Actual source code: basicsymplectic.c

  1: /*
  2:   Code for Timestepping with basic symplectic integrators for separable Hamiltonian systems
  3: */
  4: #include <petsc/private/tsimpl.h>
  5: #include <petscdm.h>

  7: static TSBasicSymplecticType TSBasicSymplecticDefault = TSBASICSYMPLECTICSIEULER;
  8: static PetscBool             TSBasicSymplecticRegisterAllCalled;
  9: static PetscBool             TSBasicSymplecticPackageInitialized;

 11: typedef struct _BasicSymplecticScheme     *BasicSymplecticScheme;
 12: typedef struct _BasicSymplecticSchemeLink *BasicSymplecticSchemeLink;

 14: struct _BasicSymplecticScheme {
 15:   char      *name;
 16:   PetscInt   order;
 17:   PetscInt   s; /* number of stages */
 18:   PetscReal *c, *d;
 19: };
 20: struct _BasicSymplecticSchemeLink {
 21:   struct _BasicSymplecticScheme sch;
 22:   BasicSymplecticSchemeLink     next;
 23: };
 24: static BasicSymplecticSchemeLink BasicSymplecticSchemeList;
 25: typedef struct {
 26:   TS                    subts_p, subts_q; /* sub TS contexts that holds the RHSFunction pointers */
 27:   IS                    is_p, is_q;       /* IS sets for position and momentum respectively */
 28:   Vec                   update;           /* a nest work vector for generalized coordinates */
 29:   BasicSymplecticScheme scheme;
 30: } TS_BasicSymplectic;

 32: /*MC
 33:   TSBASICSYMPLECTICSIEULER - first order semi-implicit Euler method

 35:   Level: intermediate

 37: .seealso: [](chapter_ts), `TSBASICSYMPLECTIC`
 38: M*/

 40: /*MC
 41:   TSBASICSYMPLECTICVELVERLET - second order Velocity Verlet method (leapfrog method with starting process and determining velocity and position at the same time)

 43: Level: intermediate

 45: .seealso: [](chapter_ts), `TSBASICSYMPLECTIC`
 46: M*/

 48: /*@C
 49:   TSBasicSymplecticRegisterAll - Registers all of the basic symplectic integration methods in `TSBASICSYMPLECTIC`

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

 53:   Level: advanced

 55: .seealso: [](chapter_ts), `TSBASICSYMPLECTIC`, `TSBasicSymplecticRegisterDestroy()`
 56: @*/
 57: PetscErrorCode TSBasicSymplecticRegisterAll(void)
 58: {
 59:   PetscFunctionBegin;
 60:   if (TSBasicSymplecticRegisterAllCalled) PetscFunctionReturn(PETSC_SUCCESS);
 61:   TSBasicSymplecticRegisterAllCalled = PETSC_TRUE;
 62:   {
 63:     PetscReal c[1] = {1.0}, d[1] = {1.0};
 64:     PetscCall(TSBasicSymplecticRegister(TSBASICSYMPLECTICSIEULER, 1, 1, c, d));
 65:   }
 66:   {
 67:     PetscReal c[2] = {0, 1.0}, d[2] = {0.5, 0.5};
 68:     PetscCall(TSBasicSymplecticRegister(TSBASICSYMPLECTICVELVERLET, 2, 2, c, d));
 69:   }
 70:   {
 71:     PetscReal c[3] = {1, -2.0 / 3.0, 2.0 / 3.0}, d[3] = {-1.0 / 24.0, 3.0 / 4.0, 7.0 / 24.0};
 72:     PetscCall(TSBasicSymplecticRegister(TSBASICSYMPLECTIC3, 3, 3, c, d));
 73:   }
 74:   {
 75: #define CUBE../../../../..OFTWO 1.2599210498948731647672106
 76:     PetscReal c[4] = {1.0 / 2.0 / (2.0 - CUBE../../../../..OFTWO), (1.0 - CUBE../../../../..OFTWO) / 2.0 / (2.0 - CUBE../../../../..OFTWO), (1.0 - CUBE../../../../..OFTWO) / 2.0 / (2.0 - CUBE../../../../..OFTWO), 1.0 / 2.0 / (2.0 - CUBE../../../../..OFTWO)}, d[4] = {1.0 / (2.0 - CUBE../../../../..OFTWO), -CUBE../../../../..OFTWO / (2.0 - CUBE../../../../..OFTWO), 1.0 / (2.0 - CUBE../../../../..OFTWO), 0};
 77:     PetscCall(TSBasicSymplecticRegister(TSBASICSYMPLECTIC4, 4, 4, c, d));
 78:   }
 79:   PetscFunctionReturn(PETSC_SUCCESS);
 80: }

 82: /*@C
 83:    TSBasicSymplecticRegisterDestroy - Frees the list of schemes that were registered by `TSBasicSymplecticRegister()`.

 85:    Not Collective

 87:    Level: advanced

 89: .seealso: [](chapter_ts), `TSBasicSymplecticRegister()`, `TSBasicSymplecticRegisterAll()`, `TSBASICSYMPLECTIC`
 90: @*/
 91: PetscErrorCode TSBasicSymplecticRegisterDestroy(void)
 92: {
 93:   BasicSymplecticSchemeLink link;

 95:   PetscFunctionBegin;
 96:   while ((link = BasicSymplecticSchemeList)) {
 97:     BasicSymplecticScheme scheme = &link->sch;
 98:     BasicSymplecticSchemeList    = link->next;
 99:     PetscCall(PetscFree2(scheme->c, scheme->d));
100:     PetscCall(PetscFree(scheme->name));
101:     PetscCall(PetscFree(link));
102:   }
103:   TSBasicSymplecticRegisterAllCalled = PETSC_FALSE;
104:   PetscFunctionReturn(PETSC_SUCCESS);
105: }

107: /*@C
108:   TSBasicSymplecticInitializePackage - This function initializes everything in the `TSBASICSYMPLECTIC` package. It is called
109:   from `TSInitializePackage()`.

111:   Level: developer

113: .seealso: [](chapter_ts), `PetscInitialize()`, `TSBASICSYMPLECTIC`
114: @*/
115: PetscErrorCode TSBasicSymplecticInitializePackage(void)
116: {
117:   PetscFunctionBegin;
118:   if (TSBasicSymplecticPackageInitialized) PetscFunctionReturn(PETSC_SUCCESS);
119:   TSBasicSymplecticPackageInitialized = PETSC_TRUE;
120:   PetscCall(TSBasicSymplecticRegisterAll());
121:   PetscCall(PetscRegisterFinalize(TSBasicSymplecticFinalizePackage));
122:   PetscFunctionReturn(PETSC_SUCCESS);
123: }

125: /*@C
126:   TSBasicSymplecticFinalizePackage - This function destroys everything in the `TSBASICSYMPLECTIC` package. It is
127:   called from `PetscFinalize()`.

129:   Level: developer

131: .seealso: [](chapter_ts), `PetscFinalize()`, `TSBASICSYMPLECTIC`
132: @*/
133: PetscErrorCode TSBasicSymplecticFinalizePackage(void)
134: {
135:   PetscFunctionBegin;
136:   TSBasicSymplecticPackageInitialized = PETSC_FALSE;
137:   PetscCall(TSBasicSymplecticRegisterDestroy());
138:   PetscFunctionReturn(PETSC_SUCCESS);
139: }

141: /*@C
142:    TSBasicSymplecticRegister - register a basic symplectic integration scheme by providing the coefficients.

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

146:    Input Parameters:
147: +  name - identifier for method
148: .  order - approximation order of method
149: .  s - number of stages, this is the dimension of the matrices below
150: .  c - coefficients for updating generalized position (dimension s)
151: -  d - coefficients for updating generalized momentum (dimension s)

153:    Level: advanced

155:    Notes:
156:    Several symplectic methods are provided, this function is only needed to create new methods.

158: .seealso: [](chapter_ts), `TSBASICSYMPLECTIC`
159: @*/
160: PetscErrorCode TSBasicSymplecticRegister(TSRosWType name, PetscInt order, PetscInt s, PetscReal c[], PetscReal d[])
161: {
162:   BasicSymplecticSchemeLink link;
163:   BasicSymplecticScheme     scheme;

165:   PetscFunctionBegin;

170:   PetscCall(TSBasicSymplecticInitializePackage());
171:   PetscCall(PetscNew(&link));
172:   scheme = &link->sch;
173:   PetscCall(PetscStrallocpy(name, &scheme->name));
174:   scheme->order = order;
175:   scheme->s     = s;
176:   PetscCall(PetscMalloc2(s, &scheme->c, s, &scheme->d));
177:   PetscCall(PetscArraycpy(scheme->c, c, s));
178:   PetscCall(PetscArraycpy(scheme->d, d, s));
179:   link->next                = BasicSymplecticSchemeList;
180:   BasicSymplecticSchemeList = link;
181:   PetscFunctionReturn(PETSC_SUCCESS);
182: }

184: /*
185: The simplified form of the equations are:

187: .vb
188:  p_{i+1} = p_i + c_i*g(q_i)*h
189:  q_{i+1} = q_i + d_i*f(p_{i+1},t_{i+1})*h
190: .ve

192: Several symplectic integrators are given below. An illustrative way to use them is to consider a particle with position q and velocity p.

194: To apply a timestep with values c_{1,2},d_{1,2} to the particle, carry out the following steps:
195: .vb
196: - Update the velocity of the particle by adding to it its acceleration multiplied by c_1
197: - Update the position of the particle by adding to it its (updated) velocity multiplied by d_1
198: - Update the velocity of the particle by adding to it its acceleration (at the updated position) multiplied by c_2
199: - Update the position of the particle by adding to it its (double-updated) velocity multiplied by d_2
200: .ve

202: */
203: static PetscErrorCode TSStep_BasicSymplectic(TS ts)
204: {
205:   TS_BasicSymplectic   *bsymp    = (TS_BasicSymplectic *)ts->data;
206:   BasicSymplecticScheme scheme   = bsymp->scheme;
207:   Vec                   solution = ts->vec_sol, update = bsymp->update, q, p, q_update, p_update;
208:   IS                    is_q = bsymp->is_q, is_p = bsymp->is_p;
209:   TS                    subts_q = bsymp->subts_q, subts_p = bsymp->subts_p;
210:   PetscBool             stageok;
211:   PetscReal             next_time_step = ts->time_step;
212:   PetscInt              iter;

214:   PetscFunctionBegin;
215:   PetscCall(VecGetSubVector(solution, is_q, &q));
216:   PetscCall(VecGetSubVector(solution, is_p, &p));
217:   PetscCall(VecGetSubVector(update, is_q, &q_update));
218:   PetscCall(VecGetSubVector(update, is_p, &p_update));

220:   for (iter = 0; iter < scheme->s; iter++) {
221:     PetscCall(TSPreStage(ts, ts->ptime));
222:     /* update velocity p */
223:     if (scheme->c[iter]) {
224:       PetscCall(TSComputeRHSFunction(subts_p, ts->ptime, q, p_update));
225:       PetscCall(VecAXPY(p, scheme->c[iter] * ts->time_step, p_update));
226:     }
227:     /* update position q */
228:     if (scheme->d[iter]) {
229:       PetscCall(TSComputeRHSFunction(subts_q, ts->ptime, p, q_update));
230:       PetscCall(VecAXPY(q, scheme->d[iter] * ts->time_step, q_update));
231:       ts->ptime = ts->ptime + scheme->d[iter] * ts->time_step;
232:     }
233:     PetscCall(TSPostStage(ts, ts->ptime, 0, &solution));
234:     PetscCall(TSAdaptCheckStage(ts->adapt, ts, ts->ptime, solution, &stageok));
235:     if (!stageok) {
236:       ts->reason = TS_DIVERGED_STEP_REJECTED;
237:       PetscFunctionReturn(PETSC_SUCCESS);
238:     }
239:     PetscCall(TSFunctionDomainError(ts, ts->ptime + ts->time_step, update, &stageok));
240:     if (!stageok) {
241:       ts->reason = TS_DIVERGED_STEP_REJECTED;
242:       PetscFunctionReturn(PETSC_SUCCESS);
243:     }
244:   }

246:   ts->time_step = next_time_step;
247:   PetscCall(VecRestoreSubVector(solution, is_q, &q));
248:   PetscCall(VecRestoreSubVector(solution, is_p, &p));
249:   PetscCall(VecRestoreSubVector(update, is_q, &q_update));
250:   PetscCall(VecRestoreSubVector(update, is_p, &p_update));
251:   PetscFunctionReturn(PETSC_SUCCESS);
252: }

254: static PetscErrorCode DMCoarsenHook_BasicSymplectic(DM fine, DM coarse, void *ctx)
255: {
256:   PetscFunctionBegin;
257:   PetscFunctionReturn(PETSC_SUCCESS);
258: }

260: static PetscErrorCode DMRestrictHook_BasicSymplectic(DM fine, Mat restrct, Vec rscale, Mat inject, DM coarse, void *ctx)
261: {
262:   PetscFunctionBegin;
263:   PetscFunctionReturn(PETSC_SUCCESS);
264: }

266: static PetscErrorCode DMSubDomainHook_BasicSymplectic(DM dm, DM subdm, void *ctx)
267: {
268:   PetscFunctionBegin;
269:   PetscFunctionReturn(PETSC_SUCCESS);
270: }

272: static PetscErrorCode DMSubDomainRestrictHook_BasicSymplectic(DM dm, VecScatter gscat, VecScatter lscat, DM subdm, void *ctx)
273: {
274:   PetscFunctionBegin;
275:   PetscFunctionReturn(PETSC_SUCCESS);
276: }

278: static PetscErrorCode TSSetUp_BasicSymplectic(TS ts)
279: {
280:   TS_BasicSymplectic *bsymp = (TS_BasicSymplectic *)ts->data;
281:   DM                  dm;

283:   PetscFunctionBegin;
284:   PetscCall(TSRHSSplitGetIS(ts, "position", &bsymp->is_q));
285:   PetscCall(TSRHSSplitGetIS(ts, "momentum", &bsymp->is_p));
286:   PetscCheck(bsymp->is_q && bsymp->is_p, PetscObjectComm((PetscObject)ts), PETSC_ERR_USER, "Must set up RHSSplits with TSRHSSplitSetIS() using split names position and momentum respectively in order to use -ts_type basicsymplectic");
287:   PetscCall(TSRHSSplitGetSubTS(ts, "position", &bsymp->subts_q));
288:   PetscCall(TSRHSSplitGetSubTS(ts, "momentum", &bsymp->subts_p));
289:   PetscCheck(bsymp->subts_q && bsymp->subts_p, PetscObjectComm((PetscObject)ts), PETSC_ERR_USER, "Must set up the RHSFunctions for position and momentum using TSRHSSplitSetRHSFunction() or calling TSSetRHSFunction() for each sub-TS");

291:   PetscCall(VecDuplicate(ts->vec_sol, &bsymp->update));

293:   PetscCall(TSGetAdapt(ts, &ts->adapt));
294:   PetscCall(TSAdaptCandidatesClear(ts->adapt)); /* make sure to use fixed time stepping */
295:   PetscCall(TSGetDM(ts, &dm));
296:   if (dm) {
297:     PetscCall(DMCoarsenHookAdd(dm, DMCoarsenHook_BasicSymplectic, DMRestrictHook_BasicSymplectic, ts));
298:     PetscCall(DMSubDomainHookAdd(dm, DMSubDomainHook_BasicSymplectic, DMSubDomainRestrictHook_BasicSymplectic, ts));
299:   }
300:   PetscFunctionReturn(PETSC_SUCCESS);
301: }

303: static PetscErrorCode TSReset_BasicSymplectic(TS ts)
304: {
305:   TS_BasicSymplectic *bsymp = (TS_BasicSymplectic *)ts->data;

307:   PetscFunctionBegin;
308:   PetscCall(VecDestroy(&bsymp->update));
309:   PetscFunctionReturn(PETSC_SUCCESS);
310: }

312: static PetscErrorCode TSDestroy_BasicSymplectic(TS ts)
313: {
314:   PetscFunctionBegin;
315:   PetscCall(TSReset_BasicSymplectic(ts));
316:   PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSBasicSymplecticSetType_C", NULL));
317:   PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSBasicSymplecticGetType_C", NULL));
318:   PetscCall(PetscFree(ts->data));
319:   PetscFunctionReturn(PETSC_SUCCESS);
320: }

322: static PetscErrorCode TSSetFromOptions_BasicSymplectic(TS ts, PetscOptionItems *PetscOptionsObject)
323: {
324:   TS_BasicSymplectic *bsymp = (TS_BasicSymplectic *)ts->data;

326:   PetscFunctionBegin;
327:   PetscOptionsHeadBegin(PetscOptionsObject, "Basic symplectic integrator options");
328:   {
329:     BasicSymplecticSchemeLink link;
330:     PetscInt                  count, choice;
331:     PetscBool                 flg;
332:     const char              **namelist;

334:     for (link = BasicSymplecticSchemeList, count = 0; link; link = link->next, count++)
335:       ;
336:     PetscCall(PetscMalloc1(count, (char ***)&namelist));
337:     for (link = BasicSymplecticSchemeList, count = 0; link; link = link->next, count++) namelist[count] = link->sch.name;
338:     PetscCall(PetscOptionsEList("-ts_basicsymplectic_type", "Family of basic symplectic integration method", "TSBasicSymplecticSetType", (const char *const *)namelist, count, bsymp->scheme->name, &choice, &flg));
339:     if (flg) PetscCall(TSBasicSymplecticSetType(ts, namelist[choice]));
340:     PetscCall(PetscFree(namelist));
341:   }
342:   PetscOptionsHeadEnd();
343:   PetscFunctionReturn(PETSC_SUCCESS);
344: }

346: static PetscErrorCode TSView_BasicSymplectic(TS ts, PetscViewer viewer)
347: {
348:   PetscFunctionBegin;
349:   PetscFunctionReturn(PETSC_SUCCESS);
350: }

352: static PetscErrorCode TSInterpolate_BasicSymplectic(TS ts, PetscReal t, Vec X)
353: {
354:   TS_BasicSymplectic *bsymp  = (TS_BasicSymplectic *)ts->data;
355:   Vec                 update = bsymp->update;
356:   PetscReal           alpha  = (ts->ptime - t) / ts->time_step;

358:   PetscFunctionBegin;
359:   PetscCall(VecWAXPY(X, -ts->time_step, update, ts->vec_sol));
360:   PetscCall(VecAXPBY(X, 1.0 - alpha, alpha, ts->vec_sol));
361:   PetscFunctionReturn(PETSC_SUCCESS);
362: }

364: static PetscErrorCode TSComputeLinearStability_BasicSymplectic(TS ts, PetscReal xr, PetscReal xi, PetscReal *yr, PetscReal *yi)
365: {
366:   PetscFunctionBegin;
367:   *yr = 1.0 + xr;
368:   *yi = xi;
369:   PetscFunctionReturn(PETSC_SUCCESS);
370: }

372: /*@C
373:   TSBasicSymplecticSetType - Set the type of the basic symplectic method

375:   Logically Collective

377:   Input Parameters:
378: +  ts - timestepping context
379: -  bsymptype - type of the symplectic scheme

381:   Options Database Key:
382: .  -ts_basicsymplectic_type <scheme> - select the scheme

384:   Level: intermediate

386:   Note:
387:     The symplectic solver always expects a two-way splitting with the split names being "position" and "momentum". Each split is associated with an `IS` object and a sub-`TS`
388:     that is intended to store the user-provided RHS function.

390: .seealso: [](chapter_ts), `TSBASICSYMPLECTIC`, `TSBasicSymplecticType`, `TSBasicSymplecticSetType()`
391: @*/
392: PetscErrorCode TSBasicSymplecticSetType(TS ts, TSBasicSymplecticType bsymptype)
393: {
394:   PetscFunctionBegin;
396:   PetscTryMethod(ts, "TSBasicSymplecticSetType_C", (TS, TSBasicSymplecticType), (ts, bsymptype));
397:   PetscFunctionReturn(PETSC_SUCCESS);
398: }

400: /*@C
401:   TSBasicSymplecticGetType - Get the type of the basic symplectic method

403:   Logically Collective

405:   Input Parameters:
406: +  ts - timestepping context
407: -  bsymptype - type of the basic symplectic scheme

409:   Level: intermediate

411: .seealso: [](chapter_ts), `TSBASICSYMPLECTIC`, `TSBasicSymplecticType`, `TSBasicSymplecticSetType()`
412: @*/
413: PetscErrorCode TSBasicSymplecticGetType(TS ts, TSBasicSymplecticType *bsymptype)
414: {
415:   PetscFunctionBegin;
417:   PetscUseMethod(ts, "TSBasicSymplecticGetType_C", (TS, TSBasicSymplecticType *), (ts, bsymptype));
418:   PetscFunctionReturn(PETSC_SUCCESS);
419: }

421: static PetscErrorCode TSBasicSymplecticSetType_BasicSymplectic(TS ts, TSBasicSymplecticType bsymptype)
422: {
423:   TS_BasicSymplectic       *bsymp = (TS_BasicSymplectic *)ts->data;
424:   BasicSymplecticSchemeLink link;
425:   PetscBool                 match;

427:   PetscFunctionBegin;
428:   if (bsymp->scheme) {
429:     PetscCall(PetscStrcmp(bsymp->scheme->name, bsymptype, &match));
430:     if (match) PetscFunctionReturn(PETSC_SUCCESS);
431:   }
432:   for (link = BasicSymplecticSchemeList; link; link = link->next) {
433:     PetscCall(PetscStrcmp(link->sch.name, bsymptype, &match));
434:     if (match) {
435:       bsymp->scheme = &link->sch;
436:       PetscFunctionReturn(PETSC_SUCCESS);
437:     }
438:   }
439:   SETERRQ(PetscObjectComm((PetscObject)ts), PETSC_ERR_ARG_UNKNOWN_TYPE, "Could not find '%s'", bsymptype);
440: }

442: static PetscErrorCode TSBasicSymplecticGetType_BasicSymplectic(TS ts, TSBasicSymplecticType *bsymptype)
443: {
444:   TS_BasicSymplectic *bsymp = (TS_BasicSymplectic *)ts->data;

446:   PetscFunctionBegin;
447:   *bsymptype = bsymp->scheme->name;
448:   PetscFunctionReturn(PETSC_SUCCESS);
449: }

451: /*MC
452:   TSBASICSYMPLECTIC - ODE solver using basic symplectic integration schemes

454:   These methods are intended for separable Hamiltonian systems
455: .vb
456:   qdot = dH(q,p,t)/dp
457:   pdot = -dH(q,p,t)/dq
458: .ve

460:   where the Hamiltonian can be split into the sum of kinetic energy and potential energy
461: .vb
462:   H(q,p,t) = T(p,t) + V(q,t).
463: .ve

465:   As a result, the system can be genearlly represented by
466: .vb
467:   qdot = f(p,t) = dT(p,t)/dp
468:   pdot = g(q,t) = -dV(q,t)/dq
469: .ve

471:   and solved iteratively with
472: .vb
473:   q_new = q_old + d_i*h*f(p_old,t_old)
474:   t_new = t_old + d_i*h
475:   p_new = p_old + c_i*h*g(p_new,t_new)
476:   i=0,1,...,n.
477: .ve

479:   The solution vector should contain both q and p, which correspond to (generalized) position and momentum respectively. Note that the momentum component
480:   could simply be velocity in some representations. The symplectic solver always expects a two-way splitting with the split names being "position" and "momentum".
481:   Each split is associated with an `IS` object and a sub-`TS` that is intended to store the user-provided RHS function.

483:   Level: beginner

485:   Reference:
486: . * -  wikipedia (https://en.wikipedia.org/wiki/Symplectic_integrator)

488: .seealso: [](chapter_ts), `TSCreate()`, `TSSetType()`, `TSRHSSplitSetIS()`, `TSRHSSplitSetRHSFunction()`, `TSType`
489: M*/
490: PETSC_EXTERN PetscErrorCode TSCreate_BasicSymplectic(TS ts)
491: {
492:   TS_BasicSymplectic *bsymp;

494:   PetscFunctionBegin;
495:   PetscCall(TSBasicSymplecticInitializePackage());
496:   PetscCall(PetscNew(&bsymp));
497:   ts->data = (void *)bsymp;

499:   ts->ops->setup           = TSSetUp_BasicSymplectic;
500:   ts->ops->step            = TSStep_BasicSymplectic;
501:   ts->ops->reset           = TSReset_BasicSymplectic;
502:   ts->ops->destroy         = TSDestroy_BasicSymplectic;
503:   ts->ops->setfromoptions  = TSSetFromOptions_BasicSymplectic;
504:   ts->ops->view            = TSView_BasicSymplectic;
505:   ts->ops->interpolate     = TSInterpolate_BasicSymplectic;
506:   ts->ops->linearstability = TSComputeLinearStability_BasicSymplectic;

508:   PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSBasicSymplecticSetType_C", TSBasicSymplecticSetType_BasicSymplectic));
509:   PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSBasicSymplecticGetType_C", TSBasicSymplecticGetType_BasicSymplectic));

511:   PetscCall(TSBasicSymplecticSetType(ts, TSBasicSymplecticDefault));
512:   PetscFunctionReturn(PETSC_SUCCESS);
513: }