Actual source code: theta.c

petsc-master 2020-06-02
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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 stages and time derivative */
 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,th->X,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,th->X,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,th->X,VecsDeltaLam,ts->vec_sensip_col,ts->vecs_fuu);
333:     /* lambda_s^T F_UP w_2 */
334:     TSComputeIHessianProductFunctionUP(ts,th->stage_time,th->X,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,th->X,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:     TSComputeIJacobianP(ts,th->stage_time,th->X,th->Xdot,1./adjoint_time_step,ts->Jacp,PETSC_FALSE); /* get -f_p */
375:     if (quadts) {
376:       TSComputeRHSJacobianP(quadts,th->stage_time,th->X,quadJp);
377:     }
378:     if (ts->vecs_sensi2p) {
379:       /* lambda_s^T F_PU w_1 */
380:       TSComputeIHessianProductFunctionPU(ts,th->stage_time,th->X,VecsDeltaLam,ts->vec_sensip_col,ts->vecs_fpu);
381:       /* lambda_s^T F_PP w_2 */
382:       TSComputeIHessianProductFunctionPP(ts,th->stage_time,th->X,VecsDeltaLam,ts->vec_dir,ts->vecs_fpp);
383:     }

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

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

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

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

447:   /* Build RHS for first-order adjoint */
448:   /* Cost function has an integral term */
449:   if (quadts) {
450:     if (th->endpoint) {
451:       TSComputeRHSJacobian(quadts,th->stage_time,ts->vec_sol,quadJ,NULL);
452:     } else {
453:       TSComputeRHSJacobian(quadts,th->stage_time,th->X,quadJ,NULL);
454:     }
455:   }

457:   for (nadj=0; nadj<ts->numcost; nadj++) {
458:     VecCopy(ts->vecs_sensi[nadj],VecsSensiTemp[nadj]);
459:     VecScale(VecsSensiTemp[nadj],1./(th->Theta*adjoint_time_step));
460:     if (quadJ) {
461:       MatDenseGetColumn(quadJ,nadj,&xarr);
462:       VecPlaceArray(ts->vec_drdu_col,xarr);
463:       VecAXPY(VecsSensiTemp[nadj],1.,ts->vec_drdu_col);
464:       VecResetArray(ts->vec_drdu_col);
465:       MatDenseRestoreColumn(quadJ,&xarr);
466:     }
467:   }

469:   /* Build LHS for first-order adjoint */
470:   th->shift = 1./(th->Theta*adjoint_time_step);
471:   if (th->endpoint) {
472:     TSComputeSNESJacobian(ts,ts->vec_sol,J,Jpre);
473:   } else {
474:     TSComputeSNESJacobian(ts,th->X,J,Jpre);
475:   }
476:   KSPSetOperators(ksp,J,Jpre);

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

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

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

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

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

567:     if (ts->vecs_sensip) { /* sensitivities wrt parameters */
568:       /* U_{n+1} */
569:       TSComputeIJacobianP(ts,th->stage_time,ts->vec_sol,th->Xdot,-1./(th->Theta*adjoint_time_step),ts->Jacp,PETSC_FALSE);
570:       if (quadts) {
571:         TSComputeRHSJacobianP(quadts,th->stage_time,ts->vec_sol,quadJp);
572:       }
573:       for (nadj=0; nadj<ts->numcost; nadj++) {
574:         MatMultTranspose(ts->Jacp,VecsDeltaLam[nadj],VecsDeltaMu[nadj]);
575:         VecAXPY(ts->vecs_sensip[nadj],-adjoint_time_step*th->Theta,VecsDeltaMu[nadj]);
576:       }
577:       if (ts->vecs_sensi2p) { /* second-order */
578:         /* Get w1 at t_{n+1} from TLM matrix */
579:         MatDenseGetColumn(ts->mat_sensip,0,&xarr);
580:         VecPlaceArray(ts->vec_sensip_col,xarr);
581:         /* lambda_s^T F_PU w_1 */
582:         TSComputeIHessianProductFunctionPU(ts,th->stage_time,ts->vec_sol,VecsDeltaLam,ts->vec_sensip_col,ts->vecs_fpu);
583:         VecResetArray(ts->vec_sensip_col);
584:         MatDenseRestoreColumn(ts->mat_sensip,&xarr);

586:         /* lambda_s^T F_PP w_2 */
587:         TSComputeIHessianProductFunctionPP(ts,th->stage_time,ts->vec_sol,VecsDeltaLam,ts->vec_dir,ts->vecs_fpp);
588:         for (nadj=0; nadj<ts->numcost; nadj++) {
589:           /* 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)  */
590:           MatMultTranspose(ts->Jacp,VecsDeltaLam2[nadj],VecsDeltaMu2[nadj]);
591:           VecAXPY(ts->vecs_sensi2p[nadj],-adjoint_time_step*th->Theta,VecsDeltaMu2[nadj]);
592:           if (ts->vecs_fpu) {
593:             VecAXPY(ts->vecs_sensi2p[nadj],-adjoint_time_step*th->Theta,ts->vecs_fpu[nadj]);
594:           }
595:           if (ts->vecs_fpp) {
596:             VecAXPY(ts->vecs_sensi2p[nadj],-adjoint_time_step*th->Theta,ts->vecs_fpp[nadj]);
597:           }
598:         }
599:       }

601:       /* U_s */
602:       TSComputeIJacobianP(ts,adjoint_ptime,th->X0,th->Xdot,1./((th->Theta-1.0)*adjoint_time_step),ts->Jacp,PETSC_FALSE);
603:       if (quadts) {
604:         TSComputeRHSJacobianP(quadts,adjoint_ptime,th->X0,quadJp);
605:       }
606:       for (nadj=0; nadj<ts->numcost; nadj++) {
607:         MatMultTranspose(ts->Jacp,VecsDeltaLam[nadj],VecsDeltaMu[nadj]);
608:         VecAXPY(ts->vecs_sensip[nadj],-adjoint_time_step*(1.0-th->Theta),VecsDeltaMu[nadj]);
609:         if (ts->vecs_sensi2p) { /* second-order */
610:           /* Get w1 at t_n from TLM matrix */
611:           MatDenseGetColumn(th->MatFwdSensip0,0,&xarr);
612:           VecPlaceArray(ts->vec_sensip_col,xarr);
613:           /* lambda_s^T F_PU w_1 */
614:           TSComputeIHessianProductFunctionPU(ts,adjoint_ptime,th->X0,VecsDeltaLam,ts->vec_sensip_col,ts->vecs_fpu);
615:           VecResetArray(ts->vec_sensip_col);
616:           MatDenseRestoreColumn(th->MatFwdSensip0,&xarr);
617:           /* lambda_s^T F_PP w_2 */
618:           TSComputeIHessianProductFunctionPP(ts,adjoint_ptime,th->X0,VecsDeltaLam,ts->vec_dir,ts->vecs_fpp);
619:           for (nadj=0; nadj<ts->numcost; nadj++) {
620:             /* 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) */
621:             MatMultTranspose(ts->Jacp,VecsDeltaLam2[nadj],VecsDeltaMu2[nadj]);
622:             VecAXPY(ts->vecs_sensi2p[nadj],-adjoint_time_step*(1.0-th->Theta),VecsDeltaMu2[nadj]);
623:             if (ts->vecs_fpu) {
624:               VecAXPY(ts->vecs_sensi2p[nadj],-adjoint_time_step*(1.0-th->Theta),ts->vecs_fpu[nadj]);
625:             }
626:             if (ts->vecs_fpp) {
627:               VecAXPY(ts->vecs_sensi2p[nadj],-adjoint_time_step*(1.0-th->Theta),ts->vecs_fpp[nadj]);
628:             }
629:           }
630:         }
631:       }
632:     }
633:   } else { /* one-stage case */
634:     th->shift = 0.0;
635:     TSComputeSNESJacobian(ts,th->X,J,Jpre); /* get -f_y */
636:     KSPSetOperators(ksp,J,Jpre);
637:     if (quadts) {
638:       TSComputeRHSJacobian(quadts,th->stage_time,th->X,quadJ,NULL);
639:     }
640:     for (nadj=0; nadj<ts->numcost; nadj++) {
641:       MatMultTranspose(J,VecsDeltaLam[nadj],VecsSensiTemp[nadj]);
642:       VecAXPY(ts->vecs_sensi[nadj],-adjoint_time_step,VecsSensiTemp[nadj]);
643:       if (quadJ) {
644:         MatDenseGetColumn(quadJ,nadj,&xarr);
645:         VecPlaceArray(ts->vec_drdu_col,xarr);
646:         VecAXPY(ts->vecs_sensi[nadj],adjoint_time_step,ts->vec_drdu_col);
647:         VecResetArray(ts->vec_drdu_col);
648:         MatDenseRestoreColumn(quadJ,&xarr);
649:       }
650:     }
651:     if (ts->vecs_sensip) {
652:       TSComputeIJacobianP(ts,th->stage_time,th->X,th->Xdot,th->shift,ts->Jacp,PETSC_FALSE);
653:       if (quadts) {
654:         TSComputeRHSJacobianP(quadts,th->stage_time,th->X,quadJp);
655:       }
656:       for (nadj=0; nadj<ts->numcost; nadj++) {
657:         MatMultTranspose(ts->Jacp,VecsDeltaLam[nadj],VecsDeltaMu[nadj]);
658:         VecAXPY(ts->vecs_sensip[nadj],-adjoint_time_step,VecsDeltaMu[nadj]);
659:         if (quadJp) {
660:           MatDenseGetColumn(quadJp,nadj,&xarr);
661:           VecPlaceArray(ts->vec_drdp_col,xarr);
662:           VecAXPY(ts->vecs_sensip[nadj],adjoint_time_step,ts->vec_drdp_col);
663:           VecResetArray(ts->vec_drdp_col);
664:           MatDenseRestoreColumn(quadJp,&xarr);
665:         }
666:       }
667:     }
668:   }

670:   th->status = TS_STEP_COMPLETE;
671:   return(0);
672: }

674: static PetscErrorCode TSInterpolate_Theta(TS ts,PetscReal t,Vec X)
675: {
676:   TS_Theta       *th = (TS_Theta*)ts->data;
677:   PetscReal      dt  = t - ts->ptime;

681:   VecCopy(ts->vec_sol,th->X);
682:   if (th->endpoint) dt *= th->Theta;
683:   VecWAXPY(X,dt,th->Xdot,th->X);
684:   return(0);
685: }

687: static PetscErrorCode TSEvaluateWLTE_Theta(TS ts,NormType wnormtype,PetscInt *order,PetscReal *wlte)
688: {
689:   TS_Theta       *th = (TS_Theta*)ts->data;
690:   Vec            X = ts->vec_sol;      /* X = solution */
691:   Vec            Y = th->vec_lte_work; /* Y = X + LTE  */
692:   PetscReal      wltea,wlter;

696:   if (!th->vec_sol_prev) {*wlte = -1; return(0);}
697:   /* Cannot compute LTE in first step or in restart after event */
698:   if (ts->steprestart) {*wlte = -1; return(0);}
699:   /* Compute LTE using backward differences with non-constant time step */
700:   {
701:     PetscReal   h = ts->time_step, h_prev = ts->ptime - ts->ptime_prev;
702:     PetscReal   a = 1 + h_prev/h;
703:     PetscScalar scal[3]; Vec vecs[3];
704:     scal[0] = +1/a; scal[1] = -1/(a-1); scal[2] = +1/(a*(a-1));
705:     vecs[0] = X;    vecs[1] = th->X0;   vecs[2] = th->vec_sol_prev;
706:     VecCopy(X,Y);
707:     VecMAXPY(Y,3,scal,vecs);
708:     TSErrorWeightedNorm(ts,X,Y,wnormtype,wlte,&wltea,&wlter);
709:   }
710:   if (order) *order = 2;
711:   return(0);
712: }

714: static PetscErrorCode TSRollBack_Theta(TS ts)
715: {
716:   TS_Theta       *th = (TS_Theta*)ts->data;
717:   TS             quadts = ts->quadraturets;

721:   VecCopy(th->X0,ts->vec_sol);
722:   if (quadts && ts->costintegralfwd) {
723:     VecCopy(th->VecCostIntegral0,quadts->vec_sol);
724:   }
725:   th->status = TS_STEP_INCOMPLETE;
726:   if (ts->mat_sensip) {
727:     MatCopy(th->MatFwdSensip0,ts->mat_sensip,SAME_NONZERO_PATTERN);
728:   }
729:   if (quadts && quadts->mat_sensip) {
730:     MatCopy(th->MatIntegralSensip0,quadts->mat_sensip,SAME_NONZERO_PATTERN);
731:   }
732:   return(0);
733: }

735: static PetscErrorCode TSForwardStep_Theta(TS ts)
736: {
737:   TS_Theta       *th = (TS_Theta*)ts->data;
738:   TS             quadts = ts->quadraturets;
739:   Mat            MatDeltaFwdSensip = th->MatDeltaFwdSensip;
740:   Vec            VecDeltaFwdSensipCol = th->VecDeltaFwdSensipCol;
741:   PetscInt       ntlm;
742:   KSP            ksp;
743:   Mat            J,Jpre,quadJ = NULL,quadJp = NULL;
744:   PetscScalar    *barr,*xarr;
745:   PetscReal      previous_shift;

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

752:   if (quadts && quadts->mat_sensip) {
753:     MatCopy(quadts->mat_sensip,th->MatIntegralSensip0,SAME_NONZERO_PATTERN);
754:   }
755:   SNESGetKSP(ts->snes,&ksp);
756:   TSGetIJacobian(ts,&J,&Jpre,NULL,NULL);
757:   if (quadts) {
758:     TSGetRHSJacobian(quadts,&quadJ,NULL,NULL,NULL);
759:     TSGetRHSJacobianP(quadts,&quadJp,NULL,NULL);
760:   }

762:   /* Build RHS */
763:   if (th->endpoint) { /* 2-stage method*/
764:     th->shift = 1./((th->Theta-1.)*th->time_step0);
765:     TSComputeIJacobian(ts,th->ptime0,th->X0,th->Xdot,th->shift,J,Jpre,PETSC_FALSE);
766:     MatMatMult(J,ts->mat_sensip,MAT_REUSE_MATRIX,PETSC_DEFAULT,&MatDeltaFwdSensip);
767:     MatScale(MatDeltaFwdSensip,(th->Theta-1.)/th->Theta);

769:     /* Add the f_p forcing terms */
770:     if (ts->Jacp) {
771:       TSComputeIJacobianP(ts,th->ptime0,th->X0,th->Xdot,th->shift,ts->Jacp,PETSC_FALSE);
772:       MatAXPY(MatDeltaFwdSensip,(th->Theta-1.)/th->Theta,ts->Jacp,SUBSET_NONZERO_PATTERN);
773:       TSComputeIJacobianP(ts,th->stage_time,ts->vec_sol,th->Xdot,th->shift,ts->Jacp,PETSC_FALSE);
774:       MatAXPY(MatDeltaFwdSensip,-1.,ts->Jacp,SUBSET_NONZERO_PATTERN);
775:     }
776:   } else { /* 1-stage method */
777:     th->shift = 0.0;
778:     TSComputeIJacobian(ts,th->stage_time,th->X,th->Xdot,th->shift,J,Jpre,PETSC_FALSE);
779:     MatMatMult(J,ts->mat_sensip,MAT_REUSE_MATRIX,PETSC_DEFAULT,&MatDeltaFwdSensip);
780:     MatScale(MatDeltaFwdSensip,-1.);

782:     /* Add the f_p forcing terms */
783:     if (ts->Jacp) {
784:       TSComputeIJacobianP(ts,th->stage_time,th->X,th->Xdot,th->shift,ts->Jacp,PETSC_FALSE);
785:       MatAXPY(MatDeltaFwdSensip,-1.,ts->Jacp,SUBSET_NONZERO_PATTERN);
786:     }
787:   }

789:   /* Build LHS */
790:   th->shift = previous_shift; /* recover the previous shift used in TSStep_Theta() */
791:   if (th->endpoint) {
792:     TSComputeIJacobian(ts,th->stage_time,ts->vec_sol,th->Xdot,th->shift,J,Jpre,PETSC_FALSE);
793:   } else {
794:     TSComputeIJacobian(ts,th->stage_time,th->X,th->Xdot,th->shift,J,Jpre,PETSC_FALSE);
795:   }
796:   KSPSetOperators(ksp,J,Jpre);

798:   /*
799:     Evaluate the first stage of integral gradients with the 2-stage method:
800:     drdu|t_n*S(t_n) + drdp|t_n
801:     This is done before the linear solve because the sensitivity variable S(t_n) will be propagated to S(t_{n+1})
802:   */
803:   if (th->endpoint) { /* 2-stage method only */
804:     if (quadts && quadts->mat_sensip) {
805:       TSComputeRHSJacobian(quadts,th->ptime0,th->X0,quadJ,NULL);
806:       TSComputeRHSJacobianP(quadts,th->ptime0,th->X0,quadJp);
807:       MatTransposeMatMult(ts->mat_sensip,quadJ,MAT_REUSE_MATRIX,PETSC_DEFAULT,&th->MatIntegralSensipTemp);
808:       MatAXPY(th->MatIntegralSensipTemp,1,quadJp,SAME_NONZERO_PATTERN);
809:       MatAXPY(quadts->mat_sensip,th->time_step0*(1.-th->Theta),th->MatIntegralSensipTemp,SAME_NONZERO_PATTERN);
810:     }
811:   }

813:   /* Solve the tangent linear equation for forward sensitivities to parameters */
814:   for (ntlm=0; ntlm<th->num_tlm; ntlm++) {
815:     KSPConvergedReason kspreason;
816:     MatDenseGetColumn(MatDeltaFwdSensip,ntlm,&barr);
817:     VecPlaceArray(VecDeltaFwdSensipCol,barr);
818:     if (th->endpoint) {
819:       MatDenseGetColumn(ts->mat_sensip,ntlm,&xarr);
820:       VecPlaceArray(ts->vec_sensip_col,xarr);
821:       KSPSolve(ksp,VecDeltaFwdSensipCol,ts->vec_sensip_col);
822:       VecResetArray(ts->vec_sensip_col);
823:       MatDenseRestoreColumn(ts->mat_sensip,&xarr);
824:     } else {
825:       KSPSolve(ksp,VecDeltaFwdSensipCol,VecDeltaFwdSensipCol);
826:     }
827:     KSPGetConvergedReason(ksp,&kspreason);
828:     if (kspreason < 0) {
829:       ts->reason = TSFORWARD_DIVERGED_LINEAR_SOLVE;
830:       PetscInfo2(ts,"Step=%D, %Dth tangent linear solve, linear solve fails, stopping tangent linear solve\n",ts->steps,ntlm);
831:     }
832:     VecResetArray(VecDeltaFwdSensipCol);
833:     MatDenseRestoreColumn(MatDeltaFwdSensip,&barr);
834:   }

836:   /*
837:     Evaluate the second stage of integral gradients with the 2-stage method:
838:     drdu|t_{n+1}*S(t_{n+1}) + drdp|t_{n+1}
839:   */
840:   if (quadts && quadts->mat_sensip) {
841:     if (!th->endpoint) {
842:       MatAXPY(ts->mat_sensip,1,MatDeltaFwdSensip,SAME_NONZERO_PATTERN); /* stage sensitivity */
843:       TSComputeRHSJacobian(quadts,th->stage_time,th->X,quadJ,NULL);
844:       TSComputeRHSJacobianP(quadts,th->stage_time,th->X,quadJp);
845:       MatTransposeMatMult(ts->mat_sensip,quadJ,MAT_REUSE_MATRIX,PETSC_DEFAULT,&th->MatIntegralSensipTemp);
846:       MatAXPY(th->MatIntegralSensipTemp,1,quadJp,SAME_NONZERO_PATTERN);
847:       MatAXPY(quadts->mat_sensip,th->time_step0,th->MatIntegralSensipTemp,SAME_NONZERO_PATTERN);
848:       MatAXPY(ts->mat_sensip,(1.-th->Theta)/th->Theta,MatDeltaFwdSensip,SAME_NONZERO_PATTERN);
849:     } else {
850:       TSComputeRHSJacobian(quadts,th->stage_time,ts->vec_sol,quadJ,NULL);
851:       TSComputeRHSJacobianP(quadts,th->stage_time,ts->vec_sol,quadJp);
852:       MatTransposeMatMult(ts->mat_sensip,quadJ,MAT_REUSE_MATRIX,PETSC_DEFAULT,&th->MatIntegralSensipTemp);
853:       MatAXPY(th->MatIntegralSensipTemp,1,quadJp,SAME_NONZERO_PATTERN);
854:       MatAXPY(quadts->mat_sensip,th->time_step0*th->Theta,th->MatIntegralSensipTemp,SAME_NONZERO_PATTERN);
855:     }
856:   } else {
857:     if (!th->endpoint) {
858:       MatAXPY(ts->mat_sensip,1./th->Theta,MatDeltaFwdSensip,SAME_NONZERO_PATTERN);
859:     }
860:   }
861:   return(0);
862: }

864: static PetscErrorCode TSForwardGetStages_Theta(TS ts,PetscInt *ns,Mat **stagesensip)
865: {
866:   TS_Theta *th = (TS_Theta*)ts->data;

869:   if (ns) *ns = 1;
870:   if (stagesensip) *stagesensip = th->endpoint ? &(th->MatFwdSensip0) : &(th->MatDeltaFwdSensip);
871:   return(0);
872: }

874: /*------------------------------------------------------------*/
875: static PetscErrorCode TSReset_Theta(TS ts)
876: {
877:   TS_Theta       *th = (TS_Theta*)ts->data;

881:   VecDestroy(&th->X);
882:   VecDestroy(&th->Xdot);
883:   VecDestroy(&th->X0);
884:   VecDestroy(&th->affine);

886:   VecDestroy(&th->vec_sol_prev);
887:   VecDestroy(&th->vec_lte_work);

889:   VecDestroy(&th->VecCostIntegral0);
890:   return(0);
891: }

893: static PetscErrorCode TSAdjointReset_Theta(TS ts)
894: {
895:   TS_Theta       *th = (TS_Theta*)ts->data;

899:   VecDestroyVecs(ts->numcost,&th->VecsDeltaLam);
900:   VecDestroyVecs(ts->numcost,&th->VecsDeltaMu);
901:   VecDestroyVecs(ts->numcost,&th->VecsDeltaLam2);
902:   VecDestroyVecs(ts->numcost,&th->VecsDeltaMu2);
903:   VecDestroyVecs(ts->numcost,&th->VecsSensiTemp);
904:   VecDestroyVecs(ts->numcost,&th->VecsSensi2Temp);
905:   return(0);
906: }

908: static PetscErrorCode TSDestroy_Theta(TS ts)
909: {

913:   TSReset_Theta(ts);
914:   if (ts->dm) {
915:     DMCoarsenHookRemove(ts->dm,DMCoarsenHook_TSTheta,DMRestrictHook_TSTheta,ts);
916:     DMSubDomainHookRemove(ts->dm,DMSubDomainHook_TSTheta,DMSubDomainRestrictHook_TSTheta,ts);
917:   }
918:   PetscFree(ts->data);
919:   PetscObjectComposeFunction((PetscObject)ts,"TSThetaGetTheta_C",NULL);
920:   PetscObjectComposeFunction((PetscObject)ts,"TSThetaSetTheta_C",NULL);
921:   PetscObjectComposeFunction((PetscObject)ts,"TSThetaGetEndpoint_C",NULL);
922:   PetscObjectComposeFunction((PetscObject)ts,"TSThetaSetEndpoint_C",NULL);
923:   return(0);
924: }

926: /*
927:   This defines the nonlinear equation that is to be solved with SNES
928:   G(U) = F[t0+Theta*dt, U, (U-U0)*shift] = 0
929: */
930: static PetscErrorCode SNESTSFormFunction_Theta(SNES snes,Vec x,Vec y,TS ts)
931: {
932:   TS_Theta       *th = (TS_Theta*)ts->data;
934:   Vec            X0,Xdot;
935:   DM             dm,dmsave;
936:   PetscReal      shift = th->shift;

939:   SNESGetDM(snes,&dm);
940:   /* When using the endpoint variant, this is actually 1/Theta * Xdot */
941:   TSThetaGetX0AndXdot(ts,dm,&X0,&Xdot);
942:   if (x != X0) {
943:     VecAXPBYPCZ(Xdot,-shift,shift,0,X0,x);
944:   } else {
945:     VecZeroEntries(Xdot);
946:   }
947:   /* DM monkey-business allows user code to call TSGetDM() inside of functions evaluated on levels of FAS */
948:   dmsave = ts->dm;
949:   ts->dm = dm;
950:   TSComputeIFunction(ts,th->stage_time,x,Xdot,y,PETSC_FALSE);
951:   ts->dm = dmsave;
952:   TSThetaRestoreX0AndXdot(ts,dm,&X0,&Xdot);
953:   return(0);
954: }

956: static PetscErrorCode SNESTSFormJacobian_Theta(SNES snes,Vec x,Mat A,Mat B,TS ts)
957: {
958:   TS_Theta       *th = (TS_Theta*)ts->data;
960:   Vec            Xdot;
961:   DM             dm,dmsave;
962:   PetscReal      shift = th->shift;

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

969:   dmsave = ts->dm;
970:   ts->dm = dm;
971:   TSComputeIJacobian(ts,th->stage_time,x,Xdot,shift,A,B,PETSC_FALSE);
972:   ts->dm = dmsave;
973:   TSThetaRestoreX0AndXdot(ts,dm,NULL,&Xdot);
974:   return(0);
975: }

977: static PetscErrorCode TSForwardSetUp_Theta(TS ts)
978: {
979:   TS_Theta       *th = (TS_Theta*)ts->data;
980:   TS             quadts = ts->quadraturets;

984:   /* combine sensitivities to parameters and sensitivities to initial values into one array */
985:   th->num_tlm = ts->num_parameters;
986:   MatDuplicate(ts->mat_sensip,MAT_DO_NOT_COPY_VALUES,&th->MatDeltaFwdSensip);
987:   if (quadts && quadts->mat_sensip) {
988:     MatDuplicate(quadts->mat_sensip,MAT_DO_NOT_COPY_VALUES,&th->MatIntegralSensipTemp);
989:     MatDuplicate(quadts->mat_sensip,MAT_DO_NOT_COPY_VALUES,&th->MatIntegralSensip0);
990:   }
991:   /* backup sensitivity results for roll-backs */
992:   MatDuplicate(ts->mat_sensip,MAT_DO_NOT_COPY_VALUES,&th->MatFwdSensip0);

994:   VecDuplicate(ts->vec_sol,&th->VecDeltaFwdSensipCol);
995:   return(0);
996: }

998: static PetscErrorCode TSForwardReset_Theta(TS ts)
999: {
1000:   TS_Theta       *th = (TS_Theta*)ts->data;
1001:   TS             quadts = ts->quadraturets;

1005:   if (quadts && quadts->mat_sensip) {
1006:     MatDestroy(&th->MatIntegralSensipTemp);
1007:     MatDestroy(&th->MatIntegralSensip0);
1008:   }
1009:   VecDestroy(&th->VecDeltaFwdSensipCol);
1010:   MatDestroy(&th->MatDeltaFwdSensip);
1011:   MatDestroy(&th->MatFwdSensip0);
1012:   return(0);
1013: }

1015: static PetscErrorCode TSSetUp_Theta(TS ts)
1016: {
1017:   TS_Theta       *th = (TS_Theta*)ts->data;
1018:   TS             quadts = ts->quadraturets;
1019:   PetscBool      match;

1023:   if (!th->VecCostIntegral0 && quadts && ts->costintegralfwd) { /* back up cost integral */
1024:     VecDuplicate(quadts->vec_sol,&th->VecCostIntegral0);
1025:   }
1026:   if (!th->X) {
1027:     VecDuplicate(ts->vec_sol,&th->X);
1028:   }
1029:   if (!th->Xdot) {
1030:     VecDuplicate(ts->vec_sol,&th->Xdot);
1031:   }
1032:   if (!th->X0) {
1033:     VecDuplicate(ts->vec_sol,&th->X0);
1034:   }
1035:   if (th->endpoint) {
1036:     VecDuplicate(ts->vec_sol,&th->affine);
1037:   }

1039:   th->order = (th->Theta == 0.5) ? 2 : 1;
1040:   th->shift = 1/(th->Theta*ts->time_step);

1042:   TSGetDM(ts,&ts->dm);
1043:   DMCoarsenHookAdd(ts->dm,DMCoarsenHook_TSTheta,DMRestrictHook_TSTheta,ts);
1044:   DMSubDomainHookAdd(ts->dm,DMSubDomainHook_TSTheta,DMSubDomainRestrictHook_TSTheta,ts);

1046:   TSGetAdapt(ts,&ts->adapt);
1047:   TSAdaptCandidatesClear(ts->adapt);
1048:   PetscObjectTypeCompare((PetscObject)ts->adapt,TSADAPTNONE,&match);
1049:   if (!match) {
1050:     VecDuplicate(ts->vec_sol,&th->vec_sol_prev);
1051:     VecDuplicate(ts->vec_sol,&th->vec_lte_work);
1052:   }
1053:   TSGetSNES(ts,&ts->snes);
1054:   return(0);
1055: }

1057: /*------------------------------------------------------------*/

1059: static PetscErrorCode TSAdjointSetUp_Theta(TS ts)
1060: {
1061:   TS_Theta       *th = (TS_Theta*)ts->data;

1065:   VecDuplicateVecs(ts->vecs_sensi[0],ts->numcost,&th->VecsDeltaLam);
1066:   VecDuplicateVecs(ts->vecs_sensi[0],ts->numcost,&th->VecsSensiTemp);
1067:   if (ts->vecs_sensip) {
1068:     VecDuplicateVecs(ts->vecs_sensip[0],ts->numcost,&th->VecsDeltaMu);
1069:   }
1070:   if (ts->vecs_sensi2) {
1071:     VecDuplicateVecs(ts->vecs_sensi[0],ts->numcost,&th->VecsDeltaLam2);
1072:     VecDuplicateVecs(ts->vecs_sensi2[0],ts->numcost,&th->VecsSensi2Temp);
1073:     /* hack ts to make implicit TS solver work when users provide only explicit versions of callbacks (RHSFunction,RHSJacobian,RHSHessian etc.) */
1074:     if (!ts->ihessianproduct_fuu) ts->vecs_fuu = ts->vecs_guu;
1075:     if (!ts->ihessianproduct_fup) ts->vecs_fup = ts->vecs_gup;
1076:   }
1077:   if (ts->vecs_sensi2p) {
1078:     VecDuplicateVecs(ts->vecs_sensi2p[0],ts->numcost,&th->VecsDeltaMu2);
1079:     /* hack ts to make implicit TS solver work when users provide only explicit versions of callbacks (RHSFunction,RHSJacobian,RHSHessian etc.) */
1080:     if (!ts->ihessianproduct_fpu) ts->vecs_fpu = ts->vecs_gpu;
1081:     if (!ts->ihessianproduct_fpp) ts->vecs_fpp = ts->vecs_gpp;
1082:   }
1083:   return(0);
1084: }

1086: static PetscErrorCode TSSetFromOptions_Theta(PetscOptionItems *PetscOptionsObject,TS ts)
1087: {
1088:   TS_Theta       *th = (TS_Theta*)ts->data;

1092:   PetscOptionsHead(PetscOptionsObject,"Theta ODE solver options");
1093:   {
1094:     PetscOptionsReal("-ts_theta_theta","Location of stage (0<Theta<=1)","TSThetaSetTheta",th->Theta,&th->Theta,NULL);
1095:     PetscOptionsBool("-ts_theta_endpoint","Use the endpoint instead of midpoint form of the Theta method","TSThetaSetEndpoint",th->endpoint,&th->endpoint,NULL);
1096:     PetscOptionsBool("-ts_theta_initial_guess_extrapolate","Extrapolate stage initial guess from previous solution (sometimes unstable)","TSThetaSetExtrapolate",th->extrapolate,&th->extrapolate,NULL);
1097:   }
1098:   PetscOptionsTail();
1099:   return(0);
1100: }

1102: static PetscErrorCode TSView_Theta(TS ts,PetscViewer viewer)
1103: {
1104:   TS_Theta       *th = (TS_Theta*)ts->data;
1105:   PetscBool      iascii;

1109:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);
1110:   if (iascii) {
1111:     PetscViewerASCIIPrintf(viewer,"  Theta=%g\n",(double)th->Theta);
1112:     PetscViewerASCIIPrintf(viewer,"  Extrapolation=%s\n",th->extrapolate ? "yes" : "no");
1113:   }
1114:   return(0);
1115: }

1117: static PetscErrorCode TSThetaGetTheta_Theta(TS ts,PetscReal *theta)
1118: {
1119:   TS_Theta *th = (TS_Theta*)ts->data;

1122:   *theta = th->Theta;
1123:   return(0);
1124: }

1126: static PetscErrorCode TSThetaSetTheta_Theta(TS ts,PetscReal theta)
1127: {
1128:   TS_Theta *th = (TS_Theta*)ts->data;

1131:   if (theta <= 0 || 1 < theta) SETERRQ1(PetscObjectComm((PetscObject)ts),PETSC_ERR_ARG_OUTOFRANGE,"Theta %g not in range (0,1]",(double)theta);
1132:   th->Theta = theta;
1133:   th->order = (th->Theta == 0.5) ? 2 : 1;
1134:   return(0);
1135: }

1137: static PetscErrorCode TSThetaGetEndpoint_Theta(TS ts,PetscBool *endpoint)
1138: {
1139:   TS_Theta *th = (TS_Theta*)ts->data;

1142:   *endpoint = th->endpoint;
1143:   return(0);
1144: }

1146: static PetscErrorCode TSThetaSetEndpoint_Theta(TS ts,PetscBool flg)
1147: {
1148:   TS_Theta *th = (TS_Theta*)ts->data;

1151:   th->endpoint = flg;
1152:   return(0);
1153: }

1155: #if defined(PETSC_HAVE_COMPLEX)
1156: static PetscErrorCode TSComputeLinearStability_Theta(TS ts,PetscReal xr,PetscReal xi,PetscReal *yr,PetscReal *yi)
1157: {
1158:   PetscComplex   z   = xr + xi*PETSC_i,f;
1159:   TS_Theta       *th = (TS_Theta*)ts->data;
1160:   const PetscReal one = 1.0;

1163:   f   = (one + (one - th->Theta)*z)/(one - th->Theta*z);
1164:   *yr = PetscRealPartComplex(f);
1165:   *yi = PetscImaginaryPartComplex(f);
1166:   return(0);
1167: }
1168: #endif

1170: static PetscErrorCode TSGetStages_Theta(TS ts,PetscInt *ns,Vec **Y)
1171: {
1172:   TS_Theta     *th = (TS_Theta*)ts->data;

1175:   if (ns) *ns = 1;
1176:   if (Y)  *Y  = th->endpoint ? &(th->X0) : &(th->X);
1177:   return(0);
1178: }

1180: /* ------------------------------------------------------------ */
1181: /*MC
1182:       TSTHETA - DAE solver using the implicit Theta method

1184:    Level: beginner

1186:    Options Database:
1187: +  -ts_theta_theta <Theta> - Location of stage (0<Theta<=1)
1188: .  -ts_theta_endpoint <flag> - Use the endpoint (like Crank-Nicholson) instead of midpoint form of the Theta method
1189: -  -ts_theta_initial_guess_extrapolate <flg> - Extrapolate stage initial guess from previous solution (sometimes unstable)

1191:    Notes:
1192: $  -ts_type theta -ts_theta_theta 1.0 corresponds to backward Euler (TSBEULER)
1193: $  -ts_type theta -ts_theta_theta 0.5 corresponds to the implicit midpoint rule
1194: $  -ts_type theta -ts_theta_theta 0.5 -ts_theta_endpoint corresponds to Crank-Nicholson (TSCN)

1196:    This method can be applied to DAE.

1198:    This method is cast as a 1-stage implicit Runge-Kutta method.

1200: .vb
1201:   Theta | Theta
1202:   -------------
1203:         |  1
1204: .ve

1206:    For the default Theta=0.5, this is also known as the implicit midpoint rule.

1208:    When the endpoint variant is chosen, the method becomes a 2-stage method with first stage explicit:

1210: .vb
1211:   0 | 0         0
1212:   1 | 1-Theta   Theta
1213:   -------------------
1214:     | 1-Theta   Theta
1215: .ve

1217:    For the default Theta=0.5, this is the trapezoid rule (also known as Crank-Nicolson, see TSCN).

1219:    To apply a diagonally implicit RK method to DAE, the stage formula

1221: $  Y_i = X + h sum_j a_ij Y'_j

1223:    is interpreted as a formula for Y'_i in terms of Y_i and known values (Y'_j, j<i)

1225: .seealso:  TSCreate(), TS, TSSetType(), TSCN, TSBEULER, TSThetaSetTheta(), TSThetaSetEndpoint()

1227: M*/
1228: PETSC_EXTERN PetscErrorCode TSCreate_Theta(TS ts)
1229: {
1230:   TS_Theta       *th;

1234:   ts->ops->reset           = TSReset_Theta;
1235:   ts->ops->adjointreset    = TSAdjointReset_Theta;
1236:   ts->ops->destroy         = TSDestroy_Theta;
1237:   ts->ops->view            = TSView_Theta;
1238:   ts->ops->setup           = TSSetUp_Theta;
1239:   ts->ops->adjointsetup    = TSAdjointSetUp_Theta;
1240:   ts->ops->adjointreset    = TSAdjointReset_Theta;
1241:   ts->ops->step            = TSStep_Theta;
1242:   ts->ops->interpolate     = TSInterpolate_Theta;
1243:   ts->ops->evaluatewlte    = TSEvaluateWLTE_Theta;
1244:   ts->ops->rollback        = TSRollBack_Theta;
1245:   ts->ops->setfromoptions  = TSSetFromOptions_Theta;
1246:   ts->ops->snesfunction    = SNESTSFormFunction_Theta;
1247:   ts->ops->snesjacobian    = SNESTSFormJacobian_Theta;
1248: #if defined(PETSC_HAVE_COMPLEX)
1249:   ts->ops->linearstability = TSComputeLinearStability_Theta;
1250: #endif
1251:   ts->ops->getstages       = TSGetStages_Theta;
1252:   ts->ops->adjointstep     = TSAdjointStep_Theta;
1253:   ts->ops->adjointintegral = TSAdjointCostIntegral_Theta;
1254:   ts->ops->forwardintegral = TSForwardCostIntegral_Theta;
1255:   ts->default_adapt_type   = TSADAPTNONE;

1257:   ts->ops->forwardsetup     = TSForwardSetUp_Theta;
1258:   ts->ops->forwardreset     = TSForwardReset_Theta;
1259:   ts->ops->forwardstep      = TSForwardStep_Theta;
1260:   ts->ops->forwardgetstages = TSForwardGetStages_Theta;

1262:   ts->usessnes = PETSC_TRUE;

1264:   PetscNewLog(ts,&th);
1265:   ts->data = (void*)th;

1267:   th->VecsDeltaLam    = NULL;
1268:   th->VecsDeltaMu     = NULL;
1269:   th->VecsSensiTemp   = NULL;
1270:   th->VecsSensi2Temp  = NULL;

1272:   th->extrapolate = PETSC_FALSE;
1273:   th->Theta       = 0.5;
1274:   th->order       = 2;
1275:   PetscObjectComposeFunction((PetscObject)ts,"TSThetaGetTheta_C",TSThetaGetTheta_Theta);
1276:   PetscObjectComposeFunction((PetscObject)ts,"TSThetaSetTheta_C",TSThetaSetTheta_Theta);
1277:   PetscObjectComposeFunction((PetscObject)ts,"TSThetaGetEndpoint_C",TSThetaGetEndpoint_Theta);
1278:   PetscObjectComposeFunction((PetscObject)ts,"TSThetaSetEndpoint_C",TSThetaSetEndpoint_Theta);
1279:   return(0);
1280: }

1282: /*@
1283:   TSThetaGetTheta - Get the abscissa of the stage in (0,1].

1285:   Not Collective

1287:   Input Parameter:
1288: .  ts - timestepping context

1290:   Output Parameter:
1291: .  theta - stage abscissa

1293:   Note:
1294:   Use of this function is normally only required to hack TSTHETA to use a modified integration scheme.

1296:   Level: Advanced

1298: .seealso: TSThetaSetTheta()
1299: @*/
1300: PetscErrorCode  TSThetaGetTheta(TS ts,PetscReal *theta)
1301: {

1307:   PetscUseMethod(ts,"TSThetaGetTheta_C",(TS,PetscReal*),(ts,theta));
1308:   return(0);
1309: }

1311: /*@
1312:   TSThetaSetTheta - Set the abscissa of the stage in (0,1].

1314:   Not Collective

1316:   Input Parameter:
1317: +  ts - timestepping context
1318: -  theta - stage abscissa

1320:   Options Database:
1321: .  -ts_theta_theta <theta>

1323:   Level: Intermediate

1325: .seealso: TSThetaGetTheta()
1326: @*/
1327: PetscErrorCode  TSThetaSetTheta(TS ts,PetscReal theta)
1328: {

1333:   PetscTryMethod(ts,"TSThetaSetTheta_C",(TS,PetscReal),(ts,theta));
1334:   return(0);
1335: }

1337: /*@
1338:   TSThetaGetEndpoint - Gets whether to use the endpoint variant of the method (e.g. trapezoid/Crank-Nicolson instead of midpoint rule).

1340:   Not Collective

1342:   Input Parameter:
1343: .  ts - timestepping context

1345:   Output Parameter:
1346: .  endpoint - PETSC_TRUE when using the endpoint variant

1348:   Level: Advanced

1350: .seealso: TSThetaSetEndpoint(), TSTHETA, TSCN
1351: @*/
1352: PetscErrorCode TSThetaGetEndpoint(TS ts,PetscBool *endpoint)
1353: {

1359:   PetscUseMethod(ts,"TSThetaGetEndpoint_C",(TS,PetscBool*),(ts,endpoint));
1360:   return(0);
1361: }

1363: /*@
1364:   TSThetaSetEndpoint - Sets whether to use the endpoint variant of the method (e.g. trapezoid/Crank-Nicolson instead of midpoint rule).

1366:   Not Collective

1368:   Input Parameter:
1369: +  ts - timestepping context
1370: -  flg - PETSC_TRUE to use the endpoint variant

1372:   Options Database:
1373: .  -ts_theta_endpoint <flg>

1375:   Level: Intermediate

1377: .seealso: TSTHETA, TSCN
1378: @*/
1379: PetscErrorCode TSThetaSetEndpoint(TS ts,PetscBool flg)
1380: {

1385:   PetscTryMethod(ts,"TSThetaSetEndpoint_C",(TS,PetscBool),(ts,flg));
1386:   return(0);
1387: }

1389: /*
1390:  * TSBEULER and TSCN are straightforward specializations of TSTHETA.
1391:  * The creation functions for these specializations are below.
1392:  */

1394: static PetscErrorCode TSSetUp_BEuler(TS ts)
1395: {
1396:   TS_Theta       *th = (TS_Theta*)ts->data;

1400:   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");
1401:   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");
1402:   TSSetUp_Theta(ts);
1403:   return(0);
1404: }

1406: static PetscErrorCode TSView_BEuler(TS ts,PetscViewer viewer)
1407: {
1409:   return(0);
1410: }

1412: /*MC
1413:       TSBEULER - ODE solver using the implicit backward Euler method

1415:   Level: beginner

1417:   Notes:
1418:   TSBEULER is equivalent to TSTHETA with Theta=1.0

1420: $  -ts_type theta -ts_theta_theta 1.0

1422: .seealso:  TSCreate(), TS, TSSetType(), TSEULER, TSCN, TSTHETA

1424: M*/
1425: PETSC_EXTERN PetscErrorCode TSCreate_BEuler(TS ts)
1426: {

1430:   TSCreate_Theta(ts);
1431:   TSThetaSetTheta(ts,1.0);
1432:   TSThetaSetEndpoint(ts,PETSC_FALSE);
1433:   ts->ops->setup = TSSetUp_BEuler;
1434:   ts->ops->view  = TSView_BEuler;
1435:   return(0);
1436: }

1438: static PetscErrorCode TSSetUp_CN(TS ts)
1439: {
1440:   TS_Theta       *th = (TS_Theta*)ts->data;

1444:   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");
1445:   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");
1446:   TSSetUp_Theta(ts);
1447:   return(0);
1448: }

1450: static PetscErrorCode TSView_CN(TS ts,PetscViewer viewer)
1451: {
1453:   return(0);
1454: }

1456: /*MC
1457:       TSCN - ODE solver using the implicit Crank-Nicolson method.

1459:   Level: beginner

1461:   Notes:
1462:   TSCN is equivalent to TSTHETA with Theta=0.5 and the "endpoint" option set. I.e.

1464: $  -ts_type theta -ts_theta_theta 0.5 -ts_theta_endpoint

1466: .seealso:  TSCreate(), TS, TSSetType(), TSBEULER, TSTHETA

1468: M*/
1469: PETSC_EXTERN PetscErrorCode TSCreate_CN(TS ts)
1470: {

1474:   TSCreate_Theta(ts);
1475:   TSThetaSetTheta(ts,0.5);
1476:   TSThetaSetEndpoint(ts,PETSC_TRUE);
1477:   ts->ops->setup = TSSetUp_CN;
1478:   ts->ops->view  = TSView_CN;
1479:   return(0);
1480: }