Date: 2022-03-04T17:39:33+00:00

Actual source code: ssp.c

      1: /*
      2:        Code for Timestepping with explicit SSP.
      3: */
      4: #include <petsc/private/tsimpl.h>

      6: PetscFunctionList TSSSPList = NULL;
      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;

     18: static PetscErrorCode TSSSPGetWorkVectors(TS ts,PetscInt n,Vec **work)
     19: {
     20:   TS_SSP         *ssp = (TS_SSP*)ts->data;

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

     37: static PetscErrorCode TSSSPRestoreWorkVectors(TS ts,PetscInt n,Vec **work)
     38: {
     39:   TS_SSP *ssp = (TS_SSP*)ts->data;

     42:   if (!ssp->workout) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ORDER,"Work vectors have not been gotten");
     43:   if (*work != ssp->work) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Wrong work vectors checked out");
     44:   ssp->workout = PETSC_FALSE;
     45:   *work = NULL;
     46:   return(0);
     47: }

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

     52:    Pseudocode 2 of Ketcheson 2008

     54:    Level: beginner

     56: .seealso: TSSSP, TSSSPSetType(), TSSSPSetNumStages()
     57: M*/
     58: static PetscErrorCode TSSSPStep_RK_2(TS ts,PetscReal t0,PetscReal dt,Vec sol)
     59: {
     60:   TS_SSP         *ssp = (TS_SSP*)ts->data;
     61:   Vec            *work,F;
     62:   PetscInt       i,s;

     66:   s    = ssp->nstages;
     67:   TSSSPGetWorkVectors(ts,2,&work);
     68:   F    = work[1];
     69:   VecCopy(sol,work[0]);
     70:   for (i=0; i<s-1; i++) {
     71:     PetscReal stage_time = t0+dt*(i/(s-1.));
     72:     TSPreStage(ts,stage_time);
     73:     TSComputeRHSFunction(ts,stage_time,work[0],F);
     74:     VecAXPY(work[0],dt/(s-1.),F);
     75:   }
     76:   TSComputeRHSFunction(ts,t0+dt,work[0],F);
     77:   VecAXPBYPCZ(sol,(s-1.)/s,dt/s,1./s,work[0],F);
     78:   TSSSPRestoreWorkVectors(ts,2,&work);
     79:   return(0);
     80: }

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

     85:    Pseudocode 2 of Ketcheson 2008

     87:    Level: beginner

     89: .seealso: TSSSP, TSSSPSetType(), TSSSPSetNumStages()
     90: M*/
     91: static PetscErrorCode TSSSPStep_RK_3(TS ts,PetscReal t0,PetscReal dt,Vec sol)
     92: {
     93:   TS_SSP         *ssp = (TS_SSP*)ts->data;
     94:   Vec            *work,F;
     95:   PetscInt       i,s,n,r;
     96:   PetscReal      c,stage_time;

    100:   s = ssp->nstages;
    101:   n = (PetscInt)(PetscSqrtReal((PetscReal)s)+0.001);
    102:   r = s-n;
    103:   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);
    104:   TSSSPGetWorkVectors(ts,3,&work);
    105:   F    = work[2];
    106:   VecCopy(sol,work[0]);
    107:   for (i=0; i<(n-1)*(n-2)/2; i++) {
    108:     c          = (i<n*(n+1)/2) ? 1.*i/(s-n) : (1.*i-n)/(s-n);
    109:     stage_time = t0+c*dt;
    110:     TSPreStage(ts,stage_time);
    111:     TSComputeRHSFunction(ts,stage_time,work[0],F);
    112:     VecAXPY(work[0],dt/r,F);
    113:   }
    114:   VecCopy(work[0],work[1]);
    115:   for (; i<n*(n+1)/2-1; i++) {
    116:     c          = (i<n*(n+1)/2) ? 1.*i/(s-n) : (1.*i-n)/(s-n);
    117:     stage_time = t0+c*dt;
    118:     TSPreStage(ts,stage_time);
    119:     TSComputeRHSFunction(ts,stage_time,work[0],F);
    120:     VecAXPY(work[0],dt/r,F);
    121:   }
    122:   {
    123:     c          = (i<n*(n+1)/2) ? 1.*i/(s-n) : (1.*i-n)/(s-n);
    124:     stage_time = t0+c*dt;
    125:     TSPreStage(ts,stage_time);
    126:     TSComputeRHSFunction(ts,stage_time,work[0],F);
    127:     VecAXPBYPCZ(work[0],1.*n/(2*n-1.),(n-1.)*dt/(r*(2*n-1)),(n-1.)/(2*n-1.),work[1],F);
    128:     i++;
    129:   }
    130:   for (; i<s; i++) {
    131:     c          = (i<n*(n+1)/2) ? 1.*i/(s-n) : (1.*i-n)/(s-n);
    132:     stage_time = t0+c*dt;
    133:     TSPreStage(ts,stage_time);
    134:     TSComputeRHSFunction(ts,stage_time,work[0],F);
    135:     VecAXPY(work[0],dt/r,F);
    136:   }
    137:   VecCopy(work[0],sol);
    138:   TSSSPRestoreWorkVectors(ts,3,&work);
    139:   return(0);
    140: }

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

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

    147:    Level: beginner

    149: .seealso: TSSSP, TSSSPSetType()
    150: M*/
    151: static PetscErrorCode TSSSPStep_RK_10_4(TS ts,PetscReal t0,PetscReal dt,Vec sol)
    152: {
    153:   const PetscReal c[10] = {0, 1./6, 2./6, 3./6, 4./6, 2./6, 3./6, 4./6, 5./6, 1};
    154:   Vec             *work,F;
    155:   PetscInt        i;
    156:   PetscReal       stage_time;
    157:   PetscErrorCode  ierr;

    160:   TSSSPGetWorkVectors(ts,3,&work);
    161:   F    = work[2];
    162:   VecCopy(sol,work[0]);
    163:   for (i=0; i<5; i++) {
    164:     stage_time = t0+c[i]*dt;
    165:     TSPreStage(ts,stage_time);
    166:     TSComputeRHSFunction(ts,stage_time,work[0],F);
    167:     VecAXPY(work[0],dt/6,F);
    168:   }
    169:   VecAXPBYPCZ(work[1],1./25,9./25,0,sol,work[0]);
    170:   VecAXPBY(work[0],15,-5,work[1]);
    171:   for (; i<9; i++) {
    172:     stage_time = t0+c[i]*dt;
    173:     TSPreStage(ts,stage_time);
    174:     TSComputeRHSFunction(ts,stage_time,work[0],F);
    175:     VecAXPY(work[0],dt/6,F);
    176:   }
    177:   stage_time = t0+dt;
    178:   TSPreStage(ts,stage_time);
    179:   TSComputeRHSFunction(ts,stage_time,work[0],F);
    180:   VecAXPBYPCZ(work[1],3./5,dt/10,1,work[0],F);
    181:   VecCopy(work[1],sol);
    182:   TSSSPRestoreWorkVectors(ts,3,&work);
    183:   return(0);
    184: }

    186: static PetscErrorCode TSSetUp_SSP(TS ts)
    187: {

    191:   TSCheckImplicitTerm(ts);
    192:   TSGetAdapt(ts,&ts->adapt);
    193:   TSAdaptCandidatesClear(ts->adapt);
    194:   return(0);
    195: }

    197: static PetscErrorCode TSStep_SSP(TS ts)
    198: {
    199:   TS_SSP         *ssp = (TS_SSP*)ts->data;
    200:   Vec            sol  = ts->vec_sol;
    201:   PetscBool      stageok,accept = PETSC_TRUE;
    202:   PetscReal      next_time_step = ts->time_step;

    206:   (*ssp->onestep)(ts,ts->ptime,ts->time_step,sol);
    207:   TSPostStage(ts,ts->ptime,0,&sol);
    208:   TSAdaptCheckStage(ts->adapt,ts,ts->ptime+ts->time_step,sol,&stageok);
    209:   if (!stageok) {ts->reason = TS_DIVERGED_STEP_REJECTED; return(0);}

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

    214:   ts->ptime += ts->time_step;
    215:   ts->time_step = next_time_step;
    216:   return(0);
    217: }
    218: /*------------------------------------------------------------*/

    220: static PetscErrorCode TSReset_SSP(TS ts)
    221: {
    222:   TS_SSP         *ssp = (TS_SSP*)ts->data;

    226:   if (ssp->work) {VecDestroyVecs(ssp->nwork,&ssp->work);}
    227:   ssp->nwork   = 0;
    228:   ssp->workout = PETSC_FALSE;
    229:   return(0);
    230: }

    232: static PetscErrorCode TSDestroy_SSP(TS ts)
    233: {
    234:   TS_SSP         *ssp = (TS_SSP*)ts->data;

    238:   TSReset_SSP(ts);
    239:   PetscFree(ssp->type_name);
    240:   PetscFree(ts->data);
    241:   PetscObjectComposeFunction((PetscObject)ts,"TSSSPGetType_C",NULL);
    242:   PetscObjectComposeFunction((PetscObject)ts,"TSSSPSetType_C",NULL);
    243:   PetscObjectComposeFunction((PetscObject)ts,"TSSSPGetNumStages_C",NULL);
    244:   PetscObjectComposeFunction((PetscObject)ts,"TSSSPSetNumStages_C",NULL);
    245:   return(0);
    246: }
    247: /*------------------------------------------------------------*/

    249: /*@C
    250:    TSSSPSetType - set the SSP time integration scheme to use

    252:    Logically Collective

    254:    Input Parameters:
    255: +  ts - time stepping object
    256: -  ssptype - type of scheme to use

    258:    Options Database Keys:
    259:    -ts_ssp_type <rks2>: Type of SSP method (one of) rks2 rks3 rk104
    260:    -ts_ssp_nstages <5>: Number of stages

    262:    Level: beginner

    264: .seealso: TSSSP, TSSSPGetType(), TSSSPSetNumStages(), TSSSPRKS2, TSSSPRKS3, TSSSPRK104
    265: @*/
    266: PetscErrorCode TSSSPSetType(TS ts,TSSSPType ssptype)
    267: {

    273:   PetscTryMethod(ts,"TSSSPSetType_C",(TS,TSSSPType),(ts,ssptype));
    274:   return(0);
    275: }

    277: /*@C
    278:    TSSSPGetType - get the SSP time integration scheme

    280:    Logically Collective

    282:    Input Parameter:
    283: .  ts - time stepping object

    285:    Output Parameter:
    286: .  type - type of scheme being used

    288:    Level: beginner

    290: .seealso: TSSSP, TSSSPSettype(), TSSSPSetNumStages(), TSSSPRKS2, TSSSPRKS3, TSSSPRK104
    291: @*/
    292: PetscErrorCode TSSSPGetType(TS ts,TSSSPType *type)
    293: {

    298:   PetscUseMethod(ts,"TSSSPGetType_C",(TS,TSSSPType*),(ts,type));
    299:   return(0);
    300: }

    302: /*@
    303:    TSSSPSetNumStages - set the number of stages to use with the SSP method

    305:    Logically Collective

    307:    Input Parameters:
    308: +  ts - time stepping object
    309: -  nstages - number of stages

    311:    Options Database Keys:
    312:    -ts_ssp_type <rks2>: NumStages of SSP method (one of) rks2 rks3 rk104
    313:    -ts_ssp_nstages <5>: Number of stages

    315:    Level: beginner

    317: .seealso: TSSSP, TSSSPGetNumStages(), TSSSPSetNumStages(), TSSSPRKS2, TSSSPRKS3, TSSSPRK104
    318: @*/
    319: PetscErrorCode TSSSPSetNumStages(TS ts,PetscInt nstages)
    320: {

    325:   PetscTryMethod(ts,"TSSSPSetNumStages_C",(TS,PetscInt),(ts,nstages));
    326:   return(0);
    327: }

    329: /*@
    330:    TSSSPGetNumStages - get the number of stages in the SSP time integration scheme

    332:    Logically Collective

    334:    Input Parameter:
    335: .  ts - time stepping object

    337:    Output Parameter:
    338: .  nstages - number of stages

    340:    Level: beginner

    342: .seealso: TSSSP, TSSSPGetType(), TSSSPSetNumStages(), TSSSPRKS2, TSSSPRKS3, TSSSPRK104
    343: @*/
    344: PetscErrorCode TSSSPGetNumStages(TS ts,PetscInt *nstages)
    345: {

    350:   PetscUseMethod(ts,"TSSSPGetNumStages_C",(TS,PetscInt*),(ts,nstages));
    351:   return(0);
    352: }

    354: static PetscErrorCode TSSSPSetType_SSP(TS ts,TSSSPType type)
    355: {
    356:   PetscErrorCode ierr,(*r)(TS,PetscReal,PetscReal,Vec);
    357:   TS_SSP         *ssp = (TS_SSP*)ts->data;

    360:   PetscFunctionListFind(TSSSPList,type,&r);
    361:   if (!r) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_UNKNOWN_TYPE,"Unknown TS_SSP type %s given",type);
    362:   ssp->onestep = r;
    363:   PetscFree(ssp->type_name);
    364:   PetscStrallocpy(type,&ssp->type_name);
    365:   ts->default_adapt_type = TSADAPTNONE;
    366:   return(0);
    367: }
    368: static PetscErrorCode TSSSPGetType_SSP(TS ts,TSSSPType *type)
    369: {
    370:   TS_SSP *ssp = (TS_SSP*)ts->data;

    373:   *type = ssp->type_name;
    374:   return(0);
    375: }
    376: static PetscErrorCode TSSSPSetNumStages_SSP(TS ts,PetscInt nstages)
    377: {
    378:   TS_SSP *ssp = (TS_SSP*)ts->data;

    381:   ssp->nstages = nstages;
    382:   return(0);
    383: }
    384: static PetscErrorCode TSSSPGetNumStages_SSP(TS ts,PetscInt *nstages)
    385: {
    386:   TS_SSP *ssp = (TS_SSP*)ts->data;

    389:   *nstages = ssp->nstages;
    390:   return(0);
    391: }

    393: static PetscErrorCode TSSetFromOptions_SSP(PetscOptionItems *PetscOptionsObject,TS ts)
    394: {
    395:   char           tname[256] = TSSSPRKS2;
    396:   TS_SSP         *ssp       = (TS_SSP*)ts->data;
    398:   PetscBool      flg;

    401:   PetscOptionsHead(PetscOptionsObject,"SSP ODE solver options");
    402:   {
    403:     PetscOptionsFList("-ts_ssp_type","Type of SSP method","TSSSPSetType",TSSSPList,tname,tname,sizeof(tname),&flg);
    404:     if (flg) {
    405:       TSSSPSetType(ts,tname);
    406:     }
    407:     PetscOptionsInt("-ts_ssp_nstages","Number of stages","TSSSPSetNumStages",ssp->nstages,&ssp->nstages,NULL);
    408:   }
    409:   PetscOptionsTail();
    410:   return(0);
    411: }

    413: static PetscErrorCode TSView_SSP(TS ts,PetscViewer viewer)
    414: {
    415:   TS_SSP         *ssp = (TS_SSP*)ts->data;
    416:   PetscBool      ascii;

    420:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&ascii);
    421:   if (ascii) {PetscViewerASCIIPrintf(viewer,"  Scheme: %s\n",ssp->type_name);}
    422:   return(0);
    423: }

    425: /* ------------------------------------------------------------ */

    427: /*MC
    428:       TSSSP - Explicit strong stability preserving ODE solver

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

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

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

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

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

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

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

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

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

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

    460:   Level: beginner

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

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

    468: M*/
    469: PETSC_EXTERN PetscErrorCode TSCreate_SSP(TS ts)
    470: {
    471:   TS_SSP         *ssp;

    475:   TSSSPInitializePackage();

    477:   ts->ops->setup          = TSSetUp_SSP;
    478:   ts->ops->step           = TSStep_SSP;
    479:   ts->ops->reset          = TSReset_SSP;
    480:   ts->ops->destroy        = TSDestroy_SSP;
    481:   ts->ops->setfromoptions = TSSetFromOptions_SSP;
    482:   ts->ops->view           = TSView_SSP;

    484:   PetscNewLog(ts,&ssp);
    485:   ts->data = (void*)ssp;

    487:   PetscObjectComposeFunction((PetscObject)ts,"TSSSPGetType_C",TSSSPGetType_SSP);
    488:   PetscObjectComposeFunction((PetscObject)ts,"TSSSPSetType_C",TSSSPSetType_SSP);
    489:   PetscObjectComposeFunction((PetscObject)ts,"TSSSPGetNumStages_C",TSSSPGetNumStages_SSP);
    490:   PetscObjectComposeFunction((PetscObject)ts,"TSSSPSetNumStages_C",TSSSPSetNumStages_SSP);

    492:   TSSSPSetType(ts,TSSSPRKS2);
    493:   ssp->nstages = 5;
    494:   return(0);
    495: }

    497: /*@C
    498:   TSSSPInitializePackage - This function initializes everything in the TSSSP package. It is called
    499:   from TSInitializePackage().

    501:   Level: developer

    503: .seealso: PetscInitialize()
    504: @*/
    505: PetscErrorCode TSSSPInitializePackage(void)
    506: {

    510:   if (TSSSPPackageInitialized) return(0);
    511:   TSSSPPackageInitialized = PETSC_TRUE;
    512:   PetscFunctionListAdd(&TSSSPList,TSSSPRKS2, TSSSPStep_RK_2);
    513:   PetscFunctionListAdd(&TSSSPList,TSSSPRKS3, TSSSPStep_RK_3);
    514:   PetscFunctionListAdd(&TSSSPList,TSSSPRK104,TSSSPStep_RK_10_4);
    515:   PetscRegisterFinalize(TSSSPFinalizePackage);
    516:   return(0);
    517: }

    519: /*@C
    520:   TSSSPFinalizePackage - This function destroys everything in the TSSSP package. It is
    521:   called from PetscFinalize().

    523:   Level: developer

    525: .seealso: PetscFinalize()
    526: @*/
    527: PetscErrorCode TSSSPFinalizePackage(void)
    528: {

    532:   TSSSPPackageInitialized = PETSC_FALSE;
    533:   PetscFunctionListDestroy(&TSSSPList);
    534:   return(0);
    535: }