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;

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

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

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

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

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

     53:    Pseudocode 2 of Ketcheson 2008

     55:    Level: beginner

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

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

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

     86:    Pseudocode 2 of Ketcheson 2008

     88:    Level: beginner

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

    101:   s = ssp->nstages;
    102:   n = (PetscInt)(PetscSqrtReal((PetscReal)s)+0.001);
    103:   r = s-n;
    104:   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);
    105:   TSSSPGetWorkVectors(ts,3,&work);
    106:   F    = work[2];
    107:   VecCopy(sol,work[0]);
    108:   for (i=0; i<(n-1)*(n-2)/2; i++) {
    109:     c          = (i<n*(n+1)/2) ? 1.*i/(s-n) : (1.*i-n)/(s-n);
    110:     stage_time = t0+c*dt;
    111:     TSPreStage(ts,stage_time);
    112:     TSComputeRHSFunction(ts,stage_time,work[0],F);
    113:     VecAXPY(work[0],dt/r,F);
    114:   }
    115:   VecCopy(work[0],work[1]);
    116:   for (; i<n*(n+1)/2-1; 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:   {
    124:     c          = (i<n*(n+1)/2) ? 1.*i/(s-n) : (1.*i-n)/(s-n);
    125:     stage_time = t0+c*dt;
    126:     TSPreStage(ts,stage_time);
    127:     TSComputeRHSFunction(ts,stage_time,work[0],F);
    128:     VecAXPBYPCZ(work[0],1.*n/(2*n-1.),(n-1.)*dt/(r*(2*n-1)),(n-1.)/(2*n-1.),work[1],F);
    129:     i++;
    130:   }
    131:   for (; i<s; i++) {
    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:     VecAXPY(work[0],dt/r,F);
    137:   }
    138:   VecCopy(work[0],sol);
    139:   TSSSPRestoreWorkVectors(ts,3,&work);
    140:   return(0);
    141: }

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

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

    148:    Level: beginner

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

    161:   TSSSPGetWorkVectors(ts,3,&work);
    162:   F    = work[2];
    163:   VecCopy(sol,work[0]);
    164:   for (i=0; i<5; i++) {
    165:     stage_time = t0+c[i]*dt;
    166:     TSPreStage(ts,stage_time);
    167:     TSComputeRHSFunction(ts,stage_time,work[0],F);
    168:     VecAXPY(work[0],dt/6,F);
    169:   }
    170:   VecAXPBYPCZ(work[1],1./25,9./25,0,sol,work[0]);
    171:   VecAXPBY(work[0],15,-5,work[1]);
    172:   for (; i<9; i++) {
    173:     stage_time = t0+c[i]*dt;
    174:     TSPreStage(ts,stage_time);
    175:     TSComputeRHSFunction(ts,stage_time,work[0],F);
    176:     VecAXPY(work[0],dt/6,F);
    177:   }
    178:   stage_time = t0+dt;
    179:   TSPreStage(ts,stage_time);
    180:   TSComputeRHSFunction(ts,stage_time,work[0],F);
    181:   VecAXPBYPCZ(work[1],3./5,dt/10,1,work[0],F);
    182:   VecCopy(work[1],sol);
    183:   TSSSPRestoreWorkVectors(ts,3,&work);
    184:   return(0);
    185: }

    188: static PetscErrorCode TSSetUp_SSP(TS ts)
    189: {

    193:   TSCheckImplicitTerm(ts);
    194:   TSGetAdapt(ts,&ts->adapt);
    195:   TSAdaptCandidatesClear(ts->adapt);
    196:   return(0);
    197: }

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

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

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

    216:   ts->ptime += ts->time_step;
    217:   ts->time_step = next_time_step;
    218:   return(0);
    219: }
    220: /*------------------------------------------------------------*/

    222: static PetscErrorCode TSReset_SSP(TS ts)
    223: {
    224:   TS_SSP         *ssp = (TS_SSP*)ts->data;

    228:   if (ssp->work) {VecDestroyVecs(ssp->nwork,&ssp->work);}
    229:   ssp->nwork   = 0;
    230:   ssp->workout = PETSC_FALSE;
    231:   return(0);
    232: }

    234: static PetscErrorCode TSDestroy_SSP(TS ts)
    235: {
    236:   TS_SSP         *ssp = (TS_SSP*)ts->data;

    240:   TSReset_SSP(ts);
    241:   PetscFree(ssp->type_name);
    242:   PetscFree(ts->data);
    243:   PetscObjectComposeFunction((PetscObject)ts,"TSSSPGetType_C",NULL);
    244:   PetscObjectComposeFunction((PetscObject)ts,"TSSSPSetType_C",NULL);
    245:   PetscObjectComposeFunction((PetscObject)ts,"TSSSPGetNumStages_C",NULL);
    246:   PetscObjectComposeFunction((PetscObject)ts,"TSSSPSetNumStages_C",NULL);
    247:   return(0);
    248: }
    249: /*------------------------------------------------------------*/

    251: /*@C
    252:    TSSSPSetType - set the SSP time integration scheme to use

    254:    Logically Collective

    256:    Input Arguments:
    257:    ts - time stepping object
    258:    ssptype - type of scheme to use

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

    264:    Level: beginner

    266: .seealso: TSSSP, TSSSPGetType(), TSSSPSetNumStages(), TSSSPRKS2, TSSSPRKS3, TSSSPRK104
    267: @*/
    268: PetscErrorCode TSSSPSetType(TS ts,TSSSPType ssptype)
    269: {

    275:   PetscTryMethod(ts,"TSSSPSetType_C",(TS,TSSSPType),(ts,ssptype));
    276:   return(0);
    277: }

    279: /*@C
    280:    TSSSPGetType - get the SSP time integration scheme

    282:    Logically Collective

    284:    Input Argument:
    285:    ts - time stepping object

    287:    Output Argument:
    288:    type - type of scheme being used

    290:    Level: beginner

    292: .seealso: TSSSP, TSSSPSettype(), TSSSPSetNumStages(), TSSSPRKS2, TSSSPRKS3, TSSSPRK104
    293: @*/
    294: PetscErrorCode TSSSPGetType(TS ts,TSSSPType *type)
    295: {

    300:   PetscUseMethod(ts,"TSSSPGetType_C",(TS,TSSSPType*),(ts,type));
    301:   return(0);
    302: }

    304: /*@
    305:    TSSSPSetNumStages - set the number of stages to use with the SSP method

    307:    Logically Collective

    309:    Input Arguments:
    310:    ts - time stepping object
    311:    nstages - number of stages

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

    317:    Level: beginner

    319: .seealso: TSSSP, TSSSPGetNumStages(), TSSSPSetNumStages(), TSSSPRKS2, TSSSPRKS3, TSSSPRK104
    320: @*/
    321: PetscErrorCode TSSSPSetNumStages(TS ts,PetscInt nstages)
    322: {

    327:   PetscTryMethod(ts,"TSSSPSetNumStages_C",(TS,PetscInt),(ts,nstages));
    328:   return(0);
    329: }

    331: /*@
    332:    TSSSPGetNumStages - get the number of stages in the SSP time integration scheme

    334:    Logically Collective

    336:    Input Argument:
    337:    ts - time stepping object

    339:    Output Argument:
    340:    nstages - number of stages

    342:    Level: beginner

    344: .seealso: TSSSP, TSSSPGetType(), TSSSPSetNumStages(), TSSSPRKS2, TSSSPRKS3, TSSSPRK104
    345: @*/
    346: PetscErrorCode TSSSPGetNumStages(TS ts,PetscInt *nstages)
    347: {

    352:   PetscUseMethod(ts,"TSSSPGetNumStages_C",(TS,PetscInt*),(ts,nstages));
    353:   return(0);
    354: }

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

    362:   PetscFunctionListFind(TSSSPList,type,&r);
    363:   if (!r) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_UNKNOWN_TYPE,"Unknown TS_SSP type %s given",type);
    364:   ssp->onestep = r;
    365:   PetscFree(ssp->type_name);
    366:   PetscStrallocpy(type,&ssp->type_name);
    367:   ts->default_adapt_type = TSADAPTNONE;
    368:   return(0);
    369: }
    370: static PetscErrorCode TSSSPGetType_SSP(TS ts,TSSSPType *type)
    371: {
    372:   TS_SSP *ssp = (TS_SSP*)ts->data;

    375:   *type = ssp->type_name;
    376:   return(0);
    377: }
    378: static PetscErrorCode TSSSPSetNumStages_SSP(TS ts,PetscInt nstages)
    379: {
    380:   TS_SSP *ssp = (TS_SSP*)ts->data;

    383:   ssp->nstages = nstages;
    384:   return(0);
    385: }
    386: static PetscErrorCode TSSSPGetNumStages_SSP(TS ts,PetscInt *nstages)
    387: {
    388:   TS_SSP *ssp = (TS_SSP*)ts->data;

    391:   *nstages = ssp->nstages;
    392:   return(0);
    393: }

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

    403:   PetscOptionsHead(PetscOptionsObject,"SSP ODE solver options");
    404:   {
    405:     PetscOptionsFList("-ts_ssp_type","Type of SSP method","TSSSPSetType",TSSSPList,tname,tname,sizeof(tname),&flg);
    406:     if (flg) {
    407:       TSSSPSetType(ts,tname);
    408:     }
    409:     PetscOptionsInt("-ts_ssp_nstages","Number of stages","TSSSPSetNumStages",ssp->nstages,&ssp->nstages,NULL);
    410:   }
    411:   PetscOptionsTail();
    412:   return(0);
    413: }

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

    422:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&ascii);
    423:   if (ascii) {PetscViewerASCIIPrintf(viewer,"  Scheme: %s\n",ssp->type_name);}
    424:   return(0);
    425: }

    427: /* ------------------------------------------------------------ */

    429: /*MC
    430:       TSSSP - Explicit strong stability preserving ODE solver

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

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

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

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

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

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

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

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

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

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

    462:   Level: beginner

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

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

    470: M*/
    471: PETSC_EXTERN PetscErrorCode TSCreate_SSP(TS ts)
    472: {
    473:   TS_SSP         *ssp;

    477:   TSSSPInitializePackage();

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

    486:   PetscNewLog(ts,&ssp);
    487:   ts->data = (void*)ssp;

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

    494:   TSSSPSetType(ts,TSSSPRKS2);
    495:   ssp->nstages = 5;
    496:   return(0);
    497: }

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

    503:   Level: developer

    505: .seealso: PetscInitialize()
    506: @*/
    507: PetscErrorCode TSSSPInitializePackage(void)
    508: {

    512:   if (TSSSPPackageInitialized) return(0);
    513:   TSSSPPackageInitialized = PETSC_TRUE;
    514:   PetscFunctionListAdd(&TSSSPList,TSSSPRKS2, TSSSPStep_RK_2);
    515:   PetscFunctionListAdd(&TSSSPList,TSSSPRKS3, TSSSPStep_RK_3);
    516:   PetscFunctionListAdd(&TSSSPList,TSSSPRK104,TSSSPStep_RK_10_4);
    517:   PetscRegisterFinalize(TSSSPFinalizePackage);
    518:   return(0);
    519: }

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

    525:   Level: developer

    527: .seealso: PetscFinalize()
    528: @*/
    529: PetscErrorCode TSSSPFinalizePackage(void)
    530: {

    534:   TSSSPPackageInitialized = PETSC_FALSE;
    535:   PetscFunctionListDestroy(&TSSSPList);
    536:   return(0);
    537: }