Actual source code: ssp.c

petsc-3.5.1 2014-08-06
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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: {

204:   return(0);
205: }

209: static PetscErrorCode TSStep_SSP(TS ts)
210: {
211:   TS_SSP         *ssp = (TS_SSP*)ts->data;
212:   Vec            sol  = ts->vec_sol;

216:   TSPreStep(ts);
217:   (*ssp->onestep)(ts,ts->ptime,ts->time_step,sol);
218:   ts->ptime += ts->time_step;
219:   ts->steps++;
220:   return(0);
221: }
222: /*------------------------------------------------------------*/
225: static PetscErrorCode TSReset_SSP(TS ts)
226: {
227:   TS_SSP         *ssp = (TS_SSP*)ts->data;

231:   if (ssp->work) {VecDestroyVecs(ssp->nwork,&ssp->work);}
232:   ssp->nwork   = 0;
233:   ssp->workout = PETSC_FALSE;
234:   return(0);
235: }

239: static PetscErrorCode TSDestroy_SSP(TS ts)
240: {
241:   TS_SSP         *ssp = (TS_SSP*)ts->data;

245:   TSReset_SSP(ts);
246:   PetscFree(ssp->type_name);
247:   PetscFree(ts->data);
248:   PetscObjectComposeFunction((PetscObject)ts,"TSSSPGetType_C",NULL);
249:   PetscObjectComposeFunction((PetscObject)ts,"TSSSPSetType_C",NULL);
250:   PetscObjectComposeFunction((PetscObject)ts,"TSSSPGetNumStages_C",NULL);
251:   PetscObjectComposeFunction((PetscObject)ts,"TSSSPSetNumStages_C",NULL);
252:   return(0);
253: }
254: /*------------------------------------------------------------*/

258: /*@C
259:    TSSSPSetType - set the SSP time integration scheme to use

261:    Logically Collective

263:    Input Arguments:
264:    ts - time stepping object
265:    type - type of scheme to use

267:    Options Database Keys:
268:    -ts_ssp_type <rks2>: Type of SSP method (one of) rks2 rks3 rk104
269:    -ts_ssp_nstages <5>: Number of stages

271:    Level: beginner

273: .seealso: TSSSP, TSSSPGetType(), TSSSPSetNumStages(), TSSSPRKS2, TSSSPRKS3, TSSSPRK104
274: @*/
275: PetscErrorCode TSSSPSetType(TS ts,TSSSPType type)
276: {

281:   PetscTryMethod(ts,"TSSSPSetType_C",(TS,TSSSPType),(ts,type));
282:   return(0);
283: }

287: /*@C
288:    TSSSPGetType - get the SSP time integration scheme

290:    Logically Collective

292:    Input Argument:
293:    ts - time stepping object

295:    Output Argument:
296:    type - type of scheme being used

298:    Level: beginner

300: .seealso: TSSSP, TSSSPSettype(), TSSSPSetNumStages(), TSSSPRKS2, TSSSPRKS3, TSSSPRK104
301: @*/
302: PetscErrorCode TSSSPGetType(TS ts,TSSSPType *type)
303: {

308:   PetscTryMethod(ts,"TSSSPGetType_C",(TS,TSSSPType*),(ts,type));
309:   return(0);
310: }

314: /*@
315:    TSSSPSetNumStages - set the number of stages to use with the SSP method

317:    Logically Collective

319:    Input Arguments:
320:    ts - time stepping object
321:    nstages - number of stages

323:    Options Database Keys:
324:    -ts_ssp_type <rks2>: NumStages of SSP method (one of) rks2 rks3 rk104
325:    -ts_ssp_nstages <5>: Number of stages

327:    Level: beginner

329: .seealso: TSSSP, TSSSPGetNumStages(), TSSSPSetNumStages(), TSSSPRKS2, TSSSPRKS3, TSSSPRK104
330: @*/
331: PetscErrorCode TSSSPSetNumStages(TS ts,PetscInt nstages)
332: {

337:   PetscTryMethod(ts,"TSSSPSetNumStages_C",(TS,PetscInt),(ts,nstages));
338:   return(0);
339: }

343: /*@
344:    TSSSPGetNumStages - get the number of stages in the SSP time integration scheme

346:    Logically Collective

348:    Input Argument:
349:    ts - time stepping object

351:    Output Argument:
352:    nstages - number of stages

354:    Level: beginner

356: .seealso: TSSSP, TSSSPGetType(), TSSSPSetNumStages(), TSSSPRKS2, TSSSPRKS3, TSSSPRK104
357: @*/
358: PetscErrorCode TSSSPGetNumStages(TS ts,PetscInt *nstages)
359: {

364:   PetscTryMethod(ts,"TSSSPGetNumStages_C",(TS,PetscInt*),(ts,nstages));
365:   return(0);
366: }

370: PETSC_EXTERN PetscErrorCode TSSSPSetType_SSP(TS ts,TSSSPType type)
371: {
372:   PetscErrorCode ierr,(*r)(TS,PetscReal,PetscReal,Vec);
373:   TS_SSP         *ssp = (TS_SSP*)ts->data;

376:   PetscFunctionListFind(TSSSPList,type,&r);
377:   if (!r) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_UNKNOWN_TYPE,"Unknown TS_SSP type %s given",type);
378:   ssp->onestep = r;
379:   PetscFree(ssp->type_name);
380:   PetscStrallocpy(type,&ssp->type_name);
381:   return(0);
382: }
385: PetscErrorCode TSSSPGetType_SSP(TS ts,TSSSPType *type)
386: {
387:   TS_SSP *ssp = (TS_SSP*)ts->data;

390:   *type = ssp->type_name;
391:   return(0);
392: }
395: PetscErrorCode TSSSPSetNumStages_SSP(TS ts,PetscInt nstages)
396: {
397:   TS_SSP *ssp = (TS_SSP*)ts->data;

400:   ssp->nstages = nstages;
401:   return(0);
402: }
405: PetscErrorCode TSSSPGetNumStages_SSP(TS ts,PetscInt *nstages)
406: {
407:   TS_SSP *ssp = (TS_SSP*)ts->data;

410:   *nstages = ssp->nstages;
411:   return(0);
412: }

416: static PetscErrorCode TSSetFromOptions_SSP(TS ts)
417: {
418:   char           tname[256] = TSSSPRKS2;
419:   TS_SSP         *ssp       = (TS_SSP*)ts->data;
421:   PetscBool      flg;

424:   PetscOptionsHead("SSP ODE solver options");
425:   {
426:     PetscOptionsFList("-ts_ssp_type","Type of SSP method","TSSSPSetType",TSSSPList,tname,tname,sizeof(tname),&flg);
427:     if (flg) {
428:       TSSSPSetType(ts,tname);
429:     }
430:     PetscOptionsInt("-ts_ssp_nstages","Number of stages","TSSSPSetNumStages",ssp->nstages,&ssp->nstages,NULL);
431:   }
432:   PetscOptionsTail();
433:   return(0);
434: }

438: static PetscErrorCode TSView_SSP(TS ts,PetscViewer viewer)
439: {
441:   return(0);
442: }

444: /* ------------------------------------------------------------ */

446: /*MC
447:       TSSSP - Explicit strong stability preserving ODE solver

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

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

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

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

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

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

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

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

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

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

479:   Level: beginner

481:   References:
482:   Ketcheson, Highly efficient strong stability preserving Runge-Kutta methods with low-storage implementations, SISC, 2008.

484:   Gottlieb, Ketcheson, and Shu, High order strong stability preserving time discretizations, J Scientific Computing, 2009.

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

488: M*/
491: PETSC_EXTERN PetscErrorCode TSCreate_SSP(TS ts)
492: {
493:   TS_SSP         *ssp;

497:   TSSSPInitializePackage();

499:   ts->ops->setup          = TSSetUp_SSP;
500:   ts->ops->step           = TSStep_SSP;
501:   ts->ops->reset          = TSReset_SSP;
502:   ts->ops->destroy        = TSDestroy_SSP;
503:   ts->ops->setfromoptions = TSSetFromOptions_SSP;
504:   ts->ops->view           = TSView_SSP;

506:   PetscNewLog(ts,&ssp);
507:   ts->data = (void*)ssp;

509:   PetscObjectComposeFunction((PetscObject)ts,"TSSSPGetType_C",TSSSPGetType_SSP);
510:   PetscObjectComposeFunction((PetscObject)ts,"TSSSPSetType_C",TSSSPSetType_SSP);
511:   PetscObjectComposeFunction((PetscObject)ts,"TSSSPGetNumStages_C",TSSSPGetNumStages_SSP);
512:   PetscObjectComposeFunction((PetscObject)ts,"TSSSPSetNumStages_C",TSSSPSetNumStages_SSP);

514:   TSSSPSetType(ts,TSSSPRKS2);
515:   ssp->nstages = 5;
516:   return(0);
517: }

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

526:   Level: developer

528: .keywords: TS, TSSSP, initialize, package
529: .seealso: PetscInitialize()
530: @*/
531: PetscErrorCode TSSSPInitializePackage(void)
532: {

536:   if (TSSSPPackageInitialized) return(0);
537:   TSSSPPackageInitialized = PETSC_TRUE;
538:   PetscFunctionListAdd(&TSSSPList,TSSSPRKS2, TSSSPStep_RK_2);
539:   PetscFunctionListAdd(&TSSSPList,TSSSPRKS3, TSSSPStep_RK_3);
540:   PetscFunctionListAdd(&TSSSPList,TSSSPRK104,TSSSPStep_RK_10_4);
541:   PetscRegisterFinalize(TSSSPFinalizePackage);
542:   return(0);
543: }

547: /*@C
548:   TSSSPFinalizePackage - This function destroys everything in the TSSSP package. It is
549:   called from PetscFinalize().

551:   Level: developer

553: .keywords: Petsc, destroy, package
554: .seealso: PetscFinalize()
555: @*/
556: PetscErrorCode TSSSPFinalizePackage(void)
557: {

561:   TSSSPPackageInitialized = PETSC_FALSE;
562:   PetscFunctionListDestroy(&TSSSPList);
563:   return(0);
564: }