Actual source code: bdf.c
petsc-3.13.6 2020-09-29
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      1: /*
      2:   Code for timestepping with BDF methods
      3: */
      4:  #include <petsc/private/tsimpl.h>
      5:  #include <petscdm.h>

      7: static PetscBool  cited = PETSC_FALSE;
      8: static const char citation[] =
      9:   "@book{Brenan1995,\n"
     10:   "  title     = {Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations},\n"
     11:   "  author    = {Brenan, K. and Campbell, S. and Petzold, L.},\n"
     12:   "  publisher = {Society for Industrial and Applied Mathematics},\n"
     13:   "  year      = {1995},\n"
     14:   "  doi       = {10.1137/1.9781611971224},\n}\n";

     16: typedef struct {
     17:   PetscInt  k,n;
     18:   PetscReal time[6+2];
     19:   Vec       work[6+2];
     20:   Vec       tvwork[6+2];
     21:   PetscReal shift;
     22:   Vec       vec_dot;            /* Xdot when !transientvar, else Cdot where C(X) is the transient variable. */
     23:   Vec       vec_wrk;
     24:   Vec       vec_lte;

     26:   PetscBool    transientvar;
     27:   PetscInt     order;
     28:   TSStepStatus status;
     29: } TS_BDF;

     32: /* Compute Lagrange polynomials on T[:n] evaluated at t.
     33:  * If one has data (T[i], Y[i]), then the interpolation/extrapolation is f(t) = \sum_i L[i]*Y[i].
     34:  */
     35: PETSC_STATIC_INLINE void LagrangeBasisVals(PetscInt n,PetscReal t,const PetscReal T[],PetscScalar L[])
     36: {
     37:   PetscInt k,j;
     38:   for (k=0; k<n; k++)
     39:     for (L[k]=1, j=0; j<n; j++)
     40:       if (j != k)
     41:         L[k] *= (t - T[j])/(T[k] - T[j]);
     42: }

     44: PETSC_STATIC_INLINE void LagrangeBasisDers(PetscInt n,PetscReal t,const PetscReal T[],PetscScalar dL[])
     45: {
     46:   PetscInt  k,j,i;
     47:   for (k=0; k<n; k++)
     48:     for (dL[k]=0, j=0; j<n; j++)
     49:       if (j != k) {
     50:         PetscReal L = 1/(T[k] - T[j]);
     51:         for (i=0; i<n; i++)
     52:           if (i != j && i != k)
     53:             L *= (t - T[i])/(T[k] - T[i]);
     54:         dL[k] += L;
     55:       }
     56: }

     58: static PetscErrorCode TSBDF_GetVecs(TS ts,DM dm,Vec *Xdot,Vec *Ydot)
     59: {
     60:   TS_BDF         *bdf = (TS_BDF*)ts->data;

     64:   if (dm && dm != ts->dm) {
     65:     DMGetNamedGlobalVector(dm,"TSBDF_Vec_Xdot",Xdot);
     66:     DMGetNamedGlobalVector(dm,"TSBDF_Vec_Ydot",Ydot);
     67:   } else {
     68:     *Xdot = bdf->vec_dot;
     69:     *Ydot = bdf->vec_wrk;
     70:   }
     71:   return(0);
     72: }

     74: static PetscErrorCode TSBDF_RestoreVecs(TS ts,DM dm,Vec *Xdot,Vec *Ydot)
     75: {
     76:   TS_BDF         *bdf = (TS_BDF*)ts->data;

     80:   if (dm && dm != ts->dm) {
     81:     DMRestoreNamedGlobalVector(dm,"TSBDF_Vec_Xdot",Xdot);
     82:     DMRestoreNamedGlobalVector(dm,"TSBDF_Vec_Ydot",Ydot);
     83:   } else {
     84:     if (*Xdot != bdf->vec_dot) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_ARG_INCOMP,"Vec does not match the cache");
     85:     if (*Ydot != bdf->vec_wrk) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_ARG_INCOMP,"Vec does not match the cache");
     86:     *Xdot = NULL;
     87:     *Ydot = NULL;
     88:   }
     89:   return(0);
     90: }

     92: static PetscErrorCode DMCoarsenHook_TSBDF(DM fine,DM coarse,void *ctx)
     93: {
     95:   return(0);
     96: }

     98: static PetscErrorCode DMRestrictHook_TSBDF(DM fine,Mat restrct,Vec rscale,Mat inject,DM coarse,void *ctx)
     99: {
    100:   TS             ts = (TS)ctx;
    101:   Vec            Ydot,Ydot_c;
    102:   Vec            Xdot,Xdot_c;

    106:   TSBDF_GetVecs(ts,fine,&Xdot,&Ydot);
    107:   TSBDF_GetVecs(ts,coarse,&Xdot_c,&Ydot_c);

    109:   MatRestrict(restrct,Ydot,Ydot_c);
    110:   VecPointwiseMult(Ydot_c,rscale,Ydot_c);

    112:   TSBDF_RestoreVecs(ts,fine,&Xdot,&Ydot);
    113:   TSBDF_RestoreVecs(ts,coarse,&Xdot_c,&Ydot_c);
    114:   return(0);
    115: }

    117: static PetscErrorCode TSBDF_Advance(TS ts,PetscReal t,Vec X)
    118: {
    119:   TS_BDF         *bdf = (TS_BDF*)ts->data;
    120:   PetscInt       i,n = (PetscInt)(sizeof(bdf->work)/sizeof(Vec));
    121:   Vec            tail = bdf->work[n-1],tvtail = bdf->tvwork[n-1];

    125:   for (i=n-1; i>=2; i--) {
    126:     bdf->time[i] = bdf->time[i-1];
    127:     bdf->work[i] = bdf->work[i-1];
    128:     bdf->tvwork[i] = bdf->tvwork[i-1];
    129:   }
    130:   bdf->n       = PetscMin(bdf->n+1,n-1);
    131:   bdf->time[1] = t;
    132:   bdf->work[1] = tail;
    133:   bdf->tvwork[1] = tvtail;
    134:   VecCopy(X,tail);
    135:   TSComputeTransientVariable(ts,tail,tvtail);
    136:   return(0);
    137: }

    139: static PetscErrorCode TSBDF_VecLTE(TS ts,PetscInt order,Vec lte)
    140: {
    141:   TS_BDF         *bdf = (TS_BDF*)ts->data;
    142:   PetscInt       i,n = order+1;
    143:   PetscReal      *time = bdf->time;
    144:   Vec            *vecs = bdf->work;
    145:   PetscScalar    a[8],b[8],alpha[8];

    149:   LagrangeBasisDers(n+0,time[0],time,a); a[n] =0;
    150:   LagrangeBasisDers(n+1,time[0],time,b);
    151:   for (i=0; i<n+1; i++) alpha[i] = (a[i]-b[i])/a[0];
    152:   VecZeroEntries(lte);
    153:   VecMAXPY(lte,n+1,alpha,vecs);
    154:   return(0);
    155: }

    157: static PetscErrorCode TSBDF_Extrapolate(TS ts,PetscInt order,PetscReal t,Vec X)
    158: {
    159:   TS_BDF         *bdf = (TS_BDF*)ts->data;
    160:   PetscInt       n = order+1;
    161:   PetscReal      *time = bdf->time+1;
    162:   Vec            *vecs = bdf->work+1;
    163:   PetscScalar    alpha[7];

    167:   n = PetscMin(n,bdf->n);
    168:   LagrangeBasisVals(n,t,time,alpha);
    169:   VecZeroEntries(X);
    170:   VecMAXPY(X,n,alpha,vecs);
    171:   return(0);
    172: }

    174: static PetscErrorCode TSBDF_Interpolate(TS ts,PetscInt order,PetscReal t,Vec X)
    175: {
    176:   TS_BDF         *bdf = (TS_BDF*)ts->data;
    177:   PetscInt       n = order+1;
    178:   PetscReal      *time = bdf->time;
    179:   Vec            *vecs = bdf->work;
    180:   PetscScalar    alpha[7];

    184:   LagrangeBasisVals(n,t,time,alpha);
    185:   VecZeroEntries(X);
    186:   VecMAXPY(X,n,alpha,vecs);
    187:   return(0);
    188: }

    190: /* Compute the affine term V0 such that Xdot = shift*X + V0.
    191:  *
    192:  * When using transient variables, we're computing Cdot = shift*C(X) + V0, and thus choose a linear combination of tvwork.
    193:  */
    194: static PetscErrorCode TSBDF_PreSolve(TS ts)
    195: {
    196:   TS_BDF         *bdf = (TS_BDF*)ts->data;
    197:   PetscInt       i,n = PetscMax(bdf->k,1) + 1;
    198:   Vec            V,V0;
    199:   Vec            vecs[7];
    200:   PetscScalar    alpha[7];

    204:   TSBDF_GetVecs(ts,NULL,&V,&V0);
    205:   LagrangeBasisDers(n,bdf->time[0],bdf->time,alpha);
    206:   for (i=1; i<n; i++) {
    207:     vecs[i] = bdf->transientvar ? bdf->tvwork[i] : bdf->work[i];
    208:   }
    209:   VecZeroEntries(V0);
    210:   VecMAXPY(V0,n-1,alpha+1,vecs+1);
    211:   bdf->shift = PetscRealPart(alpha[0]);
    212:   TSBDF_RestoreVecs(ts,NULL,&V,&V0);
    213:   return(0);
    214: }

    216: static PetscErrorCode TSBDF_SNESSolve(TS ts,Vec b,Vec x)
    217: {
    218:   PetscInt       nits,lits;

    222:   TSBDF_PreSolve(ts);
    223:   SNESSolve(ts->snes,b,x);
    224:   SNESGetIterationNumber(ts->snes,&nits);
    225:   SNESGetLinearSolveIterations(ts->snes,&lits);
    226:   ts->snes_its += nits; ts->ksp_its += lits;
    227:   return(0);
    228: }

    230: static PetscErrorCode TSBDF_Restart(TS ts,PetscBool *accept)
    231: {
    232:   TS_BDF         *bdf = (TS_BDF*)ts->data;

    236:   bdf->k = 1; bdf->n = 0;
    237:   TSBDF_Advance(ts,ts->ptime,ts->vec_sol);

    239:   bdf->time[0] = ts->ptime + ts->time_step/2;
    240:   VecCopy(bdf->work[1],bdf->work[0]);
    241:   TSPreStage(ts,bdf->time[0]);
    242:   TSBDF_SNESSolve(ts,NULL,bdf->work[0]);
    243:   TSPostStage(ts,bdf->time[0],0,&bdf->work[0]);
    244:   TSAdaptCheckStage(ts->adapt,ts,bdf->time[0],bdf->work[0],accept);
    245:   if (!*accept) return(0);

    247:   bdf->k = PetscMin(2,bdf->order); bdf->n++;
    248:   VecCopy(bdf->work[0],bdf->work[2]);
    249:   bdf->time[2] = bdf->time[0];
    250:   TSComputeTransientVariable(ts,bdf->work[2],bdf->tvwork[2]);
    251:   return(0);
    252: }

    254: static const char *const BDF_SchemeName[] = {"", "1", "2", "3", "4", "5", "6"};

    256: static PetscErrorCode TSStep_BDF(TS ts)
    257: {
    258:   TS_BDF         *bdf = (TS_BDF*)ts->data;
    259:   PetscInt       rejections = 0;
    260:   PetscBool      stageok,accept = PETSC_TRUE;
    261:   PetscReal      next_time_step = ts->time_step;

    265:   PetscCitationsRegister(citation,&cited);

    267:   if (!ts->steprollback && !ts->steprestart) {
    268:     bdf->k = PetscMin(bdf->k+1,bdf->order);
    269:     TSBDF_Advance(ts,ts->ptime,ts->vec_sol);
    270:   }

    272:   bdf->status = TS_STEP_INCOMPLETE;
    273:   while (!ts->reason && bdf->status != TS_STEP_COMPLETE) {

    275:     if (ts->steprestart) {
    276:       TSBDF_Restart(ts,&stageok);
    277:       if (!stageok) goto reject_step;
    278:     }

    280:     bdf->time[0] = ts->ptime + ts->time_step;
    281:     TSBDF_Extrapolate(ts,bdf->k-(accept?0:1),bdf->time[0],bdf->work[0]);
    282:     TSPreStage(ts,bdf->time[0]);
    283:     TSBDF_SNESSolve(ts,NULL,bdf->work[0]);
    284:     TSPostStage(ts,bdf->time[0],0,&bdf->work[0]);
    285:     TSAdaptCheckStage(ts->adapt,ts,bdf->time[0],bdf->work[0],&stageok);
    286:     if (!stageok) goto reject_step;

    288:     bdf->status = TS_STEP_PENDING;
    289:     TSAdaptCandidatesClear(ts->adapt);
    290:     TSAdaptCandidateAdd(ts->adapt,BDF_SchemeName[bdf->k],bdf->k,1,1.0,1.0,PETSC_TRUE);
    291:     TSAdaptChoose(ts->adapt,ts,ts->time_step,NULL,&next_time_step,&accept);
    292:     bdf->status = accept ? TS_STEP_COMPLETE : TS_STEP_INCOMPLETE;
    293:     if (!accept) { ts->time_step = next_time_step; goto reject_step; }

    295:     VecCopy(bdf->work[0],ts->vec_sol);
    296:     ts->ptime += ts->time_step;
    297:     ts->time_step = next_time_step;
    298:     break;

    300:   reject_step:
    301:     ts->reject++; accept = PETSC_FALSE;
    302:     if (!ts->reason && ++rejections > ts->max_reject && ts->max_reject >= 0) {
    303:       PetscInfo2(ts,"Step=%D, step rejections %D greater than current TS allowed, stopping solve\n",ts->steps,rejections);
    304:       ts->reason = TS_DIVERGED_STEP_REJECTED;
    305:     }
    306:   }
    307:   return(0);
    308: }

    310: static PetscErrorCode TSInterpolate_BDF(TS ts,PetscReal t,Vec X)
    311: {
    312:   TS_BDF         *bdf = (TS_BDF*)ts->data;

    316:   TSBDF_Interpolate(ts,bdf->k,t,X);
    317:   return(0);
    318: }

    320: static PetscErrorCode TSEvaluateWLTE_BDF(TS ts,NormType wnormtype,PetscInt *order,PetscReal *wlte)
    321: {
    322:   TS_BDF         *bdf = (TS_BDF*)ts->data;
    323:   PetscInt       k = bdf->k;
    324:   PetscReal      wltea,wlter;
    325:   Vec            X = bdf->work[0], Y = bdf->vec_lte;

    329:   k = PetscMin(k,bdf->n-1);
    330:   TSBDF_VecLTE(ts,k,Y);
    331:   VecAXPY(Y,1,X);
    332:   TSErrorWeightedNorm(ts,X,Y,wnormtype,wlte,&wltea,&wlter);
    333:   if (order) *order = k + 1;
    334:   return(0);
    335: }

    337: static PetscErrorCode TSRollBack_BDF(TS ts)
    338: {
    339:   TS_BDF         *bdf = (TS_BDF*)ts->data;

    343:   VecCopy(bdf->work[1],ts->vec_sol);
    344:   return(0);
    345: }

    347: static PetscErrorCode SNESTSFormFunction_BDF(SNES snes,Vec X,Vec F,TS ts)
    348: {
    349:   TS_BDF         *bdf = (TS_BDF*)ts->data;
    350:   DM             dm, dmsave = ts->dm;
    351:   PetscReal      t = bdf->time[0];
    352:   PetscReal      shift = bdf->shift;
    353:   Vec            V,V0;

    357:   SNESGetDM(snes,&dm);
    358:   TSBDF_GetVecs(ts,dm,&V,&V0);
    359:   if (bdf->transientvar) {      /* shift*C(X) + V0 */
    360:     TSComputeTransientVariable(ts,X,V);
    361:     VecAYPX(V,shift,V0);
    362:   } else {                      /* shift*X + V0 */
    363:     VecWAXPY(V,shift,X,V0);
    364:   }

    366:   /* F = Function(t,X,V) */
    367:   ts->dm = dm;
    368:   TSComputeIFunction(ts,t,X,V,F,PETSC_FALSE);
    369:   ts->dm = dmsave;

    371:   TSBDF_RestoreVecs(ts,dm,&V,&V0);
    372:   return(0);
    373: }

    375: static PetscErrorCode SNESTSFormJacobian_BDF(SNES snes,Vec X,Mat J,Mat P,TS ts)
    376: {
    377:   TS_BDF         *bdf = (TS_BDF*)ts->data;
    378:   DM             dm, dmsave = ts->dm;
    379:   PetscReal      t = bdf->time[0];
    380:   PetscReal      shift = bdf->shift;
    381:   Vec            V,V0;

    385:   SNESGetDM(snes,&dm);
    386:   TSBDF_GetVecs(ts,dm,&V,&V0);

    388:   /* J,P = Jacobian(t,X,V) */
    389:   ts->dm = dm;
    390:   TSComputeIJacobian(ts,t,X,V,shift,J,P,PETSC_FALSE);
    391:   ts->dm = dmsave;

    393:   TSBDF_RestoreVecs(ts,dm,&V,&V0);
    394:   return(0);
    395: }

    397: static PetscErrorCode TSReset_BDF(TS ts)
    398: {
    399:   TS_BDF         *bdf = (TS_BDF*)ts->data;
    400:   size_t         i,n = sizeof(bdf->work)/sizeof(Vec);

    404:   bdf->k = bdf->n = 0;
    405:   for (i=0; i<n; i++) {
    406:     VecDestroy(&bdf->work[i]);
    407:     VecDestroy(&bdf->tvwork[i]);
    408:   }
    409:   VecDestroy(&bdf->vec_dot);
    410:   VecDestroy(&bdf->vec_wrk);
    411:   VecDestroy(&bdf->vec_lte);
    412:   if (ts->dm) {DMCoarsenHookRemove(ts->dm,DMCoarsenHook_TSBDF,DMRestrictHook_TSBDF,ts);}
    413:   return(0);
    414: }

    416: static PetscErrorCode TSDestroy_BDF(TS ts)
    417: {

    421:   TSReset_BDF(ts);
    422:   PetscFree(ts->data);
    423:   PetscObjectComposeFunction((PetscObject)ts,"TSBDFSetOrder_C",NULL);
    424:   PetscObjectComposeFunction((PetscObject)ts,"TSBDFGetOrder_C",NULL);
    425:   return(0);
    426: }

    428: static PetscErrorCode TSSetUp_BDF(TS ts)
    429: {
    430:   TS_BDF         *bdf = (TS_BDF*)ts->data;
    431:   size_t         i,n = sizeof(bdf->work)/sizeof(Vec);
    432:   PetscReal      low,high,two = 2;

    436:   TSHasTransientVariable(ts,&bdf->transientvar);
    437:   bdf->k = bdf->n = 0;
    438:   for (i=0; i<n; i++) {
    439:     VecDuplicate(ts->vec_sol,&bdf->work[i]);
    440:     if (i && bdf->transientvar) {
    441:       VecDuplicate(ts->vec_sol,&bdf->tvwork[i]);
    442:     }
    443:   }
    444:   VecDuplicate(ts->vec_sol,&bdf->vec_dot);
    445:   VecDuplicate(ts->vec_sol,&bdf->vec_wrk);
    446:   VecDuplicate(ts->vec_sol,&bdf->vec_lte);
    447:   TSGetDM(ts,&ts->dm);
    448:   DMCoarsenHookAdd(ts->dm,DMCoarsenHook_TSBDF,DMRestrictHook_TSBDF,ts);

    450:   TSGetAdapt(ts,&ts->adapt);
    451:   TSAdaptCandidatesClear(ts->adapt);
    452:   TSAdaptGetClip(ts->adapt,&low,&high);
    453:   TSAdaptSetClip(ts->adapt,low,PetscMin(high,two));

    455:   TSGetSNES(ts,&ts->snes);
    456:   return(0);
    457: }

    459: static PetscErrorCode TSSetFromOptions_BDF(PetscOptionItems *PetscOptionsObject,TS ts)
    460: {
    461:   TS_BDF         *bdf = (TS_BDF*)ts->data;

    465:   PetscOptionsHead(PetscOptionsObject,"BDF ODE solver options");
    466:   {
    467:     PetscBool flg;
    468:     PetscInt  order = bdf->order;
    469:     PetscOptionsInt("-ts_bdf_order","Order of the BDF method","TSBDFSetOrder",order,&order,&flg);
    470:     if (flg) {TSBDFSetOrder(ts,order);}
    471:   }
    472:   PetscOptionsTail();
    473:   return(0);
    474: }

    476: static PetscErrorCode TSView_BDF(TS ts,PetscViewer viewer)
    477: {
    478:   TS_BDF         *bdf = (TS_BDF*)ts->data;
    479:   PetscBool      iascii;

    483:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);
    484:   if (iascii) {
    485:     PetscViewerASCIIPrintf(viewer,"  Order=%D\n",bdf->order);
    486:   }
    487:   return(0);
    488: }

    490: /* ------------------------------------------------------------ */

    492: static PetscErrorCode TSBDFSetOrder_BDF(TS ts,PetscInt order)
    493: {
    494:   TS_BDF *bdf = (TS_BDF*)ts->data;

    497:   if (order == bdf->order) return(0);
    498:   if (order < 1 || order > 6) SETERRQ1(PetscObjectComm((PetscObject)ts),PETSC_ERR_ARG_OUTOFRANGE,"BDF Order %D not implemented",order);
    499:   bdf->order = order;
    500:   return(0);
    501: }

    503: static PetscErrorCode TSBDFGetOrder_BDF(TS ts,PetscInt *order)
    504: {
    505:   TS_BDF *bdf = (TS_BDF*)ts->data;

    508:   *order = bdf->order;
    509:   return(0);
    510: }

    512: /* ------------------------------------------------------------ */

    514: /*MC
    515:       TSBDF - DAE solver using BDF methods

    517:   Level: beginner

    519: .seealso:  TS, TSCreate(), TSSetType()
    520: M*/
    521: PETSC_EXTERN PetscErrorCode TSCreate_BDF(TS ts)
    522: {
    523:   TS_BDF         *bdf;

    527:   ts->ops->reset          = TSReset_BDF;
    528:   ts->ops->destroy        = TSDestroy_BDF;
    529:   ts->ops->view           = TSView_BDF;
    530:   ts->ops->setup          = TSSetUp_BDF;
    531:   ts->ops->setfromoptions = TSSetFromOptions_BDF;
    532:   ts->ops->step           = TSStep_BDF;
    533:   ts->ops->evaluatewlte   = TSEvaluateWLTE_BDF;
    534:   ts->ops->rollback       = TSRollBack_BDF;
    535:   ts->ops->interpolate    = TSInterpolate_BDF;
    536:   ts->ops->snesfunction   = SNESTSFormFunction_BDF;
    537:   ts->ops->snesjacobian   = SNESTSFormJacobian_BDF;
    538:   ts->default_adapt_type  = TSADAPTBASIC;

    540:   ts->usessnes = PETSC_TRUE;

    542:   PetscNewLog(ts,&bdf);
    543:   ts->data = (void*)bdf;

    545:   bdf->order  = 2;
    546:   bdf->status = TS_STEP_COMPLETE;

    548:   PetscObjectComposeFunction((PetscObject)ts,"TSBDFSetOrder_C",TSBDFSetOrder_BDF);
    549:   PetscObjectComposeFunction((PetscObject)ts,"TSBDFGetOrder_C",TSBDFGetOrder_BDF);
    550:   return(0);
    551: }

    553: /* ------------------------------------------------------------ */

    555: /*@
    556:   TSBDFSetOrder - Set the order of the BDF method

    558:   Logically Collective on TS

    560:   Input Parameter:
    561: +  ts - timestepping context
    562: -  order - order of the method

    564:   Options Database:
    565: .  -ts_bdf_order <order>

    567:   Level: intermediate

    569: @*/
    570: PetscErrorCode TSBDFSetOrder(TS ts,PetscInt order)
    571: {

    577:   PetscTryMethod(ts,"TSBDFSetOrder_C",(TS,PetscInt),(ts,order));
    578:   return(0);
    579: }

    581: /*@
    582:   TSBDFGetOrder - Get the order of the BDF method

    584:   Not Collective

    586:   Input Parameter:
    587: .  ts - timestepping context

    589:   Output Parameter:
    590: .  order - order of the method

    592:   Level: intermediate

    594: @*/
    595: PetscErrorCode TSBDFGetOrder(TS ts,PetscInt *order)
    596: {

    602:   PetscUseMethod(ts,"TSBDFGetOrder_C",(TS,PetscInt*),(ts,order));
    603:   return(0);
    604: }