Actual source code: alpha1.c
petsc-3.7.1 2016-05-15
Report Typos and Errors

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

      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:   PetscBool adapt;
     33:   Vec       vec_sol_prev;
     34:   Vec       vec_lte_work;

     36:   TSStepStatus status;
     37: } TS_Alpha;

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

     51:   th->stage_time = t + Alpha_f*dt;
     52:   th->shift_V = Alpha_m/(Alpha_f*Gamma*dt);
     53:   th->scale_F = 1/Alpha_f;
     54:   return(0);
     55: }

     59: static PetscErrorCode TSAlpha_StageVecs(TS ts,Vec X)
     60: {
     61:   TS_Alpha       *th = (TS_Alpha*)ts->data;
     62:   Vec            X1 = X,      V1 = th->V1;
     63:   Vec            Xa = th->Xa, Va = th->Va;
     64:   Vec            X0 = th->X0, V0 = th->V0;
     65:   PetscReal      dt = ts->time_step;
     66:   PetscReal      Alpha_m = th->Alpha_m;
     67:   PetscReal      Alpha_f = th->Alpha_f;
     68:   PetscReal      Gamma   = th->Gamma;

     72:   /* V1 = 1/(Gamma*dT)*(X1-X0) + (1-1/Gamma)*V0 */
     73:   VecWAXPY(V1,-1.0,X0,X1);
     74:   VecAXPBY(V1,1-1/Gamma,1/(Gamma*dt),V0);
     75:   /* Xa = X0 + Alpha_f*(X1-X0) */
     76:   VecWAXPY(Xa,-1.0,X0,X1);
     77:   VecAYPX(Xa,Alpha_f,X0);
     78:   /* Va = V0 + Alpha_m*(V1-V0) */
     79:   VecWAXPY(Va,-1.0,V0,V1);
     80:   VecAYPX(Va,Alpha_m,V0);
     81:   return(0);
     82: }

     86: static PetscErrorCode TS_SNESSolve(TS ts,Vec b,Vec x)
     87: {
     88:   PetscInt       nits,lits;

     92:   SNESSolve(ts->snes,b,x);
     93:   SNESGetIterationNumber(ts->snes,&nits);
     94:   SNESGetLinearSolveIterations(ts->snes,&lits);
     95:   ts->snes_its += nits; ts->ksp_its += lits;
     96:   return(0);
     97: }

     99: /*
    100:   Compute a consistent initial state for the generalized-alpha method.
    101:   - Solve two successive backward Euler steps with halved time step.
    102:   - Compute the initial time derivative using backward differences.
    103:   - If using adaptivity, estimate the LTE of the initial step.
    104: */
    107: static PetscErrorCode TSAlpha_Restart(TS ts,PetscBool *initok)
    108: {
    109:   TS_Alpha       *th = (TS_Alpha*)ts->data;
    110:   PetscReal      time_step;
    111:   PetscReal      alpha_m,alpha_f,gamma;
    112:   Vec            X0 = ts->vec_sol, X1, X2 = th->X1;
    113:   PetscBool      stageok;

    117:   VecDuplicate(X0,&X1);

    119:   /* Setup backward Euler with halved time step */
    120:   TSAlphaGetParams(ts,&alpha_m,&alpha_f,&gamma);
    121:   TSAlphaSetParams(ts,1,1,1);
    122:   TSGetTimeStep(ts,&time_step);
    123:   ts->time_step = time_step/2;
    124:   TSAlpha_StageTime(ts);
    125:   th->stage_time = ts->ptime;
    126:   VecZeroEntries(th->V0);

    128:   /* First BE step, (t0,X0) -> (t1,X1) */
    129:   th->stage_time += ts->time_step;
    130:   VecCopy(X0,th->X0);
    131:   TSPreStage(ts,th->stage_time);
    132:   VecCopy(th->X0,X1);
    133:   TS_SNESSolve(ts,NULL,X1);
    134:   TSPostStage(ts,th->stage_time,0,&X1);
    135:   TSAdaptCheckStage(ts->adapt,ts,th->stage_time,X1,&stageok);
    136:   if (!stageok) goto finally;

    138:   /* Second BE step, (t1,X1) -> (t2,X2) */
    139:   th->stage_time += ts->time_step;
    140:   VecCopy(X1,th->X0);
    141:   TSPreStage(ts,th->stage_time);
    142:   VecCopy(th->X0,X2);
    143:   TS_SNESSolve(ts,NULL,X2);
    144:   TSPostStage(ts,th->stage_time,0,&X2);
    145:   TSAdaptCheckStage(ts->adapt,ts,th->stage_time,X2,&stageok);
    146:   if (!stageok) goto finally;

    148:   /* Compute V0 ~ dX/dt at t0 with backward differences */
    149:   VecZeroEntries(th->V0);
    150:   VecAXPY(th->V0,-3/ts->time_step,X0);
    151:   VecAXPY(th->V0,+4/ts->time_step,X1);
    152:   VecAXPY(th->V0,-1/ts->time_step,X2);

    154:   /* Rough, lower-order estimate LTE of the initial step */
    155:   if (th->adapt) {
    156:     VecZeroEntries(th->vec_lte_work);
    157:     VecAXPY(th->vec_lte_work,+2,X2);
    158:     VecAXPY(th->vec_lte_work,-4,X1);
    159:     VecAXPY(th->vec_lte_work,+2,X0);
    160:   }

    162:  finally:
    163:   /* Revert TSAlpha to the initial state (t0,X0) */
    164:   if (initok) *initok = stageok;
    165:   TSSetTimeStep(ts,time_step);
    166:   TSAlphaSetParams(ts,alpha_m,alpha_f,gamma);
    167:   VecCopy(ts->vec_sol,th->X0);

    169:   VecDestroy(&X1);
    170:   return(0);
    171: }

    175: static PetscErrorCode TSStep_Alpha(TS ts)
    176: {
    177:   TS_Alpha       *th = (TS_Alpha*)ts->data;
    178:   PetscInt       rejections = 0;
    179:   PetscBool      stageok,accept = PETSC_TRUE;
    180:   PetscReal      next_time_step = ts->time_step;

    184:   PetscCitationsRegister(citation,&cited);

    186:   if (!ts->steprollback) {
    187:     if (th->adapt) { VecCopy(th->X0,th->vec_sol_prev); }
    188:     VecCopy(ts->vec_sol,th->X0);
    189:     VecCopy(th->V1,th->V0);
    190:   }

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

    195:     if (ts->steprestart) {
    196:       TSAlpha_Restart(ts,&stageok);
    197:       if (!stageok) goto reject_step;
    198:     }

    200:     TSAlpha_StageTime(ts);
    201:     VecCopy(th->X0,th->X1);
    202:     TSPreStage(ts,th->stage_time);
    203:     TS_SNESSolve(ts,NULL,th->X1);
    204:     TSPostStage(ts,th->stage_time,0,&th->Xa);
    205:     TSAdaptCheckStage(ts->adapt,ts,th->stage_time,th->Xa,&stageok);
    206:     if (!stageok) goto reject_step;

    208:     th->status = TS_STEP_PENDING;
    209:     VecCopy(th->X1,ts->vec_sol);
    210:     TSAdaptChoose(ts->adapt,ts,ts->time_step,NULL,&next_time_step,&accept);
    211:     th->status = accept ? TS_STEP_COMPLETE : TS_STEP_INCOMPLETE;
    212:     if (!accept) {
    213:       VecCopy(th->X0,ts->vec_sol);
    214:       ts->time_step = next_time_step;
    215:       goto reject_step;
    216:     }

    218:     ts->ptime += ts->time_step;
    219:     ts->time_step = next_time_step;
    220:     break;

    222:   reject_step:
    223:     ts->reject++; accept = PETSC_FALSE;
    224:     if (!ts->reason && ++rejections > ts->max_reject && ts->max_reject >= 0) {
    225:       ts->reason = TS_DIVERGED_STEP_REJECTED;
    226:       PetscInfo2(ts,"Step=%D, step rejections %D greater than current TS allowed, stopping solve\n",ts->steps,rejections);
    227:     }

    229:   }
    230:   return(0);
    231: }

    235: static PetscErrorCode TSEvaluateWLTE_Alpha(TS ts,NormType wnormtype,PetscInt *order,PetscReal *wlte)
    236: {
    237:   TS_Alpha       *th = (TS_Alpha*)ts->data;
    238:   Vec            X = th->X1;           /* X = solution */
    239:   Vec            Y = th->vec_lte_work; /* Y = X + LTE  */

    243:   if (ts->steprestart) {
    244:     /* th->vec_lte_work is set to the LTE in TSAlpha_Restart() */
    245:     VecAXPY(Y,1,X);
    246:   } else {
    247:     /* Compute LTE using backward differences with non-constant time step */
    248:     PetscReal   h = ts->time_step, h_prev = ts->ptime - ts->ptime_prev;
    249:     PetscReal   a = 1 + h_prev/h;
    250:     PetscScalar scal[3]; Vec vecs[3];
    251:     scal[0] = +1/a;   scal[1] = -1/(a-1); scal[2] = +1/(a*(a-1));
    252:     vecs[0] = th->X1; vecs[1] = th->X0;   vecs[2] = th->vec_sol_prev;
    253:     VecCopy(X,Y);
    254:     VecMAXPY(Y,3,scal,vecs);
    255:   }
    256:   TSErrorWeightedNorm(ts,X,Y,wnormtype,wlte);
    257:   if (order) *order = 2;
    258:   return(0);
    259: }

    263: static PetscErrorCode TSRollBack_Alpha(TS ts)
    264: {
    265:   TS_Alpha       *th = (TS_Alpha*)ts->data;

    269:   VecCopy(th->X0,ts->vec_sol);
    270:   return(0);
    271: }

    275: static PetscErrorCode TSInterpolate_Alpha(TS ts,PetscReal t,Vec X)
    276: {
    277:   TS_Alpha       *th = (TS_Alpha*)ts->data;
    278:   PetscReal      dt  = t - ts->ptime;

    282:   VecCopy(ts->vec_sol,X);
    283:   VecAXPY(X,th->Gamma*dt,th->V1);
    284:   VecAXPY(X,(1-th->Gamma)*dt,th->V0);
    285:   return(0);
    286: }

    290: static PetscErrorCode SNESTSFormFunction_Alpha(PETSC_UNUSED SNES snes,Vec X,Vec F,TS ts)
    291: {
    292:   TS_Alpha       *th = (TS_Alpha*)ts->data;
    293:   PetscReal      ta = th->stage_time;
    294:   Vec            Xa = th->Xa, Va = th->Va;

    298:   TSAlpha_StageVecs(ts,X);
    299:   /* F = Function(ta,Xa,Va) */
    300:   TSComputeIFunction(ts,ta,Xa,Va,F,PETSC_FALSE);
    301:   VecScale(F,th->scale_F);
    302:   return(0);
    303: }

    307: static PetscErrorCode SNESTSFormJacobian_Alpha(PETSC_UNUSED SNES snes,PETSC_UNUSED Vec X,Mat J,Mat P,TS ts)
    308: {
    309:   TS_Alpha       *th = (TS_Alpha*)ts->data;
    310:   PetscReal      ta = th->stage_time;
    311:   Vec            Xa = th->Xa, Va = th->Va;
    312:   PetscReal      dVdX = th->shift_V;

    316:   /* J,P = Jacobian(ta,Xa,Va) */
    317:   TSComputeIJacobian(ts,ta,Xa,Va,dVdX,J,P,PETSC_FALSE);
    318:   return(0);
    319: }

    323: static PetscErrorCode TSReset_Alpha(TS ts)
    324: {
    325:   TS_Alpha       *th = (TS_Alpha*)ts->data;

    329:   VecDestroy(&th->X0);
    330:   VecDestroy(&th->Xa);
    331:   VecDestroy(&th->X1);
    332:   VecDestroy(&th->V0);
    333:   VecDestroy(&th->Va);
    334:   VecDestroy(&th->V1);
    335:   VecDestroy(&th->vec_sol_prev);
    336:   VecDestroy(&th->vec_lte_work);
    337:   return(0);
    338: }

    342: static PetscErrorCode TSDestroy_Alpha(TS ts)
    343: {

    347:   TSReset_Alpha(ts);
    348:   PetscFree(ts->data);

    350:   PetscObjectComposeFunction((PetscObject)ts,"TSAlphaUseAdapt_C",NULL);
    351:   PetscObjectComposeFunction((PetscObject)ts,"TSAlphaSetRadius_C",NULL);
    352:   PetscObjectComposeFunction((PetscObject)ts,"TSAlphaSetParams_C",NULL);
    353:   PetscObjectComposeFunction((PetscObject)ts,"TSAlphaGetParams_C",NULL);
    354:   return(0);
    355: }

    359: static PetscErrorCode TSSetUp_Alpha(TS ts)
    360: {
    361:   TS_Alpha       *th = (TS_Alpha*)ts->data;

    365:   VecDuplicate(ts->vec_sol,&th->X0);
    366:   VecDuplicate(ts->vec_sol,&th->Xa);
    367:   VecDuplicate(ts->vec_sol,&th->X1);
    368:   VecDuplicate(ts->vec_sol,&th->V0);
    369:   VecDuplicate(ts->vec_sol,&th->Va);
    370:   VecDuplicate(ts->vec_sol,&th->V1);

    372:   TSGetAdapt(ts,&ts->adapt);
    373:   TSAdaptCandidatesClear(ts->adapt);
    374:   if (!th->adapt) {
    375:     TSAdaptSetType(ts->adapt,TSADAPTNONE);
    376:   } else {
    377:     VecDuplicate(ts->vec_sol,&th->vec_sol_prev);
    378:     VecDuplicate(ts->vec_sol,&th->vec_lte_work);
    379:     if (ts->exact_final_time == TS_EXACTFINALTIME_UNSPECIFIED)
    380:       ts->exact_final_time = TS_EXACTFINALTIME_MATCHSTEP;
    381:   }

    383:   TSGetSNES(ts,&ts->snes);
    384:   return(0);
    385: }

    389: static PetscErrorCode TSSetFromOptions_Alpha(PetscOptionItems *PetscOptionsObject,TS ts)
    390: {
    391:   TS_Alpha       *th = (TS_Alpha*)ts->data;

    395:   PetscOptionsHead(PetscOptionsObject,"Generalized-Alpha ODE solver options");
    396:   {
    397:     PetscBool flg;
    398:     PetscReal radius = 1;
    399:     PetscBool adapt  = th->adapt;
    400:     PetscOptionsReal("-ts_alpha_radius","Spectral radius (high-frequency dissipation)","TSAlphaSetRadius",radius,&radius,&flg);
    401:     if (flg) {TSAlphaSetRadius(ts,radius);}
    402:     PetscOptionsReal("-ts_alpha_alpha_m","Algoritmic parameter alpha_m","TSAlphaSetParams",th->Alpha_m,&th->Alpha_m,NULL);
    403:     PetscOptionsReal("-ts_alpha_alpha_f","Algoritmic parameter alpha_f","TSAlphaSetParams",th->Alpha_f,&th->Alpha_f,NULL);
    404:     PetscOptionsReal("-ts_alpha_gamma","Algoritmic parameter gamma","TSAlphaSetParams",th->Gamma,&th->Gamma,NULL);
    405:     TSAlphaSetParams(ts,th->Alpha_m,th->Alpha_f,th->Gamma);
    406:     PetscOptionsBool("-ts_alpha_adapt","Use time-step adaptivity with the Alpha method","TSAlpha2UseAdapt",adapt,&adapt,&flg);
    407:     if (flg) {TSAlphaUseAdapt(ts,adapt);}
    408:   }
    409:   PetscOptionsTail();
    410:   return(0);
    411: }

    415: static PetscErrorCode TSView_Alpha(TS ts,PetscViewer viewer)
    416: {
    417:   TS_Alpha       *th = (TS_Alpha*)ts->data;
    418:   PetscBool      iascii;

    422:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);
    423:   if (iascii) {
    424:     PetscViewerASCIIPrintf(viewer,"  Alpha_m=%g, Alpha_f=%g, Gamma=%g\n",(double)th->Alpha_m,(double)th->Alpha_f,(double)th->Gamma);
    425:   }
    426:   if (ts->adapt) {TSAdaptView(ts->adapt,viewer);}
    427:   if (ts->snes)  {SNESView(ts->snes,viewer);}
    428:   return(0);
    429: }

    433: static PetscErrorCode TSAlphaUseAdapt_Alpha(TS ts,PetscBool use)
    434: {
    435:   TS_Alpha *th = (TS_Alpha*)ts->data;

    438:   if (use == th->adapt) return(0);
    439:   if (ts->setupcalled) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_ORDER,"Cannot change adaptivity after TSSetUp()");
    440:   th->adapt = use;
    441:   return(0);
    442: }

    446: static PetscErrorCode TSAlphaSetRadius_Alpha(TS ts,PetscReal radius)
    447: {
    448:   PetscReal      alpha_m,alpha_f,gamma;

    452:   if (radius < 0 || radius > 1) SETERRQ1(PetscObjectComm((PetscObject)ts),PETSC_ERR_ARG_OUTOFRANGE,"Radius %g not in range [0,1]",(double)radius);
    453:   alpha_m = (PetscReal)0.5*(3-radius)/(1+radius);
    454:   alpha_f = 1/(1+radius);
    455:   gamma   = (PetscReal)0.5 + alpha_m - alpha_f;
    456:   TSAlphaSetParams(ts,alpha_m,alpha_f,gamma);
    457:   return(0);
    458: }

    462: static PetscErrorCode TSAlphaSetParams_Alpha(TS ts,PetscReal alpha_m,PetscReal alpha_f,PetscReal gamma)
    463: {
    464:   TS_Alpha  *th = (TS_Alpha*)ts->data;
    465:   PetscReal tol = 100*PETSC_MACHINE_EPSILON;
    466:   PetscReal res = ((PetscReal)0.5 + alpha_m - alpha_f) - gamma;

    469:   th->Alpha_m = alpha_m;
    470:   th->Alpha_f = alpha_f;
    471:   th->Gamma   = gamma;
    472:   th->order   = (PetscAbsReal(res) < tol) ? 2 : 1;
    473:   return(0);
    474: }

    478: static PetscErrorCode TSAlphaGetParams_Alpha(TS ts,PetscReal *alpha_m,PetscReal *alpha_f,PetscReal *gamma)
    479: {
    480:   TS_Alpha *th = (TS_Alpha*)ts->data;

    483:   if (alpha_m) *alpha_m = th->Alpha_m;
    484:   if (alpha_f) *alpha_f = th->Alpha_f;
    485:   if (gamma)   *gamma   = th->Gamma;
    486:   return(0);
    487: }

    489: /*MC
    490:       TSALPHA - ODE/DAE solver using the implicit Generalized-Alpha method
    491:                 for first-order systems

    493:   Level: beginner

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

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

    506: .seealso:  TS, TSCreate(), TSSetType(), TSAlphaSetRadius(), TSAlphaSetParams()
    507: M*/
    510: PETSC_EXTERN PetscErrorCode TSCreate_Alpha(TS ts)
    511: {
    512:   TS_Alpha       *th;

    516:   ts->ops->reset          = TSReset_Alpha;
    517:   ts->ops->destroy        = TSDestroy_Alpha;
    518:   ts->ops->view           = TSView_Alpha;
    519:   ts->ops->setup          = TSSetUp_Alpha;
    520:   ts->ops->setfromoptions = TSSetFromOptions_Alpha;
    521:   ts->ops->step           = TSStep_Alpha;
    522:   ts->ops->evaluatewlte   = TSEvaluateWLTE_Alpha;
    523:   ts->ops->rollback       = TSRollBack_Alpha;
    524:   ts->ops->interpolate    = TSInterpolate_Alpha;
    525:   ts->ops->snesfunction   = SNESTSFormFunction_Alpha;
    526:   ts->ops->snesjacobian   = SNESTSFormJacobian_Alpha;

    528:   PetscNewLog(ts,&th);
    529:   ts->data = (void*)th;

    531:   th->Alpha_m = 0.5;
    532:   th->Alpha_f = 0.5;
    533:   th->Gamma   = 0.5;
    534:   th->order   = 2;

    536:   th->adapt = PETSC_FALSE;

    538:   PetscObjectComposeFunction((PetscObject)ts,"TSAlphaUseAdapt_C",TSAlphaUseAdapt_Alpha);
    539:   PetscObjectComposeFunction((PetscObject)ts,"TSAlphaSetRadius_C",TSAlphaSetRadius_Alpha);
    540:   PetscObjectComposeFunction((PetscObject)ts,"TSAlphaSetParams_C",TSAlphaSetParams_Alpha);
    541:   PetscObjectComposeFunction((PetscObject)ts,"TSAlphaGetParams_C",TSAlphaGetParams_Alpha);
    542:   return(0);
    543: }

    547: /*@
    548:   TSAlphaUseAdapt - Use time-step adaptivity with the Alpha method

    550:   Logically Collective on TS

    552:   Input Parameter:
    553: +  ts - timestepping context
    554: -  use - flag to use adaptivity

    556:   Options Database:
    557: .  -ts_alpha_adapt

    559:   Level: intermediate

    561: .seealso: TSAdapt, TSADAPTBASIC
    562: @*/
    563: PetscErrorCode TSAlphaUseAdapt(TS ts,PetscBool use)
    564: {

    570:   PetscTryMethod(ts,"TSAlphaUseAdapt_C",(TS,PetscBool),(ts,use));
    571:   return(0);
    572: }

    576: /*@
    577:   TSAlphaSetRadius - sets the desired spectral radius of the method
    578:                      (i.e. high-frequency numerical damping)

    580:   Logically Collective on TS

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

    589:   Input Parameter:
    590: +  ts - timestepping context
    591: -  radius - the desired spectral radius

    593:   Options Database:
    594: .  -ts_alpha_radius <radius>

    596:   Level: intermediate

    598: .seealso: TSAlphaSetParams(), TSAlphaGetParams()
    599: @*/
    600: PetscErrorCode TSAlphaSetRadius(TS ts,PetscReal radius)
    601: {

    607:   if (radius < 0 || radius > 1) SETERRQ1(((PetscObject)ts)->comm,PETSC_ERR_ARG_OUTOFRANGE,"Radius %g not in range [0,1]",(double)radius);
    608:   PetscTryMethod(ts,"TSAlphaSetRadius_C",(TS,PetscReal),(ts,radius));
    609:   return(0);
    610: }

    614: /*@
    615:   TSAlphaSetParams - sets the algorithmic parameters for TSALPHA

    617:   Logically Collective on TS

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

    622:   Unconditional stability requires:
    623:     \alpha_m >= \alpha_f >= 0.5

    625:   Backward Euler method is recovered with:
    626:     \alpha_m = \alpha_f = gamma = 1

    628:   Input Parameter:
    629: +  ts - timestepping context
    630: .  \alpha_m - algorithmic paramenter
    631: .  \alpha_f - algorithmic paramenter
    632: -  \gamma   - algorithmic paramenter

    634:    Options Database:
    635: +  -ts_alpha_alpha_m <alpha_m>
    636: .  -ts_alpha_alpha_f <alpha_f>
    637: -  -ts_alpha_gamma   <gamma>

    639:   Note:
    640:   Use of this function is normally only required to hack TSALPHA to
    641:   use a modified integration scheme. Users should call
    642:   TSAlphaSetRadius() to set the desired spectral radius of the methods
    643:   (i.e. high-frequency damping) in order so select optimal values for
    644:   these parameters.

    646:   Level: advanced

    648: .seealso: TSAlphaSetRadius(), TSAlphaGetParams()
    649: @*/
    650: PetscErrorCode TSAlphaSetParams(TS ts,PetscReal alpha_m,PetscReal alpha_f,PetscReal gamma)
    651: {

    659:   PetscTryMethod(ts,"TSAlphaSetParams_C",(TS,PetscReal,PetscReal,PetscReal),(ts,alpha_m,alpha_f,gamma));
    660:   return(0);
    661: }

    665: /*@
    666:   TSAlphaGetParams - gets the algorithmic parameters for TSALPHA

    668:   Not Collective

    670:   Input Parameter:
    671: .  ts - timestepping context

    673:   Output Parameters:
    674: +  \alpha_m - algorithmic parameter
    675: .  \alpha_f - algorithmic parameter
    676: -  \gamma   - algorithmic parameter

    678:   Note:
    679:   Use of this function is normally only required to hack TSALPHA to
    680:   use a modified integration scheme. Users should call
    681:   TSAlphaSetRadius() to set the high-frequency damping (i.e. spectral
    682:   radius of the method) in order so select optimal values for these
    683:   parameters.

    685:   Level: advanced

    687: .seealso: TSAlphaSetRadius(), TSAlphaSetParams()
    688: @*/
    689: PetscErrorCode TSAlphaGetParams(TS ts,PetscReal *alpha_m,PetscReal *alpha_f,PetscReal *gamma)
    690: {

    698:   PetscUseMethod(ts,"TSAlphaGetParams_C",(TS,PetscReal*,PetscReal*,PetscReal*),(ts,alpha_m,alpha_f,gamma));
    699:   return(0);
    700: }