Actual source code: ms.c

petsc-3.9.0 2018-04-07
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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:   PetscNew(&link);
214:   t             = &link->tab;
215:   PetscStrallocpy(name,&t->name);
216:   t->nstages    = nstages;
217:   t->nregisters = nregisters;
218:   t->stability  = stability;

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

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

230: /*
231:   X - initial state, updated in-place.
232:   F - residual, computed at the initial X on input
233: */
234: static PetscErrorCode SNESMSStep_3Sstar(SNES snes,Vec X,Vec F)
235: {
236:   PetscErrorCode  ierr;
237:   SNES_MS         *ms    = (SNES_MS*)snes->data;
238:   SNESMSTableau   t      = ms->tableau;
239:   const PetscReal *gamma = t->gamma,*delta = t->delta,*betasub = t->betasub;
240:   Vec             S1,S2,S3,Y;
241:   PetscInt        i,nstages = t->nstages;;


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

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

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

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

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

281:   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);

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

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

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

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

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

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

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

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

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

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

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

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

365:   return(0);
366: }

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

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

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

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

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

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

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

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

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

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

448:   Logically collective

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

454:   Level: beginner

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

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

468: /* -------------------------------------------------------------------------- */
469: /*MC
470:       SNESMS - multi-stage smoothers

472:       Options Database:

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

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

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

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

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

490:       Level: beginner

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

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

501:   SNESMSInitializePackage();

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

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

513:   snes->alwayscomputesfinalresidual = PETSC_FALSE;

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

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