Actual source code: alpha1.c

petsc-3.11.2 2019-05-18
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  1: /*
  2:   Code for timestepping with implicit generalized-\alpha method
  3:   for first order systems.
  4: */
  5:  #include <petsc/private/tsimpl.h>

  7: static PetscBool  cited = PETSC_FALSE;
  8: static const char citation[] =
  9:   "@article{Jansen2000,\n"
 10:   "  title   = {A generalized-$\\alpha$ method for integrating the filtered {N}avier--{S}tokes equations with a stabilized finite element method},\n"
 11:   "  author  = {Kenneth E. Jansen and Christian H. Whiting and Gregory M. Hulbert},\n"
 12:   "  journal = {Computer Methods in Applied Mechanics and Engineering},\n"
 13:   "  volume  = {190},\n"
 14:   "  number  = {3--4},\n"
 15:   "  pages   = {305--319},\n"
 16:   "  year    = {2000},\n"
 17:   "  issn    = {0045-7825},\n"
 18:   "  doi     = {http://dx.doi.org/10.1016/S0045-7825(00)00203-6}\n}\n";

 20: typedef struct {
 21:   PetscReal stage_time;
 22:   PetscReal shift_V;
 23:   PetscReal scale_F;
 24:   Vec       X0,Xa,X1;
 25:   Vec       V0,Va,V1;

 27:   PetscReal Alpha_m;
 28:   PetscReal Alpha_f;
 29:   PetscReal Gamma;
 30:   PetscInt  order;

 32:   Vec       vec_sol_prev;
 33:   Vec       vec_lte_work;

 35:   TSStepStatus status;
 36: } TS_Alpha;

 38: static PetscErrorCode TSAlpha_StageTime(TS ts)
 39: {
 40:   TS_Alpha  *th = (TS_Alpha*)ts->data;
 41:   PetscReal t  = ts->ptime;
 42:   PetscReal dt = ts->time_step;
 43:   PetscReal Alpha_m = th->Alpha_m;
 44:   PetscReal Alpha_f = th->Alpha_f;
 45:   PetscReal Gamma   = th->Gamma;

 48:   th->stage_time = t + Alpha_f*dt;
 49:   th->shift_V = Alpha_m/(Alpha_f*Gamma*dt);
 50:   th->scale_F = 1/Alpha_f;
 51:   return(0);
 52: }

 54: static PetscErrorCode TSAlpha_StageVecs(TS ts,Vec X)
 55: {
 56:   TS_Alpha       *th = (TS_Alpha*)ts->data;
 57:   Vec            X1 = X,      V1 = th->V1;
 58:   Vec            Xa = th->Xa, Va = th->Va;
 59:   Vec            X0 = th->X0, V0 = th->V0;
 60:   PetscReal      dt = ts->time_step;
 61:   PetscReal      Alpha_m = th->Alpha_m;
 62:   PetscReal      Alpha_f = th->Alpha_f;
 63:   PetscReal      Gamma   = th->Gamma;

 67:   /* V1 = 1/(Gamma*dT)*(X1-X0) + (1-1/Gamma)*V0 */
 68:   VecWAXPY(V1,-1.0,X0,X1);
 69:   VecAXPBY(V1,1-1/Gamma,1/(Gamma*dt),V0);
 70:   /* Xa = X0 + Alpha_f*(X1-X0) */
 71:   VecWAXPY(Xa,-1.0,X0,X1);
 72:   VecAYPX(Xa,Alpha_f,X0);
 73:   /* Va = V0 + Alpha_m*(V1-V0) */
 74:   VecWAXPY(Va,-1.0,V0,V1);
 75:   VecAYPX(Va,Alpha_m,V0);
 76:   return(0);
 77: }

 79: static PetscErrorCode TSAlpha_SNESSolve(TS ts,Vec b,Vec x)
 80: {
 81:   PetscInt       nits,lits;

 85:   SNESSolve(ts->snes,b,x);
 86:   SNESGetIterationNumber(ts->snes,&nits);
 87:   SNESGetLinearSolveIterations(ts->snes,&lits);
 88:   ts->snes_its += nits; ts->ksp_its += lits;
 89:   return(0);
 90: }

 92: /*
 93:   Compute a consistent initial state for the generalized-alpha method.
 94:   - Solve two successive backward Euler steps with halved time step.
 95:   - Compute the initial time derivative using backward differences.
 96:   - If using adaptivity, estimate the LTE of the initial step.
 97: */
 98: static PetscErrorCode TSAlpha_Restart(TS ts,PetscBool *initok)
 99: {
100:   TS_Alpha       *th = (TS_Alpha*)ts->data;
101:   PetscReal      time_step;
102:   PetscReal      alpha_m,alpha_f,gamma;
103:   Vec            X0 = ts->vec_sol, X1, X2 = th->X1;
104:   PetscBool      stageok;

108:   VecDuplicate(X0,&X1);

110:   /* Setup backward Euler with halved time step */
111:   TSAlphaGetParams(ts,&alpha_m,&alpha_f,&gamma);
112:   TSAlphaSetParams(ts,1,1,1);
113:   TSGetTimeStep(ts,&time_step);
114:   ts->time_step = time_step/2;
115:   TSAlpha_StageTime(ts);
116:   th->stage_time = ts->ptime;
117:   VecZeroEntries(th->V0);

119:   /* First BE step, (t0,X0) -> (t1,X1) */
120:   th->stage_time += ts->time_step;
121:   VecCopy(X0,th->X0);
122:   TSPreStage(ts,th->stage_time);
123:   VecCopy(th->X0,X1);
124:   TSAlpha_SNESSolve(ts,NULL,X1);
125:   TSPostStage(ts,th->stage_time,0,&X1);
126:   TSAdaptCheckStage(ts->adapt,ts,th->stage_time,X1,&stageok);
127:   if (!stageok) goto finally;

129:   /* Second BE step, (t1,X1) -> (t2,X2) */
130:   th->stage_time += ts->time_step;
131:   VecCopy(X1,th->X0);
132:   TSPreStage(ts,th->stage_time);
133:   VecCopy(th->X0,X2);
134:   TSAlpha_SNESSolve(ts,NULL,X2);
135:   TSPostStage(ts,th->stage_time,0,&X2);
136:   TSAdaptCheckStage(ts->adapt,ts,th->stage_time,X2,&stageok);
137:   if (!stageok) goto finally;

139:   /* Compute V0 ~ dX/dt at t0 with backward differences */
140:   VecZeroEntries(th->V0);
141:   VecAXPY(th->V0,-3/ts->time_step,X0);
142:   VecAXPY(th->V0,+4/ts->time_step,X1);
143:   VecAXPY(th->V0,-1/ts->time_step,X2);

145:   /* Rough, lower-order estimate LTE of the initial step */
146:   if (th->vec_lte_work) {
147:     VecZeroEntries(th->vec_lte_work);
148:     VecAXPY(th->vec_lte_work,+2,X2);
149:     VecAXPY(th->vec_lte_work,-4,X1);
150:     VecAXPY(th->vec_lte_work,+2,X0);
151:   }

153:  finally:
154:   /* Revert TSAlpha to the initial state (t0,X0) */
155:   if (initok) *initok = stageok;
156:   TSSetTimeStep(ts,time_step);
157:   TSAlphaSetParams(ts,alpha_m,alpha_f,gamma);
158:   VecCopy(ts->vec_sol,th->X0);

160:   VecDestroy(&X1);
161:   return(0);
162: }

164: static PetscErrorCode TSStep_Alpha(TS ts)
165: {
166:   TS_Alpha       *th = (TS_Alpha*)ts->data;
167:   PetscInt       rejections = 0;
168:   PetscBool      stageok,accept = PETSC_TRUE;
169:   PetscReal      next_time_step = ts->time_step;

173:   PetscCitationsRegister(citation,&cited);

175:   if (!ts->steprollback) {
176:     if (th->vec_sol_prev) { VecCopy(th->X0,th->vec_sol_prev); }
177:     VecCopy(ts->vec_sol,th->X0);
178:     VecCopy(th->V1,th->V0);
179:   }

181:   th->status = TS_STEP_INCOMPLETE;
182:   while (!ts->reason && th->status != TS_STEP_COMPLETE) {

184:     if (ts->steprestart) {
185:       TSAlpha_Restart(ts,&stageok);
186:       if (!stageok) goto reject_step;
187:     }

189:     TSAlpha_StageTime(ts);
190:     VecCopy(th->X0,th->X1);
191:     TSPreStage(ts,th->stage_time);
192:     TSAlpha_SNESSolve(ts,NULL,th->X1);
193:     TSPostStage(ts,th->stage_time,0,&th->Xa);
194:     TSAdaptCheckStage(ts->adapt,ts,th->stage_time,th->Xa,&stageok);
195:     if (!stageok) goto reject_step;

197:     th->status = TS_STEP_PENDING;
198:     VecCopy(th->X1,ts->vec_sol);
199:     TSAdaptChoose(ts->adapt,ts,ts->time_step,NULL,&next_time_step,&accept);
200:     th->status = accept ? TS_STEP_COMPLETE : TS_STEP_INCOMPLETE;
201:     if (!accept) {
202:       VecCopy(th->X0,ts->vec_sol);
203:       ts->time_step = next_time_step;
204:       goto reject_step;
205:     }

207:     ts->ptime += ts->time_step;
208:     ts->time_step = next_time_step;
209:     break;

211:   reject_step:
212:     ts->reject++; accept = PETSC_FALSE;
213:     if (!ts->reason && ++rejections > ts->max_reject && ts->max_reject >= 0) {
214:       ts->reason = TS_DIVERGED_STEP_REJECTED;
215:       PetscInfo2(ts,"Step=%D, step rejections %D greater than current TS allowed, stopping solve\n",ts->steps,rejections);
216:     }

218:   }
219:   return(0);
220: }

222: static PetscErrorCode TSEvaluateWLTE_Alpha(TS ts,NormType wnormtype,PetscInt *order,PetscReal *wlte)
223: {
224:   TS_Alpha       *th = (TS_Alpha*)ts->data;
225:   Vec            X = th->X1;           /* X = solution */
226:   Vec            Y = th->vec_lte_work; /* Y = X + LTE  */
227:   PetscReal      wltea,wlter;

231:   if (!th->vec_sol_prev) {*wlte = -1; return(0);}
232:   if (!th->vec_lte_work) {*wlte = -1; return(0);}
233:   if (ts->steprestart) {
234:     /* th->vec_lte_work is set to the LTE in TSAlpha_Restart() */
235:     VecAXPY(Y,1,X);
236:   } else {
237:     /* Compute LTE using backward differences with non-constant time step */
238:     PetscReal   h = ts->time_step, h_prev = ts->ptime - ts->ptime_prev;
239:     PetscReal   a = 1 + h_prev/h;
240:     PetscScalar scal[3]; Vec vecs[3];
241:     scal[0] = +1/a;   scal[1] = -1/(a-1); scal[2] = +1/(a*(a-1));
242:     vecs[0] = th->X1; vecs[1] = th->X0;   vecs[2] = th->vec_sol_prev;
243:     VecCopy(X,Y);
244:     VecMAXPY(Y,3,scal,vecs);
245:   }
246:   TSErrorWeightedNorm(ts,X,Y,wnormtype,wlte,&wltea,&wlter);
247:   if (order) *order = 2;
248:   return(0);
249: }

251: static PetscErrorCode TSRollBack_Alpha(TS ts)
252: {
253:   TS_Alpha       *th = (TS_Alpha*)ts->data;

257:   VecCopy(th->X0,ts->vec_sol);
258:   return(0);
259: }

261: static PetscErrorCode TSInterpolate_Alpha(TS ts,PetscReal t,Vec X)
262: {
263:   TS_Alpha       *th = (TS_Alpha*)ts->data;
264:   PetscReal      dt  = t - ts->ptime;

268:   VecCopy(ts->vec_sol,X);
269:   VecAXPY(X,th->Gamma*dt,th->V1);
270:   VecAXPY(X,(1-th->Gamma)*dt,th->V0);
271:   return(0);
272: }

274: static PetscErrorCode SNESTSFormFunction_Alpha(PETSC_UNUSED SNES snes,Vec X,Vec F,TS ts)
275: {
276:   TS_Alpha       *th = (TS_Alpha*)ts->data;
277:   PetscReal      ta = th->stage_time;
278:   Vec            Xa = th->Xa, Va = th->Va;

282:   TSAlpha_StageVecs(ts,X);
283:   /* F = Function(ta,Xa,Va) */
284:   TSComputeIFunction(ts,ta,Xa,Va,F,PETSC_FALSE);
285:   VecScale(F,th->scale_F);
286:   return(0);
287: }

289: static PetscErrorCode SNESTSFormJacobian_Alpha(PETSC_UNUSED SNES snes,PETSC_UNUSED Vec X,Mat J,Mat P,TS ts)
290: {
291:   TS_Alpha       *th = (TS_Alpha*)ts->data;
292:   PetscReal      ta = th->stage_time;
293:   Vec            Xa = th->Xa, Va = th->Va;
294:   PetscReal      dVdX = th->shift_V;

298:   /* J,P = Jacobian(ta,Xa,Va) */
299:   TSComputeIJacobian(ts,ta,Xa,Va,dVdX,J,P,PETSC_FALSE);
300:   return(0);
301: }

303: static PetscErrorCode TSReset_Alpha(TS ts)
304: {
305:   TS_Alpha       *th = (TS_Alpha*)ts->data;

309:   VecDestroy(&th->X0);
310:   VecDestroy(&th->Xa);
311:   VecDestroy(&th->X1);
312:   VecDestroy(&th->V0);
313:   VecDestroy(&th->Va);
314:   VecDestroy(&th->V1);
315:   VecDestroy(&th->vec_sol_prev);
316:   VecDestroy(&th->vec_lte_work);
317:   return(0);
318: }

320: static PetscErrorCode TSDestroy_Alpha(TS ts)
321: {

325:   TSReset_Alpha(ts);
326:   PetscFree(ts->data);

328:   PetscObjectComposeFunction((PetscObject)ts,"TSAlphaSetRadius_C",NULL);
329:   PetscObjectComposeFunction((PetscObject)ts,"TSAlphaSetParams_C",NULL);
330:   PetscObjectComposeFunction((PetscObject)ts,"TSAlphaGetParams_C",NULL);
331:   return(0);
332: }

334: static PetscErrorCode TSSetUp_Alpha(TS ts)
335: {
336:   TS_Alpha       *th = (TS_Alpha*)ts->data;
337:   PetscBool      match;

341:   VecDuplicate(ts->vec_sol,&th->X0);
342:   VecDuplicate(ts->vec_sol,&th->Xa);
343:   VecDuplicate(ts->vec_sol,&th->X1);
344:   VecDuplicate(ts->vec_sol,&th->V0);
345:   VecDuplicate(ts->vec_sol,&th->Va);
346:   VecDuplicate(ts->vec_sol,&th->V1);

348:   TSGetAdapt(ts,&ts->adapt);
349:   TSAdaptCandidatesClear(ts->adapt);
350:   PetscObjectTypeCompare((PetscObject)ts->adapt,TSADAPTNONE,&match);
351:   if (!match) {
352:     VecDuplicate(ts->vec_sol,&th->vec_sol_prev);
353:     VecDuplicate(ts->vec_sol,&th->vec_lte_work);
354:   }

356:   TSGetSNES(ts,&ts->snes);
357:   return(0);
358: }

360: static PetscErrorCode TSSetFromOptions_Alpha(PetscOptionItems *PetscOptionsObject,TS ts)
361: {
362:   TS_Alpha       *th = (TS_Alpha*)ts->data;

366:   PetscOptionsHead(PetscOptionsObject,"Generalized-Alpha ODE solver options");
367:   {
368:     PetscBool flg;
369:     PetscReal radius = 1;
370:     PetscOptionsReal("-ts_alpha_radius","Spectral radius (high-frequency dissipation)","TSAlphaSetRadius",radius,&radius,&flg);
371:     if (flg) {TSAlphaSetRadius(ts,radius);}
372:     PetscOptionsReal("-ts_alpha_alpha_m","Algoritmic parameter alpha_m","TSAlphaSetParams",th->Alpha_m,&th->Alpha_m,NULL);
373:     PetscOptionsReal("-ts_alpha_alpha_f","Algoritmic parameter alpha_f","TSAlphaSetParams",th->Alpha_f,&th->Alpha_f,NULL);
374:     PetscOptionsReal("-ts_alpha_gamma","Algoritmic parameter gamma","TSAlphaSetParams",th->Gamma,&th->Gamma,NULL);
375:     TSAlphaSetParams(ts,th->Alpha_m,th->Alpha_f,th->Gamma);
376:   }
377:   PetscOptionsTail();
378:   return(0);
379: }

381: static PetscErrorCode TSView_Alpha(TS ts,PetscViewer viewer)
382: {
383:   TS_Alpha       *th = (TS_Alpha*)ts->data;
384:   PetscBool      iascii;

388:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);
389:   if (iascii) {
390:     PetscViewerASCIIPrintf(viewer,"  Alpha_m=%g, Alpha_f=%g, Gamma=%g\n",(double)th->Alpha_m,(double)th->Alpha_f,(double)th->Gamma);
391:   }
392:   return(0);
393: }

395: static PetscErrorCode TSAlphaSetRadius_Alpha(TS ts,PetscReal radius)
396: {
397:   PetscReal      alpha_m,alpha_f,gamma;

401:   if (radius < 0 || radius > 1) SETERRQ1(PetscObjectComm((PetscObject)ts),PETSC_ERR_ARG_OUTOFRANGE,"Radius %g not in range [0,1]",(double)radius);
402:   alpha_m = (PetscReal)0.5*(3-radius)/(1+radius);
403:   alpha_f = 1/(1+radius);
404:   gamma   = (PetscReal)0.5 + alpha_m - alpha_f;
405:   TSAlphaSetParams(ts,alpha_m,alpha_f,gamma);
406:   return(0);
407: }

409: static PetscErrorCode TSAlphaSetParams_Alpha(TS ts,PetscReal alpha_m,PetscReal alpha_f,PetscReal gamma)
410: {
411:   TS_Alpha  *th = (TS_Alpha*)ts->data;
412:   PetscReal tol = 100*PETSC_MACHINE_EPSILON;
413:   PetscReal res = ((PetscReal)0.5 + alpha_m - alpha_f) - gamma;

416:   th->Alpha_m = alpha_m;
417:   th->Alpha_f = alpha_f;
418:   th->Gamma   = gamma;
419:   th->order   = (PetscAbsReal(res) < tol) ? 2 : 1;
420:   return(0);
421: }

423: static PetscErrorCode TSAlphaGetParams_Alpha(TS ts,PetscReal *alpha_m,PetscReal *alpha_f,PetscReal *gamma)
424: {
425:   TS_Alpha *th = (TS_Alpha*)ts->data;

428:   if (alpha_m) *alpha_m = th->Alpha_m;
429:   if (alpha_f) *alpha_f = th->Alpha_f;
430:   if (gamma)   *gamma   = th->Gamma;
431:   return(0);
432: }

434: /*MC
435:       TSALPHA - ODE/DAE solver using the implicit Generalized-Alpha method
436:                 for first-order systems

438:   Level: beginner

440:   References:
441:   K.E. Jansen, C.H. Whiting, G.M. Hulber, "A generalized-alpha
442:   method for integrating the filtered Navier-Stokes equations with a
443:   stabilized finite element method", Computer Methods in Applied
444:   Mechanics and Engineering, 190, 305-319, 2000.
445:   DOI: 10.1016/S0045-7825(00)00203-6.

447:   J. Chung, G.M.Hubert. "A Time Integration Algorithm for Structural
448:   Dynamics with Improved Numerical Dissipation: The Generalized-alpha
449:   Method" ASME Journal of Applied Mechanics, 60, 371:375, 1993.

451: .seealso:  TS, TSCreate(), TSSetType(), TSAlphaSetRadius(), TSAlphaSetParams()
452: M*/
453: PETSC_EXTERN PetscErrorCode TSCreate_Alpha(TS ts)
454: {
455:   TS_Alpha       *th;

459:   ts->ops->reset          = TSReset_Alpha;
460:   ts->ops->destroy        = TSDestroy_Alpha;
461:   ts->ops->view           = TSView_Alpha;
462:   ts->ops->setup          = TSSetUp_Alpha;
463:   ts->ops->setfromoptions = TSSetFromOptions_Alpha;
464:   ts->ops->step           = TSStep_Alpha;
465:   ts->ops->evaluatewlte   = TSEvaluateWLTE_Alpha;
466:   ts->ops->rollback       = TSRollBack_Alpha;
467:   ts->ops->interpolate    = TSInterpolate_Alpha;
468:   ts->ops->snesfunction   = SNESTSFormFunction_Alpha;
469:   ts->ops->snesjacobian   = SNESTSFormJacobian_Alpha;
470:   ts->default_adapt_type  = TSADAPTNONE;

472:   ts->usessnes = PETSC_TRUE;

474:   PetscNewLog(ts,&th);
475:   ts->data = (void*)th;

477:   th->Alpha_m = 0.5;
478:   th->Alpha_f = 0.5;
479:   th->Gamma   = 0.5;
480:   th->order   = 2;

482:   PetscObjectComposeFunction((PetscObject)ts,"TSAlphaSetRadius_C",TSAlphaSetRadius_Alpha);
483:   PetscObjectComposeFunction((PetscObject)ts,"TSAlphaSetParams_C",TSAlphaSetParams_Alpha);
484:   PetscObjectComposeFunction((PetscObject)ts,"TSAlphaGetParams_C",TSAlphaGetParams_Alpha);
485:   return(0);
486: }

488: /*@
489:   TSAlphaSetRadius - sets the desired spectral radius of the method
490:                      (i.e. high-frequency numerical damping)

492:   Logically Collective on TS

494:   The algorithmic parameters \alpha_m and \alpha_f of the
495:   generalized-\alpha method can be computed in terms of a specified
496:   spectral radius \rho in [0,1] for infinite time step in order to
497:   control high-frequency numerical damping:
498:     \alpha_m = 0.5*(3-\rho)/(1+\rho)
499:     \alpha_f = 1/(1+\rho)

501:   Input Parameter:
502: +  ts - timestepping context
503: -  radius - the desired spectral radius

505:   Options Database:
506: .  -ts_alpha_radius <radius>

508:   Level: intermediate

510: .seealso: TSAlphaSetParams(), TSAlphaGetParams()
511: @*/
512: PetscErrorCode TSAlphaSetRadius(TS ts,PetscReal radius)
513: {

519:   if (radius < 0 || radius > 1) SETERRQ1(((PetscObject)ts)->comm,PETSC_ERR_ARG_OUTOFRANGE,"Radius %g not in range [0,1]",(double)radius);
520:   PetscTryMethod(ts,"TSAlphaSetRadius_C",(TS,PetscReal),(ts,radius));
521:   return(0);
522: }

524: /*@
525:   TSAlphaSetParams - sets the algorithmic parameters for TSALPHA

527:   Logically Collective on TS

529:   Second-order accuracy can be obtained so long as:
530:     \gamma = 0.5 + alpha_m - alpha_f

532:   Unconditional stability requires:
533:     \alpha_m >= \alpha_f >= 0.5

535:   Backward Euler method is recovered with:
536:     \alpha_m = \alpha_f = gamma = 1

538:   Input Parameter:
539: +  ts - timestepping context
540: .  \alpha_m - algorithmic paramenter
541: .  \alpha_f - algorithmic paramenter
542: -  \gamma   - algorithmic paramenter

544:    Options Database:
545: +  -ts_alpha_alpha_m <alpha_m>
546: .  -ts_alpha_alpha_f <alpha_f>
547: -  -ts_alpha_gamma   <gamma>

549:   Note:
550:   Use of this function is normally only required to hack TSALPHA to
551:   use a modified integration scheme. Users should call
552:   TSAlphaSetRadius() to set the desired spectral radius of the methods
553:   (i.e. high-frequency damping) in order so select optimal values for
554:   these parameters.

556:   Level: advanced

558: .seealso: TSAlphaSetRadius(), TSAlphaGetParams()
559: @*/
560: PetscErrorCode TSAlphaSetParams(TS ts,PetscReal alpha_m,PetscReal alpha_f,PetscReal gamma)
561: {

569:   PetscTryMethod(ts,"TSAlphaSetParams_C",(TS,PetscReal,PetscReal,PetscReal),(ts,alpha_m,alpha_f,gamma));
570:   return(0);
571: }

573: /*@
574:   TSAlphaGetParams - gets the algorithmic parameters for TSALPHA

576:   Not Collective

578:   Input Parameter:
579: .  ts - timestepping context

581:   Output Parameters:
582: +  \alpha_m - algorithmic parameter
583: .  \alpha_f - algorithmic parameter
584: -  \gamma   - algorithmic parameter

586:   Note:
587:   Use of this function is normally only required to hack TSALPHA to
588:   use a modified integration scheme. Users should call
589:   TSAlphaSetRadius() to set the high-frequency damping (i.e. spectral
590:   radius of the method) in order so select optimal values for these
591:   parameters.

593:   Level: advanced

595: .seealso: TSAlphaSetRadius(), TSAlphaSetParams()
596: @*/
597: PetscErrorCode TSAlphaGetParams(TS ts,PetscReal *alpha_m,PetscReal *alpha_f,PetscReal *gamma)
598: {

606:   PetscUseMethod(ts,"TSAlphaGetParams_C",(TS,PetscReal*,PetscReal*,PetscReal*),(ts,alpha_m,alpha_f,gamma));
607:   return(0);
608: }