Actual source code: arkimex.c

  1: /*
  2:   Code for timestepping with additive Runge-Kutta IMEX method or Diagonally Implicit Runge-Kutta methods.

  4:   Notes:
  5:   For ARK, the general system is written as

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

  9:   where F represents the stiff part of the physics and G represents the non-stiff part.

 11: */
 12: #include <petsc/private/tsimpl.h>
 13: #include <petscdm.h>

 15: static TSARKIMEXType  TSARKIMEXDefault = TSARKIMEX3;
 16: static TSDIRKType     TSDIRKDefault    = TSDIRKES213SAL;
 17: static PetscBool      TSARKIMEXRegisterAllCalled;
 18: static PetscBool      TSARKIMEXPackageInitialized;
 19: static PetscErrorCode TSExtrapolate_ARKIMEX(TS, PetscReal, Vec);

 21: typedef struct _ARKTableau *ARKTableau;
 22: struct _ARKTableau {
 23:   char      *name;
 24:   PetscBool  additive;             /* If False, it is a DIRK method */
 25:   PetscInt   order;                /* Classical approximation order of the method */
 26:   PetscInt   s;                    /* Number of stages */
 27:   PetscBool  stiffly_accurate;     /* The implicit part is stiffly accurate */
 28:   PetscBool  FSAL_implicit;        /* The implicit part is FSAL */
 29:   PetscBool  explicit_first_stage; /* The implicit part has an explicit first stage */
 30:   PetscInt   pinterp;              /* Interpolation order */
 31:   PetscReal *At, *bt, *ct;         /* Stiff tableau */
 32:   PetscReal *A, *b, *c;            /* Non-stiff tableau */
 33:   PetscReal *bembedt, *bembed;     /* Embedded formula of order one less (order-1) */
 34:   PetscReal *binterpt, *binterp;   /* Dense output formula */
 35:   PetscReal  ccfl;                 /* Placeholder for CFL coefficient relative to forward Euler */
 36: };
 37: typedef struct _ARKTableauLink *ARKTableauLink;
 38: struct _ARKTableauLink {
 39:   struct _ARKTableau tab;
 40:   ARKTableauLink     next;
 41: };
 42: static ARKTableauLink ARKTableauList;

 44: typedef struct {
 45:   ARKTableau   tableau;
 46:   Vec         *Y;            /* States computed during the step */
 47:   Vec         *YdotI;        /* Time derivatives for the stiff part */
 48:   Vec         *YdotRHS;      /* Function evaluations for the non-stiff part */
 49:   Vec         *Y_prev;       /* States computed during the previous time step */
 50:   Vec         *YdotI_prev;   /* Time derivatives for the stiff part for the previous time step*/
 51:   Vec         *YdotRHS_prev; /* Function evaluations for the non-stiff part for the previous time step*/
 52:   Vec          Ydot0;        /* Holds the slope from the previous step in FSAL case */
 53:   Vec          Ydot;         /* Work vector holding Ydot during residual evaluation */
 54:   Vec          Z;            /* Ydot = shift(Y-Z) */
 55:   PetscScalar *work;         /* Scalar work */
 56:   PetscReal    scoeff;       /* shift = scoeff/dt */
 57:   PetscReal    stage_time;
 58:   PetscBool    imex;
 59:   PetscBool    extrapolate; /* Extrapolate initial guess from previous time-step stage values */
 60:   TSStepStatus status;

 62:   /* context for sensitivity analysis */
 63:   Vec *VecsDeltaLam;   /* Increment of the adjoint sensitivity w.r.t IC at stage */
 64:   Vec *VecsSensiTemp;  /* Vectors to be multiplied with Jacobian transpose */
 65:   Vec *VecsSensiPTemp; /* Temporary Vectors to store JacobianP-transpose-vector product */
 66: } TS_ARKIMEX;

 68: /*MC
 69:      TSARKIMEXARS122 - Second order ARK IMEX scheme.

 71:      This method has one explicit stage and one implicit stage.

 73:      Options Database Key:
 74: .      -ts_arkimex_type ars122 - set arkimex type to ars122

 76:      Level: advanced

 78:      References:
 79: .    * - U. Ascher, S. Ruuth, R. J. Spiteri, Implicit explicit Runge Kutta methods for time dependent Partial Differential Equations. Appl. Numer. Math. 25, (1997).

 81: .seealso: [](ch_ts), `TSARKIMEX`, `TSARKIMEXType`, `TSARKIMEXSetType()`
 82: M*/

 84: /*MC
 85:      TSARKIMEXA2 - Second order ARK IMEX scheme with A-stable implicit part.

 87:      This method has an explicit stage and one implicit stage, and has an A-stable implicit scheme. This method was provided by Emil Constantinescu.

 89:      Options Database Key:
 90: .      -ts_arkimex_type a2 - set arkimex type to a2

 92:      Level: advanced

 94: .seealso: [](ch_ts), `TSARKIMEX`, `TSARKIMEXType`, `TSARKIMEXSetType()`
 95: M*/

 97: /*MC
 98:      TSARKIMEXL2 - Second order ARK IMEX scheme with L-stable implicit part.

100:      This method has two implicit stages, and L-stable implicit scheme.

102:      Options Database Key:
103: .      -ts_arkimex_type l2 - set arkimex type to l2

105:      Level: advanced

107:     References:
108: .   * - L. Pareschi, G. Russo, Implicit Explicit Runge Kutta schemes and applications to hyperbolic systems with relaxations. Journal of Scientific Computing Volume: 25, Issue: 1, October, 2005.

110: .seealso: [](ch_ts), `TSARKIMEX`, `TSARKIMEXType`, `TSARKIMEXSetType()`
111: M*/

113: /*MC
114:      TSARKIMEX1BEE - First order backward Euler represented as an ARK IMEX scheme with extrapolation as error estimator. This is a 3-stage method.

116:      This method is aimed at starting the integration of implicit DAEs when explicit first-stage ARK methods are used.

118:      Options Database Key:
119: .      -ts_arkimex_type 1bee - set arkimex type to 1bee

121:      Level: advanced

123: .seealso: [](ch_ts), `TSARKIMEX`, `TSARKIMEXType`, `TSARKIMEXSetType()`
124: M*/

126: /*MC
127:      TSARKIMEX2C - Second order ARK IMEX scheme with L-stable implicit part.

129:      This method has one explicit stage and two implicit stages. The implicit part is the same as in TSARKIMEX2D and TSARKIMEX2E, but the explicit part has a larger stability region on the negative real axis. This method was provided by Emil Constantinescu.

131:      Options Database Key:
132: .      -ts_arkimex_type 2c - set arkimex type to 2c

134:      Level: advanced

136: .seealso: [](ch_ts), `TSARKIMEX`, `TSARKIMEXType`, `TSARKIMEXSetType()`
137: M*/

139: /*MC
140:      TSARKIMEX2D - Second order ARK IMEX scheme with L-stable implicit part.

142:      This method has one explicit stage and two implicit stages. The stability function is independent of the explicit part in the infinity limit of the implicit component. This method was provided by Emil Constantinescu.

144:      Options Database Key:
145: .      -ts_arkimex_type 2d - set arkimex type to 2d

147:      Level: advanced

149: .seealso: [](ch_ts), `TSARKIMEX`, `TSARKIMEXType`, `TSARKIMEXSetType()`
150: M*/

152: /*MC
153:      TSARKIMEX2E - Second order ARK IMEX scheme with L-stable implicit part.

155:      This method has one explicit stage and two implicit stages. It is is an optimal method developed by Emil Constantinescu.

157:      Options Database Key:
158: .      -ts_arkimex_type 2e - set arkimex type to 2e

160:     Level: advanced

162: .seealso: [](ch_ts), `TSARKIMEX`, `TSARKIMEXType`, `TSARKIMEXSetType()`
163: M*/

165: /*MC
166:      TSARKIMEXPRSSP2 - Second order SSP ARK IMEX scheme.

168:      This method has three implicit stages.

170:      References:
171: .    * - L. Pareschi, G. Russo, Implicit Explicit Runge Kutta schemes and applications to hyperbolic systems with relaxations. Journal of Scientific Computing Volume: 25, Issue: 1, October, 2005.

173:      This method is referred to as SSP2-(3,3,2) in https://arxiv.org/abs/1110.4375

175:      Options Database Key:
176: .      -ts_arkimex_type prssp2 - set arkimex type to prssp2

178:      Level: advanced

180: .seealso: [](ch_ts), `TSARKIMEX`, `TSARKIMEXType`, `TSARKIMEXSetType()`
181: M*/

183: /*MC
184:      TSARKIMEX3 - Third order ARK IMEX scheme with L-stable implicit part.

186:      This method has one explicit stage and three implicit stages.

188:      Options Database Key:
189: .      -ts_arkimex_type 3 - set arkimex type to 3

191:      Level: advanced

193:      References:
194: .    * - Kennedy and Carpenter 2003.

196: .seealso: [](ch_ts), `TSARKIMEX`, `TSARKIMEXType`, `TSARKIMEXSetType()`
197: M*/

199: /*MC
200:      TSARKIMEXARS443 - Third order ARK IMEX scheme.

202:      This method has one explicit stage and four implicit stages.

204:      Options Database Key:
205: .      -ts_arkimex_type ars443 - set arkimex type to ars443

207:      Level: advanced

209:      References:
210: +    * - U. Ascher, S. Ruuth, R. J. Spiteri, Implicit explicit Runge Kutta methods for time dependent Partial Differential Equations. Appl. Numer. Math. 25, (1997).
211: -    * - This method is referred to as ARS(4,4,3) in https://arxiv.org/abs/1110.4375

213: .seealso: [](ch_ts), `TSARKIMEX`, `TSARKIMEXType`, `TSARKIMEXSetType()`
214: M*/

216: /*MC
217:      TSARKIMEXBPR3 - Third order ARK IMEX scheme.

219:      This method has one explicit stage and four implicit stages.

221:      Options Database Key:
222: .      -ts_arkimex_type bpr3 - set arkimex type to bpr3

224:      Level: advanced

226:      References:
227: .    * - This method is referred to as ARK3 in https://arxiv.org/abs/1110.4375

229: .seealso: [](ch_ts), `TSARKIMEX`, `TSARKIMEXType`, `TSARKIMEXSetType()`
230: M*/

232: /*MC
233:      TSARKIMEX4 - Fourth order ARK IMEX scheme with L-stable implicit part.

235:      This method has one explicit stage and four implicit stages.

237:      Options Database Key:
238: .      -ts_arkimex_type 4 - set arkimex type to4

240:      Level: advanced

242:      References:
243: .    * - Kennedy and Carpenter 2003.

245: .seealso: [](ch_ts), `TSARKIMEX`, `TSARKIMEXType`, `TSARKIMEXSetType()`
246: M*/

248: /*MC
249:      TSARKIMEX5 - Fifth order ARK IMEX scheme with L-stable implicit part.

251:      This method has one explicit stage and five implicit stages.

253:      Options Database Key:
254: .      -ts_arkimex_type 5 - set arkimex type to 5

256:      Level: advanced

258:      References:
259: .    * - Kennedy and Carpenter 2003.

261: .seealso: [](ch_ts), `TSARKIMEX`, `TSARKIMEXType`, `TSARKIMEXSetType()`
262: M*/

264: /*MC
265:      TSDIRKS212 - Second order DIRK scheme.

267:      This method has two implicit stages with an embedded method of other 1.
268:      See `TSDIRK` for additional details.

270:      Options Database Key:
271: .      -ts_dirk_type s212 - select this method.

273:      Level: advanced

275:      Note:
276:      This is the default DIRK scheme in SUNDIALS.

278: .seealso: [](ch_ts), `TSDIRK`, `TSDIRKType`, `TSDIRKSetType()`
279: M*/

281: /*MC
282:      TSDIRKES122SAL - First order DIRK scheme.

284:      Uses backward Euler as advancing method and trapezoidal rule as embedded method. See `TSDIRK` for additional details.

286:      Options Database Key:
287: .      -ts_dirk_type es122sal - select this method.

289:      Level: advanced

291:      References:
292: .    * - https://arxiv.org/abs/1803.01613

294: .seealso: [](ch_ts), `TSDIRK`, `TSDIRKType`, `TSDIRKSetType()`
295: M*/

297: /*MC
298:      TSDIRKES213SAL - Second order DIRK scheme.

300:      See `TSDIRK` for additional details.

302:      Options Database Key:
303: .      -ts_dirk_type es213sal - select this method.

305:      Level: advanced

307:      Note:
308:      This is the default DIRK scheme used in PETSc.

310:      References:
311: +    * - Kennedy and Carpenter, Diagonally Implicit Runge-Kutta methods for stiff ODEs (2016), https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf
312: -    * - This method is also known as TR-BDF2, see M.E. Hosea and L.F. Shampine, Analysis and implementation of TR-BDF2, Appl. Numer. Math., 20(1) (1996) 21-37.

314: .seealso: [](ch_ts), `TSDIRK`, `TSDIRKType`, `TSDIRKSetType()`
315: M*/

317: /*MC
318:      TSDIRKES324SAL - Third order DIRK scheme.

320:      See `TSDIRK` for additional details.

322:      Options Database Key:
323: .      -ts_dirk_type es324sal - select this method.

325:      Level: advanced

327:      References:
328: .    * - Kennedy and Carpenter, Diagonally Implicit Runge-Kutta methods for stiff ODEs (2016), https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf

330: .seealso: [](ch_ts), `TSDIRK`, `TSDIRKType`, `TSDIRKSetType()`
331: M*/

333: /*MC
334:      TSDIRKES325SAL - Third order DIRK scheme.

336:      See `TSDIRK` for additional details.

338:      Options Database Key:
339: .      -ts_dirk_type es325sal - select this method.

341:      Level: advanced

343:      References:
344: .    * - Kennedy and Carpenter, Diagonally Implicit Runge-Kutta methods for stiff ODEs (2016), https://ntrs.nasa.gov/api/citations/20160005923/downloads/20160005923.pdf

346: .seealso: [](ch_ts), `TSDIRK`, `TSDIRKType`, `TSDIRKSetType()`
347: M*/

349: /*MC
350:      TSDIRK657A - Sixth order DIRK scheme.

352:      See `TSDIRK` for additional details.

354:      Options Database Key:
355: .      -ts_dirk_type 657a - select this method.

357:      Level: advanced

359:      References:
360: .    * - https://github.com/yousefalamri55/High_Order_DIRK_Methods_Coeffs

362: .seealso: [](ch_ts), `TSDIRK`, `TSDIRKType`, `TSDIRKSetType()`
363: M*/

365: /*MC
366:      TSDIRKES648SA - Sixth order DIRK scheme.

368:      See `TSDIRK` for additional details.

370:      Options Database Key:
371: .      -ts_dirk_type es648sa - select this method.

373:      Level: advanced

375:      References:
376: .    * - https://github.com/yousefalamri55/High_Order_DIRK_Methods_Coeffs

378: .seealso: [](ch_ts), `TSDIRK`, `TSDIRKType`, `TSDIRKSetType()`
379: M*/

381: /*MC
382:      TSDIRK658A - Sixth order DIRK scheme.

384:      See `TSDIRK` for additional details.

386:      Options Database Key:
387: .      -ts_dirk_type 658a - select this method.

389:      Level: advanced

391:      References:
392: .    * - https://github.com/yousefalamri55/High_Order_DIRK_Methods_Coeffs

394: .seealso: [](ch_ts), `TSDIRK`, `TSDIRKType`, `TSDIRKSetType()`
395: M*/

397: /*MC
398:      TSDIRKS659A - Sixth order DIRK scheme.

400:      See `TSDIRK` for additional details.

402:      Options Database Key:
403: .      -ts_dirk_type s659a - select this method.

405:      Level: advanced

407:      References:
408: .    * - https://github.com/yousefalamri55/High_Order_DIRK_Methods_Coeffs

410: .seealso: [](ch_ts), `TSDIRK`, `TSDIRKType`, `TSDIRKSetType()`
411: M*/

413: /*MC
414:      TSDIRK7510SAL - Seventh order DIRK scheme.

416:      See `TSDIRK` for additional details.

418:      Options Database Key:
419: .      -ts_dirk_type 7510sal - select this method.

421:      Level: advanced

423:      References:
424: .    * - https://github.com/yousefalamri55/High_Order_DIRK_Methods_Coeffs

426: .seealso: [](ch_ts), `TSDIRK`, `TSDIRKType`, `TSDIRKSetType()`
427: M*/

429: /*MC
430:      TSDIRKES7510SA - Seventh order DIRK scheme.

432:      See `TSDIRK` for additional details.

434:      Options Database Key:
435: .      -ts_dirk_type es7510sa - select this method.

437:      Level: advanced

439:      References:
440: .    * - https://github.com/yousefalamri55/High_Order_DIRK_Methods_Coeffs

442: .seealso: [](ch_ts), `TSDIRK`, `TSDIRKType`, `TSDIRKSetType()`
443: M*/

445: /*MC
446:      TSDIRK759A - Seventh order DIRK scheme.

448:      See `TSDIRK` for additional details.

450:      Options Database Key:
451: .      -ts_dirk_type 759a - select this method.

453:      Level: advanced

455:      References:
456: .    * - https://github.com/yousefalamri55/High_Order_DIRK_Methods_Coeffs

458: .seealso: [](ch_ts), `TSDIRK`, `TSDIRKType`, `TSDIRKSetType()`
459: M*/

461: /*MC
462:      TSDIRKS7511SAL - Seventh order DIRK scheme.

464:      See `TSDIRK` for additional details.

466:      Options Database Key:
467: .      -ts_dirk_type s7511sal - select this method.

469:      Level: advanced

471:      References:
472: .    * - https://github.com/yousefalamri55/High_Order_DIRK_Methods_Coeffs

474: .seealso: [](ch_ts), `TSDIRK`, `TSDIRKType`, `TSDIRKSetType()`
475: M*/

477: /*MC
478:      TSDIRK8614A - Eighth order DIRK scheme.

480:      See `TSDIRK` for additional details.

482:      Options Database Key:
483: .      -ts_dirk_type 8614a - select this method.

485:      Level: advanced

487:      References:
488: .    * - https://github.com/yousefalamri55/High_Order_DIRK_Methods_Coeffs

490: .seealso: [](ch_ts), `TSDIRK`, `TSDIRKType`, `TSDIRKSetType()`
491: M*/

493: /*MC
494:      TSDIRK8616SAL - Eighth order DIRK scheme.

496:      See `TSDIRK` for additional details.

498:      Options Database Key:
499: .      -ts_dirk_type 8616sal - select this method.

501:      Level: advanced

503:      References:
504: .    * - https://github.com/yousefalamri55/High_Order_DIRK_Methods_Coeffs

506: .seealso: [](ch_ts), `TSDIRK`, `TSDIRKType`, `TSDIRKSetType()`
507: M*/

509: /*MC
510:      TSDIRKES8516SAL - Eighth order DIRK scheme.

512:      See `TSDIRK` for additional details.

514:      Options Database Key:
515: .      -ts_dirk_type es8516sal - select this method.

517:      Level: advanced

519:      References:
520: .    * - https://github.com/yousefalamri55/High_Order_DIRK_Methods_Coeffs

522: .seealso: [](ch_ts), `TSDIRK`, `TSDIRKType`, `TSDIRKSetType()`
523: M*/

525: static PetscErrorCode TSHasRHSFunction(TS ts, PetscBool *has)
526: {
527:   TSRHSFunction func;

529:   PetscFunctionBegin;
530:   *has = PETSC_FALSE;
531:   PetscCall(DMTSGetRHSFunction(ts->dm, &func, NULL));
532:   if (func) *has = PETSC_TRUE;
533:   PetscFunctionReturn(PETSC_SUCCESS);
534: }

536: /*@C
537:   TSARKIMEXRegisterAll - Registers all of the additive Runge-Kutta implicit-explicit methods in `TSARKIMEX`

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

541:   Level: advanced

543: .seealso: [](ch_ts), `TS`, `TSARKIMEX`, `TSARKIMEXRegisterDestroy()`
544: @*/
545: PetscErrorCode TSARKIMEXRegisterAll(void)
546: {
547:   PetscFunctionBegin;
548:   if (TSARKIMEXRegisterAllCalled) PetscFunctionReturn(PETSC_SUCCESS);
549:   TSARKIMEXRegisterAllCalled = PETSC_TRUE;

551: #define RC  PetscRealConstant
552: #define s2  RC(1.414213562373095048802)  /* PetscSqrtReal((PetscReal)2.0) */
553: #define us2 RC(0.2928932188134524755992) /* 1.0-1.0/PetscSqrtReal((PetscReal)2.0); */

555:   /* Diagonally implicit methods */
556:   {
557:     /* DIRK212, default of SUNDIALS */
558:     const PetscReal A[2][2] = {
559:       {RC(1.0),  RC(0.0)},
560:       {RC(-1.0), RC(1.0)}
561:     };
562:     const PetscReal b[2]      = {RC(0.5), RC(0.5)};
563:     const PetscReal bembed[2] = {RC(1.0), RC(0.0)};
564:     PetscCall(TSDIRKRegister(TSDIRKS212, 2, 2, &A[0][0], b, NULL, bembed, 1, b));
565:   }

567:   {
568:     /* ESDIRK12 from https://arxiv.org/pdf/1803.01613.pdf */
569:     const PetscReal A[2][2] = {
570:       {RC(0.0), RC(0.0)},
571:       {RC(0.0), RC(1.0)}
572:     };
573:     const PetscReal b[2]      = {RC(0.0), RC(1.0)};
574:     const PetscReal bembed[2] = {RC(0.5), RC(0.5)};
575:     PetscCall(TSDIRKRegister(TSDIRKES122SAL, 1, 2, &A[0][0], b, NULL, bembed, 1, b));
576:   }

578:   {
579:     /* ESDIRK213L[2]SA from KC16.
580:        TR-BDF2 from Hosea and Shampine
581:        ESDIRK23 in https://arxiv.org/pdf/1803.01613.pdf */
582:     const PetscReal A[3][3] = {
583:       {RC(0.0),      RC(0.0),      RC(0.0)},
584:       {us2,          us2,          RC(0.0)},
585:       {s2 / RC(4.0), s2 / RC(4.0), us2    },
586:     };
587:     const PetscReal b[3]      = {s2 / RC(4.0), s2 / RC(4.0), us2};
588:     const PetscReal bembed[3] = {(RC(1.0) - s2 / RC(4.0)) / RC(3.0), (RC(3.0) * s2 / RC(4.0) + RC(1.0)) / RC(3.0), us2 / RC(3.0)};
589:     PetscCall(TSDIRKRegister(TSDIRKES213SAL, 2, 3, &A[0][0], b, NULL, bembed, 1, b));
590:   }

592:   {
593: #define g   RC(0.43586652150845899941601945)
594: #define g2  PetscSqr(g)
595: #define g3  g *g2
596: #define g4  PetscSqr(g2)
597: #define g5  g *g4
598: #define c3  RC(1.0)
599: #define a32 c3 *(c3 - RC(2.0) * g) / (RC(4.0) * g)
600: #define b2  (-RC(2.0) + RC(3.0) * c3 + RC(6.0) * g * (RC(1.0) - c3)) / (RC(12.0) * g * (c3 - RC(2.0) * g))
601: #define b3  (RC(1.0) - RC(6.0) * g + RC(6.0) * g2) / (RC(3.0) * c3 * (c3 - RC(2.0) * g))
602: #if 0
603: /* This is for c3 = 3/5 */
604:   #define bh2 \
605:     c3 * (-RC(1.0) + RC(6.0) * g - RC(23.0) * g3 + RC(12.0) * g4 - RC(6.0) * g5) / (RC(4.0) * (RC(2.0) * g - c3) * (RC(1.0) - RC(6.0) * g + RC(6.0) * g2)) + (RC(3.0) - RC(27.0) * g + RC(68.0) * g2 - RC(55.0) * g3 + RC(21.0) * g4 - RC(6.0) * g5) / (RC(2.0) * (RC(2.0) * g - c3) * (RC(1.0) - RC(6.0) * g + RC(6.0) * g2))
606:   #define bh3 -g * (-RC(2.0) + RC(21.0) * g - RC(68.0) * g2 + RC(79.0) * g3 - RC(33.0) * g4 + RC(12.0) * g5) / (RC(2.0) * (RC(2.0) * g - c3) * (RC(1.0) - RC(6.0) * g + RC(6.0) * g2))
607:   #define bh4 -RC(3.0) * g2 * (-RC(1.0) + RC(4.0) * g - RC(2.0) * g2 + g3) / (RC(1.0) - RC(6.0) * g + RC(6.0) * g2)
608: #else
609:   /* This is for c3 = 1.0 */
610:   #define bh2 a32
611:   #define bh3 g
612:   #define bh4 RC(0.0)
613: #endif
614:     /* ESDIRK3(2I)4L[2]SA from KC16 with c3 = 1.0 */
615:     /* Given by Kvaerno https://link.springer.com/article/10.1023/b:bitn.0000046811.70614.38 */
616:     const PetscReal A[4][4] = {
617:       {RC(0.0),               RC(0.0), RC(0.0), RC(0.0)},
618:       {g,                     g,       RC(0.0), RC(0.0)},
619:       {c3 - a32 - g,          a32,     g,       RC(0.0)},
620:       {RC(1.0) - b2 - b3 - g, b2,      b3,      g      },
621:     };
622:     const PetscReal b[4]      = {RC(1.0) - b2 - b3 - g, b2, b3, g};
623:     const PetscReal bembed[4] = {RC(1.0) - bh2 - bh3 - bh4, bh2, bh3, bh4};
624:     PetscCall(TSDIRKRegister(TSDIRKES324SAL, 3, 4, &A[0][0], b, NULL, bembed, 1, b));
625: #undef g
626: #undef g2
627: #undef g3
628: #undef c3
629: #undef a32
630: #undef b2
631: #undef b3
632: #undef bh2
633: #undef bh3
634: #undef bh4
635:   }

637:   {
638:     /* ESDIRK3(2I)5L[2]SA from KC16 */
639:     const PetscReal A[5][5] = {
640:       {RC(0.0),                  RC(0.0),                  RC(0.0),                 RC(0.0),                   RC(0.0)           },
641:       {RC(9.0) / RC(40.0),       RC(9.0) / RC(40.0),       RC(0.0),                 RC(0.0),                   RC(0.0)           },
642:       {RC(19.0) / RC(72.0),      RC(14.0) / RC(45.0),      RC(9.0) / RC(40.0),      RC(0.0),                   RC(0.0)           },
643:       {RC(3337.0) / RC(11520.0), RC(233.0) / RC(720.0),    RC(207.0) / RC(1280.0),  RC(9.0) / RC(40.0),        RC(0.0)           },
644:       {RC(7415.0) / RC(34776.0), RC(9920.0) / RC(30429.0), RC(4845.0) / RC(9016.0), -RC(5827.0) / RC(19320.0), RC(9.0) / RC(40.0)},
645:     };
646:     const PetscReal b[5]      = {RC(7415.0) / RC(34776.0), RC(9920.0) / RC(30429.0), RC(4845.0) / RC(9016.0), -RC(5827.0) / RC(19320.0), RC(9.0) / RC(40.0)};
647:     const PetscReal bembed[5] = {RC(23705.0) / RC(104328.0), RC(29720.0) / RC(91287.0), RC(4225.0) / RC(9016.0), -RC(69304987.0) / RC(337732920.0), RC(42843.0) / RC(233080.0)};
648:     PetscCall(TSDIRKRegister(TSDIRKES325SAL, 3, 5, &A[0][0], b, NULL, bembed, 1, b));
649:   }

651:   {
652:     // DIRK(6,6)[1]A[(7,5)A] from https://github.com/yousefalamri55/High_Order_DIRK_Methods_Coeffs
653:     const PetscReal A[7][7] = {
654:       {RC(0.303487844706747),    RC(0.0),                RC(0.0),                   RC(0.0),                   RC(0.0),                 RC(0.0),                RC(0.0)              },
655:       {RC(-0.279756492709814),   RC(0.500032236020747),  RC(0.0),                   RC(0.0),                   RC(0.0),                 RC(0.0),                RC(0.0)              },
656:       {RC(0.280583215743895),    RC(-0.438560061586751), RC(0.217250734515736),     RC(0.0),                   RC(0.0),                 RC(0.0),                RC(0.0)              },
657:       {RC(-0.0677678738539846),  RC(0.984312781232293),  RC(-0.266720192540149),    RC(0.2476680834526),       RC(0.0),                 RC(0.0),                RC(0.0)              },
658:       {RC(0.125671616147993),    RC(-0.995401751002415), RC(0.761333109549059),     RC(-0.210281837202208),    RC(0.866743712636936),   RC(0.0),                RC(0.0)              },
659:       {RC(-0.368056238801488),   RC(-0.999928082701516), RC(0.534734253232519),     RC(-0.174856916279082),    RC(0.615007160285509),   RC(0.696549912132029),  RC(0.0)              },
660:       {RC(-0.00570546839653984), RC(-0.113110431835656), RC(-0.000965563207671587), RC(-0.000130490084629567), RC(0.00111737736895673), RC(-0.279385587378871), RC(0.618455906845342)}
661:     };
662:     const PetscReal b[7]      = {RC(0.257561510484877), RC(0.234281287047716), RC(0.126658904241469), RC(0.252363215441784), RC(0.396701083526306), RC(-0.267566000742152), RC(0.0)};
663:     const PetscReal bembed[7] = {RC(0.257561510484945), RC(0.387312822934391), RC(0.126658904241468), RC(0.252363215441784), RC(0.396701083526306), RC(-0.267566000742225), RC(-0.153031535886669)};
664:     PetscCall(TSDIRKRegister(TSDIRK657A, 6, 7, &A[0][0], b, NULL, bembed, 1, b));
665:   }
666:   {
667:     // ESDIRK(8,6)[2]SA[(8,4)] from https://github.com/yousefalamri55/High_Order_DIRK_Methods_Coeffs
668:     const PetscReal A[8][8] = {
669:       {RC(0.0),                RC(0.0),                 RC(0.0),                 RC(0.0),               RC(0.0),                RC(0.0),                RC(0.0),               RC(0.0)              },
670:       {RC(0.333222149217725),  RC(0.333222149217725),   RC(0.0),                 RC(0.0),               RC(0.0),                RC(0.0),                RC(0.0),               RC(0.0)              },
671:       {RC(0.0639743773182214), RC(-0.0830330224410214), RC(0.333222149217725),   RC(0.0),               RC(0.0),                RC(0.0),                RC(0.0),               RC(0.0)              },
672:       {RC(-0.728522201369326), RC(-0.210414479522485),  RC(0.532519916559342),   RC(0.333222149217725), RC(0.0),                RC(0.0),                RC(0.0),               RC(0.0)              },
673:       {RC(-0.175135269272067), RC(0.666675582067552),   RC(-0.304400907370867),  RC(0.656797712445756), RC(0.333222149217725),  RC(0.0),                RC(0.0),               RC(0.0)              },
674:       {RC(0.222695802705462),  RC(-0.0948971794681061), RC(-0.0234336346686545), RC(-0.45385925012042), RC(0.0283910313826958), RC(0.333222149217725),  RC(0.0),               RC(0.0)              },
675:       {RC(-0.132534078051299), RC(0.702597935004879),   RC(-0.433316453128078),  RC(0.893717488547587), RC(0.057381454791406),  RC(-0.207798411552402), RC(0.333222149217725), RC(0.0)              },
676:       {RC(0.0802253121418085), RC(0.281196044671022),   RC(0.406758926172157),   RC(-0.01945708512416), RC(-0.41785600088526),  RC(0.0545342658870322), RC(0.281376387919675), RC(0.333222149217725)}
677:     };
678:     const PetscReal b[8]      = {RC(0.0802253121418085), RC(0.281196044671022), RC(0.406758926172157), RC(-0.01945708512416), RC(-0.41785600088526), RC(0.0545342658870322), RC(0.281376387919675), RC(0.333222149217725)};
679:     const PetscReal bembed[8] = {RC(0.0), RC(0.292331064554014), RC(0.409676102283681), RC(-0.002094718084982), RC(-0.282771520835975), RC(0.113862336644901), RC(0.181973572260693), RC(0.287023163177669)};
680:     PetscCall(TSDIRKRegister(TSDIRKES648SA, 6, 8, &A[0][0], b, NULL, bembed, 1, b));
681:   }
682:   {
683:     // DIRK(8,6)[1]SAL[(8,5)A] from https://github.com/yousefalamri55/High_Order_DIRK_Methods_Coeffs
684:     const PetscReal A[8][8] = {
685:       {RC(0.477264457385826),    RC(0.0),                RC(0.0),                   RC(0.0),                 RC(0.0),                RC(0.0),                RC(0.0),                 RC(0.0)              },
686:       {RC(-0.197052588415002),   RC(0.476363428459584),  RC(0.0),                   RC(0.0),                 RC(0.0),                RC(0.0),                RC(0.0),                 RC(0.0)              },
687:       {RC(-0.0347674430372966),  RC(0.633051807335483),  RC(0.193634310075028),     RC(0.0),                 RC(0.0),                RC(0.0),                RC(0.0),                 RC(0.0)              },
688:       {RC(0.0967797668578702),   RC(-0.193533526466535), RC(-0.000207622945800473), RC(0.159572204849431),   RC(0.0),                RC(0.0),                RC(0.0),                 RC(0.0)              },
689:       {RC(0.162527231819875),    RC(-0.249672513547382), RC(-0.0459079972041795),   RC(0.36579476400859),    RC(0.255752838307699),  RC(0.0),                RC(0.0),                 RC(0.0)              },
690:       {RC(-0.00707603197171262), RC(0.846299854860295),  RC(0.344020016925018),     RC(-0.0720926054548865), RC(-0.215492331980875), RC(0.104341097622161),  RC(0.0),                 RC(0.0)              },
691:       {RC(0.00176857935179744),  RC(0.0779960013127515), RC(0.303333277564557),     RC(0.213160806732836),   RC(0.351769320319038),  RC(-0.381545894386538), RC(0.433517909105558),   RC(0.0)              },
692:       {RC(0.0),                  RC(0.22732353410559),   RC(0.308415837980118),     RC(0.157263419573007),   RC(0.243551137152275),  RC(-0.120953626732831), RC(-0.0802678473399899), RC(0.264667545261832)}
693:     };
694:     const PetscReal b[8]      = {RC(0.0), RC(0.22732353410559), RC(0.308415837980118), RC(0.157263419573007), RC(0.243551137152275), RC(-0.120953626732831), RC(-0.0802678473399899), RC(0.264667545261832)};
695:     const PetscReal bembed[8] = {RC(0.0), RC(0.22732353410559), RC(0.308415837980118), RC(0.157263419573007), RC(0.243551137152275), RC(-0.103483943222765), RC(-0.0103721771642262), RC(0.177302191576001)};
696:     PetscCall(TSDIRKRegister(TSDIRK658A, 6, 8, &A[0][0], b, NULL, bembed, 1, b));
697:   }
698:   {
699:     // SDIRK(9,6)[1]SAL[(9,5)A] from https://github.com/yousefalamri55/High_Order_DIRK_Methods_Coeffs
700:     const PetscReal A[9][9] = {
701:       {RC(0.218127781944908),   RC(0.0),                RC(0.0),                 RC(0.0),                 RC(0.0),                RC(0.0),                RC(0.0),                RC(0.0),                RC(0.0)              },
702:       {RC(-0.0903514856119419), RC(0.218127781944908),  RC(0.0),                 RC(0.0),                 RC(0.0),                RC(0.0),                RC(0.0),                RC(0.0),                RC(0.0)              },
703:       {RC(0.172952039138937),   RC(-0.35365501036282),  RC(0.218127781944908),   RC(0.0),                 RC(0.0),                RC(0.0),                RC(0.0),                RC(0.0),                RC(0.0)              },
704:       {RC(0.511999875919193),   RC(0.0289640332201925), RC(-0.0144030945657094), RC(0.218127781944908),   RC(0.0),                RC(0.0),                RC(0.0),                RC(0.0),                RC(0.0)              },
705:       {RC(0.00465303495506782), RC(-0.075635818766597), RC(0.217273030786712),   RC(-0.0206519428725472), RC(0.218127781944908),  RC(0.0),                RC(0.0),                RC(0.0),                RC(0.0)              },
706:       {RC(0.896145501762472),   RC(0.139267327700498),  RC(-0.186920979752805),  RC(0.0672971012371723),  RC(-0.350891963442176), RC(0.218127781944908),  RC(0.0),                RC(0.0),                RC(0.0)              },
707:       {RC(0.552959701885751),   RC(-0.439360579793662), RC(0.333704002325091),   RC(-0.0339426520778416), RC(-0.151947445912595), RC(0.0213825661026943), RC(0.218127781944908),  RC(0.0),                RC(0.0)              },
708:       {RC(0.631360374036476),   RC(0.724733619641466),  RC(-0.432170625425258),  RC(0.598611382182477),   RC(-0.709087197034345), RC(-0.483986685696934), RC(0.378391562905131),  RC(0.218127781944908),  RC(0.0)              },
709:       {RC(0.0),                 RC(-0.15504452530869),  RC(0.194518478660789),   RC(0.63515640279203),    RC(0.81172278664173),   RC(0.110736108691585),  RC(-0.495304692414479), RC(-0.319912341007872), RC(0.218127781944908)}
710:     };
711:     const PetscReal b[9]      = {RC(0.0), RC(-0.15504452530869), RC(0.194518478660789), RC(0.63515640279203), RC(0.81172278664173), RC(0.110736108691585), RC(-0.495304692414479), RC(-0.319912341007872), RC(0.218127781944908)};
712:     const PetscReal bembed[9] = {RC(3.62671059311602e-16), RC(0.0736615558278942), RC(0.103527397262229), RC(1.00247481935499), RC(0.361377289250057), RC(-0.785425929961365), RC(-0.0170499047960784), RC(0.296321252214769), RC(-0.0348864791524953)};
713:     PetscCall(TSDIRKRegister(TSDIRKS659A, 6, 9, &A[0][0], b, NULL, bembed, 1, b));
714:   }
715:   {
716:     // DIRK(10,7)[1]SAL[(10,5)A] from https://github.com/yousefalamri55/High_Order_DIRK_Methods_Coeffs
717:     const PetscReal A[10][10] = {
718:       {RC(0.233704632125264),   RC(0.0),                RC(0.0),                  RC(0.0),                  RC(0.0),                   RC(0.0),                  RC(0.0),                RC(0.0),                 RC(0.0),               RC(0.0)              },
719:       {RC(-0.0739324813149407), RC(0.200056838146104),  RC(0.0),                  RC(0.0),                  RC(0.0),                   RC(0.0),                  RC(0.0),                RC(0.0),                 RC(0.0),               RC(0.0)              },
720:       {RC(0.0943790344044812),  RC(0.264056067701605),  RC(0.133245202456465),    RC(0.0),                  RC(0.0),                   RC(0.0),                  RC(0.0),                RC(0.0),                 RC(0.0),               RC(0.0)              },
721:       {RC(0.269084810601201),   RC(-0.503479002548384), RC(-0.00486736469695022), RC(0.251518716213569),    RC(0.0),                   RC(0.0),                  RC(0.0),                RC(0.0),                 RC(0.0),               RC(0.0)              },
722:       {RC(0.145665801918423),   RC(0.204983170463176),  RC(0.407154634069484),    RC(-0.0121039135200389),  RC(0.190243622486334),     RC(0.0),                  RC(0.0),                RC(0.0),                 RC(0.0),               RC(0.0)              },
723:       {RC(0.985450198547345),   RC(0.806942652811456),  RC(-0.808130934167263),   RC(-0.669035819439391),   RC(0.0269384406756128),    RC(0.462144080607327),    RC(0.0),                RC(0.0),                 RC(0.0),               RC(0.0)              },
724:       {RC(0.163902957809563),   RC(0.228315094960095),  RC(0.0745971021260249),   RC(0.000509793400156559), RC(0.0166533681378294),    RC(-0.0229383879045797),  RC(0.103505486637336),  RC(0.0),                 RC(0.0),               RC(0.0)              },
725:       {RC(-0.162694156858437),  RC(0.0453478837428434), RC(0.997443481211424),    RC(0.200251514941093),    RC(-0.000161755458839048), RC(-0.0848134335980281),  RC(-0.36438666566666),  RC(0.158604420136055),   RC(0.0),               RC(0.0)              },
726:       {RC(0.200733156477425),   RC(0.239686443444433),  RC(0.303837014418929),    RC(-0.0534390596279896),  RC(0.0314067599640569),    RC(-0.00764032790448536), RC(0.0609191260198661), RC(-0.0736319201590642), RC(0.204602530607021), RC(0.0)              },
727:       {RC(0.0),                 RC(0.235563761744267),  RC(0.658651488684319),    RC(0.0308877804992098),   RC(-0.906514945595336),    RC(-0.0248488551739974),  RC(-0.309967582365257), RC(0.191663316925525),   RC(0.923933712199542), RC(0.200631323081727)}
728:     };
729:     const PetscReal b[10] = {RC(0.0), RC(0.235563761744267), RC(0.658651488684319), RC(0.0308877804992098), RC(-0.906514945595336), RC(-0.0248488551739974), RC(-0.309967582365257), RC(0.191663316925525), RC(0.923933712199542), RC(0.200631323081727)};
730:     const PetscReal bembed[10] =
731:       {RC(0.0), RC(0.222929376486581), RC(0.950668440138169), RC(0.0342694607044032), RC(0.362875840545746), RC(0.223572979288581), RC(-0.764361723526727), RC(0.563476909230026), RC(-0.690896961894185), RC(0.0974656790270323)};
732:     PetscCall(TSDIRKRegister(TSDIRK7510SAL, 7, 10, &A[0][0], b, NULL, bembed, 1, b));
733:   }
734:   {
735:     // ESDIRK(10,7)[2]SA[(10,5)] from https://github.com/yousefalamri55/High_Order_DIRK_Methods_Coeffs
736:     const PetscReal A[10][10] = {
737:       {RC(0.0),                 RC(0.0),                 RC(0.0),                 RC(0.0),                  RC(0.0),                  RC(0.0),                  RC(0.0),                RC(0.0),                 RC(0.0),               RC(0.0)              },
738:       {RC(0.210055790203419),   RC(0.210055790203419),   RC(0.0),                 RC(0.0),                  RC(0.0),                  RC(0.0),                  RC(0.0),                RC(0.0),                 RC(0.0),               RC(0.0)              },
739:       {RC(0.255781739921086),   RC(0.239850916980976),   RC(0.210055790203419),   RC(0.0),                  RC(0.0),                  RC(0.0),                  RC(0.0),                RC(0.0),                 RC(0.0),               RC(0.0)              },
740:       {RC(0.286789624880437),   RC(0.230494748834778),   RC(0.263925149885491),   RC(0.210055790203419),    RC(0.0),                  RC(0.0),                  RC(0.0),                RC(0.0),                 RC(0.0),               RC(0.0)              },
741:       {RC(-0.0219118128774335), RC(0.897684380345907),   RC(-0.657954605498907),  RC(0.124962304722633),    RC(0.210055790203419),    RC(0.0),                  RC(0.0),                RC(0.0),                 RC(0.0),               RC(0.0)              },
742:       {RC(-0.065614879584776),  RC(-0.0565630711859497), RC(0.0254881105065311),  RC(-0.00368981790650006), RC(-0.0115178258446329),  RC(0.210055790203419),    RC(0.0),                RC(0.0),                 RC(0.0),               RC(0.0)              },
743:       {RC(0.399860851232098),   RC(0.915588469718705),   RC(-0.0758429094934412), RC(-0.263369154872759),   RC(0.719687583564526),    RC(-0.787410407015369),   RC(0.210055790203419),  RC(0.0),                 RC(0.0),               RC(0.0)              },
744:       {RC(0.51693616104628),    RC(1.00000540846973),    RC(-0.0485110663289207), RC(-0.315208041581942),   RC(0.749742806451587),    RC(-0.990975090921248),   RC(0.0159279583407308), RC(0.210055790203419),   RC(0.0),               RC(0.0)              },
745:       {RC(-0.0303062129076945), RC(-0.297035174659034),  RC(0.184724697462164),   RC(-0.0351876079516183),  RC(-0.00324668230690761), RC(0.216151004053531),    RC(-0.126676252098317), RC(0.114040254365262),   RC(0.210055790203419), RC(0.0)              },
746:       {RC(0.0705997961586714),  RC(-0.0281516061956374), RC(0.314600470734633),   RC(-0.0907057557963371),  RC(0.168078953957742),    RC(-0.00655694984590575), RC(0.0505384497804303), RC(-0.0569572058725042), RC(0.368498056875488), RC(0.210055790203419)}
747:     };
748:     const PetscReal b[10]      = {RC(0.0705997961586714),   RC(-0.0281516061956374), RC(0.314600470734633),   RC(-0.0907057557963371), RC(0.168078953957742),
749:                                   RC(-0.00655694984590575), RC(0.0505384497804303),  RC(-0.0569572058725042), RC(0.368498056875488),   RC(0.210055790203419)};
750:     const PetscReal bembed[10] = {RC(-0.015494246543626), RC(0.167657963820093), RC(0.269858958144236),  RC(-0.0443258997755156), RC(0.150049236875266),
751:                                   RC(0.259452082755846),  RC(0.244624573502521), RC(-0.215528446920284), RC(0.0487601760292619),  RC(0.134945602112201)};
752:     PetscCall(TSDIRKRegister(TSDIRKES7510SA, 7, 10, &A[0][0], b, NULL, bembed, 1, b));
753:   }
754:   {
755:     // DIRK(9,7)[1]A[(9,5)A] from https://github.com/yousefalamri55/High_Order_DIRK_Methods_Coeffs
756:     const PetscReal A[9][9] = {
757:       {RC(0.179877789855839),   RC(0.0),                 RC(0.0),                RC(0.0),                  RC(0.0),                RC(0.0),                RC(0.0),                RC(0.0),                RC(0.0)               },
758:       {RC(-0.100405844885157),  RC(0.214948590644819),   RC(0.0),                RC(0.0),                  RC(0.0),                RC(0.0),                RC(0.0),                RC(0.0),                RC(0.0)               },
759:       {RC(0.112251360198995),   RC(-0.206162139150298),  RC(0.125159642941958),  RC(0.0),                  RC(0.0),                RC(0.0),                RC(0.0),                RC(0.0),                RC(0.0)               },
760:       {RC(-0.0335164000768257), RC(0.999942349946143),   RC(-0.491470853833294), RC(0.19820086325566),     RC(0.0),                RC(0.0),                RC(0.0),                RC(0.0),                RC(0.0)               },
761:       {RC(-0.0417345265478321), RC(0.187864510308215),   RC(0.0533789224305102), RC(-0.00822060284862916), RC(0.127670843671646),  RC(0.0),                RC(0.0),                RC(0.0),                RC(0.0)               },
762:       {RC(-0.0278257925239257), RC(0.600979340683382),   RC(-0.242632273241134), RC(-0.11318753652081),    RC(0.164326917632931),  RC(0.284116597781395),  RC(0.0),                RC(0.0),                RC(0.0)               },
763:       {RC(0.041465583858922),   RC(0.429657872601836),   RC(-0.381323410582524), RC(0.391934277498434),    RC(-0.245918275501241), RC(-0.35960669741231),  RC(0.184000022289158),  RC(0.0),                RC(0.0)               },
764:       {RC(-0.105565651574538),  RC(-0.0557833155018609), RC(0.358967568942643),  RC(-0.13489263413921),    RC(0.129553247260677),  RC(0.0992493795371489), RC(-0.15716610563461),  RC(0.17918862279814),   RC(0.0)               },
765:       {RC(0.00439696079965225), RC(0.960250486570491),   RC(0.143558372286706),  RC(0.0819015241056593),   RC(0.999562318563625),  RC(0.325203439314358),  RC(-0.679013149331228), RC(-0.990589559837246), RC(0.0773648037639896)}
766:     };

768:     const PetscReal b[9]      = {RC(0.0), RC(0.179291520437966), RC(0.115310295273026), RC(-0.857943261453138), RC(0.654911318641998), RC(1.18713633508094), RC(-0.0949482361570542), RC(-0.37661430946407), RC(0.19285633764033)};
769:     const PetscReal bembed[9] = {RC(0.0), RC(0.1897135479408), RC(0.127461414808862), RC(-0.835810807663404), RC(0.665114177777166), RC(1.16481046518346), RC(-0.11661858889792), RC(-0.387303251022099), RC(0.192633041873135)};
770:     PetscCall(TSDIRKRegister(TSDIRK759A, 7, 9, &A[0][0], b, NULL, bembed, 1, b));
771:   }
772:   {
773:     // SDIRK(11,7)[1]SAL[(11,5)A] from https://github.com/yousefalamri55/High_Order_DIRK_Methods_Coeffs
774:     const PetscReal A[11][11] = {
775:       {RC(0.200252661187742),  RC(0.0),                 RC(0.0),                  RC(0.0),                 RC(0.0),                 RC(0.0),                 RC(0.0),                 RC(0.0),                 RC(0.0),               RC(0.0),               RC(0.0)              },
776:       {RC(-0.082947368165267), RC(0.200252661187742),   RC(0.0),                  RC(0.0),                 RC(0.0),                 RC(0.0),                 RC(0.0),                 RC(0.0),                 RC(0.0),               RC(0.0),               RC(0.0)              },
777:       {RC(0.483452690540751),  RC(0.0),                 RC(0.200252661187742),    RC(0.0),                 RC(0.0),                 RC(0.0),                 RC(0.0),                 RC(0.0),                 RC(0.0),               RC(0.0),               RC(0.0)              },
778:       {RC(0.771076453481321),  RC(-0.22936926341842),   RC(0.289733373208823),    RC(0.200252661187742),   RC(0.0),                 RC(0.0),                 RC(0.0),                 RC(0.0),                 RC(0.0),               RC(0.0),               RC(0.0)              },
779:       {RC(0.0329683054968892), RC(-0.162397421903366),  RC(0.000951777538562805), RC(0.0),                 RC(0.200252661187742),   RC(0.0),                 RC(0.0),                 RC(0.0),                 RC(0.0),               RC(0.0),               RC(0.0)              },
780:       {RC(0.265888743485945),  RC(0.606743151103931),   RC(0.173443800537369),    RC(-0.0433968261546912), RC(-0.385211017224481),  RC(0.200252661187742),   RC(0.0),                 RC(0.0),                 RC(0.0),               RC(0.0),               RC(0.0)              },
781:       {RC(0.220662294551146),  RC(-0.0465078507657608), RC(-0.0333111995282464),  RC(0.011801580836998),   RC(0.169480801030105),   RC(-0.0167974432139385), RC(0.200252661187742),   RC(0.0),                 RC(0.0),               RC(0.0),               RC(0.0)              },
782:       {RC(0.323099728365267),  RC(0.0288371831672575),  RC(-0.0543404318773196),  RC(0.0137765831431662),  RC(0.0516799019060702),  RC(-0.0421359763835713), RC(0.181297932037826),   RC(0.200252661187742),   RC(0.0),               RC(0.0),               RC(0.0)              },
783:       {RC(-0.164226696476538), RC(0.187552004946792),   RC(0.0628674420973025),   RC(-0.0108886582703428), RC(-0.0117628641717889), RC(0.0432176880867965),  RC(-0.0315206836275473), RC(-0.0846007021638797), RC(0.200252661187742), RC(0.0),               RC(0.0)              },
784:       {RC(0.651428598623771),  RC(-0.10208078475356),   RC(0.198305701801888),    RC(-0.0117354096673789), RC(-0.0440385966743686), RC(-0.0358364455795087), RC(-0.0075408087654097), RC(0.160320941654639),   RC(0.017940248694499), RC(0.200252661187742), RC(0.0)              },
785:       {RC(0.0),                RC(-0.266259448580236),  RC(-0.615982357748271),   RC(0.561474126687165),   RC(0.266911112787025),   RC(0.219775952207137),   RC(0.387847665451514),   RC(0.612483137773236),   RC(0.330027015806089), RC(-0.6965298655714),  RC(0.200252661187742)}
786:     };
787:     const PetscReal b[11] =
788:       {RC(0.0), RC(-0.266259448580236), RC(-0.615982357748271), RC(0.561474126687165), RC(0.266911112787025), RC(0.219775952207137), RC(0.387847665451514), RC(0.612483137773236), RC(0.330027015806089), RC(-0.6965298655714), RC(0.200252661187742)};
789:     const PetscReal bembed[11] =
790:       {RC(0.0), RC(0.180185524442613), RC(-0.628869710835338), RC(0.186185675988647), RC(0.0484716652630425), RC(0.203927720607141), RC(0.44041662512573), RC(0.615710527731245), RC(0.0689648839032607), RC(-0.253599870605903), RC(0.138606958379488)};
791:     PetscCall(TSDIRKRegister(TSDIRKS7511SAL, 7, 11, &A[0][0], b, NULL, bembed, 1, b));
792:   }
793:   {
794:     // DIRK(13,8)[1]A[(14,6)A] from https://github.com/yousefalamri55/High_Order_DIRK_Methods_Coeffs
795:     const PetscReal A[14][14] = {
796:       {RC(0.421050745442291),   RC(0.0),                RC(0.0),                 RC(0.0),                  RC(0.0),                  RC(0.0),                RC(0.0),                 RC(0.0),                  RC(0.0),                RC(0.0),                 RC(0.0),                RC(0.0),                RC(0.0),                RC(0.0)               },
797:       {RC(-0.0761079419591268), RC(0.264353986580857),  RC(0.0),                 RC(0.0),                  RC(0.0),                  RC(0.0),                RC(0.0),                 RC(0.0),                  RC(0.0),                RC(0.0),                 RC(0.0),                RC(0.0),                RC(0.0),                RC(0.0)               },
798:       {RC(0.0727106904170694),  RC(-0.204265976977285), RC(0.181608196544136),   RC(0.0),                  RC(0.0),                  RC(0.0),                RC(0.0),                 RC(0.0),                  RC(0.0),                RC(0.0),                 RC(0.0),                RC(0.0),                RC(0.0),                RC(0.0)               },
799:       {RC(0.55763054816611),    RC(-0.409773579543499), RC(0.510926516886944),   RC(0.259892204518476),    RC(0.0),                  RC(0.0),                RC(0.0),                 RC(0.0),                  RC(0.0),                RC(0.0),                 RC(0.0),                RC(0.0),                RC(0.0),                RC(0.0)               },
800:       {RC(0.0228083864844437),  RC(-0.445569051836454), RC(-0.0915242778636248), RC(0.00450055909321655),  RC(0.6397807199983),      RC(0.0),                RC(0.0),                 RC(0.0),                  RC(0.0),                RC(0.0),                 RC(0.0),                RC(0.0),                RC(0.0),                RC(0.0)               },
801:       {RC(-0.135945849505152),  RC(0.0946509646963754), RC(-0.236110197279175),  RC(0.00318944206456517),  RC(0.255453021028118),    RC(0.174805219173446),  RC(0.0),                 RC(0.0),                  RC(0.0),                RC(0.0),                 RC(0.0),                RC(0.0),                RC(0.0),                RC(0.0)               },
802:       {RC(-0.147960260670772),  RC(-0.402188192230535), RC(-0.703014530043888),  RC(0.00941974677418186),  RC(0.885747111289207),    RC(0.261314066449028),  RC(0.16307697503668),    RC(0.0),                  RC(0.0),                RC(0.0),                 RC(0.0),                RC(0.0),                RC(0.0),                RC(0.0)               },
803:       {RC(0.165597241042244),   RC(0.824182962188923),  RC(-0.0280136160783609), RC(0.282372386631758),    RC(-0.957721354131182),   RC(0.489439550159977),  RC(0.170094415598103),   RC(0.0522519785718563),   RC(0.0),                RC(0.0),                 RC(0.0),                RC(0.0),                RC(0.0),                RC(0.0)               },
804:       {RC(0.0335292011495618),  RC(0.575750388029166),  RC(0.223289855356637),   RC(-0.00317458833242804), RC(-0.112890382135193),   RC(-0.419809267954284), RC(0.0466136902102104),  RC(-0.00115413813041085), RC(0.109685363692383),  RC(0.0),                 RC(0.0),                RC(0.0),                RC(0.0),                RC(0.0)               },
805:       {RC(-0.0512616878252355), RC(0.699261265830807),  RC(-0.117939611738769),  RC(0.0021745241931243),   RC(-0.00932826702640947), RC(-0.267575057469428), RC(0.126949139814065),   RC(0.00330353204502163),  RC(0.185949445053766),  RC(0.0938215615963721),  RC(0.0),                RC(0.0),                RC(0.0),                RC(0.0)               },
806:       {RC(-0.106521517960343),  RC(0.41835889096168),   RC(0.353585905881916),   RC(-0.0746474161579599),  RC(-0.015450626460289),   RC(-0.46224659192275),  RC(-0.0576406327329181), RC(-0.00712066942504018), RC(0.377776558014452),  RC(0.36890054338294),    RC(0.0618488746331837), RC(0.0),                RC(0.0),                RC(0.0)               },
807:       {RC(-0.163079104890997),  RC(0.644561721693806),  RC(0.636968661639572),   RC(-0.122346720085377),   RC(-0.333062564990312),   RC(-0.3054226490478),   RC(-0.357820712828352),  RC(-0.0125510510334706),  RC(0.371263681186311),  RC(0.371979640363694),   RC(0.0531090658708968), RC(0.0518279459132049), RC(0.0),                RC(0.0)               },
808:       {RC(0.579993784455521),   RC(-0.188833728676494), RC(0.999975696843775),   RC(0.0572810855901161),   RC(-0.264374735003671),   RC(0.165091739976854),  RC(-0.546675809010452),  RC(-0.0283821822291982),  RC(-0.102639860418374), RC(-0.0343251040446405), RC(0.4762598462591),    RC(-0.304153104931261), RC(0.0953911855943621), RC(0.0)               },
809:       {RC(0.0848552694007844),  RC(0.287193912340074),  RC(0.543683503004232),   RC(-0.081311059300692),   RC(-0.0328661289388557),  RC(-0.323456834372922), RC(-0.240378871658975),  RC(-0.0189913019930369),  RC(0.220663114082036),  RC(0.253029984360864),   RC(0.252011799370563),  RC(-0.154882222605423), RC(0.0315202264687415), RC(0.0514095812104714)}
810:     };
811:     const PetscReal b[14] = {RC(0.0), RC(0.516650324205117), RC(0.0773227217357826), RC(-0.12474204666975), RC(-0.0241052115180679), RC(-0.325821145180359), RC(0.0907237460123951), RC(0.0459271880596652), RC(0.221012259404702), RC(0.235510906761942), RC(0.491109674204385), RC(-0.323506525837343), RC(0.119918108821531), RC(0.0)};
812:     const PetscReal bembed[14] = {RC(2.32345691433618e-16), RC(0.499150900944401), RC(0.080991997189243), RC(-0.0359440417166322), RC(-0.0258910397441454), RC(-0.304540350278636),  RC(0.0836627473632563),
813:                                   RC(0.0417664613347638),   RC(0.223636394275293), RC(0.231569156867596), RC(0.240526201277663),   RC(-0.222933582911926),  RC(-0.0111479879597561), RC(0.19915314335888)};
814:     PetscCall(TSDIRKRegister(TSDIRK8614A, 8, 14, &A[0][0], b, NULL, bembed, 1, b));
815:   }
816:   {
817:     // DIRK(15,8)[1]SAL[(16,6)A] from https://github.com/yousefalamri55/High_Order_DIRK_Methods_Coeffs
818:     const PetscReal A[16][16] = {
819:       {RC(0.498904981271193),   RC(0.0),                  RC(0.0),                 RC(0.0),                  RC(0.0),                RC(0.0),                 RC(0.0),                RC(0.0),                 RC(0.0),                   RC(0.0),                 RC(0.0),                  RC(0.0),                 RC(0.0),               RC(0.0),                 RC(0.0),                 RC(0.0)              },
820:       {RC(-0.303806037341816),  RC(0.886299445992379),    RC(0.0),                 RC(0.0),                  RC(0.0),                RC(0.0),                 RC(0.0),                RC(0.0),                 RC(0.0),                   RC(0.0),                 RC(0.0),                  RC(0.0),                 RC(0.0),               RC(0.0),                 RC(0.0),                 RC(0.0)              },
821:       {RC(-0.581440223471476),  RC(0.371003719460259),    RC(0.43844717752802),    RC(0.0),                  RC(0.0),                RC(0.0),                 RC(0.0),                RC(0.0),                 RC(0.0),                   RC(0.0),                 RC(0.0),                  RC(0.0),                 RC(0.0),               RC(0.0),                 RC(0.0),                 RC(0.0)              },
822:       {RC(0.531852638870051),   RC(-0.339363014907108),   RC(0.422373239795441),   RC(0.223854203543397),    RC(0.0),                RC(0.0),                 RC(0.0),                RC(0.0),                 RC(0.0),                   RC(0.0),                 RC(0.0),                  RC(0.0),                 RC(0.0),               RC(0.0),                 RC(0.0),                 RC(0.0)              },
823:       {RC(0.118517891868867),   RC(-0.0756235584174296),  RC(-0.0864284870668712), RC(0.000536692838658312), RC(0.10101418329932),   RC(0.0),                 RC(0.0),                RC(0.0),                 RC(0.0),                   RC(0.0),                 RC(0.0),                  RC(0.0),                 RC(0.0),               RC(0.0),                 RC(0.0),                 RC(0.0)              },
824:       {RC(0.218733626116401),   RC(-0.139568928299635),   RC(0.30473612813488),    RC(0.00354038623073564),  RC(0.0932085751160559), RC(0.140161806097591),   RC(0.0),                RC(0.0),                 RC(0.0),                   RC(0.0),                 RC(0.0),                  RC(0.0),                 RC(0.0),               RC(0.0),                 RC(0.0),                 RC(0.0)              },
825:       {RC(0.0692944686081835),  RC(-0.0442152168939502),  RC(-0.0903375348855603), RC(0.00259030241156141),  RC(0.204514233679515),  RC(-0.0245383758960002), RC(0.199289437094059),  RC(0.0),                 RC(0.0),                   RC(0.0),                 RC(0.0),                  RC(0.0),                 RC(0.0),               RC(0.0),                 RC(0.0),                 RC(0.0)              },
826:       {RC(0.990640016505571),   RC(-0.632104756315967),   RC(0.856971425234221),   RC(0.174494099232246),    RC(-0.113715829680145), RC(-0.151494045307366),  RC(-0.438268629569005), RC(0.120578398912139),   RC(0.0),                   RC(0.0),                 RC(0.0),                  RC(0.0),                 RC(0.0),               RC(0.0),                 RC(0.0),                 RC(0.0)              },
827:       {RC(-0.099415677713136),  RC(0.211832014309207),    RC(-0.245998265866888),  RC(-0.182249672235861),   RC(0.167897635713799),  RC(0.212850335030069),   RC(-0.391739299440123), RC(-0.0118718506876767), RC(0.526293701659093),     RC(0.0),                 RC(0.0),                  RC(0.0),                 RC(0.0),               RC(0.0),                 RC(0.0),                 RC(0.0)              },
828:       {RC(0.383983914845461),   RC(-0.245011361219604),   RC(0.46717278554955),    RC(-0.0361272447593202),  RC(0.0742234660511333), RC(-0.0474816271948766), RC(-0.229859978525756), RC(0.0516283729206322),  RC(0.0),                   RC(0.193823890777594),   RC(0.0),                  RC(0.0),                 RC(0.0),               RC(0.0),                 RC(0.0),                 RC(0.0)              },
829:       {RC(0.0967855003180134),  RC(-0.0481037037916184),  RC(0.191268138832434),   RC(0.234977164564126),    RC(0.0620265921753097), RC(0.403432826534738),   RC(0.152403846687238),  RC(-0.118420429237746),  RC(0.0582141598685892),    RC(-0.13924540906863),   RC(0.106661313117545),    RC(0.0),                 RC(0.0),               RC(0.0),                 RC(0.0),                 RC(0.0)              },
830:       {RC(0.133941307432055),   RC(-0.0722076602896254),  RC(0.217086297689275),   RC(0.00495499602192887),  RC(0.0306090174933995), RC(0.26483526755746),    RC(0.204442440745605),  RC(0.196883395136708),   RC(0.056527012583996),     RC(-0.150216381356784),  RC(-0.217209415757333),   RC(0.330353722743315),   RC(0.0),               RC(0.0),                 RC(0.0),                 RC(0.0)              },
831:       {RC(0.157014274561299),   RC(-0.0883810256381874),  RC(0.117193033885034),   RC(-0.0362304243769466),  RC(0.0169030211466111), RC(-0.169835753576141),  RC(0.399749979234113),  RC(0.31806704093008),    RC(0.050340008347693),     RC(0.120284837472214),   RC(-0.235313193645423),   RC(0.232488522208926),   RC(0.117719679450729), RC(0.0),                 RC(0.0),                 RC(0.0)              },
832:       {RC(0.00276453816875833), RC(-0.00366028255231782), RC(-0.331078914515559),  RC(0.623377549031949),    RC(0.167618142989491),  RC(0.0748467945312516),  RC(0.797629286699677),  RC(-0.390714256799583),  RC(-0.00808553925131555),  RC(0.014840324980952),   RC(-0.0856180410248133),  RC(0.602943304937827),   RC(-0.5771359338496),  RC(0.112273026653282),   RC(0.0),                 RC(0.0)              },
833:       {RC(0.0),                 RC(0.0),                  RC(0.085283971980307),   RC(0.51334393454179),     RC(0.144355978013514),  RC(0.255379109487853),   RC(0.225075750790524),  RC(-0.343241323394982),  RC(0.0),                   RC(0.0798250392218852),  RC(0.0528824734082655),   RC(-0.0830350888900362), RC(0.022567388707279), RC(-0.0592631119040204), RC(0.106825878037621),   RC(0.0)              },
834:       {RC(0.173784481207652),   RC(-0.110887906116241),   RC(0.190052513365204),   RC(-0.0688345422674029),  RC(0.10326505079603),   RC(0.267127097115219),   RC(0.141703423176897),  RC(0.0117966866651728),  RC(-6.65650091812762e-15), RC(-0.0213725083662519), RC(-0.00931148598712566), RC(-0.10007679077114),   RC(0.123471797451553), RC(0.00203684241073055), RC(-0.0294320891781173), RC(0.195746619921528)}
835:     };
836:     const PetscReal b[16] = {RC(0.0), RC(0.0), RC(0.085283971980307), RC(0.51334393454179), RC(0.144355978013514), RC(0.255379109487853), RC(0.225075750790524), RC(-0.343241323394982), RC(0.0), RC(0.0798250392218852), RC(0.0528824734082655), RC(-0.0830350888900362), RC(0.022567388707279), RC(-0.0592631119040204), RC(0.106825878037621), RC(0.0)};
837:     const PetscReal bembed[16] = {RC(-1.31988512519898e-15), RC(7.53606601764004e-16), RC(0.0886789133915965),   RC(0.0968726531622137),  RC(0.143815375874267),     RC(0.335214773313601),  RC(0.221862366978063),  RC(-0.147408947987273),
838:                                   RC(4.16297599203445e-16),  RC(0.000727276166520566), RC(-0.00284892677941246), RC(0.00512492274297611), RC(-0.000275595071215218), RC(0.0136014719350733), RC(0.0165190013607726), RC(0.228116714912817)};
839:     PetscCall(TSDIRKRegister(TSDIRK8616SAL, 8, 16, &A[0][0], b, NULL, bembed, 1, b));
840:   }
841:   {
842:     // ESDIRK(16,8)[2]SAL[(16,5)] from https://github.com/yousefalamri55/High_Order_DIRK_Methods_Coeffs
843:     const PetscReal A[16][16] = {
844:       {RC(0.0),                  RC(0.0),                 RC(0.0),                  RC(0.0),                   RC(0.0),                  RC(0.0),                  RC(0.0),                  RC(0.0),                RC(0.0),                 RC(0.0),                 RC(0.0),                RC(0.0),                 RC(0.0),                 RC(0.0),                  RC(0.0),               RC(0.0)              },
845:       {RC(0.117318819358521),    RC(0.117318819358521),   RC(0.0),                  RC(0.0),                   RC(0.0),                  RC(0.0),                  RC(0.0),                  RC(0.0),                RC(0.0),                 RC(0.0),                 RC(0.0),                RC(0.0),                 RC(0.0),                 RC(0.0),                  RC(0.0),               RC(0.0)              },
846:       {RC(0.0557014605974616),   RC(0.385525646638742),   RC(0.117318819358521),    RC(0.0),                   RC(0.0),                  RC(0.0),                  RC(0.0),                  RC(0.0),                RC(0.0),                 RC(0.0),                 RC(0.0),                RC(0.0),                 RC(0.0),                 RC(0.0),                  RC(0.0),               RC(0.0)              },
847:       {RC(0.063493276428895),    RC(0.373556126263681),   RC(0.0082994166438953),   RC(0.117318819358521),     RC(0.0),                  RC(0.0),                  RC(0.0),                  RC(0.0),                RC(0.0),                 RC(0.0),                 RC(0.0),                RC(0.0),                 RC(0.0),                 RC(0.0),                  RC(0.0),               RC(0.0)              },
848:       {RC(0.0961351856230088),   RC(0.335558324517178),   RC(0.207077765910132),    RC(-0.0581917140797146),   RC(0.117318819358521),    RC(0.0),                  RC(0.0),                  RC(0.0),                RC(0.0),                 RC(0.0),                 RC(0.0),                RC(0.0),                 RC(0.0),                 RC(0.0),                  RC(0.0),               RC(0.0)              },
849:       {RC(0.0497669214238319),   RC(0.384288616546039),   RC(0.0821728117583936),   RC(0.120337007107103),     RC(0.202262782645888),    RC(0.117318819358521),    RC(0.0),                  RC(0.0),                RC(0.0),                 RC(0.0),                 RC(0.0),                RC(0.0),                 RC(0.0),                 RC(0.0),                  RC(0.0),               RC(0.0)              },
850:       {RC(0.00626710666809847),  RC(0.496491452640725),   RC(-0.111303249827358),   RC(0.170478821683603),     RC(0.166517073971103),    RC(-0.0328669811542241),  RC(0.117318819358521),    RC(0.0),                RC(0.0),                 RC(0.0),                 RC(0.0),                RC(0.0),                 RC(0.0),                 RC(0.0),                  RC(0.0),               RC(0.0)              },
851:       {RC(0.0463439767281591),   RC(0.00306724391019652), RC(-0.00816305222386205), RC(-0.0353302599538294),   RC(0.0139313601702569),   RC(-0.00992014507967429), RC(0.0210087909090165),   RC(0.117318819358521),  RC(0.0),                 RC(0.0),                 RC(0.0),                RC(0.0),                 RC(0.0),                 RC(0.0),                  RC(0.0),               RC(0.0)              },
852:       {RC(0.111574049232048),    RC(0.467639166482209),   RC(0.237773114804619),    RC(0.0798895699267508),    RC(0.109580615914593),    RC(0.0307353103825936),   RC(-0.0404391509541147),  RC(-0.16942110744293),  RC(0.117318819358521),   RC(0.0),                 RC(0.0),                RC(0.0),                 RC(0.0),                 RC(0.0),                  RC(0.0),               RC(0.0)              },
853:       {RC(-0.0107072484863877),  RC(-0.231376703354252),  RC(0.017541113036611),    RC(0.144871527682418),     RC(-0.041855459769806),   RC(0.0841832168332261),   RC(-0.0850020937282192),  RC(0.486170343825899),  RC(-0.0526717116822739), RC(0.117318819358521),   RC(0.0),                RC(0.0),                 RC(0.0),                 RC(0.0),                  RC(0.0),               RC(0.0)              },
854:       {RC(-0.0142238262314935),  RC(0.14752923682514),    RC(0.238235830732566),    RC(0.037950291904103),     RC(0.252075123381518),    RC(0.0474266904224567),   RC(-0.00363139069342027), RC(0.274081442388563),  RC(-0.0599166970745255), RC(-0.0527138812389185), RC(0.117318819358521),  RC(0.0),                 RC(0.0),                 RC(0.0),                  RC(0.0),               RC(0.0)              },
855:       {RC(-0.11837020183211),    RC(-0.635712481821264),  RC(0.239738832602538),    RC(0.330058936651707),     RC(-0.325784087988237),   RC(-0.0506514314589253),  RC(-0.281914404487009),   RC(0.852596345144291),  RC(0.651444614298805),   RC(-0.103476387303591),  RC(-0.354835880209975), RC(0.117318819358521),   RC(0.0),                 RC(0.0),                  RC(0.0),               RC(0.0)              },
856:       {RC(-0.00458164025442349), RC(0.296219694015248),   RC(0.322146049419995),    RC(0.15917778285238),      RC(0.284864871688843),    RC(0.185509526463076),    RC(-0.0784621067883274),  RC(0.166312223692047),  RC(-0.284152486083397),  RC(-0.357125104338944),  RC(0.078437074055306),  RC(0.0884129667114481),  RC(0.117318819358521),   RC(0.0),                  RC(0.0),               RC(0.0)              },
857:       {RC(-0.0545561913848106),  RC(0.675785423442753),   RC(0.423066443201941),    RC(-0.000165300126841193), RC(0.104252994793763),    RC(-0.105763019303021),   RC(-0.15988308809318),    RC(0.0515050001032011), RC(0.56013979290924),    RC(-0.45781539708603),   RC(-0.255870699752664), RC(0.026960254296416),   RC(-0.0721245985053681), RC(0.117318819358521),    RC(0.0),               RC(0.0)              },
858:       {RC(0.0649253995775223),   RC(-0.0216056457922249), RC(-0.073738139377975),   RC(0.0931033310077225),    RC(-0.0194339577299149),  RC(-0.0879623837313009),  RC(0.057125517179467),    RC(0.205120850488097),  RC(0.132576503537441),   RC(0.489416890627328),   RC(-0.1106765720501),   RC(-0.081038793996096),  RC(0.0606031613503788),  RC(-0.00241467937442272), RC(0.117318819358521), RC(0.0)              },
859:       {RC(0.0459979286336779),   RC(0.0780075394482806),  RC(0.015021874148058),    RC(0.195180277284195),     RC(-0.00246643310153235), RC(0.0473977117068314),   RC(-0.0682773558610363),  RC(0.19568019123878),   RC(-0.0876765449323747), RC(0.177874852409192),   RC(-0.337519251582222), RC(-0.0123255553640736), RC(0.311573291192553),   RC(0.0458604327754991),   RC(0.278352222645651), RC(0.117318819358521)}
860:     };
861:     const PetscReal b[16]      = {RC(0.0459979286336779),  RC(0.0780075394482806), RC(0.015021874148058),  RC(0.195180277284195),   RC(-0.00246643310153235), RC(0.0473977117068314), RC(-0.0682773558610363), RC(0.19568019123878),
862:                                   RC(-0.0876765449323747), RC(0.177874852409192),  RC(-0.337519251582222), RC(-0.0123255553640736), RC(0.311573291192553),    RC(0.0458604327754991), RC(0.278352222645651),   RC(0.117318819358521)};
863:     const PetscReal bembed[16] = {RC(0.0603373529853206),   RC(0.175453809423998),  RC(0.0537707777611352), RC(0.195309248607308),  RC(0.0135893741970232), RC(-0.0221160259296707), RC(-0.00726526156430691), RC(0.102961059369124),
864:                                   RC(0.000900215457460583), RC(0.0547959465692338), RC(-0.334995726863153), RC(0.0464409662093384), RC(0.301388101652194),  RC(0.00524851570622031), RC(0.229538601845236),    RC(0.124643044573514)};
865:     PetscCall(TSDIRKRegister(TSDIRKES8516SAL, 8, 16, &A[0][0], b, NULL, bembed, 1, b));
866:   }

868:   /* Additive methods */
869:   {
870:     const PetscReal A[3][3] = {
871:       {0.0, 0.0, 0.0},
872:       {0.0, 0.0, 0.0},
873:       {0.0, 0.5, 0.0}
874:     };
875:     const PetscReal At[3][3] = {
876:       {1.0, 0.0, 0.0},
877:       {0.0, 0.5, 0.0},
878:       {0.0, 0.5, 0.5}
879:     };
880:     const PetscReal b[3]       = {0.0, 0.5, 0.5};
881:     const PetscReal bembedt[3] = {1.0, 0.0, 0.0};
882:     PetscCall(TSARKIMEXRegister(TSARKIMEX1BEE, 2, 3, &At[0][0], b, NULL, &A[0][0], b, NULL, bembedt, bembedt, 1, b, NULL));
883:   }
884:   {
885:     const PetscReal A[2][2] = {
886:       {0.0, 0.0},
887:       {0.5, 0.0}
888:     };
889:     const PetscReal At[2][2] = {
890:       {0.0, 0.0},
891:       {0.0, 0.5}
892:     };
893:     const PetscReal b[2]       = {0.0, 1.0};
894:     const PetscReal bembedt[2] = {0.5, 0.5};
895:     /* binterpt[2][2] = {{1.0,-1.0},{0.0,1.0}};  second order dense output has poor stability properties and hence it is not currently in use */
896:     PetscCall(TSARKIMEXRegister(TSARKIMEXARS122, 2, 2, &At[0][0], b, NULL, &A[0][0], b, NULL, bembedt, bembedt, 1, b, NULL));
897:   }
898:   {
899:     const PetscReal A[2][2] = {
900:       {0.0, 0.0},
901:       {1.0, 0.0}
902:     };
903:     const PetscReal At[2][2] = {
904:       {0.0, 0.0},
905:       {0.5, 0.5}
906:     };
907:     const PetscReal b[2]       = {0.5, 0.5};
908:     const PetscReal bembedt[2] = {0.0, 1.0};
909:     /* binterpt[2][2] = {{1.0,-0.5},{0.0,0.5}}  second order dense output has poor stability properties and hence it is not currently in use */
910:     PetscCall(TSARKIMEXRegister(TSARKIMEXA2, 2, 2, &At[0][0], b, NULL, &A[0][0], b, NULL, bembedt, bembedt, 1, b, NULL));
911:   }
912:   {
913:     const PetscReal A[2][2] = {
914:       {0.0, 0.0},
915:       {1.0, 0.0}
916:     };
917:     const PetscReal At[2][2] = {
918:       {us2,             0.0},
919:       {1.0 - 2.0 * us2, us2}
920:     };
921:     const PetscReal b[2]           = {0.5, 0.5};
922:     const PetscReal bembedt[2]     = {0.0, 1.0};
923:     const PetscReal binterpt[2][2] = {
924:       {(us2 - 1.0) / (2.0 * us2 - 1.0),     -1 / (2.0 * (1.0 - 2.0 * us2))},
925:       {1 - (us2 - 1.0) / (2.0 * us2 - 1.0), -1 / (2.0 * (1.0 - 2.0 * us2))}
926:     };
927:     const PetscReal binterp[2][2] = {
928:       {1.0, -0.5},
929:       {0.0, 0.5 }
930:     };
931:     PetscCall(TSARKIMEXRegister(TSARKIMEXL2, 2, 2, &At[0][0], b, NULL, &A[0][0], b, NULL, bembedt, bembedt, 2, binterpt[0], binterp[0]));
932:   }
933:   {
934:     const PetscReal A[3][3] = {
935:       {0,      0,   0},
936:       {2 - s2, 0,   0},
937:       {0.5,    0.5, 0}
938:     };
939:     const PetscReal At[3][3] = {
940:       {0,            0,            0         },
941:       {1 - 1 / s2,   1 - 1 / s2,   0         },
942:       {1 / (2 * s2), 1 / (2 * s2), 1 - 1 / s2}
943:     };
944:     const PetscReal bembedt[3]     = {(4. - s2) / 8., (4. - s2) / 8., 1 / (2. * s2)};
945:     const PetscReal binterpt[3][2] = {
946:       {1.0 / s2, -1.0 / (2.0 * s2)},
947:       {1.0 / s2, -1.0 / (2.0 * s2)},
948:       {1.0 - s2, 1.0 / s2         }
949:     };
950:     PetscCall(TSARKIMEXRegister(TSARKIMEX2C, 2, 3, &At[0][0], NULL, NULL, &A[0][0], NULL, NULL, bembedt, bembedt, 2, binterpt[0], NULL));
951:   }
952:   {
953:     const PetscReal A[3][3] = {
954:       {0,      0,    0},
955:       {2 - s2, 0,    0},
956:       {0.75,   0.25, 0}
957:     };
958:     const PetscReal At[3][3] = {
959:       {0,            0,            0         },
960:       {1 - 1 / s2,   1 - 1 / s2,   0         },
961:       {1 / (2 * s2), 1 / (2 * s2), 1 - 1 / s2}
962:     };
963:     const PetscReal bembedt[3]     = {(4. - s2) / 8., (4. - s2) / 8., 1 / (2. * s2)};
964:     const PetscReal binterpt[3][2] = {
965:       {1.0 / s2, -1.0 / (2.0 * s2)},
966:       {1.0 / s2, -1.0 / (2.0 * s2)},
967:       {1.0 - s2, 1.0 / s2         }
968:     };
969:     PetscCall(TSARKIMEXRegister(TSARKIMEX2D, 2, 3, &At[0][0], NULL, NULL, &A[0][0], NULL, NULL, bembedt, bembedt, 2, binterpt[0], NULL));
970:   }
971:   { /* Optimal for linear implicit part */
972:     const PetscReal A[3][3] = {
973:       {0,                0,                0},
974:       {2 - s2,           0,                0},
975:       {(3 - 2 * s2) / 6, (3 + 2 * s2) / 6, 0}
976:     };
977:     const PetscReal At[3][3] = {
978:       {0,            0,            0         },
979:       {1 - 1 / s2,   1 - 1 / s2,   0         },
980:       {1 / (2 * s2), 1 / (2 * s2), 1 - 1 / s2}
981:     };
982:     const PetscReal bembedt[3]     = {(4. - s2) / 8., (4. - s2) / 8., 1 / (2. * s2)};
983:     const PetscReal binterpt[3][2] = {
984:       {1.0 / s2, -1.0 / (2.0 * s2)},
985:       {1.0 / s2, -1.0 / (2.0 * s2)},
986:       {1.0 - s2, 1.0 / s2         }
987:     };
988:     PetscCall(TSARKIMEXRegister(TSARKIMEX2E, 2, 3, &At[0][0], NULL, NULL, &A[0][0], NULL, NULL, bembedt, bembedt, 2, binterpt[0], NULL));
989:   }
990:   { /* Optimal for linear implicit part */
991:     const PetscReal A[3][3] = {
992:       {0,   0,   0},
993:       {0.5, 0,   0},
994:       {0.5, 0.5, 0}
995:     };
996:     const PetscReal At[3][3] = {
997:       {0.25,   0,      0     },
998:       {0,      0.25,   0     },
999:       {1. / 3, 1. / 3, 1. / 3}
1000:     };
1001:     PetscCall(TSARKIMEXRegister(TSARKIMEXPRSSP2, 2, 3, &At[0][0], NULL, NULL, &A[0][0], NULL, NULL, NULL, NULL, 0, NULL, NULL));
1002:   }
1003:   {
1004:     const PetscReal A[4][4] = {
1005:       {0,                                0,                                0,                                 0},
1006:       {1767732205903. / 2027836641118.,  0,                                0,                                 0},
1007:       {5535828885825. / 10492691773637., 788022342437. / 10882634858940.,  0,                                 0},
1008:       {6485989280629. / 16251701735622., -4246266847089. / 9704473918619., 10755448449292. / 10357097424841., 0}
1009:     };
1010:     const PetscReal At[4][4] = {
1011:       {0,                                0,                                0,                                 0                              },
1012:       {1767732205903. / 4055673282236.,  1767732205903. / 4055673282236.,  0,                                 0                              },
1013:       {2746238789719. / 10658868560708., -640167445237. / 6845629431997.,  1767732205903. / 4055673282236.,   0                              },
1014:       {1471266399579. / 7840856788654.,  -4482444167858. / 7529755066697., 11266239266428. / 11593286722821., 1767732205903. / 4055673282236.}
1015:     };
1016:     const PetscReal bembedt[4]     = {2756255671327. / 12835298489170., -10771552573575. / 22201958757719., 9247589265047. / 10645013368117., 2193209047091. / 5459859503100.};
1017:     const PetscReal binterpt[4][2] = {
1018:       {4655552711362. / 22874653954995.,  -215264564351. / 13552729205753.  },
1019:       {-18682724506714. / 9892148508045., 17870216137069. / 13817060693119. },
1020:       {34259539580243. / 13192909600954., -28141676662227. / 17317692491321.},
1021:       {584795268549. / 6622622206610.,    2508943948391. / 7218656332882.   }
1022:     };
1023:     PetscCall(TSARKIMEXRegister(TSARKIMEX3, 3, 4, &At[0][0], NULL, NULL, &A[0][0], NULL, NULL, bembedt, bembedt, 2, binterpt[0], NULL));
1024:   }
1025:   {
1026:     const PetscReal A[5][5] = {
1027:       {0,        0,       0,      0,       0},
1028:       {1. / 2,   0,       0,      0,       0},
1029:       {11. / 18, 1. / 18, 0,      0,       0},
1030:       {5. / 6,   -5. / 6, .5,     0,       0},
1031:       {1. / 4,   7. / 4,  3. / 4, -7. / 4, 0}
1032:     };
1033:     const PetscReal At[5][5] = {
1034:       {0, 0,       0,       0,      0     },
1035:       {0, 1. / 2,  0,       0,      0     },
1036:       {0, 1. / 6,  1. / 2,  0,      0     },
1037:       {0, -1. / 2, 1. / 2,  1. / 2, 0     },
1038:       {0, 3. / 2,  -3. / 2, 1. / 2, 1. / 2}
1039:     };
1040:     PetscCall(TSARKIMEXRegister(TSARKIMEXARS443, 3, 5, &At[0][0], NULL, NULL, &A[0][0], NULL, NULL, NULL, NULL, 0, NULL, NULL));
1041:   }
1042:   {
1043:     const PetscReal A[5][5] = {
1044:       {0,      0,      0,      0, 0},
1045:       {1,      0,      0,      0, 0},
1046:       {4. / 9, 2. / 9, 0,      0, 0},
1047:       {1. / 4, 0,      3. / 4, 0, 0},
1048:       {1. / 4, 0,      3. / 5, 0, 0}
1049:     };
1050:     const PetscReal At[5][5] = {
1051:       {0,       0,       0,   0,   0 },
1052:       {.5,      .5,      0,   0,   0 },
1053:       {5. / 18, -1. / 9, .5,  0,   0 },
1054:       {.5,      0,       0,   .5,  0 },
1055:       {.25,     0,       .75, -.5, .5}
1056:     };
1057:     PetscCall(TSARKIMEXRegister(TSARKIMEXBPR3, 3, 5, &At[0][0], NULL, NULL, &A[0][0], NULL, NULL, NULL, NULL, 0, NULL, NULL));
1058:   }
1059:   {
1060:     const PetscReal A[6][6] = {
1061:       {0,                               0,                                 0,                                 0,                                0,              0},
1062:       {1. / 2,                          0,                                 0,                                 0,                                0,              0},
1063:       {13861. / 62500.,                 6889. / 62500.,                    0,                                 0,                                0,              0},
1064:       {-116923316275. / 2393684061468., -2731218467317. / 15368042101831., 9408046702089. / 11113171139209.,  0,                                0,              0},
1065:       {-451086348788. / 2902428689909., -2682348792572. / 7519795681897.,  12662868775082. / 11960479115383., 3355817975965. / 11060851509271., 0,              0},
1066:       {647845179188. / 3216320057751.,  73281519250. / 8382639484533.,     552539513391. / 3454668386233.,    3354512671639. / 8306763924573.,  4040. / 17871., 0}
1067:     };
1068:     const PetscReal At[6][6] = {
1069:       {0,                            0,                       0,                       0,                   0,             0     },
1070:       {1. / 4,                       1. / 4,                  0,                       0,                   0,             0     },
1071:       {8611. / 62500.,               -1743. / 31250.,         1. / 4,                  0,                   0,             0     },
1072:       {5012029. / 34652500.,         -654441. / 2922500.,     174375. / 388108.,       1. / 4,              0,             0     },
1073:       {15267082809. / 155376265600., -71443401. / 120774400., 730878875. / 902184768., 2285395. / 8070912., 1. / 4,        0     },
1074:       {82889. / 524892.,             0,                       15625. / 83664.,         69875. / 102672.,    -2260. / 8211, 1. / 4}
1075:     };
1076:     const PetscReal bembedt[6]     = {4586570599. / 29645900160., 0, 178811875. / 945068544., 814220225. / 1159782912., -3700637. / 11593932., 61727. / 225920.};
1077:     const PetscReal binterpt[6][3] = {
1078:       {6943876665148. / 7220017795957.,   -54480133. / 30881146., 6818779379841. / 7100303317025.  },
1079:       {0,                                 0,                      0                                },
1080:       {7640104374378. / 9702883013639.,   -11436875. / 14766696., 2173542590792. / 12501825683035. },
1081:       {-20649996744609. / 7521556579894., 174696575. / 18121608., -31592104683404. / 5083833661969.},
1082:       {8854892464581. / 2390941311638.,   -12120380. / 966161.,   61146701046299. / 7138195549469. },
1083:       {-11397109935349. / 6675773540249., 3843. / 706.,           -17219254887155. / 4939391667607.}
1084:     };
1085:     PetscCall(TSARKIMEXRegister(TSARKIMEX4, 4, 6, &At[0][0], NULL, NULL, &A[0][0], NULL, NULL, bembedt, bembedt, 3, binterpt[0], NULL));
1086:   }
1087:   {
1088:     const PetscReal A[8][8] = {
1089:       {0,                                  0,                              0,                                 0,                                  0,                               0,                                 0,                               0},
1090:       {41. / 100,                          0,                              0,                                 0,                                  0,                               0,                                 0,                               0},
1091:       {367902744464. / 2072280473677.,     677623207551. / 8224143866563., 0,                                 0,                                  0,                               0,                                 0,                               0},
1092:       {1268023523408. / 10340822734521.,   0,                              1029933939417. / 13636558850479.,  0,                                  0,                               0,                                 0,                               0},
1093:       {14463281900351. / 6315353703477.,   0,                              66114435211212. / 5879490589093.,  -54053170152839. / 4284798021562.,  0,                               0,                                 0,                               0},
1094:       {14090043504691. / 34967701212078.,  0,                              15191511035443. / 11219624916014., -18461159152457. / 12425892160975., -281667163811. / 9011619295870., 0,                                 0,                               0},
1095:       {19230459214898. / 13134317526959.,  0,                              21275331358303. / 2942455364971.,  -38145345988419. / 4862620318723.,  -1. / 8,                         -1. / 8,                           0,                               0},
1096:       {-19977161125411. / 11928030595625., 0,                              -40795976796054. / 6384907823539., 177454434618887. / 12078138498510., 782672205425. / 8267701900261.,  -69563011059811. / 9646580694205., 7356628210526. / 4942186776405., 0}
1097:     };
1098:     const PetscReal At[8][8] = {
1099:       {0,                                0,                                0,                                 0,                                  0,                                0,                                  0,                                 0         },
1100:       {41. / 200.,                       41. / 200.,                       0,                                 0,                                  0,                                0,                                  0,                                 0         },
1101:       {41. / 400.,                       -567603406766. / 11931857230679., 41. / 200.,                        0,                                  0,                                0,                                  0,                                 0         },
1102:       {683785636431. / 9252920307686.,   0,                                -110385047103. / 1367015193373.,   41. / 200.,                         0,                                0,                                  0,                                 0         },
1103:       {3016520224154. / 10081342136671., 0,                                30586259806659. / 12414158314087., -22760509404356. / 11113319521817., 41. / 200.,                       0,                                  0,                                 0         },
1104:       {218866479029. / 1489978393911.,   0,                                638256894668. / 5436446318841.,    -1179710474555. / 5321154724896.,   -60928119172. / 8023461067671.,   41. / 200.,                         0,                                 0         },
1105:       {1020004230633. / 5715676835656.,  0,                                25762820946817. / 25263940353407., -2161375909145. / 9755907335909.,   -211217309593. / 5846859502534.,  -4269925059573. / 7827059040749.,   41. / 200,                         0         },
1106:       {-872700587467. / 9133579230613.,  0,                                0,                                 22348218063261. / 9555858737531.,   -1143369518992. / 8141816002931., -39379526789629. / 19018526304540., 32727382324388. / 42900044865799., 41. / 200.}
1107:     };
1108:     const PetscReal bembedt[8]     = {-975461918565. / 9796059967033., 0, 0, 78070527104295. / 32432590147079., -548382580838. / 3424219808633., -33438840321285. / 15594753105479., 3629800801594. / 4656183773603., 4035322873751. / 18575991585200.};
1109:     const PetscReal binterpt[8][3] = {
1110:       {-17674230611817. / 10670229744614., 43486358583215. / 12773830924787.,  -9257016797708. / 5021505065439. },
1111:       {0,                                  0,                                  0                                },
1112:       {0,                                  0,                                  0                                },
1113:       {65168852399939. / 7868540260826.,   -91478233927265. / 11067650958493., 26096422576131. / 11239449250142.},
1114:       {15494834004392. / 5936557850923.,   -79368583304911. / 10890268929626., 92396832856987. / 20362823103730.},
1115:       {-99329723586156. / 26959484932159., -12239297817655. / 9152339842473.,  30029262896817. / 10175596800299.},
1116:       {-19024464361622. / 5461577185407.,  115839755401235. / 10719374521269., -26136350496073. / 3983972220547.},
1117:       {-6511271360970. / 6095937251113.,   5843115559534. / 2180450260947.,    -5289405421727. / 3760307252460. }
1118:     };
1119:     PetscCall(TSARKIMEXRegister(TSARKIMEX5, 5, 8, &At[0][0], NULL, NULL, &A[0][0], NULL, NULL, bembedt, bembedt, 3, binterpt[0], NULL));
1120:   }
1121: #undef RC
1122: #undef us2
1123: #undef s2
1124:   PetscFunctionReturn(PETSC_SUCCESS);
1125: }

1127: /*@C
1128:   TSARKIMEXRegisterDestroy - Frees the list of schemes that were registered by `TSARKIMEXRegister()`.

1130:   Not Collective

1132:   Level: advanced

1134: .seealso: [](ch_ts), `TSARKIMEX`, `TSARKIMEXRegister()`, `TSARKIMEXRegisterAll()`
1135: @*/
1136: PetscErrorCode TSARKIMEXRegisterDestroy(void)
1137: {
1138:   ARKTableauLink link;

1140:   PetscFunctionBegin;
1141:   while ((link = ARKTableauList)) {
1142:     ARKTableau t   = &link->tab;
1143:     ARKTableauList = link->next;
1144:     PetscCall(PetscFree6(t->At, t->bt, t->ct, t->A, t->b, t->c));
1145:     PetscCall(PetscFree2(t->bembedt, t->bembed));
1146:     PetscCall(PetscFree2(t->binterpt, t->binterp));
1147:     PetscCall(PetscFree(t->name));
1148:     PetscCall(PetscFree(link));
1149:   }
1150:   TSARKIMEXRegisterAllCalled = PETSC_FALSE;
1151:   PetscFunctionReturn(PETSC_SUCCESS);
1152: }

1154: /*@C
1155:   TSARKIMEXInitializePackage - This function initializes everything in the `TSARKIMEX` package. It is called
1156:   from `TSInitializePackage()`.

1158:   Level: developer

1160: .seealso: [](ch_ts), `PetscInitialize()`, `TSARKIMEXFinalizePackage()`
1161: @*/
1162: PetscErrorCode TSARKIMEXInitializePackage(void)
1163: {
1164:   PetscFunctionBegin;
1165:   if (TSARKIMEXPackageInitialized) PetscFunctionReturn(PETSC_SUCCESS);
1166:   TSARKIMEXPackageInitialized = PETSC_TRUE;
1167:   PetscCall(TSARKIMEXRegisterAll());
1168:   PetscCall(PetscRegisterFinalize(TSARKIMEXFinalizePackage));
1169:   PetscFunctionReturn(PETSC_SUCCESS);
1170: }

1172: /*@C
1173:   TSARKIMEXFinalizePackage - This function destroys everything in the `TSARKIMEX` package. It is
1174:   called from `PetscFinalize()`.

1176:   Level: developer

1178: .seealso: [](ch_ts), `PetscFinalize()`, `TSARKIMEXInitializePackage()`
1179: @*/
1180: PetscErrorCode TSARKIMEXFinalizePackage(void)
1181: {
1182:   PetscFunctionBegin;
1183:   TSARKIMEXPackageInitialized = PETSC_FALSE;
1184:   PetscCall(TSARKIMEXRegisterDestroy());
1185:   PetscFunctionReturn(PETSC_SUCCESS);
1186: }

1188: /*@C
1189:   TSARKIMEXRegister - register a `TSARKIMEX` scheme by providing the entries in the Butcher tableau and optionally embedded approximations and interpolation

1191:   Logically Collective.

1193:   Input Parameters:
1194: + name     - identifier for method
1195: . order    - approximation order of method
1196: . s        - number of stages, this is the dimension of the matrices below
1197: . At       - Butcher table of stage coefficients for stiff part (dimension s*s, row-major)
1198: . bt       - Butcher table for completing the stiff part of the step (dimension s; NULL to use the last row of At)
1199: . ct       - Abscissa of each stiff stage (dimension s, NULL to use row sums of At)
1200: . A        - Non-stiff stage coefficients (dimension s*s, row-major)
1201: . b        - Non-stiff step completion table (dimension s; NULL to use last row of At)
1202: . c        - Non-stiff abscissa (dimension s; NULL to use row sums of A)
1203: . bembedt  - Stiff part of completion table for embedded method (dimension s; NULL if not available)
1204: . bembed   - Non-stiff part of completion table for embedded method (dimension s; NULL to use bembedt if provided)
1205: . pinterp  - Order of the interpolation scheme, equal to the number of columns of binterpt and binterp
1206: . binterpt - Coefficients of the interpolation formula for the stiff part (dimension s*pinterp)
1207: - binterp  - Coefficients of the interpolation formula for the non-stiff part (dimension s*pinterp; NULL to reuse binterpt)

1209:   Level: advanced

1211:   Note:
1212:   Several `TSARKIMEX` methods are provided, this function is only needed to create new methods.

1214: .seealso: [](ch_ts), `TSARKIMEX`, `TSType`, `TS`
1215: @*/
1216: PetscErrorCode TSARKIMEXRegister(TSARKIMEXType name, PetscInt order, PetscInt s, const PetscReal At[], const PetscReal bt[], const PetscReal ct[], const PetscReal A[], const PetscReal b[], const PetscReal c[], const PetscReal bembedt[], const PetscReal bembed[], PetscInt pinterp, const PetscReal binterpt[], const PetscReal binterp[])
1217: {
1218:   ARKTableauLink link;
1219:   ARKTableau     t;
1220:   PetscInt       i, j;

1222:   PetscFunctionBegin;
1223:   PetscCall(TSARKIMEXInitializePackage());
1224:   for (link = ARKTableauList; link; link = link->next) {
1225:     PetscBool match;

1227:     PetscCall(PetscStrcmp(link->tab.name, name, &match));
1228:     PetscCheck(!match, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Method with name \"%s\" already registered", name);
1229:   }
1230:   PetscCall(PetscNew(&link));
1231:   t = &link->tab;
1232:   PetscCall(PetscStrallocpy(name, &t->name));
1233:   t->order = order;
1234:   t->s     = s;
1235:   PetscCall(PetscMalloc6(s * s, &t->At, s, &t->bt, s, &t->ct, s * s, &t->A, s, &t->b, s, &t->c));
1236:   PetscCall(PetscArraycpy(t->At, At, s * s));
1237:   if (A) {
1238:     PetscCall(PetscArraycpy(t->A, A, s * s));
1239:     t->additive = PETSC_TRUE;
1240:   }

1242:   if (bt) PetscCall(PetscArraycpy(t->bt, bt, s));
1243:   else
1244:     for (i = 0; i < s; i++) t->bt[i] = At[(s - 1) * s + i];

1246:   if (t->additive) {
1247:     if (b) PetscCall(PetscArraycpy(t->b, b, s));
1248:     else
1249:       for (i = 0; i < s; i++) t->b[i] = t->bt[i];
1250:   } else PetscCall(PetscArrayzero(t->b, s));

1252:   if (ct) PetscCall(PetscArraycpy(t->ct, ct, s));
1253:   else
1254:     for (i = 0; i < s; i++)
1255:       for (j = 0, t->ct[i] = 0; j < s; j++) t->ct[i] += At[i * s + j];

1257:   if (t->additive) {
1258:     if (c) PetscCall(PetscArraycpy(t->c, c, s));
1259:     else
1260:       for (i = 0; i < s; i++)
1261:         for (j = 0, t->c[i] = 0; j < s; j++) t->c[i] += A[i * s + j];
1262:   } else PetscCall(PetscArrayzero(t->c, s));

1264:   t->stiffly_accurate = PETSC_TRUE;
1265:   for (i = 0; i < s; i++)
1266:     if (t->At[(s - 1) * s + i] != t->bt[i]) t->stiffly_accurate = PETSC_FALSE;

1268:   t->explicit_first_stage = PETSC_TRUE;
1269:   for (i = 0; i < s; i++)
1270:     if (t->At[i] != 0.0) t->explicit_first_stage = PETSC_FALSE;

1272:   /* def of FSAL can be made more precise */
1273:   t->FSAL_implicit = (PetscBool)(t->explicit_first_stage && t->stiffly_accurate);

1275:   if (bembedt) {
1276:     PetscCall(PetscMalloc2(s, &t->bembedt, s, &t->bembed));
1277:     PetscCall(PetscArraycpy(t->bembedt, bembedt, s));
1278:     PetscCall(PetscArraycpy(t->bembed, bembed ? bembed : bembedt, s));
1279:   }

1281:   t->pinterp = pinterp;
1282:   PetscCall(PetscMalloc2(s * pinterp, &t->binterpt, s * pinterp, &t->binterp));
1283:   PetscCall(PetscArraycpy(t->binterpt, binterpt, s * pinterp));
1284:   PetscCall(PetscArraycpy(t->binterp, binterp ? binterp : binterpt, s * pinterp));

1286:   link->next     = ARKTableauList;
1287:   ARKTableauList = link;
1288:   PetscFunctionReturn(PETSC_SUCCESS);
1289: }

1291: /*@C
1292:   TSDIRKRegister - register a `TSDIRK` scheme by providing the entries in its Butcher tableau and, optionally, embedded approximations and interpolation

1294:   Logically Collective.

1296:   Input Parameters:
1297: + name     - identifier for method
1298: . order    - approximation order of method
1299: . s        - number of stages, this is the dimension of the matrices below
1300: . At       - Butcher table of stage coefficients (dimension `s`*`s`, row-major order)
1301: . bt       - Butcher table for completing the step (dimension `s`; pass `NULL` to use the last row of `At`)
1302: . ct       - Abscissa of each stage (dimension s, NULL to use row sums of At)
1303: . bembedt  - Stiff part of completion table for embedded method (dimension s; `NULL` if not available)
1304: . pinterp  - Order of the interpolation scheme, equal to the number of columns of `binterpt` and `binterp`
1305: - binterpt - Coefficients of the interpolation formula (dimension s*pinterp)

1307:   Level: advanced

1309:   Note:
1310:   Several `TSDIRK` methods are provided, the use of this function is only needed to create new methods.

1312: .seealso: [](ch_ts), `TSDIRK`, `TSType`, `TS`
1313: @*/
1314: PetscErrorCode TSDIRKRegister(TSDIRKType name, PetscInt order, PetscInt s, const PetscReal At[], const PetscReal bt[], const PetscReal ct[], const PetscReal bembedt[], PetscInt pinterp, const PetscReal binterpt[])
1315: {
1316:   PetscFunctionBegin;
1317:   PetscCall(TSARKIMEXRegister(name, order, s, At, bt, ct, NULL, NULL, NULL, bembedt, NULL, pinterp, binterpt, NULL));
1318:   PetscFunctionReturn(PETSC_SUCCESS);
1319: }

1321: /*
1322:  The step completion formula is

1324:  x1 = x0 - h bt^T YdotI + h b^T YdotRHS

1326:  This function can be called before or after ts->vec_sol has been updated.
1327:  Suppose we have a completion formula (bt,b) and an embedded formula (bet,be) of different order.
1328:  We can write

1330:  x1e = x0 - h bet^T YdotI + h be^T YdotRHS
1331:      = x1 + h bt^T YdotI - h b^T YdotRHS - h bet^T YdotI + h be^T YdotRHS
1332:      = x1 - h (bet - bt)^T YdotI + h (be - b)^T YdotRHS

1334:  so we can evaluate the method with different order even after the step has been optimistically completed.
1335: */
1336: static PetscErrorCode TSEvaluateStep_ARKIMEX(TS ts, PetscInt order, Vec X, PetscBool *done)
1337: {
1338:   TS_ARKIMEX  *ark = (TS_ARKIMEX *)ts->data;
1339:   ARKTableau   tab = ark->tableau;
1340:   PetscScalar *w   = ark->work;
1341:   PetscReal    h;
1342:   PetscInt     s = tab->s, j;
1343:   PetscBool    hasE;

1345:   PetscFunctionBegin;
1346:   switch (ark->status) {
1347:   case TS_STEP_INCOMPLETE:
1348:   case TS_STEP_PENDING:
1349:     h = ts->time_step;
1350:     break;
1351:   case TS_STEP_COMPLETE:
1352:     h = ts->ptime - ts->ptime_prev;
1353:     break;
1354:   default:
1355:     SETERRQ(PetscObjectComm((PetscObject)ts), PETSC_ERR_PLIB, "Invalid TSStepStatus");
1356:   }
1357:   if (order == tab->order) {
1358:     if (ark->status == TS_STEP_INCOMPLETE) {
1359:       if (!ark->imex && tab->stiffly_accurate) { /* Only the stiffly accurate implicit formula is used */
1360:         PetscCall(VecCopy(ark->Y[s - 1], X));
1361:       } else { /* Use the standard completion formula (bt,b) */
1362:         PetscCall(VecCopy(ts->vec_sol, X));
1363:         for (j = 0; j < s; j++) w[j] = h * tab->bt[j];
1364:         PetscCall(VecMAXPY(X, s, w, ark->YdotI));
1365:         if (tab->additive && ark->imex) { /* Method is IMEX, complete the explicit formula */
1366:           PetscCall(TSHasRHSFunction(ts, &hasE));
1367:           if (hasE) {
1368:             for (j = 0; j < s; j++) w[j] = h * tab->b[j];
1369:             PetscCall(VecMAXPY(X, s, w, ark->YdotRHS));
1370:           }
1371:         }
1372:       }
1373:     } else PetscCall(VecCopy(ts->vec_sol, X));
1374:     if (done) *done = PETSC_TRUE;
1375:     PetscFunctionReturn(PETSC_SUCCESS);
1376:   } else if (order == tab->order - 1) {
1377:     if (!tab->bembedt) goto unavailable;
1378:     if (ark->status == TS_STEP_INCOMPLETE) { /* Complete with the embedded method (bet,be) */
1379:       PetscCall(VecCopy(ts->vec_sol, X));
1380:       for (j = 0; j < s; j++) w[j] = h * tab->bembedt[j];
1381:       PetscCall(VecMAXPY(X, s, w, ark->YdotI));
1382:       if (tab->additive) {
1383:         PetscCall(TSHasRHSFunction(ts, &hasE));
1384:         if (hasE) {
1385:           for (j = 0; j < s; j++) w[j] = h * tab->bembed[j];
1386:           PetscCall(VecMAXPY(X, s, w, ark->YdotRHS));
1387:         }
1388:       }
1389:     } else { /* Rollback and re-complete using (bet-be,be-b) */
1390:       PetscCall(VecCopy(ts->vec_sol, X));
1391:       for (j = 0; j < s; j++) w[j] = h * (tab->bembedt[j] - tab->bt[j]);
1392:       PetscCall(VecMAXPY(X, tab->s, w, ark->YdotI));
1393:       if (tab->additive) {
1394:         PetscCall(TSHasRHSFunction(ts, &hasE));
1395:         if (hasE) {
1396:           for (j = 0; j < s; j++) w[j] = h * (tab->bembed[j] - tab->b[j]);
1397:           PetscCall(VecMAXPY(X, s, w, ark->YdotRHS));
1398:         }
1399:       }
1400:     }
1401:     if (done) *done = PETSC_TRUE;
1402:     PetscFunctionReturn(PETSC_SUCCESS);
1403:   }
1404: unavailable:
1405:   if (done) *done = PETSC_FALSE;
1406:   else
1407:     SETERRQ(PetscObjectComm((PetscObject)ts), PETSC_ERR_SUP, "ARKIMEX '%s' of order %" PetscInt_FMT " cannot evaluate step at order %" PetscInt_FMT ". Consider using -ts_adapt_type none or a different method that has an embedded estimate.", tab->name,
1408:             tab->order, order);
1409:   PetscFunctionReturn(PETSC_SUCCESS);
1410: }

1412: static PetscErrorCode TSARKIMEXTestMassIdentity(TS ts, PetscBool *id)
1413: {
1414:   Vec         Udot, Y1, Y2;
1415:   TS_ARKIMEX *ark = (TS_ARKIMEX *)ts->data;
1416:   PetscReal   norm;

1418:   PetscFunctionBegin;
1419:   PetscCall(VecDuplicate(ts->vec_sol, &Udot));
1420:   PetscCall(VecDuplicate(ts->vec_sol, &Y1));
1421:   PetscCall(VecDuplicate(ts->vec_sol, &Y2));
1422:   PetscCall(TSComputeIFunction(ts, ts->ptime, ts->vec_sol, Udot, Y1, ark->imex));
1423:   PetscCall(VecSetRandom(Udot, NULL));
1424:   PetscCall(TSComputeIFunction(ts, ts->ptime, ts->vec_sol, Udot, Y2, ark->imex));
1425:   PetscCall(VecAXPY(Y2, -1.0, Y1));
1426:   PetscCall(VecAXPY(Y2, -1.0, Udot));
1427:   PetscCall(VecNorm(Y2, NORM_2, &norm));
1428:   if (norm < 100.0 * PETSC_MACHINE_EPSILON) {
1429:     *id = PETSC_TRUE;
1430:   } else {
1431:     *id = PETSC_FALSE;
1432:     PetscCall(PetscInfo((PetscObject)ts, "IFunction(Udot = random) - IFunction(Udot = 0) is not near Udot, %g, suspect mass matrix implied in IFunction() is not the identity as required\n", (double)norm));
1433:   }
1434:   PetscCall(VecDestroy(&Udot));
1435:   PetscCall(VecDestroy(&Y1));
1436:   PetscCall(VecDestroy(&Y2));
1437:   PetscFunctionReturn(PETSC_SUCCESS);
1438: }

1440: static PetscErrorCode TSRollBack_ARKIMEX(TS ts)
1441: {
1442:   TS_ARKIMEX      *ark = (TS_ARKIMEX *)ts->data;
1443:   ARKTableau       tab = ark->tableau;
1444:   const PetscInt   s   = tab->s;
1445:   const PetscReal *bt = tab->bt, *b = tab->b;
1446:   PetscScalar     *w     = ark->work;
1447:   Vec             *YdotI = ark->YdotI, *YdotRHS = ark->YdotRHS;
1448:   PetscInt         j;
1449:   PetscReal        h;

1451:   PetscFunctionBegin;
1452:   switch (ark->status) {
1453:   case TS_STEP_INCOMPLETE:
1454:   case TS_STEP_PENDING:
1455:     h = ts->time_step;
1456:     break;
1457:   case TS_STEP_COMPLETE:
1458:     h = ts->ptime - ts->ptime_prev;
1459:     break;
1460:   default:
1461:     SETERRQ(PetscObjectComm((PetscObject)ts), PETSC_ERR_PLIB, "Invalid TSStepStatus");
1462:   }
1463:   for (j = 0; j < s; j++) w[j] = -h * bt[j];
1464:   PetscCall(VecMAXPY(ts->vec_sol, s, w, YdotI));
1465:   if (tab->additive) {
1466:     PetscBool hasE;

1468:     PetscCall(TSHasRHSFunction(ts, &hasE));
1469:     if (hasE) {
1470:       for (j = 0; j < s; j++) w[j] = -h * b[j];
1471:       PetscCall(VecMAXPY(ts->vec_sol, s, w, YdotRHS));
1472:     }
1473:   }
1474:   PetscFunctionReturn(PETSC_SUCCESS);
1475: }

1477: static PetscErrorCode TSStep_ARKIMEX(TS ts)
1478: {
1479:   TS_ARKIMEX      *ark = (TS_ARKIMEX *)ts->data;
1480:   ARKTableau       tab = ark->tableau;
1481:   const PetscInt   s   = tab->s;
1482:   const PetscReal *At = tab->At, *A = tab->A, *ct = tab->ct, *c = tab->c;
1483:   PetscScalar     *w = ark->work;
1484:   Vec             *Y = ark->Y, *YdotI = ark->YdotI, *YdotRHS = ark->YdotRHS, Ydot = ark->Ydot, Ydot0 = ark->Ydot0, Z = ark->Z;
1485:   PetscBool        extrapolate = ark->extrapolate;
1486:   TSAdapt          adapt;
1487:   SNES             snes;
1488:   PetscInt         i, j, its, lits;
1489:   PetscInt         rejections = 0;
1490:   PetscBool        hasE = PETSC_FALSE, dirk = (PetscBool)(!tab->additive), stageok, accept = PETSC_TRUE;
1491:   PetscReal        next_time_step = ts->time_step;

1493:   PetscFunctionBegin;
1494:   if (ark->extrapolate && !ark->Y_prev) {
1495:     PetscCall(VecDuplicateVecs(ts->vec_sol, tab->s, &ark->Y_prev));
1496:     PetscCall(VecDuplicateVecs(ts->vec_sol, tab->s, &ark->YdotI_prev));
1497:     if (tab->additive) PetscCall(VecDuplicateVecs(ts->vec_sol, tab->s, &ark->YdotRHS_prev));
1498:   }

1500:   if (!dirk) PetscCall(TSHasRHSFunction(ts, &hasE));
1501:   if (!hasE) dirk = PETSC_TRUE;

1503:   if (!ts->steprollback) {
1504:     if (dirk || ts->equation_type >= TS_EQ_IMPLICIT) { /* Save the initial slope for the next step */
1505:       PetscCall(VecCopy(YdotI[s - 1], Ydot0));
1506:     }
1507:     if (ark->extrapolate && !ts->steprestart) { /* Save the Y, YdotI, YdotRHS for extrapolation initial guess */
1508:       for (i = 0; i < s; i++) {
1509:         PetscCall(VecCopy(Y[i], ark->Y_prev[i]));
1510:         PetscCall(VecCopy(YdotI[i], ark->YdotI_prev[i]));
1511:         if (tab->additive && hasE) PetscCall(VecCopy(YdotRHS[i], ark->YdotRHS_prev[i]));
1512:       }
1513:     }
1514:   }

1516:   /* For fully implicit formulations we can solve the equations
1517:        F(tn,xn,xdot) = 0
1518:      for the explicit first stage */
1519:   if (dirk && tab->explicit_first_stage && ts->steprestart) {
1520:     ark->scoeff = PETSC_MAX_REAL;
1521:     PetscCall(VecCopy(ts->vec_sol, Z));
1522:     PetscCall(TSGetSNES(ts, &snes));
1523:     PetscCall(SNESSolve(snes, NULL, Ydot0));
1524:   }

1526:   /* For IMEX we compute a step */
1527:   if (!dirk && ts->equation_type >= TS_EQ_IMPLICIT && tab->explicit_first_stage && ts->steprestart) {
1528:     TS ts_start;
1529:     if (PetscDefined(USE_DEBUG) && hasE) {
1530:       PetscBool id = PETSC_FALSE;
1531:       PetscCall(TSARKIMEXTestMassIdentity(ts, &id));
1532:       PetscCheck(id, PetscObjectComm((PetscObject)ts), PETSC_ERR_ARG_INCOMP, "This scheme requires an identity mass matrix, however the TSIFunction you provided does not utilize an identity mass matrix");
1533:     }
1534:     PetscCall(TSClone(ts, &ts_start));
1535:     PetscCall(TSSetSolution(ts_start, ts->vec_sol));
1536:     PetscCall(TSSetTime(ts_start, ts->ptime));
1537:     PetscCall(TSSetMaxSteps(ts_start, ts->steps + 1));
1538:     PetscCall(TSSetMaxTime(ts_start, ts->ptime + ts->time_step));
1539:     PetscCall(TSSetExactFinalTime(ts_start, TS_EXACTFINALTIME_STEPOVER));
1540:     PetscCall(TSSetTimeStep(ts_start, ts->time_step));
1541:     PetscCall(TSSetType(ts_start, TSARKIMEX));
1542:     PetscCall(TSARKIMEXSetFullyImplicit(ts_start, PETSC_TRUE));
1543:     PetscCall(TSARKIMEXSetType(ts_start, TSARKIMEX1BEE));

1545:     PetscCall(TSRestartStep(ts_start));
1546:     PetscCall(TSSolve(ts_start, ts->vec_sol));
1547:     PetscCall(TSGetTime(ts_start, &ts->ptime));
1548:     PetscCall(TSGetTimeStep(ts_start, &ts->time_step));

1550:     { /* Save the initial slope for the next step */
1551:       TS_ARKIMEX *ark_start = (TS_ARKIMEX *)ts_start->data;
1552:       PetscCall(VecCopy(ark_start->YdotI[ark_start->tableau->s - 1], Ydot0));
1553:     }
1554:     ts->steps++;

1556:     /* Set the correct TS in SNES */
1557:     /* We'll try to bypass this by changing the method on the fly */
1558:     {
1559:       PetscCall(TSGetSNES(ts, &snes));
1560:       PetscCall(TSSetSNES(ts, snes));
1561:     }
1562:     PetscCall(TSDestroy(&ts_start));
1563:   }

1565:   ark->status = TS_STEP_INCOMPLETE;
1566:   while (!ts->reason && ark->status != TS_STEP_COMPLETE) {
1567:     PetscReal t = ts->ptime;
1568:     PetscReal h = ts->time_step;
1569:     for (i = 0; i < s; i++) {
1570:       ark->stage_time = t + h * ct[i];
1571:       PetscCall(TSPreStage(ts, ark->stage_time));
1572:       if (At[i * s + i] == 0) { /* This stage is explicit */
1573:         PetscCheck(i == 0 || ts->equation_type < TS_EQ_IMPLICIT, PetscObjectComm((PetscObject)ts), PETSC_ERR_SUP, "Explicit stages other than the first one are not supported for implicit problems");
1574:         PetscCall(VecCopy(ts->vec_sol, Y[i]));
1575:         for (j = 0; j < i; j++) w[j] = h * At[i * s + j];
1576:         PetscCall(VecMAXPY(Y[i], i, w, YdotI));
1577:         if (tab->additive && hasE) {
1578:           for (j = 0; j < i; j++) w[j] = h * A[i * s + j];
1579:           PetscCall(VecMAXPY(Y[i], i, w, YdotRHS));
1580:         }
1581:       } else {
1582:         ark->scoeff = 1. / At[i * s + i];
1583:         /* Ydot = shift*(Y-Z) */
1584:         PetscCall(VecCopy(ts->vec_sol, Z));
1585:         for (j = 0; j < i; j++) w[j] = h * At[i * s + j];
1586:         PetscCall(VecMAXPY(Z, i, w, YdotI));
1587:         if (tab->additive && hasE) {
1588:           for (j = 0; j < i; j++) w[j] = h * A[i * s + j];
1589:           PetscCall(VecMAXPY(Z, i, w, YdotRHS));
1590:         }
1591:         if (extrapolate && !ts->steprestart) {
1592:           /* Initial guess extrapolated from previous time step stage values */
1593:           PetscCall(TSExtrapolate_ARKIMEX(ts, c[i], Y[i]));
1594:         } else {
1595:           /* Initial guess taken from last stage */
1596:           PetscCall(VecCopy(i > 0 ? Y[i - 1] : ts->vec_sol, Y[i]));
1597:         }
1598:         PetscCall(TSGetSNES(ts, &snes));
1599:         PetscCall(SNESSolve(snes, NULL, Y[i]));
1600:         PetscCall(SNESGetIterationNumber(snes, &its));
1601:         PetscCall(SNESGetLinearSolveIterations(snes, &lits));
1602:         ts->snes_its += its;
1603:         ts->ksp_its += lits;
1604:         PetscCall(TSGetAdapt(ts, &adapt));
1605:         PetscCall(TSAdaptCheckStage(adapt, ts, ark->stage_time, Y[i], &stageok));
1606:         if (!stageok) {
1607:           /* We are likely rejecting the step because of solver or function domain problems so we should not attempt to
1608:            * use extrapolation to initialize the solves on the next attempt. */
1609:           extrapolate = PETSC_FALSE;
1610:           goto reject_step;
1611:         }
1612:       }
1613:       if (dirk || ts->equation_type >= TS_EQ_IMPLICIT) {
1614:         if (i == 0 && tab->explicit_first_stage) {
1615:           PetscCheck(tab->stiffly_accurate, PetscObjectComm((PetscObject)ts), PETSC_ERR_SUP, "%s %s is not stiffly accurate and therefore explicit-first stage methods cannot be used if the equation is implicit because the slope cannot be evaluated",
1616:                      ((PetscObject)ts)->type_name, ark->tableau->name);
1617:           PetscCall(VecCopy(Ydot0, YdotI[0])); /* YdotI = YdotI(tn-1) */
1618:         } else {
1619:           PetscCall(VecAXPBYPCZ(YdotI[i], -ark->scoeff / h, ark->scoeff / h, 0, Z, Y[i])); /* YdotI = shift*(X-Z) */
1620:         }
1621:       } else {
1622:         if (i == 0 && tab->explicit_first_stage) {
1623:           PetscCall(VecZeroEntries(Ydot));
1624:           PetscCall(TSComputeIFunction(ts, t + h * ct[i], Y[i], Ydot, YdotI[i], ark->imex)); /* YdotI = -G(t,Y,0)   */
1625:           PetscCall(VecScale(YdotI[i], -1.0));
1626:         } else {
1627:           PetscCall(VecAXPBYPCZ(YdotI[i], -ark->scoeff / h, ark->scoeff / h, 0, Z, Y[i])); /* YdotI = shift*(X-Z) */
1628:         }
1629:         if (hasE) {
1630:           if (ark->imex) {
1631:             PetscCall(TSComputeRHSFunction(ts, t + h * c[i], Y[i], YdotRHS[i]));
1632:           } else {
1633:             PetscCall(VecZeroEntries(YdotRHS[i]));
1634:           }
1635:         }
1636:       }
1637:       PetscCall(TSPostStage(ts, ark->stage_time, i, Y));
1638:     }

1640:     ark->status = TS_STEP_INCOMPLETE;
1641:     PetscCall(TSEvaluateStep_ARKIMEX(ts, tab->order, ts->vec_sol, NULL));
1642:     ark->status = TS_STEP_PENDING;
1643:     PetscCall(TSGetAdapt(ts, &adapt));
1644:     PetscCall(TSAdaptCandidatesClear(adapt));
1645:     PetscCall(TSAdaptCandidateAdd(adapt, tab->name, tab->order, 1, tab->ccfl, (PetscReal)tab->s, PETSC_TRUE));
1646:     PetscCall(TSAdaptChoose(adapt, ts, ts->time_step, NULL, &next_time_step, &accept));
1647:     ark->status = accept ? TS_STEP_COMPLETE : TS_STEP_INCOMPLETE;
1648:     if (!accept) { /* Roll back the current step */
1649:       PetscCall(TSRollBack_ARKIMEX(ts));
1650:       ts->time_step = next_time_step;
1651:       goto reject_step;
1652:     }

1654:     ts->ptime += ts->time_step;
1655:     ts->time_step = next_time_step;
1656:     break;

1658:   reject_step:
1659:     ts->reject++;
1660:     accept = PETSC_FALSE;
1661:     if (!ts->reason && ++rejections > ts->max_reject && ts->max_reject >= 0) {
1662:       ts->reason = TS_DIVERGED_STEP_REJECTED;
1663:       PetscCall(PetscInfo(ts, "Step=%" PetscInt_FMT ", step rejections %" PetscInt_FMT " greater than current TS allowed, stopping solve\n", ts->steps, rejections));
1664:     }
1665:   }
1666:   PetscFunctionReturn(PETSC_SUCCESS);
1667: }

1669: /*
1670:   This adjoint step function assumes the partitioned ODE system has an identity mass matrix and thus can be represented in the form
1671:   Udot = H(t,U) + G(t,U)
1672:   This corresponds to F(t,U,Udot) = Udot-H(t,U).

1674:   The complete adjoint equations are
1675:   (shift*I - dHdu) lambda_s[i]   = 1/at[i][i] (
1676:     dGdU (b_i lambda_{n+1} + \sum_{j=i+1}^s a[j][i] lambda_s[j])
1677:     + dHdU (bt[i] lambda_{n+1} +  \sum_{j=i+1}^s at[j][i] lambda_s[j])), i = s-1,...,0
1678:   lambda_n = lambda_{n+1} + \sum_{j=1}^s lambda_s[j]
1679:   mu_{n+1}[i]   = h (at[i][i] dHdP lambda_s[i]
1680:     + dGdP (b_i lambda_{n+1} + \sum_{j=i+1}^s a[j][i] lambda_s[j])
1681:     + dHdP (bt[i] lambda_{n+1} + \sum_{j=i+1}^s at[j][i] lambda_s[j])), i = s-1,...,0
1682:   mu_n = mu_{n+1} + \sum_{j=1}^s mu_{n+1}[j]
1683:   where shift = 1/(at[i][i]*h)

1685:   If at[i][i] is 0, the first equation falls back to
1686:   lambda_s[i] = h (
1687:     (b_i dGdU + bt[i] dHdU) lambda_{n+1} + dGdU \sum_{j=i+1}^s a[j][i] lambda_s[j]
1688:     + dHdU \sum_{j=i+1}^s at[j][i] lambda_s[j])

1690: */
1691: static PetscErrorCode TSAdjointStep_ARKIMEX(TS ts)
1692: {
1693:   TS_ARKIMEX      *ark = (TS_ARKIMEX *)ts->data;
1694:   ARKTableau       tab = ark->tableau;
1695:   const PetscInt   s   = tab->s;
1696:   const PetscReal *At = tab->At, *A = tab->A, *ct = tab->ct, *c = tab->c, *b = tab->b, *bt = tab->bt;
1697:   PetscScalar     *w = ark->work;
1698:   Vec             *Y = ark->Y, Ydot = ark->Ydot, *VecsDeltaLam = ark->VecsDeltaLam, *VecsSensiTemp = ark->VecsSensiTemp, *VecsSensiPTemp = ark->VecsSensiPTemp;
1699:   Mat              Jex, Jim, Jimpre;
1700:   PetscInt         i, j, nadj;
1701:   PetscReal        t                 = ts->ptime, stage_time_ex;
1702:   PetscReal        adjoint_time_step = -ts->time_step; /* always positive since ts->time_step is negative */
1703:   KSP              ksp;

1705:   PetscFunctionBegin;
1706:   ark->status = TS_STEP_INCOMPLETE;
1707:   PetscCall(SNESGetKSP(ts->snes, &ksp));
1708:   PetscCall(TSGetRHSMats_Private(ts, &Jex, NULL));
1709:   PetscCall(TSGetIJacobian(ts, &Jim, &Jimpre, NULL, NULL));

1711:   for (i = s - 1; i >= 0; i--) {
1712:     ark->stage_time = t - adjoint_time_step * (1.0 - ct[i]);
1713:     stage_time_ex   = t - adjoint_time_step * (1.0 - c[i]);
1714:     if (At[i * s + i] == 0) { // This stage is explicit
1715:       ark->scoeff = 0.;
1716:     } else {
1717:       ark->scoeff = -1. / At[i * s + i]; // this makes shift=ark->scoeff/ts->time_step positive since ts->time_step is negative
1718:     }
1719:     PetscCall(TSComputeSNESJacobian(ts, Y[i], Jim, Jimpre));
1720:     PetscCall(TSComputeRHSJacobian(ts, stage_time_ex, Y[i], Jex, Jex));
1721:     if (ts->vecs_sensip) {
1722:       PetscCall(TSComputeIJacobianP(ts, ark->stage_time, Y[i], Ydot, ark->scoeff / adjoint_time_step, ts->Jacp, PETSC_TRUE)); // get dFdP (-dHdP), Ydot not really used since mass matrix is identity
1723:       PetscCall(TSComputeRHSJacobianP(ts, stage_time_ex, Y[i], ts->Jacprhs));                                                 // get dGdP
1724:     }
1725:     /* Build RHS (stored in VecsDeltaLam) for first-order adjoint */
1726:     for (nadj = 0; nadj < ts->numcost; nadj++) {
1727:       /* build implicit part */
1728:       PetscCall(VecSet(VecsSensiTemp[nadj], 0));
1729:       if (s - i - 1 > 0) {
1730:         /* Temp = -\sum_{j=i+1}^s at[j][i] lambda_s[j] */
1731:         for (j = i + 1; j < s; j++) w[j - i - 1] = -At[j * s + i];
1732:         PetscCall(VecMAXPY(VecsSensiTemp[nadj], s - i - 1, w, &VecsDeltaLam[nadj * s + i + 1]));
1733:       }
1734:       /* Temp = Temp - bt[i] lambda_{n+1} */
1735:       PetscCall(VecAXPY(VecsSensiTemp[nadj], -bt[i], ts->vecs_sensi[nadj]));
1736:       if (bt[i] || s - i - 1 > 0) {
1737:         /* (shift I - dHdU) Temp */
1738:         PetscCall(MatMultTranspose(Jim, VecsSensiTemp[nadj], VecsDeltaLam[nadj * s + i]));
1739:         /* cancel out shift Temp where shift=-scoeff/h */
1740:         PetscCall(VecAXPY(VecsDeltaLam[nadj * s + i], ark->scoeff / adjoint_time_step, VecsSensiTemp[nadj]));
1741:         if (ts->vecs_sensip) {
1742:           /* - dHdP Temp */
1743:           PetscCall(MatMultTranspose(ts->Jacp, VecsSensiTemp[nadj], VecsSensiPTemp[nadj]));
1744:           /* mu_n += -h dHdP Temp */
1745:           PetscCall(VecAXPY(ts->vecs_sensip[nadj], adjoint_time_step, VecsSensiPTemp[nadj]));
1746:         }
1747:       } else {
1748:         PetscCall(VecSet(VecsDeltaLam[nadj * s + i], 0)); // make sure it is initialized
1749:       }
1750:       /* build explicit part */
1751:       PetscCall(VecSet(VecsSensiTemp[nadj], 0));
1752:       if (s - i - 1 > 0) {
1753:         /* Temp = \sum_{j=i+1}^s a[j][i] lambda_s[j] */
1754:         for (j = i + 1; j < s; j++) w[j - i - 1] = A[j * s + i];
1755:         PetscCall(VecMAXPY(VecsSensiTemp[nadj], s - i - 1, w, &VecsDeltaLam[nadj * s + i + 1]));
1756:       }
1757:       /* Temp = Temp + b[i] lambda_{n+1} */
1758:       PetscCall(VecAXPY(VecsSensiTemp[nadj], b[i], ts->vecs_sensi[nadj]));
1759:       if (b[i] || s - i - 1 > 0) {
1760:         /* dGdU Temp */
1761:         PetscCall(MatMultTransposeAdd(Jex, VecsSensiTemp[nadj], VecsDeltaLam[nadj * s + i], VecsDeltaLam[nadj * s + i]));
1762:         if (ts->vecs_sensip) {
1763:           /* dGdP Temp */
1764:           PetscCall(MatMultTranspose(ts->Jacprhs, VecsSensiTemp[nadj], VecsSensiPTemp[nadj]));
1765:           /* mu_n += h dGdP Temp */
1766:           PetscCall(VecAXPY(ts->vecs_sensip[nadj], adjoint_time_step, VecsSensiPTemp[nadj]));
1767:         }
1768:       }
1769:       /* Build LHS for first-order adjoint */
1770:       if (At[i * s + i] == 0) { // This stage is explicit
1771:         PetscCall(VecScale(VecsDeltaLam[nadj * s + i], adjoint_time_step));
1772:       } else {
1773:         KSP                ksp;
1774:         KSPConvergedReason kspreason;
1775:         PetscCall(SNESGetKSP(ts->snes, &ksp));
1776:         PetscCall(KSPSetOperators(ksp, Jim, Jimpre));
1777:         PetscCall(VecScale(VecsDeltaLam[nadj * s + i], 1. / At[i * s + i]));
1778:         PetscCall(KSPSolveTranspose(ksp, VecsDeltaLam[nadj * s + i], VecsDeltaLam[nadj * s + i]));
1779:         PetscCall(KSPGetConvergedReason(ksp, &kspreason));
1780:         if (kspreason < 0) {
1781:           ts->reason = TSADJOINT_DIVERGED_LINEAR_SOLVE;
1782:           PetscCall(PetscInfo(ts, "Step=%" PetscInt_FMT ", %" PetscInt_FMT "th cost function, transposed linear solve fails, stopping 1st-order adjoint solve\n", ts->steps, nadj));
1783:         }
1784:         if (ts->vecs_sensip) {
1785:           /* -dHdP lambda_s[i] */
1786:           PetscCall(MatMultTranspose(ts->Jacp, VecsDeltaLam[nadj * s + i], VecsSensiPTemp[nadj]));
1787:           /* mu_n += h at[i][i] dHdP lambda_s[i] */
1788:           PetscCall(VecAXPY(ts->vecs_sensip[nadj], -At[i * s + i] * adjoint_time_step, VecsSensiPTemp[nadj]));
1789:         }
1790:       }
1791:     }
1792:   }
1793:   for (j = 0; j < s; j++) w[j] = 1.0;
1794:   for (nadj = 0; nadj < ts->numcost; nadj++) // no need to do this for mu's
1795:     PetscCall(VecMAXPY(ts->vecs_sensi[nadj], s, w, &VecsDeltaLam[nadj * s]));
1796:   ark->status = TS_STEP_COMPLETE;
1797:   PetscFunctionReturn(PETSC_SUCCESS);
1798: }

1800: static PetscErrorCode TSInterpolate_ARKIMEX(TS ts, PetscReal itime, Vec X)
1801: {
1802:   TS_ARKIMEX      *ark = (TS_ARKIMEX *)ts->data;
1803:   ARKTableau       tab = ark->tableau;
1804:   PetscInt         s = tab->s, pinterp = tab->pinterp, i, j;
1805:   PetscReal        h;
1806:   PetscReal        tt, t;
1807:   PetscScalar     *bt = ark->work, *b = ark->work + s;
1808:   const PetscReal *Bt = tab->binterpt, *B = tab->binterp;

1810:   PetscFunctionBegin;
1811:   PetscCheck(Bt && B, PetscObjectComm((PetscObject)ts), PETSC_ERR_SUP, "%s %s does not have an interpolation formula", ((PetscObject)ts)->type_name, ark->tableau->name);
1812:   switch (ark->status) {
1813:   case TS_STEP_INCOMPLETE:
1814:   case TS_STEP_PENDING:
1815:     h = ts->time_step;
1816:     t = (itime - ts->ptime) / h;
1817:     break;
1818:   case TS_STEP_COMPLETE:
1819:     h = ts->ptime - ts->ptime_prev;
1820:     t = (itime - ts->ptime) / h + 1; /* In the interval [0,1] */
1821:     break;
1822:   default:
1823:     SETERRQ(PetscObjectComm((PetscObject)ts), PETSC_ERR_PLIB, "Invalid TSStepStatus");
1824:   }
1825:   for (i = 0; i < s; i++) bt[i] = b[i] = 0;
1826:   for (j = 0, tt = t; j < pinterp; j++, tt *= t) {
1827:     for (i = 0; i < s; i++) {
1828:       bt[i] += h * Bt[i * pinterp + j] * tt;
1829:       b[i] += h * B[i * pinterp + j] * tt;
1830:     }
1831:   }
1832:   PetscCall(VecCopy(ark->Y[0], X));
1833:   PetscCall(VecMAXPY(X, s, bt, ark->YdotI));
1834:   if (tab->additive) {
1835:     PetscBool hasE;
1836:     PetscCall(TSHasRHSFunction(ts, &hasE));
1837:     if (hasE) PetscCall(VecMAXPY(X, s, b, ark->YdotRHS));
1838:   }
1839:   PetscFunctionReturn(PETSC_SUCCESS);
1840: }

1842: static PetscErrorCode TSExtrapolate_ARKIMEX(TS ts, PetscReal c, Vec X)
1843: {
1844:   TS_ARKIMEX      *ark = (TS_ARKIMEX *)ts->data;
1845:   ARKTableau       tab = ark->tableau;
1846:   PetscInt         s = tab->s, pinterp = tab->pinterp, i, j;
1847:   PetscReal        h, h_prev, t, tt;
1848:   PetscScalar     *bt = ark->work, *b = ark->work + s;
1849:   const PetscReal *Bt = tab->binterpt, *B = tab->binterp;

1851:   PetscFunctionBegin;
1852:   PetscCheck(Bt && B, PetscObjectComm((PetscObject)ts), PETSC_ERR_SUP, "TSARKIMEX %s does not have an interpolation formula", ark->tableau->name);
1853:   h      = ts->time_step;
1854:   h_prev = ts->ptime - ts->ptime_prev;
1855:   t      = 1 + h / h_prev * c;
1856:   for (i = 0; i < s; i++) bt[i] = b[i] = 0;
1857:   for (j = 0, tt = t; j < pinterp; j++, tt *= t) {
1858:     for (i = 0; i < s; i++) {
1859:       bt[i] += h * Bt[i * pinterp + j] * tt;
1860:       b[i] += h * B[i * pinterp + j] * tt;
1861:     }
1862:   }
1863:   PetscCheck(ark->Y_prev, PetscObjectComm((PetscObject)ts), PETSC_ERR_SUP, "Stages from previous step have not been stored");
1864:   PetscCall(VecCopy(ark->Y_prev[0], X));
1865:   PetscCall(VecMAXPY(X, s, bt, ark->YdotI_prev));
1866:   if (tab->additive) {
1867:     PetscBool hasE;
1868:     PetscCall(TSHasRHSFunction(ts, &hasE));
1869:     if (hasE) PetscCall(VecMAXPY(X, s, b, ark->YdotRHS_prev));
1870:   }
1871:   PetscFunctionReturn(PETSC_SUCCESS);
1872: }

1874: static PetscErrorCode TSARKIMEXTableauReset(TS ts)
1875: {
1876:   TS_ARKIMEX *ark = (TS_ARKIMEX *)ts->data;
1877:   ARKTableau  tab = ark->tableau;

1879:   PetscFunctionBegin;
1880:   if (!tab) PetscFunctionReturn(PETSC_SUCCESS);
1881:   PetscCall(PetscFree(ark->work));
1882:   PetscCall(VecDestroyVecs(tab->s, &ark->Y));
1883:   PetscCall(VecDestroyVecs(tab->s, &ark->YdotI));
1884:   PetscCall(VecDestroyVecs(tab->s, &ark->YdotRHS));
1885:   PetscCall(VecDestroyVecs(tab->s, &ark->Y_prev));
1886:   PetscCall(VecDestroyVecs(tab->s, &ark->YdotI_prev));
1887:   PetscCall(VecDestroyVecs(tab->s, &ark->YdotRHS_prev));
1888:   PetscFunctionReturn(PETSC_SUCCESS);
1889: }

1891: static PetscErrorCode TSReset_ARKIMEX(TS ts)
1892: {
1893:   TS_ARKIMEX *ark = (TS_ARKIMEX *)ts->data;

1895:   PetscFunctionBegin;
1896:   PetscCall(TSARKIMEXTableauReset(ts));
1897:   PetscCall(VecDestroy(&ark->Ydot));
1898:   PetscCall(VecDestroy(&ark->Ydot0));
1899:   PetscCall(VecDestroy(&ark->Z));
1900:   PetscFunctionReturn(PETSC_SUCCESS);
1901: }

1903: static PetscErrorCode TSAdjointReset_ARKIMEX(TS ts)
1904: {
1905:   TS_ARKIMEX *ark = (TS_ARKIMEX *)ts->data;
1906:   ARKTableau  tab = ark->tableau;

1908:   PetscFunctionBegin;
1909:   PetscCall(VecDestroyVecs(tab->s * ts->numcost, &ark->VecsDeltaLam));
1910:   PetscCall(VecDestroyVecs(ts->numcost, &ark->VecsSensiTemp));
1911:   PetscCall(VecDestroyVecs(ts->numcost, &ark->VecsSensiPTemp));
1912:   PetscFunctionReturn(PETSC_SUCCESS);
1913: }

1915: static PetscErrorCode TSARKIMEXGetVecs(TS ts, DM dm, Vec *Z, Vec *Ydot)
1916: {
1917:   TS_ARKIMEX *ax = (TS_ARKIMEX *)ts->data;

1919:   PetscFunctionBegin;
1920:   if (Z) {
1921:     if (dm && dm != ts->dm) {
1922:       PetscCall(DMGetNamedGlobalVector(dm, "TSARKIMEX_Z", Z));
1923:     } else *Z = ax->Z;
1924:   }
1925:   if (Ydot) {
1926:     if (dm && dm != ts->dm) {
1927:       PetscCall(DMGetNamedGlobalVector(dm, "TSARKIMEX_Ydot", Ydot));
1928:     } else *Ydot = ax->Ydot;
1929:   }
1930:   PetscFunctionReturn(PETSC_SUCCESS);
1931: }

1933: static PetscErrorCode TSARKIMEXRestoreVecs(TS ts, DM dm, Vec *Z, Vec *Ydot)
1934: {
1935:   PetscFunctionBegin;
1936:   if (Z) {
1937:     if (dm && dm != ts->dm) PetscCall(DMRestoreNamedGlobalVector(dm, "TSARKIMEX_Z", Z));
1938:   }
1939:   if (Ydot) {
1940:     if (dm && dm != ts->dm) PetscCall(DMRestoreNamedGlobalVector(dm, "TSARKIMEX_Ydot", Ydot));
1941:   }
1942:   PetscFunctionReturn(PETSC_SUCCESS);
1943: }

1945: /*
1946:   This defines the nonlinear equation that is to be solved with SNES
1947:   G(U) = F[t0+Theta*dt, U, (U-U0)*shift] = 0
1948: */
1949: static PetscErrorCode SNESTSFormFunction_ARKIMEX(SNES snes, Vec X, Vec F, TS ts)
1950: {
1951:   TS_ARKIMEX *ark = (TS_ARKIMEX *)ts->data;
1952:   DM          dm, dmsave;
1953:   Vec         Z, Ydot;

1955:   PetscFunctionBegin;
1956:   PetscCall(SNESGetDM(snes, &dm));
1957:   PetscCall(TSARKIMEXGetVecs(ts, dm, &Z, &Ydot));
1958:   dmsave = ts->dm;
1959:   ts->dm = dm;

1961:   if (ark->scoeff == PETSC_MAX_REAL) {
1962:     /* We are solving F(t,x_n,xdot) = 0 to start the method */
1963:     PetscCall(TSComputeIFunction(ts, ark->stage_time, Z, X, F, ark->imex));
1964:   } else {
1965:     PetscReal shift = ark->scoeff / ts->time_step;
1966:     PetscCall(VecAXPBYPCZ(Ydot, -shift, shift, 0, Z, X)); /* Ydot = shift*(X-Z) */
1967:     PetscCall(TSComputeIFunction(ts, ark->stage_time, X, Ydot, F, ark->imex));
1968:   }

1970:   ts->dm = dmsave;
1971:   PetscCall(TSARKIMEXRestoreVecs(ts, dm, &Z, &Ydot));
1972:   PetscFunctionReturn(PETSC_SUCCESS);
1973: }

1975: static PetscErrorCode SNESTSFormJacobian_ARKIMEX(SNES snes, Vec X, Mat A, Mat B, TS ts)
1976: {
1977:   TS_ARKIMEX *ark = (TS_ARKIMEX *)ts->data;
1978:   DM          dm, dmsave;
1979:   Vec         Ydot, Z;
1980:   PetscReal   shift;

1982:   PetscFunctionBegin;
1983:   PetscCall(SNESGetDM(snes, &dm));
1984:   PetscCall(TSARKIMEXGetVecs(ts, dm, &Z, &Ydot));
1985:   /* ark->Ydot has already been computed in SNESTSFormFunction_ARKIMEX (SNES guarantees this) */
1986:   dmsave = ts->dm;
1987:   ts->dm = dm;

1989:   if (ark->scoeff == PETSC_MAX_REAL) {
1990:     /* We are solving F(t,x_n,xdot) = 0 to start the method, we only only dF/dXdot
1991:        Jed's proposal is to compute with a very large shift and scale back the matrix */
1992:     shift = 1.0 / PETSC_MACHINE_EPSILON;
1993:     PetscCall(TSComputeIJacobian(ts, ark->stage_time, Z, X, shift, A, B, ark->imex));
1994:     PetscCall(MatScale(B, PETSC_MACHINE_EPSILON));
1995:     if (A != B) PetscCall(MatScale(A, PETSC_MACHINE_EPSILON));
1996:   } else {
1997:     shift = ark->scoeff / ts->time_step;
1998:     PetscCall(TSComputeIJacobian(ts, ark->stage_time, X, Ydot, shift, A, B, ark->imex));
1999:   }
2000:   ts->dm = dmsave;
2001:   PetscCall(TSARKIMEXRestoreVecs(ts, dm, &Z, &Ydot));
2002:   PetscFunctionReturn(PETSC_SUCCESS);
2003: }

2005: static PetscErrorCode TSGetStages_ARKIMEX(TS ts, PetscInt *ns, Vec *Y[])
2006: {
2007:   TS_ARKIMEX *ark = (TS_ARKIMEX *)ts->data;

2009:   PetscFunctionBegin;
2010:   if (ns) *ns = ark->tableau->s;
2011:   if (Y) *Y = ark->Y;
2012:   PetscFunctionReturn(PETSC_SUCCESS);
2013: }

2015: static PetscErrorCode DMCoarsenHook_TSARKIMEX(DM fine, DM coarse, void *ctx)
2016: {
2017:   PetscFunctionBegin;
2018:   PetscFunctionReturn(PETSC_SUCCESS);
2019: }

2021: static PetscErrorCode DMRestrictHook_TSARKIMEX(DM fine, Mat restrct, Vec rscale, Mat inject, DM coarse, void *ctx)
2022: {
2023:   TS  ts = (TS)ctx;
2024:   Vec Z, Z_c;

2026:   PetscFunctionBegin;
2027:   PetscCall(TSARKIMEXGetVecs(ts, fine, &Z, NULL));
2028:   PetscCall(TSARKIMEXGetVecs(ts, coarse, &Z_c, NULL));
2029:   PetscCall(MatRestrict(restrct, Z, Z_c));
2030:   PetscCall(VecPointwiseMult(Z_c, rscale, Z_c));
2031:   PetscCall(TSARKIMEXRestoreVecs(ts, fine, &Z, NULL));
2032:   PetscCall(TSARKIMEXRestoreVecs(ts, coarse, &Z_c, NULL));
2033:   PetscFunctionReturn(PETSC_SUCCESS);
2034: }

2036: static PetscErrorCode DMSubDomainHook_TSARKIMEX(DM dm, DM subdm, void *ctx)
2037: {
2038:   PetscFunctionBegin;
2039:   PetscFunctionReturn(PETSC_SUCCESS);
2040: }

2042: static PetscErrorCode DMSubDomainRestrictHook_TSARKIMEX(DM dm, VecScatter gscat, VecScatter lscat, DM subdm, void *ctx)
2043: {
2044:   TS  ts = (TS)ctx;
2045:   Vec Z, Z_c;

2047:   PetscFunctionBegin;
2048:   PetscCall(TSARKIMEXGetVecs(ts, dm, &Z, NULL));
2049:   PetscCall(TSARKIMEXGetVecs(ts, subdm, &Z_c, NULL));

2051:   PetscCall(VecScatterBegin(gscat, Z, Z_c, INSERT_VALUES, SCATTER_FORWARD));
2052:   PetscCall(VecScatterEnd(gscat, Z, Z_c, INSERT_VALUES, SCATTER_FORWARD));

2054:   PetscCall(TSARKIMEXRestoreVecs(ts, dm, &Z, NULL));
2055:   PetscCall(TSARKIMEXRestoreVecs(ts, subdm, &Z_c, NULL));
2056:   PetscFunctionReturn(PETSC_SUCCESS);
2057: }

2059: static PetscErrorCode TSARKIMEXTableauSetUp(TS ts)
2060: {
2061:   TS_ARKIMEX *ark = (TS_ARKIMEX *)ts->data;
2062:   ARKTableau  tab = ark->tableau;

2064:   PetscFunctionBegin;
2065:   PetscCall(PetscMalloc1(2 * tab->s, &ark->work));
2066:   PetscCall(VecDuplicateVecs(ts->vec_sol, tab->s, &ark->Y));
2067:   PetscCall(VecDuplicateVecs(ts->vec_sol, tab->s, &ark->YdotI));
2068:   if (tab->additive) PetscCall(VecDuplicateVecs(ts->vec_sol, tab->s, &ark->YdotRHS));
2069:   if (ark->extrapolate) {
2070:     PetscCall(VecDuplicateVecs(ts->vec_sol, tab->s, &ark->Y_prev));
2071:     PetscCall(VecDuplicateVecs(ts->vec_sol, tab->s, &ark->YdotI_prev));
2072:     if (tab->additive) PetscCall(VecDuplicateVecs(ts->vec_sol, tab->s, &ark->YdotRHS_prev));
2073:   }
2074:   PetscFunctionReturn(PETSC_SUCCESS);
2075: }

2077: static PetscErrorCode TSSetUp_ARKIMEX(TS ts)
2078: {
2079:   TS_ARKIMEX *ark = (TS_ARKIMEX *)ts->data;
2080:   DM          dm;
2081:   SNES        snes;

2083:   PetscFunctionBegin;
2084:   PetscCall(TSARKIMEXTableauSetUp(ts));
2085:   PetscCall(VecDuplicate(ts->vec_sol, &ark->Ydot));
2086:   PetscCall(VecDuplicate(ts->vec_sol, &ark->Ydot0));
2087:   PetscCall(VecDuplicate(ts->vec_sol, &ark->Z));
2088:   PetscCall(TSGetDM(ts, &dm));
2089:   PetscCall(DMCoarsenHookAdd(dm, DMCoarsenHook_TSARKIMEX, DMRestrictHook_TSARKIMEX, ts));
2090:   PetscCall(DMSubDomainHookAdd(dm, DMSubDomainHook_TSARKIMEX, DMSubDomainRestrictHook_TSARKIMEX, ts));
2091:   PetscCall(TSGetSNES(ts, &snes));
2092:   PetscFunctionReturn(PETSC_SUCCESS);
2093: }

2095: static PetscErrorCode TSAdjointSetUp_ARKIMEX(TS ts)
2096: {
2097:   TS_ARKIMEX *ark = (TS_ARKIMEX *)ts->data;
2098:   ARKTableau  tab = ark->tableau;

2100:   PetscFunctionBegin;
2101:   PetscCall(VecDuplicateVecs(ts->vecs_sensi[0], tab->s * ts->numcost, &ark->VecsDeltaLam));
2102:   PetscCall(VecDuplicateVecs(ts->vecs_sensi[0], ts->numcost, &ark->VecsSensiTemp));
2103:   if (ts->vecs_sensip) { PetscCall(VecDuplicateVecs(ts->vecs_sensip[0], ts->numcost, &ark->VecsSensiPTemp)); }
2104:   if (PetscDefined(USE_DEBUG)) {
2105:     PetscBool id = PETSC_FALSE;
2106:     PetscCall(TSARKIMEXTestMassIdentity(ts, &id));
2107:     PetscCheck(id, PetscObjectComm((PetscObject)ts), PETSC_ERR_ARG_INCOMP, "Adjoint ARKIMEX requires an identity mass matrix, however the TSIFunction you provided does not utilize an identity mass matrix");
2108:   }
2109:   PetscFunctionReturn(PETSC_SUCCESS);
2110: }

2112: static PetscErrorCode TSSetFromOptions_ARKIMEX(TS ts, PetscOptionItems *PetscOptionsObject)
2113: {
2114:   TS_ARKIMEX *ark = (TS_ARKIMEX *)ts->data;
2115:   PetscBool   dirk;

2117:   PetscFunctionBegin;
2118:   PetscCall(PetscObjectTypeCompare((PetscObject)ts, TSDIRK, &dirk));
2119:   PetscOptionsHeadBegin(PetscOptionsObject, dirk ? "DIRK ODE solver options" : "ARKIMEX ODE solver options");
2120:   {
2121:     ARKTableauLink link;
2122:     PetscInt       count, choice;
2123:     PetscBool      flg;
2124:     const char   **namelist;
2125:     for (link = ARKTableauList, count = 0; link; link = link->next) {
2126:       if (!dirk && link->tab.additive) count++;
2127:       if (dirk && !link->tab.additive) count++;
2128:     }
2129:     PetscCall(PetscMalloc1(count, (char ***)&namelist));
2130:     for (link = ARKTableauList, count = 0; link; link = link->next) {
2131:       if (!dirk && link->tab.additive) namelist[count++] = link->tab.name;
2132:       if (dirk && !link->tab.additive) namelist[count++] = link->tab.name;
2133:     }
2134:     if (dirk) {
2135:       PetscCall(PetscOptionsEList("-ts_dirk_type", "Family of DIRK method", "TSDIRKSetType", (const char *const *)namelist, count, ark->tableau->name, &choice, &flg));
2136:       if (flg) PetscCall(TSDIRKSetType(ts, namelist[choice]));
2137:     } else {
2138:       PetscCall(PetscOptionsEList("-ts_arkimex_type", "Family of ARK IMEX method", "TSARKIMEXSetType", (const char *const *)namelist, count, ark->tableau->name, &choice, &flg));
2139:       if (flg) PetscCall(TSARKIMEXSetType(ts, namelist[choice]));
2140:       flg = (PetscBool)!ark->imex;
2141:       PetscCall(PetscOptionsBool("-ts_arkimex_fully_implicit", "Solve the problem fully implicitly", "TSARKIMEXSetFullyImplicit", flg, &flg, NULL));
2142:       ark->imex = (PetscBool)!flg;
2143:     }
2144:     PetscCall(PetscFree(namelist));
2145:     PetscCall(PetscOptionsBool("-ts_arkimex_initial_guess_extrapolate", "Extrapolate the initial guess for the stage solution from stage values of the previous time step", "", ark->extrapolate, &ark->extrapolate, NULL));
2146:   }
2147:   PetscOptionsHeadEnd();
2148:   PetscFunctionReturn(PETSC_SUCCESS);
2149: }

2151: static PetscErrorCode TSView_ARKIMEX(TS ts, PetscViewer viewer)
2152: {
2153:   TS_ARKIMEX *ark = (TS_ARKIMEX *)ts->data;
2154:   PetscBool   iascii, dirk;

2156:   PetscFunctionBegin;
2157:   PetscCall(PetscObjectTypeCompare((PetscObject)ts, TSDIRK, &dirk));
2158:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &iascii));
2159:   if (iascii) {
2160:     PetscViewerFormat format;
2161:     ARKTableau        tab = ark->tableau;
2162:     TSARKIMEXType     arktype;
2163:     char              buf[2048];
2164:     PetscBool         flg;

2166:     PetscCall(TSARKIMEXGetType(ts, &arktype));
2167:     PetscCall(TSARKIMEXGetFullyImplicit(ts, &flg));
2168:     PetscCall(PetscViewerASCIIPrintf(viewer, "  %s %s\n", dirk ? "DIRK" : "ARK IMEX", arktype));
2169:     PetscCall(PetscFormatRealArray(buf, sizeof(buf), "% 8.6f", tab->s, tab->ct));
2170:     PetscCall(PetscViewerASCIIPrintf(viewer, "  %sabscissa       ct = %s\n", dirk ? "" : "Stiff ", buf));
2171:     PetscCall(PetscViewerGetFormat(viewer, &format));
2172:     if (format == PETSC_VIEWER_ASCII_INFO_DETAIL) {
2173:       PetscCall(PetscViewerASCIIPrintf(viewer, "  %sAt =\n", dirk ? "" : "Stiff "));
2174:       for (PetscInt i = 0; i < tab->s; i++) {
2175:         PetscCall(PetscFormatRealArray(buf, sizeof(buf), "% 8.6f", tab->s, tab->At + i * tab->s));
2176:         PetscCall(PetscViewerASCIIPrintf(viewer, "    %s\n", buf));
2177:       }
2178:       PetscCall(PetscFormatRealArray(buf, sizeof(buf), "% 8.6f", tab->s, tab->bt));
2179:       PetscCall(PetscViewerASCIIPrintf(viewer, "  %sbt = %s\n", dirk ? "" : "Stiff ", buf));
2180:       PetscCall(PetscFormatRealArray(buf, sizeof(buf), "% 8.6f", tab->s, tab->bembedt));
2181:       PetscCall(PetscViewerASCIIPrintf(viewer, "  %sbet = %s\n", dirk ? "" : "Stiff ", buf));
2182:     }
2183:     PetscCall(PetscViewerASCIIPrintf(viewer, "Fully implicit: %s\n", flg ? "yes" : "no"));
2184:     PetscCall(PetscViewerASCIIPrintf(viewer, "Stiffly accurate: %s\n", tab->stiffly_accurate ? "yes" : "no"));
2185:     PetscCall(PetscViewerASCIIPrintf(viewer, "Explicit first stage: %s\n", tab->explicit_first_stage ? "yes" : "no"));
2186:     PetscCall(PetscViewerASCIIPrintf(viewer, "FSAL property: %s\n", tab->FSAL_implicit ? "yes" : "no"));
2187:     if (!dirk) {
2188:       PetscCall(PetscFormatRealArray(buf, sizeof(buf), "% 8.6f", tab->s, tab->c));
2189:       PetscCall(PetscViewerASCIIPrintf(viewer, "  Nonstiff abscissa     c = %s\n", buf));
2190:     }
2191:   }
2192:   PetscFunctionReturn(PETSC_SUCCESS);
2193: }

2195: static PetscErrorCode TSLoad_ARKIMEX(TS ts, PetscViewer viewer)
2196: {
2197:   SNES    snes;
2198:   TSAdapt adapt;

2200:   PetscFunctionBegin;
2201:   PetscCall(TSGetAdapt(ts, &adapt));
2202:   PetscCall(TSAdaptLoad(adapt, viewer));
2203:   PetscCall(TSGetSNES(ts, &snes));
2204:   PetscCall(SNESLoad(snes, viewer));
2205:   /* function and Jacobian context for SNES when used with TS is always ts object */
2206:   PetscCall(SNESSetFunction(snes, NULL, NULL, ts));
2207:   PetscCall(SNESSetJacobian(snes, NULL, NULL, NULL, ts));
2208:   PetscFunctionReturn(PETSC_SUCCESS);
2209: }

2211: /*@C
2212:   TSARKIMEXSetType - Set the type of `TSARKIMEX` scheme

2214:   Logically Collective

2216:   Input Parameters:
2217: + ts      - timestepping context
2218: - arktype - type of `TSARKIMEX` scheme

2220:   Options Database Key:
2221: . -ts_arkimex_type <1bee,a2,l2,ars122,2c,2d,2e,prssp2,3,bpr3,ars443,4,5> - set `TSARKIMEX` scheme type

2223:   Level: intermediate

2225: .seealso: [](ch_ts), `TSARKIMEXGetType()`, `TSARKIMEX`, `TSARKIMEXType`, `TSARKIMEX1BEE`, `TSARKIMEXA2`, `TSARKIMEXL2`, `TSARKIMEXARS122`, `TSARKIMEX2C`, `TSARKIMEX2D`, `TSARKIMEX2E`, `TSARKIMEXPRSSP2`,
2226:           `TSARKIMEX3`, `TSARKIMEXBPR3`, `TSARKIMEXARS443`, `TSARKIMEX4`, `TSARKIMEX5`
2227: @*/
2228: PetscErrorCode TSARKIMEXSetType(TS ts, TSARKIMEXType arktype)
2229: {
2230:   PetscFunctionBegin;
2232:   PetscAssertPointer(arktype, 2);
2233:   PetscTryMethod(ts, "TSARKIMEXSetType_C", (TS, TSARKIMEXType), (ts, arktype));
2234:   PetscFunctionReturn(PETSC_SUCCESS);
2235: }

2237: /*@C
2238:   TSARKIMEXGetType - Get the type of `TSARKIMEX` scheme

2240:   Logically Collective

2242:   Input Parameter:
2243: . ts - timestepping context

2245:   Output Parameter:
2246: . arktype - type of `TSARKIMEX` scheme

2248:   Level: intermediate

2250: .seealso: [](ch_ts), `TSARKIMEXc`
2251: @*/
2252: PetscErrorCode TSARKIMEXGetType(TS ts, TSARKIMEXType *arktype)
2253: {
2254:   PetscFunctionBegin;
2256:   PetscUseMethod(ts, "TSARKIMEXGetType_C", (TS, TSARKIMEXType *), (ts, arktype));
2257:   PetscFunctionReturn(PETSC_SUCCESS);
2258: }

2260: /*@
2261:   TSARKIMEXSetFullyImplicit - Solve both parts of the equation implicitly, including the part that is normally solved explicitly

2263:   Logically Collective

2265:   Input Parameters:
2266: + ts  - timestepping context
2267: - flg - `PETSC_TRUE` for fully implicit

2269:   Level: intermediate

2271: .seealso: [](ch_ts), `TSARKIMEX`, `TSARKIMEXGetType()`, `TSARKIMEXGetFullyImplicit()`
2272: @*/
2273: PetscErrorCode TSARKIMEXSetFullyImplicit(TS ts, PetscBool flg)
2274: {
2275:   PetscFunctionBegin;
2278:   PetscTryMethod(ts, "TSARKIMEXSetFullyImplicit_C", (TS, PetscBool), (ts, flg));
2279:   PetscFunctionReturn(PETSC_SUCCESS);
2280: }

2282: /*@
2283:   TSARKIMEXGetFullyImplicit - Inquires if both parts of the equation are solved implicitly

2285:   Logically Collective

2287:   Input Parameter:
2288: . ts - timestepping context

2290:   Output Parameter:
2291: . flg - `PETSC_TRUE` for fully implicit

2293:   Level: intermediate

2295: .seealso: [](ch_ts), `TSARKIMEXGetType()`, `TSARKIMEXSetFullyImplicit()`
2296: @*/
2297: PetscErrorCode TSARKIMEXGetFullyImplicit(TS ts, PetscBool *flg)
2298: {
2299:   PetscFunctionBegin;
2301:   PetscAssertPointer(flg, 2);
2302:   PetscUseMethod(ts, "TSARKIMEXGetFullyImplicit_C", (TS, PetscBool *), (ts, flg));
2303:   PetscFunctionReturn(PETSC_SUCCESS);
2304: }

2306: static PetscErrorCode TSARKIMEXGetType_ARKIMEX(TS ts, TSARKIMEXType *arktype)
2307: {
2308:   TS_ARKIMEX *ark = (TS_ARKIMEX *)ts->data;

2310:   PetscFunctionBegin;
2311:   *arktype = ark->tableau->name;
2312:   PetscFunctionReturn(PETSC_SUCCESS);
2313: }

2315: static PetscErrorCode TSARKIMEXSetType_ARKIMEX(TS ts, TSARKIMEXType arktype)
2316: {
2317:   TS_ARKIMEX    *ark = (TS_ARKIMEX *)ts->data;
2318:   PetscBool      match;
2319:   ARKTableauLink link;

2321:   PetscFunctionBegin;
2322:   if (ark->tableau) {
2323:     PetscCall(PetscStrcmp(ark->tableau->name, arktype, &match));
2324:     if (match) PetscFunctionReturn(PETSC_SUCCESS);
2325:   }
2326:   for (link = ARKTableauList; link; link = link->next) {
2327:     PetscCall(PetscStrcmp(link->tab.name, arktype, &match));
2328:     if (match) {
2329:       if (ts->setupcalled) PetscCall(TSARKIMEXTableauReset(ts));
2330:       ark->tableau = &link->tab;
2331:       if (ts->setupcalled) PetscCall(TSARKIMEXTableauSetUp(ts));
2332:       ts->default_adapt_type = ark->tableau->bembed ? TSADAPTBASIC : TSADAPTNONE;
2333:       PetscFunctionReturn(PETSC_SUCCESS);
2334:     }
2335:   }
2336:   SETERRQ(PetscObjectComm((PetscObject)ts), PETSC_ERR_ARG_UNKNOWN_TYPE, "Could not find '%s'", arktype);
2337: }

2339: static PetscErrorCode TSARKIMEXSetFullyImplicit_ARKIMEX(TS ts, PetscBool flg)
2340: {
2341:   TS_ARKIMEX *ark = (TS_ARKIMEX *)ts->data;

2343:   PetscFunctionBegin;
2344:   ark->imex = (PetscBool)!flg;
2345:   PetscFunctionReturn(PETSC_SUCCESS);
2346: }

2348: static PetscErrorCode TSARKIMEXGetFullyImplicit_ARKIMEX(TS ts, PetscBool *flg)
2349: {
2350:   TS_ARKIMEX *ark = (TS_ARKIMEX *)ts->data;

2352:   PetscFunctionBegin;
2353:   *flg = (PetscBool)!ark->imex;
2354:   PetscFunctionReturn(PETSC_SUCCESS);
2355: }

2357: static PetscErrorCode TSDestroy_ARKIMEX(TS ts)
2358: {
2359:   PetscFunctionBegin;
2360:   PetscCall(TSReset_ARKIMEX(ts));
2361:   if (ts->dm) {
2362:     PetscCall(DMCoarsenHookRemove(ts->dm, DMCoarsenHook_TSARKIMEX, DMRestrictHook_TSARKIMEX, ts));
2363:     PetscCall(DMSubDomainHookRemove(ts->dm, DMSubDomainHook_TSARKIMEX, DMSubDomainRestrictHook_TSARKIMEX, ts));
2364:   }
2365:   PetscCall(PetscFree(ts->data));
2366:   PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSDIRKGetType_C", NULL));
2367:   PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSDIRKSetType_C", NULL));
2368:   PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSARKIMEXGetType_C", NULL));
2369:   PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSARKIMEXSetType_C", NULL));
2370:   PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSARKIMEXSetFullyImplicit_C", NULL));
2371:   PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSARKIMEXGetFullyImplicit_C", NULL));
2372:   PetscFunctionReturn(PETSC_SUCCESS);
2373: }

2375: /* ------------------------------------------------------------ */
2376: /*MC
2377:       TSARKIMEX - ODE and DAE solver using additive Runge-Kutta IMEX schemes

2379:   These methods are intended for problems with well-separated time scales, especially when a slow scale is strongly
2380:   nonlinear such that it is expensive to solve with a fully implicit method. The user should provide the stiff part
2381:   of the equation using `TSSetIFunction()` and the non-stiff part with `TSSetRHSFunction()`.

2383:   Level: beginner

2385:   Notes:
2386:   The default is `TSARKIMEX3`, it can be changed with `TSARKIMEXSetType()` or -ts_arkimex_type

2388:   If the equation is implicit or a DAE, then `TSSetEquationType()` needs to be set accordingly. Refer to the manual for further information.

2390:   Methods with an explicit stage can only be used with ODE in which the stiff part G(t,X,Xdot) has the form Xdot + Ghat(t,X).

2392:   Consider trying `TSROSW` if the stiff part is linear or weakly nonlinear.

2394: .seealso: [](ch_ts), `TSCreate()`, `TS`, `TSSetType()`, `TSARKIMEXSetType()`, `TSARKIMEXGetType()`, `TSARKIMEXSetFullyImplicit()`, `TSARKIMEXGetFullyImplicit()`,
2395:           `TSARKIMEX1BEE`, `TSARKIMEX2C`, `TSARKIMEX2D`, `TSARKIMEX2E`, `TSARKIMEX3`, `TSARKIMEXL2`, `TSARKIMEXA2`, `TSARKIMEXARS122`,
2396:           `TSARKIMEX4`, `TSARKIMEX5`, `TSARKIMEXPRSSP2`, `TSARKIMEXARS443`, `TSARKIMEXBPR3`, `TSARKIMEXType`, `TSARKIMEXRegister()`, `TSType`
2397: M*/
2398: PETSC_EXTERN PetscErrorCode TSCreate_ARKIMEX(TS ts)
2399: {
2400:   TS_ARKIMEX *ark;
2401:   PetscBool   dirk;

2403:   PetscFunctionBegin;
2404:   PetscCall(TSARKIMEXInitializePackage());
2405:   PetscCall(PetscObjectTypeCompare((PetscObject)ts, TSDIRK, &dirk));

2407:   ts->ops->reset          = TSReset_ARKIMEX;
2408:   ts->ops->adjointreset   = TSAdjointReset_ARKIMEX;
2409:   ts->ops->destroy        = TSDestroy_ARKIMEX;
2410:   ts->ops->view           = TSView_ARKIMEX;
2411:   ts->ops->load           = TSLoad_ARKIMEX;
2412:   ts->ops->setup          = TSSetUp_ARKIMEX;
2413:   ts->ops->adjointsetup   = TSAdjointSetUp_ARKIMEX;
2414:   ts->ops->step           = TSStep_ARKIMEX;
2415:   ts->ops->interpolate    = TSInterpolate_ARKIMEX;
2416:   ts->ops->evaluatestep   = TSEvaluateStep_ARKIMEX;
2417:   ts->ops->rollback       = TSRollBack_ARKIMEX;
2418:   ts->ops->setfromoptions = TSSetFromOptions_ARKIMEX;
2419:   ts->ops->snesfunction   = SNESTSFormFunction_ARKIMEX;
2420:   ts->ops->snesjacobian   = SNESTSFormJacobian_ARKIMEX;
2421:   ts->ops->getstages      = TSGetStages_ARKIMEX;
2422:   ts->ops->adjointstep    = TSAdjointStep_ARKIMEX;

2424:   ts->usessnes = PETSC_TRUE;

2426:   PetscCall(PetscNew(&ark));
2427:   ts->data  = (void *)ark;
2428:   ark->imex = dirk ? PETSC_FALSE : PETSC_TRUE;

2430:   ark->VecsDeltaLam   = NULL;
2431:   ark->VecsSensiTemp  = NULL;
2432:   ark->VecsSensiPTemp = NULL;

2434:   PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSARKIMEXGetType_C", TSARKIMEXGetType_ARKIMEX));
2435:   PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSARKIMEXGetFullyImplicit_C", TSARKIMEXGetFullyImplicit_ARKIMEX));
2436:   if (!dirk) {
2437:     PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSARKIMEXSetType_C", TSARKIMEXSetType_ARKIMEX));
2438:     PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSARKIMEXSetFullyImplicit_C", TSARKIMEXSetFullyImplicit_ARKIMEX));
2439:     PetscCall(TSARKIMEXSetType(ts, TSARKIMEXDefault));
2440:   }
2441:   PetscFunctionReturn(PETSC_SUCCESS);
2442: }

2444: /* ------------------------------------------------------------ */

2446: static PetscErrorCode TSDIRKSetType_DIRK(TS ts, TSDIRKType dirktype)
2447: {
2448:   TS_ARKIMEX *ark = (TS_ARKIMEX *)ts->data;

2450:   PetscFunctionBegin;
2451:   PetscCall(TSARKIMEXSetType_ARKIMEX(ts, dirktype));
2452:   PetscCheck(!ark->tableau->additive, PetscObjectComm((PetscObject)ts), PETSC_ERR_ARG_WRONG, "Method \"%s\" is not DIRK", dirktype);
2453:   PetscFunctionReturn(PETSC_SUCCESS);
2454: }

2456: /*@C
2457:   TSDIRKSetType - Set the type of `TSDIRK` scheme

2459:   Logically Collective

2461:   Input Parameters:
2462: + ts       - timestepping context
2463: - dirktype - type of `TSDIRK` scheme

2465:   Options Database Key:
2466: . -ts_dirkimex_type - set `TSDIRK` scheme type

2468:   Level: intermediate

2470: .seealso: [](ch_ts), `TSDIRKGetType()`, `TSDIRK`, `TSDIRKType`
2471: @*/
2472: PetscErrorCode TSDIRKSetType(TS ts, TSDIRKType dirktype)
2473: {
2474:   PetscFunctionBegin;
2476:   PetscAssertPointer(dirktype, 2);
2477:   PetscTryMethod(ts, "TSDIRKSetType_C", (TS, TSDIRKType), (ts, dirktype));
2478:   PetscFunctionReturn(PETSC_SUCCESS);
2479: }

2481: /*@C
2482:   TSDIRKGetType - Get the type of `TSDIRK` scheme

2484:   Logically Collective

2486:   Input Parameter:
2487: . ts - timestepping context

2489:   Output Parameter:
2490: . dirktype - type of `TSDIRK` scheme

2492:   Level: intermediate

2494: .seealso: [](ch_ts), `TSDIRKSetType()`
2495: @*/
2496: PetscErrorCode TSDIRKGetType(TS ts, TSDIRKType *dirktype)
2497: {
2498:   PetscFunctionBegin;
2500:   PetscUseMethod(ts, "TSDIRKGetType_C", (TS, TSDIRKType *), (ts, dirktype));
2501:   PetscFunctionReturn(PETSC_SUCCESS);
2502: }

2504: /*MC
2505:       TSDIRK - ODE and DAE solver using Diagonally implicit Runge-Kutta schemes.

2507:   Level: beginner

2509:   Notes:
2510:   The default is `TSDIRKES213SAL`, it can be changed with `TSDIRKSetType()` or -ts_dirk_type.
2511:   The convention used in PETSc to name the DIRK methods is TSDIRK[E][S]PQS[SA][L][A] with:
2512: + E - whether the method has an explicit first stage
2513: . S - whether the method is single diagonal
2514: . P - order of the advancing method
2515: . Q - order of the embedded method
2516: . S - number of stages
2517: . SA - whether the method is stiffly accurate
2518: . L - whether the method is L-stable
2519: - A - whether the method is A-stable

2521: .seealso: [](ch_ts), `TSCreate()`, `TS`, `TSSetType()`, `TSDIRKSetType()`, `TSDIRKGetType()`, `TSDIRKRegister()`.
2522: M*/
2523: PETSC_EXTERN PetscErrorCode TSCreate_DIRK(TS ts)
2524: {
2525:   PetscFunctionBegin;
2526:   PetscCall(TSCreate_ARKIMEX(ts));
2527:   PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSDIRKGetType_C", TSARKIMEXGetType_ARKIMEX));
2528:   PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSDIRKSetType_C", TSDIRKSetType_DIRK));
2529:   PetscCall(TSDIRKSetType(ts, TSDIRKDefault));
2530:   PetscFunctionReturn(PETSC_SUCCESS);
2531: }