Actual source code: ms.c
petsc-3.10.5 2019-03-28
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      1:  #include <petsc/private/snesimpl.h>

      3: static SNESMSType SNESMSDefault = SNESMSM62;
      4: static PetscBool  SNESMSRegisterAllCalled;
      5: static PetscBool  SNESMSPackageInitialized;

      7: typedef struct _SNESMSTableau *SNESMSTableau;
      8: struct _SNESMSTableau {
      9:   char      *name;
     10:   PetscInt  nstages;            /* Number of stages */
     11:   PetscInt  nregisters;         /* Number of registers */
     12:   PetscReal stability;          /* Scaled stability region */
     13:   PetscReal *gamma;             /* Coefficients of 3S* method */
     14:   PetscReal *delta;             /* Coefficients of 3S* method */
     15:   PetscReal *betasub;           /* Subdiagonal of beta in Shu-Osher form */
     16: };

     18: typedef struct _SNESMSTableauLink *SNESMSTableauLink;
     19: struct _SNESMSTableauLink {
     20:   struct _SNESMSTableau tab;
     21:   SNESMSTableauLink     next;
     22: };
     23: static SNESMSTableauLink SNESMSTableauList;

     25: typedef struct {
     26:   SNESMSTableau tableau;        /* Tableau in low-storage form */
     27:   PetscReal     damping;        /* Damping parameter, like length of (pseudo) time step */
     28:   PetscBool     norms;          /* Compute norms, usually only for monitoring purposes */
     29: } SNES_MS;

     31: /*@C
     32:   SNESMSRegisterAll - Registers all of the multi-stage methods in SNESMS

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

     36:   Level: advanced

     38: .keywords: SNES, SNESMS, register, all

     40: .seealso:  SNESMSRegisterDestroy()
     41: @*/
     42: PetscErrorCode SNESMSRegisterAll(void)
     43: {

     47:   if (SNESMSRegisterAllCalled) return(0);
     48:   SNESMSRegisterAllCalled = PETSC_TRUE;

     50:   {
     51:     PetscReal gamma[3][1] = {{1.0},{0.0},{0.0}};
     52:     PetscReal delta[1]    = {0.0};
     53:     PetscReal betasub[1]  = {1.0};
     54:     SNESMSRegister(SNESMSEULER,1,3,1.0,&gamma[0][0],delta,betasub);
     55:   }

     57:   {
     58:     PetscReal gamma[3][6] = {
     59:       {0.0000000000000000E+00,  -7.0304722367110606E-01, -1.9836719667506464E-01, -1.6023843981863788E+00, 9.4483822882855284E-02,  -1.4204296130641869E-01},
     60:       {1.0000000000000000E+00,  1.1111025767083920E+00,  5.6150921583923230E-01,  7.4151723494934041E-01,  3.1714538168600587E-01,  4.6479276238548706E-01},
     61:       {0.0000000000000000E+00,  0.0000000000000000E+00,  0.0000000000000000E+00,  6.7968174970583317E-01,  -4.1755042846051737E-03, -1.9115668129923846E-01}
     62:     };
     63:     PetscReal delta[6]   = {1.0000000000000000E+00, 5.3275427433201750E-01, 6.0143544663985238E-01, 4.5874077053842177E-01, 2.7544386906104651E-01, 0.0000000000000000E+00};
     64:     PetscReal betasub[6] = {8.4753115429481929E-01, 7.4018896368655618E-01, 6.5963574086583309E-03, 4.6747795645517759E-01, 1.3314545813643919E-01, 5.3260800028018784E-01};
     65:     SNESMSRegister(SNESMSM62,6,3,1.0,&gamma[0][0],delta,betasub);
     66:   }
     67:   {
     68:     PetscReal gamma[3][4] = {{0,0,0,0},{0,0,0,0},{1,1,1,1}};
     69:     PetscReal delta[4]    = {0,0,0,0};
     70:     PetscReal betasub[4]  = {0.25, 0.5, 0.55, 1.0};
     71:     SNESMSRegister(SNESMSJAMESON83,4,3,1.0,&gamma[0][0],delta,betasub);
     72:   }
     73:   {                             /* Van Leer, Tai, and Powell (1989) 2 stage, order 1 */
     74:     PetscReal gamma[3][2] = {{0,0},{0,0},{1,1}};
     75:     PetscReal delta[2]    = {0,0};
     76:     PetscReal betasub[2]  = {0.3333,1.0};
     77:     SNESMSRegister(SNESMSVLTP21,2,3,1.0,&gamma[0][0],delta,betasub);
     78:   }
     79:   {                             /* Van Leer, Tai, and Powell (1989) 3 stage, order 1 */
     80:     PetscReal gamma[3][3] = {{0,0,0},{0,0,0},{1,1,1}};
     81:     PetscReal delta[3]    = {0,0,0};
     82:     PetscReal betasub[3]  = {0.1481,0.4000,1.0};
     83:     SNESMSRegister(SNESMSVLTP31,3,3,1.5,&gamma[0][0],delta,betasub);
     84:   }
     85:   {                             /* Van Leer, Tai, and Powell (1989) 4 stage, order 1 */
     86:     PetscReal gamma[3][4] = {{0,0,0,0},{0,0,0,0},{1,1,1,1}};
     87:     PetscReal delta[4]    = {0,0,0,0};
     88:     PetscReal betasub[4]  = {0.0833,0.2069,0.4265,1.0};
     89:     SNESMSRegister(SNESMSVLTP41,4,3,2.0,&gamma[0][0],delta,betasub);
     90:   }
     91:   {                             /* Van Leer, Tai, and Powell (1989) 5 stage, order 1 */
     92:     PetscReal gamma[3][5] = {{0,0,0,0,0},{0,0,0,0,0},{1,1,1,1,1}};
     93:     PetscReal delta[5]    = {0,0,0,0,0};
     94:     PetscReal betasub[5]  = {0.0533,0.1263,0.2375,0.4414,1.0};
     95:     SNESMSRegister(SNESMSVLTP51,5,3,2.5,&gamma[0][0],delta,betasub);
     96:   }
     97:   {                             /* Van Leer, Tai, and Powell (1989) 6 stage, order 1 */
     98:     PetscReal gamma[3][6] = {{0,0,0,0,0,0},{0,0,0,0,0,0},{1,1,1,1,1,1}};
     99:     PetscReal delta[6]    = {0,0,0,0,0,0};
    100:     PetscReal betasub[6]  = {0.0370,0.0851,0.1521,0.2562,0.4512,1.0};
    101:     SNESMSRegister(SNESMSVLTP61,6,3,3.0,&gamma[0][0],delta,betasub);
    102:   }
    103:   return(0);
    104: }

    106: /*@C
    107:    SNESMSRegisterDestroy - Frees the list of schemes that were registered by TSRosWRegister().

    109:    Not Collective

    111:    Level: advanced

    113: .keywords: TSRosW, register, destroy
    114: .seealso: TSRosWRegister(), TSRosWRegisterAll(), TSRosWRegister()
    115: @*/
    116: PetscErrorCode SNESMSRegisterDestroy(void)
    117: {
    118:   PetscErrorCode    ierr;
    119:   SNESMSTableauLink link;

    122:   while ((link = SNESMSTableauList)) {
    123:     SNESMSTableau t = &link->tab;
    124:     SNESMSTableauList = link->next;

    126:     PetscFree3(t->gamma,t->delta,t->betasub);
    127:     PetscFree(t->name);
    128:     PetscFree(link);
    129:   }
    130:   SNESMSRegisterAllCalled = PETSC_FALSE;
    131:   return(0);
    132: }

    134: /*@C
    135:   SNESMSInitializePackage - This function initializes everything in the SNESMS package. It is called
    136:   from PetscDLLibraryRegister() when using dynamic libraries, and on the first call to SNESCreate_MS()
    137:   when using static libraries.

    139:   Level: developer

    141: .keywords: SNES, SNESMS, initialize, package
    142: .seealso: PetscInitialize()
    143: @*/
    144: PetscErrorCode SNESMSInitializePackage(void)
    145: {

    149:   if (SNESMSPackageInitialized) return(0);
    150:   SNESMSPackageInitialized = PETSC_TRUE;

    152:   SNESMSRegisterAll();
    153:   PetscRegisterFinalize(SNESMSFinalizePackage);
    154:   return(0);
    155: }

    157: /*@C
    158:   SNESMSFinalizePackage - This function destroys everything in the SNESMS package. It is
    159:   called from PetscFinalize().

    161:   Level: developer

    163: .keywords: Petsc, destroy, package
    164: .seealso: PetscFinalize()
    165: @*/
    166: PetscErrorCode SNESMSFinalizePackage(void)
    167: {

    171:   SNESMSPackageInitialized = PETSC_FALSE;

    173:   SNESMSRegisterDestroy();
    174:   return(0);
    175: }

    177: /*@C
    178:    SNESMSRegister - register a multistage scheme

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

    182:    Input Parameters:
    183: +  name - identifier for method
    184: .  nstages - number of stages
    185: .  nregisters - number of registers used by low-storage implementation
    186: .  gamma - coefficients, see Ketcheson's paper
    187: .  delta - coefficients, see Ketcheson's paper
    188: -  betasub - subdiagonal of Shu-Osher form

    190:    Notes:
    191:    The notation is described in Ketcheson (2010) Runge-Kutta methods with minimum storage implementations.

    193:    Level: advanced

    195: .keywords: SNES, register

    197: .seealso: SNESMS
    198: @*/
    199: PetscErrorCode SNESMSRegister(SNESMSType name,PetscInt nstages,PetscInt nregisters,PetscReal stability,const PetscReal gamma[],const PetscReal delta[],const PetscReal betasub[])
    200: {
    201:   PetscErrorCode    ierr;
    202:   SNESMSTableauLink link;
    203:   SNESMSTableau     t;

    207:   if (nstages < 1) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Must have at least one stage");
    208:   if (nregisters != 3) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Only support for methods written in 3-register form");

    213:   SNESMSInitializePackage();
    214:   PetscNew(&link);
    215:   t             = &link->tab;
    216:   PetscStrallocpy(name,&t->name);
    217:   t->nstages    = nstages;
    218:   t->nregisters = nregisters;
    219:   t->stability  = stability;

    221:   PetscMalloc3(nstages*nregisters,&t->gamma,nstages,&t->delta,nstages,&t->betasub);
    222:   PetscMemcpy(t->gamma,gamma,nstages*nregisters*sizeof(PetscReal));
    223:   PetscMemcpy(t->delta,delta,nstages*sizeof(PetscReal));
    224:   PetscMemcpy(t->betasub,betasub,nstages*sizeof(PetscReal));

    226:   link->next        = SNESMSTableauList;
    227:   SNESMSTableauList = link;
    228:   return(0);
    229: }

    231: /*
    232:   X - initial state, updated in-place.
    233:   F - residual, computed at the initial X on input
    234: */
    235: static PetscErrorCode SNESMSStep_3Sstar(SNES snes,Vec X,Vec F)
    236: {
    237:   PetscErrorCode  ierr;
    238:   SNES_MS         *ms    = (SNES_MS*)snes->data;
    239:   SNESMSTableau   t      = ms->tableau;
    240:   const PetscReal *gamma = t->gamma,*delta = t->delta,*betasub = t->betasub;
    241:   Vec             S1,S2,S3,Y;
    242:   PetscInt        i,nstages = t->nstages;;

    246:   Y    = snes->work[0];
    247:   S1   = X;
    248:   S2   = snes->work[1];
    249:   S3   = snes->work[2];
    250:   VecZeroEntries(S2);
    251:   VecCopy(X,S3);
    252:   for (i=0; i<nstages; i++) {
    253:     Vec         Ss[4];
    254:     PetscScalar scoeff[4];

    256:     Ss[0] = S1; Ss[1] = S2; Ss[2] = S3; Ss[3] = Y;

    258:     scoeff[0] = gamma[0*nstages+i]-(PetscReal)1.0;
    259:     scoeff[1] = gamma[1*nstages+i];
    260:     scoeff[2] = gamma[2*nstages+i];
    261:     scoeff[3] = -betasub[i]*ms->damping;

    263:     VecAXPY(S2,delta[i],S1);
    264:     if (i>0) {
    265:       SNESComputeFunction(snes,S1,F);
    266:     }
    267:     KSPSolve(snes->ksp,F,Y);
    268:     VecMAXPY(S1,4,scoeff,Ss);
    269:   }
    270:   return(0);
    271: }

    273: static PetscErrorCode SNESSolve_MS(SNES snes)
    274: {
    275:   SNES_MS        *ms = (SNES_MS*)snes->data;
    276:   Vec            X   = snes->vec_sol,F = snes->vec_func;
    277:   PetscReal      fnorm;
    278:   PetscInt       i;

    282:   if (snes->xl || snes->xu || snes->ops->computevariablebounds) SETERRQ1(PetscObjectComm((PetscObject)snes),PETSC_ERR_ARG_WRONGSTATE, "SNES solver %s does not support bounds", ((PetscObject)snes)->type_name);

    284:   PetscCitationsRegister(SNESCitation,&SNEScite);
    285:   snes->reason = SNES_CONVERGED_ITERATING;
    286:   PetscObjectSAWsTakeAccess((PetscObject)snes);
    287:   snes->iter   = 0;
    288:   snes->norm   = 0.;
    289:   PetscObjectSAWsGrantAccess((PetscObject)snes);
    290:   if (!snes->vec_func_init_set) {
    291:     SNESComputeFunction(snes,X,F);
    292:   } else snes->vec_func_init_set = PETSC_FALSE;

    294:   if (snes->jacobian) {         /* This method does not require a Jacobian, but it is usually preconditioned by PBJacobi */
    295:     SNESComputeJacobian(snes,snes->vec_sol,snes->jacobian,snes->jacobian_pre);
    296:   }
    297:   if (ms->norms) {
    298:     VecNorm(F,NORM_2,&fnorm); /* fnorm <- ||F||  */
    299:     SNESCheckFunctionNorm(snes,fnorm);
    300:     /* Monitor convergence */
    301:     PetscObjectSAWsTakeAccess((PetscObject)snes);
    302:     snes->iter = 0;
    303:     snes->norm = fnorm;
    304:     PetscObjectSAWsGrantAccess((PetscObject)snes);
    305:     SNESLogConvergenceHistory(snes,snes->norm,0);
    306:     SNESMonitor(snes,snes->iter,snes->norm);

    308:     /* Test for convergence */
    309:     (*snes->ops->converged)(snes,snes->iter,0.0,0.0,fnorm,&snes->reason,snes->cnvP);
    310:     if (snes->reason) return(0);
    311:   }

    313:   /* Call general purpose update function */
    314:   if (snes->ops->update) {
    315:     (*snes->ops->update)(snes,snes->iter);
    316:   }
    317:   for (i = 0; i < snes->max_its; i++) {
    318:     SNESMSStep_3Sstar(snes,X,F);

    320:     if (i+1 < snes->max_its || ms->norms) {
    321:       SNESComputeFunction(snes,X,F);
    322:     }

    324:     if (ms->norms) {
    325:       VecNorm(F,NORM_2,&fnorm); /* fnorm <- ||F||  */
    326:       SNESCheckFunctionNorm(snes,fnorm);

    328:       /* Monitor convergence */
    329:       PetscObjectSAWsTakeAccess((PetscObject)snes);
    330:       snes->iter = i+1;
    331:       snes->norm = fnorm;
    332:       PetscObjectSAWsGrantAccess((PetscObject)snes);
    333:       SNESLogConvergenceHistory(snes,snes->norm,0);
    334:       SNESMonitor(snes,snes->iter,snes->norm);

    336:       /* Test for convergence */
    337:       (*snes->ops->converged)(snes,snes->iter,0.0,0.0,fnorm,&snes->reason,snes->cnvP);
    338:       if (snes->reason) return(0);
    339:     }

    341:     /* Call general purpose update function */
    342:     if (snes->ops->update) {
    343:       (*snes->ops->update)(snes, snes->iter);
    344:     }
    345:   }
    346:   if (!snes->reason) snes->reason = SNES_CONVERGED_ITS;
    347:   return(0);
    348: }

    350: static PetscErrorCode SNESSetUp_MS(SNES snes)
    351: {
    352:   SNES_MS        *ms = (SNES_MS*)snes->data;

    356:   if (!ms->tableau) {SNESMSSetType(snes,SNESMSDefault);}
    357:   SNESSetWorkVecs(snes,3);
    358:   SNESSetUpMatrices(snes);
    359:   return(0);
    360: }

    362: static PetscErrorCode SNESReset_MS(SNES snes)
    363: {

    366:   return(0);
    367: }

    369: static PetscErrorCode SNESDestroy_MS(SNES snes)
    370: {

    374:   PetscFree(snes->data);
    375:   PetscObjectComposeFunction((PetscObject)snes,"",NULL);
    376:   return(0);
    377: }

    379: static PetscErrorCode SNESView_MS(SNES snes,PetscViewer viewer)
    380: {
    381:   PetscBool      iascii;
    383:   SNES_MS        *ms = (SNES_MS*)snes->data;

    386:   PetscObjectTypeCompare((PetscObject) viewer, PETSCVIEWERASCII, &iascii);
    387:   if (iascii) {
    388:     SNESMSTableau tab = ms->tableau;
    389:     PetscViewerASCIIPrintf(viewer,"  multi-stage method type: %s\n",tab ? tab->name : "not yet set");
    390:   }
    391:   return(0);
    392: }

    394: static PetscErrorCode SNESSetFromOptions_MS(PetscOptionItems *PetscOptionsObject,SNES snes)
    395: {
    396:   SNES_MS        *ms = (SNES_MS*)snes->data;

    400:   PetscOptionsHead(PetscOptionsObject,"SNES MS options");
    401:   {
    402:     SNESMSTableauLink link;
    403:     PetscInt          count,choice;
    404:     PetscBool         flg;
    405:     const char        **namelist;
    406:     char              mstype[256];

    408:     PetscStrncpy(mstype,SNESMSDefault,sizeof(mstype));
    409:     for (link=SNESMSTableauList,count=0; link; link=link->next,count++) ;
    410:     PetscMalloc1(count,(char***)&namelist);
    411:     for (link=SNESMSTableauList,count=0; link; link=link->next,count++) namelist[count] = link->tab.name;
    412:     PetscOptionsEList("-snes_ms_type","Multistage smoother type","SNESMSSetType",(const char*const*)namelist,count,mstype,&choice,&flg);
    413:     SNESMSSetType(snes,flg ? namelist[choice] : mstype);
    414:     PetscFree(namelist);
    415:     PetscOptionsReal("-snes_ms_damping","Damping for multistage method","SNESMSSetDamping",ms->damping,&ms->damping,NULL);
    416:     PetscOptionsBool("-snes_ms_norms","Compute norms for monitoring","none",ms->norms,&ms->norms,NULL);
    417:   }
    418:   PetscOptionsTail();
    419:   return(0);
    420: }

    422: PetscErrorCode  SNESMSSetType_MS(SNES snes,SNESMSType mstype)
    423: {
    424:   PetscErrorCode    ierr;
    425:   SNES_MS           *ms = (SNES_MS*)snes->data;
    426:   SNESMSTableauLink link;
    427:   PetscBool         match;

    430:   if (ms->tableau) {
    431:     PetscStrcmp(ms->tableau->name,mstype,&match);
    432:     if (match) return(0);
    433:   }
    434:   for (link = SNESMSTableauList; link; link=link->next) {
    435:     PetscStrcmp(link->tab.name,mstype,&match);
    436:     if (match) {
    437:       SNESReset_MS(snes);
    438:       ms->tableau = &link->tab;
    439:       return(0);
    440:     }
    441:   }
    442:   SETERRQ1(PetscObjectComm((PetscObject)snes),PETSC_ERR_ARG_UNKNOWN_TYPE,"Could not find '%s'",mstype);
    443:   return(0);
    444: }

    446: /*@C
    447:   SNESMSSetType - Set the type of multistage smoother

    449:   Logically collective

    451:   Input Parameter:
    452: +  snes - nonlinear solver context
    453: -  mstype - type of multistage method

    455:   Level: beginner

    457: .seealso: SNESMSGetType(), SNESMS
    458: @*/
    459: PetscErrorCode SNESMSSetType(SNES snes,SNESMSType rostype)
    460: {

    465:   PetscTryMethod(snes,"SNESMSSetType_C",(SNES,SNESMSType),(snes,rostype));
    466:   return(0);
    467: }

    469: /* -------------------------------------------------------------------------- */
    470: /*MC
    471:       SNESMS - multi-stage smoothers

    473:       Options Database:

    475: +     -snes_ms_type - type of multi-stage smoother
    476: -     -snes_ms_damping - damping for multi-stage method

    478:       Notes:
    479:       These multistage methods are explicit Runge-Kutta methods that are often used as smoothers for
    480:       FAS multigrid for transport problems. In the linear case, these are equivalent to polynomial smoothers (such as Chebyshev).

    482:       Multi-stage smoothers should usually be preconditioned by point-block Jacobi to ensure proper scaling and to normalize the wave speeds.

    484:       The methods are specified in low storage form (Ketcheson 2010). New methods can be registered with SNESMSRegister().

    486:       References:
    487: +   1. -   Ketcheson (2010) Runge Kutta methods with minimum storage implementations.
    488: .   2. -   Jameson (1983) Solution of the Euler equations for two dimensional transonic flow by a multigrid method.
    489: -   3. -   Pierce and Giles (1997) Preconditioned multigrid methods for compressible flow calculations on stretched meshes.

    491:       Level: beginner

    493: .seealso:  SNESCreate(), SNES, SNESSetType(), SNESMS, SNESFAS, KSPCHEBYSHEV

    495: M*/
    496: PETSC_EXTERN PetscErrorCode SNESCreate_MS(SNES snes)
    497: {
    499:   SNES_MS        *ms;

    502:   SNESMSInitializePackage();

    504:   snes->ops->setup          = SNESSetUp_MS;
    505:   snes->ops->solve          = SNESSolve_MS;
    506:   snes->ops->destroy        = SNESDestroy_MS;
    507:   snes->ops->setfromoptions = SNESSetFromOptions_MS;
    508:   snes->ops->view           = SNESView_MS;
    509:   snes->ops->reset          = SNESReset_MS;

    511:   snes->usesnpc = PETSC_FALSE;
    512:   snes->usesksp = PETSC_TRUE;

    514:   snes->alwayscomputesfinalresidual = PETSC_FALSE;

    516:   PetscNewLog(snes,&ms);
    517:   snes->data  = (void*)ms;
    518:   ms->damping = 0.9;
    519:   ms->norms   = PETSC_FALSE;

    521:   PetscObjectComposeFunction((PetscObject)snes,"SNESMSSetType_C",SNESMSSetType_MS);
    522:   return(0);
    523: }