Actual source code: ssp.c

petsc-3.7.3 2016-07-24
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  1: /*
  2:        Code for Timestepping with explicit SSP.
  3: */
  4: #include <petsc/private/tsimpl.h>                /*I   "petscts.h"   I*/

  6: PetscFunctionList TSSSPList = 0;
  7: static PetscBool TSSSPPackageInitialized;

  9: typedef struct {
 10:   PetscErrorCode (*onestep)(TS,PetscReal,PetscReal,Vec);
 11:   char           *type_name;
 12:   PetscInt       nstages;
 13:   Vec            *work;
 14:   PetscInt       nwork;
 15:   PetscBool      workout;
 16: } TS_SSP;


 21: static PetscErrorCode TSSSPGetWorkVectors(TS ts,PetscInt n,Vec **work)
 22: {
 23:   TS_SSP         *ssp = (TS_SSP*)ts->data;

 27:   if (ssp->workout) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Work vectors already gotten");
 28:   if (ssp->nwork < n) {
 29:     if (ssp->nwork > 0) {
 30:       VecDestroyVecs(ssp->nwork,&ssp->work);
 31:     }
 32:     VecDuplicateVecs(ts->vec_sol,n,&ssp->work);
 33:     ssp->nwork = n;
 34:   }
 35:   *work = ssp->work;
 36:   ssp->workout = PETSC_TRUE;
 37:   return(0);
 38: }

 42: static PetscErrorCode TSSSPRestoreWorkVectors(TS ts,PetscInt n,Vec **work)
 43: {
 44:   TS_SSP *ssp = (TS_SSP*)ts->data;

 47:   if (!ssp->workout) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ORDER,"Work vectors have not been gotten");
 48:   if (*work != ssp->work) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Wrong work vectors checked out");
 49:   ssp->workout = PETSC_FALSE;
 50:   *work = NULL;
 51:   return(0);
 52: }

 56: /*MC
 57:    TSSSPRKS2 - Optimal second order SSP Runge-Kutta method, low-storage, c_eff=(s-1)/s

 59:    Pseudocode 2 of Ketcheson 2008

 61:    Level: beginner

 63: .seealso: TSSSP, TSSSPSetType(), TSSSPSetNumStages()
 64: M*/
 65: static PetscErrorCode TSSSPStep_RK_2(TS ts,PetscReal t0,PetscReal dt,Vec sol)
 66: {
 67:   TS_SSP         *ssp = (TS_SSP*)ts->data;
 68:   Vec            *work,F;
 69:   PetscInt       i,s;

 73:   s    = ssp->nstages;
 74:   TSSSPGetWorkVectors(ts,2,&work);
 75:   F    = work[1];
 76:   VecCopy(sol,work[0]);
 77:   for (i=0; i<s-1; i++) {
 78:     PetscReal stage_time = t0+dt*(i/(s-1.));
 79:     TSPreStage(ts,stage_time);
 80:     TSComputeRHSFunction(ts,stage_time,work[0],F);
 81:     VecAXPY(work[0],dt/(s-1.),F);
 82:   }
 83:   TSComputeRHSFunction(ts,t0+dt,work[0],F);
 84:   VecAXPBYPCZ(sol,(s-1.)/s,dt/s,1./s,work[0],F);
 85:   TSSSPRestoreWorkVectors(ts,2,&work);
 86:   return(0);
 87: }

 91: /*MC
 92:    TSSSPRKS3 - Optimal third order SSP Runge-Kutta, low-storage, c_eff=(PetscSqrtReal(s)-1)/PetscSqrtReal(s), where PetscSqrtReal(s) is an integer

 94:    Pseudocode 2 of Ketcheson 2008

 96:    Level: beginner

 98: .seealso: TSSSP, TSSSPSetType(), TSSSPSetNumStages()
 99: M*/
100: static PetscErrorCode TSSSPStep_RK_3(TS ts,PetscReal t0,PetscReal dt,Vec sol)
101: {
102:   TS_SSP         *ssp = (TS_SSP*)ts->data;
103:   Vec            *work,F;
104:   PetscInt       i,s,n,r;
105:   PetscReal      c,stage_time;

109:   s = ssp->nstages;
110:   n = (PetscInt)(PetscSqrtReal((PetscReal)s)+0.001);
111:   r = s-n;
112:   if (n*n != s) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"No support for optimal third order schemes with %d stages, must be a square number at least 4",s);
113:   TSSSPGetWorkVectors(ts,3,&work);
114:   F    = work[2];
115:   VecCopy(sol,work[0]);
116:   for (i=0; i<(n-1)*(n-2)/2; i++) {
117:     c          = (i<n*(n+1)/2) ? 1.*i/(s-n) : (1.*i-n)/(s-n);
118:     stage_time = t0+c*dt;
119:     TSPreStage(ts,stage_time);
120:     TSComputeRHSFunction(ts,stage_time,work[0],F);
121:     VecAXPY(work[0],dt/r,F);
122:   }
123:   VecCopy(work[0],work[1]);
124:   for (; i<n*(n+1)/2-1; i++) {
125:     c          = (i<n*(n+1)/2) ? 1.*i/(s-n) : (1.*i-n)/(s-n);
126:     stage_time = t0+c*dt;
127:     TSPreStage(ts,stage_time);
128:     TSComputeRHSFunction(ts,stage_time,work[0],F);
129:     VecAXPY(work[0],dt/r,F);
130:   }
131:   {
132:     c          = (i<n*(n+1)/2) ? 1.*i/(s-n) : (1.*i-n)/(s-n);
133:     stage_time = t0+c*dt;
134:     TSPreStage(ts,stage_time);
135:     TSComputeRHSFunction(ts,stage_time,work[0],F);
136:     VecAXPBYPCZ(work[0],1.*n/(2*n-1.),(n-1.)*dt/(r*(2*n-1)),(n-1.)/(2*n-1.),work[1],F);
137:     i++;
138:   }
139:   for (; i<s; i++) {
140:     c          = (i<n*(n+1)/2) ? 1.*i/(s-n) : (1.*i-n)/(s-n);
141:     stage_time = t0+c*dt;
142:     TSPreStage(ts,stage_time);
143:     TSComputeRHSFunction(ts,stage_time,work[0],F);
144:     VecAXPY(work[0],dt/r,F);
145:   }
146:   VecCopy(work[0],sol);
147:   TSSSPRestoreWorkVectors(ts,3,&work);
148:   return(0);
149: }

153: /*MC
154:    TSSSPRKS104 - Optimal fourth order SSP Runge-Kutta, low-storage (2N), c_eff=0.6

156:    SSPRK(10,4), Pseudocode 3 of Ketcheson 2008

158:    Level: beginner

160: .seealso: TSSSP, TSSSPSetType()
161: M*/
162: static PetscErrorCode TSSSPStep_RK_10_4(TS ts,PetscReal t0,PetscReal dt,Vec sol)
163: {
164:   const PetscReal c[10] = {0, 1./6, 2./6, 3./6, 4./6, 2./6, 3./6, 4./6, 5./6, 1};
165:   Vec             *work,F;
166:   PetscInt        i;
167:   PetscReal       stage_time;
168:   PetscErrorCode  ierr;

171:   TSSSPGetWorkVectors(ts,3,&work);
172:   F    = work[2];
173:   VecCopy(sol,work[0]);
174:   for (i=0; i<5; i++) {
175:     stage_time = t0+c[i]*dt;
176:     TSPreStage(ts,stage_time);
177:     TSComputeRHSFunction(ts,stage_time,work[0],F);
178:     VecAXPY(work[0],dt/6,F);
179:   }
180:   VecAXPBYPCZ(work[1],1./25,9./25,0,sol,work[0]);
181:   VecAXPBY(work[0],15,-5,work[1]);
182:   for (; i<9; i++) {
183:     stage_time = t0+c[i]*dt;
184:     TSPreStage(ts,stage_time);
185:     TSComputeRHSFunction(ts,stage_time,work[0],F);
186:     VecAXPY(work[0],dt/6,F);
187:   }
188:   stage_time = t0+dt;
189:   TSPreStage(ts,stage_time);
190:   TSComputeRHSFunction(ts,stage_time,work[0],F);
191:   VecAXPBYPCZ(work[1],3./5,dt/10,1,work[0],F);
192:   VecCopy(work[1],sol);
193:   TSSSPRestoreWorkVectors(ts,3,&work);
194:   return(0);
195: }


200: static PetscErrorCode TSSetUp_SSP(TS ts)
201: {

205:   TSGetAdapt(ts,&ts->adapt);
206:   TSAdaptCandidatesClear(ts->adapt);
207:   return(0);
208: }

212: static PetscErrorCode TSStep_SSP(TS ts)
213: {
214:   TS_SSP         *ssp = (TS_SSP*)ts->data;
215:   Vec            sol  = ts->vec_sol;
216:   PetscBool      stageok,accept = PETSC_TRUE;
217:   PetscReal      next_time_step = ts->time_step;

221:   (*ssp->onestep)(ts,ts->ptime,ts->time_step,sol);
222:   TSPostStage(ts,ts->ptime,0,&sol);
223:   TSAdaptCheckStage(ts->adapt,ts,ts->ptime+ts->time_step,sol,&stageok);
224:   if(!stageok) {ts->reason = TS_DIVERGED_STEP_REJECTED; return(0);}

226:   TSAdaptChoose(ts->adapt,ts,ts->time_step,NULL,&next_time_step,&accept);
227:   if (!accept) {ts->reason = TS_DIVERGED_STEP_REJECTED; return(0);}

229:   ts->ptime += ts->time_step;
230:   ts->time_step = next_time_step;
231:   return(0);
232: }
233: /*------------------------------------------------------------*/

237: static PetscErrorCode TSReset_SSP(TS ts)
238: {
239:   TS_SSP         *ssp = (TS_SSP*)ts->data;

243:   if (ssp->work) {VecDestroyVecs(ssp->nwork,&ssp->work);}
244:   ssp->nwork   = 0;
245:   ssp->workout = PETSC_FALSE;
246:   return(0);
247: }

251: static PetscErrorCode TSDestroy_SSP(TS ts)
252: {
253:   TS_SSP         *ssp = (TS_SSP*)ts->data;

257:   TSReset_SSP(ts);
258:   PetscFree(ssp->type_name);
259:   PetscFree(ts->data);
260:   PetscObjectComposeFunction((PetscObject)ts,"TSSSPGetType_C",NULL);
261:   PetscObjectComposeFunction((PetscObject)ts,"TSSSPSetType_C",NULL);
262:   PetscObjectComposeFunction((PetscObject)ts,"TSSSPGetNumStages_C",NULL);
263:   PetscObjectComposeFunction((PetscObject)ts,"TSSSPSetNumStages_C",NULL);
264:   return(0);
265: }
266: /*------------------------------------------------------------*/

270: /*@C
271:    TSSSPSetType - set the SSP time integration scheme to use

273:    Logically Collective

275:    Input Arguments:
276:    ts - time stepping object
277:    type - type of scheme to use

279:    Options Database Keys:
280:    -ts_ssp_type <rks2>: Type of SSP method (one of) rks2 rks3 rk104
281:    -ts_ssp_nstages <5>: Number of stages

283:    Level: beginner

285: .seealso: TSSSP, TSSSPGetType(), TSSSPSetNumStages(), TSSSPRKS2, TSSSPRKS3, TSSSPRK104
286: @*/
287: PetscErrorCode TSSSPSetType(TS ts,TSSSPType type)
288: {

293:   PetscTryMethod(ts,"TSSSPSetType_C",(TS,TSSSPType),(ts,type));
294:   return(0);
295: }

299: /*@C
300:    TSSSPGetType - get the SSP time integration scheme

302:    Logically Collective

304:    Input Argument:
305:    ts - time stepping object

307:    Output Argument:
308:    type - type of scheme being used

310:    Level: beginner

312: .seealso: TSSSP, TSSSPSettype(), TSSSPSetNumStages(), TSSSPRKS2, TSSSPRKS3, TSSSPRK104
313: @*/
314: PetscErrorCode TSSSPGetType(TS ts,TSSSPType *type)
315: {

320:   PetscUseMethod(ts,"TSSSPGetType_C",(TS,TSSSPType*),(ts,type));
321:   return(0);
322: }

326: /*@
327:    TSSSPSetNumStages - set the number of stages to use with the SSP method

329:    Logically Collective

331:    Input Arguments:
332:    ts - time stepping object
333:    nstages - number of stages

335:    Options Database Keys:
336:    -ts_ssp_type <rks2>: NumStages of SSP method (one of) rks2 rks3 rk104
337:    -ts_ssp_nstages <5>: Number of stages

339:    Level: beginner

341: .seealso: TSSSP, TSSSPGetNumStages(), TSSSPSetNumStages(), TSSSPRKS2, TSSSPRKS3, TSSSPRK104
342: @*/
343: PetscErrorCode TSSSPSetNumStages(TS ts,PetscInt nstages)
344: {

349:   PetscTryMethod(ts,"TSSSPSetNumStages_C",(TS,PetscInt),(ts,nstages));
350:   return(0);
351: }

355: /*@
356:    TSSSPGetNumStages - get the number of stages in the SSP time integration scheme

358:    Logically Collective

360:    Input Argument:
361:    ts - time stepping object

363:    Output Argument:
364:    nstages - number of stages

366:    Level: beginner

368: .seealso: TSSSP, TSSSPGetType(), TSSSPSetNumStages(), TSSSPRKS2, TSSSPRKS3, TSSSPRK104
369: @*/
370: PetscErrorCode TSSSPGetNumStages(TS ts,PetscInt *nstages)
371: {

376:   PetscUseMethod(ts,"TSSSPGetNumStages_C",(TS,PetscInt*),(ts,nstages));
377:   return(0);
378: }

382: static PetscErrorCode TSSSPSetType_SSP(TS ts,TSSSPType type)
383: {
384:   PetscErrorCode ierr,(*r)(TS,PetscReal,PetscReal,Vec);
385:   TS_SSP         *ssp = (TS_SSP*)ts->data;

388:   PetscFunctionListFind(TSSSPList,type,&r);
389:   if (!r) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_UNKNOWN_TYPE,"Unknown TS_SSP type %s given",type);
390:   ssp->onestep = r;
391:   PetscFree(ssp->type_name);
392:   PetscStrallocpy(type,&ssp->type_name);
393:   return(0);
394: }
397: static PetscErrorCode TSSSPGetType_SSP(TS ts,TSSSPType *type)
398: {
399:   TS_SSP *ssp = (TS_SSP*)ts->data;

402:   *type = ssp->type_name;
403:   return(0);
404: }
407: static PetscErrorCode TSSSPSetNumStages_SSP(TS ts,PetscInt nstages)
408: {
409:   TS_SSP *ssp = (TS_SSP*)ts->data;

412:   ssp->nstages = nstages;
413:   return(0);
414: }
417: static PetscErrorCode TSSSPGetNumStages_SSP(TS ts,PetscInt *nstages)
418: {
419:   TS_SSP *ssp = (TS_SSP*)ts->data;

422:   *nstages = ssp->nstages;
423:   return(0);
424: }

428: static PetscErrorCode TSSetFromOptions_SSP(PetscOptionItems *PetscOptionsObject,TS ts)
429: {
430:   char           tname[256] = TSSSPRKS2;
431:   TS_SSP         *ssp       = (TS_SSP*)ts->data;
433:   PetscBool      flg;

436:   PetscOptionsHead(PetscOptionsObject,"SSP ODE solver options");
437:   {
438:     PetscOptionsFList("-ts_ssp_type","Type of SSP method","TSSSPSetType",TSSSPList,tname,tname,sizeof(tname),&flg);
439:     if (flg) {
440:       TSSSPSetType(ts,tname);
441:     }
442:     PetscOptionsInt("-ts_ssp_nstages","Number of stages","TSSSPSetNumStages",ssp->nstages,&ssp->nstages,NULL);
443:   }
444:   PetscOptionsTail();
445:   return(0);
446: }

450: static PetscErrorCode TSView_SSP(TS ts,PetscViewer viewer)
451: {
452:   TS_SSP         *ssp = (TS_SSP*)ts->data;
453:   PetscBool      ascii;

457:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&ascii);
458:   if (ascii) {PetscViewerASCIIPrintf(viewer,"  Scheme: %s\n",ssp->type_name);}
459:   return(0);
460: }

462: /* ------------------------------------------------------------ */

464: /*MC
465:       TSSSP - Explicit strong stability preserving ODE solver

467:   Most hyperbolic conservation laws have exact solutions that are total variation diminishing (TVD) or total variation
468:   bounded (TVB) although these solutions often contain discontinuities.  Spatial discretizations such as Godunov's
469:   scheme and high-resolution finite volume methods (TVD limiters, ENO/WENO) are designed to preserve these properties,
470:   but they are usually formulated using a forward Euler time discretization or by coupling the space and time
471:   discretization as in the classical Lax-Wendroff scheme.  When the space and time discretization is coupled, it is very
472:   difficult to produce schemes with high temporal accuracy while preserving TVD properties.  An alternative is the
473:   semidiscrete formulation where we choose a spatial discretization that is TVD with forward Euler and then choose a
474:   time discretization that preserves the TVD property.  Such integrators are called strong stability preserving (SSP).

476:   Let c_eff be the minimum number of function evaluations required to step as far as one step of forward Euler while
477:   still being SSP.  Some theoretical bounds

479:   1. There are no explicit methods with c_eff > 1.

481:   2. There are no explicit methods beyond order 4 (for nonlinear problems) and c_eff > 0.

483:   3. There are no implicit methods with order greater than 1 and c_eff > 2.

485:   This integrator provides Runge-Kutta methods of order 2, 3, and 4 with maximal values of c_eff.  More stages allows
486:   for larger values of c_eff which improves efficiency.  These implementations are low-memory and only use 2 or 3 work
487:   vectors regardless of the total number of stages, so e.g. 25-stage 3rd order methods may be an excellent choice.

489:   Methods can be chosen with -ts_ssp_type {rks2,rks3,rk104}

491:   rks2: Second order methods with any number s>1 of stages.  c_eff = (s-1)/s

493:   rks3: Third order methods with s=n^2 stages, n>1.  c_eff = (s-n)/s

495:   rk104: A 10-stage fourth order method.  c_eff = 0.6

497:   Level: beginner

499:   References:
500: +  1. - Ketcheson, Highly efficient strong stability preserving Runge Kutta methods with low storage implementations, SISC, 2008.
501: -  2. - Gottlieb, Ketcheson, and Shu, High order strong stability preserving time discretizations, J Scientific Computing, 2009.

503: .seealso:  TSCreate(), TS, TSSetType()

505: M*/
508: PETSC_EXTERN PetscErrorCode TSCreate_SSP(TS ts)
509: {
510:   TS_SSP         *ssp;

514:   TSSSPInitializePackage();

516:   ts->ops->setup          = TSSetUp_SSP;
517:   ts->ops->step           = TSStep_SSP;
518:   ts->ops->reset          = TSReset_SSP;
519:   ts->ops->destroy        = TSDestroy_SSP;
520:   ts->ops->setfromoptions = TSSetFromOptions_SSP;
521:   ts->ops->view           = TSView_SSP;

523:   PetscNewLog(ts,&ssp);
524:   ts->data = (void*)ssp;

526:   PetscObjectComposeFunction((PetscObject)ts,"TSSSPGetType_C",TSSSPGetType_SSP);
527:   PetscObjectComposeFunction((PetscObject)ts,"TSSSPSetType_C",TSSSPSetType_SSP);
528:   PetscObjectComposeFunction((PetscObject)ts,"TSSSPGetNumStages_C",TSSSPGetNumStages_SSP);
529:   PetscObjectComposeFunction((PetscObject)ts,"TSSSPSetNumStages_C",TSSSPSetNumStages_SSP);

531:   TSSSPSetType(ts,TSSSPRKS2);
532:   ssp->nstages = 5;
533:   return(0);
534: }

538: /*@C
539:   TSSSPInitializePackage - This function initializes everything in the TSSSP package. It is called
540:   from PetscDLLibraryRegister() when using dynamic libraries, and on the first call to TSCreate_SSP()
541:   when using static libraries.

543:   Level: developer

545: .keywords: TS, TSSSP, initialize, package
546: .seealso: PetscInitialize()
547: @*/
548: PetscErrorCode TSSSPInitializePackage(void)
549: {

553:   if (TSSSPPackageInitialized) return(0);
554:   TSSSPPackageInitialized = PETSC_TRUE;
555:   PetscFunctionListAdd(&TSSSPList,TSSSPRKS2, TSSSPStep_RK_2);
556:   PetscFunctionListAdd(&TSSSPList,TSSSPRKS3, TSSSPStep_RK_3);
557:   PetscFunctionListAdd(&TSSSPList,TSSSPRK104,TSSSPStep_RK_10_4);
558:   PetscRegisterFinalize(TSSSPFinalizePackage);
559:   return(0);
560: }

564: /*@C
565:   TSSSPFinalizePackage - This function destroys everything in the TSSSP package. It is
566:   called from PetscFinalize().

568:   Level: developer

570: .keywords: Petsc, destroy, package
571: .seealso: PetscFinalize()
572: @*/
573: PetscErrorCode TSSSPFinalizePackage(void)
574: {

578:   TSSSPPackageInitialized = PETSC_FALSE;
579:   PetscFunctionListDestroy(&TSSSPList);
580:   return(0);
581: }