Actual source code: alpha1.c

      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","Algorithmic parameter alpha_m","TSAlphaSetParams",th->Alpha_m,&th->Alpha_m,NULL);
    373:     PetscOptionsReal("-ts_alpha_alpha_f","Algorithmic parameter alpha_f","TSAlphaSetParams",th->Alpha_f,&th->Alpha_f,NULL);
    374:     PetscOptionsReal("-ts_alpha_gamma","Algorithmic 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: }