,fas->rscale,Xcoarse);CHKERRQ(ierr);
537   }
538   PetscFunctionReturn(0);
539 }
540 
541 #undef __FUNCT__
542 #define __FUNCT__ "SNESFASCoarseCorrection"
543 /*
544 
545 Performs the FAS coarse correction as:
546 
547 fine problem:   F(x) = b
548 coarse problem: F^c(x^c) = b^c
549 
550 b^c = F^c(Rx) - R(F(x) - b)
551 
552  */
553 PetscErrorCode SNESFASCoarseCorrection(SNES snes, Vec X, Vec F, Vec X_new)
554 {
555   PetscErrorCode      ierr;
556   Vec                 X_c, Xo_c, F_c, B_c;
557   SNESConvergedReason reason;
558   SNES                next;
559   Mat                 restrct, interpolate;
560   SNES_FAS            *fasc;
561 
562   PetscFunctionBegin;
563   ierr = SNESFASCycleGetCorrection(snes, &next);CHKERRQ(ierr);
564   if (next) {
565     fasc = (SNES_FAS*)next->data;
566 
567     ierr = SNESFASCycleGetRestriction(snes, &restrct);CHKERRQ(ierr);
568     ierr = SNESFASCycleGetInterpolation(snes, &interpolate);CHKERRQ(ierr);
569 
570     X_c  = next->vec_sol;
571     Xo_c = next->work[0];
572     F_c  = next->vec_func;
573     B_c  = next->vec_rhs;
574 
575     if (fasc->eventinterprestrict) {ierr = PetscLogEventBegin(fasc->eventinterprestrict,0,0,0,0);CHKERRQ(ierr);}
576     ierr = SNESFASRestrict(snes,X,Xo_c);CHKERRQ(ierr);
577     /* restrict the defect: R(F(x) - b) */
578     ierr = MatRestrict(restrct, F, B_c);CHKERRQ(ierr);
579     if (fasc->eventinterprestrict) {ierr = PetscLogEventEnd(fasc->eventinterprestrict,0,0,0,0);CHKERRQ(ierr);}
580 
581     if (fasc->eventresidual) {ierr = PetscLogEventBegin(fasc->eventresidual,0,0,0,0);CHKERRQ(ierr);}
582     /* F_c = F^c(Rx) - R(F(x) - b) since the second term was sitting in next->vec_rhs */
583     ierr = SNESComputeFunction(next, Xo_c, F_c);CHKERRQ(ierr);
584     if (fasc->eventresidual) {ierr = PetscLogEventEnd(fasc->eventresidual,0,0,0,0);CHKERRQ(ierr);}
585 
586     /* solve the coarse problem corresponding to F^c(x^c) = b^c = F^c(Rx) - R(F(x) - b) */
587     ierr = VecCopy(B_c, X_c);CHKERRQ(ierr);
588     ierr = VecCopy(F_c, B_c);CHKERRQ(ierr);
589     ierr = VecCopy(X_c, F_c);CHKERRQ(ierr);
590     /* set initial guess of the coarse problem to the projected fine solution */
591     ierr = VecCopy(Xo_c, X_c);CHKERRQ(ierr);
592 
593     /* recurse to the next level */
594     ierr = SNESSetInitialFunction(next, F_c);CHKERRQ(ierr);
595     ierr = SNESSolve(next, B_c, X_c);CHKERRQ(ierr);
596     ierr = SNESGetConvergedReason(next,&reason);CHKERRQ(ierr);
597     if (reason < 0 && reason != SNES_DIVERGED_MAX_IT) {
598       snes->reason = SNES_DIVERGED_INNER;
599       PetscFunctionReturn(0);
600     }
601     /* correct as x <- x + I(x^c - Rx)*/
602     ierr = VecAXPY(X_c, -1.0, Xo_c);CHKERRQ(ierr);
603 
604     if (fasc->eventinterprestrict) {ierr = PetscLogEventBegin(fasc->eventinterprestrict,0,0,0,0);CHKERRQ(ierr);}
605     ierr = MatInterpolateAdd(interpolate, X_c, X, X_new);CHKERRQ(ierr);
606     if (fasc->eventinterprestrict) {ierr = PetscLogEventEnd(fasc->eventinterprestrict,0,0,0,0);CHKERRQ(ierr);}
607   }
608   PetscFunctionReturn(0);
609 }
610 
611 #undef __FUNCT__
612 #define __FUNCT__ "SNESFASCycle_Additive"
613 /*
614 
615 The additive cycle looks like:
616 
617 xhat = x
618 xhat = dS(x, b)
619 x = coarsecorrection(xhat, b_d)
620 x = x + nu*(xhat - x);
621 (optional) x = uS(x, b)
622 
623 With the coarse RHS (defect correction) as below.
624 
625  */
626 static PetscErrorCode SNESFASCycle_Additive(SNES snes, Vec X)
627 {
628   Vec                  F, B, Xhat;
629   Vec                  X_c, Xo_c, F_c, B_c;
630   PetscErrorCode       ierr;
631   SNESConvergedReason  reason;
632   PetscReal            xnorm, fnorm, ynorm;
633   SNESLineSearchReason lsresult;
634   SNES                 next;
635   Mat                  restrct, interpolate;
636   SNES_FAS             *fas = (SNES_FAS*)snes->data,*fasc;
637 
638   PetscFunctionBegin;
639   ierr = SNESFASCycleGetCorrection(snes, &next);CHKERRQ(ierr);
640   F    = snes->vec_func;
641   B    = snes->vec_rhs;
642   Xhat = snes->work[1];
643   ierr = VecCopy(X, Xhat);CHKERRQ(ierr);
644   /* recurse first */
645   if (next) {
646     fasc = (SNES_FAS*)next->data;
647     ierr = SNESFASCycleGetRestriction(snes, &restrct);CHKERRQ(ierr);
648     ierr = SNESFASCycleGetInterpolation(snes, &interpolate);CHKERRQ(ierr);
649     if (fas->eventresidual) {ierr = PetscLogEventBegin(fas->eventresidual,0,0,0,0);CHKERRQ(ierr);}
650     ierr = SNESComputeFunction(snes, Xhat, F);CHKERRQ(ierr);
651     if (fas->eventresidual) {ierr = PetscLogEventEnd(fas->eventresidual,0,0,0,0);CHKERRQ(ierr);}
652     ierr = VecNorm(F, NORM_2, &fnorm);CHKERRQ(ierr);
653     X_c  = next->vec_sol;
654     Xo_c = next->work[0];
655     F_c  = next->vec_func;
656     B_c  = next->vec_rhs;
657 
658     ierr = SNESFASRestrict(snes,Xhat,Xo_c);CHKERRQ(ierr);
659     /* restrict the defect */
660     ierr = MatRestrict(restrct, F, B_c);CHKERRQ(ierr);
661 
662     /* solve the coarse problem corresponding to F^c(x^c) = b^c = Rb + F^c(Rx) - RF(x) */
663     if (fasc->eventresidual) {ierr = PetscLogEventBegin(fasc->eventresidual,0,0,0,0);CHKERRQ(ierr);}
664     ierr = SNESComputeFunction(next, Xo_c, F_c);CHKERRQ(ierr);
665     if (fasc->eventresidual) {ierr = PetscLogEventEnd(fasc->eventresidual,0,0,0,0);CHKERRQ(ierr);}
666     ierr = VecCopy(B_c, X_c);CHKERRQ(ierr);
667     ierr = VecCopy(F_c, B_c);CHKERRQ(ierr);
668     ierr = VecCopy(X_c, F_c);CHKERRQ(ierr);
669     /* set initial guess of the coarse problem to the projected fine solution */
670     ierr = VecCopy(Xo_c, X_c);CHKERRQ(ierr);
671 
672     /* recurse */
673     ierr = SNESSetInitialFunction(next, F_c);CHKERRQ(ierr);
674     ierr = SNESSolve(next, B_c, X_c);CHKERRQ(ierr);
675 
676     /* smooth on this level */
677     ierr = SNESFASDownSmooth_Private(snes, B, X, F, &fnorm);CHKERRQ(ierr);
678 
679     ierr = SNESGetConvergedReason(next,&reason);CHKERRQ(ierr);
680     if (reason < 0 && reason != SNES_DIVERGED_MAX_IT) {
681       snes->reason = SNES_DIVERGED_INNER;
682       PetscFunctionReturn(0);
683     }
684 
685     /* correct as x <- x + I(x^c - Rx)*/
686     ierr = VecAYPX(X_c, -1.0, Xo_c);CHKERRQ(ierr);
687     ierr = MatInterpolate(interpolate, X_c, Xhat);CHKERRQ(ierr);
688 
689     /* additive correction of the coarse direction*/
690     ierr = SNESLineSearchApply(snes->linesearch, X, F, &fnorm, Xhat);CHKERRQ(ierr);
691     ierr = SNESLineSearchGetReason(snes->linesearch, &lsresult);CHKERRQ(ierr);
692     ierr = SNESLineSearchGetNorms(snes->linesearch, &xnorm, &snes->norm, &ynorm);CHKERRQ(ierr);
693     if (lsresult) {
694       if (++snes->numFailures >= snes->maxFailures) {
695         snes->reason = SNES_DIVERGED_LINE_SEARCH;
696         PetscFunctionReturn(0);
697       }
698     }
699   } else {
700     ierr = SNESFASDownSmooth_Private(snes, B, X, F, &snes->norm);CHKERRQ(ierr);
701   }
702   PetscFunctionReturn(0);
703 }
704 
705 #undef __FUNCT__
706 #define __FUNCT__ "SNESFASCycle_Multiplicative"
707 /*
708 
709 Defines the FAS cycle as:
710 
711 fine problem: F(x) = b
712 coarse problem: F^c(x) = b^c
713 
714 b^c = F^c(Rx) - R(F(x) - b)
715 
716 correction:
717 
718 x = x + I(x^c - Rx)
719 
720  */
721 static PetscErrorCode SNESFASCycle_Multiplicative(SNES snes, Vec X)
722 {
723 
724   PetscErrorCode ierr;
725   Vec            F,B;
726   SNES           next;
727 
728   PetscFunctionBegin;
729   F = snes->vec_func;
730   B = snes->vec_rhs;
731   /* pre-smooth -- just update using the pre-smoother */
732   ierr = SNESFASCycleGetCorrection(snes,&next);CHKERRQ(ierr);
733   ierr = SNESFASDownSmooth_Private(snes, B, X, F, &snes->norm);CHKERRQ(ierr);
734   if (next) {
735     ierr = SNESFASCoarseCorrection(snes, X, F, X);CHKERRQ(ierr);
736     ierr = SNESFASUpSmooth_Private(snes, B, X, F, &snes->norm);CHKERRQ(ierr);
737   }
738   PetscFunctionReturn(0);
739 }
740 
741 #undef __FUNCT__
742 #define __FUNCT__ "SNESFASCycleSetupPhase_Full"
743 static PetscErrorCode SNESFASCycleSetupPhase_Full(SNES snes)
744 {
745   SNES           next;
746   SNES_FAS       *fas = (SNES_FAS*)snes->data;
747   PetscBool      isFine;
748   PetscErrorCode ierr;
749 
750   PetscFunctionBegin;
751   /* pre-smooth -- just update using the pre-smoother */
752   ierr = SNESFASCycleIsFine(snes,&isFine);CHKERRQ(ierr);
753   ierr = SNESFASCycleGetCorrection(snes,&next);CHKERRQ(ierr);
754   fas->full_stage = 0;
755   if (next) {ierr = SNESFASCycleSetupPhase_Full(next);CHKERRQ(ierr);}
756   PetscFunctionReturn(0);
757 }
758 
759 #undef __FUNCT__
760 #define __FUNCT__ "SNESFASCycle_Full"
761 static PetscErrorCode SNESFASCycle_Full(SNES snes, Vec X)
762 {
763   PetscErrorCode ierr;
764   Vec            F,B;
765   SNES_FAS       *fas = (SNES_FAS*)snes->data;
766   PetscBool      isFine;
767   SNES           next;
768 
769   PetscFunctionBegin;
770   F = snes->vec_func;
771   B = snes->vec_rhs;
772   ierr = SNESFASCycleIsFine(snes,&isFine);CHKERRQ(ierr);
773   ierr = SNESFASCycleGetCorrection(snes,&next);CHKERRQ(ierr);
774 
775   if (isFine) {
776     ierr = SNESFASCycleSetupPhase_Full(snes);CHKERRQ(ierr);
777   }
778 
779   if (fas->full_stage == 0) {
780     /* downsweep */
781     if (next) {
782       if (fas->level != 1) next->max_its += 1;
783       if (fas->full_downsweep||isFine) {ierr = SNESFASDownSmooth_Private(snes,B,X,F,&snes->norm);CHKERRQ(ierr);}
784       ierr = SNESFASCoarseCorrection(snes,X,F,X);CHKERRQ(ierr);
785       ierr = SNESFASUpSmooth_Private(snes,B,X,F,&snes->norm);CHKERRQ(ierr);
786       if (fas->level != 1) next->max_its -= 1;
787     } else {
788       /* The smoother on the coarse level is the coarse solver */
789       ierr = SNESFASDownSmooth_Private(snes,B,X,F,&snes->norm);CHKERRQ(ierr);
790     }
791     fas->full_stage = 1;
792   } else if (fas->full_stage == 1) {
793     if (snes->iter == 0) {ierr = SNESFASDownSmooth_Private(snes,B,X,F,&snes->norm);CHKERRQ(ierr);}
794     if (next) {
795       ierr = SNESFASCoarseCorrection(snes,X,F,X);CHKERRQ(ierr);
796       ierr = SNESFASUpSmooth_Private(snes,B,X,F,&snes->norm);CHKERRQ(ierr);
797     }
798   }
799   /* final v-cycle */
800   if (isFine) {
801     if (next) {
802       ierr = SNESFASCoarseCorrection(snes,X,F,X);CHKERRQ(ierr);
803       ierr = SNESFASUpSmooth_Private(snes,B,X,F,&snes->norm);CHKERRQ(ierr);
804     }
805   }
806   PetscFunctionReturn(0);
807 }
808 
809 #undef __FUNCT__
810 #define __FUNCT__ "SNESFASCycle_Kaskade"
811 static PetscErrorCode SNESFASCycle_Kaskade(SNES snes, Vec X)
812 {
813   PetscErrorCode ierr;
814   Vec            F,B;
815   SNES           next;
816 
817   PetscFunctionBegin;
818   F = snes->vec_func;
819   B = snes->vec_rhs;
820   ierr = SNESFASCycleGetCorrection(snes,&next);CHKERRQ(ierr);
821   if (next) {
822     ierr = SNESFASCoarseCorrection(snes,X,F,X);CHKERRQ(ierr);
823     ierr = SNESFASUpSmooth_Private(snes,B,X,F,&snes->norm);CHKERRQ(ierr);
824   } else {
825     ierr = SNESFASDownSmooth_Private(snes,B,X,F,&snes->norm);CHKERRQ(ierr);
826   }
827   PetscFunctionReturn(0);
828 }
829 
830 PetscBool SNEScite = PETSC_FALSE;
831 const char SNESCitation[] = "@techreport{pbmkbsxt2012,\n"
832                             "  title = {Composing Scalable Nonlinear Algebraic Solvers},\n"
833                             "  author = {Peter Brune and Mathew Knepley and Barry Smith and Xuemin Tu},\n"
834                             "  year = 2013,\n"
835                             "  type = Preprint,\n"
836                             "  number = {ANL/MCS-P2010-0112},\n"
837                             "  institution = {Argonne National Laboratory}\n}\n";
838 
839 #undef __FUNCT__
840 #define __FUNCT__ "SNESSolve_FAS"
841 static PetscErrorCode SNESSolve_FAS(SNES snes)
842 {
843   PetscErrorCode ierr;
844   PetscInt       i, maxits;
845   Vec            X, F;
846   PetscReal      fnorm;
847   SNES_FAS       *fas = (SNES_FAS*)snes->data,*ffas;
848   DM             dm;
849   PetscBool      isFine;
850 
851   PetscFunctionBegin;
852 
853   if (snes->xl || snes->xu || snes->ops->computevariablebounds) SETERRQ1(PetscObjectComm((PetscObject)snes),PETSC_ERR_ARG_WRONGSTATE, "SNES solver %s does not support bounds", ((PetscObject)snes)->type_name);
854 
855   ierr = PetscCitationsRegister(SNESCitation,&SNEScite);CHKERRQ(ierr);
856   maxits       = snes->max_its;      /* maximum number of iterations */
857   snes->reason = SNES_CONVERGED_ITERATING;
858   X            = snes->vec_sol;
859   F            = snes->vec_func;
860 
861   ierr = SNESFASCycleIsFine(snes, &isFine);CHKERRQ(ierr);
862   /*norm setup */
863   ierr       = PetscObjectSAWsTakeAccess((PetscObject)snes);CHKERRQ(ierr);
864   snes->iter = 0;
865   snes->norm = 0.;
866   ierr       = PetscObjectSAWsGrantAccess((PetscObject)snes);CHKERRQ(ierr);
867   if (!snes->vec_func_init_set) {
868     if (fas->eventresidual) {ierr = PetscLogEventBegin(fas->eventresidual,0,0,0,0);CHKERRQ(ierr);}
869     ierr = SNESComputeFunction(snes,X,F);CHKERRQ(ierr);
870     if (fas->eventresidual) {ierr = PetscLogEventEnd(fas->eventresidual,0,0,0,0);CHKERRQ(ierr);}
871   } else snes->vec_func_init_set = PETSC_FALSE;
872 
873   ierr = VecNorm(F, NORM_2, &fnorm);CHKERRQ(ierr); /* fnorm <- ||F||  */
874   SNESCheckFunctionNorm(snes,fnorm);
875   ierr       = PetscObjectSAWsTakeAccess((PetscObject)snes);CHKERRQ(ierr);
876   snes->norm = fnorm;
877   ierr       = PetscObjectSAWsGrantAccess((PetscObject)snes);CHKERRQ(ierr);
878   ierr       = SNESLogConvergenceHistory(snes,fnorm,0);CHKERRQ(ierr);
879   ierr       = SNESMonitor(snes,0,fnorm);CHKERRQ(ierr);
880 
881   /* test convergence */
882   ierr = (*snes->ops->converged)(snes,0,0.0,0.0,fnorm,&snes->reason,snes->cnvP);CHKERRQ(ierr);
883   if (snes->reason) PetscFunctionReturn(0);
884 
885 
886   if (isFine) {
887     /* propagate scale-dependent data up the hierarchy */
888     ierr = SNESGetDM(snes,&dm);CHKERRQ(ierr);
889     for (ffas=fas; ffas->next; ffas=(SNES_FAS*)ffas->next->data) {
890       DM dmcoarse;
891       ierr = SNESGetDM(ffas->next,&dmcoarse);CHKERRQ(ierr);
892       ierr = DMRestrict(dm,ffas->restrct,ffas->rscale,ffas->inject,dmcoarse);CHKERRQ(ierr);
893       dm   = dmcoarse;
894     }
895   }
896 
897   for (i = 0; i < maxits; i++) {
898     /* Call general purpose update function */
899 
900     if (snes->ops->update) {
901       ierr = (*snes->ops->update)(snes, snes->iter);CHKERRQ(ierr);
902     }
903     if (fas->fastype == SNES_FAS_MULTIPLICATIVE) {
904       ierr = SNESFASCycle_Multiplicative(snes, X);CHKERRQ(ierr);
905     } else if (fas->fastype == SNES_FAS_ADDITIVE) {
906       ierr = SNESFASCycle_Additive(snes, X);CHKERRQ(ierr);
907     } else if (fas->fastype == SNES_FAS_FULL) {
908       ierr = SNESFASCycle_Full(snes, X);CHKERRQ(ierr);
909     } else if (fas->fastype ==SNES_FAS_KASKADE) {
910       ierr = SNESFASCycle_Kaskade(snes, X);CHKERRQ(ierr);
911     } else SETERRQ(PetscObjectComm((PetscObject)snes),PETSC_ERR_ARG_WRONGSTATE,"Unsupported FAS type");
912 
913     /* check for FAS cycle divergence */
914     if (snes->reason != SNES_CONVERGED_ITERATING) PetscFunctionReturn(0);
915 
916     /* Monitor convergence */
917     ierr       = PetscObjectSAWsTakeAccess((PetscObject)snes);CHKERRQ(ierr);
918     snes->iter = i+1;
919     ierr       = PetscObjectSAWsGrantAccess((PetscObject)snes);CHKERRQ(ierr);
920     ierr       = SNESLogConvergenceHistory(snes,snes->norm,0);CHKERRQ(ierr);
921     ierr       = SNESMonitor(snes,snes->iter,snes->norm);CHKERRQ(ierr);
922     /* Test for convergence */
923     if (isFine) {
924       ierr = (*snes->ops->converged)(snes,snes->iter,0.0,0.0,snes->norm,&snes->reason,snes->cnvP);CHKERRQ(ierr);
925       if (snes->reason) break;
926     }
927   }
928   if (i == maxits) {
929     ierr = PetscInfo1(snes, "Maximum number of iterations has been reached: %D\n", maxits);CHKERRQ(ierr);
930     if (!snes->reason) snes->reason = SNES_DIVERGED_MAX_IT;
931   }
932   PetscFunctionReturn(0);
933 }
934 
935 /*MC
936 
937 SNESFAS - Full Approximation Scheme nonlinear multigrid solver.
938 
939    The nonlinear problem is solved by correction using coarse versions
940    of the nonlinear problem.  This problem is perturbed so that a projected
941    solution of the fine problem elicits no correction from the coarse problem.
942 
943 Options Database:
944 +   -snes_fas_levels -  The number of levels
945 .   -snes_fas_cycles<1> -  The number of cycles -- 1 for V, 2 for W
946 .   -snes_fas_type<additive,multiplicative,full,kaskade>  -  Additive or multiplicative cycle
947 .   -snes_fas_galerkin<PETSC_FALSE> -  Form coarse problems by projection back upon the fine problem
948 .   -snes_fas_smoothup<1> -  The number of iterations of the post-smoother
949 .   -snes_fas_smoothdown<1> -  The number of iterations of the pre-smoother
950 .   -snes_fas_monitor -  Monitor progress of all of the levels
951 .   -snes_fas_full_downsweep<PETSC_FALSE> - call the downsmooth on the initial downsweep of full FAS
952 .   -fas_levels_snes_ -  SNES options for all smoothers
953 .   -fas_levels_cycle_snes_ -  SNES options for all cycles
954 .   -fas_levels_i_snes_ -  SNES options for the smoothers on level i
955 .   -fas_levels_i_cycle_snes_ - SNES options for the cycle on level i
956 -   -fas_coarse_snes_ -  SNES options for the coarsest smoother
957 
958 Notes:
959    The organization of the FAS solver is slightly different from the organization of PCMG
960    As each level has smoother SNES instances(down and potentially up) and a cycle SNES instance.
961    The cycle SNES instance may be used for monitoring convergence on a particular level.
962 
963 Level: beginner
964 
965    References:
966 . 1. -  Peter R. Brune, Matthew G. Knepley, Barry F. Smith, and Xuemin Tu, "Composing Scalable Nonlinear Algebraic Solvers",
967    SIAM Review, 57(4), 2015
968 
969 .seealso: PCMG, SNESCreate(), SNES, SNESSetType(), SNESType (for list of available types)
970 M*/
971 
972 #undef __FUNCT__
973 #define __FUNCT__ "SNESCreate_FAS"
974 PETSC_EXTERN PetscErrorCode SNESCreate_FAS(SNES snes)
975 {
976   SNES_FAS       *fas;
977   PetscErrorCode ierr;
978 
979   PetscFunctionBegin;
980   snes->ops->destroy        = SNESDestroy_FAS;
981   snes->ops->setup          = SNESSetUp_FAS;
982   snes->ops->setfromoptions = SNESSetFromOptions_FAS;
983   snes->ops->view           = SNESView_FAS;
984   snes->ops->solve          = SNESSolve_FAS;
985   snes->ops->reset          = SNESReset_FAS;
986 
987   snes->usesksp = PETSC_FALSE;
988   snes->usespc  = PETSC_FALSE;
989 
990   if (!snes->tolerancesset) {
991     snes->max_funcs = 30000;
992     snes->max_its   = 10000;
993   }
994 
995   snes->alwayscomputesfinalresidual = PETSC_TRUE;
996 
997   ierr = PetscNewLog(snes,&fas);CHKERRQ(ierr);
998 
999   snes->data                  = (void*) fas;
1000   fas->level                  = 0;
1001   fas->levels                 = 1;
1002   fas->n_cycles               = 1;
1003   fas->max_up_it              = 1;
1004   fas->max_down_it            = 1;
1005   fas->smoothu                = NULL;
1006   fas->smoothd                = NULL;
1007   fas->next                   = NULL;
1008   fas->previous               = NULL;
1009   fas->fine                   = snes;
1010   fas->interpolate            = NULL;
1011   fas->restrct                = NULL;
1012   fas->inject                 = NULL;
1013   fas->usedmfornumberoflevels = PETSC_FALSE;
1014   fas->fastype                = SNES_FAS_MULTIPLICATIVE;
1015   fas->full_downsweep         = PETSC_FALSE;
1016 
1017   fas->eventsmoothsetup    = 0;
1018   fas->eventsmoothsolve    = 0;
1019   fas->eventresidual       = 0;
1020   fas->eventinterprestrict = 0;
1021   PetscFunctionReturn(0);
1022 }
1023