Actual source code: bdf.c

  1: /*
2:   Code for timestepping with BDF methods
3: */
4: #include <petsc/private/tsimpl.h>
5: #include <petscdm.h>

7: static PetscBool  cited      = PETSC_FALSE;
8: static const char citation[] = "@book{Brenan1995,\n"
9:                                "  title     = {Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations},\n"
10:                                "  author    = {Brenan, K. and Campbell, S. and Petzold, L.},\n"
11:                                "  publisher = {Society for Industrial and Applied Mathematics},\n"
12:                                "  year      = {1995},\n"
13:                                "  doi       = {10.1137/1.9781611971224},\n}\n";

15: typedef struct {
16:   PetscInt  k, n;
17:   PetscReal time[6 + 2];
18:   Vec       work[6 + 2];
19:   Vec       tvwork[6 + 2];
20:   PetscReal shift;
21:   Vec       vec_dot; /* Xdot when !transientvar, else Cdot where C(X) is the transient variable. */
22:   Vec       vec_wrk;
23:   Vec       vec_lte;

25:   PetscBool    transientvar;
26:   PetscInt     order;
27:   TSStepStatus status;
28: } TS_BDF;

30: /* Compute Lagrange polynomials on T[:n] evaluated at t.
31:  * If one has data (T[i], Y[i]), then the interpolation/extrapolation is f(t) = \sum_i L[i]*Y[i].
32:  */
33: static inline void LagrangeBasisVals(PetscInt n, PetscReal t, const PetscReal T[], PetscScalar L[])
34: {
35:   PetscInt k, j;
36:   for (k = 0; k < n; k++)
37:     for (L[k] = 1, j = 0; j < n; j++)
38:       if (j != k) L[k] *= (t - T[j]) / (T[k] - T[j]);
39: }

41: static inline void LagrangeBasisDers(PetscInt n, PetscReal t, const PetscReal T[], PetscScalar dL[])
42: {
43:   PetscInt k, j, i;
44:   for (k = 0; k < n; k++)
45:     for (dL[k] = 0, j = 0; j < n; j++)
46:       if (j != k) {
47:         PetscReal L = 1 / (T[k] - T[j]);
48:         for (i = 0; i < n; i++)
49:           if (i != j && i != k) L *= (t - T[i]) / (T[k] - T[i]);
50:         dL[k] += L;
51:       }
52: }

54: static PetscErrorCode TSBDF_GetVecs(TS ts, DM dm, Vec *Xdot, Vec *Ydot)
55: {
56:   TS_BDF *bdf = (TS_BDF *)ts->data;

58:   PetscFunctionBegin;
59:   if (dm && dm != ts->dm) {
60:     PetscCall(DMGetNamedGlobalVector(dm, "TSBDF_Vec_Xdot", Xdot));
61:     PetscCall(DMGetNamedGlobalVector(dm, "TSBDF_Vec_Ydot", Ydot));
62:   } else {
63:     *Xdot = bdf->vec_dot;
64:     *Ydot = bdf->vec_wrk;
65:   }
66:   PetscFunctionReturn(PETSC_SUCCESS);
67: }

69: static PetscErrorCode TSBDF_RestoreVecs(TS ts, DM dm, Vec *Xdot, Vec *Ydot)
70: {
71:   TS_BDF *bdf = (TS_BDF *)ts->data;

73:   PetscFunctionBegin;
74:   if (dm && dm != ts->dm) {
75:     PetscCall(DMRestoreNamedGlobalVector(dm, "TSBDF_Vec_Xdot", Xdot));
76:     PetscCall(DMRestoreNamedGlobalVector(dm, "TSBDF_Vec_Ydot", Ydot));
77:   } else {
78:     PetscCheck(*Xdot == bdf->vec_dot, PetscObjectComm((PetscObject)ts), PETSC_ERR_ARG_INCOMP, "Vec does not match the cache");
79:     PetscCheck(*Ydot == bdf->vec_wrk, PetscObjectComm((PetscObject)ts), PETSC_ERR_ARG_INCOMP, "Vec does not match the cache");
80:     *Xdot = NULL;
81:     *Ydot = NULL;
82:   }
83:   PetscFunctionReturn(PETSC_SUCCESS);
84: }

86: static PetscErrorCode DMCoarsenHook_TSBDF(DM fine, DM coarse, void *ctx)
87: {
88:   PetscFunctionBegin;
89:   PetscFunctionReturn(PETSC_SUCCESS);
90: }

92: static PetscErrorCode DMRestrictHook_TSBDF(DM fine, Mat restrct, Vec rscale, Mat inject, DM coarse, void *ctx)
93: {
94:   TS  ts = (TS)ctx;
95:   Vec Ydot, Ydot_c;
96:   Vec Xdot, Xdot_c;

98:   PetscFunctionBegin;
99:   PetscCall(TSBDF_GetVecs(ts, fine, &Xdot, &Ydot));
100:   PetscCall(TSBDF_GetVecs(ts, coarse, &Xdot_c, &Ydot_c));

102:   PetscCall(MatRestrict(restrct, Ydot, Ydot_c));
103:   PetscCall(VecPointwiseMult(Ydot_c, rscale, Ydot_c));

105:   PetscCall(TSBDF_RestoreVecs(ts, fine, &Xdot, &Ydot));
106:   PetscCall(TSBDF_RestoreVecs(ts, coarse, &Xdot_c, &Ydot_c));
107:   PetscFunctionReturn(PETSC_SUCCESS);
108: }

110: static PetscErrorCode TSBDF_Advance(TS ts, PetscReal t, Vec X)
111: {
112:   TS_BDF  *bdf = (TS_BDF *)ts->data;
113:   PetscInt i, n = PETSC_STATIC_ARRAY_LENGTH(bdf->work);
114:   Vec      tail = bdf->work[n - 1], tvtail = bdf->tvwork[n - 1];

116:   PetscFunctionBegin;
117:   for (i = n - 1; i >= 2; i--) {
118:     bdf->time[i]   = bdf->time[i - 1];
119:     bdf->work[i]   = bdf->work[i - 1];
120:     bdf->tvwork[i] = bdf->tvwork[i - 1];
121:   }
122:   bdf->n         = PetscMin(bdf->n + 1, n - 1);
123:   bdf->time[1]   = t;
124:   bdf->work[1]   = tail;
125:   bdf->tvwork[1] = tvtail;
126:   PetscCall(VecCopy(X, tail));
127:   PetscCall(TSComputeTransientVariable(ts, tail, tvtail));
128:   PetscFunctionReturn(PETSC_SUCCESS);
129: }

131: static PetscErrorCode TSBDF_VecLTE(TS ts, PetscInt order, Vec lte)
132: {
133:   TS_BDF     *bdf = (TS_BDF *)ts->data;
134:   PetscInt    i, n = order + 1;
135:   PetscReal  *time = bdf->time;
136:   Vec        *vecs = bdf->work;
137:   PetscScalar a[8], b[8], alpha[8];

139:   PetscFunctionBegin;
140:   LagrangeBasisDers(n + 0, time[0], time, a);
141:   a[n] = 0;
142:   LagrangeBasisDers(n + 1, time[0], time, b);
143:   for (i = 0; i < n + 1; i++) alpha[i] = (a[i] - b[i]) / a[0];
144:   PetscCall(VecZeroEntries(lte));
145:   PetscCall(VecMAXPY(lte, n + 1, alpha, vecs));
146:   PetscFunctionReturn(PETSC_SUCCESS);
147: }

149: static PetscErrorCode TSBDF_Extrapolate(TS ts, PetscInt order, PetscReal t, Vec X)
150: {
151:   TS_BDF     *bdf  = (TS_BDF *)ts->data;
152:   PetscInt    n    = order + 1;
153:   PetscReal  *time = bdf->time + 1;
154:   Vec        *vecs = bdf->work + 1;
155:   PetscScalar alpha[7];

157:   PetscFunctionBegin;
158:   n = PetscMin(n, bdf->n);
159:   LagrangeBasisVals(n, t, time, alpha);
160:   PetscCall(VecZeroEntries(X));
161:   PetscCall(VecMAXPY(X, n, alpha, vecs));
162:   PetscFunctionReturn(PETSC_SUCCESS);
163: }

165: static PetscErrorCode TSBDF_Interpolate(TS ts, PetscInt order, PetscReal t, Vec X)
166: {
167:   TS_BDF     *bdf  = (TS_BDF *)ts->data;
168:   PetscInt    n    = order + 1;
169:   PetscReal  *time = bdf->time;
170:   Vec        *vecs = bdf->work;
171:   PetscScalar alpha[7];

173:   PetscFunctionBegin;
174:   LagrangeBasisVals(n, t, time, alpha);
175:   PetscCall(VecZeroEntries(X));
176:   PetscCall(VecMAXPY(X, n, alpha, vecs));
177:   PetscFunctionReturn(PETSC_SUCCESS);
178: }

180: /* Compute the affine term V0 such that Xdot = shift*X + V0.
181:  *
182:  * When using transient variables, we're computing Cdot = shift*C(X) + V0, and thus choose a linear combination of tvwork.
183:  */
184: static PetscErrorCode TSBDF_PreSolve(TS ts)
185: {
186:   TS_BDF     *bdf = (TS_BDF *)ts->data;
187:   PetscInt    i, n = PetscMax(bdf->k, 1) + 1;
188:   Vec         V, V0;
189:   Vec         vecs[7];
190:   PetscScalar alpha[7];

192:   PetscFunctionBegin;
193:   PetscCall(TSBDF_GetVecs(ts, NULL, &V, &V0));
194:   LagrangeBasisDers(n, bdf->time[0], bdf->time, alpha);
195:   for (i = 1; i < n; i++) vecs[i] = bdf->transientvar ? bdf->tvwork[i] : bdf->work[i];
196:   PetscCall(VecZeroEntries(V0));
197:   PetscCall(VecMAXPY(V0, n - 1, alpha + 1, vecs + 1));
198:   bdf->shift = PetscRealPart(alpha[0]);
199:   PetscCall(TSBDF_RestoreVecs(ts, NULL, &V, &V0));
200:   PetscFunctionReturn(PETSC_SUCCESS);
201: }

203: static PetscErrorCode TSBDF_SNESSolve(TS ts, Vec b, Vec x)
204: {
205:   PetscInt nits, lits;

207:   PetscFunctionBegin;
208:   PetscCall(TSBDF_PreSolve(ts));
209:   PetscCall(SNESSolve(ts->snes, b, x));
210:   PetscCall(SNESGetIterationNumber(ts->snes, &nits));
211:   PetscCall(SNESGetLinearSolveIterations(ts->snes, &lits));
212:   ts->snes_its += nits;
213:   ts->ksp_its += lits;
214:   PetscFunctionReturn(PETSC_SUCCESS);
215: }

217: static PetscErrorCode TSBDF_Restart(TS ts, PetscBool *accept)
218: {
219:   TS_BDF *bdf = (TS_BDF *)ts->data;

221:   PetscFunctionBegin;
222:   bdf->k = 1;
223:   bdf->n = 0;

226:   bdf->time[0] = ts->ptime + ts->time_step / 2;
227:   PetscCall(VecCopy(bdf->work[1], bdf->work[0]));
228:   PetscCall(TSPreStage(ts, bdf->time[0]));
229:   PetscCall(TSBDF_SNESSolve(ts, NULL, bdf->work[0]));
230:   PetscCall(TSPostStage(ts, bdf->time[0], 0, &bdf->work[0]));
232:   if (!*accept) PetscFunctionReturn(PETSC_SUCCESS);

234:   bdf->k = PetscMin(2, bdf->order);
235:   bdf->n++;
236:   PetscCall(VecCopy(bdf->work[0], bdf->work[2]));
237:   bdf->time[2] = bdf->time[0];
238:   PetscCall(TSComputeTransientVariable(ts, bdf->work[2], bdf->tvwork[2]));
239:   PetscFunctionReturn(PETSC_SUCCESS);
240: }

242: static const char *const BDF_SchemeName[] = {"", "1", "2", "3", "4", "5", "6"};

244: static PetscErrorCode TSStep_BDF(TS ts)
245: {
246:   TS_BDF   *bdf        = (TS_BDF *)ts->data;
247:   PetscInt  rejections = 0;
248:   PetscBool stageok, accept = PETSC_TRUE;
249:   PetscReal next_time_step = ts->time_step;

251:   PetscFunctionBegin;
252:   PetscCall(PetscCitationsRegister(citation, &cited));

254:   if (!ts->steprollback && !ts->steprestart) {
255:     bdf->k = PetscMin(bdf->k + 1, bdf->order);
257:   }

259:   bdf->status = TS_STEP_INCOMPLETE;
260:   while (!ts->reason && bdf->status != TS_STEP_COMPLETE) {
261:     if (ts->steprestart) {
262:       PetscCall(TSBDF_Restart(ts, &stageok));
263:       if (!stageok) goto reject_step;
264:     }

266:     bdf->time[0] = ts->ptime + ts->time_step;
267:     PetscCall(TSBDF_Extrapolate(ts, bdf->k - (accept ? 0 : 1), bdf->time[0], bdf->work[0]));
268:     PetscCall(TSPreStage(ts, bdf->time[0]));
269:     PetscCall(TSBDF_SNESSolve(ts, NULL, bdf->work[0]));
270:     PetscCall(TSPostStage(ts, bdf->time[0], 0, &bdf->work[0]));
272:     if (!stageok) goto reject_step;

274:     bdf->status = TS_STEP_PENDING;
278:     bdf->status = accept ? TS_STEP_COMPLETE : TS_STEP_INCOMPLETE;
279:     if (!accept) {
280:       ts->time_step = next_time_step;
281:       goto reject_step;
282:     }

284:     PetscCall(VecCopy(bdf->work[0], ts->vec_sol));
285:     ts->ptime += ts->time_step;
286:     ts->time_step = next_time_step;
287:     break;

289:   reject_step:
290:     ts->reject++;
291:     accept = PETSC_FALSE;
292:     if (!ts->reason && ++rejections > ts->max_reject && ts->max_reject >= 0) {
293:       PetscCall(PetscInfo(ts, "Step=%" PetscInt_FMT ", step rejections %" PetscInt_FMT " greater than current TS allowed, stopping solve\n", ts->steps, rejections));
294:       ts->reason = TS_DIVERGED_STEP_REJECTED;
295:     }
296:   }
297:   PetscFunctionReturn(PETSC_SUCCESS);
298: }

300: static PetscErrorCode TSInterpolate_BDF(TS ts, PetscReal t, Vec X)
301: {
302:   TS_BDF *bdf = (TS_BDF *)ts->data;

304:   PetscFunctionBegin;
305:   PetscCall(TSBDF_Interpolate(ts, bdf->k, t, X));
306:   PetscFunctionReturn(PETSC_SUCCESS);
307: }

309: static PetscErrorCode TSEvaluateWLTE_BDF(TS ts, NormType wnormtype, PetscInt *order, PetscReal *wlte)
310: {
311:   TS_BDF   *bdf = (TS_BDF *)ts->data;
312:   PetscInt  k   = bdf->k;
313:   PetscReal wltea, wlter;
314:   Vec       X = bdf->work[0], Y = bdf->vec_lte;

316:   PetscFunctionBegin;
317:   k = PetscMin(k, bdf->n - 1);
318:   PetscCall(TSBDF_VecLTE(ts, k, Y));
319:   PetscCall(VecAXPY(Y, 1, X));
320:   PetscCall(TSErrorWeightedNorm(ts, X, Y, wnormtype, wlte, &wltea, &wlter));
321:   if (order) *order = k + 1;
322:   PetscFunctionReturn(PETSC_SUCCESS);
323: }

325: static PetscErrorCode TSResizeRegister_BDF(TS ts, PetscBool reg)
326: {
327:   TS_BDF     *bdf     = (TS_BDF *)ts->data;
328:   const char *names[] = {"", "ts:bdf:1", "ts:bdf:2", "ts:bdf:3", "ts:bdf:4", "ts:bdf:5", "ts:bdf:6", "ts:bdf:7"};
329:   PetscInt    i, maxn = PETSC_STATIC_ARRAY_LENGTH(bdf->work);

331:   PetscFunctionBegin;
332:   PetscAssert(maxn == 8, PetscObjectComm((PetscObject)ts), PETSC_ERR_PLIB, "names need to be redefined");
333:   if (reg) {
334:     for (i = 1; i < PetscMin(bdf->n + 1, maxn); i++) { PetscCall(TSResizeRegisterVec(ts, names[i], bdf->work[i])); }
335:   } else {
336:     for (i = 1; i < maxn; i++) {
337:       PetscCall(TSResizeRetrieveVec(ts, names[i], &bdf->work[i]));
338:       if (!bdf->work[i]) break;
339:       PetscCall(PetscObjectReference((PetscObject)bdf->work[i]));
340:       if (bdf->transientvar) {
341:         PetscCall(VecDuplicate(bdf->work[i], &bdf->tvwork[i]));
342:         PetscCall(TSComputeTransientVariable(ts, bdf->work[i], bdf->tvwork[i]));
343:       }
344:     }
345:   }
346:   PetscFunctionReturn(PETSC_SUCCESS);
347: }

349: static PetscErrorCode SNESTSFormFunction_BDF(SNES snes, Vec X, Vec F, TS ts)
350: {
351:   TS_BDF   *bdf = (TS_BDF *)ts->data;
352:   DM        dm, dmsave = ts->dm;
353:   PetscReal t     = bdf->time[0];
354:   PetscReal shift = bdf->shift;
355:   Vec       V, V0;

357:   PetscFunctionBegin;
358:   PetscCall(SNESGetDM(snes, &dm));
359:   PetscCall(TSBDF_GetVecs(ts, dm, &V, &V0));
360:   if (bdf->transientvar) { /* shift*C(X) + V0 */
361:     PetscCall(TSComputeTransientVariable(ts, X, V));
362:     PetscCall(VecAYPX(V, shift, V0));
363:   } else { /* shift*X + V0 */
364:     PetscCall(VecWAXPY(V, shift, X, V0));
365:   }

367:   /* F = Function(t,X,V) */
368:   ts->dm = dm;
369:   PetscCall(TSComputeIFunction(ts, t, X, V, F, PETSC_FALSE));
370:   ts->dm = dmsave;

372:   PetscCall(TSBDF_RestoreVecs(ts, dm, &V, &V0));
373:   PetscFunctionReturn(PETSC_SUCCESS);
374: }

376: static PetscErrorCode SNESTSFormJacobian_BDF(SNES snes, Vec X, Mat J, Mat P, TS ts)
377: {
378:   TS_BDF   *bdf = (TS_BDF *)ts->data;
379:   DM        dm, dmsave = ts->dm;
380:   PetscReal t     = bdf->time[0];
381:   PetscReal shift = bdf->shift;
382:   Vec       V, V0;

384:   PetscFunctionBegin;
385:   PetscCall(SNESGetDM(snes, &dm));
386:   PetscCall(TSBDF_GetVecs(ts, dm, &V, &V0));

388:   /* J,P = Jacobian(t,X,V) */
389:   ts->dm = dm;
390:   PetscCall(TSComputeIJacobian(ts, t, X, V, shift, J, P, PETSC_FALSE));
391:   ts->dm = dmsave;

393:   PetscCall(TSBDF_RestoreVecs(ts, dm, &V, &V0));
394:   PetscFunctionReturn(PETSC_SUCCESS);
395: }

397: static PetscErrorCode TSReset_BDF(TS ts)
398: {
399:   TS_BDF *bdf = (TS_BDF *)ts->data;
400:   size_t  i, n = PETSC_STATIC_ARRAY_LENGTH(bdf->work);

402:   PetscFunctionBegin;
403:   for (i = 0; i < n; i++) {
404:     PetscCall(VecDestroy(&bdf->work[i]));
405:     PetscCall(VecDestroy(&bdf->tvwork[i]));
406:   }
407:   PetscCall(VecDestroy(&bdf->vec_dot));
408:   PetscCall(VecDestroy(&bdf->vec_wrk));
409:   PetscCall(VecDestroy(&bdf->vec_lte));
410:   if (ts->dm) PetscCall(DMCoarsenHookRemove(ts->dm, DMCoarsenHook_TSBDF, DMRestrictHook_TSBDF, ts));
411:   PetscFunctionReturn(PETSC_SUCCESS);
412: }

414: static PetscErrorCode TSDestroy_BDF(TS ts)
415: {
416:   PetscFunctionBegin;
417:   PetscCall(TSReset_BDF(ts));
418:   PetscCall(PetscFree(ts->data));
419:   PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSBDFSetOrder_C", NULL));
420:   PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSBDFGetOrder_C", NULL));
421:   PetscFunctionReturn(PETSC_SUCCESS);
422: }

424: static PetscErrorCode TSSetUp_BDF(TS ts)
425: {
426:   TS_BDF   *bdf = (TS_BDF *)ts->data;
427:   size_t    n   = PETSC_STATIC_ARRAY_LENGTH(bdf->work);
428:   PetscReal low, high, two = 2;
429:   PetscInt  cnt = 0;

431:   PetscFunctionBegin;
432:   PetscCall(TSHasTransientVariable(ts, &bdf->transientvar));
433:   for (size_t i = 0; i < n; i++) {
434:     if (!bdf->work[i]) PetscCall(VecDuplicate(ts->vec_sol, &bdf->work[i]));
435:     else cnt++;
436:     if (i && bdf->transientvar && !bdf->tvwork[i]) PetscCall(VecDuplicate(ts->vec_sol, &bdf->tvwork[i]));
437:   }
438:   if (!cnt) bdf->k = bdf->n = 0;
439:   PetscCall(VecDuplicate(ts->vec_sol, &bdf->vec_dot));
440:   PetscCall(VecDuplicate(ts->vec_sol, &bdf->vec_wrk));
441:   PetscCall(VecDuplicate(ts->vec_sol, &bdf->vec_lte));
442:   PetscCall(TSGetDM(ts, &ts->dm));

450:   PetscCall(TSGetSNES(ts, &ts->snes));
451:   PetscFunctionReturn(PETSC_SUCCESS);
452: }

454: static PetscErrorCode TSSetFromOptions_BDF(TS ts, PetscOptionItems *PetscOptionsObject)
455: {
456:   PetscFunctionBegin;
457:   PetscOptionsHeadBegin(PetscOptionsObject, "BDF ODE solver options");
458:   {
459:     PetscBool flg;
460:     PetscInt  order;
461:     PetscCall(TSBDFGetOrder(ts, &order));
462:     PetscCall(PetscOptionsInt("-ts_bdf_order", "Order of the BDF method", "TSBDFSetOrder", order, &order, &flg));
463:     if (flg) PetscCall(TSBDFSetOrder(ts, order));
464:   }
466:   PetscFunctionReturn(PETSC_SUCCESS);
467: }

469: static PetscErrorCode TSView_BDF(TS ts, PetscViewer viewer)
470: {
471:   TS_BDF   *bdf = (TS_BDF *)ts->data;
472:   PetscBool iascii;

474:   PetscFunctionBegin;
475:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &iascii));
476:   if (iascii) PetscCall(PetscViewerASCIIPrintf(viewer, "  Order=%" PetscInt_FMT "\n", bdf->order));
477:   PetscFunctionReturn(PETSC_SUCCESS);
478: }

480: /* ------------------------------------------------------------ */

482: static PetscErrorCode TSBDFSetOrder_BDF(TS ts, PetscInt order)
483: {
484:   TS_BDF *bdf = (TS_BDF *)ts->data;

486:   PetscFunctionBegin;
487:   if (order == bdf->order) PetscFunctionReturn(PETSC_SUCCESS);
488:   PetscCheck(order >= 1 && order <= 6, PetscObjectComm((PetscObject)ts), PETSC_ERR_ARG_OUTOFRANGE, "BDF Order %" PetscInt_FMT " not implemented", order);
489:   bdf->order = order;
490:   PetscFunctionReturn(PETSC_SUCCESS);
491: }

493: static PetscErrorCode TSBDFGetOrder_BDF(TS ts, PetscInt *order)
494: {
495:   TS_BDF *bdf = (TS_BDF *)ts->data;

497:   PetscFunctionBegin;
498:   *order = bdf->order;
499:   PetscFunctionReturn(PETSC_SUCCESS);
500: }

502: /* ------------------------------------------------------------ */

504: /*MC
505:       TSBDF - DAE solver using BDF methods

507:   Level: beginner

509: .seealso: [](ch_ts), TS, TSCreate(), TSSetType(), TSType
510: M*/
511: PETSC_EXTERN PetscErrorCode TSCreate_BDF(TS ts)
512: {
513:   TS_BDF *bdf;

515:   PetscFunctionBegin;
516:   ts->ops->reset          = TSReset_BDF;
517:   ts->ops->destroy        = TSDestroy_BDF;
518:   ts->ops->view           = TSView_BDF;
519:   ts->ops->setup          = TSSetUp_BDF;
520:   ts->ops->setfromoptions = TSSetFromOptions_BDF;
521:   ts->ops->step           = TSStep_BDF;
522:   ts->ops->evaluatewlte   = TSEvaluateWLTE_BDF;
523:   ts->ops->interpolate    = TSInterpolate_BDF;
524:   ts->ops->resizeregister = TSResizeRegister_BDF;
525:   ts->ops->snesfunction   = SNESTSFormFunction_BDF;
526:   ts->ops->snesjacobian   = SNESTSFormJacobian_BDF;

529:   ts->usessnes = PETSC_TRUE;

531:   PetscCall(PetscNew(&bdf));
532:   ts->data = (void *)bdf;

534:   bdf->status = TS_STEP_COMPLETE;
535:   for (size_t i = 0; i < PETSC_STATIC_ARRAY_LENGTH(bdf->work); i++) { bdf->work[i] = bdf->tvwork[i] = NULL; }

537:   PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSBDFSetOrder_C", TSBDFSetOrder_BDF));
538:   PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSBDFGetOrder_C", TSBDFGetOrder_BDF));
539:   PetscCall(TSBDFSetOrder(ts, 2));
540:   PetscFunctionReturn(PETSC_SUCCESS);
541: }

543: /* ------------------------------------------------------------ */

545: /*@
546:   TSBDFSetOrder - Set the order of the TSBDF method

548:   Logically Collective

550:   Input Parameters:
551: + ts    - timestepping context
552: - order - order of the method

554:   Options Database Key:
555: . -ts_bdf_order <order> - select the order

557:   Level: intermediate

559: .seealso: TSBDFGetOrder(), TS, TSBDF
560: @*/
561: PetscErrorCode TSBDFSetOrder(TS ts, PetscInt order)
562: {
563:   PetscFunctionBegin;
566:   PetscTryMethod(ts, "TSBDFSetOrder_C", (TS, PetscInt), (ts, order));
567:   PetscFunctionReturn(PETSC_SUCCESS);
568: }

570: /*@
571:   TSBDFGetOrder - Get the order of the TSBDF method

573:   Not Collective

575:   Input Parameter:
576: . ts - timestepping context

578:   Output Parameter:
579: . order - order of the method

581:   Level: intermediate

583: .seealso: TSBDFSetOrder(), TS, TSBDF
584: @*/
585: PetscErrorCode TSBDFGetOrder(TS ts, PetscInt *order)
586: {
587:   PetscFunctionBegin;
589:   PetscAssertPointer(order, 2);
590:   PetscUseMethod(ts, "TSBDFGetOrder_C", (TS, PetscInt *), (ts, order));
591:   PetscFunctionReturn(PETSC_SUCCESS);
592: }