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: {0, 0},
330: {1., 0}
331: };
332: const PetscReal Gamma[2][2] = {
333: {1.707106781186547524401, 0 },
334: {-2. * 1.707106781186547524401, 1.707106781186547524401}
335: };
336: const PetscReal b[2] = {0.5, 0.5};
337: const PetscReal b1[2] = {1.0, 0.0};
338: PetscReal binterpt[2][2];
339: binterpt[0][0] = 1.707106781186547524401 - 1.0;
340: binterpt[1][0] = 2.0 - 1.707106781186547524401;
341: binterpt[0][1] = 1.707106781186547524401 - 1.5;
342: binterpt[1][1] = 1.5 - 1.707106781186547524401;
344: PetscCall(TSRosWRegister(TSROSW2P, 2, 2, &A[0][0], &Gamma[0][0], b, b1, 2, &binterpt[0][0]));
345: }
346: {
347: /*const PetscReal g = 1. - 1./PetscSqrtReal(2.0); Direct evaluation: 0.2928932188134524755992. Used for setting up arrays of values known at compile time below. */
348: const PetscReal A[2][2] = {
349: {0, 0},
350: {1., 0}
351: };
352: const PetscReal Gamma[2][2] = {
353: {0.2928932188134524755992, 0 },
354: {-2. * 0.2928932188134524755992, 0.2928932188134524755992}
355: };
356: const PetscReal b[2] = {0.5, 0.5};
357: const PetscReal b1[2] = {1.0, 0.0};
358: PetscReal binterpt[2][2];
359: binterpt[0][0] = 0.2928932188134524755992 - 1.0;
360: binterpt[1][0] = 2.0 - 0.2928932188134524755992;
361: binterpt[0][1] = 0.2928932188134524755992 - 1.5;
362: binterpt[1][1] = 1.5 - 0.2928932188134524755992;
364: PetscCall(TSRosWRegister(TSROSW2M, 2, 2, &A[0][0], &Gamma[0][0], b, b1, 2, &binterpt[0][0]));
365: }
366: {
367: /*const PetscReal g = 7.8867513459481287e-01; Directly written in-place below */
368: PetscReal binterpt[3][2];
369: const PetscReal A[3][3] = {
370: {0, 0, 0},
371: {1.5773502691896257e+00, 0, 0},
372: {0.5, 0, 0}
373: };
374: const PetscReal Gamma[3][3] = {
375: {7.8867513459481287e-01, 0, 0 },
376: {-1.5773502691896257e+00, 7.8867513459481287e-01, 0 },
377: {-6.7075317547305480e-01, -1.7075317547305482e-01, 7.8867513459481287e-01}
378: };
379: const PetscReal b[3] = {1.0566243270259355e-01, 4.9038105676657971e-02, 8.4529946162074843e-01};
380: const PetscReal b2[3] = {-1.7863279495408180e-01, 1. / 3., 8.4529946162074843e-01};
382: binterpt[0][0] = -0.8094010767585034;
383: binterpt[1][0] = -0.5;
384: binterpt[2][0] = 2.3094010767585034;
385: binterpt[0][1] = 0.9641016151377548;
386: binterpt[1][1] = 0.5;
387: binterpt[2][1] = -1.4641016151377548;
389: PetscCall(TSRosWRegister(TSROSWRA3PW, 3, 3, &A[0][0], &Gamma[0][0], b, b2, 2, &binterpt[0][0]));
390: }
391: {
392: PetscReal binterpt[4][3];
393: /*const PetscReal g = 4.3586652150845900e-01; Directly written in-place below */
394: const PetscReal A[4][4] = {
395: {0, 0, 0, 0},
396: {8.7173304301691801e-01, 0, 0, 0},
397: {8.4457060015369423e-01, -1.1299064236484185e-01, 0, 0},
398: {0, 0, 1., 0}
399: };
400: const PetscReal Gamma[4][4] = {
401: {4.3586652150845900e-01, 0, 0, 0 },
402: {-8.7173304301691801e-01, 4.3586652150845900e-01, 0, 0 },
403: {-9.0338057013044082e-01, 5.4180672388095326e-02, 4.3586652150845900e-01, 0 },
404: {2.4212380706095346e-01, -1.2232505839045147e+00, 5.4526025533510214e-01, 4.3586652150845900e-01}
405: };
406: const PetscReal b[4] = {2.4212380706095346e-01, -1.2232505839045147e+00, 1.5452602553351020e+00, 4.3586652150845900e-01};
407: const PetscReal b2[4] = {3.7810903145819369e-01, -9.6042292212423178e-02, 5.0000000000000000e-01, 2.1793326075422950e-01};
409: binterpt[0][0] = 1.0564298455794094;
410: binterpt[1][0] = 2.296429974281067;
411: binterpt[2][0] = -1.307599564525376;
412: binterpt[3][0] = -1.045260255335102;
413: binterpt[0][1] = -1.3864882699759573;
414: binterpt[1][1] = -8.262611700275677;
415: binterpt[2][1] = 7.250979895056055;
416: binterpt[3][1] = 2.398120075195581;
417: binterpt[0][2] = 0.5721822314575016;
418: binterpt[1][2] = 4.742931142090097;
419: binterpt[2][2] = -4.398120075195578;
420: binterpt[3][2] = -0.9169932983520199;
422: PetscCall(TSRosWRegister(TSROSWRA34PW2, 3, 4, &A[0][0], &Gamma[0][0], b, b2, 3, &binterpt[0][0]));
423: }
424: {
425: /* const PetscReal g = 0.5; Directly written in-place below */
426: const PetscReal A[4][4] = {
427: {0, 0, 0, 0},
428: {0, 0, 0, 0},
429: {1., 0, 0, 0},
430: {0.75, -0.25, 0.5, 0}
431: };
432: const PetscReal Gamma[4][4] = {
433: {0.5, 0, 0, 0 },
434: {1., 0.5, 0, 0 },
435: {-0.25, -0.25, 0.5, 0 },
436: {1. / 12, 1. / 12, -2. / 3, 0.5}
437: };
438: const PetscReal b[4] = {5. / 6, -1. / 6, -1. / 6, 0.5};
439: const PetscReal b2[4] = {0.75, -0.25, 0.5, 0};
441: PetscCall(TSRosWRegister(TSROSWRODAS3, 3, 4, &A[0][0], &Gamma[0][0], b, b2, 0, NULL));
442: }
443: {
444: /*const PetscReal g = 0.43586652150845899941601945119356; Directly written in-place below */
445: const PetscReal A[3][3] = {
446: {0, 0, 0},
447: {0.43586652150845899941601945119356, 0, 0},
448: {0.43586652150845899941601945119356, 0, 0}
449: };
450: const PetscReal Gamma[3][3] = {
451: {0.43586652150845899941601945119356, 0, 0 },
452: {-0.19294655696029095575009695436041, 0.43586652150845899941601945119356, 0 },
453: {0, 1.74927148125794685173529749738960, 0.43586652150845899941601945119356}
454: };
455: const PetscReal b[3] = {-0.75457412385404315829818998646589, 1.94100407061964420292840123379419, -0.18642994676560104463021124732829};
456: const PetscReal b2[3] = {-1.53358745784149585370766523913002, 2.81745131148625772213931745457622, -0.28386385364476186843165221544619};
458: PetscReal binterpt[3][2];
459: binterpt[0][0] = 3.793692883777660870425141387941;
460: binterpt[1][0] = -2.918692883777660870425141387941;
461: binterpt[2][0] = 0.125;
462: binterpt[0][1] = -0.725741064379812106687651020584;
463: binterpt[1][1] = 0.559074397713145440020984353917;
464: binterpt[2][1] = 0.16666666666666666666666666666667;
466: PetscCall(TSRosWRegister(TSROSWSANDU3, 3, 3, &A[0][0], &Gamma[0][0], b, b2, 2, &binterpt[0][0]));
467: }
468: {
469: /*const PetscReal s3 = PetscSqrtReal(3.),g = (3.0+s3)/6.0;
470: * Direct evaluation: s3 = 1.732050807568877293527;
471: * g = 0.7886751345948128822546;
472: * Values are directly inserted below to ensure availability at compile time (compiler warnings otherwise...) */
473: const PetscReal A[3][3] = {
474: {0, 0, 0},
475: {1, 0, 0},
476: {0.25, 0.25, 0}
477: };
478: const PetscReal Gamma[3][3] = {
479: {0, 0, 0 },
480: {(-3.0 - 1.732050807568877293527) / 6.0, 0.7886751345948128822546, 0 },
481: {(-3.0 - 1.732050807568877293527) / 24.0, (-3.0 - 1.732050807568877293527) / 8.0, 0.7886751345948128822546}
482: };
483: const PetscReal b[3] = {1. / 6., 1. / 6., 2. / 3.};
484: const PetscReal b2[3] = {1. / 4., 1. / 4., 1. / 2.};
485: PetscReal binterpt[3][2];
487: binterpt[0][0] = 0.089316397477040902157517886164709;
488: binterpt[1][0] = -0.91068360252295909784248211383529;
489: binterpt[2][0] = 1.8213672050459181956849642276706;
490: binterpt[0][1] = 0.077350269189625764509148780501957;
491: binterpt[1][1] = 1.077350269189625764509148780502;
492: binterpt[2][1] = -1.1547005383792515290182975610039;
494: PetscCall(TSRosWRegister(TSROSWASSP3P3S1C, 3, 3, &A[0][0], &Gamma[0][0], b, b2, 2, &binterpt[0][0]));
495: }
497: {
498: const PetscReal A[4][4] = {
499: {0, 0, 0, 0},
500: {1. / 2., 0, 0, 0},
501: {1. / 2., 1. / 2., 0, 0},
502: {1. / 6., 1. / 6., 1. / 6., 0}
503: };
504: const PetscReal Gamma[4][4] = {
505: {1. / 2., 0, 0, 0},
506: {0.0, 1. / 4., 0, 0},
507: {-2., -2. / 3., 2. / 3., 0},
508: {1. / 2., 5. / 36., -2. / 9, 0}
509: };
510: const PetscReal b[4] = {1. / 6., 1. / 6., 1. / 6., 1. / 2.};
511: const PetscReal b2[4] = {1. / 8., 3. / 4., 1. / 8., 0};
512: PetscReal binterpt[4][3];
514: binterpt[0][0] = 6.25;
515: binterpt[1][0] = -30.25;
516: binterpt[2][0] = 1.75;
517: binterpt[3][0] = 23.25;
518: binterpt[0][1] = -9.75;
519: binterpt[1][1] = 58.75;
520: binterpt[2][1] = -3.25;
521: binterpt[3][1] = -45.75;
522: binterpt[0][2] = 3.6666666666666666666666666666667;
523: binterpt[1][2] = -28.333333333333333333333333333333;
524: binterpt[2][2] = 1.6666666666666666666666666666667;
525: binterpt[3][2] = 23.;
527: PetscCall(TSRosWRegister(TSROSWLASSP3P4S2C, 3, 4, &A[0][0], &Gamma[0][0], b, b2, 3, &binterpt[0][0]));
528: }
530: {
531: const PetscReal A[4][4] = {
532: {0, 0, 0, 0},
533: {1. / 2., 0, 0, 0},
534: {1. / 2., 1. / 2., 0, 0},
535: {1. / 6., 1. / 6., 1. / 6., 0}
536: };
537: const PetscReal Gamma[4][4] = {
538: {1. / 2., 0, 0, 0},
539: {0.0, 3. / 4., 0, 0},
540: {-2. / 3., -23. / 9., 2. / 9., 0},
541: {1. / 18., 65. / 108., -2. / 27, 0}
542: };
543: const PetscReal b[4] = {1. / 6., 1. / 6., 1. / 6., 1. / 2.};
544: const PetscReal b2[4] = {3. / 16., 10. / 16., 3. / 16., 0};
545: PetscReal binterpt[4][3];
547: binterpt[0][0] = 1.6911764705882352941176470588235;
548: binterpt[1][0] = 3.6813725490196078431372549019608;
549: binterpt[2][0] = 0.23039215686274509803921568627451;
550: binterpt[3][0] = -4.6029411764705882352941176470588;
551: binterpt[0][1] = -0.95588235294117647058823529411765;
552: binterpt[1][1] = -6.2401960784313725490196078431373;
553: binterpt[2][1] = -0.31862745098039215686274509803922;
554: binterpt[3][1] = 7.5147058823529411764705882352941;
555: binterpt[0][2] = -0.56862745098039215686274509803922;
556: binterpt[1][2] = 2.7254901960784313725490196078431;
557: binterpt[2][2] = 0.25490196078431372549019607843137;
558: binterpt[3][2] = -2.4117647058823529411764705882353;
560: PetscCall(TSRosWRegister(TSROSWLLSSP3P4S2C, 3, 4, &A[0][0], &Gamma[0][0], b, b2, 3, &binterpt[0][0]));
561: }
563: {
564: PetscReal A[4][4], Gamma[4][4], b[4], b2[4];
565: PetscReal binterpt[4][3];
567: Gamma[0][0] = 0.4358665215084589994160194475295062513822671686978816;
568: Gamma[0][1] = 0;
569: Gamma[0][2] = 0;
570: Gamma[0][3] = 0;
571: Gamma[1][0] = -1.997527830934941248426324674704153457289527280554476;
572: Gamma[1][1] = 0.4358665215084589994160194475295062513822671686978816;
573: Gamma[1][2] = 0;
574: Gamma[1][3] = 0;
575: Gamma[2][0] = -1.007948511795029620852002345345404191008352770119903;
576: Gamma[2][1] = -0.004648958462629345562774289390054679806993396798458131;
577: Gamma[2][2] = 0.4358665215084589994160194475295062513822671686978816;
578: Gamma[2][3] = 0;
579: Gamma[3][0] = -0.6685429734233467180451604600279552604364311322650783;
580: Gamma[3][1] = 0.6056625986449338476089525334450053439525178740492984;
581: Gamma[3][2] = -0.9717899277217721234705114616271378792182450260943198;
582: Gamma[3][3] = 0;
584: A[0][0] = 0;
585: A[0][1] = 0;
586: A[0][2] = 0;
587: A[0][3] = 0;
588: A[1][0] = 0.8717330430169179988320388950590125027645343373957631;
589: A[1][1] = 0;
590: A[1][2] = 0;
591: A[1][3] = 0;
592: A[2][0] = 0.5275890119763004115618079766722914408876108660811028;
593: A[2][1] = 0.07241098802369958843819203208518599088698057726988732;
594: A[2][2] = 0;
595: A[2][3] = 0;
596: A[3][0] = 0.3990960076760701320627260685975778145384666450351314;
597: A[3][1] = -0.4375576546135194437228463747348862825846903771419953;
598: A[3][2] = 1.038461646937449311660120300601880176655352737312713;
599: A[3][3] = 0;
601: b[0] = 0.1876410243467238251612921333138006734899663569186926;
602: b[1] = -0.5952974735769549480478230473706443582188442040780541;
603: b[2] = 0.9717899277217721234705114616271378792182450260943198;
604: b[3] = 0.4358665215084589994160194475295062513822671686978816;
606: b2[0] = 0.2147402862233891404862383521089097657790734483804460;
607: b2[1] = -0.4851622638849390928209050538171743017757490232519684;
608: b2[2] = 0.8687250025203875511662123688667549217531982787600080;
609: b2[3] = 0.4016969751411624011684543450940068201770721128357014;
611: binterpt[0][0] = 2.2565812720167954547104627844105;
612: binterpt[1][0] = 1.349166413351089573796243820819;
613: binterpt[2][0] = -2.4695174540533503758652847586647;
614: binterpt[3][0] = -0.13623023131453465264142184656474;
615: binterpt[0][1] = -3.0826699111559187902922463354557;
616: binterpt[1][1] = -2.4689115685996042534544925650515;
617: binterpt[2][1] = 5.7428279814696677152129332773553;
618: binterpt[3][1] = -0.19124650171414467146619437684812;
619: binterpt[0][2] = 1.0137296634858471607430756831148;
620: binterpt[1][2] = 0.52444768167155973161042570784064;
621: binterpt[2][2] = -2.3015205996945452158771370439586;
622: binterpt[3][2] = 0.76334325453713832352363565300308;
624: PetscCall(TSRosWRegister(TSROSWARK3, 3, 4, &A[0][0], &Gamma[0][0], b, b2, 3, &binterpt[0][0]));
625: }
626: PetscCall(TSRosWRegisterRos4(TSROSWGRK4T, 0.231, PETSC_DEFAULT, PETSC_DEFAULT, 0, -0.1282612945269037e+01));
627: PetscCall(TSRosWRegisterRos4(TSROSWSHAMP4, 0.5, PETSC_DEFAULT, PETSC_DEFAULT, 0, 125. / 108.));
628: PetscCall(TSRosWRegisterRos4(TSROSWVELDD4, 0.22570811482256823492, PETSC_DEFAULT, PETSC_DEFAULT, 0, -1.355958941201148));
629: PetscCall(TSRosWRegisterRos4(TSROSW4L, 0.57282, PETSC_DEFAULT, PETSC_DEFAULT, 0, -1.093502252409163));
630: PetscFunctionReturn(PETSC_SUCCESS);
631: }
633: /*@C
634: TSRosWRegisterDestroy - Frees the list of schemes that were registered by `TSRosWRegister()`.
636: Not Collective
638: Level: advanced
640: .seealso: [](ch_ts), `TSRosWRegister()`, `TSRosWRegisterAll()`
641: @*/
642: PetscErrorCode TSRosWRegisterDestroy(void)
643: {
644: RosWTableauLink link;
646: PetscFunctionBegin;
647: while ((link = RosWTableauList)) {
648: RosWTableau t = &link->tab;
649: RosWTableauList = link->next;
650: PetscCall(PetscFree5(t->A, t->Gamma, t->b, t->ASum, t->GammaSum));
651: PetscCall(PetscFree5(t->At, t->bt, t->GammaInv, t->GammaZeroDiag, t->GammaExplicitCorr));
652: PetscCall(PetscFree2(t->bembed, t->bembedt));
653: PetscCall(PetscFree(t->binterpt));
654: PetscCall(PetscFree(t->name));
655: PetscCall(PetscFree(link));
656: }
657: TSRosWRegisterAllCalled = PETSC_FALSE;
658: PetscFunctionReturn(PETSC_SUCCESS);
659: }
661: /*@C
662: TSRosWInitializePackage - This function initializes everything in the `TSROSW` package. It is called
663: from `TSInitializePackage()`.
665: Level: developer
667: .seealso: [](ch_ts), `TSROSW`, `PetscInitialize()`, `TSRosWFinalizePackage()`
668: @*/
669: PetscErrorCode TSRosWInitializePackage(void)
670: {
671: PetscFunctionBegin;
672: if (TSRosWPackageInitialized) PetscFunctionReturn(PETSC_SUCCESS);
673: TSRosWPackageInitialized = PETSC_TRUE;
674: PetscCall(TSRosWRegisterAll());
675: PetscCall(PetscRegisterFinalize(TSRosWFinalizePackage));
676: PetscFunctionReturn(PETSC_SUCCESS);
677: }
679: /*@C
680: TSRosWFinalizePackage - This function destroys everything in the `TSROSW` package. It is
681: called from `PetscFinalize()`.
683: Level: developer
685: .seealso: [](ch_ts), `TSROSW`, `PetscFinalize()`, `TSRosWInitializePackage()`
686: @*/
687: PetscErrorCode TSRosWFinalizePackage(void)
688: {
689: PetscFunctionBegin;
690: TSRosWPackageInitialized = PETSC_FALSE;
691: PetscCall(TSRosWRegisterDestroy());
692: PetscFunctionReturn(PETSC_SUCCESS);
693: }
695: /*@C
696: TSRosWRegister - register a `TSROSW`, Rosenbrock W scheme by providing the entries in the Butcher tableau and optionally embedded approximations and interpolation
698: Not Collective, but the same schemes should be registered on all processes on which they will be used
700: Input Parameters:
701: + name - identifier for method
702: . order - approximation order of method
703: . s - number of stages, this is the dimension of the matrices below
704: . A - Table of propagated stage coefficients (dimension s*s, row-major), strictly lower triangular
705: . Gamma - Table of coefficients in implicit stage equations (dimension s*s, row-major), lower triangular with nonzero diagonal
706: . b - Step completion table (dimension s)
707: . bembed - Step completion table for a scheme of order one less (dimension s, NULL if no embedded scheme is available)
708: . pinterp - Order of the interpolation scheme, equal to the number of columns of binterpt
709: - binterpt - Coefficients of the interpolation formula (dimension s*pinterp)
711: Level: advanced
713: Note:
714: Several Rosenbrock W methods are provided, this function is only needed to create new methods.
716: .seealso: [](ch_ts), `TSROSW`
717: @*/
718: 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[])
719: {
720: RosWTableauLink link;
721: RosWTableau t;
722: PetscInt i, j, k;
723: PetscScalar *GammaInv;
725: PetscFunctionBegin;
726: PetscAssertPointer(name, 1);
727: PetscAssertPointer(A, 4);
728: PetscAssertPointer(Gamma, 5);
729: PetscAssertPointer(b, 6);
730: if (bembed) PetscAssertPointer(bembed, 7);
732: PetscCall(TSRosWInitializePackage());
733: PetscCall(PetscNew(&link));
734: t = &link->tab;
735: PetscCall(PetscStrallocpy(name, &t->name));
736: t->order = order;
737: t->s = s;
738: PetscCall(PetscMalloc5(s * s, &t->A, s * s, &t->Gamma, s, &t->b, s, &t->ASum, s, &t->GammaSum));
739: PetscCall(PetscMalloc5(s * s, &t->At, s, &t->bt, s * s, &t->GammaInv, s, &t->GammaZeroDiag, s * s, &t->GammaExplicitCorr));
740: PetscCall(PetscArraycpy(t->A, A, s * s));
741: PetscCall(PetscArraycpy(t->Gamma, Gamma, s * s));
742: PetscCall(PetscArraycpy(t->GammaExplicitCorr, Gamma, s * s));
743: PetscCall(PetscArraycpy(t->b, b, s));
744: if (bembed) {
745: PetscCall(PetscMalloc2(s, &t->bembed, s, &t->bembedt));
746: PetscCall(PetscArraycpy(t->bembed, bembed, s));
747: }
748: for (i = 0; i < s; i++) {
749: t->ASum[i] = 0;
750: t->GammaSum[i] = 0;
751: for (j = 0; j < s; j++) {
752: t->ASum[i] += A[i * s + j];
753: t->GammaSum[i] += Gamma[i * s + j];
754: }
755: }
756: PetscCall(PetscMalloc1(s * s, &GammaInv)); /* Need to use Scalar for inverse, then convert back to Real */
757: for (i = 0; i < s * s; i++) GammaInv[i] = Gamma[i];
758: for (i = 0; i < s; i++) {
759: if (Gamma[i * s + i] == 0.0) {
760: GammaInv[i * s + i] = 1.0;
761: t->GammaZeroDiag[i] = PETSC_TRUE;
762: } else {
763: t->GammaZeroDiag[i] = PETSC_FALSE;
764: }
765: }
767: switch (s) {
768: case 1:
769: GammaInv[0] = 1. / GammaInv[0];
770: break;
771: case 2:
772: PetscCall(PetscKernel_A_gets_inverse_A_2(GammaInv, 0, PETSC_FALSE, NULL));
773: break;
774: case 3:
775: PetscCall(PetscKernel_A_gets_inverse_A_3(GammaInv, 0, PETSC_FALSE, NULL));
776: break;
777: case 4:
778: PetscCall(PetscKernel_A_gets_inverse_A_4(GammaInv, 0, PETSC_FALSE, NULL));
779: break;
780: case 5: {
781: PetscInt ipvt5[5];
782: MatScalar work5[5 * 5];
783: PetscCall(PetscKernel_A_gets_inverse_A_5(GammaInv, ipvt5, work5, 0, PETSC_FALSE, NULL));
784: break;
785: }
786: case 6:
787: PetscCall(PetscKernel_A_gets_inverse_A_6(GammaInv, 0, PETSC_FALSE, NULL));
788: break;
789: case 7:
790: PetscCall(PetscKernel_A_gets_inverse_A_7(GammaInv, 0, PETSC_FALSE, NULL));
791: break;
792: default:
793: SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "Not implemented for %" PetscInt_FMT " stages", s);
794: }
795: for (i = 0; i < s * s; i++) t->GammaInv[i] = PetscRealPart(GammaInv[i]);
796: PetscCall(PetscFree(GammaInv));
798: for (i = 0; i < s; i++) {
799: for (k = 0; k < i + 1; k++) {
800: t->GammaExplicitCorr[i * s + k] = (t->GammaExplicitCorr[i * s + k]) * (t->GammaInv[k * s + k]);
801: for (j = k + 1; j < i + 1; j++) t->GammaExplicitCorr[i * s + k] += (t->GammaExplicitCorr[i * s + j]) * (t->GammaInv[j * s + k]);
802: }
803: }
805: for (i = 0; i < s; i++) {
806: for (j = 0; j < s; j++) {
807: t->At[i * s + j] = 0;
808: for (k = 0; k < s; k++) t->At[i * s + j] += t->A[i * s + k] * t->GammaInv[k * s + j];
809: }
810: t->bt[i] = 0;
811: for (j = 0; j < s; j++) t->bt[i] += t->b[j] * t->GammaInv[j * s + i];
812: if (bembed) {
813: t->bembedt[i] = 0;
814: for (j = 0; j < s; j++) t->bembedt[i] += t->bembed[j] * t->GammaInv[j * s + i];
815: }
816: }
817: t->ccfl = 1.0; /* Fix this */
819: t->pinterp = pinterp;
820: PetscCall(PetscMalloc1(s * pinterp, &t->binterpt));
821: PetscCall(PetscArraycpy(t->binterpt, binterpt, s * pinterp));
822: link->next = RosWTableauList;
823: RosWTableauList = link;
824: PetscFunctionReturn(PETSC_SUCCESS);
825: }
827: /*@C
828: TSRosWRegisterRos4 - register a fourth order Rosenbrock scheme by providing parameter choices
830: Not Collective, but the same schemes should be registered on all processes on which they will be used
832: Input Parameters:
833: + name - identifier for method
834: . gamma - leading coefficient (diagonal entry)
835: . a2 - design parameter, see Table 7.2 of Hairer&Wanner
836: . a3 - design parameter or PETSC_DEFAULT to satisfy one of the order five conditions (Eq 7.22)
837: . b3 - design parameter, see Table 7.2 of Hairer&Wanner
838: - e4 - design parameter for embedded method, see coefficient E4 in ros4.f code from Hairer
840: Level: developer
842: Notes:
843: This routine encodes the design of fourth order Rosenbrock methods as described in Hairer and Wanner volume 2.
844: It is used here to implement several methods from the book and can be used to experiment with new methods.
845: It was written this way instead of by copying coefficients in order to provide better than double precision satisfaction of the order conditions.
847: .seealso: [](ch_ts), `TSRosW`, `TSRosWRegister()`
848: @*/
849: PetscErrorCode TSRosWRegisterRos4(TSRosWType name, PetscReal gamma, PetscReal a2, PetscReal a3, PetscReal b3, PetscReal e4)
850: {
851: /* Declare numeric constants so they can be quad precision without being truncated at double */
852: 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;
853: PetscReal a4, a32, a42, a43, b1, b2, b4, beta2p, beta3p, beta4p, beta32, beta42, beta43, beta32beta2p, beta4jbetajp;
854: PetscReal A[4][4], Gamma[4][4], b[4], bm[4];
855: PetscScalar M[3][3], rhs[3];
857: PetscFunctionBegin;
858: /* Step 1: choose Gamma (input) */
859: /* Step 2: choose a2,a3,a4; b1,b2,b3,b4 to satisfy order conditions */
860: if (a3 == (PetscReal)PETSC_DEFAULT) a3 = (one / five - a2 / four) / (one / four - a2 / three); /* Eq 7.22 */
861: a4 = a3; /* consequence of 7.20 */
863: /* Solve order conditions 7.15a, 7.15c, 7.15e */
864: M[0][0] = one;
865: M[0][1] = one;
866: M[0][2] = one; /* 7.15a */
867: M[1][0] = 0.0;
868: M[1][1] = a2 * a2;
869: M[1][2] = a4 * a4; /* 7.15c */
870: M[2][0] = 0.0;
871: M[2][1] = a2 * a2 * a2;
872: M[2][2] = a4 * a4 * a4; /* 7.15e */
873: rhs[0] = one - b3;
874: rhs[1] = one / three - a3 * a3 * b3;
875: rhs[2] = one / four - a3 * a3 * a3 * b3;
876: PetscCall(PetscKernel_A_gets_inverse_A_3(&M[0][0], 0, PETSC_FALSE, NULL));
877: b1 = PetscRealPart(M[0][0] * rhs[0] + M[0][1] * rhs[1] + M[0][2] * rhs[2]);
878: b2 = PetscRealPart(M[1][0] * rhs[0] + M[1][1] * rhs[1] + M[1][2] * rhs[2]);
879: b4 = PetscRealPart(M[2][0] * rhs[0] + M[2][1] * rhs[1] + M[2][2] * rhs[2]);
881: /* Step 3 */
882: beta43 = (p56 - a2 * p43) / (b4 * a3 * a3 * (a3 - a2)); /* 7.21 */
883: beta32beta2p = p44 / (b4 * beta43); /* 7.15h */
884: beta4jbetajp = (p32 - b3 * beta32beta2p) / b4;
885: M[0][0] = b2;
886: M[0][1] = b3;
887: M[0][2] = b4;
888: M[1][0] = a4 * a4 * beta32beta2p - a3 * a3 * beta4jbetajp;
889: M[1][1] = a2 * a2 * beta4jbetajp;
890: M[1][2] = -a2 * a2 * beta32beta2p;
891: M[2][0] = b4 * beta43 * a3 * a3 - p43;
892: M[2][1] = -b4 * beta43 * a2 * a2;
893: M[2][2] = 0;
894: rhs[0] = one / two - gamma;
895: rhs[1] = 0;
896: rhs[2] = -a2 * a2 * p32;
897: PetscCall(PetscKernel_A_gets_inverse_A_3(&M[0][0], 0, PETSC_FALSE, NULL));
898: beta2p = PetscRealPart(M[0][0] * rhs[0] + M[0][1] * rhs[1] + M[0][2] * rhs[2]);
899: beta3p = PetscRealPart(M[1][0] * rhs[0] + M[1][1] * rhs[1] + M[1][2] * rhs[2]);
900: beta4p = PetscRealPart(M[2][0] * rhs[0] + M[2][1] * rhs[1] + M[2][2] * rhs[2]);
902: /* Step 4: back-substitute */
903: beta32 = beta32beta2p / beta2p;
904: beta42 = (beta4jbetajp - beta43 * beta3p) / beta2p;
906: /* Step 5: 7.15f and 7.20, then 7.16 */
907: a43 = 0;
908: a32 = p42 / (b3 * a3 * beta2p + b4 * a4 * beta2p);
909: a42 = a32;
911: A[0][0] = 0;
912: A[0][1] = 0;
913: A[0][2] = 0;
914: A[0][3] = 0;
915: A[1][0] = a2;
916: A[1][1] = 0;
917: A[1][2] = 0;
918: A[1][3] = 0;
919: A[2][0] = a3 - a32;
920: A[2][1] = a32;
921: A[2][2] = 0;
922: A[2][3] = 0;
923: A[3][0] = a4 - a43 - a42;
924: A[3][1] = a42;
925: A[3][2] = a43;
926: A[3][3] = 0;
927: Gamma[0][0] = gamma;
928: Gamma[0][1] = 0;
929: Gamma[0][2] = 0;
930: Gamma[0][3] = 0;
931: Gamma[1][0] = beta2p - A[1][0];
932: Gamma[1][1] = gamma;
933: Gamma[1][2] = 0;
934: Gamma[1][3] = 0;
935: Gamma[2][0] = beta3p - beta32 - A[2][0];
936: Gamma[2][1] = beta32 - A[2][1];
937: Gamma[2][2] = gamma;
938: Gamma[2][3] = 0;
939: Gamma[3][0] = beta4p - beta42 - beta43 - A[3][0];
940: Gamma[3][1] = beta42 - A[3][1];
941: Gamma[3][2] = beta43 - A[3][2];
942: Gamma[3][3] = gamma;
943: b[0] = b1;
944: b[1] = b2;
945: b[2] = b3;
946: b[3] = b4;
948: /* Construct embedded formula using given e4. We are solving Equation 7.18. */
949: bm[3] = b[3] - e4 * gamma; /* using definition of E4 */
950: bm[2] = (p32 - beta4jbetajp * bm[3]) / (beta32 * beta2p); /* fourth row of 7.18 */
951: bm[1] = (one / two - gamma - beta3p * bm[2] - beta4p * bm[3]) / beta2p; /* second row */
952: bm[0] = one - bm[1] - bm[2] - bm[3]; /* first row */
954: {
955: const PetscReal misfit = a2 * a2 * bm[1] + a3 * a3 * bm[2] + a4 * a4 * bm[3] - one / three;
956: PetscCheck(PetscAbs(misfit) <= PETSC_SMALL, PETSC_COMM_SELF, PETSC_ERR_SUP, "Assumptions violated, could not construct a third order embedded method");
957: }
958: PetscCall(TSRosWRegister(name, 4, 4, &A[0][0], &Gamma[0][0], b, bm, 0, NULL));
959: PetscFunctionReturn(PETSC_SUCCESS);
960: }
962: /*
963: The step completion formula is
965: x1 = x0 + b^T Y
967: where Y is the multi-vector of stages corrections. This function can be called before or after ts->vec_sol has been
968: updated. Suppose we have a completion formula b and an embedded formula be of different order. We can write
970: x1e = x0 + be^T Y
971: = x1 - b^T Y + be^T Y
972: = x1 + (be - b)^T Y
974: so we can evaluate the method of different order even after the step has been optimistically completed.
975: */
976: static PetscErrorCode TSEvaluateStep_RosW(TS ts, PetscInt order, Vec U, PetscBool *done)
977: {
978: TS_RosW *ros = (TS_RosW *)ts->data;
979: RosWTableau tab = ros->tableau;
980: PetscScalar *w = ros->work;
981: PetscInt i;
983: PetscFunctionBegin;
984: if (order == tab->order) {
985: if (ros->status == TS_STEP_INCOMPLETE) { /* Use standard completion formula */
986: PetscCall(VecCopy(ts->vec_sol, U));
987: for (i = 0; i < tab->s; i++) w[i] = tab->bt[i];
988: PetscCall(VecMAXPY(U, tab->s, w, ros->Y));
989: } else PetscCall(VecCopy(ts->vec_sol, U));
990: if (done) *done = PETSC_TRUE;
991: PetscFunctionReturn(PETSC_SUCCESS);
992: } else if (order == tab->order - 1) {
993: if (!tab->bembedt) goto unavailable;
994: if (ros->status == TS_STEP_INCOMPLETE) { /* Use embedded completion formula */
995: PetscCall(VecCopy(ts->vec_sol, U));
996: for (i = 0; i < tab->s; i++) w[i] = tab->bembedt[i];
997: PetscCall(VecMAXPY(U, tab->s, w, ros->Y));
998: } else { /* Use rollback-and-recomplete formula (bembedt - bt) */
999: for (i = 0; i < tab->s; i++) w[i] = tab->bembedt[i] - tab->bt[i];
1000: PetscCall(VecCopy(ts->vec_sol, U));
1001: PetscCall(VecMAXPY(U, tab->s, w, ros->Y));
1002: }
1003: if (done) *done = PETSC_TRUE;
1004: PetscFunctionReturn(PETSC_SUCCESS);
1005: }
1006: unavailable:
1007: if (done) *done = PETSC_FALSE;
1008: else
1009: 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,
1010: tab->order, order);
1011: PetscFunctionReturn(PETSC_SUCCESS);
1012: }
1014: static PetscErrorCode TSRollBack_RosW(TS ts)
1015: {
1016: TS_RosW *ros = (TS_RosW *)ts->data;
1018: PetscFunctionBegin;
1019: PetscCall(VecCopy(ros->vec_sol_prev, ts->vec_sol));
1020: PetscFunctionReturn(PETSC_SUCCESS);
1021: }
1023: static PetscErrorCode TSStep_RosW(TS ts)
1024: {
1025: TS_RosW *ros = (TS_RosW *)ts->data;
1026: RosWTableau tab = ros->tableau;
1027: const PetscInt s = tab->s;
1028: const PetscReal *At = tab->At, *Gamma = tab->Gamma, *ASum = tab->ASum, *GammaInv = tab->GammaInv;
1029: const PetscReal *GammaExplicitCorr = tab->GammaExplicitCorr;
1030: const PetscBool *GammaZeroDiag = tab->GammaZeroDiag;
1031: PetscScalar *w = ros->work;
1032: Vec *Y = ros->Y, Ydot = ros->Ydot, Zdot = ros->Zdot, Zstage = ros->Zstage;
1033: SNES snes;
1034: TSAdapt adapt;
1035: PetscInt i, j, its, lits;
1036: PetscInt rejections = 0;
1037: PetscBool stageok, accept = PETSC_TRUE;
1038: PetscReal next_time_step = ts->time_step;
1039: PetscInt lag;
1041: PetscFunctionBegin;
1042: if (!ts->steprollback) PetscCall(VecCopy(ts->vec_sol, ros->vec_sol_prev));
1044: ros->status = TS_STEP_INCOMPLETE;
1045: while (!ts->reason && ros->status != TS_STEP_COMPLETE) {
1046: const PetscReal h = ts->time_step;
1047: for (i = 0; i < s; i++) {
1048: ros->stage_time = ts->ptime + h * ASum[i];
1049: PetscCall(TSPreStage(ts, ros->stage_time));
1050: if (GammaZeroDiag[i]) {
1051: ros->stage_explicit = PETSC_TRUE;
1052: ros->scoeff = 1.;
1053: } else {
1054: ros->stage_explicit = PETSC_FALSE;
1055: ros->scoeff = 1. / Gamma[i * s + i];
1056: }
1058: PetscCall(VecCopy(ts->vec_sol, Zstage));
1059: for (j = 0; j < i; j++) w[j] = At[i * s + j];
1060: PetscCall(VecMAXPY(Zstage, i, w, Y));
1062: for (j = 0; j < i; j++) w[j] = 1. / h * GammaInv[i * s + j];
1063: PetscCall(VecZeroEntries(Zdot));
1064: PetscCall(VecMAXPY(Zdot, i, w, Y));
1066: /* Initial guess taken from last stage */
1067: PetscCall(VecZeroEntries(Y[i]));
1069: if (!ros->stage_explicit) {
1070: PetscCall(TSGetSNES(ts, &snes));
1071: if (!ros->recompute_jacobian && !i) {
1072: PetscCall(SNESGetLagJacobian(snes, &lag));
1073: if (lag == 1) { /* use did not set a nontrivial lag, so lag over all stages */
1074: PetscCall(SNESSetLagJacobian(snes, -2)); /* Recompute the Jacobian on this solve, but not again for the rest of the stages */
1075: }
1076: }
1077: PetscCall(SNESSolve(snes, NULL, Y[i]));
1078: 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 */ }
1079: PetscCall(SNESGetIterationNumber(snes, &its));
1080: PetscCall(SNESGetLinearSolveIterations(snes, &lits));
1081: ts->snes_its += its;
1082: ts->ksp_its += lits;
1083: } else {
1084: Mat J, Jp;
1085: PetscCall(VecZeroEntries(Ydot)); /* Evaluate Y[i]=G(t,Ydot=0,Zstage) */
1086: PetscCall(TSComputeIFunction(ts, ros->stage_time, Zstage, Ydot, Y[i], PETSC_FALSE));
1087: PetscCall(VecScale(Y[i], -1.0));
1088: PetscCall(VecAXPY(Y[i], -1.0, Zdot)); /*Y[i] = F(Zstage)-Zdot[=GammaInv*Y]*/
1090: PetscCall(VecZeroEntries(Zstage)); /* Zstage = GammaExplicitCorr[i,j] * Y[j] */
1091: for (j = 0; j < i; j++) w[j] = GammaExplicitCorr[i * s + j];
1092: PetscCall(VecMAXPY(Zstage, i, w, Y));
1094: /* Y[i] = Y[i] + Jac*Zstage[=Jac*GammaExplicitCorr[i,j] * Y[j]] */
1095: PetscCall(TSGetIJacobian(ts, &J, &Jp, NULL, NULL));
1096: PetscCall(TSComputeIJacobian(ts, ros->stage_time, ts->vec_sol, Ydot, 0, J, Jp, PETSC_FALSE));
1097: PetscCall(MatMult(J, Zstage, Zdot));
1098: PetscCall(VecAXPY(Y[i], -1.0, Zdot));
1099: ts->ksp_its += 1;
1101: PetscCall(VecScale(Y[i], h));
1102: }
1103: PetscCall(TSPostStage(ts, ros->stage_time, i, Y));
1104: PetscCall(TSGetAdapt(ts, &adapt));
1105: PetscCall(TSAdaptCheckStage(adapt, ts, ros->stage_time, Y[i], &stageok));
1106: if (!stageok) goto reject_step;
1107: }
1109: ros->status = TS_STEP_INCOMPLETE;
1110: PetscCall(TSEvaluateStep_RosW(ts, tab->order, ts->vec_sol, NULL));
1111: ros->status = TS_STEP_PENDING;
1112: PetscCall(TSGetAdapt(ts, &adapt));
1113: PetscCall(TSAdaptCandidatesClear(adapt));
1114: PetscCall(TSAdaptCandidateAdd(adapt, tab->name, tab->order, 1, tab->ccfl, (PetscReal)tab->s, PETSC_TRUE));
1115: PetscCall(TSAdaptChoose(adapt, ts, ts->time_step, NULL, &next_time_step, &accept));
1116: ros->status = accept ? TS_STEP_COMPLETE : TS_STEP_INCOMPLETE;
1117: if (!accept) { /* Roll back the current step */
1118: PetscCall(TSRollBack_RosW(ts));
1119: ts->time_step = next_time_step;
1120: goto reject_step;
1121: }
1123: ts->ptime += ts->time_step;
1124: ts->time_step = next_time_step;
1125: break;
1127: reject_step:
1128: ts->reject++;
1129: accept = PETSC_FALSE;
1130: if (!ts->reason && ++rejections > ts->max_reject && ts->max_reject >= 0) {
1131: ts->reason = TS_DIVERGED_STEP_REJECTED;
1132: PetscCall(PetscInfo(ts, "Step=%" PetscInt_FMT ", step rejections %" PetscInt_FMT " greater than current TS allowed, stopping solve\n", ts->steps, rejections));
1133: }
1134: }
1135: PetscFunctionReturn(PETSC_SUCCESS);
1136: }
1138: static PetscErrorCode TSInterpolate_RosW(TS ts, PetscReal itime, Vec U)
1139: {
1140: TS_RosW *ros = (TS_RosW *)ts->data;
1141: PetscInt s = ros->tableau->s, pinterp = ros->tableau->pinterp, i, j;
1142: PetscReal h;
1143: PetscReal tt, t;
1144: PetscScalar *bt;
1145: const PetscReal *Bt = ros->tableau->binterpt;
1146: const PetscReal *GammaInv = ros->tableau->GammaInv;
1147: PetscScalar *w = ros->work;
1148: Vec *Y = ros->Y;
1150: PetscFunctionBegin;
1151: PetscCheck(Bt, PetscObjectComm((PetscObject)ts), PETSC_ERR_SUP, "TSRosW %s does not have an interpolation formula", ros->tableau->name);
1153: switch (ros->status) {
1154: case TS_STEP_INCOMPLETE:
1155: case TS_STEP_PENDING:
1156: h = ts->time_step;
1157: t = (itime - ts->ptime) / h;
1158: break;
1159: case TS_STEP_COMPLETE:
1160: h = ts->ptime - ts->ptime_prev;
1161: t = (itime - ts->ptime) / h + 1; /* In the interval [0,1] */
1162: break;
1163: default:
1164: SETERRQ(PetscObjectComm((PetscObject)ts), PETSC_ERR_PLIB, "Invalid TSStepStatus");
1165: }
1166: PetscCall(PetscMalloc1(s, &bt));
1167: for (i = 0; i < s; i++) bt[i] = 0;
1168: for (j = 0, tt = t; j < pinterp; j++, tt *= t) {
1169: for (i = 0; i < s; i++) bt[i] += Bt[i * pinterp + j] * tt;
1170: }
1172: /* y(t+tt*h) = y(t) + Sum bt(tt) * GammaInv * Ydot */
1173: /* U <- 0*/
1174: PetscCall(VecZeroEntries(U));
1175: /* U <- Sum bt_i * GammaInv(i,1:i) * Y(1:i) */
1176: for (j = 0; j < s; j++) w[j] = 0;
1177: for (j = 0; j < s; j++) {
1178: for (i = j; i < s; i++) w[j] += bt[i] * GammaInv[i * s + j];
1179: }
1180: PetscCall(VecMAXPY(U, i, w, Y));
1181: /* U <- y(t) + U */
1182: PetscCall(VecAXPY(U, 1, ros->vec_sol_prev));
1184: PetscCall(PetscFree(bt));
1185: PetscFunctionReturn(PETSC_SUCCESS);
1186: }
1188: /*------------------------------------------------------------*/
1190: static PetscErrorCode TSRosWTableauReset(TS ts)
1191: {
1192: TS_RosW *ros = (TS_RosW *)ts->data;
1193: RosWTableau tab = ros->tableau;
1195: PetscFunctionBegin;
1196: if (!tab) PetscFunctionReturn(PETSC_SUCCESS);
1197: PetscCall(VecDestroyVecs(tab->s, &ros->Y));
1198: PetscCall(PetscFree(ros->work));
1199: PetscFunctionReturn(PETSC_SUCCESS);
1200: }
1202: static PetscErrorCode TSReset_RosW(TS ts)
1203: {
1204: TS_RosW *ros = (TS_RosW *)ts->data;
1206: PetscFunctionBegin;
1207: PetscCall(TSRosWTableauReset(ts));
1208: PetscCall(VecDestroy(&ros->Ydot));
1209: PetscCall(VecDestroy(&ros->Ystage));
1210: PetscCall(VecDestroy(&ros->Zdot));
1211: PetscCall(VecDestroy(&ros->Zstage));
1212: PetscCall(VecDestroy(&ros->vec_sol_prev));
1213: PetscFunctionReturn(PETSC_SUCCESS);
1214: }
1216: static PetscErrorCode TSRosWGetVecs(TS ts, DM dm, Vec *Ydot, Vec *Zdot, Vec *Ystage, Vec *Zstage)
1217: {
1218: TS_RosW *rw = (TS_RosW *)ts->data;
1220: PetscFunctionBegin;
1221: if (Ydot) {
1222: if (dm && dm != ts->dm) {
1223: PetscCall(DMGetNamedGlobalVector(dm, "TSRosW_Ydot", Ydot));
1224: } else *Ydot = rw->Ydot;
1225: }
1226: if (Zdot) {
1227: if (dm && dm != ts->dm) {
1228: PetscCall(DMGetNamedGlobalVector(dm, "TSRosW_Zdot", Zdot));
1229: } else *Zdot = rw->Zdot;
1230: }
1231: if (Ystage) {
1232: if (dm && dm != ts->dm) {
1233: PetscCall(DMGetNamedGlobalVector(dm, "TSRosW_Ystage", Ystage));
1234: } else *Ystage = rw->Ystage;
1235: }
1236: if (Zstage) {
1237: if (dm && dm != ts->dm) {
1238: PetscCall(DMGetNamedGlobalVector(dm, "TSRosW_Zstage", Zstage));
1239: } else *Zstage = rw->Zstage;
1240: }
1241: PetscFunctionReturn(PETSC_SUCCESS);
1242: }
1244: static PetscErrorCode TSRosWRestoreVecs(TS ts, DM dm, Vec *Ydot, Vec *Zdot, Vec *Ystage, Vec *Zstage)
1245: {
1246: PetscFunctionBegin;
1247: if (Ydot) {
1248: if (dm && dm != ts->dm) PetscCall(DMRestoreNamedGlobalVector(dm, "TSRosW_Ydot", Ydot));
1249: }
1250: if (Zdot) {
1251: if (dm && dm != ts->dm) PetscCall(DMRestoreNamedGlobalVector(dm, "TSRosW_Zdot", Zdot));
1252: }
1253: if (Ystage) {
1254: if (dm && dm != ts->dm) PetscCall(DMRestoreNamedGlobalVector(dm, "TSRosW_Ystage", Ystage));
1255: }
1256: if (Zstage) {
1257: if (dm && dm != ts->dm) PetscCall(DMRestoreNamedGlobalVector(dm, "TSRosW_Zstage", Zstage));
1258: }
1259: PetscFunctionReturn(PETSC_SUCCESS);
1260: }
1262: static PetscErrorCode DMCoarsenHook_TSRosW(DM fine, DM coarse, void *ctx)
1263: {
1264: PetscFunctionBegin;
1265: PetscFunctionReturn(PETSC_SUCCESS);
1266: }
1268: static PetscErrorCode DMRestrictHook_TSRosW(DM fine, Mat restrct, Vec rscale, Mat inject, DM coarse, void *ctx)
1269: {
1270: TS ts = (TS)ctx;
1271: Vec Ydot, Zdot, Ystage, Zstage;
1272: Vec Ydotc, Zdotc, Ystagec, Zstagec;
1274: PetscFunctionBegin;
1275: PetscCall(TSRosWGetVecs(ts, fine, &Ydot, &Ystage, &Zdot, &Zstage));
1276: PetscCall(TSRosWGetVecs(ts, coarse, &Ydotc, &Ystagec, &Zdotc, &Zstagec));
1277: PetscCall(MatRestrict(restrct, Ydot, Ydotc));
1278: PetscCall(VecPointwiseMult(Ydotc, rscale, Ydotc));
1279: PetscCall(MatRestrict(restrct, Ystage, Ystagec));
1280: PetscCall(VecPointwiseMult(Ystagec, rscale, Ystagec));
1281: PetscCall(MatRestrict(restrct, Zdot, Zdotc));
1282: PetscCall(VecPointwiseMult(Zdotc, rscale, Zdotc));
1283: PetscCall(MatRestrict(restrct, Zstage, Zstagec));
1284: PetscCall(VecPointwiseMult(Zstagec, rscale, Zstagec));
1285: PetscCall(TSRosWRestoreVecs(ts, fine, &Ydot, &Ystage, &Zdot, &Zstage));
1286: PetscCall(TSRosWRestoreVecs(ts, coarse, &Ydotc, &Ystagec, &Zdotc, &Zstagec));
1287: PetscFunctionReturn(PETSC_SUCCESS);
1288: }
1290: static PetscErrorCode DMSubDomainHook_TSRosW(DM fine, DM coarse, void *ctx)
1291: {
1292: PetscFunctionBegin;
1293: PetscFunctionReturn(PETSC_SUCCESS);
1294: }
1296: static PetscErrorCode DMSubDomainRestrictHook_TSRosW(DM dm, VecScatter gscat, VecScatter lscat, DM subdm, void *ctx)
1297: {
1298: TS ts = (TS)ctx;
1299: Vec Ydot, Zdot, Ystage, Zstage;
1300: Vec Ydots, Zdots, Ystages, Zstages;
1302: PetscFunctionBegin;
1303: PetscCall(TSRosWGetVecs(ts, dm, &Ydot, &Ystage, &Zdot, &Zstage));
1304: PetscCall(TSRosWGetVecs(ts, subdm, &Ydots, &Ystages, &Zdots, &Zstages));
1306: PetscCall(VecScatterBegin(gscat, Ydot, Ydots, INSERT_VALUES, SCATTER_FORWARD));
1307: PetscCall(VecScatterEnd(gscat, Ydot, Ydots, INSERT_VALUES, SCATTER_FORWARD));
1309: PetscCall(VecScatterBegin(gscat, Ystage, Ystages, INSERT_VALUES, SCATTER_FORWARD));
1310: PetscCall(VecScatterEnd(gscat, Ystage, Ystages, INSERT_VALUES, SCATTER_FORWARD));
1312: PetscCall(VecScatterBegin(gscat, Zdot, Zdots, INSERT_VALUES, SCATTER_FORWARD));
1313: PetscCall(VecScatterEnd(gscat, Zdot, Zdots, INSERT_VALUES, SCATTER_FORWARD));
1315: PetscCall(VecScatterBegin(gscat, Zstage, Zstages, INSERT_VALUES, SCATTER_FORWARD));
1316: PetscCall(VecScatterEnd(gscat, Zstage, Zstages, INSERT_VALUES, SCATTER_FORWARD));
1318: PetscCall(TSRosWRestoreVecs(ts, dm, &Ydot, &Ystage, &Zdot, &Zstage));
1319: PetscCall(TSRosWRestoreVecs(ts, subdm, &Ydots, &Ystages, &Zdots, &Zstages));
1320: PetscFunctionReturn(PETSC_SUCCESS);
1321: }
1323: /*
1324: This defines the nonlinear equation that is to be solved with SNES
1325: G(U) = F[t0+Theta*dt, U, (U-U0)*shift] = 0
1326: */
1327: static PetscErrorCode SNESTSFormFunction_RosW(SNES snes, Vec U, Vec F, TS ts)
1328: {
1329: TS_RosW *ros = (TS_RosW *)ts->data;
1330: Vec Ydot, Zdot, Ystage, Zstage;
1331: PetscReal shift = ros->scoeff / ts->time_step;
1332: DM dm, dmsave;
1334: PetscFunctionBegin;
1335: PetscCall(SNESGetDM(snes, &dm));
1336: PetscCall(TSRosWGetVecs(ts, dm, &Ydot, &Zdot, &Ystage, &Zstage));
1337: PetscCall(VecWAXPY(Ydot, shift, U, Zdot)); /* Ydot = shift*U + Zdot */
1338: PetscCall(VecWAXPY(Ystage, 1.0, U, Zstage)); /* Ystage = U + Zstage */
1339: dmsave = ts->dm;
1340: ts->dm = dm;
1341: PetscCall(TSComputeIFunction(ts, ros->stage_time, Ystage, Ydot, F, PETSC_FALSE));
1342: ts->dm = dmsave;
1343: PetscCall(TSRosWRestoreVecs(ts, dm, &Ydot, &Zdot, &Ystage, &Zstage));
1344: PetscFunctionReturn(PETSC_SUCCESS);
1345: }
1347: static PetscErrorCode SNESTSFormJacobian_RosW(SNES snes, Vec U, Mat A, Mat B, TS ts)
1348: {
1349: TS_RosW *ros = (TS_RosW *)ts->data;
1350: Vec Ydot, Zdot, Ystage, Zstage;
1351: PetscReal shift = ros->scoeff / ts->time_step;
1352: DM dm, dmsave;
1354: PetscFunctionBegin;
1355: /* ros->Ydot and ros->Ystage have already been computed in SNESTSFormFunction_RosW (SNES guarantees this) */
1356: PetscCall(SNESGetDM(snes, &dm));
1357: PetscCall(TSRosWGetVecs(ts, dm, &Ydot, &Zdot, &Ystage, &Zstage));
1358: dmsave = ts->dm;
1359: ts->dm = dm;
1360: PetscCall(TSComputeIJacobian(ts, ros->stage_time, Ystage, Ydot, shift, A, B, PETSC_TRUE));
1361: ts->dm = dmsave;
1362: PetscCall(TSRosWRestoreVecs(ts, dm, &Ydot, &Zdot, &Ystage, &Zstage));
1363: PetscFunctionReturn(PETSC_SUCCESS);
1364: }
1366: static PetscErrorCode TSRosWTableauSetUp(TS ts)
1367: {
1368: TS_RosW *ros = (TS_RosW *)ts->data;
1369: RosWTableau tab = ros->tableau;
1371: PetscFunctionBegin;
1372: PetscCall(VecDuplicateVecs(ts->vec_sol, tab->s, &ros->Y));
1373: PetscCall(PetscMalloc1(tab->s, &ros->work));
1374: PetscFunctionReturn(PETSC_SUCCESS);
1375: }
1377: static PetscErrorCode TSSetUp_RosW(TS ts)
1378: {
1379: TS_RosW *ros = (TS_RosW *)ts->data;
1380: DM dm;
1381: SNES snes;
1382: TSRHSJacobian rhsjacobian;
1384: PetscFunctionBegin;
1385: PetscCall(TSRosWTableauSetUp(ts));
1386: PetscCall(VecDuplicate(ts->vec_sol, &ros->Ydot));
1387: PetscCall(VecDuplicate(ts->vec_sol, &ros->Ystage));
1388: PetscCall(VecDuplicate(ts->vec_sol, &ros->Zdot));
1389: PetscCall(VecDuplicate(ts->vec_sol, &ros->Zstage));
1390: PetscCall(VecDuplicate(ts->vec_sol, &ros->vec_sol_prev));
1391: PetscCall(TSGetDM(ts, &dm));
1392: PetscCall(DMCoarsenHookAdd(dm, DMCoarsenHook_TSRosW, DMRestrictHook_TSRosW, ts));
1393: PetscCall(DMSubDomainHookAdd(dm, DMSubDomainHook_TSRosW, DMSubDomainRestrictHook_TSRosW, ts));
1394: /* Rosenbrock methods are linearly implicit, so set that unless the user has specifically asked for something else */
1395: PetscCall(TSGetSNES(ts, &snes));
1396: if (!((PetscObject)snes)->type_name) PetscCall(SNESSetType(snes, SNESKSPONLY));
1397: PetscCall(DMTSGetRHSJacobian(dm, &rhsjacobian, NULL));
1398: if (rhsjacobian == TSComputeRHSJacobianConstant) {
1399: Mat Amat, Pmat;
1401: /* Set the SNES matrix to be different from the RHS matrix because there is no way to reconstruct shift*M-J */
1402: PetscCall(SNESGetJacobian(snes, &Amat, &Pmat, NULL, NULL));
1403: if (Amat && Amat == ts->Arhs) {
1404: if (Amat == Pmat) {
1405: PetscCall(MatDuplicate(ts->Arhs, MAT_COPY_VALUES, &Amat));
1406: PetscCall(SNESSetJacobian(snes, Amat, Amat, NULL, NULL));
1407: } else {
1408: PetscCall(MatDuplicate(ts->Arhs, MAT_COPY_VALUES, &Amat));
1409: PetscCall(SNESSetJacobian(snes, Amat, NULL, NULL, NULL));
1410: if (Pmat && Pmat == ts->Brhs) {
1411: PetscCall(MatDuplicate(ts->Brhs, MAT_COPY_VALUES, &Pmat));
1412: PetscCall(SNESSetJacobian(snes, NULL, Pmat, NULL, NULL));
1413: PetscCall(MatDestroy(&Pmat));
1414: }
1415: }
1416: PetscCall(MatDestroy(&Amat));
1417: }
1418: }
1419: PetscFunctionReturn(PETSC_SUCCESS);
1420: }
1421: /*------------------------------------------------------------*/
1423: static PetscErrorCode TSSetFromOptions_RosW(TS ts, PetscOptionItems *PetscOptionsObject)
1424: {
1425: TS_RosW *ros = (TS_RosW *)ts->data;
1426: SNES snes;
1428: PetscFunctionBegin;
1429: PetscOptionsHeadBegin(PetscOptionsObject, "RosW ODE solver options");
1430: {
1431: RosWTableauLink link;
1432: PetscInt count, choice;
1433: PetscBool flg;
1434: const char **namelist;
1436: for (link = RosWTableauList, count = 0; link; link = link->next, count++)
1437: ;
1438: PetscCall(PetscMalloc1(count, (char ***)&namelist));
1439: for (link = RosWTableauList, count = 0; link; link = link->next, count++) namelist[count] = link->tab.name;
1440: PetscCall(PetscOptionsEList("-ts_rosw_type", "Family of Rosenbrock-W method", "TSRosWSetType", (const char *const *)namelist, count, ros->tableau->name, &choice, &flg));
1441: if (flg) PetscCall(TSRosWSetType(ts, namelist[choice]));
1442: PetscCall(PetscFree(namelist));
1444: PetscCall(PetscOptionsBool("-ts_rosw_recompute_jacobian", "Recompute the Jacobian at each stage", "TSRosWSetRecomputeJacobian", ros->recompute_jacobian, &ros->recompute_jacobian, NULL));
1445: }
1446: PetscOptionsHeadEnd();
1447: /* Rosenbrock methods are linearly implicit, so set that unless the user has specifically asked for something else */
1448: PetscCall(TSGetSNES(ts, &snes));
1449: if (!((PetscObject)snes)->type_name) PetscCall(SNESSetType(snes, SNESKSPONLY));
1450: PetscFunctionReturn(PETSC_SUCCESS);
1451: }
1453: static PetscErrorCode TSView_RosW(TS ts, PetscViewer viewer)
1454: {
1455: TS_RosW *ros = (TS_RosW *)ts->data;
1456: PetscBool iascii;
1458: PetscFunctionBegin;
1459: PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &iascii));
1460: if (iascii) {
1461: RosWTableau tab = ros->tableau;
1462: TSRosWType rostype;
1463: char buf[512];
1464: PetscInt i;
1465: PetscReal abscissa[512];
1466: PetscCall(TSRosWGetType(ts, &rostype));
1467: PetscCall(PetscViewerASCIIPrintf(viewer, " Rosenbrock-W %s\n", rostype));
1468: PetscCall(PetscFormatRealArray(buf, sizeof(buf), "% 8.6f", tab->s, tab->ASum));
1469: PetscCall(PetscViewerASCIIPrintf(viewer, " Abscissa of A = %s\n", buf));
1470: for (i = 0; i < tab->s; i++) abscissa[i] = tab->ASum[i] + tab->Gamma[i];
1471: PetscCall(PetscFormatRealArray(buf, sizeof(buf), "% 8.6f", tab->s, abscissa));
1472: PetscCall(PetscViewerASCIIPrintf(viewer, " Abscissa of A+Gamma = %s\n", buf));
1473: }
1474: PetscFunctionReturn(PETSC_SUCCESS);
1475: }
1477: static PetscErrorCode TSLoad_RosW(TS ts, PetscViewer viewer)
1478: {
1479: SNES snes;
1480: TSAdapt adapt;
1482: PetscFunctionBegin;
1483: PetscCall(TSGetAdapt(ts, &adapt));
1484: PetscCall(TSAdaptLoad(adapt, viewer));
1485: PetscCall(TSGetSNES(ts, &snes));
1486: PetscCall(SNESLoad(snes, viewer));
1487: /* function and Jacobian context for SNES when used with TS is always ts object */
1488: PetscCall(SNESSetFunction(snes, NULL, NULL, ts));
1489: PetscCall(SNESSetJacobian(snes, NULL, NULL, NULL, ts));
1490: PetscFunctionReturn(PETSC_SUCCESS);
1491: }
1493: /*@C
1494: TSRosWSetType - Set the type of Rosenbrock-W, `TSROSW`, scheme
1496: Logically Collective
1498: Input Parameters:
1499: + ts - timestepping context
1500: - roswtype - type of Rosenbrock-W scheme
1502: Level: beginner
1504: .seealso: [](ch_ts), `TSRosWGetType()`, `TSROSW`, `TSROSW2M`, `TSROSW2P`, `TSROSWRA3PW`, `TSROSWRA34PW2`, `TSROSWRODAS3`, `TSROSWSANDU3`, `TSROSWASSP3P3S1C`, `TSROSWLASSP3P4S2C`, `TSROSWLLSSP3P4S2C`, `TSROSWARK3`
1505: @*/
1506: PetscErrorCode TSRosWSetType(TS ts, TSRosWType roswtype)
1507: {
1508: PetscFunctionBegin;
1510: PetscAssertPointer(roswtype, 2);
1511: PetscTryMethod(ts, "TSRosWSetType_C", (TS, TSRosWType), (ts, roswtype));
1512: PetscFunctionReturn(PETSC_SUCCESS);
1513: }
1515: /*@C
1516: TSRosWGetType - Get the type of Rosenbrock-W scheme
1518: Logically Collective
1520: Input Parameter:
1521: . ts - timestepping context
1523: Output Parameter:
1524: . rostype - type of Rosenbrock-W scheme
1526: Level: intermediate
1528: .seealso: [](ch_ts), `TSRosWType`, `TSRosWSetType()`
1529: @*/
1530: PetscErrorCode TSRosWGetType(TS ts, TSRosWType *rostype)
1531: {
1532: PetscFunctionBegin;
1534: PetscUseMethod(ts, "TSRosWGetType_C", (TS, TSRosWType *), (ts, rostype));
1535: PetscFunctionReturn(PETSC_SUCCESS);
1536: }
1538: /*@C
1539: TSRosWSetRecomputeJacobian - Set whether to recompute the Jacobian at each stage. The default is to update the Jacobian once per step.
1541: Logically Collective
1543: Input Parameters:
1544: + ts - timestepping context
1545: - flg - `PETSC_TRUE` to recompute the Jacobian at each stage
1547: Level: intermediate
1549: .seealso: [](ch_ts), `TSRosWType`, `TSRosWGetType()`
1550: @*/
1551: PetscErrorCode TSRosWSetRecomputeJacobian(TS ts, PetscBool flg)
1552: {
1553: PetscFunctionBegin;
1555: PetscTryMethod(ts, "TSRosWSetRecomputeJacobian_C", (TS, PetscBool), (ts, flg));
1556: PetscFunctionReturn(PETSC_SUCCESS);
1557: }
1559: static PetscErrorCode TSRosWGetType_RosW(TS ts, TSRosWType *rostype)
1560: {
1561: TS_RosW *ros = (TS_RosW *)ts->data;
1563: PetscFunctionBegin;
1564: *rostype = ros->tableau->name;
1565: PetscFunctionReturn(PETSC_SUCCESS);
1566: }
1568: static PetscErrorCode TSRosWSetType_RosW(TS ts, TSRosWType rostype)
1569: {
1570: TS_RosW *ros = (TS_RosW *)ts->data;
1571: PetscBool match;
1572: RosWTableauLink link;
1574: PetscFunctionBegin;
1575: if (ros->tableau) {
1576: PetscCall(PetscStrcmp(ros->tableau->name, rostype, &match));
1577: if (match) PetscFunctionReturn(PETSC_SUCCESS);
1578: }
1579: for (link = RosWTableauList; link; link = link->next) {
1580: PetscCall(PetscStrcmp(link->tab.name, rostype, &match));
1581: if (match) {
1582: if (ts->setupcalled) PetscCall(TSRosWTableauReset(ts));
1583: ros->tableau = &link->tab;
1584: if (ts->setupcalled) PetscCall(TSRosWTableauSetUp(ts));
1585: ts->default_adapt_type = ros->tableau->bembed ? TSADAPTBASIC : TSADAPTNONE;
1586: PetscFunctionReturn(PETSC_SUCCESS);
1587: }
1588: }
1589: SETERRQ(PetscObjectComm((PetscObject)ts), PETSC_ERR_ARG_UNKNOWN_TYPE, "Could not find '%s'", rostype);
1590: }
1592: static PetscErrorCode TSRosWSetRecomputeJacobian_RosW(TS ts, PetscBool flg)
1593: {
1594: TS_RosW *ros = (TS_RosW *)ts->data;
1596: PetscFunctionBegin;
1597: ros->recompute_jacobian = flg;
1598: PetscFunctionReturn(PETSC_SUCCESS);
1599: }
1601: static PetscErrorCode TSDestroy_RosW(TS ts)
1602: {
1603: PetscFunctionBegin;
1604: PetscCall(TSReset_RosW(ts));
1605: if (ts->dm) {
1606: PetscCall(DMCoarsenHookRemove(ts->dm, DMCoarsenHook_TSRosW, DMRestrictHook_TSRosW, ts));
1607: PetscCall(DMSubDomainHookRemove(ts->dm, DMSubDomainHook_TSRosW, DMSubDomainRestrictHook_TSRosW, ts));
1608: }
1609: PetscCall(PetscFree(ts->data));
1610: PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSRosWGetType_C", NULL));
1611: PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSRosWSetType_C", NULL));
1612: PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSRosWSetRecomputeJacobian_C", NULL));
1613: PetscFunctionReturn(PETSC_SUCCESS);
1614: }
1616: /* ------------------------------------------------------------ */
1617: /*MC
1618: TSROSW - ODE solver using Rosenbrock-W schemes
1620: These methods are intended for problems with well-separated time scales, especially when a slow scale is strongly
1621: nonlinear such that it is expensive to solve with a fully implicit method. The user should provide the stiff part
1622: of the equation using `TSSetIFunction()` and the non-stiff part with `TSSetRHSFunction()`.
1624: Level: beginner
1626: Notes:
1627: This method currently only works with autonomous ODE and DAE.
1629: Consider trying `TSARKIMEX` if the stiff part is strongly nonlinear.
1631: 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
1633: Developer Notes:
1634: Rosenbrock-W methods are typically specified for autonomous ODE
1636: $ udot = f(u)
1638: by the stage equations
1640: $ k_i = h f(u_0 + sum_j alpha_ij k_j) + h J sum_j gamma_ij k_j
1642: and step completion formula
1644: $ u_1 = u_0 + sum_j b_j k_j
1646: with step size h and coefficients alpha_ij, gamma_ij, and b_i. Implementing the method in this form would require f(u)
1647: and the Jacobian J to be available, in addition to the shifted matrix I - h gamma_ii J. Following Hairer and Wanner,
1648: we define new variables for the stage equations
1650: $ y_i = gamma_ij k_j
1652: The k_j can be recovered because Gamma is invertible. Let C be the lower triangular part of Gamma^{-1} and define
1654: $ A = Alpha Gamma^{-1}, bt^T = b^T Gamma^{-1}
1656: to rewrite the method as
1658: .vb
1659: [M/(h gamma_ii) - J] y_i = f(u_0 + sum_j a_ij y_j) + M sum_j (c_ij/h) y_j
1660: u_1 = u_0 + sum_j bt_j y_j
1661: .ve
1663: where we have introduced the mass matrix M. Continue by defining
1665: $ ydot_i = 1/(h gamma_ii) y_i - sum_j (c_ij/h) y_j
1667: or, more compactly in tensor notation
1669: $ Ydot = 1/h (Gamma^{-1} \otimes I) Y .
1671: Note that Gamma^{-1} is lower triangular. With this definition of Ydot in terms of known quantities and the current
1672: stage y_i, the stage equations reduce to performing one Newton step (typically with a lagged Jacobian) on the
1673: equation
1675: $ g(u_0 + sum_j a_ij y_j + y_i, ydot_i) = 0
1677: with initial guess y_i = 0.
1679: .seealso: [](ch_ts), `TSCreate()`, `TS`, `TSSetType()`, `TSRosWSetType()`, `TSRosWRegister()`, `TSROSWTHETA1`, `TSROSWTHETA2`, `TSROSW2M`, `TSROSW2P`, `TSROSWRA3PW`, `TSROSWRA34PW2`, `TSROSWRODAS3`,
1680: `TSROSWSANDU3`, `TSROSWASSP3P3S1C`, `TSROSWLASSP3P4S2C`, `TSROSWLLSSP3P4S2C`, `TSROSWGRK4T`, `TSROSWSHAMP4`, `TSROSWVELDD4`, `TSROSW4L`, `TSType`
1681: M*/
1682: PETSC_EXTERN PetscErrorCode TSCreate_RosW(TS ts)
1683: {
1684: TS_RosW *ros;
1686: PetscFunctionBegin;
1687: PetscCall(TSRosWInitializePackage());
1689: ts->ops->reset = TSReset_RosW;
1690: ts->ops->destroy = TSDestroy_RosW;
1691: ts->ops->view = TSView_RosW;
1692: ts->ops->load = TSLoad_RosW;
1693: ts->ops->setup = TSSetUp_RosW;
1694: ts->ops->step = TSStep_RosW;
1695: ts->ops->interpolate = TSInterpolate_RosW;
1696: ts->ops->evaluatestep = TSEvaluateStep_RosW;
1697: ts->ops->rollback = TSRollBack_RosW;
1698: ts->ops->setfromoptions = TSSetFromOptions_RosW;
1699: ts->ops->snesfunction = SNESTSFormFunction_RosW;
1700: ts->ops->snesjacobian = SNESTSFormJacobian_RosW;
1702: ts->usessnes = PETSC_TRUE;
1704: PetscCall(PetscNew(&ros));
1705: ts->data = (void *)ros;
1707: PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSRosWGetType_C", TSRosWGetType_RosW));
1708: PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSRosWSetType_C", TSRosWSetType_RosW));
1709: PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSRosWSetRecomputeJacobian_C", TSRosWSetRecomputeJacobian_RosW));
1711: PetscCall(TSRosWSetType(ts, TSRosWDefault));
1712: PetscFunctionReturn(PETSC_SUCCESS);
1713: }