Date: 2016-07-24T17:12:34+00:00

Actual source code: bdf.c
petsc-3.7.3 2016-07-24
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      1: /*
      2:   Code for timestepping with BDF methods
      3: */
      4: #include <petsc/private/tsimpl.h>  /*I "petscts.h" I*/

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

     15: typedef struct {
     16:   PetscInt  k,n;
     17:   PetscReal time[6+2];
     18:   Vec       work[6+2];
     19:   PetscReal shift;
     20:   Vec       vec_dot;
     21:   Vec       vec_lte;

     23:   PetscInt     order;
     24:   PetscBool    adapt;
     25:   TSStepStatus status;
     26: } TS_BDF;

     29: PETSC_STATIC_INLINE void LagrangeBasisVals(PetscInt n,PetscReal t,const PetscReal T[],PetscScalar L[])
     30: {
     31:   PetscInt k,j;
     32:   for (k=0; k<n; k++)
     33:     for (L[k]=1, j=0; j<n; j++)
     34:       if (j != k)
     35:         L[k] *= (t - T[j])/(T[k] - T[j]);
     36: }

     38: PETSC_STATIC_INLINE void LagrangeBasisDers(PetscInt n,PetscReal t,const PetscReal T[],PetscScalar dL[])
     39: {
     40:   PetscInt  k,j,i;
     41:   for (k=0; k<n; k++)
     42:     for (dL[k]=0, j=0; j<n; j++)
     43:       if (j != k) {
     44:         PetscReal L = 1/(T[k] - T[j]);
     45:         for (i=0; i<n; i++)
     46:           if (i != j && i != k)
     47:             L *= (t - T[i])/(T[k] - T[i]);
     48:         dL[k] += L;
     49:       }
     50: }

     54: static PetscErrorCode TSBDF_Advance(TS ts,PetscReal t,Vec X)
     55: {
     56:   TS_BDF         *bdf = (TS_BDF*)ts->data;
     57:   PetscInt       i,n = (PetscInt)(sizeof(bdf->work)/sizeof(Vec));
     58:   Vec            tail = bdf->work[n-1];

     62:   for (i=n-1; i>=2; i--) {
     63:     bdf->time[i] = bdf->time[i-1];
     64:     bdf->work[i] = bdf->work[i-1];
     65:   }
     66:   bdf->n       = PetscMin(bdf->n+1,n-1);
     67:   bdf->time[1] = t;
     68:   bdf->work[1] = tail;
     69:   VecCopy(X,tail);
     70:   return(0);
     71: }

     75: static PetscErrorCode TSBDF_VecDot(TS ts,PetscInt order,PetscReal t,Vec X,Vec Xdot,PetscReal *shift)
     76: {
     77:   TS_BDF         *bdf = (TS_BDF*)ts->data;
     78:   PetscInt       i,n = order+1;
     79:   PetscReal      time[7];
     80:   Vec            vecs[7];
     81:   PetscScalar    alpha[7];

     85:   n = PetscMax(n,2);
     86:   time[0] = t; for (i=1; i<n; i++) time[i] = bdf->time[i];
     87:   vecs[0] = X; for (i=1; i<n; i++) vecs[i] = bdf->work[i];
     88:   LagrangeBasisDers(n,t,time,alpha);
     89:   VecZeroEntries(Xdot);
     90:   VecMAXPY(Xdot,n,alpha,vecs);
     91:   if (shift) *shift = PetscRealPart(alpha[0]);
     92:   return(0);
     93: }

     97: static PetscErrorCode TSBDF_VecLTE(TS ts,PetscInt order,Vec lte)
     98: {
     99:   TS_BDF         *bdf = (TS_BDF*)ts->data;
    100:   PetscInt       i,n = order+1;
    101:   PetscReal      *time = bdf->time;
    102:   Vec            *vecs = bdf->work;
    103:   PetscScalar    a[8],b[8],alpha[8];

    107:   LagrangeBasisDers(n+0,time[0],time,a); a[n] =0;
    108:   LagrangeBasisDers(n+1,time[0],time,b);
    109:   for (i=0; i<n+1; i++) alpha[i] = (a[i]-b[i])/a[0];
    110:   VecZeroEntries(lte);
    111:   VecMAXPY(lte,n+1,alpha,vecs);
    112:   return(0);
    113: }

    117: static PetscErrorCode TSBDF_Extrapolate(TS ts,PetscInt order,PetscReal t,Vec X)
    118: {
    119:   TS_BDF         *bdf = (TS_BDF*)ts->data;
    120:   PetscInt       n = order+1;
    121:   PetscReal      *time = bdf->time+1;
    122:   Vec            *vecs = bdf->work+1;
    123:   PetscScalar    alpha[7];

    127:   n = PetscMin(n,bdf->n);
    128:   LagrangeBasisVals(n,t,time,alpha);
    129:   VecZeroEntries(X);
    130:   VecMAXPY(X,n,alpha,vecs);
    131:   return(0);
    132: }

    136: static PetscErrorCode TSBDF_Interpolate(TS ts,PetscInt order,PetscReal t,Vec X)
    137: {
    138:   TS_BDF         *bdf = (TS_BDF*)ts->data;
    139:   PetscInt       n = order+1;
    140:   PetscReal      *time = bdf->time;
    141:   Vec            *vecs = bdf->work;
    142:   PetscScalar    alpha[7];

    146:   LagrangeBasisVals(n,t,time,alpha);
    147:   VecZeroEntries(X);
    148:   VecMAXPY(X,n,alpha,vecs);
    149:   return(0);
    150: }

    154: static PetscErrorCode TS_SNESSolve(TS ts,Vec b,Vec x)
    155: {
    156:   PetscInt       nits,lits;

    160:   SNESSolve(ts->snes,b,x);
    161:   SNESGetIterationNumber(ts->snes,&nits);
    162:   SNESGetLinearSolveIterations(ts->snes,&lits);
    163:   ts->snes_its += nits; ts->ksp_its += lits;
    164:   return(0);
    165: }

    169: static PetscErrorCode TSBDF_Restart(TS ts,PetscBool *accept)
    170: {
    171:   TS_BDF         *bdf = (TS_BDF*)ts->data;

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

    178:   bdf->time[0] = ts->ptime + ts->time_step/2;
    179:   VecCopy(bdf->work[1],bdf->work[0]);
    180:   TSPreStage(ts,bdf->time[0]);
    181:   TS_SNESSolve(ts,NULL,bdf->work[0]);
    182:   TSPostStage(ts,bdf->time[0],0,&bdf->work[0]);
    183:   TSAdaptCheckStage(ts->adapt,ts,bdf->time[0],bdf->work[0],accept);
    184:   if (!*accept) return(0);

    186:   bdf->k = PetscMin(2,bdf->order); bdf->n++;
    187:   VecCopy(bdf->work[0],bdf->work[2]);
    188:   bdf->time[2] = bdf->time[0];
    189:   return(0);
    190: }

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

    196: static PetscErrorCode TSStep_BDF(TS ts)
    197: {
    198:   TS_BDF         *bdf = (TS_BDF*)ts->data;
    199:   PetscInt       rejections = 0;
    200:   PetscBool      stageok,accept = PETSC_TRUE;
    201:   PetscReal      next_time_step = ts->time_step;

    205:   PetscCitationsRegister(citation,&cited);

    207:   if (!ts->steprollback && !ts->steprestart) {
    208:     bdf->k = PetscMin(bdf->k+1,bdf->order);
    209:     TSBDF_Advance(ts,ts->ptime,ts->vec_sol);
    210:   }

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

    215:     if (ts->steprestart) {
    216:       TSBDF_Restart(ts,&stageok);
    217:       if (!stageok) goto reject_step;
    218:     }

    220:     bdf->time[0] = ts->ptime + ts->time_step;
    221:     TSBDF_Extrapolate(ts,bdf->k-(accept?0:1),bdf->time[0],bdf->work[0]);
    222:     TSPreStage(ts,bdf->time[0]);
    223:     TS_SNESSolve(ts,NULL,bdf->work[0]);
    224:     TSPostStage(ts,bdf->time[0],0,&bdf->work[0]);
    225:     TSAdaptCheckStage(ts->adapt,ts,bdf->time[0],bdf->work[0],&stageok);
    226:     if (!stageok) goto reject_step;

    228:     bdf->status = TS_STEP_PENDING;
    229:     TSAdaptCandidatesClear(ts->adapt);
    230:     TSAdaptCandidateAdd(ts->adapt,BDF_SchemeName[bdf->k],bdf->k,1,1.0,1.0,PETSC_TRUE);
    231:     TSAdaptChoose(ts->adapt,ts,ts->time_step,NULL,&next_time_step,&accept);
    232:     bdf->status = accept ? TS_STEP_COMPLETE : TS_STEP_INCOMPLETE;
    233:     if (!accept) { ts->time_step = next_time_step; goto reject_step; }

    235:     VecCopy(bdf->work[0],ts->vec_sol);
    236:     ts->ptime += ts->time_step;
    237:     ts->time_step = next_time_step;
    238:     break;

    240:   reject_step:
    241:     ts->reject++; accept = PETSC_FALSE;
    242:     if (!ts->reason && ++rejections > ts->max_reject && ts->max_reject >= 0) {
    243:       PetscInfo2(ts,"Step=%D, step rejections %D greater than current TS allowed, stopping solve\n",ts->steps,rejections);
    244:       ts->reason = TS_DIVERGED_STEP_REJECTED;
    245:     }
    246:   }
    247:   return(0);
    248: }

    252: static PetscErrorCode TSInterpolate_BDF(TS ts,PetscReal t,Vec X)
    253: {
    254:   TS_BDF         *bdf = (TS_BDF*)ts->data;

    258:   TSBDF_Interpolate(ts,bdf->k,t,X);
    259:   return(0);
    260: }

    264: static PetscErrorCode TSEvaluateWLTE_BDF(TS ts,NormType wnormtype,PetscInt *order,PetscReal *wlte)
    265: {
    266:   TS_BDF         *bdf = (TS_BDF*)ts->data;
    267:   PetscInt       k = bdf->k;
    268:   Vec            X = bdf->work[0], Y = bdf->vec_lte;

    272:   k = PetscMin(k,bdf->n-1);
    273:   TSBDF_VecLTE(ts,k,Y);
    274:   VecAXPY(Y,1,X);
    275:   TSErrorWeightedNorm(ts,X,Y,wnormtype,wlte);
    276:   if (order) *order = k + 1;
    277:   return(0);
    278: }

    282: static PetscErrorCode TSRollBack_BDF(TS ts)
    283: {
    284:   TS_BDF         *bdf = (TS_BDF*)ts->data;

    288:   VecCopy(bdf->work[1],ts->vec_sol);
    289:   return(0);
    290: }

    294: static PetscErrorCode SNESTSFormFunction_BDF(PETSC_UNUSED SNES snes,Vec X,Vec F,TS ts)
    295: {
    296:   TS_BDF         *bdf = (TS_BDF*)ts->data;
    297:   PetscInt       k = bdf->k;
    298:   PetscReal      t = bdf->time[0];
    299:   Vec            V = bdf->vec_dot;

    303:   TSBDF_VecDot(ts,k,t,X,V,&bdf->shift);
    304:   /* F = Function(t,X,V) */
    305:   TSComputeIFunction(ts,t,X,V,F,PETSC_FALSE);
    306:   return(0);
    307: }

    311: static PetscErrorCode SNESTSFormJacobian_BDF(PETSC_UNUSED SNES snes,
    312:                                              PETSC_UNUSED Vec X,
    313:                                              Mat J,Mat P,
    314:                                              TS ts)
    315: {
    316:   TS_BDF         *bdf = (TS_BDF*)ts->data;
    317:   PetscReal      t = bdf->time[0];
    318:   Vec            V = bdf->vec_dot;
    319:   PetscReal      dVdX = bdf->shift;

    323:   /* J,P = Jacobian(t,X,V) */
    324:   TSComputeIJacobian(ts,t,X,V,dVdX,J,P,PETSC_FALSE);
    325:   return(0);
    326: }

    330: static PetscErrorCode TSReset_BDF(TS ts)
    331: {
    332:   TS_BDF         *bdf = (TS_BDF*)ts->data;
    333:   size_t         i,n = sizeof(bdf->work)/sizeof(Vec);

    337:   for (i=0; i<n; i++) {VecDestroy(&bdf->work[i]);}
    338:   VecDestroy(&bdf->vec_dot);
    339:   VecDestroy(&bdf->vec_lte);
    340:   return(0);
    341: }

    345: static PetscErrorCode TSDestroy_BDF(TS ts)
    346: {

    350:   TSReset_BDF(ts);
    351:   PetscFree(ts->data);
    352:   PetscObjectComposeFunction((PetscObject)ts,"TSBDFSetOrder_C",NULL);
    353:   PetscObjectComposeFunction((PetscObject)ts,"TSBDFGetOrder_C",NULL);
    354:   PetscObjectComposeFunction((PetscObject)ts,"TSBDFUseAdapt_C",NULL);
    355:   return(0);
    356: }

    360: static PetscErrorCode TSSetUp_BDF(TS ts)
    361: {
    362:   TS_BDF         *bdf = (TS_BDF*)ts->data;
    363:   size_t         i,n = sizeof(bdf->work)/sizeof(Vec);

    367:   bdf->k = bdf->n = 0;
    368:   for (i=0; i<n; i++) {VecDuplicate(ts->vec_sol,&bdf->work[i]);}
    369:   VecDuplicate(ts->vec_sol,&bdf->vec_dot);
    370:   VecDuplicate(ts->vec_sol,&bdf->vec_lte);

    372:   TSGetAdapt(ts,&ts->adapt);
    373:   TSAdaptCandidatesClear(ts->adapt);
    374:   if (!bdf->adapt) {
    375:     TSAdaptSetType(ts->adapt,TSADAPTNONE);
    376:   } else {
    377:     PetscReal low,high;
    378:     TSAdaptBasicGetClip(ts->adapt,&low,&high);
    379:     high = PetscMin(high,2.0);
    380:     TSAdaptBasicSetClip(ts->adapt,low,high);
    381:     if (ts->exact_final_time == TS_EXACTFINALTIME_UNSPECIFIED)
    382:       ts->exact_final_time = TS_EXACTFINALTIME_MATCHSTEP;
    383:   }

    385:   TSGetSNES(ts,&ts->snes);
    386:   return(0);
    387: }

    391: static PetscErrorCode TSSetFromOptions_BDF(PetscOptionItems *PetscOptionsObject,TS ts)
    392: {
    393:   TS_BDF         *bdf = (TS_BDF*)ts->data;

    397:   PetscOptionsHead(PetscOptionsObject,"BDF ODE solver options");
    398:   {
    399:     PetscBool flg;
    400:     PetscInt  order = bdf->order;
    401:     PetscBool adapt = bdf->adapt;
    402:     PetscOptionsInt("-ts_bdf_order","Order of the BDF method","TSBDFSetOrder",order,&order,&flg);
    403:     if (flg) {TSBDFSetOrder(ts,order);}
    404:     PetscOptionsBool("-ts_bdf_adapt","Use time-step adaptivity with the BDF method","TSBDFUseAdapt",adapt,&adapt,&flg);
    405:     if (flg) {TSBDFUseAdapt(ts,adapt);}
    406:   }
    407:   PetscOptionsTail();
    408:   return(0);
    409: }

    413: static PetscErrorCode TSView_BDF(TS ts,PetscViewer viewer)
    414: {
    415:   TS_BDF         *bdf = (TS_BDF*)ts->data;
    416:   PetscBool      iascii;

    420:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);
    421:   if (iascii)    {
    422:     PetscViewerASCIIPrintf(viewer,"  Order=%D\n",bdf->order);
    423:   }
    424:   if (ts->adapt) {TSAdaptView(ts->adapt,viewer);}
    425:   if (ts->snes)  {SNESView(ts->snes,viewer);}
    426:   return(0);
    427: }

    429: /* ------------------------------------------------------------ */

    433: static PetscErrorCode TSBDFSetOrder_BDF(TS ts,PetscInt order)
    434: {
    435:   TS_BDF *bdf = (TS_BDF*)ts->data;

    438:   if (order == bdf->order) return(0);
    439:   if (order < 1 || order > 6) SETERRQ1(PetscObjectComm((PetscObject)ts),PETSC_ERR_ARG_OUTOFRANGE,"BDF Order %D not implemented",order);
    440:   bdf->order = order;
    441:   return(0);
    442: }

    446: static PetscErrorCode TSBDFGetOrder_BDF(TS ts,PetscInt *order)
    447: {
    448:   TS_BDF *bdf = (TS_BDF*)ts->data;

    451:   *order = bdf->order;
    452:   return(0);
    453: }

    457: static PetscErrorCode TSBDFUseAdapt_BDF(TS ts,PetscBool use)
    458: {
    459:   TS_BDF *bdf = (TS_BDF*)ts->data;

    462:   if (use == bdf->adapt) return(0);
    463:   if (ts->setupcalled) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_ORDER,"Cannot change adaptivity after TSSetUp()");
    464:   bdf->adapt = use;
    465:   return(0);
    466: }

    468: /* ------------------------------------------------------------ */

    470: /*MC
    471:       TSBDF - DAE solver using BDF methods

    473:   Level: beginner

    475: .seealso:  TS, TSCreate(), TSSetType()
    476: M*/
    479: PETSC_EXTERN PetscErrorCode TSCreate_BDF(TS ts)
    480: {
    481:   TS_BDF         *bdf;

    485:   ts->ops->reset          = TSReset_BDF;
    486:   ts->ops->destroy        = TSDestroy_BDF;
    487:   ts->ops->view           = TSView_BDF;
    488:   ts->ops->setup          = TSSetUp_BDF;
    489:   ts->ops->setfromoptions = TSSetFromOptions_BDF;
    490:   ts->ops->step           = TSStep_BDF;
    491:   ts->ops->evaluatewlte   = TSEvaluateWLTE_BDF;
    492:   ts->ops->rollback       = TSRollBack_BDF;
    493:   ts->ops->interpolate    = TSInterpolate_BDF;
    494:   ts->ops->snesfunction   = SNESTSFormFunction_BDF;
    495:   ts->ops->snesjacobian   = SNESTSFormJacobian_BDF;

    497:   PetscNewLog(ts,&bdf);
    498:   ts->data = (void*)bdf;

    500:   bdf->order  = 2;
    501:   bdf->adapt  = PETSC_FALSE;
    502:   bdf->status = TS_STEP_COMPLETE;

    504:   PetscObjectComposeFunction((PetscObject)ts,"TSBDFSetOrder_C",TSBDFSetOrder_BDF);
    505:   PetscObjectComposeFunction((PetscObject)ts,"TSBDFGetOrder_C",TSBDFGetOrder_BDF);
    506:   PetscObjectComposeFunction((PetscObject)ts,"TSBDFUseAdapt_C",TSBDFUseAdapt_BDF);
    507:   return(0);
    508: }

    510: /* ------------------------------------------------------------ */

    514: /*@
    515:   TSBDFSetOrder - Set the order of the BDF method

    517:   Logically Collective on TS

    519:   Input Parameter:
    520: +  ts - timestepping context
    521: -  order - order of the method

    523:   Options Database:
    524: .  -ts_bdf_order <order>

    526:   Level: intermediate

    528: @*/
    529: PetscErrorCode TSBDFSetOrder(TS ts,PetscInt order)
    530: {

    536:   PetscTryMethod(ts,"TSBDFSetOrder_C",(TS,PetscInt),(ts,order));
    537:   return(0);
    538: }

    542: /*@
    543:   TSBDFGetOrder - Get the order of the BDF method

    545:   Not Collective

    547:   Input Parameter:
    548: .  ts - timestepping context

    550:   Output Parameter:
    551: .  order - order of the method

    553:   Level: intermediate

    555: @*/
    556: PetscErrorCode TSBDFGetOrder(TS ts,PetscInt *order)
    557: {

    563:   PetscUseMethod(ts,"TSBDFGetOrder_C",(TS,PetscInt*),(ts,order));
    564:   return(0);
    565: }

    569: /*@
    570:   TSBDFUseAdapt - Use time-step adaptivity with the BDF method

    572:   Logically Collective on TS

    574:   Input Parameter:
    575: +  ts - timestepping context
    576: -  use - flag to use adaptivity

    578:   Options Database:
    579: .  -ts_bdf_adapt

    581:   Level: intermediate

    583: .seealso: TSAdapt
    584: @*/
    585: PetscErrorCode TSBDFUseAdapt(TS ts,PetscBool use)
    586: {

    592:   PetscTryMethod(ts,"TSBDFUseAdapt_C",(TS,PetscBool),(ts,use));
    593:   return(0);
    594: }