Actual source code: rosw.c

  1: /*
  2:   Code for timestepping with Rosenbrock W methods

  4:   Notes:
  5:   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.
 10:   This method is designed to be linearly implicit on F and can use an approximate and lagged Jacobian.

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

 16: #include <petsc/private/kernels/blockinvert.h>

 18: static TSRosWType TSRosWDefault = TSROSWRA34PW2;
 19: static PetscBool  TSRosWRegisterAllCalled;
 20: static PetscBool  TSRosWPackageInitialized;

 22: typedef struct _RosWTableau *RosWTableau;
 23: struct _RosWTableau {
 24:   char      *name;
 25:   PetscInt   order;             /* Classical approximation order of the method */
 26:   PetscInt   s;                 /* Number of stages */
 27:   PetscInt   pinterp;           /* Interpolation order */
 28:   PetscReal *A;                 /* Propagation table, strictly lower triangular */
 29:   PetscReal *Gamma;             /* Stage table, lower triangular with nonzero diagonal */
 30:   PetscBool *GammaZeroDiag;     /* Diagonal entries that are zero in stage table Gamma, vector indicating explicit statages */
 31:   PetscReal *GammaExplicitCorr; /* Coefficients for correction terms needed for explicit stages in transformed variables*/
 32:   PetscReal *b;                 /* Step completion table */
 33:   PetscReal *bembed;            /* Step completion table for embedded method of order one less */
 34:   PetscReal *ASum;              /* Row sum of A */
 35:   PetscReal *GammaSum;          /* Row sum of Gamma, only needed for non-autonomous systems */
 36:   PetscReal *At;                /* Propagation table in transformed variables */
 37:   PetscReal *bt;                /* Step completion table in transformed variables */
 38:   PetscReal *bembedt;           /* Step completion table of order one less in transformed variables */
 39:   PetscReal *GammaInv;          /* Inverse of Gamma, used for transformed variables */
 40:   PetscReal  ccfl;              /* Placeholder for CFL coefficient relative to forward Euler */
 41:   PetscReal *binterpt;          /* Dense output formula */
 42: };
 43: typedef struct _RosWTableauLink *RosWTableauLink;
 44: struct _RosWTableauLink {
 45:   struct _RosWTableau tab;
 46:   RosWTableauLink     next;
 47: };
 48: static RosWTableauLink RosWTableauList;

 50: typedef struct {
 51:   RosWTableau  tableau;
 52:   Vec         *Y;            /* States computed during the step, used to complete the step */
 53:   Vec          Ydot;         /* Work vector holding Ydot during residual evaluation */
 54:   Vec          Ystage;       /* Work vector for the state value at each stage */
 55:   Vec          Zdot;         /* Ydot = Zdot + shift*Y */
 56:   Vec          Zstage;       /* Y = Zstage + Y */
 57:   Vec          vec_sol_prev; /* Solution from the previous step (used for interpolation and rollback)*/
 58:   PetscScalar *work;         /* Scalar work space of length number of stages, used to prepare VecMAXPY() */
 59:   PetscReal    scoeff;       /* shift = scoeff/dt */
 60:   PetscReal    stage_time;
 61:   PetscReal    stage_explicit;     /* Flag indicates that the current stage is explicit */
 62:   PetscBool    recompute_jacobian; /* Recompute the Jacobian at each stage, default is to freeze the Jacobian at the start of each step */
 63:   TSStepStatus status;
 64: } TS_RosW;

 66: /*MC
 67:      TSROSWTHETA1 - One stage first order L-stable Rosenbrock-W scheme (aka theta method).

 69:      Only an approximate Jacobian is needed.

 71:      Level: intermediate

 73: .seealso: [](ch_ts), `TSROSW`
 74: M*/

 76: /*MC
 77:      TSROSWTHETA2 - One stage second order A-stable Rosenbrock-W scheme (aka theta method).

 79:      Only an approximate Jacobian is needed.

 81:      Level: intermediate

 83: .seealso: [](ch_ts), `TSROSW`
 84: M*/

 86: /*MC
 87:      TSROSW2M - Two stage second order L-stable Rosenbrock-W scheme.

 89:      Only an approximate Jacobian is needed. By default, it is only recomputed once per step. This method is a reflection of TSROSW2P.

 91:      Level: intermediate

 93: .seealso: [](ch_ts), `TSROSW`
 94: M*/

 96: /*MC
 97:      TSROSW2P - Two stage second order L-stable Rosenbrock-W scheme.

 99:      Only an approximate Jacobian is needed. By default, it is only recomputed once per step. This method is a reflection of TSROSW2M.

101:      Level: intermediate

103: .seealso: [](ch_ts), `TSROSW`
104: M*/

106: /*MC
107:      TSROSWRA3PW - Three stage third order Rosenbrock-W scheme for PDAE of index 1.

109:      Only an approximate Jacobian is needed. By default, it is only recomputed once per step.

111:      This is strongly A-stable with R(infty) = 0.73. The embedded method of order 2 is strongly A-stable with R(infty) = 0.73.

113:      Level: intermediate

115:      References:
116: .  * - Rang and Angermann, New Rosenbrock W methods of order 3 for partial differential algebraic equations of index 1, 2005.

118: .seealso: [](ch_ts), `TSROSW`
119: M*/

121: /*MC
122:      TSROSWRA34PW2 - Four stage third order L-stable Rosenbrock-W scheme for PDAE of index 1.

124:      Only an approximate Jacobian is needed. By default, it is only recomputed once per step.

126:      This is strongly A-stable with R(infty) = 0. The embedded method of order 2 is strongly A-stable with R(infty) = 0.48.

128:      Level: intermediate

130:      References:
131: .  * - Rang and Angermann, New Rosenbrock W methods of order 3 for partial differential algebraic equations of index 1, 2005.

133: .seealso: [](ch_ts), `TSROSW`
134: M*/

136: /*MC
137:      TSROSWRODAS3 - Four stage third order L-stable Rosenbrock scheme

139:      By default, the Jacobian is only recomputed once per step.

141:      Both the third order and embedded second order methods are stiffly accurate and L-stable.

143:      Level: intermediate

145:      References:
146: .  * - Sandu et al, Benchmarking stiff ODE solvers for atmospheric chemistry problems II, Rosenbrock solvers, 1997.

148: .seealso: [](ch_ts), `TSROSW`, `TSROSWSANDU3`
149: M*/

151: /*MC
152:      TSROSWSANDU3 - Three stage third order L-stable Rosenbrock scheme

154:      By default, the Jacobian is only recomputed once per step.

156:      The third order method is L-stable, but not stiffly accurate.
157:      The second order embedded method is strongly A-stable with R(infty) = 0.5.
158:      The internal stages are L-stable.
159:      This method is called ROS3 in the paper.

161:      Level: intermediate

163:      References:
164: .  * - Sandu et al, Benchmarking stiff ODE solvers for atmospheric chemistry problems II, Rosenbrock solvers, 1997.

166: .seealso: [](ch_ts), `TSROSW`, `TSROSWRODAS3`
167: M*/

169: /*MC
170:      TSROSWASSP3P3S1C - A-stable Rosenbrock-W method with SSP explicit part, third order, three stages

172:      By default, the Jacobian is only recomputed once per step.

174:      A-stable SPP explicit order 3, 3 stages, CFL 1 (eff = 1/3)

176:      Level: intermediate

178:      References:
179: . * - Emil Constantinescu

181: .seealso: [](ch_ts), `TSROSW`, `TSROSWLASSP3P4S2C`, `TSROSWLLSSP3P4S2C`, `SSP`
182: M*/

184: /*MC
185:      TSROSWLASSP3P4S2C - L-stable Rosenbrock-W method with SSP explicit part, third order, four stages

187:      By default, the Jacobian is only recomputed once per step.

189:      L-stable (A-stable embedded) SPP explicit order 3, 4 stages, CFL 2 (eff = 1/2)

191:      Level: intermediate

193:      References:
194: . * - Emil Constantinescu

196: .seealso: [](ch_ts), `TSROSW`, `TSROSWASSP3P3S1C`, `TSROSWLLSSP3P4S2C`, `TSSSP`
197: M*/

199: /*MC
200:      TSROSWLLSSP3P4S2C - L-stable Rosenbrock-W method with SSP explicit part, third order, four stages

202:      By default, the Jacobian is only recomputed once per step.

204:      L-stable (L-stable embedded) SPP explicit order 3, 4 stages, CFL 2 (eff = 1/2)

206:      Level: intermediate

208:      References:
209: . * - Emil Constantinescu

211: .seealso: [](ch_ts), `TSROSW`, `TSROSWASSP3P3S1C`, `TSROSWLASSP3P4S2C`, `TSSSP`
212: M*/

214: /*MC
215:      TSROSWGRK4T - four stage, fourth order Rosenbrock (not W) method from Kaps and Rentrop

217:      By default, the Jacobian is only recomputed once per step.

219:      A(89.3 degrees)-stable, |R(infty)| = 0.454.

221:      This method does not provide a dense output formula.

223:      Level: intermediate

225:      References:
226: +   * -  Kaps and Rentrop, Generalized Runge Kutta methods of order four with stepsize control for stiff ordinary differential equations, 1979.
227: -   * -  Hairer and Wanner, Solving Ordinary Differential Equations II, Section 4 Table 7.2.

229:      Hairer's code ros4.f

231: .seealso: [](ch_ts), `TSROSW`, `TSROSWSHAMP4`, `TSROSWVELDD4`, `TSROSW4L`
232: M*/

234: /*MC
235:      TSROSWSHAMP4 - four stage, fourth order Rosenbrock (not W) method from Shampine

237:      By default, the Jacobian is only recomputed once per step.

239:      A-stable, |R(infty)| = 1/3.

241:      This method does not provide a dense output formula.

243:      Level: intermediate

245:      References:
246: +   * -  Shampine, Implementation of Rosenbrock methods, 1982.
247: -   * -  Hairer and Wanner, Solving Ordinary Differential Equations II, Section 4 Table 7.2.

249:      Hairer's code ros4.f

251: .seealso: [](ch_ts), `TSROSW`, `TSROSWGRK4T`, `TSROSWVELDD4`, `TSROSW4L`
252: M*/

254: /*MC
255:      TSROSWVELDD4 - four stage, fourth order Rosenbrock (not W) method from van Veldhuizen

257:      By default, the Jacobian is only recomputed once per step.

259:      A(89.5 degrees)-stable, |R(infty)| = 0.24.

261:      This method does not provide a dense output formula.

263:      Level: intermediate

265:      References:
266: +   * -  van Veldhuizen, D stability and Kaps Rentrop methods, 1984.
267: -   * -  Hairer and Wanner, Solving Ordinary Differential Equations II, Section 4 Table 7.2.

269:      Hairer's code ros4.f

271: .seealso: [](ch_ts), `TSROSW`, `TSROSWGRK4T`, `TSROSWSHAMP4`, `TSROSW4L`
272: M*/

274: /*MC
275:      TSROSW4L - four stage, fourth order Rosenbrock (not W) method

277:      By default, the Jacobian is only recomputed once per step.

279:      A-stable and L-stable

281:      This method does not provide a dense output formula.

283:      Level: intermediate

285:      References:
286: .  * -   Hairer and Wanner, Solving Ordinary Differential Equations II, Section 4 Table 7.2.

288:      Hairer's code ros4.f

290: .seealso: [](ch_ts), `TSROSW`, `TSROSWGRK4T`, `TSROSWSHAMP4`, `TSROSW4L`
291: M*/

293: /*@C
294:   TSRosWRegisterAll - Registers all of the Rosenbrock-W methods in `TSROSW`

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

298:   Level: advanced

300: .seealso: [](ch_ts), `TSROSW`, `TSRosWRegisterDestroy()`
301: @*/
302: PetscErrorCode TSRosWRegisterAll(void)
303: {
304:   PetscFunctionBegin;
305:   if (TSRosWRegisterAllCalled) PetscFunctionReturn(PETSC_SUCCESS);
306:   TSRosWRegisterAllCalled = PETSC_TRUE;

308:   {
309:     const PetscReal A        = 0;
310:     const PetscReal Gamma    = 1;
311:     const PetscReal b        = 1;
312:     const PetscReal binterpt = 1;

314:     PetscCall(TSRosWRegister(TSROSWTHETA1, 1, 1, &A, &Gamma, &b, NULL, 1, &binterpt));
315:   }

317:   {
318:     const PetscReal A        = 0;
319:     const PetscReal Gamma    = 0.5;
320:     const PetscReal b        = 1;
321:     const PetscReal binterpt = 1;

323:     PetscCall(TSRosWRegister(TSROSWTHETA2, 2, 1, &A, &Gamma, &b, NULL, 1, &binterpt));
324:   }

326:   {
327:     /*const PetscReal g = 1. + 1./PetscSqrtReal(2.0);   Direct evaluation: 1.707106781186547524401. Used for setting up arrays of values known at compile time below. */
328:     const PetscReal A[2][2] =
329:       {
330:         {0,  0},
331:         {1., 0}
332:     },
333:                     Gamma[2][2] = {{1.707106781186547524401, 0}, {-2. * 1.707106781186547524401, 1.707106781186547524401}}, b[2] = {0.5, 0.5}, b1[2] = {1.0, 0.0};
334:     PetscReal binterpt[2][2];
335:     binterpt[0][0] = 1.707106781186547524401 - 1.0;
336:     binterpt[1][0] = 2.0 - 1.707106781186547524401;
337:     binterpt[0][1] = 1.707106781186547524401 - 1.5;
338:     binterpt[1][1] = 1.5 - 1.707106781186547524401;

340:     PetscCall(TSRosWRegister(TSROSW2P, 2, 2, &A[0][0], &Gamma[0][0], b, b1, 2, &binterpt[0][0]));
341:   }
342:   {
343:     /*const PetscReal g = 1. - 1./PetscSqrtReal(2.0);   Direct evaluation: 0.2928932188134524755992. Used for setting up arrays of values known at compile time below. */
344:     const PetscReal A[2][2] =
345:       {
346:         {0,  0},
347:         {1., 0}
348:     },
349:                     Gamma[2][2] = {{0.2928932188134524755992, 0}, {-2. * 0.2928932188134524755992, 0.2928932188134524755992}}, b[2] = {0.5, 0.5}, b1[2] = {1.0, 0.0};
350:     PetscReal binterpt[2][2];
351:     binterpt[0][0] = 0.2928932188134524755992 - 1.0;
352:     binterpt[1][0] = 2.0 - 0.2928932188134524755992;
353:     binterpt[0][1] = 0.2928932188134524755992 - 1.5;
354:     binterpt[1][1] = 1.5 - 0.2928932188134524755992;

356:     PetscCall(TSRosWRegister(TSROSW2M, 2, 2, &A[0][0], &Gamma[0][0], b, b1, 2, &binterpt[0][0]));
357:   }
358:   {
359:     /*const PetscReal g = 7.8867513459481287e-01; Directly written in-place below */
360:     PetscReal       binterpt[3][2];
361:     const PetscReal A[3][3] =
362:       {
363:         {0,                      0, 0},
364:         {1.5773502691896257e+00, 0, 0},
365:         {0.5,                    0, 0}
366:     },
367:                     Gamma[3][3] = {{7.8867513459481287e-01, 0, 0}, {-1.5773502691896257e+00, 7.8867513459481287e-01, 0}, {-6.7075317547305480e-01, -1.7075317547305482e-01, 7.8867513459481287e-01}}, b[3] = {1.0566243270259355e-01, 4.9038105676657971e-02, 8.4529946162074843e-01}, b2[3] = {-1.7863279495408180e-01, 1. / 3., 8.4529946162074843e-01};

369:     binterpt[0][0] = -0.8094010767585034;
370:     binterpt[1][0] = -0.5;
371:     binterpt[2][0] = 2.3094010767585034;
372:     binterpt[0][1] = 0.9641016151377548;
373:     binterpt[1][1] = 0.5;
374:     binterpt[2][1] = -1.4641016151377548;

376:     PetscCall(TSRosWRegister(TSROSWRA3PW, 3, 3, &A[0][0], &Gamma[0][0], b, b2, 2, &binterpt[0][0]));
377:   }
378:   {
379:     PetscReal binterpt[4][3];
380:     /*const PetscReal g = 4.3586652150845900e-01; Directly written in-place below */
381:     const PetscReal A[4][4] =
382:       {
383:         {0,                      0,                       0,  0},
384:         {8.7173304301691801e-01, 0,                       0,  0},
385:         {8.4457060015369423e-01, -1.1299064236484185e-01, 0,  0},
386:         {0,                      0,                       1., 0}
387:     },
388:                     Gamma[4][4] = {{4.3586652150845900e-01, 0, 0, 0}, {-8.7173304301691801e-01, 4.3586652150845900e-01, 0, 0}, {-9.0338057013044082e-01, 5.4180672388095326e-02, 4.3586652150845900e-01, 0}, {2.4212380706095346e-01, -1.2232505839045147e+00, 5.4526025533510214e-01, 4.3586652150845900e-01}}, b[4] = {2.4212380706095346e-01, -1.2232505839045147e+00, 1.5452602553351020e+00, 4.3586652150845900e-01}, b2[4] = {3.7810903145819369e-01, -9.6042292212423178e-02, 5.0000000000000000e-01, 2.1793326075422950e-01};

390:     binterpt[0][0] = 1.0564298455794094;
391:     binterpt[1][0] = 2.296429974281067;
392:     binterpt[2][0] = -1.307599564525376;
393:     binterpt[3][0] = -1.045260255335102;
394:     binterpt[0][1] = -1.3864882699759573;
395:     binterpt[1][1] = -8.262611700275677;
396:     binterpt[2][1] = 7.250979895056055;
397:     binterpt[3][1] = 2.398120075195581;
398:     binterpt[0][2] = 0.5721822314575016;
399:     binterpt[1][2] = 4.742931142090097;
400:     binterpt[2][2] = -4.398120075195578;
401:     binterpt[3][2] = -0.9169932983520199;

403:     PetscCall(TSRosWRegister(TSROSWRA34PW2, 3, 4, &A[0][0], &Gamma[0][0], b, b2, 3, &binterpt[0][0]));
404:   }
405:   {
406:     /* const PetscReal g = 0.5;       Directly written in-place below */
407:     const PetscReal A[4][4] =
408:       {
409:         {0,    0,     0,   0},
410:         {0,    0,     0,   0},
411:         {1.,   0,     0,   0},
412:         {0.75, -0.25, 0.5, 0}
413:     },
414:                     Gamma[4][4] = {{0.5, 0, 0, 0}, {1., 0.5, 0, 0}, {-0.25, -0.25, 0.5, 0}, {1. / 12, 1. / 12, -2. / 3, 0.5}}, b[4] = {5. / 6, -1. / 6, -1. / 6, 0.5}, b2[4] = {0.75, -0.25, 0.5, 0};

416:     PetscCall(TSRosWRegister(TSROSWRODAS3, 3, 4, &A[0][0], &Gamma[0][0], b, b2, 0, NULL));
417:   }
418:   {
419:     /*const PetscReal g = 0.43586652150845899941601945119356;       Directly written in-place below */
420:     const PetscReal A[3][3] =
421:       {
422:         {0,                                  0, 0},
423:         {0.43586652150845899941601945119356, 0, 0},
424:         {0.43586652150845899941601945119356, 0, 0}
425:     },
426:                     Gamma[3][3] = {{0.43586652150845899941601945119356, 0, 0}, {-0.19294655696029095575009695436041, 0.43586652150845899941601945119356, 0}, {0, 1.74927148125794685173529749738960, 0.43586652150845899941601945119356}}, b[3] = {-0.75457412385404315829818998646589, 1.94100407061964420292840123379419, -0.18642994676560104463021124732829}, b2[3] = {-1.53358745784149585370766523913002, 2.81745131148625772213931745457622, -0.28386385364476186843165221544619};

428:     PetscReal binterpt[3][2];
429:     binterpt[0][0] = 3.793692883777660870425141387941;
430:     binterpt[1][0] = -2.918692883777660870425141387941;
431:     binterpt[2][0] = 0.125;
432:     binterpt[0][1] = -0.725741064379812106687651020584;
433:     binterpt[1][1] = 0.559074397713145440020984353917;
434:     binterpt[2][1] = 0.16666666666666666666666666666667;

436:     PetscCall(TSRosWRegister(TSROSWSANDU3, 3, 3, &A[0][0], &Gamma[0][0], b, b2, 2, &binterpt[0][0]));
437:   }
438:   {
439:     /*const PetscReal s3 = PetscSqrtReal(3.),g = (3.0+s3)/6.0;
440:      * Direct evaluation: s3 = 1.732050807568877293527;
441:      *                     g = 0.7886751345948128822546;
442:      * Values are directly inserted below to ensure availability at compile time (compiler warnings otherwise...) */
443:     const PetscReal A[3][3] =
444:       {
445:         {0,    0,    0},
446:         {1,    0,    0},
447:         {0.25, 0.25, 0}
448:     },
449:                     Gamma[3][3] = {{0, 0, 0}, {(-3.0 - 1.732050807568877293527) / 6.0, 0.7886751345948128822546, 0}, {(-3.0 - 1.732050807568877293527) / 24.0, (-3.0 - 1.732050807568877293527) / 8.0, 0.7886751345948128822546}}, b[3] = {1. / 6., 1. / 6., 2. / 3.}, b2[3] = {1. / 4., 1. / 4., 1. / 2.};
450:     PetscReal binterpt[3][2];

452:     binterpt[0][0] = 0.089316397477040902157517886164709;
453:     binterpt[1][0] = -0.91068360252295909784248211383529;
454:     binterpt[2][0] = 1.8213672050459181956849642276706;
455:     binterpt[0][1] = 0.077350269189625764509148780501957;
456:     binterpt[1][1] = 1.077350269189625764509148780502;
457:     binterpt[2][1] = -1.1547005383792515290182975610039;

459:     PetscCall(TSRosWRegister(TSROSWASSP3P3S1C, 3, 3, &A[0][0], &Gamma[0][0], b, b2, 2, &binterpt[0][0]));
460:   }

462:   {
463:     const PetscReal A[4][4] =
464:       {
465:         {0,       0,       0,       0},
466:         {1. / 2., 0,       0,       0},
467:         {1. / 2., 1. / 2., 0,       0},
468:         {1. / 6., 1. / 6., 1. / 6., 0}
469:     },
470:                     Gamma[4][4] = {{1. / 2., 0, 0, 0}, {0.0, 1. / 4., 0, 0}, {-2., -2. / 3., 2. / 3., 0}, {1. / 2., 5. / 36., -2. / 9, 0}}, b[4] = {1. / 6., 1. / 6., 1. / 6., 1. / 2.}, b2[4] = {1. / 8., 3. / 4., 1. / 8., 0};
471:     PetscReal binterpt[4][3];

473:     binterpt[0][0] = 6.25;
474:     binterpt[1][0] = -30.25;
475:     binterpt[2][0] = 1.75;
476:     binterpt[3][0] = 23.25;
477:     binterpt[0][1] = -9.75;
478:     binterpt[1][1] = 58.75;
479:     binterpt[2][1] = -3.25;
480:     binterpt[3][1] = -45.75;
481:     binterpt[0][2] = 3.6666666666666666666666666666667;
482:     binterpt[1][2] = -28.333333333333333333333333333333;
483:     binterpt[2][2] = 1.6666666666666666666666666666667;
484:     binterpt[3][2] = 23.;

486:     PetscCall(TSRosWRegister(TSROSWLASSP3P4S2C, 3, 4, &A[0][0], &Gamma[0][0], b, b2, 3, &binterpt[0][0]));
487:   }

489:   {
490:     const PetscReal A[4][4] =
491:       {
492:         {0,       0,       0,       0},
493:         {1. / 2., 0,       0,       0},
494:         {1. / 2., 1. / 2., 0,       0},
495:         {1. / 6., 1. / 6., 1. / 6., 0}
496:     },
497:                     Gamma[4][4] = {{1. / 2., 0, 0, 0}, {0.0, 3. / 4., 0, 0}, {-2. / 3., -23. / 9., 2. / 9., 0}, {1. / 18., 65. / 108., -2. / 27, 0}}, b[4] = {1. / 6., 1. / 6., 1. / 6., 1. / 2.}, b2[4] = {3. / 16., 10. / 16., 3. / 16., 0};
498:     PetscReal binterpt[4][3];

500:     binterpt[0][0] = 1.6911764705882352941176470588235;
501:     binterpt[1][0] = 3.6813725490196078431372549019608;
502:     binterpt[2][0] = 0.23039215686274509803921568627451;
503:     binterpt[3][0] = -4.6029411764705882352941176470588;
504:     binterpt[0][1] = -0.95588235294117647058823529411765;
505:     binterpt[1][1] = -6.2401960784313725490196078431373;
506:     binterpt[2][1] = -0.31862745098039215686274509803922;
507:     binterpt[3][1] = 7.5147058823529411764705882352941;
508:     binterpt[0][2] = -0.56862745098039215686274509803922;
509:     binterpt[1][2] = 2.7254901960784313725490196078431;
510:     binterpt[2][2] = 0.25490196078431372549019607843137;
511:     binterpt[3][2] = -2.4117647058823529411764705882353;

513:     PetscCall(TSRosWRegister(TSROSWLLSSP3P4S2C, 3, 4, &A[0][0], &Gamma[0][0], b, b2, 3, &binterpt[0][0]));
514:   }

516:   {
517:     PetscReal A[4][4], Gamma[4][4], b[4], b2[4];
518:     PetscReal binterpt[4][3];

520:     Gamma[0][0] = 0.4358665215084589994160194475295062513822671686978816;
521:     Gamma[0][1] = 0;
522:     Gamma[0][2] = 0;
523:     Gamma[0][3] = 0;
524:     Gamma[1][0] = -1.997527830934941248426324674704153457289527280554476;
525:     Gamma[1][1] = 0.4358665215084589994160194475295062513822671686978816;
526:     Gamma[1][2] = 0;
527:     Gamma[1][3] = 0;
528:     Gamma[2][0] = -1.007948511795029620852002345345404191008352770119903;
529:     Gamma[2][1] = -0.004648958462629345562774289390054679806993396798458131;
530:     Gamma[2][2] = 0.4358665215084589994160194475295062513822671686978816;
531:     Gamma[2][3] = 0;
532:     Gamma[3][0] = -0.6685429734233467180451604600279552604364311322650783;
533:     Gamma[3][1] = 0.6056625986449338476089525334450053439525178740492984;
534:     Gamma[3][2] = -0.9717899277217721234705114616271378792182450260943198;
535:     Gamma[3][3] = 0;

537:     A[0][0] = 0;
538:     A[0][1] = 0;
539:     A[0][2] = 0;
540:     A[0][3] = 0;
541:     A[1][0] = 0.8717330430169179988320388950590125027645343373957631;
542:     A[1][1] = 0;
543:     A[1][2] = 0;
544:     A[1][3] = 0;
545:     A[2][0] = 0.5275890119763004115618079766722914408876108660811028;
546:     A[2][1] = 0.07241098802369958843819203208518599088698057726988732;
547:     A[2][2] = 0;
548:     A[2][3] = 0;
549:     A[3][0] = 0.3990960076760701320627260685975778145384666450351314;
550:     A[3][1] = -0.4375576546135194437228463747348862825846903771419953;
551:     A[3][2] = 1.038461646937449311660120300601880176655352737312713;
552:     A[3][3] = 0;

554:     b[0] = 0.1876410243467238251612921333138006734899663569186926;
555:     b[1] = -0.5952974735769549480478230473706443582188442040780541;
556:     b[2] = 0.9717899277217721234705114616271378792182450260943198;
557:     b[3] = 0.4358665215084589994160194475295062513822671686978816;

559:     b2[0] = 0.2147402862233891404862383521089097657790734483804460;
560:     b2[1] = -0.4851622638849390928209050538171743017757490232519684;
561:     b2[2] = 0.8687250025203875511662123688667549217531982787600080;
562:     b2[3] = 0.4016969751411624011684543450940068201770721128357014;

564:     binterpt[0][0] = 2.2565812720167954547104627844105;
565:     binterpt[1][0] = 1.349166413351089573796243820819;
566:     binterpt[2][0] = -2.4695174540533503758652847586647;
567:     binterpt[3][0] = -0.13623023131453465264142184656474;
568:     binterpt[0][1] = -3.0826699111559187902922463354557;
569:     binterpt[1][1] = -2.4689115685996042534544925650515;
570:     binterpt[2][1] = 5.7428279814696677152129332773553;
571:     binterpt[3][1] = -0.19124650171414467146619437684812;
572:     binterpt[0][2] = 1.0137296634858471607430756831148;
573:     binterpt[1][2] = 0.52444768167155973161042570784064;
574:     binterpt[2][2] = -2.3015205996945452158771370439586;
575:     binterpt[3][2] = 0.76334325453713832352363565300308;

577:     PetscCall(TSRosWRegister(TSROSWARK3, 3, 4, &A[0][0], &Gamma[0][0], b, b2, 3, &binterpt[0][0]));
578:   }
579:   PetscCall(TSRosWRegisterRos4(TSROSWGRK4T, 0.231, PETSC_DEFAULT, PETSC_DEFAULT, 0, -0.1282612945269037e+01));
580:   PetscCall(TSRosWRegisterRos4(TSROSWSHAMP4, 0.5, PETSC_DEFAULT, PETSC_DEFAULT, 0, 125. / 108.));
581:   PetscCall(TSRosWRegisterRos4(TSROSWVELDD4, 0.22570811482256823492, PETSC_DEFAULT, PETSC_DEFAULT, 0, -1.355958941201148));
582:   PetscCall(TSRosWRegisterRos4(TSROSW4L, 0.57282, PETSC_DEFAULT, PETSC_DEFAULT, 0, -1.093502252409163));
583:   PetscFunctionReturn(PETSC_SUCCESS);
584: }

586: /*@C
587:    TSRosWRegisterDestroy - Frees the list of schemes that were registered by `TSRosWRegister()`.

589:    Not Collective

591:    Level: advanced

593: .seealso: [](ch_ts), `TSRosWRegister()`, `TSRosWRegisterAll()`
594: @*/
595: PetscErrorCode TSRosWRegisterDestroy(void)
596: {
597:   RosWTableauLink link;

599:   PetscFunctionBegin;
600:   while ((link = RosWTableauList)) {
601:     RosWTableau t   = &link->tab;
602:     RosWTableauList = link->next;
603:     PetscCall(PetscFree5(t->A, t->Gamma, t->b, t->ASum, t->GammaSum));
604:     PetscCall(PetscFree5(t->At, t->bt, t->GammaInv, t->GammaZeroDiag, t->GammaExplicitCorr));
605:     PetscCall(PetscFree2(t->bembed, t->bembedt));
606:     PetscCall(PetscFree(t->binterpt));
607:     PetscCall(PetscFree(t->name));
608:     PetscCall(PetscFree(link));
609:   }
610:   TSRosWRegisterAllCalled = PETSC_FALSE;
611:   PetscFunctionReturn(PETSC_SUCCESS);
612: }

614: /*@C
615:   TSRosWInitializePackage - This function initializes everything in the `TSROSW` package. It is called
616:   from `TSInitializePackage()`.

618:   Level: developer

620: .seealso: [](ch_ts), `TSROSW`, `PetscInitialize()`, `TSRosWFinalizePackage()`
621: @*/
622: PetscErrorCode TSRosWInitializePackage(void)
623: {
624:   PetscFunctionBegin;
625:   if (TSRosWPackageInitialized) PetscFunctionReturn(PETSC_SUCCESS);
626:   TSRosWPackageInitialized = PETSC_TRUE;
627:   PetscCall(TSRosWRegisterAll());
628:   PetscCall(PetscRegisterFinalize(TSRosWFinalizePackage));
629:   PetscFunctionReturn(PETSC_SUCCESS);
630: }

632: /*@C
633:   TSRosWFinalizePackage - This function destroys everything in the `TSROSW` package. It is
634:   called from `PetscFinalize()`.

636:   Level: developer

638: .seealso: [](ch_ts), `TSROSW`, `PetscFinalize()`, `TSRosWInitializePackage()`
639: @*/
640: PetscErrorCode TSRosWFinalizePackage(void)
641: {
642:   PetscFunctionBegin;
643:   TSRosWPackageInitialized = PETSC_FALSE;
644:   PetscCall(TSRosWRegisterDestroy());
645:   PetscFunctionReturn(PETSC_SUCCESS);
646: }

648: /*@C
649:    TSRosWRegister - register a `TSROSW`, Rosenbrock W scheme by providing the entries in the Butcher tableau and optionally embedded approximations and interpolation

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

653:    Input Parameters:
654: +  name - identifier for method
655: .  order - approximation order of method
656: .  s - number of stages, this is the dimension of the matrices below
657: .  A - Table of propagated stage coefficients (dimension s*s, row-major), strictly lower triangular
658: .  Gamma - Table of coefficients in implicit stage equations (dimension s*s, row-major), lower triangular with nonzero diagonal
659: .  b - Step completion table (dimension s)
660: .  bembed - Step completion table for a scheme of order one less (dimension s, NULL if no embedded scheme is available)
661: .  pinterp - Order of the interpolation scheme, equal to the number of columns of binterpt
662: -  binterpt - Coefficients of the interpolation formula (dimension s*pinterp)

664:    Level: advanced

666:    Note:
667:    Several Rosenbrock W methods are provided, this function is only needed to create new methods.

669: .seealso: [](ch_ts), `TSROSW`
670: @*/
671: PetscErrorCode TSRosWRegister(TSRosWType name, PetscInt order, PetscInt s, const PetscReal A[], const PetscReal Gamma[], const PetscReal b[], const PetscReal bembed[], PetscInt pinterp, const PetscReal binterpt[])
672: {
673:   RosWTableauLink link;
674:   RosWTableau     t;
675:   PetscInt        i, j, k;
676:   PetscScalar    *GammaInv;

678:   PetscFunctionBegin;

685:   PetscCall(TSRosWInitializePackage());
686:   PetscCall(PetscNew(&link));
687:   t = &link->tab;
688:   PetscCall(PetscStrallocpy(name, &t->name));
689:   t->order = order;
690:   t->s     = s;
691:   PetscCall(PetscMalloc5(s * s, &t->A, s * s, &t->Gamma, s, &t->b, s, &t->ASum, s, &t->GammaSum));
692:   PetscCall(PetscMalloc5(s * s, &t->At, s, &t->bt, s * s, &t->GammaInv, s, &t->GammaZeroDiag, s * s, &t->GammaExplicitCorr));
693:   PetscCall(PetscArraycpy(t->A, A, s * s));
694:   PetscCall(PetscArraycpy(t->Gamma, Gamma, s * s));
695:   PetscCall(PetscArraycpy(t->GammaExplicitCorr, Gamma, s * s));
696:   PetscCall(PetscArraycpy(t->b, b, s));
697:   if (bembed) {
698:     PetscCall(PetscMalloc2(s, &t->bembed, s, &t->bembedt));
699:     PetscCall(PetscArraycpy(t->bembed, bembed, s));
700:   }
701:   for (i = 0; i < s; i++) {
702:     t->ASum[i]     = 0;
703:     t->GammaSum[i] = 0;
704:     for (j = 0; j < s; j++) {
705:       t->ASum[i] += A[i * s + j];
706:       t->GammaSum[i] += Gamma[i * s + j];
707:     }
708:   }
709:   PetscCall(PetscMalloc1(s * s, &GammaInv)); /* Need to use Scalar for inverse, then convert back to Real */
710:   for (i = 0; i < s * s; i++) GammaInv[i] = Gamma[i];
711:   for (i = 0; i < s; i++) {
712:     if (Gamma[i * s + i] == 0.0) {
713:       GammaInv[i * s + i] = 1.0;
714:       t->GammaZeroDiag[i] = PETSC_TRUE;
715:     } else {
716:       t->GammaZeroDiag[i] = PETSC_FALSE;
717:     }
718:   }

720:   switch (s) {
721:   case 1:
722:     GammaInv[0] = 1. / GammaInv[0];
723:     break;
724:   case 2:
725:     PetscCall(PetscKernel_A_gets_inverse_A_2(GammaInv, 0, PETSC_FALSE, NULL));
726:     break;
727:   case 3:
728:     PetscCall(PetscKernel_A_gets_inverse_A_3(GammaInv, 0, PETSC_FALSE, NULL));
729:     break;
730:   case 4:
731:     PetscCall(PetscKernel_A_gets_inverse_A_4(GammaInv, 0, PETSC_FALSE, NULL));
732:     break;
733:   case 5: {
734:     PetscInt  ipvt5[5];
735:     MatScalar work5[5 * 5];
736:     PetscCall(PetscKernel_A_gets_inverse_A_5(GammaInv, ipvt5, work5, 0, PETSC_FALSE, NULL));
737:     break;
738:   }
739:   case 6:
740:     PetscCall(PetscKernel_A_gets_inverse_A_6(GammaInv, 0, PETSC_FALSE, NULL));
741:     break;
742:   case 7:
743:     PetscCall(PetscKernel_A_gets_inverse_A_7(GammaInv, 0, PETSC_FALSE, NULL));
744:     break;
745:   default:
746:     SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "Not implemented for %" PetscInt_FMT " stages", s);
747:   }
748:   for (i = 0; i < s * s; i++) t->GammaInv[i] = PetscRealPart(GammaInv[i]);
749:   PetscCall(PetscFree(GammaInv));

751:   for (i = 0; i < s; i++) {
752:     for (k = 0; k < i + 1; k++) {
753:       t->GammaExplicitCorr[i * s + k] = (t->GammaExplicitCorr[i * s + k]) * (t->GammaInv[k * s + k]);
754:       for (j = k + 1; j < i + 1; j++) t->GammaExplicitCorr[i * s + k] += (t->GammaExplicitCorr[i * s + j]) * (t->GammaInv[j * s + k]);
755:     }
756:   }

758:   for (i = 0; i < s; i++) {
759:     for (j = 0; j < s; j++) {
760:       t->At[i * s + j] = 0;
761:       for (k = 0; k < s; k++) t->At[i * s + j] += t->A[i * s + k] * t->GammaInv[k * s + j];
762:     }
763:     t->bt[i] = 0;
764:     for (j = 0; j < s; j++) t->bt[i] += t->b[j] * t->GammaInv[j * s + i];
765:     if (bembed) {
766:       t->bembedt[i] = 0;
767:       for (j = 0; j < s; j++) t->bembedt[i] += t->bembed[j] * t->GammaInv[j * s + i];
768:     }
769:   }
770:   t->ccfl = 1.0; /* Fix this */

772:   t->pinterp = pinterp;
773:   PetscCall(PetscMalloc1(s * pinterp, &t->binterpt));
774:   PetscCall(PetscArraycpy(t->binterpt, binterpt, s * pinterp));
775:   link->next      = RosWTableauList;
776:   RosWTableauList = link;
777:   PetscFunctionReturn(PETSC_SUCCESS);
778: }

780: /*@C
781:    TSRosWRegisterRos4 - register a fourth order Rosenbrock scheme by providing parameter choices

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

785:    Input Parameters:
786: +  name - identifier for method
787: .  gamma - leading coefficient (diagonal entry)
788: .  a2 - design parameter, see Table 7.2 of Hairer&Wanner
789: .  a3 - design parameter or PETSC_DEFAULT to satisfy one of the order five conditions (Eq 7.22)
790: .  b3 - design parameter, see Table 7.2 of Hairer&Wanner
791: -  e4 - design parameter for embedded method, see coefficient E4 in ros4.f code from Hairer

793:    Level: developer

795:    Notes:
796:    This routine encodes the design of fourth order Rosenbrock methods as described in Hairer and Wanner volume 2.
797:    It is used here to implement several methods from the book and can be used to experiment with new methods.
798:    It was written this way instead of by copying coefficients in order to provide better than double precision satisfaction of the order conditions.

800: .seealso: [](ch_ts), `TSRosW`, `TSRosWRegister()`
801: @*/
802: PetscErrorCode TSRosWRegisterRos4(TSRosWType name, PetscReal gamma, PetscReal a2, PetscReal a3, PetscReal b3, PetscReal e4)
803: {
804:   /* Declare numeric constants so they can be quad precision without being truncated at double */
805:   const PetscReal one = 1, two = 2, three = 3, four = 4, five = 5, six = 6, eight = 8, twelve = 12, twenty = 20, twentyfour = 24, p32 = one / six - gamma + gamma * gamma, p42 = one / eight - gamma / three, p43 = one / twelve - gamma / three, p44 = one / twentyfour - gamma / two + three / two * gamma * gamma - gamma * gamma * gamma, p56 = one / twenty - gamma / four;
806:   PetscReal   a4, a32, a42, a43, b1, b2, b4, beta2p, beta3p, beta4p, beta32, beta42, beta43, beta32beta2p, beta4jbetajp;
807:   PetscReal   A[4][4], Gamma[4][4], b[4], bm[4];
808:   PetscScalar M[3][3], rhs[3];

810:   PetscFunctionBegin;
811:   /* Step 1: choose Gamma (input) */
812:   /* Step 2: choose a2,a3,a4; b1,b2,b3,b4 to satisfy order conditions */
813:   if (a3 == (PetscReal)PETSC_DEFAULT) a3 = (one / five - a2 / four) / (one / four - a2 / three); /* Eq 7.22 */
814:   a4 = a3;                                                                                       /* consequence of 7.20 */

816:   /* Solve order conditions 7.15a, 7.15c, 7.15e */
817:   M[0][0] = one;
818:   M[0][1] = one;
819:   M[0][2] = one; /* 7.15a */
820:   M[1][0] = 0.0;
821:   M[1][1] = a2 * a2;
822:   M[1][2] = a4 * a4; /* 7.15c */
823:   M[2][0] = 0.0;
824:   M[2][1] = a2 * a2 * a2;
825:   M[2][2] = a4 * a4 * a4; /* 7.15e */
826:   rhs[0]  = one - b3;
827:   rhs[1]  = one / three - a3 * a3 * b3;
828:   rhs[2]  = one / four - a3 * a3 * a3 * b3;
829:   PetscCall(PetscKernel_A_gets_inverse_A_3(&M[0][0], 0, PETSC_FALSE, NULL));
830:   b1 = PetscRealPart(M[0][0] * rhs[0] + M[0][1] * rhs[1] + M[0][2] * rhs[2]);
831:   b2 = PetscRealPart(M[1][0] * rhs[0] + M[1][1] * rhs[1] + M[1][2] * rhs[2]);
832:   b4 = PetscRealPart(M[2][0] * rhs[0] + M[2][1] * rhs[1] + M[2][2] * rhs[2]);

834:   /* Step 3 */
835:   beta43       = (p56 - a2 * p43) / (b4 * a3 * a3 * (a3 - a2)); /* 7.21 */
836:   beta32beta2p = p44 / (b4 * beta43);                           /* 7.15h */
837:   beta4jbetajp = (p32 - b3 * beta32beta2p) / b4;
838:   M[0][0]      = b2;
839:   M[0][1]      = b3;
840:   M[0][2]      = b4;
841:   M[1][0]      = a4 * a4 * beta32beta2p - a3 * a3 * beta4jbetajp;
842:   M[1][1]      = a2 * a2 * beta4jbetajp;
843:   M[1][2]      = -a2 * a2 * beta32beta2p;
844:   M[2][0]      = b4 * beta43 * a3 * a3 - p43;
845:   M[2][1]      = -b4 * beta43 * a2 * a2;
846:   M[2][2]      = 0;
847:   rhs[0]       = one / two - gamma;
848:   rhs[1]       = 0;
849:   rhs[2]       = -a2 * a2 * p32;
850:   PetscCall(PetscKernel_A_gets_inverse_A_3(&M[0][0], 0, PETSC_FALSE, NULL));
851:   beta2p = PetscRealPart(M[0][0] * rhs[0] + M[0][1] * rhs[1] + M[0][2] * rhs[2]);
852:   beta3p = PetscRealPart(M[1][0] * rhs[0] + M[1][1] * rhs[1] + M[1][2] * rhs[2]);
853:   beta4p = PetscRealPart(M[2][0] * rhs[0] + M[2][1] * rhs[1] + M[2][2] * rhs[2]);

855:   /* Step 4: back-substitute */
856:   beta32 = beta32beta2p / beta2p;
857:   beta42 = (beta4jbetajp - beta43 * beta3p) / beta2p;

859:   /* Step 5: 7.15f and 7.20, then 7.16 */
860:   a43 = 0;
861:   a32 = p42 / (b3 * a3 * beta2p + b4 * a4 * beta2p);
862:   a42 = a32;

864:   A[0][0]     = 0;
865:   A[0][1]     = 0;
866:   A[0][2]     = 0;
867:   A[0][3]     = 0;
868:   A[1][0]     = a2;
869:   A[1][1]     = 0;
870:   A[1][2]     = 0;
871:   A[1][3]     = 0;
872:   A[2][0]     = a3 - a32;
873:   A[2][1]     = a32;
874:   A[2][2]     = 0;
875:   A[2][3]     = 0;
876:   A[3][0]     = a4 - a43 - a42;
877:   A[3][1]     = a42;
878:   A[3][2]     = a43;
879:   A[3][3]     = 0;
880:   Gamma[0][0] = gamma;
881:   Gamma[0][1] = 0;
882:   Gamma[0][2] = 0;
883:   Gamma[0][3] = 0;
884:   Gamma[1][0] = beta2p - A[1][0];
885:   Gamma[1][1] = gamma;
886:   Gamma[1][2] = 0;
887:   Gamma[1][3] = 0;
888:   Gamma[2][0] = beta3p - beta32 - A[2][0];
889:   Gamma[2][1] = beta32 - A[2][1];
890:   Gamma[2][2] = gamma;
891:   Gamma[2][3] = 0;
892:   Gamma[3][0] = beta4p - beta42 - beta43 - A[3][0];
893:   Gamma[3][1] = beta42 - A[3][1];
894:   Gamma[3][2] = beta43 - A[3][2];
895:   Gamma[3][3] = gamma;
896:   b[0]        = b1;
897:   b[1]        = b2;
898:   b[2]        = b3;
899:   b[3]        = b4;

901:   /* Construct embedded formula using given e4. We are solving Equation 7.18. */
902:   bm[3] = b[3] - e4 * gamma;                                              /* using definition of E4 */
903:   bm[2] = (p32 - beta4jbetajp * bm[3]) / (beta32 * beta2p);               /* fourth row of 7.18 */
904:   bm[1] = (one / two - gamma - beta3p * bm[2] - beta4p * bm[3]) / beta2p; /* second row */
905:   bm[0] = one - bm[1] - bm[2] - bm[3];                                    /* first row */

907:   {
908:     const PetscReal misfit = a2 * a2 * bm[1] + a3 * a3 * bm[2] + a4 * a4 * bm[3] - one / three;
909:     PetscCheck(PetscAbs(misfit) <= PETSC_SMALL, PETSC_COMM_SELF, PETSC_ERR_SUP, "Assumptions violated, could not construct a third order embedded method");
910:   }
911:   PetscCall(TSRosWRegister(name, 4, 4, &A[0][0], &Gamma[0][0], b, bm, 0, NULL));
912:   PetscFunctionReturn(PETSC_SUCCESS);
913: }

915: /*
916:  The step completion formula is

918:  x1 = x0 + b^T Y

920:  where Y is the multi-vector of stages corrections. This function can be called before or after ts->vec_sol has been
921:  updated. Suppose we have a completion formula b and an embedded formula be of different order. We can write

923:  x1e = x0 + be^T Y
924:      = x1 - b^T Y + be^T Y
925:      = x1 + (be - b)^T Y

927:  so we can evaluate the method of different order even after the step has been optimistically completed.
928: */
929: static PetscErrorCode TSEvaluateStep_RosW(TS ts, PetscInt order, Vec U, PetscBool *done)
930: {
931:   TS_RosW     *ros = (TS_RosW *)ts->data;
932:   RosWTableau  tab = ros->tableau;
933:   PetscScalar *w   = ros->work;
934:   PetscInt     i;

936:   PetscFunctionBegin;
937:   if (order == tab->order) {
938:     if (ros->status == TS_STEP_INCOMPLETE) { /* Use standard completion formula */
939:       PetscCall(VecCopy(ts->vec_sol, U));
940:       for (i = 0; i < tab->s; i++) w[i] = tab->bt[i];
941:       PetscCall(VecMAXPY(U, tab->s, w, ros->Y));
942:     } else PetscCall(VecCopy(ts->vec_sol, U));
943:     if (done) *done = PETSC_TRUE;
944:     PetscFunctionReturn(PETSC_SUCCESS);
945:   } else if (order == tab->order - 1) {
946:     if (!tab->bembedt) goto unavailable;
947:     if (ros->status == TS_STEP_INCOMPLETE) { /* Use embedded completion formula */
948:       PetscCall(VecCopy(ts->vec_sol, U));
949:       for (i = 0; i < tab->s; i++) w[i] = tab->bembedt[i];
950:       PetscCall(VecMAXPY(U, tab->s, w, ros->Y));
951:     } else { /* Use rollback-and-recomplete formula (bembedt - bt) */
952:       for (i = 0; i < tab->s; i++) w[i] = tab->bembedt[i] - tab->bt[i];
953:       PetscCall(VecCopy(ts->vec_sol, U));
954:       PetscCall(VecMAXPY(U, tab->s, w, ros->Y));
955:     }
956:     if (done) *done = PETSC_TRUE;
957:     PetscFunctionReturn(PETSC_SUCCESS);
958:   }
959: unavailable:
960:   if (done) *done = PETSC_FALSE;
961:   else
962:     SETERRQ(PetscObjectComm((PetscObject)ts), PETSC_ERR_SUP, "Rosenbrock-W '%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,
963:             tab->order, order);
964:   PetscFunctionReturn(PETSC_SUCCESS);
965: }

967: static PetscErrorCode TSRollBack_RosW(TS ts)
968: {
969:   TS_RosW *ros = (TS_RosW *)ts->data;

971:   PetscFunctionBegin;
972:   PetscCall(VecCopy(ros->vec_sol_prev, ts->vec_sol));
973:   PetscFunctionReturn(PETSC_SUCCESS);
974: }

976: static PetscErrorCode TSStep_RosW(TS ts)
977: {
978:   TS_RosW         *ros = (TS_RosW *)ts->data;
979:   RosWTableau      tab = ros->tableau;
980:   const PetscInt   s   = tab->s;
981:   const PetscReal *At = tab->At, *Gamma = tab->Gamma, *ASum = tab->ASum, *GammaInv = tab->GammaInv;
982:   const PetscReal *GammaExplicitCorr = tab->GammaExplicitCorr;
983:   const PetscBool *GammaZeroDiag     = tab->GammaZeroDiag;
984:   PetscScalar     *w                 = ros->work;
985:   Vec             *Y = ros->Y, Ydot = ros->Ydot, Zdot = ros->Zdot, Zstage = ros->Zstage;
986:   SNES             snes;
987:   TSAdapt          adapt;
988:   PetscInt         i, j, its, lits;
989:   PetscInt         rejections = 0;
990:   PetscBool        stageok, accept = PETSC_TRUE;
991:   PetscReal        next_time_step = ts->time_step;
992:   PetscInt         lag;

994:   PetscFunctionBegin;
995:   if (!ts->steprollback) PetscCall(VecCopy(ts->vec_sol, ros->vec_sol_prev));

997:   ros->status = TS_STEP_INCOMPLETE;
998:   while (!ts->reason && ros->status != TS_STEP_COMPLETE) {
999:     const PetscReal h = ts->time_step;
1000:     for (i = 0; i < s; i++) {
1001:       ros->stage_time = ts->ptime + h * ASum[i];
1002:       PetscCall(TSPreStage(ts, ros->stage_time));
1003:       if (GammaZeroDiag[i]) {
1004:         ros->stage_explicit = PETSC_TRUE;
1005:         ros->scoeff         = 1.;
1006:       } else {
1007:         ros->stage_explicit = PETSC_FALSE;
1008:         ros->scoeff         = 1. / Gamma[i * s + i];
1009:       }

1011:       PetscCall(VecCopy(ts->vec_sol, Zstage));
1012:       for (j = 0; j < i; j++) w[j] = At[i * s + j];
1013:       PetscCall(VecMAXPY(Zstage, i, w, Y));

1015:       for (j = 0; j < i; j++) w[j] = 1. / h * GammaInv[i * s + j];
1016:       PetscCall(VecZeroEntries(Zdot));
1017:       PetscCall(VecMAXPY(Zdot, i, w, Y));

1019:       /* Initial guess taken from last stage */
1020:       PetscCall(VecZeroEntries(Y[i]));

1022:       if (!ros->stage_explicit) {
1023:         PetscCall(TSGetSNES(ts, &snes));
1024:         if (!ros->recompute_jacobian && !i) {
1025:           PetscCall(SNESGetLagJacobian(snes, &lag));
1026:           if (lag == 1) {                            /* use did not set a nontrivial lag, so lag over all stages */
1027:             PetscCall(SNESSetLagJacobian(snes, -2)); /* Recompute the Jacobian on this solve, but not again for the rest of the stages */
1028:           }
1029:         }
1030:         PetscCall(SNESSolve(snes, NULL, Y[i]));
1031:         if (!ros->recompute_jacobian && i == s - 1 && lag == 1) { PetscCall(SNESSetLagJacobian(snes, lag)); /* Set lag back to 1 so we know user did not set it */ }
1032:         PetscCall(SNESGetIterationNumber(snes, &its));
1033:         PetscCall(SNESGetLinearSolveIterations(snes, &lits));
1034:         ts->snes_its += its;
1035:         ts->ksp_its += lits;
1036:       } else {
1037:         Mat J, Jp;
1038:         PetscCall(VecZeroEntries(Ydot)); /* Evaluate Y[i]=G(t,Ydot=0,Zstage) */
1039:         PetscCall(TSComputeIFunction(ts, ros->stage_time, Zstage, Ydot, Y[i], PETSC_FALSE));
1040:         PetscCall(VecScale(Y[i], -1.0));
1041:         PetscCall(VecAXPY(Y[i], -1.0, Zdot)); /*Y[i] = F(Zstage)-Zdot[=GammaInv*Y]*/

1043:         PetscCall(VecZeroEntries(Zstage)); /* Zstage = GammaExplicitCorr[i,j] * Y[j] */
1044:         for (j = 0; j < i; j++) w[j] = GammaExplicitCorr[i * s + j];
1045:         PetscCall(VecMAXPY(Zstage, i, w, Y));

1047:         /* Y[i] = Y[i] + Jac*Zstage[=Jac*GammaExplicitCorr[i,j] * Y[j]] */
1048:         PetscCall(TSGetIJacobian(ts, &J, &Jp, NULL, NULL));
1049:         PetscCall(TSComputeIJacobian(ts, ros->stage_time, ts->vec_sol, Ydot, 0, J, Jp, PETSC_FALSE));
1050:         PetscCall(MatMult(J, Zstage, Zdot));
1051:         PetscCall(VecAXPY(Y[i], -1.0, Zdot));
1052:         ts->ksp_its += 1;

1054:         PetscCall(VecScale(Y[i], h));
1055:       }
1056:       PetscCall(TSPostStage(ts, ros->stage_time, i, Y));
1057:       PetscCall(TSGetAdapt(ts, &adapt));
1058:       PetscCall(TSAdaptCheckStage(adapt, ts, ros->stage_time, Y[i], &stageok));
1059:       if (!stageok) goto reject_step;
1060:     }

1062:     ros->status = TS_STEP_INCOMPLETE;
1063:     PetscCall(TSEvaluateStep_RosW(ts, tab->order, ts->vec_sol, NULL));
1064:     ros->status = TS_STEP_PENDING;
1065:     PetscCall(TSGetAdapt(ts, &adapt));
1066:     PetscCall(TSAdaptCandidatesClear(adapt));
1067:     PetscCall(TSAdaptCandidateAdd(adapt, tab->name, tab->order, 1, tab->ccfl, (PetscReal)tab->s, PETSC_TRUE));
1068:     PetscCall(TSAdaptChoose(adapt, ts, ts->time_step, NULL, &next_time_step, &accept));
1069:     ros->status = accept ? TS_STEP_COMPLETE : TS_STEP_INCOMPLETE;
1070:     if (!accept) { /* Roll back the current step */
1071:       PetscCall(TSRollBack_RosW(ts));
1072:       ts->time_step = next_time_step;
1073:       goto reject_step;
1074:     }

1076:     ts->ptime += ts->time_step;
1077:     ts->time_step = next_time_step;
1078:     break;

1080:   reject_step:
1081:     ts->reject++;
1082:     accept = PETSC_FALSE;
1083:     if (!ts->reason && ++rejections > ts->max_reject && ts->max_reject >= 0) {
1084:       ts->reason = TS_DIVERGED_STEP_REJECTED;
1085:       PetscCall(PetscInfo(ts, "Step=%" PetscInt_FMT ", step rejections %" PetscInt_FMT " greater than current TS allowed, stopping solve\n", ts->steps, rejections));
1086:     }
1087:   }
1088:   PetscFunctionReturn(PETSC_SUCCESS);
1089: }

1091: static PetscErrorCode TSInterpolate_RosW(TS ts, PetscReal itime, Vec U)
1092: {
1093:   TS_RosW         *ros = (TS_RosW *)ts->data;
1094:   PetscInt         s = ros->tableau->s, pinterp = ros->tableau->pinterp, i, j;
1095:   PetscReal        h;
1096:   PetscReal        tt, t;
1097:   PetscScalar     *bt;
1098:   const PetscReal *Bt       = ros->tableau->binterpt;
1099:   const PetscReal *GammaInv = ros->tableau->GammaInv;
1100:   PetscScalar     *w        = ros->work;
1101:   Vec             *Y        = ros->Y;

1103:   PetscFunctionBegin;
1104:   PetscCheck(Bt, PetscObjectComm((PetscObject)ts), PETSC_ERR_SUP, "TSRosW %s does not have an interpolation formula", ros->tableau->name);

1106:   switch (ros->status) {
1107:   case TS_STEP_INCOMPLETE:
1108:   case TS_STEP_PENDING:
1109:     h = ts->time_step;
1110:     t = (itime - ts->ptime) / h;
1111:     break;
1112:   case TS_STEP_COMPLETE:
1113:     h = ts->ptime - ts->ptime_prev;
1114:     t = (itime - ts->ptime) / h + 1; /* In the interval [0,1] */
1115:     break;
1116:   default:
1117:     SETERRQ(PetscObjectComm((PetscObject)ts), PETSC_ERR_PLIB, "Invalid TSStepStatus");
1118:   }
1119:   PetscCall(PetscMalloc1(s, &bt));
1120:   for (i = 0; i < s; i++) bt[i] = 0;
1121:   for (j = 0, tt = t; j < pinterp; j++, tt *= t) {
1122:     for (i = 0; i < s; i++) bt[i] += Bt[i * pinterp + j] * tt;
1123:   }

1125:   /* y(t+tt*h) = y(t) + Sum bt(tt) * GammaInv * Ydot */
1126:   /* U <- 0*/
1127:   PetscCall(VecZeroEntries(U));
1128:   /* U <- Sum bt_i * GammaInv(i,1:i) * Y(1:i) */
1129:   for (j = 0; j < s; j++) w[j] = 0;
1130:   for (j = 0; j < s; j++) {
1131:     for (i = j; i < s; i++) w[j] += bt[i] * GammaInv[i * s + j];
1132:   }
1133:   PetscCall(VecMAXPY(U, i, w, Y));
1134:   /* U <- y(t) + U */
1135:   PetscCall(VecAXPY(U, 1, ros->vec_sol_prev));

1137:   PetscCall(PetscFree(bt));
1138:   PetscFunctionReturn(PETSC_SUCCESS);
1139: }

1141: /*------------------------------------------------------------*/

1143: static PetscErrorCode TSRosWTableauReset(TS ts)
1144: {
1145:   TS_RosW    *ros = (TS_RosW *)ts->data;
1146:   RosWTableau tab = ros->tableau;

1148:   PetscFunctionBegin;
1149:   if (!tab) PetscFunctionReturn(PETSC_SUCCESS);
1150:   PetscCall(VecDestroyVecs(tab->s, &ros->Y));
1151:   PetscCall(PetscFree(ros->work));
1152:   PetscFunctionReturn(PETSC_SUCCESS);
1153: }

1155: static PetscErrorCode TSReset_RosW(TS ts)
1156: {
1157:   TS_RosW *ros = (TS_RosW *)ts->data;

1159:   PetscFunctionBegin;
1160:   PetscCall(TSRosWTableauReset(ts));
1161:   PetscCall(VecDestroy(&ros->Ydot));
1162:   PetscCall(VecDestroy(&ros->Ystage));
1163:   PetscCall(VecDestroy(&ros->Zdot));
1164:   PetscCall(VecDestroy(&ros->Zstage));
1165:   PetscCall(VecDestroy(&ros->vec_sol_prev));
1166:   PetscFunctionReturn(PETSC_SUCCESS);
1167: }

1169: static PetscErrorCode TSRosWGetVecs(TS ts, DM dm, Vec *Ydot, Vec *Zdot, Vec *Ystage, Vec *Zstage)
1170: {
1171:   TS_RosW *rw = (TS_RosW *)ts->data;

1173:   PetscFunctionBegin;
1174:   if (Ydot) {
1175:     if (dm && dm != ts->dm) {
1176:       PetscCall(DMGetNamedGlobalVector(dm, "TSRosW_Ydot", Ydot));
1177:     } else *Ydot = rw->Ydot;
1178:   }
1179:   if (Zdot) {
1180:     if (dm && dm != ts->dm) {
1181:       PetscCall(DMGetNamedGlobalVector(dm, "TSRosW_Zdot", Zdot));
1182:     } else *Zdot = rw->Zdot;
1183:   }
1184:   if (Ystage) {
1185:     if (dm && dm != ts->dm) {
1186:       PetscCall(DMGetNamedGlobalVector(dm, "TSRosW_Ystage", Ystage));
1187:     } else *Ystage = rw->Ystage;
1188:   }
1189:   if (Zstage) {
1190:     if (dm && dm != ts->dm) {
1191:       PetscCall(DMGetNamedGlobalVector(dm, "TSRosW_Zstage", Zstage));
1192:     } else *Zstage = rw->Zstage;
1193:   }
1194:   PetscFunctionReturn(PETSC_SUCCESS);
1195: }

1197: static PetscErrorCode TSRosWRestoreVecs(TS ts, DM dm, Vec *Ydot, Vec *Zdot, Vec *Ystage, Vec *Zstage)
1198: {
1199:   PetscFunctionBegin;
1200:   if (Ydot) {
1201:     if (dm && dm != ts->dm) PetscCall(DMRestoreNamedGlobalVector(dm, "TSRosW_Ydot", Ydot));
1202:   }
1203:   if (Zdot) {
1204:     if (dm && dm != ts->dm) PetscCall(DMRestoreNamedGlobalVector(dm, "TSRosW_Zdot", Zdot));
1205:   }
1206:   if (Ystage) {
1207:     if (dm && dm != ts->dm) PetscCall(DMRestoreNamedGlobalVector(dm, "TSRosW_Ystage", Ystage));
1208:   }
1209:   if (Zstage) {
1210:     if (dm && dm != ts->dm) PetscCall(DMRestoreNamedGlobalVector(dm, "TSRosW_Zstage", Zstage));
1211:   }
1212:   PetscFunctionReturn(PETSC_SUCCESS);
1213: }

1215: static PetscErrorCode DMCoarsenHook_TSRosW(DM fine, DM coarse, void *ctx)
1216: {
1217:   PetscFunctionBegin;
1218:   PetscFunctionReturn(PETSC_SUCCESS);
1219: }

1221: static PetscErrorCode DMRestrictHook_TSRosW(DM fine, Mat restrct, Vec rscale, Mat inject, DM coarse, void *ctx)
1222: {
1223:   TS  ts = (TS)ctx;
1224:   Vec Ydot, Zdot, Ystage, Zstage;
1225:   Vec Ydotc, Zdotc, Ystagec, Zstagec;

1227:   PetscFunctionBegin;
1228:   PetscCall(TSRosWGetVecs(ts, fine, &Ydot, &Ystage, &Zdot, &Zstage));
1229:   PetscCall(TSRosWGetVecs(ts, coarse, &Ydotc, &Ystagec, &Zdotc, &Zstagec));
1230:   PetscCall(MatRestrict(restrct, Ydot, Ydotc));
1231:   PetscCall(VecPointwiseMult(Ydotc, rscale, Ydotc));
1232:   PetscCall(MatRestrict(restrct, Ystage, Ystagec));
1233:   PetscCall(VecPointwiseMult(Ystagec, rscale, Ystagec));
1234:   PetscCall(MatRestrict(restrct, Zdot, Zdotc));
1235:   PetscCall(VecPointwiseMult(Zdotc, rscale, Zdotc));
1236:   PetscCall(MatRestrict(restrct, Zstage, Zstagec));
1237:   PetscCall(VecPointwiseMult(Zstagec, rscale, Zstagec));
1238:   PetscCall(TSRosWRestoreVecs(ts, fine, &Ydot, &Ystage, &Zdot, &Zstage));
1239:   PetscCall(TSRosWRestoreVecs(ts, coarse, &Ydotc, &Ystagec, &Zdotc, &Zstagec));
1240:   PetscFunctionReturn(PETSC_SUCCESS);
1241: }

1243: static PetscErrorCode DMSubDomainHook_TSRosW(DM fine, DM coarse, void *ctx)
1244: {
1245:   PetscFunctionBegin;
1246:   PetscFunctionReturn(PETSC_SUCCESS);
1247: }

1249: static PetscErrorCode DMSubDomainRestrictHook_TSRosW(DM dm, VecScatter gscat, VecScatter lscat, DM subdm, void *ctx)
1250: {
1251:   TS  ts = (TS)ctx;
1252:   Vec Ydot, Zdot, Ystage, Zstage;
1253:   Vec Ydots, Zdots, Ystages, Zstages;

1255:   PetscFunctionBegin;
1256:   PetscCall(TSRosWGetVecs(ts, dm, &Ydot, &Ystage, &Zdot, &Zstage));
1257:   PetscCall(TSRosWGetVecs(ts, subdm, &Ydots, &Ystages, &Zdots, &Zstages));

1259:   PetscCall(VecScatterBegin(gscat, Ydot, Ydots, INSERT_VALUES, SCATTER_FORWARD));
1260:   PetscCall(VecScatterEnd(gscat, Ydot, Ydots, INSERT_VALUES, SCATTER_FORWARD));

1262:   PetscCall(VecScatterBegin(gscat, Ystage, Ystages, INSERT_VALUES, SCATTER_FORWARD));
1263:   PetscCall(VecScatterEnd(gscat, Ystage, Ystages, INSERT_VALUES, SCATTER_FORWARD));

1265:   PetscCall(VecScatterBegin(gscat, Zdot, Zdots, INSERT_VALUES, SCATTER_FORWARD));
1266:   PetscCall(VecScatterEnd(gscat, Zdot, Zdots, INSERT_VALUES, SCATTER_FORWARD));

1268:   PetscCall(VecScatterBegin(gscat, Zstage, Zstages, INSERT_VALUES, SCATTER_FORWARD));
1269:   PetscCall(VecScatterEnd(gscat, Zstage, Zstages, INSERT_VALUES, SCATTER_FORWARD));

1271:   PetscCall(TSRosWRestoreVecs(ts, dm, &Ydot, &Ystage, &Zdot, &Zstage));
1272:   PetscCall(TSRosWRestoreVecs(ts, subdm, &Ydots, &Ystages, &Zdots, &Zstages));
1273:   PetscFunctionReturn(PETSC_SUCCESS);
1274: }

1276: /*
1277:   This defines the nonlinear equation that is to be solved with SNES
1278:   G(U) = F[t0+Theta*dt, U, (U-U0)*shift] = 0
1279: */
1280: static PetscErrorCode SNESTSFormFunction_RosW(SNES snes, Vec U, Vec F, TS ts)
1281: {
1282:   TS_RosW  *ros = (TS_RosW *)ts->data;
1283:   Vec       Ydot, Zdot, Ystage, Zstage;
1284:   PetscReal shift = ros->scoeff / ts->time_step;
1285:   DM        dm, dmsave;

1287:   PetscFunctionBegin;
1288:   PetscCall(SNESGetDM(snes, &dm));
1289:   PetscCall(TSRosWGetVecs(ts, dm, &Ydot, &Zdot, &Ystage, &Zstage));
1290:   PetscCall(VecWAXPY(Ydot, shift, U, Zdot));   /* Ydot = shift*U + Zdot */
1291:   PetscCall(VecWAXPY(Ystage, 1.0, U, Zstage)); /* Ystage = U + Zstage */
1292:   dmsave = ts->dm;
1293:   ts->dm = dm;
1294:   PetscCall(TSComputeIFunction(ts, ros->stage_time, Ystage, Ydot, F, PETSC_FALSE));
1295:   ts->dm = dmsave;
1296:   PetscCall(TSRosWRestoreVecs(ts, dm, &Ydot, &Zdot, &Ystage, &Zstage));
1297:   PetscFunctionReturn(PETSC_SUCCESS);
1298: }

1300: static PetscErrorCode SNESTSFormJacobian_RosW(SNES snes, Vec U, Mat A, Mat B, TS ts)
1301: {
1302:   TS_RosW  *ros = (TS_RosW *)ts->data;
1303:   Vec       Ydot, Zdot, Ystage, Zstage;
1304:   PetscReal shift = ros->scoeff / ts->time_step;
1305:   DM        dm, dmsave;

1307:   PetscFunctionBegin;
1308:   /* ros->Ydot and ros->Ystage have already been computed in SNESTSFormFunction_RosW (SNES guarantees this) */
1309:   PetscCall(SNESGetDM(snes, &dm));
1310:   PetscCall(TSRosWGetVecs(ts, dm, &Ydot, &Zdot, &Ystage, &Zstage));
1311:   dmsave = ts->dm;
1312:   ts->dm = dm;
1313:   PetscCall(TSComputeIJacobian(ts, ros->stage_time, Ystage, Ydot, shift, A, B, PETSC_TRUE));
1314:   ts->dm = dmsave;
1315:   PetscCall(TSRosWRestoreVecs(ts, dm, &Ydot, &Zdot, &Ystage, &Zstage));
1316:   PetscFunctionReturn(PETSC_SUCCESS);
1317: }

1319: static PetscErrorCode TSRosWTableauSetUp(TS ts)
1320: {
1321:   TS_RosW    *ros = (TS_RosW *)ts->data;
1322:   RosWTableau tab = ros->tableau;

1324:   PetscFunctionBegin;
1325:   PetscCall(VecDuplicateVecs(ts->vec_sol, tab->s, &ros->Y));
1326:   PetscCall(PetscMalloc1(tab->s, &ros->work));
1327:   PetscFunctionReturn(PETSC_SUCCESS);
1328: }

1330: static PetscErrorCode TSSetUp_RosW(TS ts)
1331: {
1332:   TS_RosW      *ros = (TS_RosW *)ts->data;
1333:   DM            dm;
1334:   SNES          snes;
1335:   TSRHSJacobian rhsjacobian;

1337:   PetscFunctionBegin;
1338:   PetscCall(TSRosWTableauSetUp(ts));
1339:   PetscCall(VecDuplicate(ts->vec_sol, &ros->Ydot));
1340:   PetscCall(VecDuplicate(ts->vec_sol, &ros->Ystage));
1341:   PetscCall(VecDuplicate(ts->vec_sol, &ros->Zdot));
1342:   PetscCall(VecDuplicate(ts->vec_sol, &ros->Zstage));
1343:   PetscCall(VecDuplicate(ts->vec_sol, &ros->vec_sol_prev));
1344:   PetscCall(TSGetDM(ts, &dm));
1345:   PetscCall(DMCoarsenHookAdd(dm, DMCoarsenHook_TSRosW, DMRestrictHook_TSRosW, ts));
1346:   PetscCall(DMSubDomainHookAdd(dm, DMSubDomainHook_TSRosW, DMSubDomainRestrictHook_TSRosW, ts));
1347:   /* Rosenbrock methods are linearly implicit, so set that unless the user has specifically asked for something else */
1348:   PetscCall(TSGetSNES(ts, &snes));
1349:   if (!((PetscObject)snes)->type_name) PetscCall(SNESSetType(snes, SNESKSPONLY));
1350:   PetscCall(DMTSGetRHSJacobian(dm, &rhsjacobian, NULL));
1351:   if (rhsjacobian == TSComputeRHSJacobianConstant) {
1352:     Mat Amat, Pmat;

1354:     /* Set the SNES matrix to be different from the RHS matrix because there is no way to reconstruct shift*M-J */
1355:     PetscCall(SNESGetJacobian(snes, &Amat, &Pmat, NULL, NULL));
1356:     if (Amat && Amat == ts->Arhs) {
1357:       if (Amat == Pmat) {
1358:         PetscCall(MatDuplicate(ts->Arhs, MAT_COPY_VALUES, &Amat));
1359:         PetscCall(SNESSetJacobian(snes, Amat, Amat, NULL, NULL));
1360:       } else {
1361:         PetscCall(MatDuplicate(ts->Arhs, MAT_COPY_VALUES, &Amat));
1362:         PetscCall(SNESSetJacobian(snes, Amat, NULL, NULL, NULL));
1363:         if (Pmat && Pmat == ts->Brhs) {
1364:           PetscCall(MatDuplicate(ts->Brhs, MAT_COPY_VALUES, &Pmat));
1365:           PetscCall(SNESSetJacobian(snes, NULL, Pmat, NULL, NULL));
1366:           PetscCall(MatDestroy(&Pmat));
1367:         }
1368:       }
1369:       PetscCall(MatDestroy(&Amat));
1370:     }
1371:   }
1372:   PetscFunctionReturn(PETSC_SUCCESS);
1373: }
1374: /*------------------------------------------------------------*/

1376: static PetscErrorCode TSSetFromOptions_RosW(TS ts, PetscOptionItems *PetscOptionsObject)
1377: {
1378:   TS_RosW *ros = (TS_RosW *)ts->data;
1379:   SNES     snes;

1381:   PetscFunctionBegin;
1382:   PetscOptionsHeadBegin(PetscOptionsObject, "RosW ODE solver options");
1383:   {
1384:     RosWTableauLink link;
1385:     PetscInt        count, choice;
1386:     PetscBool       flg;
1387:     const char    **namelist;

1389:     for (link = RosWTableauList, count = 0; link; link = link->next, count++)
1390:       ;
1391:     PetscCall(PetscMalloc1(count, (char ***)&namelist));
1392:     for (link = RosWTableauList, count = 0; link; link = link->next, count++) namelist[count] = link->tab.name;
1393:     PetscCall(PetscOptionsEList("-ts_rosw_type", "Family of Rosenbrock-W method", "TSRosWSetType", (const char *const *)namelist, count, ros->tableau->name, &choice, &flg));
1394:     if (flg) PetscCall(TSRosWSetType(ts, namelist[choice]));
1395:     PetscCall(PetscFree(namelist));

1397:     PetscCall(PetscOptionsBool("-ts_rosw_recompute_jacobian", "Recompute the Jacobian at each stage", "TSRosWSetRecomputeJacobian", ros->recompute_jacobian, &ros->recompute_jacobian, NULL));
1398:   }
1399:   PetscOptionsHeadEnd();
1400:   /* Rosenbrock methods are linearly implicit, so set that unless the user has specifically asked for something else */
1401:   PetscCall(TSGetSNES(ts, &snes));
1402:   if (!((PetscObject)snes)->type_name) PetscCall(SNESSetType(snes, SNESKSPONLY));
1403:   PetscFunctionReturn(PETSC_SUCCESS);
1404: }

1406: static PetscErrorCode TSView_RosW(TS ts, PetscViewer viewer)
1407: {
1408:   TS_RosW  *ros = (TS_RosW *)ts->data;
1409:   PetscBool iascii;

1411:   PetscFunctionBegin;
1412:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &iascii));
1413:   if (iascii) {
1414:     RosWTableau tab = ros->tableau;
1415:     TSRosWType  rostype;
1416:     char        buf[512];
1417:     PetscInt    i;
1418:     PetscReal   abscissa[512];
1419:     PetscCall(TSRosWGetType(ts, &rostype));
1420:     PetscCall(PetscViewerASCIIPrintf(viewer, "  Rosenbrock-W %s\n", rostype));
1421:     PetscCall(PetscFormatRealArray(buf, sizeof(buf), "% 8.6f", tab->s, tab->ASum));
1422:     PetscCall(PetscViewerASCIIPrintf(viewer, "  Abscissa of A       = %s\n", buf));
1423:     for (i = 0; i < tab->s; i++) abscissa[i] = tab->ASum[i] + tab->Gamma[i];
1424:     PetscCall(PetscFormatRealArray(buf, sizeof(buf), "% 8.6f", tab->s, abscissa));
1425:     PetscCall(PetscViewerASCIIPrintf(viewer, "  Abscissa of A+Gamma = %s\n", buf));
1426:   }
1427:   PetscFunctionReturn(PETSC_SUCCESS);
1428: }

1430: static PetscErrorCode TSLoad_RosW(TS ts, PetscViewer viewer)
1431: {
1432:   SNES    snes;
1433:   TSAdapt adapt;

1435:   PetscFunctionBegin;
1436:   PetscCall(TSGetAdapt(ts, &adapt));
1437:   PetscCall(TSAdaptLoad(adapt, viewer));
1438:   PetscCall(TSGetSNES(ts, &snes));
1439:   PetscCall(SNESLoad(snes, viewer));
1440:   /* function and Jacobian context for SNES when used with TS is always ts object */
1441:   PetscCall(SNESSetFunction(snes, NULL, NULL, ts));
1442:   PetscCall(SNESSetJacobian(snes, NULL, NULL, NULL, ts));
1443:   PetscFunctionReturn(PETSC_SUCCESS);
1444: }

1446: /*@C
1447:   TSRosWSetType - Set the type of Rosenbrock-W, `TSROSW`, scheme

1449:   Logically Collective

1451:   Input Parameters:
1452: +  ts - timestepping context
1453: -  roswtype - type of Rosenbrock-W scheme

1455:   Level: beginner

1457: .seealso: [](ch_ts), `TSRosWGetType()`, `TSROSW`, `TSROSW2M`, `TSROSW2P`, `TSROSWRA3PW`, `TSROSWRA34PW2`, `TSROSWRODAS3`, `TSROSWSANDU3`, `TSROSWASSP3P3S1C`, `TSROSWLASSP3P4S2C`, `TSROSWLLSSP3P4S2C`, `TSROSWARK3`
1458: @*/
1459: PetscErrorCode TSRosWSetType(TS ts, TSRosWType roswtype)
1460: {
1461:   PetscFunctionBegin;
1464:   PetscTryMethod(ts, "TSRosWSetType_C", (TS, TSRosWType), (ts, roswtype));
1465:   PetscFunctionReturn(PETSC_SUCCESS);
1466: }

1468: /*@C
1469:   TSRosWGetType - Get the type of Rosenbrock-W scheme

1471:   Logically Collective

1473:   Input Parameter:
1474: .  ts - timestepping context

1476:   Output Parameter:
1477: .  rostype - type of Rosenbrock-W scheme

1479:   Level: intermediate

1481: .seealso: [](ch_ts), `TSRosWType`, `TSRosWSetType()`
1482: @*/
1483: PetscErrorCode TSRosWGetType(TS ts, TSRosWType *rostype)
1484: {
1485:   PetscFunctionBegin;
1487:   PetscUseMethod(ts, "TSRosWGetType_C", (TS, TSRosWType *), (ts, rostype));
1488:   PetscFunctionReturn(PETSC_SUCCESS);
1489: }

1491: /*@C
1492:   TSRosWSetRecomputeJacobian - Set whether to recompute the Jacobian at each stage. The default is to update the Jacobian once per step.

1494:   Logically Collective

1496:   Input Parameters:
1497: +  ts - timestepping context
1498: -  flg - `PETSC_TRUE` to recompute the Jacobian at each stage

1500:   Level: intermediate

1502: .seealso: [](ch_ts), `TSRosWType`, `TSRosWGetType()`
1503: @*/
1504: PetscErrorCode TSRosWSetRecomputeJacobian(TS ts, PetscBool flg)
1505: {
1506:   PetscFunctionBegin;
1508:   PetscTryMethod(ts, "TSRosWSetRecomputeJacobian_C", (TS, PetscBool), (ts, flg));
1509:   PetscFunctionReturn(PETSC_SUCCESS);
1510: }

1512: static PetscErrorCode TSRosWGetType_RosW(TS ts, TSRosWType *rostype)
1513: {
1514:   TS_RosW *ros = (TS_RosW *)ts->data;

1516:   PetscFunctionBegin;
1517:   *rostype = ros->tableau->name;
1518:   PetscFunctionReturn(PETSC_SUCCESS);
1519: }

1521: static PetscErrorCode TSRosWSetType_RosW(TS ts, TSRosWType rostype)
1522: {
1523:   TS_RosW        *ros = (TS_RosW *)ts->data;
1524:   PetscBool       match;
1525:   RosWTableauLink link;

1527:   PetscFunctionBegin;
1528:   if (ros->tableau) {
1529:     PetscCall(PetscStrcmp(ros->tableau->name, rostype, &match));
1530:     if (match) PetscFunctionReturn(PETSC_SUCCESS);
1531:   }
1532:   for (link = RosWTableauList; link; link = link->next) {
1533:     PetscCall(PetscStrcmp(link->tab.name, rostype, &match));
1534:     if (match) {
1535:       if (ts->setupcalled) PetscCall(TSRosWTableauReset(ts));
1536:       ros->tableau = &link->tab;
1537:       if (ts->setupcalled) PetscCall(TSRosWTableauSetUp(ts));
1538:       ts->default_adapt_type = ros->tableau->bembed ? TSADAPTBASIC : TSADAPTNONE;
1539:       PetscFunctionReturn(PETSC_SUCCESS);
1540:     }
1541:   }
1542:   SETERRQ(PetscObjectComm((PetscObject)ts), PETSC_ERR_ARG_UNKNOWN_TYPE, "Could not find '%s'", rostype);
1543: }

1545: static PetscErrorCode TSRosWSetRecomputeJacobian_RosW(TS ts, PetscBool flg)
1546: {
1547:   TS_RosW *ros = (TS_RosW *)ts->data;

1549:   PetscFunctionBegin;
1550:   ros->recompute_jacobian = flg;
1551:   PetscFunctionReturn(PETSC_SUCCESS);
1552: }

1554: static PetscErrorCode TSDestroy_RosW(TS ts)
1555: {
1556:   PetscFunctionBegin;
1557:   PetscCall(TSReset_RosW(ts));
1558:   if (ts->dm) {
1559:     PetscCall(DMCoarsenHookRemove(ts->dm, DMCoarsenHook_TSRosW, DMRestrictHook_TSRosW, ts));
1560:     PetscCall(DMSubDomainHookRemove(ts->dm, DMSubDomainHook_TSRosW, DMSubDomainRestrictHook_TSRosW, ts));
1561:   }
1562:   PetscCall(PetscFree(ts->data));
1563:   PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSRosWGetType_C", NULL));
1564:   PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSRosWSetType_C", NULL));
1565:   PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSRosWSetRecomputeJacobian_C", NULL));
1566:   PetscFunctionReturn(PETSC_SUCCESS);
1567: }

1569: /* ------------------------------------------------------------ */
1570: /*MC
1571:       TSROSW - ODE solver using Rosenbrock-W schemes

1573:   These methods are intended for problems with well-separated time scales, especially when a slow scale is strongly
1574:   nonlinear such that it is expensive to solve with a fully implicit method. The user should provide the stiff part
1575:   of the equation using `TSSetIFunction()` and the non-stiff part with `TSSetRHSFunction()`.

1577:   Level: beginner

1579:   Notes:
1580:   This method currently only works with autonomous ODE and DAE.

1582:   Consider trying `TSARKIMEX` if the stiff part is strongly nonlinear.

1584:   Since this uses a single linear solve per time-step if you wish to lag the jacobian or preconditioner computation you must use also -snes_lag_jacobian_persists true or -snes_lag_jacobian_preconditioner true

1586:   Developer Notes:
1587:   Rosenbrock-W methods are typically specified for autonomous ODE

1589: $  udot = f(u)

1591:   by the stage equations

1593: $  k_i = h f(u_0 + sum_j alpha_ij k_j) + h J sum_j gamma_ij k_j

1595:   and step completion formula

1597: $  u_1 = u_0 + sum_j b_j k_j

1599:   with step size h and coefficients alpha_ij, gamma_ij, and b_i. Implementing the method in this form would require f(u)
1600:   and the Jacobian J to be available, in addition to the shifted matrix I - h gamma_ii J. Following Hairer and Wanner,
1601:   we define new variables for the stage equations

1603: $  y_i = gamma_ij k_j

1605:   The k_j can be recovered because Gamma is invertible. Let C be the lower triangular part of Gamma^{-1} and define

1607: $  A = Alpha Gamma^{-1}, bt^T = b^T Gamma^{-1}

1609:   to rewrite the method as

1611: .vb
1612:   [M/(h gamma_ii) - J] y_i = f(u_0 + sum_j a_ij y_j) + M sum_j (c_ij/h) y_j
1613:   u_1 = u_0 + sum_j bt_j y_j
1614: .ve

1616:    where we have introduced the mass matrix M. Continue by defining

1618: $  ydot_i = 1/(h gamma_ii) y_i - sum_j (c_ij/h) y_j

1620:    or, more compactly in tensor notation

1622: $  Ydot = 1/h (Gamma^{-1} \otimes I) Y .

1624:    Note that Gamma^{-1} is lower triangular. With this definition of Ydot in terms of known quantities and the current
1625:    stage y_i, the stage equations reduce to performing one Newton step (typically with a lagged Jacobian) on the
1626:    equation

1628: $  g(u_0 + sum_j a_ij y_j + y_i, ydot_i) = 0

1630:    with initial guess y_i = 0.

1632: .seealso: [](ch_ts), `TSCreate()`, `TS`, `TSSetType()`, `TSRosWSetType()`, `TSRosWRegister()`, `TSROSWTHETA1`, `TSROSWTHETA2`, `TSROSW2M`, `TSROSW2P`, `TSROSWRA3PW`, `TSROSWRA34PW2`, `TSROSWRODAS3`,
1633:           `TSROSWSANDU3`, `TSROSWASSP3P3S1C`, `TSROSWLASSP3P4S2C`, `TSROSWLLSSP3P4S2C`, `TSROSWGRK4T`, `TSROSWSHAMP4`, `TSROSWVELDD4`, `TSROSW4L`, `TSType`
1634: M*/
1635: PETSC_EXTERN PetscErrorCode TSCreate_RosW(TS ts)
1636: {
1637:   TS_RosW *ros;

1639:   PetscFunctionBegin;
1640:   PetscCall(TSRosWInitializePackage());

1642:   ts->ops->reset          = TSReset_RosW;
1643:   ts->ops->destroy        = TSDestroy_RosW;
1644:   ts->ops->view           = TSView_RosW;
1645:   ts->ops->load           = TSLoad_RosW;
1646:   ts->ops->setup          = TSSetUp_RosW;
1647:   ts->ops->step           = TSStep_RosW;
1648:   ts->ops->interpolate    = TSInterpolate_RosW;
1649:   ts->ops->evaluatestep   = TSEvaluateStep_RosW;
1650:   ts->ops->rollback       = TSRollBack_RosW;
1651:   ts->ops->setfromoptions = TSSetFromOptions_RosW;
1652:   ts->ops->snesfunction   = SNESTSFormFunction_RosW;
1653:   ts->ops->snesjacobian   = SNESTSFormJacobian_RosW;

1655:   ts->usessnes = PETSC_TRUE;

1657:   PetscCall(PetscNew(&ros));
1658:   ts->data = (void *)ros;

1660:   PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSRosWGetType_C", TSRosWGetType_RosW));
1661:   PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSRosWSetType_C", TSRosWSetType_RosW));
1662:   PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSRosWSetRecomputeJacobian_C", TSRosWSetRecomputeJacobian_RosW));

1664:   PetscCall(TSRosWSetType(ts, TSRosWDefault));
1665:   PetscFunctionReturn(PETSC_SUCCESS);
1666: }