Actual source code: bdf.c

petsc-3.11.2 2019-05-18
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  1: /*
  2:   Code for timestepping with BDF methods
  3: */
  4:  #include <petsc/private/tsimpl.h>

  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:   TSStepStatus status;
 25: } TS_BDF;


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

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

 51: static PetscErrorCode TSBDF_Advance(TS ts,PetscReal t,Vec X)
 52: {
 53:   TS_BDF         *bdf = (TS_BDF*)ts->data;
 54:   PetscInt       i,n = (PetscInt)(sizeof(bdf->work)/sizeof(Vec));
 55:   Vec            tail = bdf->work[n-1];

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

 70: static PetscErrorCode TSBDF_VecDot(TS ts,PetscInt order,PetscReal t,Vec X,Vec Xdot,PetscReal *shift)
 71: {
 72:   TS_BDF         *bdf = (TS_BDF*)ts->data;
 73:   PetscInt       i,n = order+1;
 74:   PetscReal      time[7];
 75:   Vec            vecs[7];
 76:   PetscScalar    alpha[7];

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

 90: static PetscErrorCode TSBDF_VecLTE(TS ts,PetscInt order,Vec lte)
 91: {
 92:   TS_BDF         *bdf = (TS_BDF*)ts->data;
 93:   PetscInt       i,n = order+1;
 94:   PetscReal      *time = bdf->time;
 95:   Vec            *vecs = bdf->work;
 96:   PetscScalar    a[8],b[8],alpha[8];

100:   LagrangeBasisDers(n+0,time[0],time,a); a[n] =0;
101:   LagrangeBasisDers(n+1,time[0],time,b);
102:   for (i=0; i<n+1; i++) alpha[i] = (a[i]-b[i])/a[0];
103:   VecZeroEntries(lte);
104:   VecMAXPY(lte,n+1,alpha,vecs);
105:   return(0);
106: }

108: static PetscErrorCode TSBDF_Extrapolate(TS ts,PetscInt order,PetscReal t,Vec X)
109: {
110:   TS_BDF         *bdf = (TS_BDF*)ts->data;
111:   PetscInt       n = order+1;
112:   PetscReal      *time = bdf->time+1;
113:   Vec            *vecs = bdf->work+1;
114:   PetscScalar    alpha[7];

118:   n = PetscMin(n,bdf->n);
119:   LagrangeBasisVals(n,t,time,alpha);
120:   VecZeroEntries(X);
121:   VecMAXPY(X,n,alpha,vecs);
122:   return(0);
123: }

125: static PetscErrorCode TSBDF_Interpolate(TS ts,PetscInt order,PetscReal t,Vec X)
126: {
127:   TS_BDF         *bdf = (TS_BDF*)ts->data;
128:   PetscInt       n = order+1;
129:   PetscReal      *time = bdf->time;
130:   Vec            *vecs = bdf->work;
131:   PetscScalar    alpha[7];

135:   LagrangeBasisVals(n,t,time,alpha);
136:   VecZeroEntries(X);
137:   VecMAXPY(X,n,alpha,vecs);
138:   return(0);
139: }

141: static PetscErrorCode TSBDF_SNESSolve(TS ts,Vec b,Vec x)
142: {
143:   PetscInt       nits,lits;

147:   SNESSolve(ts->snes,b,x);
148:   SNESGetIterationNumber(ts->snes,&nits);
149:   SNESGetLinearSolveIterations(ts->snes,&lits);
150:   ts->snes_its += nits; ts->ksp_its += lits;
151:   return(0);
152: }

154: static PetscErrorCode TSBDF_Restart(TS ts,PetscBool *accept)
155: {
156:   TS_BDF         *bdf = (TS_BDF*)ts->data;

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

163:   bdf->time[0] = ts->ptime + ts->time_step/2;
164:   VecCopy(bdf->work[1],bdf->work[0]);
165:   TSPreStage(ts,bdf->time[0]);
166:   TSBDF_SNESSolve(ts,NULL,bdf->work[0]);
167:   TSPostStage(ts,bdf->time[0],0,&bdf->work[0]);
168:   TSAdaptCheckStage(ts->adapt,ts,bdf->time[0],bdf->work[0],accept);
169:   if (!*accept) return(0);

171:   bdf->k = PetscMin(2,bdf->order); bdf->n++;
172:   VecCopy(bdf->work[0],bdf->work[2]);
173:   bdf->time[2] = bdf->time[0];
174:   return(0);
175: }

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

179: static PetscErrorCode TSStep_BDF(TS ts)
180: {
181:   TS_BDF         *bdf = (TS_BDF*)ts->data;
182:   PetscInt       rejections = 0;
183:   PetscBool      stageok,accept = PETSC_TRUE;
184:   PetscReal      next_time_step = ts->time_step;

188:   PetscCitationsRegister(citation,&cited);

190:   if (!ts->steprollback && !ts->steprestart) {
191:     bdf->k = PetscMin(bdf->k+1,bdf->order);
192:     TSBDF_Advance(ts,ts->ptime,ts->vec_sol);
193:   }

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

198:     if (ts->steprestart) {
199:       TSBDF_Restart(ts,&stageok);
200:       if (!stageok) goto reject_step;
201:     }

203:     bdf->time[0] = ts->ptime + ts->time_step;
204:     TSBDF_Extrapolate(ts,bdf->k-(accept?0:1),bdf->time[0],bdf->work[0]);
205:     TSPreStage(ts,bdf->time[0]);
206:     TSBDF_SNESSolve(ts,NULL,bdf->work[0]);
207:     TSPostStage(ts,bdf->time[0],0,&bdf->work[0]);
208:     TSAdaptCheckStage(ts->adapt,ts,bdf->time[0],bdf->work[0],&stageok);
209:     if (!stageok) goto reject_step;

211:     bdf->status = TS_STEP_PENDING;
212:     TSAdaptCandidatesClear(ts->adapt);
213:     TSAdaptCandidateAdd(ts->adapt,BDF_SchemeName[bdf->k],bdf->k,1,1.0,1.0,PETSC_TRUE);
214:     TSAdaptChoose(ts->adapt,ts,ts->time_step,NULL,&next_time_step,&accept);
215:     bdf->status = accept ? TS_STEP_COMPLETE : TS_STEP_INCOMPLETE;
216:     if (!accept) { ts->time_step = next_time_step; goto reject_step; }

218:     VecCopy(bdf->work[0],ts->vec_sol);
219:     ts->ptime += ts->time_step;
220:     ts->time_step = next_time_step;
221:     break;

223:   reject_step:
224:     ts->reject++; accept = PETSC_FALSE;
225:     if (!ts->reason && ++rejections > ts->max_reject && ts->max_reject >= 0) {
226:       PetscInfo2(ts,"Step=%D, step rejections %D greater than current TS allowed, stopping solve\n",ts->steps,rejections);
227:       ts->reason = TS_DIVERGED_STEP_REJECTED;
228:     }
229:   }
230:   return(0);
231: }

233: static PetscErrorCode TSInterpolate_BDF(TS ts,PetscReal t,Vec X)
234: {
235:   TS_BDF         *bdf = (TS_BDF*)ts->data;

239:   TSBDF_Interpolate(ts,bdf->k,t,X);
240:   return(0);
241: }

243: static PetscErrorCode TSEvaluateWLTE_BDF(TS ts,NormType wnormtype,PetscInt *order,PetscReal *wlte)
244: {
245:   TS_BDF         *bdf = (TS_BDF*)ts->data;
246:   PetscInt       k = bdf->k;
247:   PetscReal      wltea,wlter;
248:   Vec            X = bdf->work[0], Y = bdf->vec_lte;

252:   k = PetscMin(k,bdf->n-1);
253:   TSBDF_VecLTE(ts,k,Y);
254:   VecAXPY(Y,1,X);
255:   TSErrorWeightedNorm(ts,X,Y,wnormtype,wlte,&wltea,&wlter);
256:   if (order) *order = k + 1;
257:   return(0);
258: }

260: static PetscErrorCode TSRollBack_BDF(TS ts)
261: {
262:   TS_BDF         *bdf = (TS_BDF*)ts->data;

266:   VecCopy(bdf->work[1],ts->vec_sol);
267:   return(0);
268: }

270: static PetscErrorCode SNESTSFormFunction_BDF(PETSC_UNUSED SNES snes,Vec X,Vec F,TS ts)
271: {
272:   TS_BDF         *bdf = (TS_BDF*)ts->data;
273:   PetscInt       k = bdf->k;
274:   PetscReal      t = bdf->time[0];
275:   Vec            V = bdf->vec_dot;

279:   TSBDF_VecDot(ts,k,t,X,V,&bdf->shift);
280:   /* F = Function(t,X,V) */
281:   TSComputeIFunction(ts,t,X,V,F,PETSC_FALSE);
282:   return(0);
283: }

285: static PetscErrorCode SNESTSFormJacobian_BDF(PETSC_UNUSED SNES snes,
286:                                              PETSC_UNUSED Vec X,
287:                                              Mat J,Mat P,
288:                                              TS ts)
289: {
290:   TS_BDF         *bdf = (TS_BDF*)ts->data;
291:   PetscReal      t = bdf->time[0];
292:   Vec            V = bdf->vec_dot;
293:   PetscReal      dVdX = bdf->shift;

297:   /* J,P = Jacobian(t,X,V) */
298:   TSComputeIJacobian(ts,t,X,V,dVdX,J,P,PETSC_FALSE);
299:   return(0);
300: }

302: static PetscErrorCode TSReset_BDF(TS ts)
303: {
304:   TS_BDF         *bdf = (TS_BDF*)ts->data;
305:   size_t         i,n = sizeof(bdf->work)/sizeof(Vec);

309:   for (i=0; i<n; i++) {VecDestroy(&bdf->work[i]);}
310:   VecDestroy(&bdf->vec_dot);
311:   VecDestroy(&bdf->vec_lte);
312:   return(0);
313: }

315: static PetscErrorCode TSDestroy_BDF(TS ts)
316: {

320:   TSReset_BDF(ts);
321:   PetscFree(ts->data);
322:   PetscObjectComposeFunction((PetscObject)ts,"TSBDFSetOrder_C",NULL);
323:   PetscObjectComposeFunction((PetscObject)ts,"TSBDFGetOrder_C",NULL);
324:   return(0);
325: }

327: static PetscErrorCode TSSetUp_BDF(TS ts)
328: {
329:   TS_BDF         *bdf = (TS_BDF*)ts->data;
330:   size_t         i,n = sizeof(bdf->work)/sizeof(Vec);
331:   PetscReal      low,high,two = 2;

335:   bdf->k = bdf->n = 0;
336:   for (i=0; i<n; i++) {VecDuplicate(ts->vec_sol,&bdf->work[i]);}
337:   VecDuplicate(ts->vec_sol,&bdf->vec_dot);
338:   VecDuplicate(ts->vec_sol,&bdf->vec_lte);

340:   TSGetAdapt(ts,&ts->adapt);
341:   TSAdaptCandidatesClear(ts->adapt);
342:   TSAdaptGetClip(ts->adapt,&low,&high);
343:   TSAdaptSetClip(ts->adapt,low,PetscMin(high,two));

345:   TSGetSNES(ts,&ts->snes);
346:   return(0);
347: }

349: static PetscErrorCode TSSetFromOptions_BDF(PetscOptionItems *PetscOptionsObject,TS ts)
350: {
351:   TS_BDF         *bdf = (TS_BDF*)ts->data;

355:   PetscOptionsHead(PetscOptionsObject,"BDF ODE solver options");
356:   {
357:     PetscBool flg;
358:     PetscInt  order = bdf->order;
359:     PetscOptionsInt("-ts_bdf_order","Order of the BDF method","TSBDFSetOrder",order,&order,&flg);
360:     if (flg) {TSBDFSetOrder(ts,order);}
361:   }
362:   PetscOptionsTail();
363:   return(0);
364: }

366: static PetscErrorCode TSView_BDF(TS ts,PetscViewer viewer)
367: {
368:   TS_BDF         *bdf = (TS_BDF*)ts->data;
369:   PetscBool      iascii;

373:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);
374:   if (iascii) {
375:     PetscViewerASCIIPrintf(viewer,"  Order=%D\n",bdf->order);
376:   }
377:   return(0);
378: }

380: /* ------------------------------------------------------------ */

382: static PetscErrorCode TSBDFSetOrder_BDF(TS ts,PetscInt order)
383: {
384:   TS_BDF *bdf = (TS_BDF*)ts->data;

387:   if (order == bdf->order) return(0);
388:   if (order < 1 || order > 6) SETERRQ1(PetscObjectComm((PetscObject)ts),PETSC_ERR_ARG_OUTOFRANGE,"BDF Order %D not implemented",order);
389:   bdf->order = order;
390:   return(0);
391: }

393: static PetscErrorCode TSBDFGetOrder_BDF(TS ts,PetscInt *order)
394: {
395:   TS_BDF *bdf = (TS_BDF*)ts->data;

398:   *order = bdf->order;
399:   return(0);
400: }

402: /* ------------------------------------------------------------ */

404: /*MC
405:       TSBDF - DAE solver using BDF methods

407:   Level: beginner

409: .seealso:  TS, TSCreate(), TSSetType()
410: M*/
411: PETSC_EXTERN PetscErrorCode TSCreate_BDF(TS ts)
412: {
413:   TS_BDF         *bdf;

417:   ts->ops->reset          = TSReset_BDF;
418:   ts->ops->destroy        = TSDestroy_BDF;
419:   ts->ops->view           = TSView_BDF;
420:   ts->ops->setup          = TSSetUp_BDF;
421:   ts->ops->setfromoptions = TSSetFromOptions_BDF;
422:   ts->ops->step           = TSStep_BDF;
423:   ts->ops->evaluatewlte   = TSEvaluateWLTE_BDF;
424:   ts->ops->rollback       = TSRollBack_BDF;
425:   ts->ops->interpolate    = TSInterpolate_BDF;
426:   ts->ops->snesfunction   = SNESTSFormFunction_BDF;
427:   ts->ops->snesjacobian   = SNESTSFormJacobian_BDF;
428:   ts->default_adapt_type  = TSADAPTBASIC;

430:   ts->usessnes = PETSC_TRUE;

432:   PetscNewLog(ts,&bdf);
433:   ts->data = (void*)bdf;

435:   bdf->order  = 2;
436:   bdf->status = TS_STEP_COMPLETE;

438:   PetscObjectComposeFunction((PetscObject)ts,"TSBDFSetOrder_C",TSBDFSetOrder_BDF);
439:   PetscObjectComposeFunction((PetscObject)ts,"TSBDFGetOrder_C",TSBDFGetOrder_BDF);
440:   return(0);
441: }

443: /* ------------------------------------------------------------ */

445: /*@
446:   TSBDFSetOrder - Set the order of the BDF method

448:   Logically Collective on TS

450:   Input Parameter:
451: +  ts - timestepping context
452: -  order - order of the method

454:   Options Database:
455: .  -ts_bdf_order <order>

457:   Level: intermediate

459: @*/
460: PetscErrorCode TSBDFSetOrder(TS ts,PetscInt order)
461: {

467:   PetscTryMethod(ts,"TSBDFSetOrder_C",(TS,PetscInt),(ts,order));
468:   return(0);
469: }

471: /*@
472:   TSBDFGetOrder - Get the order of the BDF method

474:   Not Collective

476:   Input Parameter:
477: .  ts - timestepping context

479:   Output Parameter:
480: .  order - order of the method

482:   Level: intermediate

484: @*/
485: PetscErrorCode TSBDFGetOrder(TS ts,PetscInt *order)
486: {

492:   PetscUseMethod(ts,"TSBDFGetOrder_C",(TS,PetscInt*),(ts,order));
493:   return(0);
494: }