Actual source code: theta.c

petsc-main 2021-04-20
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  1: /*
  2:   Code for timestepping with implicit Theta method
  3: */
  4: #include <petsc/private/tsimpl.h>
  5: #include <petscsnes.h>
  6: #include <petscdm.h>
  7: #include <petscmat.h>

  9: typedef struct {
 10:   /* context for time stepping */
 11:   PetscReal    stage_time;
 12:   Vec          X0,X,Xdot;                /* Storage for stage solution, u^n + dt a_{11} k_1, and time derivative u^{n+1}_t */
 13:   Vec          affine;                   /* Affine vector needed for residual at beginning of step in endpoint formulation */
 14:   PetscReal    Theta;
 15:   PetscReal    shift;                    /* Shift parameter for SNES Jacobian, used by forward, TLM and adjoint */
 16:   PetscInt     order;
 17:   PetscBool    endpoint;
 18:   PetscBool    extrapolate;
 19:   TSStepStatus status;
 20:   Vec          VecCostIntegral0;         /* Backup for roll-backs due to events, used by cost integral */
 21:   PetscReal    ptime0;                   /* Backup for ts->ptime, the start time of current time step, used by TLM and cost integral */
 22:   PetscReal    time_step0;               /* Backup for ts->timestep, the step size of current time step, used by TLM and cost integral*/

 24:   /* context for sensitivity analysis */
 25:   PetscInt     num_tlm;                  /* Total number of tangent linear equations */
 26:   Vec          *VecsDeltaLam;            /* Increment of the adjoint sensitivity w.r.t IC at stage */
 27:   Vec          *VecsDeltaMu;             /* Increment of the adjoint sensitivity w.r.t P at stage */
 28:   Vec          *VecsSensiTemp;           /* Vector to be multiplied with Jacobian transpose */
 29:   Mat          MatDeltaFwdSensip;        /* Increment of the forward sensitivity at stage */
 30:   Vec          VecDeltaFwdSensipCol;     /* Working vector for holding one column of the sensitivity matrix */
 31:   Mat          MatFwdSensip0;            /* backup for roll-backs due to events */
 32:   Mat          MatIntegralSensipTemp;    /* Working vector for forward integral sensitivity */
 33:   Mat          MatIntegralSensip0;       /* backup for roll-backs due to events */
 34:   Vec          *VecsDeltaLam2;           /* Increment of the 2nd-order adjoint sensitivity w.r.t IC at stage */
 35:   Vec          *VecsDeltaMu2;            /* Increment of the 2nd-order adjoint sensitivity w.r.t P at stage */
 36:   Vec          *VecsSensi2Temp;          /* Working vectors that holds the residual for the second-order adjoint */
 37:   Vec          *VecsAffine;              /* Working vectors to store residuals */
 38:   /* context for error estimation */
 39:   Vec          vec_sol_prev;
 40:   Vec          vec_lte_work;
 41: } TS_Theta;

 43: static PetscErrorCode TSThetaGetX0AndXdot(TS ts,DM dm,Vec *X0,Vec *Xdot)
 44: {
 45:   TS_Theta       *th = (TS_Theta*)ts->data;

 49:   if (X0) {
 50:     if (dm && dm != ts->dm) {
 51:       DMGetNamedGlobalVector(dm,"TSTheta_X0",X0);
 52:     } else *X0 = ts->vec_sol;
 53:   }
 54:   if (Xdot) {
 55:     if (dm && dm != ts->dm) {
 56:       DMGetNamedGlobalVector(dm,"TSTheta_Xdot",Xdot);
 57:     } else *Xdot = th->Xdot;
 58:   }
 59:   return(0);
 60: }

 62: static PetscErrorCode TSThetaRestoreX0AndXdot(TS ts,DM dm,Vec *X0,Vec *Xdot)
 63: {

 67:   if (X0) {
 68:     if (dm && dm != ts->dm) {
 69:       DMRestoreNamedGlobalVector(dm,"TSTheta_X0",X0);
 70:     }
 71:   }
 72:   if (Xdot) {
 73:     if (dm && dm != ts->dm) {
 74:       DMRestoreNamedGlobalVector(dm,"TSTheta_Xdot",Xdot);
 75:     }
 76:   }
 77:   return(0);
 78: }

 80: static PetscErrorCode DMCoarsenHook_TSTheta(DM fine,DM coarse,void *ctx)
 81: {
 83:   return(0);
 84: }

 86: static PetscErrorCode DMRestrictHook_TSTheta(DM fine,Mat restrct,Vec rscale,Mat inject,DM coarse,void *ctx)
 87: {
 88:   TS             ts = (TS)ctx;
 90:   Vec            X0,Xdot,X0_c,Xdot_c;

 93:   TSThetaGetX0AndXdot(ts,fine,&X0,&Xdot);
 94:   TSThetaGetX0AndXdot(ts,coarse,&X0_c,&Xdot_c);
 95:   MatRestrict(restrct,X0,X0_c);
 96:   MatRestrict(restrct,Xdot,Xdot_c);
 97:   VecPointwiseMult(X0_c,rscale,X0_c);
 98:   VecPointwiseMult(Xdot_c,rscale,Xdot_c);
 99:   TSThetaRestoreX0AndXdot(ts,fine,&X0,&Xdot);
100:   TSThetaRestoreX0AndXdot(ts,coarse,&X0_c,&Xdot_c);
101:   return(0);
102: }

104: static PetscErrorCode DMSubDomainHook_TSTheta(DM dm,DM subdm,void *ctx)
105: {
107:   return(0);
108: }

110: static PetscErrorCode DMSubDomainRestrictHook_TSTheta(DM dm,VecScatter gscat,VecScatter lscat,DM subdm,void *ctx)
111: {
112:   TS             ts = (TS)ctx;
114:   Vec            X0,Xdot,X0_sub,Xdot_sub;

117:   TSThetaGetX0AndXdot(ts,dm,&X0,&Xdot);
118:   TSThetaGetX0AndXdot(ts,subdm,&X0_sub,&Xdot_sub);

120:   VecScatterBegin(gscat,X0,X0_sub,INSERT_VALUES,SCATTER_FORWARD);
121:   VecScatterEnd(gscat,X0,X0_sub,INSERT_VALUES,SCATTER_FORWARD);

123:   VecScatterBegin(gscat,Xdot,Xdot_sub,INSERT_VALUES,SCATTER_FORWARD);
124:   VecScatterEnd(gscat,Xdot,Xdot_sub,INSERT_VALUES,SCATTER_FORWARD);

126:   TSThetaRestoreX0AndXdot(ts,dm,&X0,&Xdot);
127:   TSThetaRestoreX0AndXdot(ts,subdm,&X0_sub,&Xdot_sub);
128:   return(0);
129: }

131: static PetscErrorCode TSThetaEvaluateCostIntegral(TS ts)
132: {
133:   TS_Theta       *th = (TS_Theta*)ts->data;
134:   TS             quadts = ts->quadraturets;

138:   if (th->endpoint) {
139:     /* Evolve ts->vec_costintegral to compute integrals */
140:     if (th->Theta!=1.0) {
141:       TSComputeRHSFunction(quadts,th->ptime0,th->X0,ts->vec_costintegrand);
142:       VecAXPY(quadts->vec_sol,th->time_step0*(1.0-th->Theta),ts->vec_costintegrand);
143:     }
144:     TSComputeRHSFunction(quadts,ts->ptime,ts->vec_sol,ts->vec_costintegrand);
145:     VecAXPY(quadts->vec_sol,th->time_step0*th->Theta,ts->vec_costintegrand);
146:   } else {
147:     TSComputeRHSFunction(quadts,th->stage_time,th->X,ts->vec_costintegrand);
148:     VecAXPY(quadts->vec_sol,th->time_step0,ts->vec_costintegrand);
149:   }
150:   return(0);
151: }

153: static PetscErrorCode TSForwardCostIntegral_Theta(TS ts)
154: {
155:   TS_Theta       *th = (TS_Theta*)ts->data;
156:   TS             quadts = ts->quadraturets;

160:   /* backup cost integral */
161:   VecCopy(quadts->vec_sol,th->VecCostIntegral0);
162:   TSThetaEvaluateCostIntegral(ts);
163:   return(0);
164: }

166: static PetscErrorCode TSAdjointCostIntegral_Theta(TS ts)
167: {
168:   TS_Theta       *th = (TS_Theta*)ts->data;

172:   /* Like TSForwardCostIntegral(), the adjoint cost integral evaluation relies on ptime0 and time_step0. */
173:   th->ptime0     = ts->ptime + ts->time_step;
174:   th->time_step0 = -ts->time_step;
175:   TSThetaEvaluateCostIntegral(ts);
176:   return(0);
177: }

179: static PetscErrorCode TSTheta_SNESSolve(TS ts,Vec b,Vec x)
180: {
181:   PetscInt       nits,lits;

185:   SNESSolve(ts->snes,b,x);
186:   SNESGetIterationNumber(ts->snes,&nits);
187:   SNESGetLinearSolveIterations(ts->snes,&lits);
188:   ts->snes_its += nits; ts->ksp_its += lits;
189:   return(0);
190: }

192: static PetscErrorCode TSStep_Theta(TS ts)
193: {
194:   TS_Theta       *th = (TS_Theta*)ts->data;
195:   PetscInt       rejections = 0;
196:   PetscBool      stageok,accept = PETSC_TRUE;
197:   PetscReal      next_time_step = ts->time_step;

201:   if (!ts->steprollback) {
202:     if (th->vec_sol_prev) { VecCopy(th->X0,th->vec_sol_prev); }
203:     VecCopy(ts->vec_sol,th->X0);
204:   }

206:   th->status     = TS_STEP_INCOMPLETE;
207:   while (!ts->reason && th->status != TS_STEP_COMPLETE) {
208:     th->shift      = 1/(th->Theta*ts->time_step);
209:     th->stage_time = ts->ptime + (th->endpoint ? (PetscReal)1 : th->Theta)*ts->time_step;
210:     VecCopy(th->X0,th->X);
211:     if (th->extrapolate && !ts->steprestart) {
212:       VecAXPY(th->X,1/th->shift,th->Xdot);
213:     }
214:     if (th->endpoint) { /* This formulation assumes linear time-independent mass matrix */
215:       if (!th->affine) {VecDuplicate(ts->vec_sol,&th->affine);}
216:       VecZeroEntries(th->Xdot);
217:       TSComputeIFunction(ts,ts->ptime,th->X0,th->Xdot,th->affine,PETSC_FALSE);
218:       VecScale(th->affine,(th->Theta-1)/th->Theta);
219:     } else if (th->affine) { /* Just in case th->endpoint is changed between calls to TSStep_Theta() */
220:       VecZeroEntries(th->affine);
221:     }
222:     TSPreStage(ts,th->stage_time);
223:     TSTheta_SNESSolve(ts,th->affine,th->X);
224:     TSPostStage(ts,th->stage_time,0,&th->X);
225:     TSAdaptCheckStage(ts->adapt,ts,th->stage_time,th->X,&stageok);
226:     if (!stageok) goto reject_step;

228:     th->status = TS_STEP_PENDING;
229:     if (th->endpoint) {
230:       VecCopy(th->X,ts->vec_sol);
231:     } else {
232:       VecAXPBYPCZ(th->Xdot,-th->shift,th->shift,0,th->X0,th->X);
233:       VecAXPY(ts->vec_sol,ts->time_step,th->Xdot);
234:     }
235:     TSAdaptChoose(ts->adapt,ts,ts->time_step,NULL,&next_time_step,&accept);
236:     th->status = accept ? TS_STEP_COMPLETE : TS_STEP_INCOMPLETE;
237:     if (!accept) {
238:       VecCopy(th->X0,ts->vec_sol);
239:       ts->time_step = next_time_step;
240:       goto reject_step;
241:     }

243:     if (ts->forward_solve || ts->costintegralfwd) { /* Save the info for the later use in cost integral evaluation */
244:       th->ptime0     = ts->ptime;
245:       th->time_step0 = ts->time_step;
246:     }
247:     ts->ptime += ts->time_step;
248:     ts->time_step = next_time_step;
249:     break;

251:   reject_step:
252:     ts->reject++; accept = PETSC_FALSE;
253:     if (!ts->reason && ++rejections > ts->max_reject && ts->max_reject >= 0) {
254:       ts->reason = TS_DIVERGED_STEP_REJECTED;
255:       PetscInfo2(ts,"Step=%D, step rejections %D greater than current TS allowed, stopping solve\n",ts->steps,rejections);
256:     }
257:   }
258:   return(0);
259: }

261: static PetscErrorCode TSAdjointStepBEuler_Private(TS ts)
262: {
263:   TS_Theta       *th = (TS_Theta*)ts->data;
264:   TS             quadts = ts->quadraturets;
265:   Vec            *VecsDeltaLam = th->VecsDeltaLam,*VecsDeltaMu = th->VecsDeltaMu,*VecsSensiTemp = th->VecsSensiTemp;
266:   Vec            *VecsDeltaLam2 = th->VecsDeltaLam2,*VecsDeltaMu2 = th->VecsDeltaMu2,*VecsSensi2Temp = th->VecsSensi2Temp;
267:   PetscInt       nadj;
268:   Mat            J,Jpre,quadJ = NULL,quadJp = NULL;
269:   KSP            ksp;
270:   PetscScalar    *xarr;
271:   TSEquationType eqtype;
272:   PetscBool      isexplicitode = PETSC_FALSE;
273:   PetscReal      adjoint_time_step;

277:   TSGetEquationType(ts,&eqtype);
278:   if (eqtype == TS_EQ_ODE_EXPLICIT) {
279:     isexplicitode  = PETSC_TRUE;
280:     VecsDeltaLam  = ts->vecs_sensi;
281:     VecsDeltaLam2 = ts->vecs_sensi2;
282:   }
283:   th->status = TS_STEP_INCOMPLETE;
284:   SNESGetKSP(ts->snes,&ksp);
285:   TSGetIJacobian(ts,&J,&Jpre,NULL,NULL);
286:   if (quadts) {
287:     TSGetRHSJacobian(quadts,&quadJ,NULL,NULL,NULL);
288:     TSGetRHSJacobianP(quadts,&quadJp,NULL,NULL);
289:   }

291:   th->stage_time    = ts->ptime;
292:   adjoint_time_step = -ts->time_step; /* always positive since time_step is negative */

294:   /* Build RHS for first-order adjoint lambda_{n+1}/h + r_u^T(n+1) */
295:   if (quadts) {
296:     TSComputeRHSJacobian(quadts,th->stage_time,ts->vec_sol,quadJ,NULL);
297:   }

299:   for (nadj=0; nadj<ts->numcost; nadj++) {
300:     VecCopy(ts->vecs_sensi[nadj],VecsSensiTemp[nadj]);
301:     VecScale(VecsSensiTemp[nadj],1./adjoint_time_step); /* lambda_{n+1}/h */
302:     if (quadJ) {
303:       MatDenseGetColumn(quadJ,nadj,&xarr);
304:       VecPlaceArray(ts->vec_drdu_col,xarr);
305:       VecAXPY(VecsSensiTemp[nadj],1.,ts->vec_drdu_col);
306:       VecResetArray(ts->vec_drdu_col);
307:       MatDenseRestoreColumn(quadJ,&xarr);
308:     }
309:   }

311:   /* Build LHS for first-order adjoint */
312:   th->shift = 1./adjoint_time_step;
313:   TSComputeSNESJacobian(ts,ts->vec_sol,J,Jpre);
314:   KSPSetOperators(ksp,J,Jpre);

316:   /* Solve stage equation LHS*lambda_s = RHS for first-order adjoint */
317:   for (nadj=0; nadj<ts->numcost; nadj++) {
318:     KSPConvergedReason kspreason;
319:     KSPSolveTranspose(ksp,VecsSensiTemp[nadj],VecsDeltaLam[nadj]);
320:     KSPGetConvergedReason(ksp,&kspreason);
321:     if (kspreason < 0) {
322:       ts->reason = TSADJOINT_DIVERGED_LINEAR_SOLVE;
323:       PetscInfo2(ts,"Step=%D, %Dth cost function, transposed linear solve fails, stopping 1st-order adjoint solve\n",ts->steps,nadj);
324:     }
325:   }

327:   if (ts->vecs_sensi2) { /* U_{n+1} */
328:     /* Get w1 at t_{n+1} from TLM matrix */
329:     MatDenseGetColumn(ts->mat_sensip,0,&xarr);
330:     VecPlaceArray(ts->vec_sensip_col,xarr);
331:     /* lambda_s^T F_UU w_1 */
332:     TSComputeIHessianProductFunctionUU(ts,th->stage_time,ts->vec_sol,VecsDeltaLam,ts->vec_sensip_col,ts->vecs_fuu);
333:     /* lambda_s^T F_UP w_2 */
334:     TSComputeIHessianProductFunctionUP(ts,th->stage_time,ts->vec_sol,VecsDeltaLam,ts->vec_dir,ts->vecs_fup);
335:     for (nadj=0; nadj<ts->numcost; nadj++) { /* compute the residual */
336:       VecCopy(ts->vecs_sensi2[nadj],VecsSensi2Temp[nadj]);
337:       VecScale(VecsSensi2Temp[nadj],1./adjoint_time_step);
338:       VecAXPY(VecsSensi2Temp[nadj],-1.,ts->vecs_fuu[nadj]);
339:       if (ts->vecs_fup) {
340:         VecAXPY(VecsSensi2Temp[nadj],-1.,ts->vecs_fup[nadj]);
341:       }
342:     }
343:     /* Solve stage equation LHS X = RHS for second-order adjoint */
344:     for (nadj=0; nadj<ts->numcost; nadj++) {
345:       KSPConvergedReason kspreason;
346:       KSPSolveTranspose(ksp,VecsSensi2Temp[nadj],VecsDeltaLam2[nadj]);
347:       KSPGetConvergedReason(ksp,&kspreason);
348:       if (kspreason < 0) {
349:         ts->reason = TSADJOINT_DIVERGED_LINEAR_SOLVE;
350:         PetscInfo2(ts,"Step=%D, %Dth cost function, transposed linear solve fails, stopping 2nd-order adjoint solve\n",ts->steps,nadj);
351:       }
352:     }
353:   }

355:   /* Update sensitivities, and evaluate integrals if there is any */
356:   if (!isexplicitode) {
357:     th->shift = 0.0;
358:     TSComputeSNESJacobian(ts,ts->vec_sol,J,Jpre);
359:     KSPSetOperators(ksp,J,Jpre);
360:     MatScale(J,-1.);
361:     for (nadj=0; nadj<ts->numcost; nadj++) {
362:       /* Add f_U \lambda_s to the original RHS */
363:       MatMultTransposeAdd(J,VecsDeltaLam[nadj],VecsSensiTemp[nadj],VecsSensiTemp[nadj]);
364:       VecScale(VecsSensiTemp[nadj],adjoint_time_step);
365:       VecCopy(VecsSensiTemp[nadj],ts->vecs_sensi[nadj]);
366:       if (ts->vecs_sensi2) {
367:         MatMultTransposeAdd(J,VecsDeltaLam2[nadj],VecsSensi2Temp[nadj],VecsSensi2Temp[nadj]);
368:         VecScale(VecsSensi2Temp[nadj],adjoint_time_step);
369:         VecCopy(VecsSensi2Temp[nadj],ts->vecs_sensi2[nadj]);
370:       }
371:     }
372:   }
373:   if (ts->vecs_sensip) {
374:     VecAXPBYPCZ(th->Xdot,-1./adjoint_time_step,1.0/adjoint_time_step,0,th->X0,ts->vec_sol);
375:     TSComputeIJacobianP(ts,th->stage_time,ts->vec_sol,th->Xdot,1./adjoint_time_step,ts->Jacp,PETSC_FALSE); /* get -f_p */
376:     if (quadts) {
377:       TSComputeRHSJacobianP(quadts,th->stage_time,ts->vec_sol,quadJp);
378:     }
379:     if (ts->vecs_sensi2p) {
380:       /* lambda_s^T F_PU w_1 */
381:       TSComputeIHessianProductFunctionPU(ts,th->stage_time,ts->vec_sol,VecsDeltaLam,ts->vec_sensip_col,ts->vecs_fpu);
382:       /* lambda_s^T F_PP w_2 */
383:       TSComputeIHessianProductFunctionPP(ts,th->stage_time,ts->vec_sol,VecsDeltaLam,ts->vec_dir,ts->vecs_fpp);
384:     }

386:     for (nadj=0; nadj<ts->numcost; nadj++) {
387:       MatMultTranspose(ts->Jacp,VecsDeltaLam[nadj],VecsDeltaMu[nadj]);
388:       VecAXPY(ts->vecs_sensip[nadj],-adjoint_time_step,VecsDeltaMu[nadj]);
389:       if (quadJp) {
390:         MatDenseGetColumn(quadJp,nadj,&xarr);
391:         VecPlaceArray(ts->vec_drdp_col,xarr);
392:         VecAXPY(ts->vecs_sensip[nadj],adjoint_time_step,ts->vec_drdp_col);
393:         VecResetArray(ts->vec_drdp_col);
394:         MatDenseRestoreColumn(quadJp,&xarr);
395:       }
396:       if (ts->vecs_sensi2p) {
397:         MatMultTranspose(ts->Jacp,VecsDeltaLam2[nadj],VecsDeltaMu2[nadj]);
398:         VecAXPY(ts->vecs_sensi2p[nadj],-adjoint_time_step,VecsDeltaMu2[nadj]);
399:         if (ts->vecs_fpu) {
400:           VecAXPY(ts->vecs_sensi2p[nadj],-adjoint_time_step,ts->vecs_fpu[nadj]);
401:         }
402:         if (ts->vecs_fpp) {
403:           VecAXPY(ts->vecs_sensi2p[nadj],-adjoint_time_step,ts->vecs_fpp[nadj]);
404:         }
405:       }
406:     }
407:   }

409:   if (ts->vecs_sensi2) {
410:     VecResetArray(ts->vec_sensip_col);
411:     MatDenseRestoreColumn(ts->mat_sensip,&xarr);
412:   }
413:   th->status = TS_STEP_COMPLETE;
414:   return(0);
415: }

417: static PetscErrorCode TSAdjointStep_Theta(TS ts)
418: {
419:   TS_Theta       *th = (TS_Theta*)ts->data;
420:   TS             quadts = ts->quadraturets;
421:   Vec            *VecsDeltaLam = th->VecsDeltaLam,*VecsDeltaMu = th->VecsDeltaMu,*VecsSensiTemp = th->VecsSensiTemp;
422:   Vec            *VecsDeltaLam2 = th->VecsDeltaLam2,*VecsDeltaMu2 = th->VecsDeltaMu2,*VecsSensi2Temp = th->VecsSensi2Temp;
423:   PetscInt       nadj;
424:   Mat            J,Jpre,quadJ = NULL,quadJp = NULL;
425:   KSP            ksp;
426:   PetscScalar    *xarr;
427:   PetscReal      adjoint_time_step;
428:   PetscReal      adjoint_ptime; /* end time of the adjoint time step (ts->ptime is the start time, ususally ts->ptime is larger than adjoint_ptime) */

432:   if (th->Theta == 1.) {
433:     TSAdjointStepBEuler_Private(ts);
434:     return(0);
435:   }
436:   th->status = TS_STEP_INCOMPLETE;
437:   SNESGetKSP(ts->snes,&ksp);
438:   TSGetIJacobian(ts,&J,&Jpre,NULL,NULL);
439:   if (quadts) {
440:     TSGetRHSJacobian(quadts,&quadJ,NULL,NULL,NULL);
441:     TSGetRHSJacobianP(quadts,&quadJp,NULL,NULL);
442:   }
443:   /* If endpoint=1, th->ptime and th->X0 will be used; if endpoint=0, th->stage_time and th->X will be used. */
444:   th->stage_time    = th->endpoint ? ts->ptime : (ts->ptime+(1.-th->Theta)*ts->time_step);
445:   adjoint_ptime     = ts->ptime + ts->time_step;
446:   adjoint_time_step = -ts->time_step;  /* always positive since time_step is negative */

448:   if (!th->endpoint) {
449:     /* recover th->X0 using vec_sol and the stage value th->X */
450:     VecAXPBYPCZ(th->X0,1.0/(1.0-th->Theta),th->Theta/(th->Theta-1.0),0,th->X,ts->vec_sol);
451:   }

453:   /* Build RHS for first-order adjoint */
454:   /* Cost function has an integral term */
455:   if (quadts) {
456:     if (th->endpoint) {
457:       TSComputeRHSJacobian(quadts,th->stage_time,ts->vec_sol,quadJ,NULL);
458:     } else {
459:       TSComputeRHSJacobian(quadts,th->stage_time,th->X,quadJ,NULL);
460:     }
461:   }

463:   for (nadj=0; nadj<ts->numcost; nadj++) {
464:     VecCopy(ts->vecs_sensi[nadj],VecsSensiTemp[nadj]);
465:     VecScale(VecsSensiTemp[nadj],1./(th->Theta*adjoint_time_step));
466:     if (quadJ) {
467:       MatDenseGetColumn(quadJ,nadj,&xarr);
468:       VecPlaceArray(ts->vec_drdu_col,xarr);
469:       VecAXPY(VecsSensiTemp[nadj],1.,ts->vec_drdu_col);
470:       VecResetArray(ts->vec_drdu_col);
471:       MatDenseRestoreColumn(quadJ,&xarr);
472:     }
473:   }

475:   /* Build LHS for first-order adjoint */
476:   th->shift = 1./(th->Theta*adjoint_time_step);
477:   if (th->endpoint) {
478:     TSComputeSNESJacobian(ts,ts->vec_sol,J,Jpre);
479:   } else {
480:     TSComputeSNESJacobian(ts,th->X,J,Jpre);
481:   }
482:   KSPSetOperators(ksp,J,Jpre);

484:   /* Solve stage equation LHS*lambda_s = RHS for first-order adjoint */
485:   for (nadj=0; nadj<ts->numcost; nadj++) {
486:     KSPConvergedReason kspreason;
487:     KSPSolveTranspose(ksp,VecsSensiTemp[nadj],VecsDeltaLam[nadj]);
488:     KSPGetConvergedReason(ksp,&kspreason);
489:     if (kspreason < 0) {
490:       ts->reason = TSADJOINT_DIVERGED_LINEAR_SOLVE;
491:       PetscInfo2(ts,"Step=%D, %Dth cost function, transposed linear solve fails, stopping 1st-order adjoint solve\n",ts->steps,nadj);
492:     }
493:   }

495:   /* Second-order adjoint */
496:   if (ts->vecs_sensi2) { /* U_{n+1} */
497:     if (!th->endpoint) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_SUP,"Operation not implemented in TS_Theta");
498:     /* Get w1 at t_{n+1} from TLM matrix */
499:     MatDenseGetColumn(ts->mat_sensip,0,&xarr);
500:     VecPlaceArray(ts->vec_sensip_col,xarr);
501:     /* lambda_s^T F_UU w_1 */
502:     TSComputeIHessianProductFunctionUU(ts,th->stage_time,ts->vec_sol,VecsDeltaLam,ts->vec_sensip_col,ts->vecs_fuu);
503:     VecResetArray(ts->vec_sensip_col);
504:     MatDenseRestoreColumn(ts->mat_sensip,&xarr);
505:     /* lambda_s^T F_UP w_2 */
506:     TSComputeIHessianProductFunctionUP(ts,th->stage_time,ts->vec_sol,VecsDeltaLam,ts->vec_dir,ts->vecs_fup);
507:     for (nadj=0; nadj<ts->numcost; nadj++) { /* compute the residual */
508:       VecCopy(ts->vecs_sensi2[nadj],VecsSensi2Temp[nadj]);
509:       VecScale(VecsSensi2Temp[nadj],th->shift);
510:       VecAXPY(VecsSensi2Temp[nadj],-1.,ts->vecs_fuu[nadj]);
511:       if (ts->vecs_fup) {
512:         VecAXPY(VecsSensi2Temp[nadj],-1.,ts->vecs_fup[nadj]);
513:       }
514:     }
515:     /* Solve stage equation LHS X = RHS for second-order adjoint */
516:     for (nadj=0; nadj<ts->numcost; nadj++) {
517:       KSPConvergedReason kspreason;
518:       KSPSolveTranspose(ksp,VecsSensi2Temp[nadj],VecsDeltaLam2[nadj]);
519:       KSPGetConvergedReason(ksp,&kspreason);
520:       if (kspreason < 0) {
521:         ts->reason = TSADJOINT_DIVERGED_LINEAR_SOLVE;
522:         PetscInfo2(ts,"Step=%D, %Dth cost function, transposed linear solve fails, stopping 2nd-order adjoint solve\n",ts->steps,nadj);
523:       }
524:     }
525:   }

527:   /* Update sensitivities, and evaluate integrals if there is any */
528:   if (th->endpoint) { /* two-stage Theta methods with th->Theta!=1, th->Theta==1 leads to BEuler */
529:     th->shift      = 1./((th->Theta-1.)*adjoint_time_step);
530:     th->stage_time = adjoint_ptime;
531:     TSComputeSNESJacobian(ts,th->X0,J,Jpre);
532:     KSPSetOperators(ksp,J,Jpre);
533:     /* R_U at t_n */
534:     if (quadts) {
535:       TSComputeRHSJacobian(quadts,adjoint_ptime,th->X0,quadJ,NULL);
536:     }
537:     for (nadj=0; nadj<ts->numcost; nadj++) {
538:       MatMultTranspose(J,VecsDeltaLam[nadj],ts->vecs_sensi[nadj]);
539:       if (quadJ) {
540:         MatDenseGetColumn(quadJ,nadj,&xarr);
541:         VecPlaceArray(ts->vec_drdu_col,xarr);
542:         VecAXPY(ts->vecs_sensi[nadj],-1.,ts->vec_drdu_col);
543:         VecResetArray(ts->vec_drdu_col);
544:         MatDenseRestoreColumn(quadJ,&xarr);
545:       }
546:       VecScale(ts->vecs_sensi[nadj],1./th->shift);
547:     }

549:     /* Second-order adjoint */
550:     if (ts->vecs_sensi2) { /* U_n */
551:       /* Get w1 at t_n from TLM matrix */
552:       MatDenseGetColumn(th->MatFwdSensip0,0,&xarr);
553:       VecPlaceArray(ts->vec_sensip_col,xarr);
554:       /* lambda_s^T F_UU w_1 */
555:       TSComputeIHessianProductFunctionUU(ts,adjoint_ptime,th->X0,VecsDeltaLam,ts->vec_sensip_col,ts->vecs_fuu);
556:       VecResetArray(ts->vec_sensip_col);
557:       MatDenseRestoreColumn(th->MatFwdSensip0,&xarr);
558:       /* lambda_s^T F_UU w_2 */
559:       TSComputeIHessianProductFunctionUP(ts,adjoint_ptime,th->X0,VecsDeltaLam,ts->vec_dir,ts->vecs_fup);
560:       for (nadj=0; nadj<ts->numcost; nadj++) {
561:         /* M^T Lambda_s + h(1-theta) F_U^T Lambda_s + h(1-theta) lambda_s^T F_UU w_1 + lambda_s^T F_UP w_2  */
562:         MatMultTranspose(J,VecsDeltaLam2[nadj],ts->vecs_sensi2[nadj]);
563:         VecAXPY(ts->vecs_sensi2[nadj],1.,ts->vecs_fuu[nadj]);
564:         if (ts->vecs_fup) {
565:           VecAXPY(ts->vecs_sensi2[nadj],1.,ts->vecs_fup[nadj]);
566:         }
567:         VecScale(ts->vecs_sensi2[nadj],1./th->shift);
568:       }
569:     }

571:     th->stage_time = ts->ptime; /* recover the old value */

573:     if (ts->vecs_sensip) { /* sensitivities wrt parameters */
574:       /* U_{n+1} */
575:       th->shift = 1.0/(adjoint_time_step*th->Theta);
576:       VecAXPBYPCZ(th->Xdot,-th->shift,th->shift,0,th->X0,ts->vec_sol);
577:       TSComputeIJacobianP(ts,th->stage_time,ts->vec_sol,th->Xdot,-1./(th->Theta*adjoint_time_step),ts->Jacp,PETSC_FALSE);
578:       if (quadts) {
579:         TSComputeRHSJacobianP(quadts,th->stage_time,ts->vec_sol,quadJp);
580:       }
581:       for (nadj=0; nadj<ts->numcost; nadj++) {
582:         MatMultTranspose(ts->Jacp,VecsDeltaLam[nadj],VecsDeltaMu[nadj]);
583:         VecAXPY(ts->vecs_sensip[nadj],-adjoint_time_step*th->Theta,VecsDeltaMu[nadj]);
584:         if (quadJp) {
585:           MatDenseGetColumn(quadJp,nadj,&xarr);
586:           VecPlaceArray(ts->vec_drdp_col,xarr);
587:           VecAXPY(ts->vecs_sensip[nadj],adjoint_time_step*th->Theta,ts->vec_drdp_col);
588:           VecResetArray(ts->vec_drdp_col);
589:           MatDenseRestoreColumn(quadJp,&xarr);
590:         }
591:       }
592:       if (ts->vecs_sensi2p) { /* second-order */
593:         /* Get w1 at t_{n+1} from TLM matrix */
594:         MatDenseGetColumn(ts->mat_sensip,0,&xarr);
595:         VecPlaceArray(ts->vec_sensip_col,xarr);
596:         /* lambda_s^T F_PU w_1 */
597:         TSComputeIHessianProductFunctionPU(ts,th->stage_time,ts->vec_sol,VecsDeltaLam,ts->vec_sensip_col,ts->vecs_fpu);
598:         VecResetArray(ts->vec_sensip_col);
599:         MatDenseRestoreColumn(ts->mat_sensip,&xarr);

601:         /* lambda_s^T F_PP w_2 */
602:         TSComputeIHessianProductFunctionPP(ts,th->stage_time,ts->vec_sol,VecsDeltaLam,ts->vec_dir,ts->vecs_fpp);
603:         for (nadj=0; nadj<ts->numcost; nadj++) {
604:           /* Mu2 <- Mu2 + h theta F_P^T Lambda_s + h theta (lambda_s^T F_UU w_1 + lambda_s^T F_UP w_2)  */
605:           MatMultTranspose(ts->Jacp,VecsDeltaLam2[nadj],VecsDeltaMu2[nadj]);
606:           VecAXPY(ts->vecs_sensi2p[nadj],-adjoint_time_step*th->Theta,VecsDeltaMu2[nadj]);
607:           if (ts->vecs_fpu) {
608:             VecAXPY(ts->vecs_sensi2p[nadj],-adjoint_time_step*th->Theta,ts->vecs_fpu[nadj]);
609:           }
610:           if (ts->vecs_fpp) {
611:             VecAXPY(ts->vecs_sensi2p[nadj],-adjoint_time_step*th->Theta,ts->vecs_fpp[nadj]);
612:           }
613:         }
614:       }

616:       /* U_s */
617:       VecZeroEntries(th->Xdot);
618:       TSComputeIJacobianP(ts,adjoint_ptime,th->X0,th->Xdot,1./((th->Theta-1.0)*adjoint_time_step),ts->Jacp,PETSC_FALSE);
619:       if (quadts) {
620:         TSComputeRHSJacobianP(quadts,adjoint_ptime,th->X0,quadJp);
621:       }
622:       for (nadj=0; nadj<ts->numcost; nadj++) {
623:         MatMultTranspose(ts->Jacp,VecsDeltaLam[nadj],VecsDeltaMu[nadj]);
624:         VecAXPY(ts->vecs_sensip[nadj],-adjoint_time_step*(1.0-th->Theta),VecsDeltaMu[nadj]);
625:         if (quadJp) {
626:           MatDenseGetColumn(quadJp,nadj,&xarr);
627:           VecPlaceArray(ts->vec_drdp_col,xarr);
628:           VecAXPY(ts->vecs_sensip[nadj],adjoint_time_step*(1.0-th->Theta),ts->vec_drdp_col);
629:           VecResetArray(ts->vec_drdp_col);
630:           MatDenseRestoreColumn(quadJp,&xarr);
631:         }
632:         if (ts->vecs_sensi2p) { /* second-order */
633:           /* Get w1 at t_n from TLM matrix */
634:           MatDenseGetColumn(th->MatFwdSensip0,0,&xarr);
635:           VecPlaceArray(ts->vec_sensip_col,xarr);
636:           /* lambda_s^T F_PU w_1 */
637:           TSComputeIHessianProductFunctionPU(ts,adjoint_ptime,th->X0,VecsDeltaLam,ts->vec_sensip_col,ts->vecs_fpu);
638:           VecResetArray(ts->vec_sensip_col);
639:           MatDenseRestoreColumn(th->MatFwdSensip0,&xarr);
640:           /* lambda_s^T F_PP w_2 */
641:           TSComputeIHessianProductFunctionPP(ts,adjoint_ptime,th->X0,VecsDeltaLam,ts->vec_dir,ts->vecs_fpp);
642:           for (nadj=0; nadj<ts->numcost; nadj++) {
643:             /* Mu2 <- Mu2 + h(1-theta) F_P^T Lambda_s + h(1-theta) (lambda_s^T F_UU w_1 + lambda_s^T F_UP w_2) */
644:             MatMultTranspose(ts->Jacp,VecsDeltaLam2[nadj],VecsDeltaMu2[nadj]);
645:             VecAXPY(ts->vecs_sensi2p[nadj],-adjoint_time_step*(1.0-th->Theta),VecsDeltaMu2[nadj]);
646:             if (ts->vecs_fpu) {
647:               VecAXPY(ts->vecs_sensi2p[nadj],-adjoint_time_step*(1.0-th->Theta),ts->vecs_fpu[nadj]);
648:             }
649:             if (ts->vecs_fpp) {
650:               VecAXPY(ts->vecs_sensi2p[nadj],-adjoint_time_step*(1.0-th->Theta),ts->vecs_fpp[nadj]);
651:             }
652:           }
653:         }
654:       }
655:     }
656:   } else { /* one-stage case */
657:     th->shift = 0.0;
658:     TSComputeSNESJacobian(ts,th->X,J,Jpre); /* get -f_y */
659:     KSPSetOperators(ksp,J,Jpre);
660:     if (quadts) {
661:       TSComputeRHSJacobian(quadts,th->stage_time,th->X,quadJ,NULL);
662:     }
663:     for (nadj=0; nadj<ts->numcost; nadj++) {
664:       MatMultTranspose(J,VecsDeltaLam[nadj],VecsSensiTemp[nadj]);
665:       VecAXPY(ts->vecs_sensi[nadj],-adjoint_time_step,VecsSensiTemp[nadj]);
666:       if (quadJ) {
667:         MatDenseGetColumn(quadJ,nadj,&xarr);
668:         VecPlaceArray(ts->vec_drdu_col,xarr);
669:         VecAXPY(ts->vecs_sensi[nadj],adjoint_time_step,ts->vec_drdu_col);
670:         VecResetArray(ts->vec_drdu_col);
671:         MatDenseRestoreColumn(quadJ,&xarr);
672:       }
673:     }
674:     if (ts->vecs_sensip) {
675:       th->shift = 1.0/(adjoint_time_step*th->Theta);
676:       VecAXPBYPCZ(th->Xdot,-th->shift,th->shift,0,th->X0,th->X);
677:       TSComputeIJacobianP(ts,th->stage_time,th->X,th->Xdot,th->shift,ts->Jacp,PETSC_FALSE);
678:       if (quadts) {
679:         TSComputeRHSJacobianP(quadts,th->stage_time,th->X,quadJp);
680:       }
681:       for (nadj=0; nadj<ts->numcost; nadj++) {
682:         MatMultTranspose(ts->Jacp,VecsDeltaLam[nadj],VecsDeltaMu[nadj]);
683:         VecAXPY(ts->vecs_sensip[nadj],-adjoint_time_step,VecsDeltaMu[nadj]);
684:         if (quadJp) {
685:           MatDenseGetColumn(quadJp,nadj,&xarr);
686:           VecPlaceArray(ts->vec_drdp_col,xarr);
687:           VecAXPY(ts->vecs_sensip[nadj],adjoint_time_step,ts->vec_drdp_col);
688:           VecResetArray(ts->vec_drdp_col);
689:           MatDenseRestoreColumn(quadJp,&xarr);
690:         }
691:       }
692:     }
693:   }

695:   th->status = TS_STEP_COMPLETE;
696:   return(0);
697: }

699: static PetscErrorCode TSInterpolate_Theta(TS ts,PetscReal t,Vec X)
700: {
701:   TS_Theta       *th = (TS_Theta*)ts->data;
702:   PetscReal      dt  = t - ts->ptime;

706:   VecCopy(ts->vec_sol,th->X);
707:   if (th->endpoint) dt *= th->Theta;
708:   VecWAXPY(X,dt,th->Xdot,th->X);
709:   return(0);
710: }

712: static PetscErrorCode TSEvaluateWLTE_Theta(TS ts,NormType wnormtype,PetscInt *order,PetscReal *wlte)
713: {
714:   TS_Theta       *th = (TS_Theta*)ts->data;
715:   Vec            X = ts->vec_sol;      /* X = solution */
716:   Vec            Y = th->vec_lte_work; /* Y = X + LTE  */
717:   PetscReal      wltea,wlter;

721:   if (!th->vec_sol_prev) {*wlte = -1; return(0);}
722:   /* Cannot compute LTE in first step or in restart after event */
723:   if (ts->steprestart) {*wlte = -1; return(0);}
724:   /* Compute LTE using backward differences with non-constant time step */
725:   {
726:     PetscReal   h = ts->time_step, h_prev = ts->ptime - ts->ptime_prev;
727:     PetscReal   a = 1 + h_prev/h;
728:     PetscScalar scal[3]; Vec vecs[3];
729:     scal[0] = +1/a; scal[1] = -1/(a-1); scal[2] = +1/(a*(a-1));
730:     vecs[0] = X;    vecs[1] = th->X0;   vecs[2] = th->vec_sol_prev;
731:     VecCopy(X,Y);
732:     VecMAXPY(Y,3,scal,vecs);
733:     TSErrorWeightedNorm(ts,X,Y,wnormtype,wlte,&wltea,&wlter);
734:   }
735:   if (order) *order = 2;
736:   return(0);
737: }

739: static PetscErrorCode TSRollBack_Theta(TS ts)
740: {
741:   TS_Theta       *th = (TS_Theta*)ts->data;
742:   TS             quadts = ts->quadraturets;

746:   VecCopy(th->X0,ts->vec_sol);
747:   if (quadts && ts->costintegralfwd) {
748:     VecCopy(th->VecCostIntegral0,quadts->vec_sol);
749:   }
750:   th->status = TS_STEP_INCOMPLETE;
751:   if (ts->mat_sensip) {
752:     MatCopy(th->MatFwdSensip0,ts->mat_sensip,SAME_NONZERO_PATTERN);
753:   }
754:   if (quadts && quadts->mat_sensip) {
755:     MatCopy(th->MatIntegralSensip0,quadts->mat_sensip,SAME_NONZERO_PATTERN);
756:   }
757:   return(0);
758: }

760: static PetscErrorCode TSForwardStep_Theta(TS ts)
761: {
762:   TS_Theta       *th = (TS_Theta*)ts->data;
763:   TS             quadts = ts->quadraturets;
764:   Mat            MatDeltaFwdSensip = th->MatDeltaFwdSensip;
765:   Vec            VecDeltaFwdSensipCol = th->VecDeltaFwdSensipCol;
766:   PetscInt       ntlm;
767:   KSP            ksp;
768:   Mat            J,Jpre,quadJ = NULL,quadJp = NULL;
769:   PetscScalar    *barr,*xarr;
770:   PetscReal      previous_shift;

774:   previous_shift = th->shift;
775:   MatCopy(ts->mat_sensip,th->MatFwdSensip0,SAME_NONZERO_PATTERN);

777:   if (quadts && quadts->mat_sensip) {
778:     MatCopy(quadts->mat_sensip,th->MatIntegralSensip0,SAME_NONZERO_PATTERN);
779:   }
780:   SNESGetKSP(ts->snes,&ksp);
781:   TSGetIJacobian(ts,&J,&Jpre,NULL,NULL);
782:   if (quadts) {
783:     TSGetRHSJacobian(quadts,&quadJ,NULL,NULL,NULL);
784:     TSGetRHSJacobianP(quadts,&quadJp,NULL,NULL);
785:   }

787:   /* Build RHS */
788:   if (th->endpoint) { /* 2-stage method*/
789:     th->shift = 1./((th->Theta-1.)*th->time_step0);
790:     TSComputeIJacobian(ts,th->ptime0,th->X0,th->Xdot,th->shift,J,Jpre,PETSC_FALSE);
791:     MatMatMult(J,ts->mat_sensip,MAT_REUSE_MATRIX,PETSC_DEFAULT,&MatDeltaFwdSensip);
792:     MatScale(MatDeltaFwdSensip,(th->Theta-1.)/th->Theta);

794:     /* Add the f_p forcing terms */
795:     if (ts->Jacp) {
796:       VecZeroEntries(th->Xdot);
797:       TSComputeIJacobianP(ts,th->ptime0,th->X0,th->Xdot,th->shift,ts->Jacp,PETSC_FALSE);
798:       MatAXPY(MatDeltaFwdSensip,(th->Theta-1.)/th->Theta,ts->Jacp,SUBSET_NONZERO_PATTERN);
799:       th->shift = previous_shift;
800:       VecAXPBYPCZ(th->Xdot,-th->shift,th->shift,0,th->X0,ts->vec_sol);
801:       TSComputeIJacobianP(ts,th->stage_time,ts->vec_sol,th->Xdot,th->shift,ts->Jacp,PETSC_FALSE);
802:       MatAXPY(MatDeltaFwdSensip,-1.,ts->Jacp,SUBSET_NONZERO_PATTERN);
803:     }
804:   } else { /* 1-stage method */
805:     th->shift = 0.0;
806:     TSComputeIJacobian(ts,th->stage_time,th->X,th->Xdot,th->shift,J,Jpre,PETSC_FALSE);
807:     MatMatMult(J,ts->mat_sensip,MAT_REUSE_MATRIX,PETSC_DEFAULT,&MatDeltaFwdSensip);
808:     MatScale(MatDeltaFwdSensip,-1.);

810:     /* Add the f_p forcing terms */
811:     if (ts->Jacp) {
812:       th->shift = previous_shift;
813:       VecAXPBYPCZ(th->Xdot,-th->shift,th->shift,0,th->X0,th->X);
814:       TSComputeIJacobianP(ts,th->stage_time,th->X,th->Xdot,th->shift,ts->Jacp,PETSC_FALSE);
815:       MatAXPY(MatDeltaFwdSensip,-1.,ts->Jacp,SUBSET_NONZERO_PATTERN);
816:     }
817:   }

819:   /* Build LHS */
820:   th->shift = previous_shift; /* recover the previous shift used in TSStep_Theta() */
821:   if (th->endpoint) {
822:     TSComputeIJacobian(ts,th->stage_time,ts->vec_sol,th->Xdot,th->shift,J,Jpre,PETSC_FALSE);
823:   } else {
824:     TSComputeIJacobian(ts,th->stage_time,th->X,th->Xdot,th->shift,J,Jpre,PETSC_FALSE);
825:   }
826:   KSPSetOperators(ksp,J,Jpre);

828:   /*
829:     Evaluate the first stage of integral gradients with the 2-stage method:
830:     drdu|t_n*S(t_n) + drdp|t_n
831:     This is done before the linear solve because the sensitivity variable S(t_n) will be propagated to S(t_{n+1})
832:   */
833:   if (th->endpoint) { /* 2-stage method only */
834:     if (quadts && quadts->mat_sensip) {
835:       TSComputeRHSJacobian(quadts,th->ptime0,th->X0,quadJ,NULL);
836:       TSComputeRHSJacobianP(quadts,th->ptime0,th->X0,quadJp);
837:       MatTransposeMatMult(ts->mat_sensip,quadJ,MAT_REUSE_MATRIX,PETSC_DEFAULT,&th->MatIntegralSensipTemp);
838:       MatAXPY(th->MatIntegralSensipTemp,1,quadJp,SAME_NONZERO_PATTERN);
839:       MatAXPY(quadts->mat_sensip,th->time_step0*(1.-th->Theta),th->MatIntegralSensipTemp,SAME_NONZERO_PATTERN);
840:     }
841:   }

843:   /* Solve the tangent linear equation for forward sensitivities to parameters */
844:   for (ntlm=0; ntlm<th->num_tlm; ntlm++) {
845:     KSPConvergedReason kspreason;
846:     MatDenseGetColumn(MatDeltaFwdSensip,ntlm,&barr);
847:     VecPlaceArray(VecDeltaFwdSensipCol,barr);
848:     if (th->endpoint) {
849:       MatDenseGetColumn(ts->mat_sensip,ntlm,&xarr);
850:       VecPlaceArray(ts->vec_sensip_col,xarr);
851:       KSPSolve(ksp,VecDeltaFwdSensipCol,ts->vec_sensip_col);
852:       VecResetArray(ts->vec_sensip_col);
853:       MatDenseRestoreColumn(ts->mat_sensip,&xarr);
854:     } else {
855:       KSPSolve(ksp,VecDeltaFwdSensipCol,VecDeltaFwdSensipCol);
856:     }
857:     KSPGetConvergedReason(ksp,&kspreason);
858:     if (kspreason < 0) {
859:       ts->reason = TSFORWARD_DIVERGED_LINEAR_SOLVE;
860:       PetscInfo2(ts,"Step=%D, %Dth tangent linear solve, linear solve fails, stopping tangent linear solve\n",ts->steps,ntlm);
861:     }
862:     VecResetArray(VecDeltaFwdSensipCol);
863:     MatDenseRestoreColumn(MatDeltaFwdSensip,&barr);
864:   }

866:   /*
867:     Evaluate the second stage of integral gradients with the 2-stage method:
868:     drdu|t_{n+1}*S(t_{n+1}) + drdp|t_{n+1}
869:   */
870:   if (quadts && quadts->mat_sensip) {
871:     if (!th->endpoint) {
872:       MatAXPY(ts->mat_sensip,1,MatDeltaFwdSensip,SAME_NONZERO_PATTERN); /* stage sensitivity */
873:       TSComputeRHSJacobian(quadts,th->stage_time,th->X,quadJ,NULL);
874:       TSComputeRHSJacobianP(quadts,th->stage_time,th->X,quadJp);
875:       MatTransposeMatMult(ts->mat_sensip,quadJ,MAT_REUSE_MATRIX,PETSC_DEFAULT,&th->MatIntegralSensipTemp);
876:       MatAXPY(th->MatIntegralSensipTemp,1,quadJp,SAME_NONZERO_PATTERN);
877:       MatAXPY(quadts->mat_sensip,th->time_step0,th->MatIntegralSensipTemp,SAME_NONZERO_PATTERN);
878:       MatAXPY(ts->mat_sensip,(1.-th->Theta)/th->Theta,MatDeltaFwdSensip,SAME_NONZERO_PATTERN);
879:     } else {
880:       TSComputeRHSJacobian(quadts,th->stage_time,ts->vec_sol,quadJ,NULL);
881:       TSComputeRHSJacobianP(quadts,th->stage_time,ts->vec_sol,quadJp);
882:       MatTransposeMatMult(ts->mat_sensip,quadJ,MAT_REUSE_MATRIX,PETSC_DEFAULT,&th->MatIntegralSensipTemp);
883:       MatAXPY(th->MatIntegralSensipTemp,1,quadJp,SAME_NONZERO_PATTERN);
884:       MatAXPY(quadts->mat_sensip,th->time_step0*th->Theta,th->MatIntegralSensipTemp,SAME_NONZERO_PATTERN);
885:     }
886:   } else {
887:     if (!th->endpoint) {
888:       MatAXPY(ts->mat_sensip,1./th->Theta,MatDeltaFwdSensip,SAME_NONZERO_PATTERN);
889:     }
890:   }
891:   return(0);
892: }

894: static PetscErrorCode TSForwardGetStages_Theta(TS ts,PetscInt *ns,Mat **stagesensip)
895: {
896:   TS_Theta *th = (TS_Theta*)ts->data;

899:   if (ns) *ns = 1;
900:   if (stagesensip) {
901:     *stagesensip = (!th->endpoint && th->Theta != 1.0) ? &(th->MatDeltaFwdSensip) : &(th->MatFwdSensip0);
902:   }
903:   return(0);
904: }

906: /*------------------------------------------------------------*/
907: static PetscErrorCode TSReset_Theta(TS ts)
908: {
909:   TS_Theta       *th = (TS_Theta*)ts->data;

913:   VecDestroy(&th->X);
914:   VecDestroy(&th->Xdot);
915:   VecDestroy(&th->X0);
916:   VecDestroy(&th->affine);

918:   VecDestroy(&th->vec_sol_prev);
919:   VecDestroy(&th->vec_lte_work);

921:   VecDestroy(&th->VecCostIntegral0);
922:   return(0);
923: }

925: static PetscErrorCode TSAdjointReset_Theta(TS ts)
926: {
927:   TS_Theta       *th = (TS_Theta*)ts->data;

931:   VecDestroyVecs(ts->numcost,&th->VecsDeltaLam);
932:   VecDestroyVecs(ts->numcost,&th->VecsDeltaMu);
933:   VecDestroyVecs(ts->numcost,&th->VecsDeltaLam2);
934:   VecDestroyVecs(ts->numcost,&th->VecsDeltaMu2);
935:   VecDestroyVecs(ts->numcost,&th->VecsSensiTemp);
936:   VecDestroyVecs(ts->numcost,&th->VecsSensi2Temp);
937:   return(0);
938: }

940: static PetscErrorCode TSDestroy_Theta(TS ts)
941: {

945:   TSReset_Theta(ts);
946:   if (ts->dm) {
947:     DMCoarsenHookRemove(ts->dm,DMCoarsenHook_TSTheta,DMRestrictHook_TSTheta,ts);
948:     DMSubDomainHookRemove(ts->dm,DMSubDomainHook_TSTheta,DMSubDomainRestrictHook_TSTheta,ts);
949:   }
950:   PetscFree(ts->data);
951:   PetscObjectComposeFunction((PetscObject)ts,"TSThetaGetTheta_C",NULL);
952:   PetscObjectComposeFunction((PetscObject)ts,"TSThetaSetTheta_C",NULL);
953:   PetscObjectComposeFunction((PetscObject)ts,"TSThetaGetEndpoint_C",NULL);
954:   PetscObjectComposeFunction((PetscObject)ts,"TSThetaSetEndpoint_C",NULL);
955:   return(0);
956: }

958: /*
959:   This defines the nonlinear equation that is to be solved with SNES
960:   G(U) = F[t0+Theta*dt, U, (U-U0)*shift] = 0

962:   Note that U here is the stage argument. This means that U = U_{n+1} only if endpoint = true,
963:   otherwise U = theta U_{n+1} + (1 - theta) U0, which for the case of implicit midpoint is
964:   U = (U_{n+1} + U0)/2
965: */
966: static PetscErrorCode SNESTSFormFunction_Theta(SNES snes,Vec x,Vec y,TS ts)
967: {
968:   TS_Theta       *th = (TS_Theta*)ts->data;
970:   Vec            X0,Xdot;
971:   DM             dm,dmsave;
972:   PetscReal      shift = th->shift;

975:   SNESGetDM(snes,&dm);
976:   /* When using the endpoint variant, this is actually 1/Theta * Xdot */
977:   TSThetaGetX0AndXdot(ts,dm,&X0,&Xdot);
978:   if (x != X0) {
979:     VecAXPBYPCZ(Xdot,-shift,shift,0,X0,x);
980:   } else {
981:     VecZeroEntries(Xdot);
982:   }
983:   /* DM monkey-business allows user code to call TSGetDM() inside of functions evaluated on levels of FAS */
984:   dmsave = ts->dm;
985:   ts->dm = dm;
986:   TSComputeIFunction(ts,th->stage_time,x,Xdot,y,PETSC_FALSE);
987:   ts->dm = dmsave;
988:   TSThetaRestoreX0AndXdot(ts,dm,&X0,&Xdot);
989:   return(0);
990: }

992: static PetscErrorCode SNESTSFormJacobian_Theta(SNES snes,Vec x,Mat A,Mat B,TS ts)
993: {
994:   TS_Theta       *th = (TS_Theta*)ts->data;
996:   Vec            Xdot;
997:   DM             dm,dmsave;
998:   PetscReal      shift = th->shift;

1001:   SNESGetDM(snes,&dm);
1002:   /* Xdot has already been computed in SNESTSFormFunction_Theta (SNES guarantees this) */
1003:   TSThetaGetX0AndXdot(ts,dm,NULL,&Xdot);

1005:   dmsave = ts->dm;
1006:   ts->dm = dm;
1007:   TSComputeIJacobian(ts,th->stage_time,x,Xdot,shift,A,B,PETSC_FALSE);
1008:   ts->dm = dmsave;
1009:   TSThetaRestoreX0AndXdot(ts,dm,NULL,&Xdot);
1010:   return(0);
1011: }

1013: static PetscErrorCode TSForwardSetUp_Theta(TS ts)
1014: {
1015:   TS_Theta       *th = (TS_Theta*)ts->data;
1016:   TS             quadts = ts->quadraturets;

1020:   /* combine sensitivities to parameters and sensitivities to initial values into one array */
1021:   th->num_tlm = ts->num_parameters;
1022:   MatDuplicate(ts->mat_sensip,MAT_DO_NOT_COPY_VALUES,&th->MatDeltaFwdSensip);
1023:   if (quadts && quadts->mat_sensip) {
1024:     MatDuplicate(quadts->mat_sensip,MAT_DO_NOT_COPY_VALUES,&th->MatIntegralSensipTemp);
1025:     MatDuplicate(quadts->mat_sensip,MAT_DO_NOT_COPY_VALUES,&th->MatIntegralSensip0);
1026:   }
1027:   /* backup sensitivity results for roll-backs */
1028:   MatDuplicate(ts->mat_sensip,MAT_DO_NOT_COPY_VALUES,&th->MatFwdSensip0);

1030:   VecDuplicate(ts->vec_sol,&th->VecDeltaFwdSensipCol);
1031:   return(0);
1032: }

1034: static PetscErrorCode TSForwardReset_Theta(TS ts)
1035: {
1036:   TS_Theta       *th = (TS_Theta*)ts->data;
1037:   TS             quadts = ts->quadraturets;

1041:   if (quadts && quadts->mat_sensip) {
1042:     MatDestroy(&th->MatIntegralSensipTemp);
1043:     MatDestroy(&th->MatIntegralSensip0);
1044:   }
1045:   VecDestroy(&th->VecDeltaFwdSensipCol);
1046:   MatDestroy(&th->MatDeltaFwdSensip);
1047:   MatDestroy(&th->MatFwdSensip0);
1048:   return(0);
1049: }

1051: static PetscErrorCode TSSetUp_Theta(TS ts)
1052: {
1053:   TS_Theta       *th = (TS_Theta*)ts->data;
1054:   TS             quadts = ts->quadraturets;
1055:   PetscBool      match;

1059:   if (!th->VecCostIntegral0 && quadts && ts->costintegralfwd) { /* back up cost integral */
1060:     VecDuplicate(quadts->vec_sol,&th->VecCostIntegral0);
1061:   }
1062:   if (!th->X) {
1063:     VecDuplicate(ts->vec_sol,&th->X);
1064:   }
1065:   if (!th->Xdot) {
1066:     VecDuplicate(ts->vec_sol,&th->Xdot);
1067:   }
1068:   if (!th->X0) {
1069:     VecDuplicate(ts->vec_sol,&th->X0);
1070:   }
1071:   if (th->endpoint) {
1072:     VecDuplicate(ts->vec_sol,&th->affine);
1073:   }

1075:   th->order = (th->Theta == 0.5) ? 2 : 1;
1076:   th->shift = 1/(th->Theta*ts->time_step);

1078:   TSGetDM(ts,&ts->dm);
1079:   DMCoarsenHookAdd(ts->dm,DMCoarsenHook_TSTheta,DMRestrictHook_TSTheta,ts);
1080:   DMSubDomainHookAdd(ts->dm,DMSubDomainHook_TSTheta,DMSubDomainRestrictHook_TSTheta,ts);

1082:   TSGetAdapt(ts,&ts->adapt);
1083:   TSAdaptCandidatesClear(ts->adapt);
1084:   PetscObjectTypeCompare((PetscObject)ts->adapt,TSADAPTNONE,&match);
1085:   if (!match) {
1086:     VecDuplicate(ts->vec_sol,&th->vec_sol_prev);
1087:     VecDuplicate(ts->vec_sol,&th->vec_lte_work);
1088:   }
1089:   TSGetSNES(ts,&ts->snes);
1090:   return(0);
1091: }

1093: /*------------------------------------------------------------*/

1095: static PetscErrorCode TSAdjointSetUp_Theta(TS ts)
1096: {
1097:   TS_Theta       *th = (TS_Theta*)ts->data;

1101:   VecDuplicateVecs(ts->vecs_sensi[0],ts->numcost,&th->VecsDeltaLam);
1102:   VecDuplicateVecs(ts->vecs_sensi[0],ts->numcost,&th->VecsSensiTemp);
1103:   if (ts->vecs_sensip) {
1104:     VecDuplicateVecs(ts->vecs_sensip[0],ts->numcost,&th->VecsDeltaMu);
1105:   }
1106:   if (ts->vecs_sensi2) {
1107:     VecDuplicateVecs(ts->vecs_sensi[0],ts->numcost,&th->VecsDeltaLam2);
1108:     VecDuplicateVecs(ts->vecs_sensi2[0],ts->numcost,&th->VecsSensi2Temp);
1109:     /* hack ts to make implicit TS solver work when users provide only explicit versions of callbacks (RHSFunction,RHSJacobian,RHSHessian etc.) */
1110:     if (!ts->ihessianproduct_fuu) ts->vecs_fuu = ts->vecs_guu;
1111:     if (!ts->ihessianproduct_fup) ts->vecs_fup = ts->vecs_gup;
1112:   }
1113:   if (ts->vecs_sensi2p) {
1114:     VecDuplicateVecs(ts->vecs_sensi2p[0],ts->numcost,&th->VecsDeltaMu2);
1115:     /* hack ts to make implicit TS solver work when users provide only explicit versions of callbacks (RHSFunction,RHSJacobian,RHSHessian etc.) */
1116:     if (!ts->ihessianproduct_fpu) ts->vecs_fpu = ts->vecs_gpu;
1117:     if (!ts->ihessianproduct_fpp) ts->vecs_fpp = ts->vecs_gpp;
1118:   }
1119:   return(0);
1120: }

1122: static PetscErrorCode TSSetFromOptions_Theta(PetscOptionItems *PetscOptionsObject,TS ts)
1123: {
1124:   TS_Theta       *th = (TS_Theta*)ts->data;

1128:   PetscOptionsHead(PetscOptionsObject,"Theta ODE solver options");
1129:   {
1130:     PetscOptionsReal("-ts_theta_theta","Location of stage (0<Theta<=1)","TSThetaSetTheta",th->Theta,&th->Theta,NULL);
1131:     PetscOptionsBool("-ts_theta_endpoint","Use the endpoint instead of midpoint form of the Theta method","TSThetaSetEndpoint",th->endpoint,&th->endpoint,NULL);
1132:     PetscOptionsBool("-ts_theta_initial_guess_extrapolate","Extrapolate stage initial guess from previous solution (sometimes unstable)","TSThetaSetExtrapolate",th->extrapolate,&th->extrapolate,NULL);
1133:   }
1134:   PetscOptionsTail();
1135:   return(0);
1136: }

1138: static PetscErrorCode TSView_Theta(TS ts,PetscViewer viewer)
1139: {
1140:   TS_Theta       *th = (TS_Theta*)ts->data;
1141:   PetscBool      iascii;

1145:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);
1146:   if (iascii) {
1147:     PetscViewerASCIIPrintf(viewer,"  Theta=%g\n",(double)th->Theta);
1148:     PetscViewerASCIIPrintf(viewer,"  Extrapolation=%s\n",th->extrapolate ? "yes" : "no");
1149:   }
1150:   return(0);
1151: }

1153: static PetscErrorCode TSThetaGetTheta_Theta(TS ts,PetscReal *theta)
1154: {
1155:   TS_Theta *th = (TS_Theta*)ts->data;

1158:   *theta = th->Theta;
1159:   return(0);
1160: }

1162: static PetscErrorCode TSThetaSetTheta_Theta(TS ts,PetscReal theta)
1163: {
1164:   TS_Theta *th = (TS_Theta*)ts->data;

1167:   if (theta <= 0 || 1 < theta) SETERRQ1(PetscObjectComm((PetscObject)ts),PETSC_ERR_ARG_OUTOFRANGE,"Theta %g not in range (0,1]",(double)theta);
1168:   th->Theta = theta;
1169:   th->order = (th->Theta == 0.5) ? 2 : 1;
1170:   return(0);
1171: }

1173: static PetscErrorCode TSThetaGetEndpoint_Theta(TS ts,PetscBool *endpoint)
1174: {
1175:   TS_Theta *th = (TS_Theta*)ts->data;

1178:   *endpoint = th->endpoint;
1179:   return(0);
1180: }

1182: static PetscErrorCode TSThetaSetEndpoint_Theta(TS ts,PetscBool flg)
1183: {
1184:   TS_Theta *th = (TS_Theta*)ts->data;

1187:   th->endpoint = flg;
1188:   return(0);
1189: }

1191: #if defined(PETSC_HAVE_COMPLEX)
1192: static PetscErrorCode TSComputeLinearStability_Theta(TS ts,PetscReal xr,PetscReal xi,PetscReal *yr,PetscReal *yi)
1193: {
1194:   PetscComplex   z   = xr + xi*PETSC_i,f;
1195:   TS_Theta       *th = (TS_Theta*)ts->data;
1196:   const PetscReal one = 1.0;

1199:   f   = (one + (one - th->Theta)*z)/(one - th->Theta*z);
1200:   *yr = PetscRealPartComplex(f);
1201:   *yi = PetscImaginaryPartComplex(f);
1202:   return(0);
1203: }
1204: #endif

1206: static PetscErrorCode TSGetStages_Theta(TS ts,PetscInt *ns,Vec **Y)
1207: {
1208:   TS_Theta     *th = (TS_Theta*)ts->data;

1211:   if (ns) *ns = 1;
1212:   if (Y) {
1213:     *Y = (!th->endpoint && th->Theta != 1.0) ? &(th->X) : &(th->X0);
1214:   }
1215:   return(0);
1216: }

1218: /* ------------------------------------------------------------ */
1219: /*MC
1220:       TSTHETA - DAE solver using the implicit Theta method

1222:    Level: beginner

1224:    Options Database:
1225: +  -ts_theta_theta <Theta> - Location of stage (0<Theta<=1)
1226: .  -ts_theta_endpoint <flag> - Use the endpoint (like Crank-Nicholson) instead of midpoint form of the Theta method
1227: -  -ts_theta_initial_guess_extrapolate <flg> - Extrapolate stage initial guess from previous solution (sometimes unstable)

1229:    Notes:
1230: $  -ts_type theta -ts_theta_theta 1.0 corresponds to backward Euler (TSBEULER)
1231: $  -ts_type theta -ts_theta_theta 0.5 corresponds to the implicit midpoint rule
1232: $  -ts_type theta -ts_theta_theta 0.5 -ts_theta_endpoint corresponds to Crank-Nicholson (TSCN)

1234:    This method can be applied to DAE.

1236:    This method is cast as a 1-stage implicit Runge-Kutta method.

1238: .vb
1239:   Theta | Theta
1240:   -------------
1241:         |  1
1242: .ve

1244:    For the default Theta=0.5, this is also known as the implicit midpoint rule.

1246:    When the endpoint variant is chosen, the method becomes a 2-stage method with first stage explicit:

1248: .vb
1249:   0 | 0         0
1250:   1 | 1-Theta   Theta
1251:   -------------------
1252:     | 1-Theta   Theta
1253: .ve

1255:    For the default Theta=0.5, this is the trapezoid rule (also known as Crank-Nicolson, see TSCN).

1257:    To apply a diagonally implicit RK method to DAE, the stage formula

1259: $  Y_i = X + h sum_j a_ij Y'_j

1261:    is interpreted as a formula for Y'_i in terms of Y_i and known values (Y'_j, j<i)

1263: .seealso:  TSCreate(), TS, TSSetType(), TSCN, TSBEULER, TSThetaSetTheta(), TSThetaSetEndpoint()

1265: M*/
1266: PETSC_EXTERN PetscErrorCode TSCreate_Theta(TS ts)
1267: {
1268:   TS_Theta       *th;

1272:   ts->ops->reset           = TSReset_Theta;
1273:   ts->ops->adjointreset    = TSAdjointReset_Theta;
1274:   ts->ops->destroy         = TSDestroy_Theta;
1275:   ts->ops->view            = TSView_Theta;
1276:   ts->ops->setup           = TSSetUp_Theta;
1277:   ts->ops->adjointsetup    = TSAdjointSetUp_Theta;
1278:   ts->ops->adjointreset    = TSAdjointReset_Theta;
1279:   ts->ops->step            = TSStep_Theta;
1280:   ts->ops->interpolate     = TSInterpolate_Theta;
1281:   ts->ops->evaluatewlte    = TSEvaluateWLTE_Theta;
1282:   ts->ops->rollback        = TSRollBack_Theta;
1283:   ts->ops->setfromoptions  = TSSetFromOptions_Theta;
1284:   ts->ops->snesfunction    = SNESTSFormFunction_Theta;
1285:   ts->ops->snesjacobian    = SNESTSFormJacobian_Theta;
1286: #if defined(PETSC_HAVE_COMPLEX)
1287:   ts->ops->linearstability = TSComputeLinearStability_Theta;
1288: #endif
1289:   ts->ops->getstages       = TSGetStages_Theta;
1290:   ts->ops->adjointstep     = TSAdjointStep_Theta;
1291:   ts->ops->adjointintegral = TSAdjointCostIntegral_Theta;
1292:   ts->ops->forwardintegral = TSForwardCostIntegral_Theta;
1293:   ts->default_adapt_type   = TSADAPTNONE;

1295:   ts->ops->forwardsetup     = TSForwardSetUp_Theta;
1296:   ts->ops->forwardreset     = TSForwardReset_Theta;
1297:   ts->ops->forwardstep      = TSForwardStep_Theta;
1298:   ts->ops->forwardgetstages = TSForwardGetStages_Theta;

1300:   ts->usessnes = PETSC_TRUE;

1302:   PetscNewLog(ts,&th);
1303:   ts->data = (void*)th;

1305:   th->VecsDeltaLam    = NULL;
1306:   th->VecsDeltaMu     = NULL;
1307:   th->VecsSensiTemp   = NULL;
1308:   th->VecsSensi2Temp  = NULL;

1310:   th->extrapolate = PETSC_FALSE;
1311:   th->Theta       = 0.5;
1312:   th->order       = 2;
1313:   PetscObjectComposeFunction((PetscObject)ts,"TSThetaGetTheta_C",TSThetaGetTheta_Theta);
1314:   PetscObjectComposeFunction((PetscObject)ts,"TSThetaSetTheta_C",TSThetaSetTheta_Theta);
1315:   PetscObjectComposeFunction((PetscObject)ts,"TSThetaGetEndpoint_C",TSThetaGetEndpoint_Theta);
1316:   PetscObjectComposeFunction((PetscObject)ts,"TSThetaSetEndpoint_C",TSThetaSetEndpoint_Theta);
1317:   return(0);
1318: }

1320: /*@
1321:   TSThetaGetTheta - Get the abscissa of the stage in (0,1].

1323:   Not Collective

1325:   Input Parameter:
1326: .  ts - timestepping context

1328:   Output Parameter:
1329: .  theta - stage abscissa

1331:   Note:
1332:   Use of this function is normally only required to hack TSTHETA to use a modified integration scheme.

1334:   Level: Advanced

1336: .seealso: TSThetaSetTheta()
1337: @*/
1338: PetscErrorCode  TSThetaGetTheta(TS ts,PetscReal *theta)
1339: {

1345:   PetscUseMethod(ts,"TSThetaGetTheta_C",(TS,PetscReal*),(ts,theta));
1346:   return(0);
1347: }

1349: /*@
1350:   TSThetaSetTheta - Set the abscissa of the stage in (0,1].

1352:   Not Collective

1354:   Input Parameter:
1355: +  ts - timestepping context
1356: -  theta - stage abscissa

1358:   Options Database:
1359: .  -ts_theta_theta <theta>

1361:   Level: Intermediate

1363: .seealso: TSThetaGetTheta()
1364: @*/
1365: PetscErrorCode  TSThetaSetTheta(TS ts,PetscReal theta)
1366: {

1371:   PetscTryMethod(ts,"TSThetaSetTheta_C",(TS,PetscReal),(ts,theta));
1372:   return(0);
1373: }

1375: /*@
1376:   TSThetaGetEndpoint - Gets whether to use the endpoint variant of the method (e.g. trapezoid/Crank-Nicolson instead of midpoint rule).

1378:   Not Collective

1380:   Input Parameter:
1381: .  ts - timestepping context

1383:   Output Parameter:
1384: .  endpoint - PETSC_TRUE when using the endpoint variant

1386:   Level: Advanced

1388: .seealso: TSThetaSetEndpoint(), TSTHETA, TSCN
1389: @*/
1390: PetscErrorCode TSThetaGetEndpoint(TS ts,PetscBool *endpoint)
1391: {

1397:   PetscUseMethod(ts,"TSThetaGetEndpoint_C",(TS,PetscBool*),(ts,endpoint));
1398:   return(0);
1399: }

1401: /*@
1402:   TSThetaSetEndpoint - Sets whether to use the endpoint variant of the method (e.g. trapezoid/Crank-Nicolson instead of midpoint rule).

1404:   Not Collective

1406:   Input Parameter:
1407: +  ts - timestepping context
1408: -  flg - PETSC_TRUE to use the endpoint variant

1410:   Options Database:
1411: .  -ts_theta_endpoint <flg>

1413:   Level: Intermediate

1415: .seealso: TSTHETA, TSCN
1416: @*/
1417: PetscErrorCode TSThetaSetEndpoint(TS ts,PetscBool flg)
1418: {

1423:   PetscTryMethod(ts,"TSThetaSetEndpoint_C",(TS,PetscBool),(ts,flg));
1424:   return(0);
1425: }

1427: /*
1428:  * TSBEULER and TSCN are straightforward specializations of TSTHETA.
1429:  * The creation functions for these specializations are below.
1430:  */

1432: static PetscErrorCode TSSetUp_BEuler(TS ts)
1433: {
1434:   TS_Theta       *th = (TS_Theta*)ts->data;

1438:   if (th->Theta != 1.0) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_OPT_OVERWRITE,"Can not change the default value (1) of theta when using backward Euler\n");
1439:   if (th->endpoint) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_OPT_OVERWRITE,"Can not change to the endpoint form of the Theta methods when using backward Euler\n");
1440:   TSSetUp_Theta(ts);
1441:   return(0);
1442: }

1444: static PetscErrorCode TSView_BEuler(TS ts,PetscViewer viewer)
1445: {
1447:   return(0);
1448: }

1450: /*MC
1451:       TSBEULER - ODE solver using the implicit backward Euler method

1453:   Level: beginner

1455:   Notes:
1456:   TSBEULER is equivalent to TSTHETA with Theta=1.0

1458: $  -ts_type theta -ts_theta_theta 1.0

1460: .seealso:  TSCreate(), TS, TSSetType(), TSEULER, TSCN, TSTHETA

1462: M*/
1463: PETSC_EXTERN PetscErrorCode TSCreate_BEuler(TS ts)
1464: {

1468:   TSCreate_Theta(ts);
1469:   TSThetaSetTheta(ts,1.0);
1470:   TSThetaSetEndpoint(ts,PETSC_FALSE);
1471:   ts->ops->setup = TSSetUp_BEuler;
1472:   ts->ops->view  = TSView_BEuler;
1473:   return(0);
1474: }

1476: static PetscErrorCode TSSetUp_CN(TS ts)
1477: {
1478:   TS_Theta       *th = (TS_Theta*)ts->data;

1482:   if (th->Theta != 0.5) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_OPT_OVERWRITE,"Can not change the default value (0.5) of theta when using Crank-Nicolson\n");
1483:   if (!th->endpoint) SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_OPT_OVERWRITE,"Can not change to the midpoint form of the Theta methods when using Crank-Nicolson\n");
1484:   TSSetUp_Theta(ts);
1485:   return(0);
1486: }

1488: static PetscErrorCode TSView_CN(TS ts,PetscViewer viewer)
1489: {
1491:   return(0);
1492: }

1494: /*MC
1495:       TSCN - ODE solver using the implicit Crank-Nicolson method.

1497:   Level: beginner

1499:   Notes:
1500:   TSCN is equivalent to TSTHETA with Theta=0.5 and the "endpoint" option set. I.e.

1502: $  -ts_type theta -ts_theta_theta 0.5 -ts_theta_endpoint

1504: .seealso:  TSCreate(), TS, TSSetType(), TSBEULER, TSTHETA

1506: M*/
1507: PETSC_EXTERN PetscErrorCode TSCreate_CN(TS ts)
1508: {

1512:   TSCreate_Theta(ts);
1513:   TSThetaSetTheta(ts,0.5);
1514:   TSThetaSetEndpoint(ts,PETSC_TRUE);
1515:   ts->ops->setup = TSSetUp_CN;
1516:   ts->ops->view  = TSView_CN;
1517:   return(0);
1518: }