Actual source code: bdf.c

petsc-master 2020-09-24
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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: {

464:   PetscOptionsHead(PetscOptionsObject,"BDF ODE solver options");
465:   {
466:     PetscBool flg;
467:     PetscInt  order;
468:     TSBDFGetOrder(ts,&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->status = TS_STEP_COMPLETE;

547:   PetscObjectComposeFunction((PetscObject)ts,"TSBDFSetOrder_C",TSBDFSetOrder_BDF);
548:   PetscObjectComposeFunction((PetscObject)ts,"TSBDFGetOrder_C",TSBDFGetOrder_BDF);
549:   TSBDFSetOrder(ts,2);
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: }