Actual source code: eimex.c

petsc-3.6.2 2015-10-02
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```  1: /*
2:  * eimex.c
3:  *
4:  *  Created on: Jun 21, 2012
5:  *      Written by Hong Zhang (zhang@vt.edu), Virginia Tech
6:  *                 Emil Constantinescu (emconsta@mcs.anl.gov), Argonne National Laboratory
7:  */
8: /*MC
9:       EIMEX - Time stepping with Extrapolated IMEX methods.

11:   Notes:
12:   The general system is written as

14:   G(t,X,Xdot) = F(t,X)

16:   where G represents the stiff part and F represents the non-stiff part. The user should provide the stiff part
17:   of the equation using TSSetIFunction() and the non-stiff part with TSSetRHSFunction().
18:   This method is designed to be linearly implicit on G and can use an approximate and lagged Jacobian.

20:   Another common form for the system is

22:   y'=f(x)+g(x)

24:   The relationship between F,G and f,g is

26:   G = y'-g(x), F = f(x)

28:  References
29:   E. Constantinescu and A. Sandu, Extrapolated implicit-explicit time stepping, SIAM Journal on Scientific
30: Computing, 31 (2010), pp. 4452-4477.

32:       Level: beginner

34: .seealso:  TSCreate(), TS, TSSetType(), TSEIMEXSetMaxRows(), TSEIMEXSetRowCol(), TSEIMEXSetOrdAdapt()

36:  M*/
37: #include <petsc/private/tsimpl.h>                /*I   "petscts.h"   I*/
38: #include <petscdm.h>

40: static const PetscInt TSEIMEXDefault = 3;

42: typedef struct {
43:   PetscInt     row_ind;         /* Return the term T[row_ind][col_ind] */
44:   PetscInt     col_ind;         /* Return the term T[row_ind][col_ind] */
45:   PetscInt     nstages;         /* Numbers of stages in current scheme */
46:   PetscInt     max_rows;        /* Maximum number of rows */
47:   PetscInt     *N;              /* Harmonic sequence N[max_rows] */
48:   Vec          Y;               /* States computed during the step, used to complete the step */
49:   Vec          Z;               /* For shift*(Y-Z) */
50:   Vec          *T;              /* Working table, size determined by nstages */
51:   Vec          YdotRHS;         /* f(x) Work vector holding YdotRHS during residual evaluation */
52:   Vec          YdotI;           /* xdot-g(x) Work vector holding YdotI = G(t,x,xdot) when xdot =0 */
53:   Vec          Ydot;            /* f(x)+g(x) Work vector */
54:   Vec          VecSolPrev;      /* Work vector holding the solution from the previous step (used for interpolation) */
55:   PetscReal    shift;
56:   PetscReal    ctime;
57:   PetscBool    recompute_jacobian; /* Recompute the Jacobian at each stage, default is to freeze the Jacobian at the start of each step */
59:   TSStepStatus status;
60: } TS_EIMEX;

62: /* This function is pure */
63: static PetscInt Map(PetscInt i, PetscInt j, PetscInt s)
64: {
65:   return ((2*s-j+1)*j/2+i-j);
66: }

71: static PetscErrorCode TSEvaluateStep_EIMEX(TS ts,PetscInt order,Vec X,PetscBool *done)
72: {
73:   TS_EIMEX        *ext = (TS_EIMEX*)ts->data;
74:   const PetscInt  ns = ext->nstages;
77:   VecCopy(ext->T[Map(ext->row_ind,ext->col_ind,ns)],X);
78:   return(0);
79: }

84: static PetscErrorCode TSStage_EIMEX(TS ts,PetscInt istage)
85: {
86:   TS_EIMEX        *ext = (TS_EIMEX*)ts->data;
87:   PetscReal       h;
88:   Vec             Y=ext->Y, Z=ext->Z;
89:   SNES            snes;
91:   PetscInt        i,its,lits;
92:   PetscBool       accept;
93:   PetscErrorCode  ierr;

96:   TSGetSNES(ts,&snes);
97:   h = ts->time_step/ext->N[istage];/* step size for the istage-th stage */
98:   ext->shift = 1./h;
99:   SNESSetLagJacobian(snes,-2); /* Recompute the Jacobian on this solve, but not again */
100:   VecCopy(ext->VecSolPrev,Y); /* Take the previous solution as intial step */

102:   for(i=0; i<ext->N[istage]; i++){
103:     ext->ctime = ts->ptime + h*i;
104:     VecCopy(Y,Z);/* Save the solution of the previous substep */
105:     SNESSolve(snes,NULL,Y);
106:     SNESGetIterationNumber(snes,&its);
107:     SNESGetLinearSolveIterations(snes,&lits);
108:     ts->snes_its += its; ts->ksp_its += lits;
111:   }

113:   return(0);
114: }

119: static PetscErrorCode TSStep_EIMEX(TS ts)
120: {
121:   TS_EIMEX        *ext = (TS_EIMEX*)ts->data;
122:   const PetscInt  ns = ext->nstages;
123:   Vec             *T=ext->T, Y=ext->Y;

125:   SNES            snes;
126:   PetscInt        i,j;
127:   PetscBool       accept = PETSC_FALSE;
128:   PetscErrorCode  ierr;
129:   PetscReal       alpha,local_error;

132:   TSGetSNES(ts,&snes);
133:   SNESSetType(snes,"ksponly");
134:   ext->status = TS_STEP_INCOMPLETE;

136:   VecCopy(ts->vec_sol,ext->VecSolPrev);

138:   /* Apply n_j steps of the base method to obtain solutions of T(j,1),1<=j<=s */
139:   for(j=0; j<ns; j++){
140:         TSStage_EIMEX(ts,j);
141:         VecCopy(Y,T[j]);
142:   }

144:   for(i=1;i<ns;i++){
145:     for(j=i;j<ns;j++){
146:       alpha = -(PetscReal)ext->N[j]/ext->N[j-i];
147:       VecAXPBYPCZ(T[Map(j,i,ns)],alpha,1.0,0,T[Map(j,i-1,ns)],T[Map(j-1,i-1,ns)]);/* T[j][i]=alpha*T[j][i-1]+T[j-1][i-1] */
148:       alpha = 1.0/(1.0 + alpha);
149:       VecScale(T[Map(j,i,ns)],alpha);
150:     }
151:   }

153:   TSEvaluateStep(ts,ns,ts->vec_sol,NULL);/*update ts solution */

155:   if(ext->ord_adapt && ext->nstages < ext->max_rows){
156:         accept = PETSC_FALSE;
157:         while(!accept && ext->nstages < ext->max_rows){
159:           accept = (local_error < 1.0)? PETSC_TRUE : PETSC_FALSE;

161:           if(!accept){/* add one more stage*/
162:             TSStage_EIMEX(ts,ext->nstages);
163:             ext->nstages++; ext->row_ind++; ext->col_ind++;
164:             /*T table need to be recycled*/
165:             VecDuplicateVecs(ts->vec_sol,(1+ext->nstages)*ext->nstages/2,&ext->T);
166:             for(i=0; i<ext->nstages-1; i++){
167:               for(j=0; j<=i; j++){
168:                 VecCopy(T[Map(i,j,ext->nstages-1)],ext->T[Map(i,j,ext->nstages)]);
169:               }
170:             }
171:             VecDestroyVecs(ext->nstages*(ext->nstages-1)/2,&T);
172:             T = ext->T; /*reset the pointer*/
173:             /*recycling finished, store the new solution*/
174:             VecCopy(Y,T[ext->nstages-1]);
175:             /*extrapolation for the newly added stage*/
176:             for(i=1;i<ext->nstages;i++){
177:               alpha = -(PetscReal)ext->N[ext->nstages-1]/ext->N[ext->nstages-1-i];
178:               VecAXPBYPCZ(T[Map(ext->nstages-1,i,ext->nstages)],alpha,1.0,0,T[Map(ext->nstages-1,i-1,ext->nstages)],T[Map(ext->nstages-1-1,i-1,ext->nstages)]);/*T[ext->nstages-1][i]=alpha*T[ext->nstages-1][i-1]+T[ext->nstages-1-1][i-1]*/
179:               alpha = 1.0/(1.0 + alpha);
180:               VecScale(T[Map(ext->nstages-1,i,ext->nstages)],alpha);
181:             }
182:             /*update ts solution */
183:             TSEvaluateStep(ts,ext->nstages,ts->vec_sol,NULL);
184:           }/*end if !accept*/
185:         }/*end while*/

187:         if(ext->nstages == ext->max_rows){
188:                 PetscInfo(ts,"Max number of rows has been used\n");
189:         }
191:   ts->ptime += ts->time_step;
192:   ts->steps++;
193:   ext->status = TS_STEP_COMPLETE;

195:   if (ext->status != TS_STEP_COMPLETE && !ts->reason) ts->reason = TS_DIVERGED_STEP_REJECTED;
196:   return(0);
197: }

199: /* cubic Hermit spline */
202: static PetscErrorCode TSInterpolate_EIMEX(TS ts,PetscReal itime,Vec X)
203: {
204:   TS_EIMEX       *ext = (TS_EIMEX*)ts->data;
205:   PetscReal      t,a,b;
206:   Vec            Y0=ext->VecSolPrev,Y1=ext->Y,
207:                          Ydot=ext->Ydot,YdotI=ext->YdotI;
208:   const PetscReal h = ts->time_step_prev;
211:   t = (itime -ts->ptime + h)/h;
212:   /* YdotI = -f(x)-g(x) */

214:   VecZeroEntries(Ydot);
215:   TSComputeIFunction(ts,ts->ptime-h,Y0,Ydot,YdotI,PETSC_FALSE);

217:   a    = 2.0*t*t*t - 3.0*t*t + 1.0;
218:   b    = -(t*t*t - 2.0*t*t + t)*h;
219:   VecAXPBYPCZ(X,a,b,0.0,Y0,YdotI);

221:   TSComputeIFunction(ts,ts->ptime,Y1,Ydot,YdotI,PETSC_FALSE);
222:   a    = -2.0*t*t*t+3.0*t*t;
223:   b    = -(t*t*t - t*t)*h;
224:   VecAXPBYPCZ(X,a,b,1.0,Y1,YdotI);

226:   return(0);
227: }

232: static PetscErrorCode TSReset_EIMEX(TS ts)
233: {
234:   TS_EIMEX        *ext = (TS_EIMEX*)ts->data;
235:   PetscInt        ns;
236:   PetscErrorCode  ierr;

239:   ns = ext->nstages;
240:   VecDestroyVecs((1+ns)*ns/2,&ext->T);
241:   VecDestroy(&ext->Y);
242:   VecDestroy(&ext->Z);
243:   VecDestroy(&ext->YdotRHS);
244:   VecDestroy(&ext->YdotI);
245:   VecDestroy(&ext->Ydot);
246:   VecDestroy(&ext->VecSolPrev);
247:   PetscFree(ext->N);
248:   return(0);
249: }

253: static PetscErrorCode TSDestroy_EIMEX(TS ts)
254: {
255:   PetscErrorCode  ierr;

258:   TSReset_EIMEX(ts);
259:   PetscFree(ts->data);
260:   PetscObjectComposeFunction((PetscObject)ts,"TSEIMEXSetMaxRows_C",NULL);
261:   PetscObjectComposeFunction((PetscObject)ts,"TSEIMEXSetRowCol_C",NULL);

264:   return(0);
265: }

270: static PetscErrorCode TSEIMEXGetVecs(TS ts,DM dm,Vec *Z,Vec *Ydot,Vec *YdotI, Vec *YdotRHS)
271: {
272:   TS_EIMEX       *ext = (TS_EIMEX*)ts->data;

276:   if (Z) {
277:     if (dm && dm != ts->dm) {
278:       DMGetNamedGlobalVector(dm,"TSEIMEX_Z",Z);
279:     } else *Z = ext->Z;
280:   }
281:   if (Ydot) {
282:     if (dm && dm != ts->dm) {
283:       DMGetNamedGlobalVector(dm,"TSEIMEX_Ydot",Ydot);
284:     } else *Ydot = ext->Ydot;
285:   }
286:   if (YdotI) {
287:     if (dm && dm != ts->dm) {
288:       DMGetNamedGlobalVector(dm,"TSEIMEX_YdotI",YdotI);
289:     } else *YdotI = ext->YdotI;
290:   }
291:   if (YdotRHS) {
292:     if (dm && dm != ts->dm) {
293:       DMGetNamedGlobalVector(dm,"TSEIMEX_YdotRHS",YdotRHS);
294:     } else *YdotRHS = ext->YdotRHS;
295:   }
296:   return(0);
297: }

302: static PetscErrorCode TSEIMEXRestoreVecs(TS ts,DM dm,Vec *Z,Vec *Ydot,Vec *YdotI,Vec *YdotRHS)
303: {

307:   if (Z) {
308:     if (dm && dm != ts->dm) {
309:       DMRestoreNamedGlobalVector(dm,"TSEIMEX_Z",Z);
310:     }
311:   }
312:   if (Ydot) {
313:     if (dm && dm != ts->dm) {
314:       DMRestoreNamedGlobalVector(dm,"TSEIMEX_Ydot",Ydot);
315:     }
316:   }
317:   if (YdotI) {
318:     if (dm && dm != ts->dm) {
319:       DMRestoreNamedGlobalVector(dm,"TSEIMEX_YdotI",YdotI);
320:     }
321:   }
322:   if (YdotRHS) {
323:     if (dm && dm != ts->dm) {
324:       DMRestoreNamedGlobalVector(dm,"TSEIMEX_YdotRHS",YdotRHS);
325:     }
326:   }
327:   return(0);
328: }

331: /*
332:   This defines the nonlinear equation that is to be solved with SNES
333:   Fn[t0+Theta*dt, U, (U-U0)*shift] = 0
334:   In the case of Backward Euler, Fn = (U-U0)/h-g(t1,U))
335:   Since FormIFunction calculates G = ydot - g(t,y), ydot will be set to (U-U0)/h
336: */
339: static PetscErrorCode SNESTSFormFunction_EIMEX(SNES snes,Vec X,Vec G,TS ts)
340: {
341:   TS_EIMEX        *ext = (TS_EIMEX*)ts->data;
342:   PetscErrorCode  ierr;
343:   Vec             Ydot,Z;
344:   DM              dm,dmsave;

347:   VecZeroEntries(G);

349:   SNESGetDM(snes,&dm);
350:   TSEIMEXGetVecs(ts,dm,&Z,&Ydot,NULL,NULL);
351:   VecZeroEntries(Ydot);
352:   dmsave = ts->dm;
353:   ts->dm = dm;
354:   TSComputeIFunction(ts,ext->ctime,X,Ydot,G,PETSC_FALSE);
355:   /* PETSC_FALSE indicates non-imex, adding explicit RHS to the implicit I function.  */
356:   VecCopy(G,Ydot);
357:   ts->dm = dmsave;
358:   TSEIMEXRestoreVecs(ts,dm,&Z,&Ydot,NULL,NULL);

360:   return(0);
361: }

363: /*
364:  This defined the Jacobian matrix for SNES. Jn = (I/h-g'(t,y))
365:  */
368: static PetscErrorCode SNESTSFormJacobian_EIMEX(SNES snes,Vec X,Mat A,Mat B,TS ts)
369: {
370:   TS_EIMEX        *ext = (TS_EIMEX*)ts->data;
371:   Vec             Ydot;
372:   PetscErrorCode  ierr;
373:   DM              dm,dmsave;
375:   SNESGetDM(snes,&dm);
376:   TSEIMEXGetVecs(ts,dm,NULL,&Ydot,NULL,NULL);
377:   /*  VecZeroEntries(Ydot); */
378:   /* ext->Ydot have already been computed in SNESTSFormFunction_EIMEX (SNES guarantees this) */
379:   dmsave = ts->dm;
380:   ts->dm = dm;
381:   TSComputeIJacobian(ts,ts->ptime,X,Ydot,ext->shift,A,B,PETSC_TRUE);
382:   ts->dm = dmsave;
383:   TSEIMEXRestoreVecs(ts,dm,NULL,&Ydot,NULL,NULL);
384:   return(0);
385: }

389: static PetscErrorCode DMCoarsenHook_TSEIMEX(DM fine,DM coarse,void *ctx)
390: {

393:   return(0);
394: }

398: static PetscErrorCode DMRestrictHook_TSEIMEX(DM fine,Mat restrct,Vec rscale,Mat inject,DM coarse,void *ctx)
399: {
400:   TS ts = (TS)ctx;
402:   Vec Z,Z_c;

405:   TSEIMEXGetVecs(ts,fine,&Z,NULL,NULL,NULL);
406:   TSEIMEXGetVecs(ts,coarse,&Z_c,NULL,NULL,NULL);
407:   MatRestrict(restrct,Z,Z_c);
408:   VecPointwiseMult(Z_c,rscale,Z_c);
409:   TSEIMEXRestoreVecs(ts,fine,&Z,NULL,NULL,NULL);
410:   TSEIMEXRestoreVecs(ts,coarse,&Z_c,NULL,NULL,NULL);
411:   return(0);
412: }

417: static PetscErrorCode TSSetUp_EIMEX(TS ts)
418: {
419:   TS_EIMEX       *ext = (TS_EIMEX*)ts->data;
421:   DM             dm;

424:   if (!ext->N){ /* ext->max_rows not set */
425:     TSEIMEXSetMaxRows(ts,TSEIMEXDefault);
426:   }
427:   if(-1 == ext->row_ind && -1 == ext->col_ind){
428:         TSEIMEXSetRowCol(ts,ext->max_rows,ext->max_rows);
429:   } else{/* ext->row_ind and col_ind already set */
431:       PetscInfo(ts,"Order adaptivity is enabled and TSEIMEXSetRowCol or -ts_eimex_row_col option will take no effect\n");
432:     }
433:   }

437:     TSEIMEXSetRowCol(ts,ext->nstages,ext->nstages);
438:   } else{
439:     ext->nstages = ext->max_rows; /* by default nstages is the same as max_rows, this can be changed by setting order adaptivity */
440:   }

442:   VecDuplicateVecs(ts->vec_sol,(1+ext->nstages)*ext->nstages/2,&ext->T);/* full T table */
443:   VecDuplicate(ts->vec_sol,&ext->YdotI);
444:   VecDuplicate(ts->vec_sol,&ext->YdotRHS);
445:   VecDuplicate(ts->vec_sol,&ext->Ydot);
446:   VecDuplicate(ts->vec_sol,&ext->VecSolPrev);
447:   VecDuplicate(ts->vec_sol,&ext->Y);
448:   VecDuplicate(ts->vec_sol,&ext->Z);
449:   TSGetDM(ts,&dm);
450:   if (dm) {
452:   }
453:   return(0);
454: }

458: static PetscErrorCode TSSetFromOptions_EIMEX(PetscOptions *PetscOptionsObject,TS ts)
459: {
460:   TS_EIMEX       *ext = (TS_EIMEX*)ts->data;
462:   PetscInt       tindex[2];
463:   PetscInt       np = 2, nrows=TSEIMEXDefault;

466:   tindex[0] = TSEIMEXDefault;
467:   tindex[1] = TSEIMEXDefault;
469:   {
470:     PetscBool flg;
471:     PetscOptionsInt("-ts_eimex_max_rows","Define the maximum number of rows used","TSEIMEXSetMaxRows",nrows,&nrows,&flg); /* default value 3 */
472:     if(flg){
473:       TSEIMEXSetMaxRows(ts,nrows);
474:     }
475:     PetscOptionsIntArray("-ts_eimex_row_col","Return the specific term in the T table","TSEIMEXSetRowCol",tindex,&np,&flg);
476:     if(flg){
477:       TSEIMEXSetRowCol(ts,tindex[0],tindex[1]);
478:     }
480:     SNESSetFromOptions(ts->snes);
481:   }
482:   PetscOptionsTail();
483:   return(0);
484: }

488: static PetscErrorCode TSView_EIMEX(TS ts,PetscViewer viewer)
489: {
490:   /*  TS_EIMEX         *ext = (TS_EIMEX*)ts->data; */
491:   PetscBool        iascii;
492:   PetscErrorCode   ierr;

495:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);
496:   if (iascii) {
497:     PetscViewerASCIIPrintf(viewer,"  EIMEX\n");
498:   }
499:   SNESView(ts->snes,viewer);
500:   return(0);
501: }

506: /*@C
507:   TSEIMEXSetMaxRows - Set the maximum number of rows for EIMEX schemes

509:   Logically collective

511:   Input Parameter:
512: +  ts - timestepping context
513: -  nrows - maximum number of rows

515:   Level: intermediate

518: @*/
519: PetscErrorCode TSEIMEXSetMaxRows(TS ts, PetscInt nrows)
520: {
524:   PetscTryMethod(ts,"TSEIMEXSetMaxRows_C",(TS,PetscInt),(ts,nrows));
525:   return(0);
526: }

531: /*@C
532:   TSEIMEXSetRowCol - Set the type index in the T table for the return value

534:   Logically collective

536:   Input Parameter:
537: +  ts - timestepping context
538: -  tindex - index in the T table

540:   Level: intermediate

543: @*/
544: PetscErrorCode TSEIMEXSetRowCol(TS ts, PetscInt row, PetscInt col)
545: {
549:   PetscTryMethod(ts,"TSEIMEXSetRowCol_C",(TS,PetscInt, PetscInt),(ts,row,col));
550:   return(0);
551: }

556: /*@C

559:   Logically collective

561:   Input Parameter:
562: +  ts - timestepping context
563: -  tindex - index in the T table

565:   Level: intermediate

568: @*/
569: PetscErrorCode TSEIMEXSetOrdAdapt(TS ts, PetscBool flg)
570: {
575:   return(0);
576: }

581: static PetscErrorCode TSEIMEXSetMaxRows_EIMEX(TS ts,PetscInt nrows)
582: {
583:   TS_EIMEX *ext = (TS_EIMEX*)ts->data;
585:   PetscInt       i;

588:   if (nrows < 0 || nrows > 100) SETERRQ1(((PetscObject)ts)->comm,PETSC_ERR_ARG_OUTOFRANGE,"Max number of rows (current value %D) should be an integer number between 1 and 100\n",nrows);
589:   PetscFree(ext->N);
590:   ext->max_rows = nrows;
591:   PetscMalloc1(nrows,&ext->N);
592:   for(i=0;i<nrows;i++) ext->N[i]=i+1;
593:   return(0);
594: }

598: static PetscErrorCode TSEIMEXSetRowCol_EIMEX(TS ts,PetscInt row,PetscInt col)
599: {
600:   TS_EIMEX *ext = (TS_EIMEX*)ts->data;

603:   if (row < 1 || col < 1) SETERRQ2(((PetscObject)ts)->comm,PETSC_ERR_ARG_OUTOFRANGE,"The row or column index (current value %d,%d) should not be less than 1 \n",row,col);
604:   if (row > ext->max_rows || col > ext->max_rows) SETERRQ3(((PetscObject)ts)->comm,PETSC_ERR_ARG_OUTOFRANGE,"The row or column index (current value %d,%d) exceeds the maximum number of rows %d\n",row,col,ext->max_rows);
605:   if (col > row) SETERRQ2(((PetscObject)ts)->comm,PETSC_ERR_ARG_OUTOFRANGE,"The column index (%d) exceeds the row index (%d)\n",col,row);

607:   ext->row_ind = row - 1;
608:   ext->col_ind = col - 1; /* Array index in C starts from 0 */
609:   return(0);
610: }

614: static PetscErrorCode TSEIMEXSetOrdAdapt_EIMEX(TS ts,PetscBool flg)
615: {
616:   TS_EIMEX *ext = (TS_EIMEX*)ts->data;
619:   return(0);
620: }

622: /* ------------------------------------------------------------ */
623: /*MC
624:       TSEIMEX - ODE solver using extrapolated IMEX schemes
625:   These methods are intended for problems with well-separated time scales, especially when a slow scale is strongly nonlinear such that it is expensive to solve with a fully implicit method. The user should provide the stiff part of the equation using TSSetIFunction() and the non-stiff part with TSSetRHSFunction().

627:    Notes:
628:   The default is a 3-stage scheme, it can be changed with TSEIMEXSetMaxRows() or -ts_eimex_max_rows

630:   This method currently only works with ODE, for which the stiff part G(t,X,Xdot) has the form Xdot + Ghat(t,X).

632:   Level: beginner

634: .seealso:  TSCreate(), TS
635: M*/
638: PETSC_EXTERN PetscErrorCode TSCreate_EIMEX(TS ts)
639: {
640:   TS_EIMEX       *ext;

645:   ts->ops->reset          = TSReset_EIMEX;
646:   ts->ops->destroy        = TSDestroy_EIMEX;
647:   ts->ops->view           = TSView_EIMEX;
648:   ts->ops->setup          = TSSetUp_EIMEX;
649:   ts->ops->step           = TSStep_EIMEX;
650:   ts->ops->interpolate    = TSInterpolate_EIMEX;
651:   ts->ops->evaluatestep   = TSEvaluateStep_EIMEX;
652:   ts->ops->setfromoptions = TSSetFromOptions_EIMEX;
653:   ts->ops->snesfunction   = SNESTSFormFunction_EIMEX;
654:   ts->ops->snesjacobian   = SNESTSFormJacobian_EIMEX;

656:   PetscNewLog(ts,&ext);
657:   ts->data = (void*)ext;