Actual source code: rk.c

petsc-3.8.2 2017-11-09
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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>
 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:   PetscInt   p;                   /* Interpolation order                                        */
 23:   PetscBool  FSAL;                /* flag to indicate if tableau is FSAL                        */
 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:      TSRK1FE - First order forward Euler scheme.

 54:      This method has one stage.

 56:      Options database:
 57: .     -ts_rk_type 1fe

 59:      Level: advanced

 61: .seealso: TSRK, TSRKType, TSRKSetType()
 62: M*/
 63: /*MC
 64:      TSRK2A - Second order RK scheme.

 66:      This method has two stages.

 68:      Options database:
 69: .     -ts_rk_type 2a

 71:      Level: advanced

 73: .seealso: TSRK, TSRKType, TSRKSetType()
 74: M*/
 75: /*MC
 76:      TSRK3 - Third order RK scheme.

 78:      This method has three stages.

 80:      Options database:
 81: .     -ts_rk_type 3

 83:      Level: advanced

 85: .seealso: TSRK, TSRKType, TSRKSetType()
 86: M*/
 87: /*MC
 88:      TSRK3BS - Third order RK scheme of Bogacki-Shampine with 2nd order embedded method.

 90:      This method has four stages with the First Same As Last (FSAL) property.

 92:      Options database:
 93: .     -ts_rk_type 3bs

 95:      Level: advanced

 97:      References: https://doi.org/10.1016/0893-9659(89)90079-7

 99: .seealso: TSRK, TSRKType, TSRKSetType()
100: M*/
101: /*MC
102:      TSRK4 - Fourth order RK scheme.

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

106:      Options database:
107: .     -ts_rk_type 4

109:      Level: advanced

111: .seealso: TSRK, TSRKType, TSRKSetType()
112: M*/
113: /*MC
114:      TSRK5F - Fifth order Fehlberg RK scheme with a 4th order embedded method.

116:      This method has six stages.

118:      Options database:
119: .     -ts_rk_type 5f

121:      Level: advanced

123: .seealso: TSRK, TSRKType, TSRKSetType()
124: M*/
125: /*MC
126:      TSRK5DP - Fifth order Dormand-Prince RK scheme with the 4th order embedded method.

128:      This method has seven stages with the First Same As Last (FSAL) property.

130:      Options database:
131: .     -ts_rk_type 5dp

133:      Level: advanced

135:      References: https://doi.org/10.1016/0771-050X(80)90013-3

137: .seealso: TSRK, TSRKType, TSRKSetType()
138: M*/
139: /*MC
140:      TSRK5BS - Fifth order Bogacki-Shampine RK scheme with 4th order embedded method.

142:      This method has eight stages with the First Same As Last (FSAL) property.

144:      Options database:
145: .     -ts_rk_type 5bs

147:      Level: advanced

149:      References: https://doi.org/10.1016/0898-1221(96)00141-1

151: .seealso: TSRK, TSRKType, TSRKSetType()
152: M*/

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

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

159:   Level: advanced

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

163: .seealso:  TSRKRegisterDestroy()
164: @*/
165: PetscErrorCode TSRKRegisterAll(void)
166: {

170:   if (TSRKRegisterAllCalled) return(0);
171:   TSRKRegisterAllCalled = PETSC_TRUE;

173: #define RC PetscRealConstant
174:   {
175:     const PetscReal
176:       A[1][1] = {{0}},
177:       b[1]    = {RC(1.0)};
178:     TSRKRegister(TSRK1FE,1,1,&A[0][0],b,NULL,NULL,0,NULL);
179:   }
180:   {
181:     const PetscReal
182:       A[2][2]   = {{0,0},
183:                    {RC(1.0),0}},
184:       b[2]      =  {RC(0.5),RC(0.5)},
185:       bembed[2] =  {RC(1.0),0};
186:     TSRKRegister(TSRK2A,2,2,&A[0][0],b,NULL,bembed,0,NULL);
187:   }
188:   {
189:     const PetscReal
190:       A[3][3] = {{0,0,0},
191:                  {RC(2.0)/RC(3.0),0,0},
192:                  {RC(-1.0)/RC(3.0),RC(1.0),0}},
193:       b[3]    =  {RC(0.25),RC(0.5),RC(0.25)};
194:     TSRKRegister(TSRK3,3,3,&A[0][0],b,NULL,NULL,0,NULL);
195:   }
196:   {
197:     const PetscReal
198:       A[4][4]   = {{0,0,0,0},
199:                    {RC(1.0)/RC(2.0),0,0,0},
200:                    {0,RC(3.0)/RC(4.0),0,0},
201:                    {RC(2.0)/RC(9.0),RC(1.0)/RC(3.0),RC(4.0)/RC(9.0),0}},
202:       b[4]      =  {RC(2.0)/RC(9.0),RC(1.0)/RC(3.0),RC(4.0)/RC(9.0),0},
203:       bembed[4] =  {RC(7.0)/RC(24.0),RC(1.0)/RC(4.0),RC(1.0)/RC(3.0),RC(1.0)/RC(8.0)};
204:     TSRKRegister(TSRK3BS,3,4,&A[0][0],b,NULL,bembed,0,NULL);
205:   }
206:   {
207:     const PetscReal
208:       A[4][4] = {{0,0,0,0},
209:                  {RC(0.5),0,0,0},
210:                  {0,RC(0.5),0,0},
211:                  {0,0,RC(1.0),0}},
212:       b[4]    =  {RC(1.0)/RC(6.0),RC(1.0)/RC(3.0),RC(1.0)/RC(3.0),RC(1.0)/RC(6.0)};
213:     TSRKRegister(TSRK4,4,4,&A[0][0],b,NULL,NULL,0,NULL);
214:   }
215:   {
216:     const PetscReal
217:       A[6][6]   = {{0,0,0,0,0,0},
218:                    {RC(0.25),0,0,0,0,0},
219:                    {RC(3.0)/RC(32.0),RC(9.0)/RC(32.0),0,0,0,0},
220:                    {RC(1932.0)/RC(2197.0),RC(-7200.0)/RC(2197.0),RC(7296.0)/RC(2197.0),0,0,0},
221:                    {RC(439.0)/RC(216.0),RC(-8.0),RC(3680.0)/RC(513.0),RC(-845.0)/RC(4104.0),0,0},
222:                    {RC(-8.0)/RC(27.0),RC(2.0),RC(-3544.0)/RC(2565.0),RC(1859.0)/RC(4104.0),RC(-11.0)/RC(40.0),0}},
223:       b[6]      =  {RC(16.0)/RC(135.0),0,RC(6656.0)/RC(12825.0),RC(28561.0)/RC(56430.0),RC(-9.0)/RC(50.0),RC(2.0)/RC(55.0)},
224:       bembed[6] =  {RC(25.0)/RC(216.0),0,RC(1408.0)/RC(2565.0),RC(2197.0)/RC(4104.0),RC(-1.0)/RC(5.0),0};
225:     TSRKRegister(TSRK5F,5,6,&A[0][0],b,NULL,bembed,0,NULL);
226:   }
227:   {
228:     const PetscReal
229:       A[7][7]   = {{0,0,0,0,0,0,0},
230:                    {RC(1.0)/RC(5.0),0,0,0,0,0,0},
231:                    {RC(3.0)/RC(40.0),RC(9.0)/RC(40.0),0,0,0,0,0},
232:                    {RC(44.0)/RC(45.0),RC(-56.0)/RC(15.0),RC(32.0)/RC(9.0),0,0,0,0},
233:                    {RC(19372.0)/RC(6561.0),RC(-25360.0)/RC(2187.0),RC(64448.0)/RC(6561.0),RC(-212.0)/RC(729.0),0,0,0},
234:                    {RC(9017.0)/RC(3168.0),RC(-355.0)/RC(33.0),RC(46732.0)/RC(5247.0),RC(49.0)/RC(176.0),RC(-5103.0)/RC(18656.0),0,0},
235:                    {RC(35.0)/RC(384.0),0,RC(500.0)/RC(1113.0),RC(125.0)/RC(192.0),RC(-2187.0)/RC(6784.0),RC(11.0)/RC(84.0),0}},
236:       b[7]      =  {RC(35.0)/RC(384.0),0,RC(500.0)/RC(1113.0),RC(125.0)/RC(192.0),RC(-2187.0)/RC(6784.0),RC(11.0)/RC(84.0),0},
237:       bembed[7] =  {RC(5179.0)/RC(57600.0),0,RC(7571.0)/RC(16695.0),RC(393.0)/RC(640.0),RC(-92097.0)/RC(339200.0),RC(187.0)/RC(2100.0),RC(1.0)/RC(40.0)};
238:     TSRKRegister(TSRK5DP,5,7,&A[0][0],b,NULL,bembed,0,NULL);
239:   }
240:   {
241:     const PetscReal
242:       A[8][8]   = {{0,0,0,0,0,0,0,0},
243:                    {RC(1.0)/RC(6.0),0,0,0,0,0,0,0},
244:                    {RC(2.0)/RC(27.0),RC(4.0)/RC(27.0),0,0,0,0,0,0},
245:                    {RC(183.0)/RC(1372.0),RC(-162.0)/RC(343.0),RC(1053.0)/RC(1372.0),0,0,0,0,0},
246:                    {RC(68.0)/RC(297.0),RC(-4.0)/RC(11.0),RC(42.0)/RC(143.0),RC(1960.0)/RC(3861.0),0,0,0,0},
247:                    {RC(597.0)/RC(22528.0),RC(81.0)/RC(352.0),RC(63099.0)/RC(585728.0),RC(58653.0)/RC(366080.0),RC(4617.0)/RC(20480.0),0,0,0},
248:                    {RC(174197.0)/RC(959244.0),RC(-30942.0)/RC(79937.0),RC(8152137.0)/RC(19744439.0),RC(666106.0)/RC(1039181.0),RC(-29421.0)/RC(29068.0),RC(482048.0)/RC(414219.0),0,0},
249:                    {RC(587.0)/RC(8064.0),0,RC(4440339.0)/RC(15491840.0),RC(24353.0)/RC(124800.0),RC(387.0)/RC(44800.0),RC(2152.0)/RC(5985.0),RC(7267.0)/RC(94080.0),0}},
250:       b[8]      =  {RC(587.0)/RC(8064.0),0,RC(4440339.0)/RC(15491840.0),RC(24353.0)/RC(124800.0),RC(387.0)/RC(44800.0),RC(2152.0)/RC(5985.0),RC(7267.0)/RC(94080.0),0},
251:       bembed[8] =  {RC(2479.0)/RC(34992.0),0,RC(123.0)/RC(416.0),RC(612941.0)/RC(3411720.0),RC(43.0)/RC(1440.0),RC(2272.0)/RC(6561.0),RC(79937.0)/RC(1113912.0),RC(3293.0)/RC(556956.0)};
252:     TSRKRegister(TSRK5BS,5,8,&A[0][0],b,NULL,bembed,0,NULL);
253:   }
254: #undef RC
255:   return(0);
256: }

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

261:    Not Collective

263:    Level: advanced

265: .keywords: TSRK, register, destroy
266: .seealso: TSRKRegister(), TSRKRegisterAll()
267: @*/
268: PetscErrorCode TSRKRegisterDestroy(void)
269: {
271:   RKTableauLink link;

274:   while ((link = RKTableauList)) {
275:     RKTableau t = &link->tab;
276:     RKTableauList = link->next;
277:     PetscFree3(t->A,t->b,t->c);
278:     PetscFree (t->bembed);
279:     PetscFree (t->binterp);
280:     PetscFree (t->name);
281:     PetscFree (link);
282:   }
283:   TSRKRegisterAllCalled = PETSC_FALSE;
284:   return(0);
285: }

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

292:   Level: developer

294: .keywords: TS, TSRK, initialize, package
295: .seealso: PetscInitialize()
296: @*/
297: PetscErrorCode TSRKInitializePackage(void)
298: {

302:   if (TSRKPackageInitialized) return(0);
303:   TSRKPackageInitialized = PETSC_TRUE;
304:   TSRKRegisterAll();
305:   PetscRegisterFinalize(TSRKFinalizePackage);
306:   return(0);
307: }

309: /*@C
310:   TSRKFinalizePackage - This function destroys everything in the TSRK package. It is
311:   called from PetscFinalize().

313:   Level: developer

315: .keywords: Petsc, destroy, package
316: .seealso: PetscFinalize()
317: @*/
318: PetscErrorCode TSRKFinalizePackage(void)
319: {

323:   TSRKPackageInitialized = PETSC_FALSE;
324:   TSRKRegisterDestroy();
325:   return(0);
326: }

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

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

333:    Input Parameters:
334: +  name - identifier for method
335: .  order - approximation order of method
336: .  s - number of stages, this is the dimension of the matrices below
337: .  A - stage coefficients (dimension s*s, row-major)
338: .  b - step completion table (dimension s; NULL to use last row of A)
339: .  c - abscissa (dimension s; NULL to use row sums of A)
340: .  bembed - completion table for embedded method (dimension s; NULL if not available)
341: .  p - Order of the interpolation scheme, equal to the number of columns of binterp
342: -  binterp - Coefficients of the interpolation formula (dimension s*p; NULL to reuse b with p=1)

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

347:    Level: advanced

349: .keywords: TS, register

351: .seealso: TSRK
352: @*/
353: PetscErrorCode TSRKRegister(TSRKType name,PetscInt order,PetscInt s,
354:                             const PetscReal A[],const PetscReal b[],const PetscReal c[],
355:                             const PetscReal bembed[],PetscInt p,const PetscReal binterp[])
356: {
357:   PetscErrorCode  ierr;
358:   RKTableauLink   link;
359:   RKTableau       t;
360:   PetscInt        i,j;


370:   PetscNew(&link);
371:   t = &link->tab;

373:   PetscStrallocpy(name,&t->name);
374:   t->order = order;
375:   t->s = s;
376:   PetscMalloc3(s*s,&t->A,s,&t->b,s,&t->c);
377:   PetscMemcpy(t->A,A,s*s*sizeof(A[0]));
378:   if (b)  { PetscMemcpy(t->b,b,s*sizeof(b[0])); }
379:   else for (i=0; i<s; i++) t->b[i] = A[(s-1)*s+i];
380:   if (c)  { PetscMemcpy(t->c,c,s*sizeof(c[0])); }
381:   else for (i=0; i<s; i++) for (j=0,t->c[i]=0; j<s; j++) t->c[i] += A[i*s+j];
382:   t->FSAL = PETSC_TRUE;
383:   for (i=0; i<s; i++) if (t->A[(s-1)*s+i] != t->b[i]) t->FSAL = PETSC_FALSE;

385:   if (bembed) {
386:     PetscMalloc1(s,&t->bembed);
387:     PetscMemcpy(t->bembed,bembed,s*sizeof(bembed[0]));
388:   }

390:   if (!binterp) { p = 1; binterp = t->b; }
391:   t->p = p;
392:   PetscMalloc1(s*p,&t->binterp);
393:   PetscMemcpy(t->binterp,binterp,s*p*sizeof(binterp[0]));

395:   link->next = RKTableauList;
396:   RKTableauList = link;
397:   return(0);
398: }

400: /*
401:  The step completion formula is

403:  x1 = x0 + h b^T YdotRHS

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

409:  x1e = x0 + h be^T YdotRHS
410:      = x1 - h b^T YdotRHS + h be^T YdotRHS
411:      = x1 + h (be - b)^T YdotRHS

413:  so we can evaluate the method with different order even after the step has been optimistically completed.
414: */
415: static PetscErrorCode TSEvaluateStep_RK(TS ts,PetscInt order,Vec X,PetscBool *done)
416: {
417:   TS_RK         *rk   = (TS_RK*)ts->data;
418:   RKTableau      tab  = rk->tableau;
419:   PetscScalar   *w    = rk->work;
420:   PetscReal      h;
421:   PetscInt       s    = tab->s,j;

425:   switch (rk->status) {
426:   case TS_STEP_INCOMPLETE:
427:   case TS_STEP_PENDING:
428:     h = ts->time_step; break;
429:   case TS_STEP_COMPLETE:
430:     h = ts->ptime - ts->ptime_prev; break;
431:   default: SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_PLIB,"Invalid TSStepStatus");
432:   }
433:   if (order == tab->order) {
434:     if (rk->status == TS_STEP_INCOMPLETE) {
435:       VecCopy(ts->vec_sol,X);
436:       for (j=0; j<s; j++) w[j] = h*tab->b[j];
437:       VecMAXPY(X,s,w,rk->YdotRHS);
438:     } else {VecCopy(ts->vec_sol,X);}
439:     return(0);
440:   } else if (order == tab->order-1) {
441:     if (!tab->bembed) goto unavailable;
442:     if (rk->status == TS_STEP_INCOMPLETE) { /* Complete with the embedded method (be) */
443:       VecCopy(ts->vec_sol,X);
444:       for (j=0; j<s; j++) w[j] = h*tab->bembed[j];
445:       VecMAXPY(X,s,w,rk->YdotRHS);
446:     } else { /* Rollback and re-complete using (be-b) */
447:       VecCopy(ts->vec_sol,X);
448:       for (j=0; j<s; j++) w[j] = h*(tab->bembed[j] - tab->b[j]);
449:       VecMAXPY(X,s,w,rk->YdotRHS);
450:       if (ts->vec_costintegral && ts->costintegralfwd) {
451:         VecCopy(rk->VecCostIntegral0,ts->vec_costintegral);
452:       }
453:     }
454:     if (done) *done = PETSC_TRUE;
455:     return(0);
456:   }
457: unavailable:
458:   if (done) *done = PETSC_FALSE;
459:   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);
460:   return(0);
461: }

463: static PetscErrorCode TSForwardCostIntegral_RK(TS ts)
464: {
465:   TS_RK           *rk = (TS_RK*)ts->data;
466:   RKTableau       tab = rk->tableau;
467:   const PetscInt  s = tab->s;
468:   const PetscReal *b = tab->b,*c = tab->c;
469:   Vec             *Y = rk->Y;
470:   PetscInt        i;
471:   PetscErrorCode  ierr;

474:   /* backup cost integral */
475:   VecCopy(ts->vec_costintegral,rk->VecCostIntegral0);
476:   for (i=s-1; i>=0; i--) {
477:     /* Evolve ts->vec_costintegral to compute integrals */
478:     TSComputeCostIntegrand(ts,rk->ptime+rk->time_step*(1.0-c[i]),Y[i],ts->vec_costintegrand);
479:     VecAXPY(ts->vec_costintegral,rk->time_step*b[i],ts->vec_costintegrand);
480:   }
481:   return(0);
482: }

484: static PetscErrorCode TSAdjointCostIntegral_RK(TS ts)
485: {
486:   TS_RK           *rk = (TS_RK*)ts->data;
487:   RKTableau       tab = rk->tableau;
488:   const PetscInt  s = tab->s;
489:   const PetscReal *b = tab->b,*c = tab->c;
490:   Vec             *Y = rk->Y;
491:   PetscInt        i;
492:   PetscErrorCode  ierr;

495:   for (i=s-1; i>=0; i--) {
496:     /* Evolve ts->vec_costintegral to compute integrals */
497:     TSComputeCostIntegrand(ts,ts->ptime-ts->time_step*(1.0-c[i]),Y[i],ts->vec_costintegrand);
498:     VecAXPY(ts->vec_costintegral,-ts->time_step*b[i],ts->vec_costintegrand);
499:   }
500:   return(0);
501: }

503: static PetscErrorCode TSRollBack_RK(TS ts)
504: {
505:   TS_RK           *rk = (TS_RK*)ts->data;
506:   RKTableau       tab = rk->tableau;
507:   const PetscInt  s  = tab->s;
508:   const PetscReal *b = tab->b;
509:   PetscScalar     *w = rk->work;
510:   Vec             *YdotRHS = rk->YdotRHS;
511:   PetscInt        j;
512:   PetscReal       h;
513:   PetscErrorCode  ierr;

516:   switch (rk->status) {
517:   case TS_STEP_INCOMPLETE:
518:   case TS_STEP_PENDING:
519:     h = ts->time_step; break;
520:   case TS_STEP_COMPLETE:
521:     h = ts->ptime - ts->ptime_prev; break;
522:   default: SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_PLIB,"Invalid TSStepStatus");
523:   }
524:   for (j=0; j<s; j++) w[j] = -h*b[j];
525:   VecMAXPY(ts->vec_sol,s,w,YdotRHS);
526:   return(0);
527: }

529: static PetscErrorCode TSStep_RK(TS ts)
530: {
531:   TS_RK           *rk   = (TS_RK*)ts->data;
532:   RKTableau        tab  = rk->tableau;
533:   const PetscInt   s = tab->s;
534:   const PetscReal *A = tab->A,*c = tab->c;
535:   PetscScalar     *w = rk->work;
536:   Vec             *Y = rk->Y,*YdotRHS = rk->YdotRHS;
537:   PetscBool        FSAL = tab->FSAL;
538:   TSAdapt          adapt;
539:   PetscInt         i,j;
540:   PetscInt         rejections = 0;
541:   PetscBool        stageok,accept = PETSC_TRUE;
542:   PetscReal        next_time_step = ts->time_step;
543:   PetscErrorCode   ierr;

546:   if (ts->steprollback || ts->steprestart) FSAL = PETSC_FALSE;
547:   if (FSAL) { VecCopy(YdotRHS[s-1],YdotRHS[0]); }

549:   rk->status = TS_STEP_INCOMPLETE;
550:   while (!ts->reason && rk->status != TS_STEP_COMPLETE) {
551:     PetscReal t = ts->ptime;
552:     PetscReal h = ts->time_step;
553:     for (i=0; i<s; i++) {
554:       rk->stage_time = t + h*c[i];
555:       TSPreStage(ts,rk->stage_time);
556:       VecCopy(ts->vec_sol,Y[i]);
557:       for (j=0; j<i; j++) w[j] = h*A[i*s+j];
558:       VecMAXPY(Y[i],i,w,YdotRHS);
559:       TSPostStage(ts,rk->stage_time,i,Y);
560:       TSGetAdapt(ts,&adapt);
561:       TSAdaptCheckStage(adapt,ts,rk->stage_time,Y[i],&stageok);
562:       if (!stageok) goto reject_step;
563:       if (FSAL && !i) continue;
564:       TSComputeRHSFunction(ts,t+h*c[i],Y[i],YdotRHS[i]);
565:     }

567:     rk->status = TS_STEP_INCOMPLETE;
568:     TSEvaluateStep(ts,tab->order,ts->vec_sol,NULL);
569:     rk->status = TS_STEP_PENDING;
570:     TSGetAdapt(ts,&adapt);
571:     TSAdaptCandidatesClear(adapt);
572:     TSAdaptCandidateAdd(adapt,tab->name,tab->order,1,tab->ccfl,(PetscReal)tab->s,PETSC_TRUE);
573:     TSAdaptChoose(adapt,ts,ts->time_step,NULL,&next_time_step,&accept);
574:     rk->status = accept ? TS_STEP_COMPLETE : TS_STEP_INCOMPLETE;
575:     if (!accept) { /* Roll back the current step */
576:       TSRollBack_RK(ts);
577:       ts->time_step = next_time_step;
578:       goto reject_step;
579:     }

581:     if (ts->costintegralfwd) { /* Save the info for the later use in cost integral evaluation*/
582:       rk->ptime     = ts->ptime;
583:       rk->time_step = ts->time_step;
584:     }

586:     ts->ptime += ts->time_step;
587:     ts->time_step = next_time_step;
588:     break;

590:   reject_step:
591:     ts->reject++; accept = PETSC_FALSE;
592:     if (!ts->reason && ++rejections > ts->max_reject && ts->max_reject >= 0) {
593:       ts->reason = TS_DIVERGED_STEP_REJECTED;
594:       PetscInfo2(ts,"Step=%D, step rejections %D greater than current TS allowed, stopping solve\n",ts->steps,rejections);
595:     }
596:   }
597:   return(0);
598: }

600: static PetscErrorCode TSAdjointSetUp_RK(TS ts)
601: {
602:   TS_RK         *rk  = (TS_RK*)ts->data;
603:   RKTableau      tab = rk->tableau;
604:   PetscInt       s   = tab->s;

608:   if (ts->adjointsetupcalled++) return(0);
609:   VecDuplicateVecs(ts->vecs_sensi[0],s*ts->numcost,&rk->VecDeltaLam);
610:   if(ts->vecs_sensip) {
611:     VecDuplicateVecs(ts->vecs_sensip[0],s*ts->numcost,&rk->VecDeltaMu);
612:   }
613:   VecDuplicateVecs(ts->vecs_sensi[0],ts->numcost,&rk->VecSensiTemp);
614:   return(0);
615: }

617: static PetscErrorCode TSAdjointStep_RK(TS ts)
618: {
619:   TS_RK           *rk   = (TS_RK*)ts->data;
620:   RKTableau        tab  = rk->tableau;
621:   const PetscInt   s    = tab->s;
622:   const PetscReal *A = tab->A,*b = tab->b,*c = tab->c;
623:   PetscScalar     *w    = rk->work;
624:   Vec             *Y    = rk->Y,*VecDeltaLam = rk->VecDeltaLam,*VecDeltaMu = rk->VecDeltaMu,*VecSensiTemp = rk->VecSensiTemp;
625:   PetscInt         i,j,nadj;
626:   PetscReal        t = ts->ptime;
627:   PetscErrorCode   ierr;
628:   PetscReal        h = ts->time_step;
629:   Mat              J,Jp;

632:   rk->status = TS_STEP_INCOMPLETE;
633:   for (i=s-1; i>=0; i--) {
634:     rk->stage_time = t + h*(1.0-c[i]);
635:     for (nadj=0; nadj<ts->numcost; nadj++) {
636:       VecCopy(ts->vecs_sensi[nadj],VecSensiTemp[nadj]);
637:       VecScale(VecSensiTemp[nadj],-h*b[i]);
638:       for (j=i+1; j<s; j++) {
639:         VecAXPY(VecSensiTemp[nadj],-h*A[j*s+i],VecDeltaLam[nadj*s+j]);
640:       }
641:     }
642:     /* Stage values of lambda */
643:     TSGetRHSJacobian(ts,&J,&Jp,NULL,NULL);
644:     TSComputeRHSJacobian(ts,rk->stage_time,Y[i],J,Jp);
645:     if (ts->vec_costintegral) {
646:       TSAdjointComputeDRDYFunction(ts,rk->stage_time,Y[i],ts->vecs_drdy);
647:     }
648:     for (nadj=0; nadj<ts->numcost; nadj++) {
649:       MatMultTranspose(J,VecSensiTemp[nadj],VecDeltaLam[nadj*s+i]);
650:       if (ts->vec_costintegral) {
651:         VecAXPY(VecDeltaLam[nadj*s+i],-h*b[i],ts->vecs_drdy[nadj]);
652:       }
653:     }

655:     /* Stage values of mu */
656:     if(ts->vecs_sensip) {
657:       TSAdjointComputeRHSJacobian(ts,rk->stage_time,Y[i],ts->Jacp);
658:       if (ts->vec_costintegral) {
659:         TSAdjointComputeDRDPFunction(ts,rk->stage_time,Y[i],ts->vecs_drdp);
660:       }

662:       for (nadj=0; nadj<ts->numcost; nadj++) {
663:         MatMultTranspose(ts->Jacp,VecSensiTemp[nadj],VecDeltaMu[nadj*s+i]);
664:         if (ts->vec_costintegral) {
665:           VecAXPY(VecDeltaMu[nadj*s+i],-h*b[i],ts->vecs_drdp[nadj]);
666:         }
667:       }
668:     }
669:   }

671:   for (j=0; j<s; j++) w[j] = 1.0;
672:   for (nadj=0; nadj<ts->numcost; nadj++) {
673:     VecMAXPY(ts->vecs_sensi[nadj],s,w,&VecDeltaLam[nadj*s]);
674:     if(ts->vecs_sensip) {
675:       VecMAXPY(ts->vecs_sensip[nadj],s,w,&VecDeltaMu[nadj*s]);
676:     }
677:   }
678:   rk->status = TS_STEP_COMPLETE;
679:   return(0);
680: }

682: static PetscErrorCode TSInterpolate_RK(TS ts,PetscReal itime,Vec X)
683: {
684:   TS_RK           *rk = (TS_RK*)ts->data;
685:   PetscInt         s  = rk->tableau->s,p = rk->tableau->p,i,j;
686:   PetscReal        h;
687:   PetscReal        tt,t;
688:   PetscScalar     *b;
689:   const PetscReal *B = rk->tableau->binterp;
690:   PetscErrorCode   ierr;

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

695:   switch (rk->status) {
696:   case TS_STEP_INCOMPLETE:
697:   case TS_STEP_PENDING:
698:     h = ts->time_step;
699:     t = (itime - ts->ptime)/h;
700:     break;
701:   case TS_STEP_COMPLETE:
702:     h = ts->ptime - ts->ptime_prev;
703:     t = (itime - ts->ptime)/h + 1; /* In the interval [0,1] */
704:     break;
705:   default: SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_PLIB,"Invalid TSStepStatus");
706:   }
707:   PetscMalloc1(s,&b);
708:   for (i=0; i<s; i++) b[i] = 0;
709:   for (j=0,tt=t; j<p; j++,tt*=t) {
710:     for (i=0; i<s; i++) {
711:       b[i]  += h * B[i*p+j] * tt;
712:     }
713:   }

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

718:   PetscFree(b);
719:   return(0);
720: }

722: /*------------------------------------------------------------*/

724: static PetscErrorCode TSRKTableauReset(TS ts)
725: {
726:   TS_RK          *rk = (TS_RK*)ts->data;
727:   RKTableau      tab = rk->tableau;

731:   if (!tab) return(0);
732:   PetscFree(rk->work);
733:   VecDestroyVecs(tab->s,&rk->Y);
734:   VecDestroyVecs(tab->s,&rk->YdotRHS);
735:   VecDestroyVecs(tab->s*ts->numcost,&rk->VecDeltaLam);
736:   VecDestroyVecs(tab->s*ts->numcost,&rk->VecDeltaMu);
737:   return(0);
738: }

740: static PetscErrorCode TSReset_RK(TS ts)
741: {
742:   TS_RK         *rk = (TS_RK*)ts->data;

746:   TSRKTableauReset(ts);
747:   VecDestroy(&rk->VecCostIntegral0);
748:   VecDestroyVecs(ts->numcost,&rk->VecSensiTemp);
749:   return(0);
750: }

752: static PetscErrorCode DMCoarsenHook_TSRK(DM fine,DM coarse,void *ctx)
753: {
755:   return(0);
756: }

758: static PetscErrorCode DMRestrictHook_TSRK(DM fine,Mat restrct,Vec rscale,Mat inject,DM coarse,void *ctx)
759: {
761:   return(0);
762: }


765: static PetscErrorCode DMSubDomainHook_TSRK(DM dm,DM subdm,void *ctx)
766: {
768:   return(0);
769: }

771: static PetscErrorCode DMSubDomainRestrictHook_TSRK(DM dm,VecScatter gscat,VecScatter lscat,DM subdm,void *ctx)
772: {

775:   return(0);
776: }
777: /*
778: static PetscErrorCode RKSetAdjCoe(RKTableau tab)
779: {
780:   PetscReal *A,*b;
781:   PetscInt        s,i,j;
782:   PetscErrorCode  ierr;

785:   s    = tab->s;
786:   PetscMalloc2(s*s,&A,s,&b);

788:   for (i=0; i<s; i++)
789:     for (j=0; j<s; j++) {
790:       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];
791:       PetscPrintf(PETSC_COMM_WORLD,"Coefficients: A[%D][%D]=%.6f\n",i,j,A[i*s+j]);
792:     }

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

796:   PetscMemcpy(tab->A,A,s*s*sizeof(A[0]));
797:   PetscMemcpy(tab->b,b,s*sizeof(b[0]));
798:   PetscFree2(A,b);
799:   return(0);
800: }
801: */

803: static PetscErrorCode TSRKTableauSetUp(TS ts)
804: {
805:   TS_RK         *rk  = (TS_RK*)ts->data;
806:   RKTableau      tab = rk->tableau;

810:   PetscMalloc1(tab->s,&rk->work);
811:   VecDuplicateVecs(ts->vec_sol,tab->s,&rk->Y);
812:   VecDuplicateVecs(ts->vec_sol,tab->s,&rk->YdotRHS);
813:   return(0);
814: }


817: static PetscErrorCode TSSetUp_RK(TS ts)
818: {
819:   TS_RK         *rk = (TS_RK*)ts->data;
821:   DM             dm;

824:   TSCheckImplicitTerm(ts);
825:   TSRKTableauSetUp(ts);
826:   if (!rk->VecCostIntegral0 && ts->vec_costintegral && ts->costintegralfwd) { /* back up cost integral */
827:     VecDuplicate(ts->vec_costintegral,&rk->VecCostIntegral0);
828:   }
829:   TSGetDM(ts,&dm);
830:   DMCoarsenHookAdd(dm,DMCoarsenHook_TSRK,DMRestrictHook_TSRK,ts);
831:   DMSubDomainHookAdd(dm,DMSubDomainHook_TSRK,DMSubDomainRestrictHook_TSRK,ts);
832:   return(0);
833: }


836: /*------------------------------------------------------------*/

838: static PetscErrorCode TSSetFromOptions_RK(PetscOptionItems *PetscOptionsObject,TS ts)
839: {
840:   TS_RK         *rk = (TS_RK*)ts->data;

844:   PetscOptionsHead(PetscOptionsObject,"RK ODE solver options");
845:   {
846:     RKTableauLink  link;
847:     PetscInt       count,choice;
848:     PetscBool      flg;
849:     const char   **namelist;
850:     for (link=RKTableauList,count=0; link; link=link->next,count++) ;
851:     PetscMalloc1(count,&namelist);
852:     for (link=RKTableauList,count=0; link; link=link->next,count++) namelist[count] = link->tab.name;
853:     PetscOptionsEList("-ts_rk_type","Family of RK method","TSRKSetType",(const char*const*)namelist,count,rk->tableau->name,&choice,&flg);
854:     if (flg) {TSRKSetType(ts,namelist[choice]);}
855:     PetscFree(namelist);
856:   }
857:   PetscOptionsTail();
858:   return(0);
859: }

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

869:   for (i=0,p=buf,left=len; i<n; i++) {
870:     PetscSNPrintfCount(p,left,fmt,&count,x[i]);
871:     if (count >= left) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Insufficient space in buffer");
872:     left -= count;
873:     p    += count;
874:     *p++  = ' ';
875:   }
876:   p[i ? 0 : -1] = 0;
877:   return(0);
878: }

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

887:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);
888:   if (iascii) {
889:     RKTableau tab  = rk->tableau;
890:     TSRKType  rktype;
891:     char      buf[512];
892:     TSRKGetType(ts,&rktype);
893:     PetscViewerASCIIPrintf(viewer,"  RK type %s\n",rktype);
894:     PetscViewerASCIIPrintf(viewer,"  Order: %D\n",tab->order);
895:     PetscViewerASCIIPrintf(viewer,"  FSAL property: %s\n",tab->FSAL ? "yes" : "no");
896:     PetscFormatRealArray(buf,sizeof(buf),"% 8.6f",tab->s,tab->c);
897:     PetscViewerASCIIPrintf(viewer,"  Abscissa c = %s\n",buf);
898:   }
899:   return(0);
900: }

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: }

913: /*@C
914:   TSRKSetType - Set the type of RK scheme

916:   Logically collective

918:   Input Parameter:
919: +  ts - timestepping context
920: -  rktype - type of RK-scheme

922:   Options Database:
923: .   -ts_rk_type - <1fe,2a,3,3bs,4,5f,5dp,5bs>

925:   Level: intermediate

927: .seealso: TSRKGetType(), TSRK, TSRKType, TSRK1FE, TSRK2A, TSRK3, TSRK3BS, TSRK4, TSRK5F, TSRK5DP, TSRK5BS
928: @*/
929: PetscErrorCode TSRKSetType(TS ts,TSRKType rktype)
930: {

936:   PetscTryMethod(ts,"TSRKSetType_C",(TS,TSRKType),(ts,rktype));
937:   return(0);
938: }

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: }

965: static PetscErrorCode TSRKGetType_RK(TS ts,TSRKType *rktype)
966: {
967:   TS_RK *rk = (TS_RK*)ts->data;

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

981:   if (rk->tableau) {
982:     PetscStrcmp(rk->tableau->name,rktype,&match);
983:     if (match) return(0);
984:   }
985:   for (link = RKTableauList; link; link=link->next) {
986:     PetscStrcmp(link->tab.name,rktype,&match);
987:     if (match) {
988:       if (ts->setupcalled) {TSRKTableauReset(ts);}
989:       rk->tableau = &link->tab;
990:       if (ts->setupcalled) {TSRKTableauSetUp(ts);}
991:       ts->default_adapt_type = rk->tableau->bembed ? TSADAPTBASIC : TSADAPTNONE;
992:       return(0);
993:     }
994:   }
995:   SETERRQ1(PetscObjectComm((PetscObject)ts),PETSC_ERR_ARG_UNKNOWN_TYPE,"Could not find '%s'",rktype);
996:   return(0);
997: }

999: static PetscErrorCode  TSGetStages_RK(TS ts,PetscInt *ns,Vec **Y)
1000: {
1001:   TS_RK          *rk = (TS_RK*)ts->data;

1004:   *ns = rk->tableau->s;
1005:   if(Y) *Y  = rk->Y;
1006:   return(0);
1007: }

1009: static PetscErrorCode TSDestroy_RK(TS ts)
1010: {

1014:   TSReset_RK(ts);
1015:   if (ts->dm) {
1016:     DMCoarsenHookRemove(ts->dm,DMCoarsenHook_TSRK,DMRestrictHook_TSRK,ts);
1017:     DMSubDomainHookRemove(ts->dm,DMSubDomainHook_TSRK,DMSubDomainRestrictHook_TSRK,ts);
1018:   }
1019:   PetscFree(ts->data);
1020:   PetscObjectComposeFunction((PetscObject)ts,"TSRKGetType_C",NULL);
1021:   PetscObjectComposeFunction((PetscObject)ts,"TSRKSetType_C",NULL);
1022:   return(0);
1023: }

1025: /* ------------------------------------------------------------ */
1026: /*MC
1027:       TSRK - ODE and DAE solver using Runge-Kutta schemes

1029:   The user should provide the right hand side of the equation
1030:   using TSSetRHSFunction().

1032:   Notes:
1033:   The default is TSRK3BS, it can be changed with TSRKSetType() or -ts_rk_type

1035:   Level: beginner

1037: .seealso:  TSCreate(), TS, TSSetType(), TSRKSetType(), TSRKGetType(), TSRKSetFullyImplicit(), TSRK2D, TTSRK2E, TSRK3,
1038:            TSRK4, TSRK5, TSRKPRSSP2, TSRKBPR3, TSRKType, TSRKRegister()

1040: M*/
1041: PETSC_EXTERN PetscErrorCode TSCreate_RK(TS ts)
1042: {
1043:   TS_RK          *rk;

1047:   TSRKInitializePackage();

1049:   ts->ops->reset          = TSReset_RK;
1050:   ts->ops->destroy        = TSDestroy_RK;
1051:   ts->ops->view           = TSView_RK;
1052:   ts->ops->load           = TSLoad_RK;
1053:   ts->ops->setup          = TSSetUp_RK;
1054:   ts->ops->adjointsetup   = TSAdjointSetUp_RK;
1055:   ts->ops->step           = TSStep_RK;
1056:   ts->ops->interpolate    = TSInterpolate_RK;
1057:   ts->ops->evaluatestep   = TSEvaluateStep_RK;
1058:   ts->ops->rollback       = TSRollBack_RK;
1059:   ts->ops->setfromoptions = TSSetFromOptions_RK;
1060:   ts->ops->getstages      = TSGetStages_RK;
1061:   ts->ops->adjointstep    = TSAdjointStep_RK;

1063:   ts->ops->adjointintegral = TSAdjointCostIntegral_RK;
1064:   ts->ops->forwardintegral = TSForwardCostIntegral_RK;

1066:   PetscNewLog(ts,&rk);
1067:   ts->data = (void*)rk;

1069:   PetscObjectComposeFunction((PetscObject)ts,"TSRKGetType_C",TSRKGetType_RK);
1070:   PetscObjectComposeFunction((PetscObject)ts,"TSRKSetType_C",TSRKSetType_RK);

1072:   TSRKSetType(ts,TSRKDefault);
1073:   return(0);
1074: }