Actual source code: theta.c

petsc-dev 2014-02-02
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  1: /*
  2:   Code for timestepping with implicit Theta method
  3: */
  4: #define PETSC_DESIRE_COMPLEX
  5: #include <petsc-private/tsimpl.h>                /*I   "petscts.h"   I*/
  6: #include <petscsnesfas.h>
  7: #include <petscdm.h>

  9: typedef struct {
 10:   Vec          X,Xdot;                   /* Storage for one stage */
 11:   Vec          X0;                       /* work vector to store X0 */
 12:   Vec          affine;                   /* Affine vector needed for residual at beginning of step */
 13:   PetscBool    extrapolate;
 14:   PetscBool    endpoint;
 15:   PetscReal    Theta;
 16:   PetscReal    stage_time;
 17:   TSStepStatus status;
 18:   char         *name;
 19:   PetscInt     order;
 20:   PetscReal    ccfl;               /* Placeholder for CFL coefficient relative to forward Euler */
 21:   PetscBool    adapt;  /* use time-step adaptivity ? */
 22: } TS_Theta;

 26: static PetscErrorCode TSThetaGetX0AndXdot(TS ts,DM dm,Vec *X0,Vec *Xdot)
 27: {
 28:   TS_Theta       *th = (TS_Theta*)ts->data;

 32:   if (X0) {
 33:     if (dm && dm != ts->dm) {
 34:       DMGetNamedGlobalVector(dm,"TSTheta_X0",X0);
 35:     } else *X0 = ts->vec_sol;
 36:   }
 37:   if (Xdot) {
 38:     if (dm && dm != ts->dm) {
 39:       DMGetNamedGlobalVector(dm,"TSTheta_Xdot",Xdot);
 40:     } else *Xdot = th->Xdot;
 41:   }
 42:   return(0);
 43: }


 48: static PetscErrorCode TSThetaRestoreX0AndXdot(TS ts,DM dm,Vec *X0,Vec *Xdot)
 49: {

 53:   if (X0) {
 54:     if (dm && dm != ts->dm) {
 55:       DMRestoreNamedGlobalVector(dm,"TSTheta_X0",X0);
 56:     }
 57:   }
 58:   if (Xdot) {
 59:     if (dm && dm != ts->dm) {
 60:       DMRestoreNamedGlobalVector(dm,"TSTheta_Xdot",Xdot);
 61:     }
 62:   }
 63:   return(0);
 64: }

 68: static PetscErrorCode DMCoarsenHook_TSTheta(DM fine,DM coarse,void *ctx)
 69: {

 72:   return(0);
 73: }

 77: static PetscErrorCode DMRestrictHook_TSTheta(DM fine,Mat restrct,Vec rscale,Mat inject,DM coarse,void *ctx)
 78: {
 79:   TS             ts = (TS)ctx;
 81:   Vec            X0,Xdot,X0_c,Xdot_c;

 84:   TSThetaGetX0AndXdot(ts,fine,&X0,&Xdot);
 85:   TSThetaGetX0AndXdot(ts,coarse,&X0_c,&Xdot_c);
 86:   MatRestrict(restrct,X0,X0_c);
 87:   MatRestrict(restrct,Xdot,Xdot_c);
 88:   VecPointwiseMult(X0_c,rscale,X0_c);
 89:   VecPointwiseMult(Xdot_c,rscale,Xdot_c);
 90:   TSThetaRestoreX0AndXdot(ts,fine,&X0,&Xdot);
 91:   TSThetaRestoreX0AndXdot(ts,coarse,&X0_c,&Xdot_c);
 92:   return(0);
 93: }

 97: static PetscErrorCode DMSubDomainHook_TSTheta(DM dm,DM subdm,void *ctx)
 98: {

101:   return(0);
102: }

106: static PetscErrorCode DMSubDomainRestrictHook_TSTheta(DM dm,VecScatter gscat,VecScatter lscat,DM subdm,void *ctx)
107: {
108:   TS             ts = (TS)ctx;
110:   Vec            X0,Xdot,X0_sub,Xdot_sub;

113:   TSThetaGetX0AndXdot(ts,dm,&X0,&Xdot);
114:   TSThetaGetX0AndXdot(ts,subdm,&X0_sub,&Xdot_sub);

116:   VecScatterBegin(gscat,X0,X0_sub,INSERT_VALUES,SCATTER_FORWARD);
117:   VecScatterEnd(gscat,X0,X0_sub,INSERT_VALUES,SCATTER_FORWARD);

119:   VecScatterBegin(gscat,Xdot,Xdot_sub,INSERT_VALUES,SCATTER_FORWARD);
120:   VecScatterEnd(gscat,Xdot,Xdot_sub,INSERT_VALUES,SCATTER_FORWARD);

122:   TSThetaRestoreX0AndXdot(ts,dm,&X0,&Xdot);
123:   TSThetaRestoreX0AndXdot(ts,subdm,&X0_sub,&Xdot_sub);
124:   return(0);
125: }

129: static PetscErrorCode TSEvaluateStep_Theta(TS ts,PetscInt order,Vec U,PetscBool *done)
130: {
132:   TS_Theta       *th = (TS_Theta*)ts->data;

135:   if (order == 0) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_USER,"No time-step adaptivity implemented for 1st order theta method; Run with -ts_adapt_type none");
136:   if (order == th->order) {
137:     if (th->endpoint) {
138:       VecCopy(th->X,U);
139:     } else {
140:       PetscReal shift = 1./(th->Theta*ts->time_step);
141:       VecAXPBYPCZ(th->Xdot,-shift,shift,0,U,th->X);
142:       VecAXPY(U,ts->time_step,th->Xdot);
143:     }
144:   } else if (order == th->order-1 && order) {
145:     VecWAXPY(U,ts->time_step,th->Xdot,th->X0);
146:   }
147:   return(0);
148: }

152: static PetscErrorCode TSStep_Theta(TS ts)
153: {
154:   TS_Theta            *th = (TS_Theta*)ts->data;
155:   PetscInt            its,lits,reject,next_scheme;
156:   PetscReal           next_time_step;
157:   SNESConvergedReason snesreason;
158:   PetscErrorCode      ierr;
159:   TSAdapt             adapt;
160:   PetscBool           accept;

163:   th->status = TS_STEP_INCOMPLETE;
164:   VecCopy(ts->vec_sol,th->X0);
165:   for (reject=0; reject<ts->max_reject && !ts->reason && th->status != TS_STEP_COMPLETE; reject++,ts->reject++) {
166:     PetscReal shift = 1./(th->Theta*ts->time_step);
167:     next_time_step = ts->time_step;
168:     th->stage_time = ts->ptime + (th->endpoint ? 1. : th->Theta)*ts->time_step;
169:     TSPreStep(ts);
170:     TSPreStage(ts,th->stage_time);

172:     if (th->endpoint) {           /* This formulation assumes linear time-independent mass matrix */
173:       VecZeroEntries(th->Xdot);
174:       if (!th->affine) {VecDuplicate(ts->vec_sol,&th->affine);}
175:       TSComputeIFunction(ts,ts->ptime,ts->vec_sol,th->Xdot,th->affine,PETSC_FALSE);
176:       VecScale(th->affine,(th->Theta-1.)/th->Theta);
177:     }
178:     if (th->extrapolate) {
179:       VecWAXPY(th->X,1./shift,th->Xdot,ts->vec_sol);
180:     } else {
181:       VecCopy(ts->vec_sol,th->X);
182:     }
183:     SNESSolve(ts->snes,th->affine,th->X);
184:     SNESGetIterationNumber(ts->snes,&its);
185:     SNESGetLinearSolveIterations(ts->snes,&lits);
186:     SNESGetConvergedReason(ts->snes,&snesreason);
187:     TSPostStage(ts,th->stage_time,0,&(th->X));
188:     ts->snes_its += its; ts->ksp_its += lits;
189:     TSGetAdapt(ts,&adapt);
190:     TSAdaptCheckStage(adapt,ts,&accept);
191:     if (!accept) continue;
192:     TSEvaluateStep(ts,th->order,ts->vec_sol,NULL);
193:     /* Register only the current method as a candidate because we're not supporting multiple candidates yet. */
194:     TSGetAdapt(ts,&adapt);
195:     TSAdaptCandidatesClear(adapt);
196:     TSAdaptCandidateAdd(adapt,NULL,th->order,1,th->ccfl,1.0,PETSC_TRUE);
197:     TSAdaptChoose(adapt,ts,ts->time_step,&next_scheme,&next_time_step,&accept);

199:     if (accept) {
200:       /* ignore next_scheme for now */
201:       ts->ptime    += ts->time_step;
202:       ts->time_step = next_time_step;
203:       ts->steps++;
204:       th->status = TS_STEP_COMPLETE;
205:     } else {                    /* Roll back the current step */
206:       VecCopy(th->X0,ts->vec_sol);
207:       ts->time_step = next_time_step;
208:       th->status    = TS_STEP_INCOMPLETE;
209:     }
210:   }
211:   return(0);
212: }

216: static PetscErrorCode TSInterpolate_Theta(TS ts,PetscReal t,Vec X)
217: {
218:   TS_Theta       *th   = (TS_Theta*)ts->data;
219:   PetscReal      alpha = t - ts->ptime;

223:   VecCopy(ts->vec_sol,th->X);
224:   if (th->endpoint) alpha *= th->Theta;
225:   VecWAXPY(X,alpha,th->Xdot,th->X);
226:   return(0);
227: }

229: /*------------------------------------------------------------*/
232: static PetscErrorCode TSReset_Theta(TS ts)
233: {
234:   TS_Theta       *th = (TS_Theta*)ts->data;

238:   VecDestroy(&th->X);
239:   VecDestroy(&th->Xdot);
240:   VecDestroy(&th->X0);
241:   VecDestroy(&th->affine);
242:   return(0);
243: }

247: static PetscErrorCode TSDestroy_Theta(TS ts)
248: {

252:   TSReset_Theta(ts);
253:   PetscFree(ts->data);
254:   PetscObjectComposeFunction((PetscObject)ts,"TSThetaGetTheta_C",NULL);
255:   PetscObjectComposeFunction((PetscObject)ts,"TSThetaSetTheta_C",NULL);
256:   PetscObjectComposeFunction((PetscObject)ts,"TSThetaGetEndpoint_C",NULL);
257:   PetscObjectComposeFunction((PetscObject)ts,"TSThetaSetEndpoint_C",NULL);
258:   return(0);
259: }

261: /*
262:   This defines the nonlinear equation that is to be solved with SNES
263:   G(U) = F[t0+Theta*dt, U, (U-U0)*shift] = 0
264: */
267: static PetscErrorCode SNESTSFormFunction_Theta(SNES snes,Vec x,Vec y,TS ts)
268: {
269:   TS_Theta       *th = (TS_Theta*)ts->data;
271:   Vec            X0,Xdot;
272:   DM             dm,dmsave;
273:   PetscReal      shift = 1./(th->Theta*ts->time_step);

276:   SNESGetDM(snes,&dm);
277:   /* When using the endpoint variant, this is actually 1/Theta * Xdot */
278:   TSThetaGetX0AndXdot(ts,dm,&X0,&Xdot);
279:   VecAXPBYPCZ(Xdot,-shift,shift,0,X0,x);

281:   /* DM monkey-business allows user code to call TSGetDM() inside of functions evaluated on levels of FAS */
282:   dmsave = ts->dm;
283:   ts->dm = dm;
284:   TSComputeIFunction(ts,th->stage_time,x,Xdot,y,PETSC_FALSE);
285:   ts->dm = dmsave;
286:   TSThetaRestoreX0AndXdot(ts,dm,&X0,&Xdot);
287:   return(0);
288: }

292: static PetscErrorCode SNESTSFormJacobian_Theta(SNES snes,Vec x,Mat *A,Mat *B,MatStructure *str,TS ts)
293: {
294:   TS_Theta       *th = (TS_Theta*)ts->data;
296:   Vec            Xdot;
297:   DM             dm,dmsave;
298:   PetscReal      shift = 1./(th->Theta*ts->time_step);

301:   SNESGetDM(snes,&dm);

303:   /* th->Xdot has already been computed in SNESTSFormFunction_Theta (SNES guarantees this) */
304:   TSThetaGetX0AndXdot(ts,dm,NULL,&Xdot);

306:   dmsave = ts->dm;
307:   ts->dm = dm;
308:   TSComputeIJacobian(ts,th->stage_time,x,Xdot,shift,A,B,str,PETSC_FALSE);
309:   ts->dm = dmsave;
310:   TSThetaRestoreX0AndXdot(ts,dm,NULL,&Xdot);
311:   return(0);
312: }

316: static PetscErrorCode TSSetUp_Theta(TS ts)
317: {
318:   TS_Theta       *th = (TS_Theta*)ts->data;
320:   SNES           snes;
321:   DM             dm;

324:   VecDuplicate(ts->vec_sol,&th->X);
325:   VecDuplicate(ts->vec_sol,&th->Xdot);
326:   VecDuplicate(ts->vec_sol,&th->X0);
327:   TSGetSNES(ts,&snes);
328:   TSGetDM(ts,&dm);
329:   if (dm) {
330:     DMCoarsenHookAdd(dm,DMCoarsenHook_TSTheta,DMRestrictHook_TSTheta,ts);
331:     DMSubDomainHookAdd(dm,DMSubDomainHook_TSTheta,DMSubDomainRestrictHook_TSTheta,ts);
332:   }
333:   if (th->Theta == 0.5 && th->endpoint) th->order = 2;
334:   else th->order = 1;

336:   if (!th->adapt) {
337:     TSAdapt adapt;
338:     TSAdaptDestroy(&ts->adapt);
339:     TSGetAdapt(ts,&adapt);
340:     TSAdaptSetType(adapt,TSADAPTNONE);
341:   }
342:   return(0);
343: }
344: /*------------------------------------------------------------*/

348: static PetscErrorCode TSSetFromOptions_Theta(TS ts)
349: {
350:   TS_Theta       *th = (TS_Theta*)ts->data;

354:   PetscOptionsHead("Theta ODE solver options");
355:   {
356:     PetscOptionsReal("-ts_theta_theta","Location of stage (0<Theta<=1)","TSThetaSetTheta",th->Theta,&th->Theta,NULL);
357:     PetscOptionsBool("-ts_theta_extrapolate","Extrapolate stage solution from previous solution (sometimes unstable)","TSThetaSetExtrapolate",th->extrapolate,&th->extrapolate,NULL);
358:     PetscOptionsBool("-ts_theta_endpoint","Use the endpoint instead of midpoint form of the Theta method","TSThetaSetEndpoint",th->endpoint,&th->endpoint,NULL);
359:     PetscOptionsBool("-ts_theta_adapt","Use time-step adaptivity with the Theta method","",th->adapt,&th->adapt,NULL);
360:     SNESSetFromOptions(ts->snes);
361:   }
362:   PetscOptionsTail();
363:   return(0);
364: }

368: static PetscErrorCode TSView_Theta(TS ts,PetscViewer viewer)
369: {
370:   TS_Theta       *th = (TS_Theta*)ts->data;
371:   PetscBool      iascii;

375:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);
376:   if (iascii) {
377:     PetscViewerASCIIPrintf(viewer,"  Theta=%g\n",(double)th->Theta);
378:     PetscViewerASCIIPrintf(viewer,"  Extrapolation=%s\n",th->extrapolate ? "yes" : "no");
379:   }
380:   SNESView(ts->snes,viewer);
381:   return(0);
382: }

386: PetscErrorCode  TSThetaGetTheta_Theta(TS ts,PetscReal *theta)
387: {
388:   TS_Theta *th = (TS_Theta*)ts->data;

391:   *theta = th->Theta;
392:   return(0);
393: }

397: PetscErrorCode  TSThetaSetTheta_Theta(TS ts,PetscReal theta)
398: {
399:   TS_Theta *th = (TS_Theta*)ts->data;

402:   if (theta <= 0 || 1 < theta) SETERRQ1(PetscObjectComm((PetscObject)ts),PETSC_ERR_ARG_OUTOFRANGE,"Theta %g not in range (0,1]",(double)theta);
403:   th->Theta = theta;
404:   return(0);
405: }

409: PetscErrorCode  TSThetaGetEndpoint_Theta(TS ts,PetscBool *endpoint)
410: {
411:   TS_Theta *th = (TS_Theta*)ts->data;

414:   *endpoint = th->endpoint;
415:   return(0);
416: }

420: PetscErrorCode  TSThetaSetEndpoint_Theta(TS ts,PetscBool flg)
421: {
422:   TS_Theta *th = (TS_Theta*)ts->data;

425:   th->endpoint = flg;
426:   return(0);
427: }

429: #if defined(PETSC_HAVE_COMPLEX)
432: static PetscErrorCode TSComputeLinearStability_Theta(TS ts,PetscReal xr,PetscReal xi,PetscReal *yr,PetscReal *yi)
433: {
434:   PetscComplex z   = xr + xi*PETSC_i,f;
435:   TS_Theta     *th = (TS_Theta*)ts->data;
436:   const PetscReal one = 1.0;

439:   f   = (one + (one - th->Theta)*z)/(one - th->Theta*z);
440:   *yr = PetscRealPartComplex(f);
441:   *yi = PetscImaginaryPartComplex(f);
442:   return(0);
443: }
444: #endif


447: /* ------------------------------------------------------------ */
448: /*MC
449:       TSTHETA - DAE solver using the implicit Theta method

451:    Level: beginner

453:    Options Database:
454:       -ts_theta_theta <Theta> - Location of stage (0<Theta<=1)
455:       -ts_theta_extrapolate <flg> Extrapolate stage solution from previous solution (sometimes unstable)
456:       -ts_theta_endpoint <flag> - Use the endpoint (like Crank-Nicholson) instead of midpoint form of the Theta method

458:    Notes:
459: $  -ts_type theta -ts_theta_theta 1.0 corresponds to backward Euler (TSBEULER)
460: $  -ts_type theta -ts_theta_theta 0.5 corresponds to the implicit midpoint rule
461: $  -ts_type theta -ts_theta_theta 0.5 -ts_theta_endpoint corresponds to Crank-Nicholson (TSCN)



465:    This method can be applied to DAE.

467:    This method is cast as a 1-stage implicit Runge-Kutta method.

469: .vb
470:   Theta | Theta
471:   -------------
472:         |  1
473: .ve

475:    For the default Theta=0.5, this is also known as the implicit midpoint rule.

477:    When the endpoint variant is chosen, the method becomes a 2-stage method with first stage explicit:

479: .vb
480:   0 | 0         0
481:   1 | 1-Theta   Theta
482:   -------------------
483:     | 1-Theta   Theta
484: .ve

486:    For the default Theta=0.5, this is the trapezoid rule (also known as Crank-Nicolson, see TSCN).

488:    To apply a diagonally implicit RK method to DAE, the stage formula

490: $  Y_i = X + h sum_j a_ij Y'_j

492:    is interpreted as a formula for Y'_i in terms of Y_i and known values (Y'_j, j<i)

494: .seealso:  TSCreate(), TS, TSSetType(), TSCN, TSBEULER, TSThetaSetTheta(), TSThetaSetEndpoint()

496: M*/
499: PETSC_EXTERN PetscErrorCode TSCreate_Theta(TS ts)
500: {
501:   TS_Theta       *th;

505:   ts->ops->reset          = TSReset_Theta;
506:   ts->ops->destroy        = TSDestroy_Theta;
507:   ts->ops->view           = TSView_Theta;
508:   ts->ops->setup          = TSSetUp_Theta;
509:   ts->ops->step           = TSStep_Theta;
510:   ts->ops->interpolate    = TSInterpolate_Theta;
511:   ts->ops->evaluatestep   = TSEvaluateStep_Theta;
512:   ts->ops->setfromoptions = TSSetFromOptions_Theta;
513:   ts->ops->snesfunction   = SNESTSFormFunction_Theta;
514:   ts->ops->snesjacobian   = SNESTSFormJacobian_Theta;
515: #if defined(PETSC_HAVE_COMPLEX)
516:   ts->ops->linearstability = TSComputeLinearStability_Theta;
517: #endif

519:   PetscNewLog(ts,&th);
520:   ts->data = (void*)th;

522:   th->extrapolate = PETSC_FALSE;
523:   th->Theta       = 0.5;
524:   th->ccfl        = 1.0;
525:   th->adapt       = PETSC_FALSE;
526:   PetscObjectComposeFunction((PetscObject)ts,"TSThetaGetTheta_C",TSThetaGetTheta_Theta);
527:   PetscObjectComposeFunction((PetscObject)ts,"TSThetaSetTheta_C",TSThetaSetTheta_Theta);
528:   PetscObjectComposeFunction((PetscObject)ts,"TSThetaGetEndpoint_C",TSThetaGetEndpoint_Theta);
529:   PetscObjectComposeFunction((PetscObject)ts,"TSThetaSetEndpoint_C",TSThetaSetEndpoint_Theta);
530:   return(0);
531: }

535: /*@
536:   TSThetaGetTheta - Get the abscissa of the stage in (0,1].

538:   Not Collective

540:   Input Parameter:
541: .  ts - timestepping context

543:   Output Parameter:
544: .  theta - stage abscissa

546:   Note:
547:   Use of this function is normally only required to hack TSTHETA to use a modified integration scheme.

549:   Level: Advanced

551: .seealso: TSThetaSetTheta()
552: @*/
553: PetscErrorCode  TSThetaGetTheta(TS ts,PetscReal *theta)
554: {

560:   PetscUseMethod(ts,"TSThetaGetTheta_C",(TS,PetscReal*),(ts,theta));
561:   return(0);
562: }

566: /*@
567:   TSThetaSetTheta - Set the abscissa of the stage in (0,1].

569:   Not Collective

571:   Input Parameter:
572: +  ts - timestepping context
573: -  theta - stage abscissa

575:   Options Database:
576: .  -ts_theta_theta <theta>

578:   Level: Intermediate

580: .seealso: TSThetaGetTheta()
581: @*/
582: PetscErrorCode  TSThetaSetTheta(TS ts,PetscReal theta)
583: {

588:   PetscTryMethod(ts,"TSThetaSetTheta_C",(TS,PetscReal),(ts,theta));
589:   return(0);
590: }

594: /*@
595:   TSThetaGetEndpoint - Gets whether to use the endpoint variant of the method (e.g. trapezoid/Crank-Nicolson instead of midpoint rule).

597:   Not Collective

599:   Input Parameter:
600: .  ts - timestepping context

602:   Output Parameter:
603: .  endpoint - PETSC_TRUE when using the endpoint variant

605:   Level: Advanced

607: .seealso: TSThetaSetEndpoint(), TSTHETA, TSCN
608: @*/
609: PetscErrorCode TSThetaGetEndpoint(TS ts,PetscBool *endpoint)
610: {

616:   PetscTryMethod(ts,"TSThetaGetEndpoint_C",(TS,PetscBool*),(ts,endpoint));
617:   return(0);
618: }

622: /*@
623:   TSThetaSetEndpoint - Sets whether to use the endpoint variant of the method (e.g. trapezoid/Crank-Nicolson instead of midpoint rule).

625:   Not Collective

627:   Input Parameter:
628: +  ts - timestepping context
629: -  flg - PETSC_TRUE to use the endpoint variant

631:   Options Database:
632: .  -ts_theta_endpoint <flg>

634:   Level: Intermediate

636: .seealso: TSTHETA, TSCN
637: @*/
638: PetscErrorCode TSThetaSetEndpoint(TS ts,PetscBool flg)
639: {

644:   PetscTryMethod(ts,"TSThetaSetEndpoint_C",(TS,PetscBool),(ts,flg));
645:   return(0);
646: }

648: /*
649:  * TSBEULER and TSCN are straightforward specializations of TSTHETA.
650:  * The creation functions for these specializations are below.
651:  */

655: static PetscErrorCode TSView_BEuler(TS ts,PetscViewer viewer)
656: {

660:   SNESView(ts->snes,viewer);
661:   return(0);
662: }

664: /*MC
665:       TSBEULER - ODE solver using the implicit backward Euler method

667:   Level: beginner

669:   Notes:
670:   TSBEULER is equivalent to TSTHETA with Theta=1.0

672: $  -ts_type theta -ts_theta_theta 1.

674: .seealso:  TSCreate(), TS, TSSetType(), TSEULER, TSCN, TSTHETA

676: M*/
679: PETSC_EXTERN PetscErrorCode TSCreate_BEuler(TS ts)
680: {

684:   TSCreate_Theta(ts);
685:   TSThetaSetTheta(ts,1.0);
686:   ts->ops->view = TSView_BEuler;
687:   return(0);
688: }

692: static PetscErrorCode TSView_CN(TS ts,PetscViewer viewer)
693: {

697:   SNESView(ts->snes,viewer);
698:   return(0);
699: }

701: /*MC
702:       TSCN - ODE solver using the implicit Crank-Nicolson method.

704:   Level: beginner

706:   Notes:
707:   TSCN is equivalent to TSTHETA with Theta=0.5 and the "endpoint" option set. I.e.

709: $  -ts_type theta -ts_theta_theta 0.5 -ts_theta_endpoint

711: .seealso:  TSCreate(), TS, TSSetType(), TSBEULER, TSTHETA

713: M*/
716: PETSC_EXTERN PetscErrorCode TSCreate_CN(TS ts)
717: {

721:   TSCreate_Theta(ts);
722:   TSThetaSetTheta(ts,0.5);
723:   TSThetaSetEndpoint(ts,PETSC_TRUE);
724:   ts->ops->view = TSView_CN;
725:   return(0);
726: }