Actual source code: irk.c

      1: /*
      2:   Code for timestepping with implicit Runge-Kutta method

      4:   Notes:
      5:   The general system is written as

      7:   F(t,U,Udot) = 0

      9: */
     10: #include <petsc/private/tsimpl.h>
     11: #include <petscdm.h>
     12: #include <petscdt.h>

     14: static TSIRKType         TSIRKDefault = TSIRKGAUSS;
     15: static PetscBool         TSIRKRegisterAllCalled;
     16: static PetscBool         TSIRKPackageInitialized;
     17: static PetscFunctionList TSIRKList;

     19: struct _IRKTableau{
     20:   PetscReal   *A,*b,*c;
     21:   PetscScalar *A_inv,*A_inv_rowsum,*I_s;
     22:   PetscReal   *binterp;   /* Dense output formula */
     23: };

     25: typedef struct _IRKTableau *IRKTableau;

     27: typedef struct {
     28:   char         *method_name;
     29:   PetscInt     order;            /* Classical approximation order of the method */
     30:   PetscInt     nstages;          /* Number of stages */
     31:   PetscBool    stiffly_accurate;
     32:   PetscInt     pinterp;          /* Interpolation order */
     33:   IRKTableau   tableau;
     34:   Vec          U0;               /* Backup vector */
     35:   Vec          Z;                /* Combined stage vector */
     36:   Vec          *Y;               /* States computed during the step */
     37:   Vec          Ydot;             /* Work vector holding time derivatives during residual evaluation */
     38:   Vec          U;                /* U is used to compute Ydot = shift(Y-U) */
     39:   Vec          *YdotI;           /* Work vectors to hold the residual evaluation */
     40:   Mat          TJ;               /* KAIJ matrix for the Jacobian of the combined system */
     41:   PetscScalar  *work;            /* Scalar work */
     42:   TSStepStatus status;
     43:   PetscBool    rebuild_completion;
     44:   PetscReal    ccfl;
     45: } TS_IRK;

     47: /*@C
     48:    TSIRKTableauCreate - create the tableau for TSIRK and provide the entries

     50:    Not Collective

     52:    Input Parameters:
     53: +  ts - timestepping context
     54: .  nstages - number of stages, this is the dimension of the matrices below
     55: .  A - stage coefficients (dimension nstages*nstages, row-major)
     56: .  b - step completion table (dimension nstages)
     57: .  c - abscissa (dimension nstages)
     58: .  binterp - coefficients of the interpolation formula (dimension nstages)
     59: .  A_inv - inverse of A (dimension nstages*nstages, row-major)
     60: .  A_inv_rowsum - row sum of the inverse of A (dimension nstages)
     61: -  I_s - identity matrix (dimension nstages*nstages)

     63:    Level: advanced

     65: .seealso: TSIRK, TSIRKRegister()
     66: @*/
     67: PetscErrorCode TSIRKTableauCreate(TS ts,PetscInt nstages,const PetscReal *A,const PetscReal *b,const PetscReal *c,const PetscReal *binterp,const PetscScalar *A_inv,const PetscScalar *A_inv_rowsum,const PetscScalar *I_s)
     68: {
     69:   TS_IRK         *irk = (TS_IRK*)ts->data;
     70:   IRKTableau     tab = irk->tableau;

     72:   irk->order = nstages;
     73:   PetscMalloc3(PetscSqr(nstages),&tab->A,PetscSqr(nstages),&tab->A_inv,PetscSqr(nstages),&tab->I_s);
     74:   PetscMalloc4(nstages,&tab->b,nstages,&tab->c,nstages,&tab->binterp,nstages,&tab->A_inv_rowsum);
     75:   PetscArraycpy(tab->A,A,PetscSqr(nstages));
     76:   PetscArraycpy(tab->b,b,nstages);
     77:   PetscArraycpy(tab->c,c,nstages);
     78:   /* optional coefficient arrays */
     79:   if (binterp) {
     80:     PetscArraycpy(tab->binterp,binterp,nstages);
     81:   }
     82:   if (A_inv) {
     83:     PetscArraycpy(tab->A_inv,A_inv,PetscSqr(nstages));
     84:   }
     85:   if (A_inv_rowsum) {
     86:     PetscArraycpy(tab->A_inv_rowsum,A_inv_rowsum,nstages);
     87:   }
     88:   if (I_s) {
     89:     PetscArraycpy(tab->I_s,I_s,PetscSqr(nstages));
     90:   }
     91:   return 0;
     92: }

     94: /* Arrays should be freed with PetscFree3(A,b,c) */
     95: static PetscErrorCode TSIRKCreate_Gauss(TS ts)
     96: {
     97:   PetscInt       nstages;
     98:   PetscReal      *gauss_A_real,*gauss_b,*b,*gauss_c;
     99:   PetscScalar    *gauss_A,*gauss_A_inv,*gauss_A_inv_rowsum,*I_s;
    100:   PetscScalar    *G0,*G1;
    101:   PetscInt       i,j;
    102:   Mat            G0mat,G1mat,Amat;

    104:   TSIRKGetNumStages(ts,&nstages);
    105:   PetscMalloc3(PetscSqr(nstages),&gauss_A_real,nstages,&gauss_b,nstages,&gauss_c);
    106:   PetscMalloc4(PetscSqr(nstages),&gauss_A,PetscSqr(nstages),&gauss_A_inv,nstages,&gauss_A_inv_rowsum,PetscSqr(nstages),&I_s);
    107:   PetscMalloc3(nstages,&b,PetscSqr(nstages),&G0,PetscSqr(nstages),&G1);
    108:   PetscDTGaussQuadrature(nstages,0.,1.,gauss_c,b);
    109:   for (i=0; i<nstages; i++) gauss_b[i] = b[i]; /* copy to possibly-complex array */

    111:   /* A^T = G0^{-1} G1 */
    112:   for (i=0; i<nstages; i++) {
    113:     for (j=0; j<nstages; j++) {
    114:       G0[i*nstages+j] = PetscPowRealInt(gauss_c[i],j);
    115:       G1[i*nstages+j] = PetscPowRealInt(gauss_c[i],j+1)/(j+1);
    116:     }
    117:   }
    118:   /* The arrays above are row-aligned, but we create dense matrices as the transpose */
    119:   MatCreateSeqDense(PETSC_COMM_SELF,nstages,nstages,G0,&G0mat);
    120:   MatCreateSeqDense(PETSC_COMM_SELF,nstages,nstages,G1,&G1mat);
    121:   MatCreateSeqDense(PETSC_COMM_SELF,nstages,nstages,gauss_A,&Amat);
    122:   MatLUFactor(G0mat,NULL,NULL,NULL);
    123:   MatMatSolve(G0mat,G1mat,Amat);
    124:   MatTranspose(Amat,MAT_INPLACE_MATRIX,&Amat);
    125:   for (i=0; i<nstages; i++)
    126:     for (j=0; j<nstages; j++)
    127:       gauss_A_real[i*nstages+j] = PetscRealPart(gauss_A[i*nstages+j]);

    129:   MatDestroy(&G0mat);
    130:   MatDestroy(&G1mat);
    131:   MatDestroy(&Amat);
    132:   PetscFree3(b,G0,G1);

    134:   {/* Invert A */
    135:     /* PETSc does not provide a routine to calculate the inverse of a general matrix.
    136:      * To get the inverse of A, we form a sequential BAIJ matrix from it, consisting of a single block with block size
    137:      * equal to the dimension of A, and then use MatInvertBlockDiagonal(). */
    138:     Mat               A_baij;
    139:     PetscInt          idxm[1]={0},idxn[1]={0};
    140:     const PetscScalar *A_inv;

    142:     MatCreateSeqBAIJ(PETSC_COMM_SELF,nstages,nstages,nstages,1,NULL,&A_baij);
    143:     MatSetOption(A_baij,MAT_ROW_ORIENTED,PETSC_FALSE);
    144:     MatSetValuesBlocked(A_baij,1,idxm,1,idxn,gauss_A,INSERT_VALUES);
    145:     MatAssemblyBegin(A_baij,MAT_FINAL_ASSEMBLY);
    146:     MatAssemblyEnd(A_baij,MAT_FINAL_ASSEMBLY);
    147:     MatInvertBlockDiagonal(A_baij,&A_inv);
    148:     PetscMemcpy(gauss_A_inv,A_inv,nstages*nstages*sizeof(PetscScalar));
    149:     MatDestroy(&A_baij);
    150:   }

    152:   /* Compute row sums A_inv_rowsum and identity I_s */
    153:   for (i=0; i<nstages; i++) {
    154:     gauss_A_inv_rowsum[i] = 0;
    155:     for (j=0; j<nstages; j++) {
    156:       gauss_A_inv_rowsum[i] += gauss_A_inv[i+nstages*j];
    157:       I_s[i+nstages*j] = 1.*(i == j);
    158:     }
    159:   }
    160:   TSIRKTableauCreate(ts,nstages,gauss_A_real,gauss_b,gauss_c,NULL,gauss_A_inv,gauss_A_inv_rowsum,I_s);
    161:   PetscFree3(gauss_A_real,gauss_b,gauss_c);
    162:   PetscFree4(gauss_A,gauss_A_inv,gauss_A_inv_rowsum,I_s);
    163:   return 0;
    164: }

    166: /*@C
    167:    TSIRKRegister -  adds a TSIRK implementation

    169:    Not Collective

    171:    Input Parameters:
    172: +  sname - name of user-defined IRK scheme
    173: -  function - function to create method context

    175:    Notes:
    176:    TSIRKRegister() may be called multiple times to add several user-defined families.

    178:    Sample usage:
    179: .vb
    180:    TSIRKRegister("my_scheme",MySchemeCreate);
    181: .ve

    183:    Then, your scheme can be chosen with the procedural interface via
    184: $     TSIRKSetType(ts,"my_scheme")
    185:    or at runtime via the option
    186: $     -ts_irk_type my_scheme

    188:    Level: advanced

    190: .seealso: TSIRKRegisterAll()
    191: @*/
    192: PetscErrorCode TSIRKRegister(const char sname[],PetscErrorCode (*function)(TS))
    193: {
    194:   TSIRKInitializePackage();
    195:   PetscFunctionListAdd(&TSIRKList,sname,function);
    196:   return 0;
    197: }

    199: /*@C
    200:   TSIRKRegisterAll - Registers all of the implicit Runge-Kutta methods in TSIRK

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

    204:   Level: advanced

    206: .seealso:  TSIRKRegisterDestroy()
    207: @*/
    208: PetscErrorCode TSIRKRegisterAll(void)
    209: {
    210:   if (TSIRKRegisterAllCalled) return 0;
    211:   TSIRKRegisterAllCalled = PETSC_TRUE;

    213:   TSIRKRegister(TSIRKGAUSS,TSIRKCreate_Gauss);
    214:   return 0;
    215: }

    217: /*@C
    218:    TSIRKRegisterDestroy - Frees the list of schemes that were registered by TSIRKRegister().

    220:    Not Collective

    222:    Level: advanced

    224: .seealso: TSIRKRegister(), TSIRKRegisterAll()
    225: @*/
    226: PetscErrorCode TSIRKRegisterDestroy(void)
    227: {
    228:   TSIRKRegisterAllCalled = PETSC_FALSE;
    229:   return 0;
    230: }

    232: /*@C
    233:   TSIRKInitializePackage - This function initializes everything in the TSIRK package. It is called
    234:   from TSInitializePackage().

    236:   Level: developer

    238: .seealso: PetscInitialize()
    239: @*/
    240: PetscErrorCode TSIRKInitializePackage(void)
    241: {
    242:   if (TSIRKPackageInitialized) return 0;
    243:   TSIRKPackageInitialized = PETSC_TRUE;
    244:   TSIRKRegisterAll();
    245:   PetscRegisterFinalize(TSIRKFinalizePackage);
    246:   return 0;
    247: }

    249: /*@C
    250:   TSIRKFinalizePackage - This function destroys everything in the TSIRK package. It is
    251:   called from PetscFinalize().

    253:   Level: developer

    255: .seealso: PetscFinalize()
    256: @*/
    257: PetscErrorCode TSIRKFinalizePackage(void)
    258: {
    259:   PetscFunctionListDestroy(&TSIRKList);
    260:   TSIRKPackageInitialized = PETSC_FALSE;
    261:   return 0;
    262: }

    264: /*
    265:  This function can be called before or after ts->vec_sol has been updated.
    266: */
    267: static PetscErrorCode TSEvaluateStep_IRK(TS ts,PetscInt order,Vec U,PetscBool *done)
    268: {
    269:   TS_IRK         *irk = (TS_IRK*)ts->data;
    270:   IRKTableau     tab = irk->tableau;
    271:   Vec            *YdotI = irk->YdotI;
    272:   PetscScalar    *w = irk->work;
    273:   PetscReal      h;
    274:   PetscInt       j;

    276:   switch (irk->status) {
    277:   case TS_STEP_INCOMPLETE:
    278:   case TS_STEP_PENDING:
    279:     h = ts->time_step; break;
    280:   case TS_STEP_COMPLETE:
    281:     h = ts->ptime - ts->ptime_prev; break;
    282:   default: SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_PLIB,"Invalid TSStepStatus");
    283:   }

    285:   VecCopy(ts->vec_sol,U);
    286:   for (j=0; j<irk->nstages; j++) w[j] = h*tab->b[j];
    287:   VecMAXPY(U,irk->nstages,w,YdotI);
    288:   return 0;
    289: }

    291: static PetscErrorCode TSRollBack_IRK(TS ts)
    292: {
    293:   TS_IRK         *irk = (TS_IRK*)ts->data;

    295:   VecCopy(irk->U0,ts->vec_sol);
    296:   return 0;
    297: }

    299: static PetscErrorCode TSStep_IRK(TS ts)
    300: {
    301:   TS_IRK          *irk = (TS_IRK*)ts->data;
    302:   IRKTableau      tab = irk->tableau;
    303:   PetscScalar     *A_inv = tab->A_inv,*A_inv_rowsum = tab->A_inv_rowsum;
    304:   const PetscInt  nstages = irk->nstages;
    305:   SNES            snes;
    306:   PetscInt        i,j,its,lits,bs;
    307:   TSAdapt         adapt;
    308:   PetscInt        rejections = 0;
    309:   PetscBool       accept = PETSC_TRUE;
    310:   PetscReal       next_time_step = ts->time_step;

    312:   if (!ts->steprollback) {
    313:     VecCopy(ts->vec_sol,irk->U0);
    314:   }
    315:   VecGetBlockSize(ts->vec_sol,&bs);
    316:   for (i=0; i<nstages; i++) {
    317:     VecStrideScatter(ts->vec_sol,i*bs,irk->Z,INSERT_VALUES);
    318:   }

    320:   irk->status = TS_STEP_INCOMPLETE;
    321:   while (!ts->reason && irk->status != TS_STEP_COMPLETE) {
    322:     VecCopy(ts->vec_sol,irk->U);
    323:     TSGetSNES(ts,&snes);
    324:     SNESSolve(snes,NULL,irk->Z);
    325:     SNESGetIterationNumber(snes,&its);
    326:     SNESGetLinearSolveIterations(snes,&lits);
    327:     ts->snes_its += its; ts->ksp_its += lits;
    328:     VecStrideGatherAll(irk->Z,irk->Y,INSERT_VALUES);
    329:     for (i=0; i<nstages; i++) {
    330:       VecZeroEntries(irk->YdotI[i]);
    331:       for (j=0; j<nstages; j++) {
    332:         VecAXPY(irk->YdotI[i],A_inv[i+j*nstages]/ts->time_step,irk->Y[j]);
    333:       }
    334:       VecAXPY(irk->YdotI[i],-A_inv_rowsum[i]/ts->time_step,irk->U);
    335:     }
    336:     irk->status = TS_STEP_INCOMPLETE;
    337:     TSEvaluateStep_IRK(ts,irk->order,ts->vec_sol,NULL);
    338:     irk->status = TS_STEP_PENDING;
    339:     TSGetAdapt(ts,&adapt);
    340:     TSAdaptChoose(adapt,ts,ts->time_step,NULL,&next_time_step,&accept);
    341:     irk->status = accept ? TS_STEP_COMPLETE : TS_STEP_INCOMPLETE;
    342:     if (!accept) {
    343:       TSRollBack_IRK(ts);
    344:       ts->time_step = next_time_step;
    345:       goto reject_step;
    346:     }

    348:     ts->ptime += ts->time_step;
    349:     ts->time_step = next_time_step;
    350:     break;
    351:   reject_step:
    352:     ts->reject++; accept = PETSC_FALSE;
    353:     if (!ts->reason && ++rejections > ts->max_reject && ts->max_reject >= 0) {
    354:       ts->reason = TS_DIVERGED_STEP_REJECTED;
    355:       PetscInfo(ts,"Step=%D, step rejections %D greater than current TS allowed, stopping solve\n",ts->steps,rejections);
    356:     }
    357:   }
    358:   return 0;
    359: }

    361: static PetscErrorCode TSInterpolate_IRK(TS ts,PetscReal itime,Vec U)
    362: {
    363:   TS_IRK          *irk = (TS_IRK*)ts->data;
    364:   PetscInt        nstages = irk->nstages,pinterp = irk->pinterp,i,j;
    365:   PetscReal       h;
    366:   PetscReal       tt,t;
    367:   PetscScalar     *bt;
    368:   const PetscReal *B = irk->tableau->binterp;

    371:   switch (irk->status) {
    372:   case TS_STEP_INCOMPLETE:
    373:   case TS_STEP_PENDING:
    374:     h = ts->time_step;
    375:     t = (itime - ts->ptime)/h;
    376:     break;
    377:   case TS_STEP_COMPLETE:
    378:     h = ts->ptime - ts->ptime_prev;
    379:     t = (itime - ts->ptime)/h + 1; /* In the interval [0,1] */
    380:     break;
    381:   default: SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_PLIB,"Invalid TSStepStatus");
    382:   }
    383:   PetscMalloc1(nstages,&bt);
    384:   for (i=0; i<nstages; i++) bt[i] = 0;
    385:   for (j=0,tt=t; j<pinterp; j++,tt*=t) {
    386:     for (i=0; i<nstages; i++) {
    387:       bt[i] += h * B[i*pinterp+j] * tt;
    388:     }
    389:   }
    390:   VecMAXPY(U,nstages,bt,irk->YdotI);
    391:   return 0;
    392: }

    394: static PetscErrorCode TSIRKTableauReset(TS ts)
    395: {
    396:   TS_IRK         *irk = (TS_IRK*)ts->data;
    397:   IRKTableau     tab = irk->tableau;

    399:   if (!tab) return 0;
    400:   PetscFree3(tab->A,tab->A_inv,tab->I_s);
    401:   PetscFree4(tab->b,tab->c,tab->binterp,tab->A_inv_rowsum);
    402:   return 0;
    403: }

    405: static PetscErrorCode TSReset_IRK(TS ts)
    406: {
    407:   TS_IRK         *irk = (TS_IRK*)ts->data;

    409:   TSIRKTableauReset(ts);
    410:   if (irk->tableau) {
    411:     PetscFree(irk->tableau);
    412:   }
    413:   if (irk->method_name) {
    414:     PetscFree(irk->method_name);
    415:   }
    416:   if (irk->work) {
    417:     PetscFree(irk->work);
    418:   }
    419:   VecDestroyVecs(irk->nstages,&irk->Y);
    420:   VecDestroyVecs(irk->nstages,&irk->YdotI);
    421:   VecDestroy(&irk->Ydot);
    422:   VecDestroy(&irk->Z);
    423:   VecDestroy(&irk->U);
    424:   VecDestroy(&irk->U0);
    425:   MatDestroy(&irk->TJ);
    426:   return 0;
    427: }

    429: static PetscErrorCode TSIRKGetVecs(TS ts,DM dm,Vec *U)
    430: {
    431:   TS_IRK         *irk = (TS_IRK*)ts->data;

    433:   if (U) {
    434:     if (dm && dm != ts->dm) {
    435:       DMGetNamedGlobalVector(dm,"TSIRK_U",U);
    436:     } else *U = irk->U;
    437:   }
    438:   return 0;
    439: }

    441: static PetscErrorCode TSIRKRestoreVecs(TS ts,DM dm,Vec *U)
    442: {
    443:   if (U) {
    444:     if (dm && dm != ts->dm) {
    445:       DMRestoreNamedGlobalVector(dm,"TSIRK_U",U);
    446:     }
    447:   }
    448:   return 0;
    449: }

    451: /*
    452:   This defines the nonlinear equations that is to be solved with SNES
    453:     G[e\otimes t + C*dt, Z, Zdot] = 0
    454:     Zdot = (In \otimes S)*Z - (In \otimes Se) U
    455:   where S = 1/(dt*A)
    456: */
    457: static PetscErrorCode SNESTSFormFunction_IRK(SNES snes,Vec ZC,Vec FC,TS ts)
    458: {
    459:   TS_IRK            *irk = (TS_IRK*)ts->data;
    460:   IRKTableau        tab  = irk->tableau;
    461:   const PetscInt    nstages = irk->nstages;
    462:   const PetscReal   *c = tab->c;
    463:   const PetscScalar *A_inv = tab->A_inv,*A_inv_rowsum = tab->A_inv_rowsum;
    464:   DM                dm,dmsave;
    465:   Vec               U,*YdotI = irk->YdotI,Ydot = irk->Ydot,*Y = irk->Y;
    466:   PetscReal         h = ts->time_step;
    467:   PetscInt          i,j;

    469:   SNESGetDM(snes,&dm);
    470:   TSIRKGetVecs(ts,dm,&U);
    471:   VecStrideGatherAll(ZC,Y,INSERT_VALUES);
    472:   dmsave = ts->dm;
    473:   ts->dm = dm;
    474:   for (i=0; i<nstages; i++) {
    475:     VecZeroEntries(Ydot);
    476:     for (j=0; j<nstages; j++) {
    477:       VecAXPY(Ydot,A_inv[j*nstages+i]/h,Y[j]);
    478:     }
    479:     VecAXPY(Ydot,-A_inv_rowsum[i]/h,U); /* Ydot = (S \otimes In)*Z - (Se \otimes In) U */
    480:     TSComputeIFunction(ts,ts->ptime+ts->time_step*c[i],Y[i],Ydot,YdotI[i],PETSC_FALSE);
    481:   }
    482:   VecStrideScatterAll(YdotI,FC,INSERT_VALUES);
    483:   ts->dm = dmsave;
    484:   TSIRKRestoreVecs(ts,dm,&U);
    485:   return 0;
    486: }

    488: /*
    489:    For explicit ODE, the Jacobian is
    490:      JC = I_n \otimes S - J \otimes I_s
    491:    For DAE, the Jacobian is
    492:      JC = M_n \otimes S - J \otimes I_s
    493: */
    494: static PetscErrorCode SNESTSFormJacobian_IRK(SNES snes,Vec ZC,Mat JC,Mat JCpre,TS ts)
    495: {
    496:   TS_IRK          *irk = (TS_IRK*)ts->data;
    497:   IRKTableau      tab  = irk->tableau;
    498:   const PetscInt  nstages = irk->nstages;
    499:   const PetscReal *c = tab->c;
    500:   DM              dm,dmsave;
    501:   Vec             *Y = irk->Y,Ydot = irk->Ydot;
    502:   Mat             J;
    503:   PetscScalar     *S;
    504:   PetscInt        i,j,bs;

    506:   SNESGetDM(snes,&dm);
    507:   /* irk->Ydot has already been computed in SNESTSFormFunction_IRK (SNES guarantees this) */
    508:   dmsave = ts->dm;
    509:   ts->dm = dm;
    510:   VecGetBlockSize(Y[nstages-1],&bs);
    511:   if (ts->equation_type <= TS_EQ_ODE_EXPLICIT) { /* Support explicit formulas only */
    512:     VecStrideGather(ZC,(nstages-1)*bs,Y[nstages-1],INSERT_VALUES);
    513:     MatKAIJGetAIJ(JC,&J);
    514:     TSComputeIJacobian(ts,ts->ptime+ts->time_step*c[nstages-1],Y[nstages-1],Ydot,0,J,J,PETSC_FALSE);
    515:     MatKAIJGetS(JC,NULL,NULL,&S);
    516:     for (i=0; i<nstages; i++)
    517:       for (j=0; j<nstages; j++)
    518:         S[i+nstages*j] = tab->A_inv[i+nstages*j]/ts->time_step;
    519:     MatKAIJRestoreS(JC,&S);
    520:   } else SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_SUP,"TSIRK %s does not support implicit formula",irk->method_name); /* TODO: need the mass matrix for DAE  */
    521:   ts->dm = dmsave;
    522:   return 0;
    523: }

    525: static PetscErrorCode DMCoarsenHook_TSIRK(DM fine,DM coarse,void *ctx)
    526: {
    527:   return 0;
    528: }

    530: static PetscErrorCode DMRestrictHook_TSIRK(DM fine,Mat restrct,Vec rscale,Mat inject,DM coarse,void *ctx)
    531: {
    532:   TS             ts = (TS)ctx;
    533:   Vec            U,U_c;

    535:   TSIRKGetVecs(ts,fine,&U);
    536:   TSIRKGetVecs(ts,coarse,&U_c);
    537:   MatRestrict(restrct,U,U_c);
    538:   VecPointwiseMult(U_c,rscale,U_c);
    539:   TSIRKRestoreVecs(ts,fine,&U);
    540:   TSIRKRestoreVecs(ts,coarse,&U_c);
    541:   return 0;
    542: }

    544: static PetscErrorCode DMSubDomainHook_TSIRK(DM dm,DM subdm,void *ctx)
    545: {
    546:   return 0;
    547: }

    549: static PetscErrorCode DMSubDomainRestrictHook_TSIRK(DM dm,VecScatter gscat,VecScatter lscat,DM subdm,void *ctx)
    550: {
    551:   TS             ts = (TS)ctx;
    552:   Vec            U,U_c;

    554:   TSIRKGetVecs(ts,dm,&U);
    555:   TSIRKGetVecs(ts,subdm,&U_c);

    557:   VecScatterBegin(gscat,U,U_c,INSERT_VALUES,SCATTER_FORWARD);
    558:   VecScatterEnd(gscat,U,U_c,INSERT_VALUES,SCATTER_FORWARD);

    560:   TSIRKRestoreVecs(ts,dm,&U);
    561:   TSIRKRestoreVecs(ts,subdm,&U_c);
    562:   return 0;
    563: }

    565: static PetscErrorCode TSSetUp_IRK(TS ts)
    566: {
    567:   TS_IRK         *irk = (TS_IRK*)ts->data;
    568:   IRKTableau     tab = irk->tableau;
    569:   DM             dm;
    570:   Mat            J;
    571:   Vec            R;
    572:   const PetscInt nstages = irk->nstages;
    573:   PetscInt       vsize,bs;

    575:   if (!irk->work) {
    576:     PetscMalloc1(irk->nstages,&irk->work);
    577:   }
    578:   if (!irk->Y) {
    579:     VecDuplicateVecs(ts->vec_sol,irk->nstages,&irk->Y);
    580:   }
    581:   if (!irk->YdotI) {
    582:     VecDuplicateVecs(ts->vec_sol,irk->nstages,&irk->YdotI);
    583:   }
    584:   if (!irk->Ydot) {
    585:     VecDuplicate(ts->vec_sol,&irk->Ydot);
    586:   }
    587:   if (!irk->U) {
    588:     VecDuplicate(ts->vec_sol,&irk->U);
    589:   }
    590:   if (!irk->U0) {
    591:     VecDuplicate(ts->vec_sol,&irk->U0);
    592:   }
    593:   if (!irk->Z) {
    594:     VecCreate(PetscObjectComm((PetscObject)ts->vec_sol),&irk->Z);
    595:     VecGetSize(ts->vec_sol,&vsize);
    596:     VecSetSizes(irk->Z,PETSC_DECIDE,vsize*irk->nstages);
    597:     VecGetBlockSize(ts->vec_sol,&bs);
    598:     VecSetBlockSize(irk->Z,irk->nstages*bs);
    599:     VecSetFromOptions(irk->Z);
    600:   }
    601:   TSGetDM(ts,&dm);
    602:   DMCoarsenHookAdd(dm,DMCoarsenHook_TSIRK,DMRestrictHook_TSIRK,ts);
    603:   DMSubDomainHookAdd(dm,DMSubDomainHook_TSIRK,DMSubDomainRestrictHook_TSIRK,ts);

    605:   TSGetSNES(ts,&ts->snes);
    606:   VecDuplicate(irk->Z,&R);
    607:   SNESSetFunction(ts->snes,R,SNESTSFormFunction,ts);
    608:   TSGetIJacobian(ts,&J,NULL,NULL,NULL);
    609:   if (!irk->TJ) {
    610:     /* Create the KAIJ matrix for solving the stages */
    611:     MatCreateKAIJ(J,nstages,nstages,tab->A_inv,tab->I_s,&irk->TJ);
    612:   }
    613:   SNESSetJacobian(ts->snes,irk->TJ,irk->TJ,SNESTSFormJacobian,ts);
    614:   VecDestroy(&R);
    615:   return 0;
    616: }

    618: static PetscErrorCode TSSetFromOptions_IRK(PetscOptionItems *PetscOptionsObject,TS ts)
    619: {
    620:   TS_IRK         *irk = (TS_IRK*)ts->data;
    621:   char           tname[256] = TSIRKGAUSS;

    623:   PetscOptionsHead(PetscOptionsObject,"IRK ODE solver options");
    624:   {
    625:     PetscBool flg1,flg2;
    626:     PetscOptionsInt("-ts_irk_nstages","Stages of the IRK method","TSIRKSetNumStages",irk->nstages,&irk->nstages,&flg1);
    627:     PetscOptionsFList("-ts_irk_type","Type of IRK method","TSIRKSetType",TSIRKList,irk->method_name[0] ? irk->method_name : tname,tname,sizeof(tname),&flg2);
    628:     if (flg1 ||flg2 || !irk->method_name[0]) { /* Create the method tableau after nstages or method is set */
    629:       TSIRKSetType(ts,tname);
    630:     }
    631:   }
    632:   PetscOptionsTail();
    633:   return 0;
    634: }

    636: static PetscErrorCode TSView_IRK(TS ts,PetscViewer viewer)
    637: {
    638:   TS_IRK         *irk = (TS_IRK*)ts->data;
    639:   PetscBool      iascii;

    641:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);
    642:   if (iascii) {
    643:     IRKTableau    tab = irk->tableau;
    644:     TSIRKType irktype;
    645:     char          buf[512];

    647:     TSIRKGetType(ts,&irktype);
    648:     PetscViewerASCIIPrintf(viewer,"  IRK type %s\n",irktype);
    649:     PetscFormatRealArray(buf,sizeof(buf),"% 8.6f",irk->nstages,tab->c);
    650:     PetscViewerASCIIPrintf(viewer,"  Abscissa       c = %s\n",buf);
    651:     PetscViewerASCIIPrintf(viewer,"Stiffly accurate: %s\n",irk->stiffly_accurate ? "yes" : "no");
    652:     PetscFormatRealArray(buf,sizeof(buf),"% 8.6f",PetscSqr(irk->nstages),tab->A);
    653:     PetscViewerASCIIPrintf(viewer,"  A coefficients       A = %s\n",buf);
    654:   }
    655:   return 0;
    656: }

    658: static PetscErrorCode TSLoad_IRK(TS ts,PetscViewer viewer)
    659: {
    660:   SNES           snes;
    661:   TSAdapt        adapt;

    663:   TSGetAdapt(ts,&adapt);
    664:   TSAdaptLoad(adapt,viewer);
    665:   TSGetSNES(ts,&snes);
    666:   SNESLoad(snes,viewer);
    667:   /* function and Jacobian context for SNES when used with TS is always ts object */
    668:   SNESSetFunction(snes,NULL,NULL,ts);
    669:   SNESSetJacobian(snes,NULL,NULL,NULL,ts);
    670:   return 0;
    671: }

    673: /*@C
    674:   TSIRKSetType - Set the type of IRK scheme

    676:   Logically collective

    678:   Input Parameters:
    679: +  ts - timestepping context
    680: -  irktype - type of IRK scheme

    682:   Options Database:
    683: .  -ts_irk_type <gauss> - set irk type

    685:   Level: intermediate

    687: .seealso: TSIRKGetType(), TSIRK, TSIRKType, TSIRKGAUSS
    688: @*/
    689: PetscErrorCode TSIRKSetType(TS ts,TSIRKType irktype)
    690: {
    693:   PetscTryMethod(ts,"TSIRKSetType_C",(TS,TSIRKType),(ts,irktype));
    694:   return 0;
    695: }

    697: /*@C
    698:   TSIRKGetType - Get the type of IRK IMEX scheme

    700:   Logically collective

    702:   Input Parameter:
    703: .  ts - timestepping context

    705:   Output Parameter:
    706: .  irktype - type of IRK-IMEX scheme

    708:   Level: intermediate

    710: .seealso: TSIRKGetType()
    711: @*/
    712: PetscErrorCode TSIRKGetType(TS ts,TSIRKType *irktype)
    713: {
    715:   PetscUseMethod(ts,"TSIRKGetType_C",(TS,TSIRKType*),(ts,irktype));
    716:   return 0;
    717: }

    719: /*@C
    720:   TSIRKSetNumStages - Set the number of stages of IRK scheme

    722:   Logically collective

    724:   Input Parameters:
    725: +  ts - timestepping context
    726: -  nstages - number of stages of IRK scheme

    728:   Options Database:
    729: .  -ts_irk_nstages <int> - set number of stages

    731:   Level: intermediate

    733: .seealso: TSIRKGetNumStages(), TSIRK
    734: @*/
    735: PetscErrorCode TSIRKSetNumStages(TS ts,PetscInt nstages)
    736: {
    738:   PetscTryMethod(ts,"TSIRKSetNumStages_C",(TS,PetscInt),(ts,nstages));
    739:   return 0;
    740: }

    742: /*@C
    743:   TSIRKGetNumStages - Get the number of stages of IRK scheme

    745:   Logically collective

    747:   Input Parameters:
    748: +  ts - timestepping context
    749: -  nstages - number of stages of IRK scheme

    751:   Level: intermediate

    753: .seealso: TSIRKSetNumStages(), TSIRK
    754: @*/
    755: PetscErrorCode TSIRKGetNumStages(TS ts,PetscInt *nstages)
    756: {
    759:   PetscTryMethod(ts,"TSIRKGetNumStages_C",(TS,PetscInt*),(ts,nstages));
    760:   return 0;
    761: }

    763: static PetscErrorCode TSIRKGetType_IRK(TS ts,TSIRKType *irktype)
    764: {
    765:   TS_IRK *irk = (TS_IRK*)ts->data;

    767:   *irktype = irk->method_name;
    768:   return 0;
    769: }

    771: static PetscErrorCode TSIRKSetType_IRK(TS ts,TSIRKType irktype)
    772: {
    773:   TS_IRK         *irk = (TS_IRK*)ts->data;
    774:   PetscErrorCode (*irkcreate)(TS);

    776:   if (irk->method_name) {
    777:     PetscFree(irk->method_name);
    778:     TSIRKTableauReset(ts);
    779:   }
    780:   PetscFunctionListFind(TSIRKList,irktype,&irkcreate);
    782:   (*irkcreate)(ts);
    783:   PetscStrallocpy(irktype,&irk->method_name);
    784:   return 0;
    785: }

    787: static PetscErrorCode TSIRKSetNumStages_IRK(TS ts,PetscInt nstages)
    788: {
    789:   TS_IRK *irk = (TS_IRK*)ts->data;

    792:   irk->nstages = nstages;
    793:   return 0;
    794: }

    796: static PetscErrorCode TSIRKGetNumStages_IRK(TS ts,PetscInt *nstages)
    797: {
    798:   TS_IRK *irk = (TS_IRK*)ts->data;

    801:   *nstages = irk->nstages;
    802:   return 0;
    803: }

    805: static PetscErrorCode TSDestroy_IRK(TS ts)
    806: {
    807:   TSReset_IRK(ts);
    808:   if (ts->dm) {
    809:     DMCoarsenHookRemove(ts->dm,DMCoarsenHook_TSIRK,DMRestrictHook_TSIRK,ts);
    810:     DMSubDomainHookRemove(ts->dm,DMSubDomainHook_TSIRK,DMSubDomainRestrictHook_TSIRK,ts);
    811:   }
    812:   PetscFree(ts->data);
    813:   PetscObjectComposeFunction((PetscObject)ts,"TSIRKSetType_C",NULL);
    814:   PetscObjectComposeFunction((PetscObject)ts,"TSIRKGetType_C",NULL);
    815:   PetscObjectComposeFunction((PetscObject)ts,"TSIRKSetNumStages_C",NULL);
    816:   PetscObjectComposeFunction((PetscObject)ts,"TSIRKGetNumStages_C",NULL);
    817:   return 0;
    818: }

    820: /*MC
    821:       TSIRK - ODE and DAE solver using Implicit Runge-Kutta schemes

    823:   Notes:

    825:   TSIRK uses the sparse Kronecker product matrix implementation of MATKAIJ to achieve good arithmetic intensity.

    827:   Gauss-Legrendre methods are currently supported. These are A-stable symplectic methods with an arbitrary number of stages. The order of accuracy is 2s when using s stages. The default method uses three stages and thus has an order of six. The number of stages (thus order) can be set with -ts_irk_nstages or TSIRKSetNumStages().

    829:   Level: beginner

    831: .seealso:  TSCreate(), TS, TSSetType(), TSIRKSetType(), TSIRKGetType(), TSIRKGAUSS, TSIRKRegister(), TSIRKSetNumStages()

    833: M*/
    834: PETSC_EXTERN PetscErrorCode TSCreate_IRK(TS ts)
    835: {
    836:   TS_IRK         *irk;

    838:   TSIRKInitializePackage();

    840:   ts->ops->reset          = TSReset_IRK;
    841:   ts->ops->destroy        = TSDestroy_IRK;
    842:   ts->ops->view           = TSView_IRK;
    843:   ts->ops->load           = TSLoad_IRK;
    844:   ts->ops->setup          = TSSetUp_IRK;
    845:   ts->ops->step           = TSStep_IRK;
    846:   ts->ops->interpolate    = TSInterpolate_IRK;
    847:   ts->ops->evaluatestep   = TSEvaluateStep_IRK;
    848:   ts->ops->rollback       = TSRollBack_IRK;
    849:   ts->ops->setfromoptions = TSSetFromOptions_IRK;
    850:   ts->ops->snesfunction   = SNESTSFormFunction_IRK;
    851:   ts->ops->snesjacobian   = SNESTSFormJacobian_IRK;

    853:   ts->usessnes = PETSC_TRUE;

    855:   PetscNewLog(ts,&irk);
    856:   ts->data = (void*)irk;

    858:   PetscObjectComposeFunction((PetscObject)ts,"TSIRKSetType_C",TSIRKSetType_IRK);
    859:   PetscObjectComposeFunction((PetscObject)ts,"TSIRKGetType_C",TSIRKGetType_IRK);
    860:   PetscObjectComposeFunction((PetscObject)ts,"TSIRKSetNumStages_C",TSIRKSetNumStages_IRK);
    861:   PetscObjectComposeFunction((PetscObject)ts,"TSIRKGetNumStages_C",TSIRKGetNumStages_IRK);
    862:   /* 3-stage IRK_Gauss is the default */
    863:   PetscNew(&irk->tableau);
    864:   irk->nstages = 3;
    865:   TSIRKSetType(ts,TSIRKDefault);
    866:   return 0;
    867: }