Actual source code: rk.c

petsc-3.7.3 2016-07-24
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  1: /*
  2:   Code for time stepping with the Runge-Kutta method

  4:   Notes:
  5:   The general system is written as

  7:   Udot = F(t,U)

  9: */
 10: #include <petsc/private/tsimpl.h>                /*I   "petscts.h"   I*/
 11: #include <petscdm.h>

 13: static TSRKType  TSRKDefault = TSRK3BS;
 14: static PetscBool TSRKRegisterAllCalled;
 15: static PetscBool TSRKPackageInitialized;

 17: typedef struct _RKTableau *RKTableau;
 18: struct _RKTableau {
 19:   char      *name;
 20:   PetscInt   order;               /* Classical approximation order of the method i              */
 21:   PetscInt   s;                   /* Number of stages                                           */
 22:   PetscBool  FSAL;                /* flag to indicate if tableau is FSAL                        */
 23:   PetscInt   pinterp;             /* Interpolation order                                        */
 24:   PetscReal *A,*b,*c;             /* Tableau                                                    */
 25:   PetscReal *bembed;              /* Embedded formula of order one less (order-1)               */
 26:   PetscReal *binterp;             /* Dense output formula                                       */
 27:   PetscReal  ccfl;                /* Placeholder for CFL coefficient relative to forward Euler  */
 28: };
 29: typedef struct _RKTableauLink *RKTableauLink;
 30: struct _RKTableauLink {
 31:   struct _RKTableau tab;
 32:   RKTableauLink     next;
 33: };
 34: static RKTableauLink RKTableauList;

 36: typedef struct {
 37:   RKTableau    tableau;
 38:   Vec          *Y;               /* States computed during the step */
 39:   Vec          *YdotRHS;         /* Function evaluations for the non-stiff part */
 40:   Vec          *VecDeltaLam;     /* Increment of the adjoint sensitivity w.r.t IC at stage */
 41:   Vec          *VecDeltaMu;      /* Increment of the adjoint sensitivity w.r.t P at stage */
 42:   Vec          *VecSensiTemp;    /* Vector to be timed with Jacobian transpose */
 43:   Vec          VecCostIntegral0; /* backup for roll-backs due to events */
 44:   PetscScalar  *work;            /* Scalar work */
 45:   PetscReal    stage_time;
 46:   TSStepStatus status;
 47:   PetscReal    ptime;
 48:   PetscReal    time_step;
 49: } TS_RK;

 51: /*MC
 52:      TSRK1 - First order forward Euler scheme.

 54:      This method has one stage.

 56:      Level: advanced

 58: .seealso: TSRK
 59: M*/
 60: /*MC
 61:      TSRK2A - Second order RK scheme.

 63:      This method has two stages.

 65:      Level: advanced

 67: .seealso: TSRK
 68: M*/
 69: /*MC
 70:      TSRK3 - Third order RK scheme.

 72:      This method has three stages.

 74:      Level: advanced

 76: .seealso: TSRK
 77: M*/
 78: /*MC
 79:      TSRK3BS - Third order RK scheme of Bogacki-Shampine with 2nd order embedded method.

 81:      This method has four stages.

 83:      Level: advanced

 85: .seealso: TSRK
 86: M*/
 87: /*MC
 88:      TSRK4 - Fourth order RK scheme.

 90:      This is the classical Runge-Kutta method with four stages.

 92:      Level: advanced

 94: .seealso: TSRK
 95: M*/
 96: /*MC
 97:      TSRK5F - Fifth order Fehlberg RK scheme with a 4th order embedded method.

 99:      This method has six stages.

101:      Level: advanced

103: .seealso: TSRK
104: M*/
105: /*MC
106:      TSRK5DP - Fifth order Dormand-Prince RK scheme with the 4th order embedded method.

108:      This method has seven stages.

110:      Level: advanced

112: .seealso: TSRK
113: M*/

117: /*@C
118:   TSRKRegisterAll - Registers all of the Runge-Kutta explicit methods in TSRK

120:   Not Collective, but should be called by all processes which will need the schemes to be registered

122:   Level: advanced

124: .keywords: TS, TSRK, register, all

126: .seealso:  TSRKRegisterDestroy()
127: @*/
128: PetscErrorCode TSRKRegisterAll(void)
129: {

133:   if (TSRKRegisterAllCalled) return(0);
134:   TSRKRegisterAllCalled = PETSC_TRUE;

136:   {
137:     const PetscReal
138:       A[1][1] = {{0.0}},
139:       b[1]    = {1.0};
140:     TSRKRegister(TSRK1FE,1,1,&A[0][0],b,NULL,NULL,1,b);
141:   }
142:   {
143:     const PetscReal
144:       A[2][2]     = {{0.0,0.0},
145:                     {1.0,0.0}},
146:       b[2]        = {0.5,0.5},
147:       bembed[2]   = {1.0,0};
148:     TSRKRegister(TSRK2A,2,2,&A[0][0],b,NULL,bembed,2,b);
149:   }
150:   {
151:     const PetscReal
152:       A[3][3] = {{0,0,0},
153:                  {2.0/3.0,0,0},
154:                  {-1.0/3.0,1.0,0}},
155:       b[3]    = {0.25,0.5,0.25};
156:     TSRKRegister(TSRK3,3,3,&A[0][0],b,NULL,NULL,3,b);
157:   }
158:   {
159:     const PetscReal
160:       A[4][4] = {{0,0,0,0},
161:                  {1.0/2.0,0,0,0},
162:                  {0,3.0/4.0,0,0},
163:                  {2.0/9.0,1.0/3.0,4.0/9.0,0}},
164:       b[4]    = {2.0/9.0,1.0/3.0,4.0/9.0,0},
165:       bembed[4] = {7.0/24.0,1.0/4.0,1.0/3.0,1.0/8.0};
166:     TSRKRegister(TSRK3BS,3,4,&A[0][0],b,NULL,bembed,3,b);
167:   }
168:   {
169:     const PetscReal
170:       A[4][4] = {{0,0,0,0},
171:                  {0.5,0,0,0},
172:                  {0,0.5,0,0},
173:                  {0,0,1.0,0}},
174:       b[4]    = {1.0/6.0,1.0/3.0,1.0/3.0,1.0/6.0};
175:     TSRKRegister(TSRK4,4,4,&A[0][0],b,NULL,NULL,4,b);
176:   }
177:   {
178:     const PetscReal
179:       A[6][6]   = {{0,0,0,0,0,0},
180:                    {0.25,0,0,0,0,0},
181:                    {3.0/32.0,9.0/32.0,0,0,0,0},
182:                    {1932.0/2197.0,-7200.0/2197.0,7296.0/2197.0,0,0,0},
183:                    {439.0/216.0,-8.0,3680.0/513.0,-845.0/4104.0,0,0},
184:                    {-8.0/27.0,2.0,-3544.0/2565.0,1859.0/4104.0,-11.0/40.0,0}},
185:       b[6]      = {16.0/135.0,0,6656.0/12825.0,28561.0/56430.0,-9.0/50.0,2.0/55.0},
186:       bembed[6] = {25.0/216.0,0,1408.0/2565.0,2197.0/4104.0,-1.0/5.0,0};
187:     TSRKRegister(TSRK5F,5,6,&A[0][0],b,NULL,bembed,5,b);
188:   }
189:   {
190:     const PetscReal
191:       A[7][7]   = {{0,0,0,0,0,0,0},
192:                    {1.0/5.0,0,0,0,0,0,0},
193:                    {3.0/40.0,9.0/40.0,0,0,0,0,0},
194:                    {44.0/45.0,-56.0/15.0,32.0/9.0,0,0,0,0},
195:                    {19372.0/6561.0,-25360.0/2187.0,64448.0/6561.0,-212.0/729.0,0,0,0},
196:                    {9017.0/3168.0,-355.0/33.0,46732.0/5247.0,49.0/176.0,-5103.0/18656.0,0,0},
197:                    {35.0/384.0,0,500.0/1113.0,125.0/192.0,-2187.0/6784.0,11.0/84.0,0}},
198:       b[7]      = {35.0/384.0,0,500.0/1113.0,125.0/192.0,-2187.0/6784.0,11.0/84.0,0},
199:       bembed[7] = {5179.0/57600.0,0,7571.0/16695.0,393.0/640.0,-92097.0/339200.0,187.0/2100.0,1.0/40.0};
200:     TSRKRegister(TSRK5DP,5,7,&A[0][0],b,NULL,bembed,5,b);
201:   }
202:   return(0);
203: }

207: /*@C
208:    TSRKRegisterDestroy - Frees the list of schemes that were registered by TSRKRegister().

210:    Not Collective

212:    Level: advanced

214: .keywords: TSRK, register, destroy
215: .seealso: TSRKRegister(), TSRKRegisterAll()
216: @*/
217: PetscErrorCode TSRKRegisterDestroy(void)
218: {
220:   RKTableauLink link;

223:   while ((link = RKTableauList)) {
224:     RKTableau t = &link->tab;
225:     RKTableauList = link->next;
226:     PetscFree3(t->A,t->b,t->c);
227:     PetscFree (t->bembed);
228:     PetscFree (t->binterp);
229:     PetscFree (t->name);
230:     PetscFree (link);
231:   }
232:   TSRKRegisterAllCalled = PETSC_FALSE;
233:   return(0);
234: }

238: /*@C
239:   TSRKInitializePackage - This function initializes everything in the TSRK package. It is called
240:   from PetscDLLibraryRegister() when using dynamic libraries, and on the first call to TSCreate_RK()
241:   when using static libraries.

243:   Level: developer

245: .keywords: TS, TSRK, initialize, package
246: .seealso: PetscInitialize()
247: @*/
248: PetscErrorCode TSRKInitializePackage(void)
249: {

253:   if (TSRKPackageInitialized) return(0);
254:   TSRKPackageInitialized = PETSC_TRUE;
255:   TSRKRegisterAll();
256:   PetscRegisterFinalize(TSRKFinalizePackage);
257:   return(0);
258: }

262: /*@C
263:   TSRKFinalizePackage - This function destroys everything in the TSRK package. It is
264:   called from PetscFinalize().

266:   Level: developer

268: .keywords: Petsc, destroy, package
269: .seealso: PetscFinalize()
270: @*/
271: PetscErrorCode TSRKFinalizePackage(void)
272: {

276:   TSRKPackageInitialized = PETSC_FALSE;
277:   TSRKRegisterDestroy();
278:   return(0);
279: }

283: /*@C
284:    TSRKRegister - register an RK scheme by providing the entries in the Butcher tableau and optionally embedded approximations and interpolation

286:    Not Collective, but the same schemes should be registered on all processes on which they will be used

288:    Input Parameters:
289: +  name - identifier for method
290: .  order - approximation order of method
291: .  s - number of stages, this is the dimension of the matrices below
292: .  A - stage coefficients (dimension s*s, row-major)
293: .  b - step completion table (dimension s; NULL to use last row of A)
294: .  c - abscissa (dimension s; NULL to use row sums of A)
295: .  bembed - completion table for embedded method (dimension s; NULL if not available)
296: .  pinterp - Order of the interpolation scheme, equal to the number of columns of binterp
297: -  binterp - Coefficients of the interpolation formula (dimension s*pinterp; NULL to reuse binterpt)

299:    Notes:
300:    Several RK methods are provided, this function is only needed to create new methods.

302:    Level: advanced

304: .keywords: TS, register

306: .seealso: TSRK
307: @*/
308: PetscErrorCode TSRKRegister(TSRKType name,PetscInt order,PetscInt s,
309:                                  const PetscReal A[],const PetscReal b[],const PetscReal c[],
310:                                  const PetscReal bembed[],
311:                                  PetscInt pinterp,const PetscReal binterp[])
312: {
313:   PetscErrorCode  ierr;
314:   RKTableauLink   link;
315:   RKTableau       t;
316:   PetscInt        i,j;

319:   PetscMalloc(sizeof(*link),&link);
320:   PetscMemzero(link,sizeof(*link));
321:   t        = &link->tab;
322:   PetscStrallocpy(name,&t->name);
323:   t->order = order;
324:   t->s     = s;
325:   PetscMalloc3(s*s,&t->A,s,&t->b,s,&t->c);
326:   PetscMemcpy(t->A,A,s*s*sizeof(A[0]));
327:   if (b)  { PetscMemcpy(t->b,b,s*sizeof(b[0])); }
328:   else for (i=0; i<s; i++) t->b[i] = A[(s-1)*s+i];
329:   if (c)  { PetscMemcpy(t->c,c,s*sizeof(c[0])); }
330:   else for (i=0; i<s; i++) for (j=0,t->c[i]=0; j<s; j++) t->c[i] += A[i*s+j];
331:   t->FSAL = PETSC_TRUE;
332:   for (i=0; i<s; i++) if (t->A[(s-1)*s+i] != t->b[i]) t->FSAL = PETSC_FALSE;
333:   if (bembed) {
334:     PetscMalloc1(s,&t->bembed);
335:     PetscMemcpy(t->bembed,bembed,s*sizeof(bembed[0]));
336:   }

338:   t->pinterp     = pinterp;
339:   PetscMalloc1(s*pinterp,&t->binterp);
340:   PetscMemcpy(t->binterp,binterp,s*pinterp*sizeof(binterp[0]));
341:   link->next     = RKTableauList;
342:   RKTableauList = link;
343:   return(0);
344: }

348: /*
349:  The step completion formula is

351:  x1 = x0 + h b^T YdotRHS

353:  This function can be called before or after ts->vec_sol has been updated.
354:  Suppose we have a completion formula (b) and an embedded formula (be) of different order.
355:  We can write

357:  x1e = x0 + h be^T YdotRHS
358:      = x1 - h b^T YdotRHS + h be^T YdotRHS
359:      = x1 + h (be - b)^T YdotRHS

361:  so we can evaluate the method with different order even after the step has been optimistically completed.
362: */
363: static PetscErrorCode TSEvaluateStep_RK(TS ts,PetscInt order,Vec X,PetscBool *done)
364: {
365:   TS_RK         *rk   = (TS_RK*)ts->data;
366:   RKTableau      tab  = rk->tableau;
367:   PetscScalar   *w    = rk->work;
368:   PetscReal      h;
369:   PetscInt       s    = tab->s,j;

373:   switch (rk->status) {
374:   case TS_STEP_INCOMPLETE:
375:   case TS_STEP_PENDING:
376:     h = ts->time_step; break;
377:   case TS_STEP_COMPLETE:
378:     h = ts->ptime - ts->ptime_prev; break;
379:   default: SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_PLIB,"Invalid TSStepStatus");
380:   }
381:   if (order == tab->order) {
382:     if (rk->status == TS_STEP_INCOMPLETE) {
383:       VecCopy(ts->vec_sol,X);
384:       for (j=0; j<s; j++) w[j] = h*tab->b[j];
385:       VecMAXPY(X,s,w,rk->YdotRHS);
386:     } else {VecCopy(ts->vec_sol,X);}
387:     return(0);
388:   } else if (order == tab->order-1) {
389:     if (!tab->bembed) goto unavailable;
390:     if (rk->status == TS_STEP_INCOMPLETE) { /* Complete with the embedded method (be) */
391:       VecCopy(ts->vec_sol,X);
392:       for (j=0; j<s; j++) w[j] = h*tab->bembed[j];
393:       VecMAXPY(X,s,w,rk->YdotRHS);
394:     } else { /* Rollback and re-complete using (be-b) */
395:       VecCopy(ts->vec_sol,X);
396:       for (j=0; j<s; j++) w[j] = h*(tab->bembed[j] - tab->b[j]);
397:       VecMAXPY(X,s,w,rk->YdotRHS);
398:       if (ts->vec_costintegral && ts->costintegralfwd) {
399:         VecCopy(rk->VecCostIntegral0,ts->vec_costintegral);
400:       }
401:     }
402:     if (done) *done = PETSC_TRUE;
403:     return(0);
404:   }
405: unavailable:
406:   if (done) *done = PETSC_FALSE;
407:   else SETERRQ3(PetscObjectComm((PetscObject)ts),PETSC_ERR_SUP,"RK '%s' of order %D cannot evaluate step at order %D. Consider using -ts_adapt_type none or a different method that has an embedded estimate.",tab->name,tab->order,order);
408:   return(0);
409: }

413: static PetscErrorCode TSForwardCostIntegral_RK(TS ts)
414: {
415:   TS_RK           *rk = (TS_RK*)ts->data;
416:   RKTableau       tab = rk->tableau;
417:   const PetscInt  s = tab->s;
418:   const PetscReal *b = tab->b,*c = tab->c;
419:   Vec             *Y = rk->Y;
420:   PetscInt        i;
421:   PetscErrorCode  ierr;

424:   /* backup cost integral */
425:   VecCopy(ts->vec_costintegral,rk->VecCostIntegral0);
426:   for (i=s-1; i>=0; i--) {
427:     /* Evolve ts->vec_costintegral to compute integrals */
428:     TSAdjointComputeCostIntegrand(ts,rk->ptime+rk->time_step*(1.0-c[i]),Y[i],ts->vec_costintegrand);
429:     VecAXPY(ts->vec_costintegral,rk->time_step*b[i],ts->vec_costintegrand);
430:   }
431:   return(0);
432: }

436: static PetscErrorCode TSAdjointCostIntegral_RK(TS ts)
437: {
438:   TS_RK           *rk = (TS_RK*)ts->data;
439:   RKTableau       tab = rk->tableau;
440:   const PetscInt  s = tab->s;
441:   const PetscReal *b = tab->b,*c = tab->c;
442:   Vec             *Y = rk->Y;
443:   PetscInt        i;
444:   PetscErrorCode  ierr;

447:   for (i=s-1; i>=0; i--) {
448:     /* Evolve ts->vec_costintegral to compute integrals */
449:     TSAdjointComputeCostIntegrand(ts,ts->ptime-ts->time_step*(1.0-c[i]),Y[i],ts->vec_costintegrand);
450:     VecAXPY(ts->vec_costintegral,-ts->time_step*b[i],ts->vec_costintegrand);
451:   }
452:   return(0);
453: }

457: static PetscErrorCode TSRollBack_RK(TS ts)
458: {
459:   TS_RK           *rk = (TS_RK*)ts->data;
460:   RKTableau       tab = rk->tableau;
461:   const PetscInt  s  = tab->s;
462:   const PetscReal *b = tab->b;
463:   PetscScalar     *w = rk->work;
464:   Vec             *YdotRHS = rk->YdotRHS;
465:   PetscInt        j;
466:   PetscReal       h;
467:   PetscErrorCode  ierr;

470:   switch (rk->status) {
471:   case TS_STEP_INCOMPLETE:
472:   case TS_STEP_PENDING:
473:     h = ts->time_step; break;
474:   case TS_STEP_COMPLETE:
475:     h = ts->ptime - ts->ptime_prev; break;
476:   default: SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_PLIB,"Invalid TSStepStatus");
477:   }
478:   for (j=0; j<s; j++) w[j] = -h*b[j];
479:   VecMAXPY(ts->vec_sol,s,w,YdotRHS);
480:   return(0);
481: }

485: static PetscErrorCode TSStep_RK(TS ts)
486: {
487:   TS_RK           *rk   = (TS_RK*)ts->data;
488:   RKTableau        tab  = rk->tableau;
489:   const PetscInt   s = tab->s;
490:   const PetscReal *A = tab->A,*c = tab->c;
491:   PetscScalar     *w = rk->work;
492:   Vec             *Y = rk->Y,*YdotRHS = rk->YdotRHS;
493:   TSAdapt          adapt;
494:   PetscInt         i,j;
495:   PetscInt         rejections = 0;
496:   PetscBool        stageok,accept = PETSC_TRUE;
497:   PetscReal        next_time_step = ts->time_step;
498:   PetscErrorCode   ierr;


502:   rk->status = TS_STEP_INCOMPLETE;
503:   while (!ts->reason && rk->status != TS_STEP_COMPLETE) {
504:     PetscReal t = ts->ptime;
505:     PetscReal h = ts->time_step;
506:     for (i=0; i<s; i++) {
507:       rk->stage_time = t + h*c[i];
508:       TSPreStage(ts,rk->stage_time);
509:       VecCopy(ts->vec_sol,Y[i]);
510:       for (j=0; j<i; j++) w[j] = h*A[i*s+j];
511:       VecMAXPY(Y[i],i,w,YdotRHS);
512:       TSPostStage(ts,rk->stage_time,i,Y);
513:       TSGetAdapt(ts,&adapt);
514:       TSAdaptCheckStage(adapt,ts,rk->stage_time,Y[i],&stageok);
515:       if (!stageok) goto reject_step;
516:       TSComputeRHSFunction(ts,t+h*c[i],Y[i],YdotRHS[i]);
517:     }

519:     rk->status = TS_STEP_INCOMPLETE;
520:     TSEvaluateStep(ts,tab->order,ts->vec_sol,NULL);
521:     rk->status = TS_STEP_PENDING;
522:     TSGetAdapt(ts,&adapt);
523:     TSAdaptCandidatesClear(adapt);
524:     TSAdaptCandidateAdd(adapt,tab->name,tab->order,1,tab->ccfl,1.*tab->s,PETSC_TRUE);
525:     TSAdaptChoose(adapt,ts,ts->time_step,NULL,&next_time_step,&accept);
526:     rk->status = accept ? TS_STEP_COMPLETE : TS_STEP_INCOMPLETE;
527:     if (!accept) { /* Roll back the current step */
528:       TSRollBack_RK(ts);
529:       ts->time_step = next_time_step;
530:       goto reject_step;
531:     }

533:     if (ts->costintegralfwd) { /* Save the info for the later use in cost integral evaluation*/
534:       rk->ptime     = ts->ptime;
535:       rk->time_step = ts->time_step;
536:     }

538:     ts->ptime += ts->time_step;
539:     ts->time_step = next_time_step;
540:     break;

542:   reject_step:
543:     ts->reject++; accept = PETSC_FALSE;
544:     if (!ts->reason && ++rejections > ts->max_reject && ts->max_reject >= 0) {
545:       ts->reason = TS_DIVERGED_STEP_REJECTED;
546:       PetscInfo2(ts,"Step=%D, step rejections %D greater than current TS allowed, stopping solve\n",ts->steps,rejections);
547:     }
548:   }
549:   return(0);
550: }

554: static PetscErrorCode TSAdjointSetUp_RK(TS ts)
555: {
556:   TS_RK         *rk  = (TS_RK*)ts->data;
557:   RKTableau      tab = rk->tableau;
558:   PetscInt       s   = tab->s;

562:   if (ts->adjointsetupcalled++) return(0);
563:   VecDuplicateVecs(ts->vecs_sensi[0],s*ts->numcost,&rk->VecDeltaLam);
564:   if(ts->vecs_sensip) {
565:     VecDuplicateVecs(ts->vecs_sensip[0],s*ts->numcost,&rk->VecDeltaMu);
566:   }
567:   VecDuplicateVecs(ts->vecs_sensi[0],ts->numcost,&rk->VecSensiTemp);
568:   return(0);
569: }

573: static PetscErrorCode TSAdjointStep_RK(TS ts)
574: {
575:   TS_RK           *rk   = (TS_RK*)ts->data;
576:   RKTableau        tab  = rk->tableau;
577:   const PetscInt   s    = tab->s;
578:   const PetscReal *A = tab->A,*b = tab->b,*c = tab->c;
579:   PetscScalar     *w    = rk->work;
580:   Vec             *Y    = rk->Y,*VecDeltaLam = rk->VecDeltaLam,*VecDeltaMu = rk->VecDeltaMu,*VecSensiTemp = rk->VecSensiTemp;
581:   PetscInt         i,j,nadj;
582:   PetscReal        t = ts->ptime;
583:   PetscErrorCode   ierr;
584:   PetscReal        h = ts->time_step;
585:   Mat              J,Jp;

588:   rk->status = TS_STEP_INCOMPLETE;
589:   for (i=s-1; i>=0; i--) {
590:     rk->stage_time = t + h*(1.0-c[i]);
591:     for (nadj=0; nadj<ts->numcost; nadj++) {
592:       VecCopy(ts->vecs_sensi[nadj],VecSensiTemp[nadj]);
593:       VecScale(VecSensiTemp[nadj],-h*b[i]);
594:       for (j=i+1; j<s; j++) {
595:         VecAXPY(VecSensiTemp[nadj],-h*A[j*s+i],VecDeltaLam[nadj*s+j]);
596:       }
597:     }
598:     /* Stage values of lambda */
599:     TSGetRHSJacobian(ts,&J,&Jp,NULL,NULL);
600:     TSComputeRHSJacobian(ts,rk->stage_time,Y[i],J,Jp);
601:     if (ts->vec_costintegral) {
602:       TSAdjointComputeDRDYFunction(ts,rk->stage_time,Y[i],ts->vecs_drdy);
603:     }
604:     for (nadj=0; nadj<ts->numcost; nadj++) {
605:       MatMultTranspose(J,VecSensiTemp[nadj],VecDeltaLam[nadj*s+i]);
606:       if (ts->vec_costintegral) {
607:         VecAXPY(VecDeltaLam[nadj*s+i],-h*b[i],ts->vecs_drdy[nadj]);
608:       }
609:     }

611:     /* Stage values of mu */
612:     if(ts->vecs_sensip) {
613:       TSAdjointComputeRHSJacobian(ts,rk->stage_time,Y[i],ts->Jacp);
614:       if (ts->vec_costintegral) {
615:         TSAdjointComputeDRDPFunction(ts,rk->stage_time,Y[i],ts->vecs_drdp);
616:       }

618:       for (nadj=0; nadj<ts->numcost; nadj++) {
619:         MatMultTranspose(ts->Jacp,VecSensiTemp[nadj],VecDeltaMu[nadj*s+i]);
620:         if (ts->vec_costintegral) {
621:           VecAXPY(VecDeltaMu[nadj*s+i],-h*b[i],ts->vecs_drdp[nadj]);
622:         }
623:       }
624:     }
625:   }

627:   for (j=0; j<s; j++) w[j] = 1.0;
628:   for (nadj=0; nadj<ts->numcost; nadj++) {
629:     VecMAXPY(ts->vecs_sensi[nadj],s,w,&VecDeltaLam[nadj*s]);
630:     if(ts->vecs_sensip) {
631:       VecMAXPY(ts->vecs_sensip[nadj],s,w,&VecDeltaMu[nadj*s]);
632:     }
633:   }
634:   rk->status = TS_STEP_COMPLETE;
635:   return(0);
636: }

640: static PetscErrorCode TSInterpolate_RK(TS ts,PetscReal itime,Vec X)
641: {
642:   TS_RK           *rk = (TS_RK*)ts->data;
643:   PetscInt         s  = rk->tableau->s,pinterp = rk->tableau->pinterp,i,j;
644:   PetscReal        h;
645:   PetscReal        tt,t;
646:   PetscScalar     *b;
647:   const PetscReal *B = rk->tableau->binterp;
648:   PetscErrorCode   ierr;

651:   if (!B) SETERRQ1(PetscObjectComm((PetscObject)ts),PETSC_ERR_SUP,"TSRK %s does not have an interpolation formula",rk->tableau->name);

653:   switch (rk->status) {
654:   case TS_STEP_INCOMPLETE:
655:   case TS_STEP_PENDING:
656:     h = ts->time_step;
657:     t = (itime - ts->ptime)/h;
658:     break;
659:   case TS_STEP_COMPLETE:
660:     h = ts->ptime - ts->ptime_prev;
661:     t = (itime - ts->ptime)/h + 1; /* In the interval [0,1] */
662:     break;
663:   default: SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_PLIB,"Invalid TSStepStatus");
664:   }
665:   PetscMalloc1(s,&b);
666:   for (i=0; i<s; i++) b[i] = 0;
667:   for (j=0,tt=t; j<pinterp; j++,tt*=t) {
668:     for (i=0; i<s; i++) {
669:       b[i]  += h * B[i*pinterp+j] * tt;
670:     }
671:   }

673:   VecCopy(rk->Y[0],X);
674:   VecMAXPY(X,s,b,rk->YdotRHS);

676:   PetscFree(b);
677:   return(0);
678: }

680: /*------------------------------------------------------------*/

684: static PetscErrorCode TSRKTableauReset(TS ts)
685: {
686:   TS_RK          *rk = (TS_RK*)ts->data;
687:   RKTableau      tab = rk->tableau;

691:   if (!tab) return(0);
692:   PetscFree(rk->work);
693:   VecDestroyVecs(tab->s,&rk->Y);
694:   VecDestroyVecs(tab->s,&rk->YdotRHS);
695:   VecDestroyVecs(tab->s*ts->numcost,&rk->VecDeltaLam);
696:   VecDestroyVecs(tab->s*ts->numcost,&rk->VecDeltaMu);
697:   return(0);
698: }

702: static PetscErrorCode TSReset_RK(TS ts)
703: {
704:   TS_RK         *rk = (TS_RK*)ts->data;

708:   TSRKTableauReset(ts);
709:   VecDestroy(&rk->VecCostIntegral0);
710:   VecDestroyVecs(ts->numcost,&rk->VecSensiTemp);
711:   return(0);
712: }

716: static PetscErrorCode TSDestroy_RK(TS ts)
717: {

721:   TSReset_RK(ts);
722:   PetscFree(ts->data);
723:   PetscObjectComposeFunction((PetscObject)ts,"TSRKGetType_C",NULL);
724:   PetscObjectComposeFunction((PetscObject)ts,"TSRKSetType_C",NULL);
725:   return(0);
726: }


731: static PetscErrorCode DMCoarsenHook_TSRK(DM fine,DM coarse,void *ctx)
732: {
734:   return(0);
735: }

739: static PetscErrorCode DMRestrictHook_TSRK(DM fine,Mat restrct,Vec rscale,Mat inject,DM coarse,void *ctx)
740: {
742:   return(0);
743: }


748: static PetscErrorCode DMSubDomainHook_TSRK(DM dm,DM subdm,void *ctx)
749: {
751:   return(0);
752: }

756: static PetscErrorCode DMSubDomainRestrictHook_TSRK(DM dm,VecScatter gscat,VecScatter lscat,DM subdm,void *ctx)
757: {

760:   return(0);
761: }
762: /*
765: static PetscErrorCode RKSetAdjCoe(RKTableau tab)
766: {
767:   PetscReal *A,*b;
768:   PetscInt        s,i,j;
769:   PetscErrorCode  ierr;

772:   s    = tab->s;
773:   PetscMalloc2(s*s,&A,s,&b);

775:   for (i=0; i<s; i++)
776:     for (j=0; j<s; j++) {
777:       A[i*s+j] = (tab->b[s-1-i]==0) ? 0: -tab->A[s-1-i+(s-1-j)*s] * tab->b[s-1-j] / tab->b[s-1-i];
778:       PetscPrintf(PETSC_COMM_WORLD,"Coefficients: A[%D][%D]=%.6f\n",i,j,A[i*s+j]);
779:     }

781:   for (i=0; i<s; i++) b[i] = (tab->b[s-1-i]==0)? 0: -tab->b[s-1-i];

783:   PetscMemcpy(tab->A,A,s*s*sizeof(A[0]));
784:   PetscMemcpy(tab->b,b,s*sizeof(b[0]));
785:   PetscFree2(A,b);
786:   return(0);
787: }
788: */

792: static PetscErrorCode TSRKTableauSetUp(TS ts)
793: {
794:   TS_RK         *rk  = (TS_RK*)ts->data;
795:   RKTableau      tab = rk->tableau;

799:   PetscMalloc1(tab->s,&rk->work);
800:   VecDuplicateVecs(ts->vec_sol,tab->s,&rk->Y);
801:   VecDuplicateVecs(ts->vec_sol,tab->s,&rk->YdotRHS);
802:   return(0);
803: }


808: static PetscErrorCode TSSetUp_RK(TS ts)
809: {
810:   TS_RK         *rk = (TS_RK*)ts->data;
812:   DM             dm;

815:   TSRKTableauSetUp(ts);
816:   if (!rk->VecCostIntegral0 && ts->vec_costintegral && ts->costintegralfwd) { /* back up cost integral */
817:     VecDuplicate(ts->vec_costintegral,&rk->VecCostIntegral0);
818:   }
819:   TSGetDM(ts,&dm);
820:   if (dm) {
821:     DMCoarsenHookAdd(dm,DMCoarsenHook_TSRK,DMRestrictHook_TSRK,ts);
822:     DMSubDomainHookAdd(dm,DMSubDomainHook_TSRK,DMSubDomainRestrictHook_TSRK,ts);
823:   }
824:   return(0);
825: }


828: /*------------------------------------------------------------*/

832: static PetscErrorCode TSSetFromOptions_RK(PetscOptionItems *PetscOptionsObject,TS ts)
833: {
834:   TS_RK         *rk = (TS_RK*)ts->data;

838:   PetscOptionsHead(PetscOptionsObject,"RK ODE solver options");
839:   {
840:     RKTableauLink  link;
841:     PetscInt       count,choice;
842:     PetscBool      flg;
843:     const char   **namelist;
844:     for (link=RKTableauList,count=0; link; link=link->next,count++) ;
845:     PetscMalloc1(count,&namelist);
846:     for (link=RKTableauList,count=0; link; link=link->next,count++) namelist[count] = link->tab.name;
847:     PetscOptionsEList("-ts_rk_type","Family of RK method","TSRKSetType",(const char*const*)namelist,count,rk->tableau->name,&choice,&flg);
848:     if (flg) {TSRKSetType(ts,namelist[choice]);}
849:     PetscFree(namelist);
850:   }
851:   PetscOptionsTail();
852:   return(0);
853: }

857: static PetscErrorCode PetscFormatRealArray(char buf[],size_t len,const char *fmt,PetscInt n,const PetscReal x[])
858: {
860:   PetscInt       i;
861:   size_t         left,count;
862:   char           *p;

865:   for (i=0,p=buf,left=len; i<n; i++) {
866:     PetscSNPrintfCount(p,left,fmt,&count,x[i]);
867:     if (count >= left) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Insufficient space in buffer");
868:     left -= count;
869:     p    += count;
870:     *p++  = ' ';
871:   }
872:   p[i ? 0 : -1] = 0;
873:   return(0);
874: }

878: static PetscErrorCode TSView_RK(TS ts,PetscViewer viewer)
879: {
880:   TS_RK          *rk = (TS_RK*)ts->data;
881:   PetscBool      iascii;

885:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);
886:   if (iascii) {
887:     RKTableau tab  = rk->tableau;
888:     TSRKType  rktype;
889:     char      buf[512];
890:     TSRKGetType(ts,&rktype);
891:     PetscViewerASCIIPrintf(viewer,"  RK %s\n",rktype);
892:     PetscFormatRealArray(buf,sizeof(buf),"% 8.6f",tab->s,tab->c);
893:     PetscViewerASCIIPrintf(viewer,"  Abscissa     c = %s\n",buf);
894:     PetscViewerASCIIPrintf(viewer,"FSAL: %s\n",tab->FSAL ? "yes" : "no");
895:   }
896:   if (ts->adapt) {TSAdaptView(ts->adapt,viewer);}
897:   return(0);
898: }

902: static PetscErrorCode TSLoad_RK(TS ts,PetscViewer viewer)
903: {
905:   TSAdapt        adapt;

908:   TSGetAdapt(ts,&adapt);
909:   TSAdaptLoad(adapt,viewer);
910:   return(0);
911: }

915: /*@C
916:   TSRKSetType - Set the type of RK scheme

918:   Logically collective

920:   Input Parameter:
921: +  ts - timestepping context
922: -  rktype - type of RK-scheme

924:   Level: intermediate

926: .seealso: TSRKGetType(), TSRK, TSRK2, TSRK3, TSRKPRSSP2, TSRK4, TSRK5
927: @*/
928: PetscErrorCode TSRKSetType(TS ts,TSRKType rktype)
929: {

934:   PetscTryMethod(ts,"TSRKSetType_C",(TS,TSRKType),(ts,rktype));
935:   return(0);
936: }

940: /*@C
941:   TSRKGetType - Get the type of RK scheme

943:   Logically collective

945:   Input Parameter:
946: .  ts - timestepping context

948:   Output Parameter:
949: .  rktype - type of RK-scheme

951:   Level: intermediate

953: .seealso: TSRKGetType()
954: @*/
955: PetscErrorCode TSRKGetType(TS ts,TSRKType *rktype)
956: {

961:   PetscUseMethod(ts,"TSRKGetType_C",(TS,TSRKType*),(ts,rktype));
962:   return(0);
963: }

967: static PetscErrorCode TSRKGetType_RK(TS ts,TSRKType *rktype)
968: {
969:   TS_RK *rk = (TS_RK*)ts->data;

972:   *rktype = rk->tableau->name;
973:   return(0);
974: }
977: static PetscErrorCode TSRKSetType_RK(TS ts,TSRKType rktype)
978: {
979:   TS_RK          *rk = (TS_RK*)ts->data;
981:   PetscBool      match;
982:   RKTableauLink  link;

985:   if (rk->tableau) {
986:     PetscStrcmp(rk->tableau->name,rktype,&match);
987:     if (match) return(0);
988:   }
989:   for (link = RKTableauList; link; link=link->next) {
990:     PetscStrcmp(link->tab.name,rktype,&match);
991:     if (match) {
992:       if (ts->setupcalled) {TSRKTableauReset(ts);}
993:       rk->tableau = &link->tab;
994:       if (ts->setupcalled) {TSRKTableauSetUp(ts);}
995:       return(0);
996:     }
997:   }
998:   SETERRQ1(PetscObjectComm((PetscObject)ts),PETSC_ERR_ARG_UNKNOWN_TYPE,"Could not find '%s'",rktype);
999:   return(0);
1000: }

1004: static PetscErrorCode  TSGetStages_RK(TS ts,PetscInt *ns,Vec **Y)
1005: {
1006:   TS_RK          *rk = (TS_RK*)ts->data;

1009:   *ns = rk->tableau->s;
1010:   if(Y) *Y  = rk->Y;
1011:   return(0);
1012: }


1015: /* ------------------------------------------------------------ */
1016: /*MC
1017:       TSRK - ODE and DAE solver using Runge-Kutta schemes

1019:   The user should provide the right hand side of the equation
1020:   using TSSetRHSFunction().

1022:   Notes:
1023:   The default is TSRK3, it can be changed with TSRKSetType() or -ts_rk_type

1025:   Level: beginner

1027: .seealso:  TSCreate(), TS, TSSetType(), TSRKSetType(), TSRKGetType(), TSRKSetFullyImplicit(), TSRK2D, TTSRK2E, TSRK3,
1028:            TSRK4, TSRK5, TSRKPRSSP2, TSRKBPR3, TSRKType, TSRKRegister()

1030: M*/
1033: PETSC_EXTERN PetscErrorCode TSCreate_RK(TS ts)
1034: {
1035:   TS_RK          *rk;

1039:   TSRKInitializePackage();

1041:   ts->ops->reset          = TSReset_RK;
1042:   ts->ops->destroy        = TSDestroy_RK;
1043:   ts->ops->view           = TSView_RK;
1044:   ts->ops->load           = TSLoad_RK;
1045:   ts->ops->setup          = TSSetUp_RK;
1046:   ts->ops->adjointsetup   = TSAdjointSetUp_RK;
1047:   ts->ops->step           = TSStep_RK;
1048:   ts->ops->interpolate    = TSInterpolate_RK;
1049:   ts->ops->evaluatestep   = TSEvaluateStep_RK;
1050:   ts->ops->rollback       = TSRollBack_RK;
1051:   ts->ops->setfromoptions = TSSetFromOptions_RK;
1052:   ts->ops->getstages      = TSGetStages_RK;
1053:   ts->ops->adjointstep    = TSAdjointStep_RK;

1055:   ts->ops->adjointintegral = TSAdjointCostIntegral_RK;
1056:   ts->ops->forwardintegral = TSForwardCostIntegral_RK;

1058:   PetscNewLog(ts,&rk);
1059:   ts->data = (void*)rk;

1061:   PetscObjectComposeFunction((PetscObject)ts,"TSRKGetType_C",TSRKGetType_RK);
1062:   PetscObjectComposeFunction((PetscObject)ts,"TSRKSetType_C",TSRKSetType_RK);

1064:   TSRKSetType(ts,TSRKDefault);
1065:   return(0);
1066: }