Actual source code: alpha2.c
petsc-3.7.1 2016-05-15
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      1: /*
      2:   Code for timestepping with implicit generalized-\alpha method
      3:   for second 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{Chung1993,\n"
     10:   "  title   = {A Time Integration Algorithm for Structural Dynamics with Improved Numerical Dissipation: The Generalized-$\\alpha$ Method},\n"
     11:   "  author  = {J. Chung, G. M. Hubert},\n"
     12:   "  journal = {ASME Journal of Applied Mechanics},\n"
     13:   "  volume  = {60},\n"
     14:   "  number  = {2},\n"
     15:   "  pages   = {371--375},\n"
     16:   "  year    = {1993},\n"
     17:   "  issn    = {0021-8936},\n"
     18:   "  doi     = {http://dx.doi.org/10.1115/1.2900803}\n}\n";

     20: typedef struct {
     21:   PetscReal stage_time;
     22:   PetscReal shift_V;
     23:   PetscReal shift_A;
     24:   PetscReal scale_F;
     25:   Vec       X0,Xa,X1;
     26:   Vec       V0,Va,V1;
     27:   Vec       A0,Aa,A1;

     29:   Vec       vec_dot;

     31:   PetscReal Alpha_m;
     32:   PetscReal Alpha_f;
     33:   PetscReal Gamma;
     34:   PetscReal Beta;
     35:   PetscInt  order;

     37:   PetscBool adapt;
     38:   Vec       vec_sol_prev;
     39:   Vec       vec_dot_prev;
     40:   Vec       vec_lte_work[2];

     42:   TSStepStatus status;
     43: } TS_Alpha;

     47: static PetscErrorCode TSAlpha_StageTime(TS ts)
     48: {
     49:   TS_Alpha  *th = (TS_Alpha*)ts->data;
     50:   PetscReal t  = ts->ptime;
     51:   PetscReal dt = ts->time_step;
     52:   PetscReal Alpha_m = th->Alpha_m;
     53:   PetscReal Alpha_f = th->Alpha_f;
     54:   PetscReal Gamma   = th->Gamma;
     55:   PetscReal Beta    = th->Beta;

     58:   th->stage_time = t + Alpha_f*dt;
     59:   th->shift_V = Gamma/(dt*Beta);
     60:   th->shift_A = Alpha_m/(Alpha_f*dt*dt*Beta);
     61:   th->scale_F = 1/Alpha_f;
     62:   return(0);
     63: }

     67: static PetscErrorCode TSAlpha_StageVecs(TS ts,Vec X)
     68: {
     69:   TS_Alpha       *th = (TS_Alpha*)ts->data;
     70:   Vec            X1 = X,      V1 = th->V1, A1 = th->A1;
     71:   Vec            Xa = th->Xa, Va = th->Va, Aa = th->Aa;
     72:   Vec            X0 = th->X0, V0 = th->V0, A0 = th->A0;
     73:   PetscReal      dt = ts->time_step;
     74:   PetscReal      Alpha_m = th->Alpha_m;
     75:   PetscReal      Alpha_f = th->Alpha_f;
     76:   PetscReal      Gamma   = th->Gamma;
     77:   PetscReal      Beta    = th->Beta;

     81:   /* A1 = ... */
     82:   VecWAXPY(A1,-1.0,X0,X1);
     83:   VecAXPY (A1,-dt,V0);
     84:   VecAXPBY(A1,-(1-2*Beta)/(2*Beta),1/(dt*dt*Beta),A0);
     85:   /* V1 = ... */
     86:   VecWAXPY(V1,(1.0-Gamma)/Gamma,A0,A1);
     87:   VecAYPX (V1,dt*Gamma,V0);
     88:   /* Xa = X0 + Alpha_f*(X1-X0) */
     89:   VecWAXPY(Xa,-1.0,X0,X1);
     90:   VecAYPX (Xa,Alpha_f,X0);
     91:   /* Va = V0 + Alpha_f*(V1-V0) */
     92:   VecWAXPY(Va,-1.0,V0,V1);
     93:   VecAYPX (Va,Alpha_f,V0);
     94:   /* Aa = A0 + Alpha_m*(A1-A0) */
     95:   VecWAXPY(Aa,-1.0,A0,A1);
     96:   VecAYPX (Aa,Alpha_m,A0);
     97:   return(0);
     98: }

    102: static PetscErrorCode TS_SNESSolve(TS ts,Vec b,Vec x)
    103: {
    104:   PetscInt       nits,lits;

    108:   SNESSolve(ts->snes,b,x);
    109:   SNESGetIterationNumber(ts->snes,&nits);
    110:   SNESGetLinearSolveIterations(ts->snes,&lits);
    111:   ts->snes_its += nits; ts->ksp_its += lits;
    112:   return(0);
    113: }

    115: /*
    116:   Compute a consistent initial state for the generalized-alpha method.
    117:   - Solve two successive backward Euler steps with halved time step.
    118:   - Compute the initial second time derivative using backward differences.
    119:   - If using adaptivity, estimate the LTE of the initial step.
    120: */
    123: static PetscErrorCode TSAlpha_Restart(TS ts,PetscBool *initok)
    124: {
    125:   TS_Alpha       *th = (TS_Alpha*)ts->data;
    126:   PetscReal      time_step;
    127:   PetscReal      alpha_m,alpha_f,gamma,beta;
    128:   Vec            X0 = ts->vec_sol, X1, X2 = th->X1;
    129:   Vec            V0 = ts->vec_dot, V1, V2 = th->V1;
    130:   PetscBool      stageok;

    134:   VecDuplicate(X0,&X1);
    135:   VecDuplicate(V0,&V1);

    137:   /* Setup backward Euler with halved time step */
    138:   TSAlpha2GetParams(ts,&alpha_m,&alpha_f,&gamma,&beta);
    139:   TSAlpha2SetParams(ts,1,1,1,0.5);
    140:   TSGetTimeStep(ts,&time_step);
    141:   ts->time_step = time_step/2;
    142:   TSAlpha_StageTime(ts);
    143:   th->stage_time = ts->ptime;
    144:   VecZeroEntries(th->A0);

    146:   /* First BE step, (t0,X0,V0) -> (t1,X1,V1) */
    147:   th->stage_time += ts->time_step;
    148:   VecCopy(X0,th->X0);
    149:   VecCopy(V0,th->V0);
    150:   TSPreStage(ts,th->stage_time);
    151:   VecCopy(th->X0,X1);
    152:   TS_SNESSolve(ts,NULL,X1);
    153:   VecCopy(th->V1,V1);
    154:   TSPostStage(ts,th->stage_time,0,&X1);
    155:   TSAdaptCheckStage(ts->adapt,ts,th->stage_time,X1,&stageok);
    156:   if (!stageok) goto finally;

    158:   /* Second BE step, (t1,X1,V1) -> (t2,X2,V2) */
    159:   th->stage_time += ts->time_step;
    160:   VecCopy(X1,th->X0);
    161:   VecCopy(V1,th->V0);
    162:   TSPreStage(ts,th->stage_time);
    163:   VecCopy(th->X0,X2);
    164:   TS_SNESSolve(ts,NULL,X2);
    165:   VecCopy(th->V1,V2);
    166:   TSPostStage(ts,th->stage_time,0,&X2);
    167:   TSAdaptCheckStage(ts->adapt,ts,th->stage_time,X1,&stageok);
    168:   if (!stageok) goto finally;

    170:   /* Compute A0 ~ dV/dt at t0 with backward differences */
    171:   VecZeroEntries(th->A0);
    172:   VecAXPY(th->A0,-3/ts->time_step,V0);
    173:   VecAXPY(th->A0,+4/ts->time_step,V1);
    174:   VecAXPY(th->A0,-1/ts->time_step,V2);

    176:   /* Rough, lower-order estimate LTE of the initial step */
    177:   if (th->adapt) {
    178:     VecZeroEntries(th->vec_lte_work[0]);
    179:     VecAXPY(th->vec_lte_work[0],+2,X2);
    180:     VecAXPY(th->vec_lte_work[0],-4,X1);
    181:     VecAXPY(th->vec_lte_work[0],+2,X0);
    182:   }
    183:   if (th->adapt) {
    184:     VecZeroEntries(th->vec_lte_work[1]);
    185:     VecAXPY(th->vec_lte_work[1],+2,V2);
    186:     VecAXPY(th->vec_lte_work[1],-4,V1);
    187:     VecAXPY(th->vec_lte_work[1],+2,V0);
    188:   }

    190:  finally:
    191:   /* Revert TSAlpha to the initial state (t0,X0,V0) */
    192:   if (initok) *initok = stageok;
    193:   TSSetTimeStep(ts,time_step);
    194:   TSAlpha2SetParams(ts,alpha_m,alpha_f,gamma,beta);
    195:   VecCopy(ts->vec_sol,th->X0);
    196:   VecCopy(ts->vec_dot,th->V0);

    198:   VecDestroy(&X1);
    199:   VecDestroy(&V1);
    200:   return(0);
    201: }

    205: static PetscErrorCode TSStep_Alpha(TS ts)
    206: {
    207:   TS_Alpha       *th = (TS_Alpha*)ts->data;
    208:   PetscInt       rejections = 0;
    209:   PetscBool      stageok,accept = PETSC_TRUE;
    210:   PetscReal      next_time_step = ts->time_step;

    214:   PetscCitationsRegister(citation,&cited);

    216:   if (!ts->steprollback) {
    217:     if (th->adapt) { VecCopy(th->X0,th->vec_sol_prev); }
    218:     if (th->adapt) { VecCopy(th->V0,th->vec_dot_prev); }
    219:     VecCopy(ts->vec_sol,th->X0);
    220:     VecCopy(ts->vec_dot,th->V0);
    221:     VecCopy(th->A1,th->A0);
    222:   }

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

    227:     if (ts->steprestart) {
    228:       TSAlpha_Restart(ts,&stageok);
    229:       if (!stageok) goto reject_step;
    230:     }

    232:     TSAlpha_StageTime(ts);
    233:     VecCopy(th->X0,th->X1);
    234:     TSPreStage(ts,th->stage_time);
    235:     TS_SNESSolve(ts,NULL,th->X1);
    236:     TSPostStage(ts,th->stage_time,0,&th->Xa);
    237:     TSAdaptCheckStage(ts->adapt,ts,th->stage_time,th->Xa,&stageok);
    238:     if (!stageok) goto reject_step;

    240:     th->status = TS_STEP_PENDING;
    241:     VecCopy(th->X1,ts->vec_sol);
    242:     VecCopy(th->V1,ts->vec_dot);
    243:     TSAdaptChoose(ts->adapt,ts,ts->time_step,NULL,&next_time_step,&accept);
    244:     th->status = accept ? TS_STEP_COMPLETE : TS_STEP_INCOMPLETE;
    245:     if (!accept) {
    246:       VecCopy(th->X0,ts->vec_sol);
    247:       VecCopy(th->V0,ts->vec_dot);
    248:       ts->time_step = next_time_step;
    249:       goto reject_step;
    250:     }

    252:     ts->ptime += ts->time_step;
    253:     ts->time_step = next_time_step;
    254:     break;

    256:   reject_step:
    257:     ts->reject++; accept = PETSC_FALSE;
    258:     if (!ts->reason && ++rejections > ts->max_reject && ts->max_reject >= 0) {
    259:       ts->reason = TS_DIVERGED_STEP_REJECTED;
    260:       PetscInfo2(ts,"Step=%D, step rejections %D greater than current TS allowed, stopping solve\n",ts->steps,rejections);
    261:     }

    263:   }
    264:   return(0);
    265: }

    269: static PetscErrorCode TSEvaluateWLTE_Alpha(TS ts,NormType wnormtype,PetscInt *order,PetscReal *wlte)
    270: {
    271:   TS_Alpha       *th = (TS_Alpha*)ts->data;
    272:   Vec            X = th->X1;              /* X = solution */
    273:   Vec            V = th->V1;              /* V = solution */
    274:   Vec            Y = th->vec_lte_work[0]; /* Y = X + LTE  */
    275:   Vec            Z = th->vec_lte_work[1]; /* Z = V + LTE  */
    276:   PetscReal      enormX,enormV;

    280:   if (ts->steprestart) {
    281:     /* th->vec_{sol|dot}_prev is set to the LTE in TSAlpha_Restart() */
    282:     VecAXPY(Y,1,X);
    283:     VecAXPY(Z,1,V);
    284:   } else {
    285:     /* Compute LTE using backward differences with non-constant time step */
    286:     PetscReal   h = ts->time_step, h_prev = ts->ptime - ts->ptime_prev;
    287:     PetscReal   a = 1 + h_prev/h;
    288:     PetscScalar scal[3]; Vec vecX[3],vecV[3];
    289:     scal[0] = +1/a;   scal[1] = -1/(a-1); scal[2] = +1/(a*(a-1));
    290:     vecX[0] = th->X1; vecX[1] = th->X0;   vecX[2] = th->vec_sol_prev;
    291:     vecV[0] = th->V1; vecV[1] = th->V0;   vecV[2] = th->vec_dot_prev;
    292:     VecCopy(X,Y);
    293:     VecMAXPY(Y,3,scal,vecX);
    294:     VecCopy(V,Z);
    295:     VecMAXPY(Z,3,scal,vecV);
    296:   }
    297:   /* XXX ts->atol and ts->vatol are not appropriate for computing enormV */
    298:   TSErrorWeightedNorm(ts,X,Y,wnormtype,&enormX);
    299:   TSErrorWeightedNorm(ts,V,Z,wnormtype,&enormV);
    300:   if (wnormtype == NORM_2)
    301:     *wlte = PetscSqrtReal(PetscSqr(enormX)/2 + PetscSqr(enormV)/2);
    302:   else
    303:     *wlte = PetscMax(enormX,enormV);
    304:   if (order) *order = 2;
    305:   return(0);
    306: }

    310: static PetscErrorCode TSRollBack_Alpha(TS ts)
    311: {
    312:   TS_Alpha       *th = (TS_Alpha*)ts->data;

    316:   VecCopy(th->X0,ts->vec_sol);
    317:   VecCopy(th->V0,ts->vec_dot);
    318:   return(0);
    319: }

    321: /*
    324: static PetscErrorCode TSInterpolate_Alpha(TS ts,PetscReal t,Vec X,Vec V)
    325: {
    326:   TS_Alpha       *th = (TS_Alpha*)ts->data;
    327:   PetscReal      dt  = t - ts->ptime;

    331:   VecCopy(ts->vec_dot,V);
    332:   VecAXPY(V,dt*(1-th->Gamma),th->A0);
    333:   VecAXPY(V,dt*th->Gamma,th->A1);
    334:   VecCopy(ts->vec_sol,X);
    335:   VecAXPY(X,dt,V);
    336:   VecAXPY(X,dt*dt*((PetscReal)0.5-th->Beta),th->A0);
    337:   VecAXPY(X,dt*dt*th->Beta,th->A1);
    338:   return(0);
    339: }
    340: */

    344: static PetscErrorCode SNESTSFormFunction_Alpha(PETSC_UNUSED SNES snes,Vec X,Vec F,TS ts)
    345: {
    346:   TS_Alpha       *th = (TS_Alpha*)ts->data;
    347:   PetscReal      ta = th->stage_time;
    348:   Vec            Xa = th->Xa, Va = th->Va, Aa = th->Aa;

    352:   TSAlpha_StageVecs(ts,X);
    353:   /* F = Function(ta,Xa,Va,Aa) */
    354:   TSComputeI2Function(ts,ta,Xa,Va,Aa,F);
    355:   VecScale(F,th->scale_F);
    356:   return(0);
    357: }

    361: static PetscErrorCode SNESTSFormJacobian_Alpha(PETSC_UNUSED SNES snes,PETSC_UNUSED Vec X,Mat J,Mat P,TS ts)
    362: {
    363:   TS_Alpha       *th = (TS_Alpha*)ts->data;
    364:   PetscReal      ta = th->stage_time;
    365:   Vec            Xa = th->Xa, Va = th->Va, Aa = th->Aa;
    366:   PetscReal      dVdX = th->shift_V, dAdX = th->shift_A;

    370:   /* J,P = Jacobian(ta,Xa,Va,Aa) */
    371:   TSComputeI2Jacobian(ts,ta,Xa,Va,Aa,dVdX,dAdX,J,P);
    372:   return(0);
    373: }

    377: static PetscErrorCode TSReset_Alpha(TS ts)
    378: {
    379:   TS_Alpha       *th = (TS_Alpha*)ts->data;

    383:   VecDestroy(&th->X0);
    384:   VecDestroy(&th->Xa);
    385:   VecDestroy(&th->X1);
    386:   VecDestroy(&th->V0);
    387:   VecDestroy(&th->Va);
    388:   VecDestroy(&th->V1);
    389:   VecDestroy(&th->A0);
    390:   VecDestroy(&th->Aa);
    391:   VecDestroy(&th->A1);
    392:   VecDestroy(&th->vec_sol_prev);
    393:   VecDestroy(&th->vec_dot_prev);
    394:   VecDestroy(&th->vec_lte_work[0]);
    395:   VecDestroy(&th->vec_lte_work[1]);
    396:   return(0);
    397: }

    401: static PetscErrorCode TSDestroy_Alpha(TS ts)
    402: {

    406:   TSReset_Alpha(ts);
    407:   PetscFree(ts->data);

    409:   PetscObjectComposeFunction((PetscObject)ts,"TSAlpha2UseAdapt_C",NULL);
    410:   PetscObjectComposeFunction((PetscObject)ts,"TSAlpha2SetRadius_C",NULL);
    411:   PetscObjectComposeFunction((PetscObject)ts,"TSAlpha2SetParams_C",NULL);
    412:   PetscObjectComposeFunction((PetscObject)ts,"TSAlpha2GetParams_C",NULL);
    413:   return(0);
    414: }

    418: static PetscErrorCode TSSetUp_Alpha(TS ts)
    419: {
    420:   TS_Alpha       *th = (TS_Alpha*)ts->data;

    424:   VecDuplicate(ts->vec_sol,&th->X0);
    425:   VecDuplicate(ts->vec_sol,&th->Xa);
    426:   VecDuplicate(ts->vec_sol,&th->X1);
    427:   VecDuplicate(ts->vec_sol,&th->V0);
    428:   VecDuplicate(ts->vec_sol,&th->Va);
    429:   VecDuplicate(ts->vec_sol,&th->V1);
    430:   VecDuplicate(ts->vec_sol,&th->A0);
    431:   VecDuplicate(ts->vec_sol,&th->Aa);
    432:   VecDuplicate(ts->vec_sol,&th->A1);

    434:   TSGetAdapt(ts,&ts->adapt);
    435:   TSAdaptCandidatesClear(ts->adapt);
    436:   if (!th->adapt) {
    437:     TSAdaptSetType(ts->adapt,TSADAPTNONE);
    438:   } else {
    439:     VecDuplicate(ts->vec_sol,&th->vec_sol_prev);
    440:     VecDuplicate(ts->vec_sol,&th->vec_dot_prev);
    441:     VecDuplicate(ts->vec_sol,&th->vec_lte_work[0]);
    442:     VecDuplicate(ts->vec_sol,&th->vec_lte_work[1]);
    443:     if (ts->exact_final_time == TS_EXACTFINALTIME_UNSPECIFIED)
    444:       ts->exact_final_time = TS_EXACTFINALTIME_MATCHSTEP;
    445:   }

    447:   TSGetSNES(ts,&ts->snes);
    448:   return(0);
    449: }

    453: static PetscErrorCode TSSetFromOptions_Alpha(PetscOptionItems *PetscOptionsObject,TS ts)
    454: {
    455:   TS_Alpha       *th = (TS_Alpha*)ts->data;

    459:   PetscOptionsHead(PetscOptionsObject,"Generalized-Alpha ODE solver options");
    460:   {
    461:     PetscBool flg;
    462:     PetscReal radius = 1;
    463:     PetscBool adapt  = th->adapt;
    464:     PetscOptionsReal("-ts_alpha_radius","Spectral radius (high-frequency dissipation)","TSAlpha2SetRadius",radius,&radius,&flg);
    465:     if (flg) {TSAlpha2SetRadius(ts,radius);}
    466:     PetscOptionsReal("-ts_alpha_alpha_m","Algoritmic parameter alpha_m","TSAlpha2SetParams",th->Alpha_m,&th->Alpha_m,NULL);
    467:     PetscOptionsReal("-ts_alpha_alpha_f","Algoritmic parameter alpha_f","TSAlpha2SetParams",th->Alpha_f,&th->Alpha_f,NULL);
    468:     PetscOptionsReal("-ts_alpha_gamma","Algoritmic parameter gamma","TSAlpha2SetParams",th->Gamma,&th->Gamma,NULL);
    469:     PetscOptionsReal("-ts_alpha_beta","Algoritmic parameter beta","TSAlpha2SetParams",th->Beta,&th->Beta,NULL);
    470:     TSAlpha2SetParams(ts,th->Alpha_m,th->Alpha_f,th->Gamma,th->Beta);
    471:     PetscOptionsBool("-ts_alpha_adapt","Use time-step adaptivity with the Alpha method","TSAlpha2UseAdapt",adapt,&adapt,&flg);
    472:     if (flg) {TSAlpha2UseAdapt(ts,adapt);}
    473:   }
    474:   PetscOptionsTail();
    475:   return(0);
    476: }

    480: static PetscErrorCode TSView_Alpha(TS ts,PetscViewer viewer)
    481: {
    482:   TS_Alpha       *th = (TS_Alpha*)ts->data;
    483:   PetscBool      iascii;

    487:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);
    488:   if (iascii) {
    489:     PetscViewerASCIIPrintf(viewer,"  Alpha_m=%g, Alpha_f=%g, Gamma=%g, Beta=%g\n",(double)th->Alpha_m,(double)th->Alpha_f,(double)th->Gamma,(double)th->Beta);
    490:   }
    491:   if (ts->adapt) {TSAdaptView(ts->adapt,viewer);}
    492:   if (ts->snes)  {SNESView(ts->snes,viewer);}
    493:   return(0);
    494: }

    498: static PetscErrorCode TSAlpha2UseAdapt_Alpha(TS ts,PetscBool use)
    499: {
    500:   TS_Alpha *th = (TS_Alpha*)ts->data;

    503:   if (use == th->adapt) return(0);
    504:   if (ts->setupcalled) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_ORDER,"Cannot change adaptivity after TSSetUp()");
    505:   th->adapt = use;
    506:   return(0);
    507: }

    511: static PetscErrorCode TSAlpha2SetRadius_Alpha(TS ts,PetscReal radius)
    512: {
    513:   PetscReal      alpha_m,alpha_f,gamma,beta;

    517:   if (radius < 0 || radius > 1) SETERRQ1(PetscObjectComm((PetscObject)ts),PETSC_ERR_ARG_OUTOFRANGE,"Radius %g not in range [0,1]",(double)radius);
    518:   alpha_m = (2-radius)/(1+radius);
    519:   alpha_f = 1/(1+radius);
    520:   gamma   = (PetscReal)0.5 + alpha_m - alpha_f;
    521:   beta    = (PetscReal)0.5 * (1 + alpha_m - alpha_f); beta *= beta;
    522:   TSAlpha2SetParams(ts,alpha_m,alpha_f,gamma,beta);
    523:   return(0);
    524: }

    528: static PetscErrorCode TSAlpha2SetParams_Alpha(TS ts,PetscReal alpha_m,PetscReal alpha_f,PetscReal gamma,PetscReal beta)
    529: {
    530:   TS_Alpha  *th = (TS_Alpha*)ts->data;
    531:   PetscReal tol = 100*PETSC_MACHINE_EPSILON;
    532:   PetscReal res = ((PetscReal)0.5 + alpha_m - alpha_f) - gamma;

    535:   th->Alpha_m = alpha_m;
    536:   th->Alpha_f = alpha_f;
    537:   th->Gamma   = gamma;
    538:   th->Beta    = beta;
    539:   th->order   = (PetscAbsReal(res) < tol) ? 2 : 1;
    540:   return(0);
    541: }

    545: static PetscErrorCode TSAlpha2GetParams_Alpha(TS ts,PetscReal *alpha_m,PetscReal *alpha_f,PetscReal *gamma,PetscReal *beta)
    546: {
    547:   TS_Alpha *th = (TS_Alpha*)ts->data;

    550:   if (alpha_m) *alpha_m = th->Alpha_m;
    551:   if (alpha_f) *alpha_f = th->Alpha_f;
    552:   if (gamma)   *gamma   = th->Gamma;
    553:   if (beta)    *beta    = th->Beta;
    554:   return(0);
    555: }

    557: /*MC
    558:       TSALPHA2 - ODE/DAE solver using the implicit Generalized-Alpha method
    559:                  for second-order systems

    561:   Level: beginner

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

    568: .seealso:  TS, TSCreate(), TSSetType(), TSAlpha2SetRadius(), TSAlpha2SetParams()
    569: M*/
    572: PETSC_EXTERN PetscErrorCode TSCreate_Alpha2(TS ts)
    573: {
    574:   TS_Alpha       *th;

    578:   ts->ops->reset          = TSReset_Alpha;
    579:   ts->ops->destroy        = TSDestroy_Alpha;
    580:   ts->ops->view           = TSView_Alpha;
    581:   ts->ops->setup          = TSSetUp_Alpha;
    582:   ts->ops->setfromoptions = TSSetFromOptions_Alpha;
    583:   ts->ops->step           = TSStep_Alpha;
    584:   ts->ops->evaluatewlte   = TSEvaluateWLTE_Alpha;
    585:   ts->ops->rollback       = TSRollBack_Alpha;
    586:   /*ts->ops->interpolate  = TSInterpolate_Alpha;*/
    587:   ts->ops->snesfunction   = SNESTSFormFunction_Alpha;
    588:   ts->ops->snesjacobian   = SNESTSFormJacobian_Alpha;

    590:   PetscNewLog(ts,&th);
    591:   ts->data = (void*)th;

    593:   th->Alpha_m = 0.5;
    594:   th->Alpha_f = 0.5;
    595:   th->Gamma   = 0.5;
    596:   th->Beta    = 0.25;
    597:   th->order   = 2;

    599:   th->adapt = PETSC_FALSE;

    601:   PetscObjectComposeFunction((PetscObject)ts,"TSAlpha2UseAdapt_C",TSAlpha2UseAdapt_Alpha);
    602:   PetscObjectComposeFunction((PetscObject)ts,"TSAlpha2SetRadius_C",TSAlpha2SetRadius_Alpha);
    603:   PetscObjectComposeFunction((PetscObject)ts,"TSAlpha2SetParams_C",TSAlpha2SetParams_Alpha);
    604:   PetscObjectComposeFunction((PetscObject)ts,"TSAlpha2GetParams_C",TSAlpha2GetParams_Alpha);
    605:   return(0);
    606: }

    610: /*@
    611:   TSAlpha2UseAdapt - Use time-step adaptivity with the Alpha method

    613:   Logically Collective on TS

    615:   Input Parameter:
    616: +  ts - timestepping context
    617: -  use - flag to use adaptivity

    619:   Options Database:
    620: .  -ts_alpha_adapt

    622:   Level: intermediate

    624: .seealso: TSAdapt, TSADAPTBASIC
    625: @*/
    626: PetscErrorCode TSAlpha2UseAdapt(TS ts,PetscBool use)
    627: {

    633:   PetscTryMethod(ts,"TSAlpha2UseAdapt_C",(TS,PetscBool),(ts,use));
    634:   return(0);
    635: }

    639: /*@
    640:   TSAlpha2SetRadius - sets the desired spectral radius of the method
    641:                       (i.e. high-frequency numerical damping)

    643:   Logically Collective on TS

    645:   The algorithmic parameters \alpha_m and \alpha_f of the
    646:   generalized-\alpha method can be computed in terms of a specified
    647:   spectral radius \rho in [0,1] for infinite time step in order to
    648:   control high-frequency numerical damping:
    649:     \alpha_m = (2-\rho)/(1+\rho)
    650:     \alpha_f = 1/(1+\rho)

    652:   Input Parameter:
    653: +  ts - timestepping context
    654: -  radius - the desired spectral radius

    656:   Options Database:
    657: .  -ts_alpha_radius <radius>

    659:   Level: intermediate

    661: .seealso: TSAlpha2SetParams(), TSAlpha2GetParams()
    662: @*/
    663: PetscErrorCode TSAlpha2SetRadius(TS ts,PetscReal radius)
    664: {

    670:   if (radius < 0 || radius > 1) SETERRQ1(((PetscObject)ts)->comm,PETSC_ERR_ARG_OUTOFRANGE,"Radius %g not in range [0,1]",(double)radius);
    671:   PetscTryMethod(ts,"TSAlpha2SetRadius_C",(TS,PetscReal),(ts,radius));
    672:   return(0);
    673: }

    677: /*@
    678:   TSAlpha2SetParams - sets the algorithmic parameters for TSALPHA2

    680:   Logically Collective on TS

    682:   Second-order accuracy can be obtained so long as:
    683:     \gamma = 1/2 + alpha_m - alpha_f
    684:     \beta  = 1/4 (1 + alpha_m - alpha_f)^2

    686:   Unconditional stability requires:
    687:     \alpha_m >= \alpha_f >= 1/2

    690:   Input Parameter:
    691: + ts - timestepping context
    692: . \alpha_m - algorithmic paramenter
    693: . \alpha_f - algorithmic paramenter
    694: . \gamma   - algorithmic paramenter
    695: - \beta    - algorithmic paramenter

    697:   Options Database:
    698: + -ts_alpha_alpha_m <alpha_m>
    699: . -ts_alpha_alpha_f <alpha_f>
    700: . -ts_alpha_gamma   <gamma>
    701: - -ts_alpha_beta    <beta>

    703:   Note:
    704:   Use of this function is normally only required to hack TSALPHA2 to
    705:   use a modified integration scheme. Users should call
    706:   TSAlpha2SetRadius() to set the desired spectral radius of the methods
    707:   (i.e. high-frequency damping) in order so select optimal values for
    708:   these parameters.

    710:   Level: advanced

    712: .seealso: TSAlpha2SetRadius(), TSAlpha2GetParams()
    713: @*/
    714: PetscErrorCode TSAlpha2SetParams(TS ts,PetscReal alpha_m,PetscReal alpha_f,PetscReal gamma,PetscReal beta)
    715: {

    724:   PetscTryMethod(ts,"TSAlpha2SetParams_C",(TS,PetscReal,PetscReal,PetscReal,PetscReal),(ts,alpha_m,alpha_f,gamma,beta));
    725:   return(0);
    726: }

    730: /*@
    731:   TSAlpha2GetParams - gets the algorithmic parameters for TSALPHA2

    733:   Not Collective

    735:   Input Parameter:
    736: . ts - timestepping context

    738:   Output Parameters:
    739: + \alpha_m - algorithmic parameter
    740: . \alpha_f - algorithmic parameter
    741: . \gamma   - algorithmic parameter
    742: - \beta    - algorithmic parameter

    744:   Note:
    745:   Use of this function is normally only required to hack TSALPHA2 to
    746:   use a modified integration scheme. Users should call
    747:   TSAlpha2SetRadius() to set the high-frequency damping (i.e. spectral
    748:   radius of the method) in order so select optimal values for these
    749:   parameters.

    751:   Level: advanced

    753: .seealso: TSAlpha2SetRadius(), TSAlpha2SetParams()
    754: @*/
    755: PetscErrorCode TSAlpha2GetParams(TS ts,PetscReal *alpha_m,PetscReal *alpha_f,PetscReal *gamma,PetscReal *beta)
    756: {

    765:   PetscUseMethod(ts,"TSAlpha2GetParams_C",(TS,PetscReal*,PetscReal*,PetscReal*,PetscReal*),(ts,alpha_m,alpha_f,gamma,beta));
    766:   return(0);
    767: }