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 {cite}`rang_2005`
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: .seealso: [](ch_ts), `TSROSW`
116: M*/
118: /*MC
119: TSROSWRA34PW2 - Four stage third order L-stable Rosenbrock-W scheme for PDAE of index 1 {cite}`rang_2005`.
121: Only an approximate Jacobian is needed. By default, it is only recomputed once per step.
123: This is strongly A-stable with R(infty) = 0. The embedded method of order 2 is strongly A-stable with R(infty) = 0.48.
125: Level: intermediate
127: .seealso: [](ch_ts), `TSROSW`
128: M*/
130: /*MC
131: TSROSWRODAS3 - Four stage third order L-stable Rosenbrock scheme {cite}`sandu_1997`
133: By default, the Jacobian is only recomputed once per step.
135: Both the third order and embedded second order methods are stiffly accurate and L-stable.
137: Level: intermediate
139: .seealso: [](ch_ts), `TSROSW`, `TSROSWSANDU3`
140: M*/
142: /*MC
143: TSROSWSANDU3 - Three stage third order L-stable Rosenbrock scheme {cite}`sandu_1997`
145: By default, the Jacobian is only recomputed once per step.
147: The third order method is L-stable, but not stiffly accurate.
148: The second order embedded method is strongly A-stable with R(infty) = 0.5.
149: The internal stages are L-stable.
150: This method is called ROS3 in {cite}`sandu_1997`.
152: Level: intermediate
154: .seealso: [](ch_ts), `TSROSW`, `TSROSWRODAS3`
155: M*/
157: /*MC
158: TSROSWASSP3P3S1C - A-stable Rosenbrock-W method with SSP explicit part, third order, three stages
160: By default, the Jacobian is only recomputed once per step.
162: A-stable SPP explicit order 3, 3 stages, CFL 1 (eff = 1/3)
164: Level: intermediate
166: .seealso: [](ch_ts), `TSROSW`, `TSROSWLASSP3P4S2C`, `TSROSWLLSSP3P4S2C`, `SSP`
167: M*/
169: /*MC
170: TSROSWLASSP3P4S2C - L-stable Rosenbrock-W method with SSP explicit part, third order, four stages
172: By default, the Jacobian is only recomputed once per step.
174: L-stable (A-stable embedded) SPP explicit order 3, 4 stages, CFL 2 (eff = 1/2)
176: Level: intermediate
178: .seealso: [](ch_ts), `TSROSW`, `TSROSWASSP3P3S1C`, `TSROSWLLSSP3P4S2C`, `TSSSP`
179: M*/
181: /*MC
182: TSROSWLLSSP3P4S2C - L-stable Rosenbrock-W method with SSP explicit part, third order, four stages
184: By default, the Jacobian is only recomputed once per step.
186: L-stable (L-stable embedded) SPP explicit order 3, 4 stages, CFL 2 (eff = 1/2)
188: Level: intermediate
190: .seealso: [](ch_ts), `TSROSW`, `TSROSWASSP3P3S1C`, `TSROSWLASSP3P4S2C`, `TSSSP`
191: M*/
193: /*MC
194: TSROSWGRK4T - four stage, fourth order Rosenbrock (not W) method from Kaps and Rentrop {cite}`kaps1979generalized`
196: By default, the Jacobian is only recomputed once per step.
198: A(89.3 degrees)-stable, |R(infty)| = 0.454.
200: This method does not provide a dense output formula.
202: Level: intermediate
204: Note:
205: See Section 4 Table 7.2 in {cite}`wanner1996solving`
207: .seealso: [](ch_ts), `TSROSW`, `TSROSWSHAMP4`, `TSROSWVELDD4`, `TSROSW4L`
208: M*/
210: /*MC
211: TSROSWSHAMP4 - four stage, fourth order Rosenbrock (not W) method from Shampine {cite}`shampine1982implementation`
213: By default, the Jacobian is only recomputed once per step.
215: A-stable, |R(infty)| = 1/3.
217: This method does not provide a dense output formula.
219: Level: intermediate
221: Note:
222: See Section 4 Table 7.2 in in {cite}`wanner1996solving`
224: .seealso: [](ch_ts), `TSROSW`, `TSROSWGRK4T`, `TSROSWVELDD4`, `TSROSW4L`
225: M*/
227: /*MC
228: TSROSWVELDD4 - four stage, fourth order Rosenbrock (not W) method from van Veldhuizen {cite}`veldhuizen1984d`
230: By default, the Jacobian is only recomputed once per step.
232: A(89.5 degrees)-stable, |R(infty)| = 0.24.
234: This method does not provide a dense output formula.
236: Level: intermediate
238: Note:
239: See Section 4 Table 7.2 in {cite}`wanner1996solving`
241: .seealso: [](ch_ts), `TSROSW`, `TSROSWGRK4T`, `TSROSWSHAMP4`, `TSROSW4L`
242: M*/
244: /*MC
245: TSROSW4L - four stage, fourth order Rosenbrock (not W) method
247: By default, the Jacobian is only recomputed once per step.
249: A-stable and L-stable
251: This method does not provide a dense output formula.
253: Level: intermediate
255: Note:
256: See Section 4 Table 7.2 in in {cite}`wanner1996solving`
258: .seealso: [](ch_ts), `TSROSW`, `TSROSWGRK4T`, `TSROSWSHAMP4`, `TSROSW4L`
259: M*/
261: /*@C
262: TSRosWRegisterAll - Registers all of the Rosenbrock-W methods in `TSROSW`
264: Not Collective, but should be called by all MPI processes which will need the schemes to be registered
266: Level: advanced
268: .seealso: [](ch_ts), `TSROSW`, `TSRosWRegisterDestroy()`
269: @*/
270: PetscErrorCode TSRosWRegisterAll(void)
271: {
272: PetscFunctionBegin;
273: if (TSRosWRegisterAllCalled) PetscFunctionReturn(PETSC_SUCCESS);
274: TSRosWRegisterAllCalled = PETSC_TRUE;
276: {
277: const PetscReal A = 0;
278: const PetscReal Gamma = 1;
279: const PetscReal b = 1;
280: const PetscReal binterpt = 1;
282: PetscCall(TSRosWRegister(TSROSWTHETA1, 1, 1, &A, &Gamma, &b, NULL, 1, &binterpt));
283: }
285: {
286: const PetscReal A = 0;
287: const PetscReal Gamma = 0.5;
288: const PetscReal b = 1;
289: const PetscReal binterpt = 1;
291: PetscCall(TSRosWRegister(TSROSWTHETA2, 2, 1, &A, &Gamma, &b, NULL, 1, &binterpt));
292: }
294: {
295: /*const PetscReal g = 1. + 1./PetscSqrtReal(2.0); Direct evaluation: 1.707106781186547524401. Used for setting up arrays of values known at compile time below. */
296: const PetscReal A[2][2] = {
297: {0, 0},
298: {1., 0}
299: };
300: const PetscReal Gamma[2][2] = {
301: {1.707106781186547524401, 0 },
302: {-2. * 1.707106781186547524401, 1.707106781186547524401}
303: };
304: const PetscReal b[2] = {0.5, 0.5};
305: const PetscReal b1[2] = {1.0, 0.0};
306: PetscReal binterpt[2][2];
307: binterpt[0][0] = 1.707106781186547524401 - 1.0;
308: binterpt[1][0] = 2.0 - 1.707106781186547524401;
309: binterpt[0][1] = 1.707106781186547524401 - 1.5;
310: binterpt[1][1] = 1.5 - 1.707106781186547524401;
312: PetscCall(TSRosWRegister(TSROSW2P, 2, 2, &A[0][0], &Gamma[0][0], b, b1, 2, &binterpt[0][0]));
313: }
314: {
315: /*const PetscReal g = 1. - 1./PetscSqrtReal(2.0); Direct evaluation: 0.2928932188134524755992. Used for setting up arrays of values known at compile time below. */
316: const PetscReal A[2][2] = {
317: {0, 0},
318: {1., 0}
319: };
320: const PetscReal Gamma[2][2] = {
321: {0.2928932188134524755992, 0 },
322: {-2. * 0.2928932188134524755992, 0.2928932188134524755992}
323: };
324: const PetscReal b[2] = {0.5, 0.5};
325: const PetscReal b1[2] = {1.0, 0.0};
326: PetscReal binterpt[2][2];
327: binterpt[0][0] = 0.2928932188134524755992 - 1.0;
328: binterpt[1][0] = 2.0 - 0.2928932188134524755992;
329: binterpt[0][1] = 0.2928932188134524755992 - 1.5;
330: binterpt[1][1] = 1.5 - 0.2928932188134524755992;
332: PetscCall(TSRosWRegister(TSROSW2M, 2, 2, &A[0][0], &Gamma[0][0], b, b1, 2, &binterpt[0][0]));
333: }
334: {
335: /*const PetscReal g = 7.8867513459481287e-01; Directly written in-place below */
336: PetscReal binterpt[3][2];
337: const PetscReal A[3][3] = {
338: {0, 0, 0},
339: {1.5773502691896257e+00, 0, 0},
340: {0.5, 0, 0}
341: };
342: const PetscReal Gamma[3][3] = {
343: {7.8867513459481287e-01, 0, 0 },
344: {-1.5773502691896257e+00, 7.8867513459481287e-01, 0 },
345: {-6.7075317547305480e-01, -1.7075317547305482e-01, 7.8867513459481287e-01}
346: };
347: const PetscReal b[3] = {1.0566243270259355e-01, 4.9038105676657971e-02, 8.4529946162074843e-01};
348: const PetscReal b2[3] = {-1.7863279495408180e-01, 1. / 3., 8.4529946162074843e-01};
350: binterpt[0][0] = -0.8094010767585034;
351: binterpt[1][0] = -0.5;
352: binterpt[2][0] = 2.3094010767585034;
353: binterpt[0][1] = 0.9641016151377548;
354: binterpt[1][1] = 0.5;
355: binterpt[2][1] = -1.4641016151377548;
357: PetscCall(TSRosWRegister(TSROSWRA3PW, 3, 3, &A[0][0], &Gamma[0][0], b, b2, 2, &binterpt[0][0]));
358: }
359: {
360: PetscReal binterpt[4][3];
361: /*const PetscReal g = 4.3586652150845900e-01; Directly written in-place below */
362: const PetscReal A[4][4] = {
363: {0, 0, 0, 0},
364: {8.7173304301691801e-01, 0, 0, 0},
365: {8.4457060015369423e-01, -1.1299064236484185e-01, 0, 0},
366: {0, 0, 1., 0}
367: };
368: const PetscReal Gamma[4][4] = {
369: {4.3586652150845900e-01, 0, 0, 0 },
370: {-8.7173304301691801e-01, 4.3586652150845900e-01, 0, 0 },
371: {-9.0338057013044082e-01, 5.4180672388095326e-02, 4.3586652150845900e-01, 0 },
372: {2.4212380706095346e-01, -1.2232505839045147e+00, 5.4526025533510214e-01, 4.3586652150845900e-01}
373: };
374: const PetscReal b[4] = {2.4212380706095346e-01, -1.2232505839045147e+00, 1.5452602553351020e+00, 4.3586652150845900e-01};
375: const PetscReal b2[4] = {3.7810903145819369e-01, -9.6042292212423178e-02, 5.0000000000000000e-01, 2.1793326075422950e-01};
377: binterpt[0][0] = 1.0564298455794094;
378: binterpt[1][0] = 2.296429974281067;
379: binterpt[2][0] = -1.307599564525376;
380: binterpt[3][0] = -1.045260255335102;
381: binterpt[0][1] = -1.3864882699759573;
382: binterpt[1][1] = -8.262611700275677;
383: binterpt[2][1] = 7.250979895056055;
384: binterpt[3][1] = 2.398120075195581;
385: binterpt[0][2] = 0.5721822314575016;
386: binterpt[1][2] = 4.742931142090097;
387: binterpt[2][2] = -4.398120075195578;
388: binterpt[3][2] = -0.9169932983520199;
390: PetscCall(TSRosWRegister(TSROSWRA34PW2, 3, 4, &A[0][0], &Gamma[0][0], b, b2, 3, &binterpt[0][0]));
391: }
392: {
393: /* const PetscReal g = 0.5; Directly written in-place below */
394: const PetscReal A[4][4] = {
395: {0, 0, 0, 0},
396: {0, 0, 0, 0},
397: {1., 0, 0, 0},
398: {0.75, -0.25, 0.5, 0}
399: };
400: const PetscReal Gamma[4][4] = {
401: {0.5, 0, 0, 0 },
402: {1., 0.5, 0, 0 },
403: {-0.25, -0.25, 0.5, 0 },
404: {1. / 12, 1. / 12, -2. / 3, 0.5}
405: };
406: const PetscReal b[4] = {5. / 6, -1. / 6, -1. / 6, 0.5};
407: const PetscReal b2[4] = {0.75, -0.25, 0.5, 0};
409: PetscCall(TSRosWRegister(TSROSWRODAS3, 3, 4, &A[0][0], &Gamma[0][0], b, b2, 0, NULL));
410: }
411: {
412: /*const PetscReal g = 0.43586652150845899941601945119356; Directly written in-place below */
413: const PetscReal A[3][3] = {
414: {0, 0, 0},
415: {0.43586652150845899941601945119356, 0, 0},
416: {0.43586652150845899941601945119356, 0, 0}
417: };
418: const PetscReal Gamma[3][3] = {
419: {0.43586652150845899941601945119356, 0, 0 },
420: {-0.19294655696029095575009695436041, 0.43586652150845899941601945119356, 0 },
421: {0, 1.74927148125794685173529749738960, 0.43586652150845899941601945119356}
422: };
423: const PetscReal b[3] = {-0.75457412385404315829818998646589, 1.94100407061964420292840123379419, -0.18642994676560104463021124732829};
424: const PetscReal b2[3] = {-1.53358745784149585370766523913002, 2.81745131148625772213931745457622, -0.28386385364476186843165221544619};
426: PetscReal binterpt[3][2];
427: binterpt[0][0] = 3.793692883777660870425141387941;
428: binterpt[1][0] = -2.918692883777660870425141387941;
429: binterpt[2][0] = 0.125;
430: binterpt[0][1] = -0.725741064379812106687651020584;
431: binterpt[1][1] = 0.559074397713145440020984353917;
432: binterpt[2][1] = 0.16666666666666666666666666666667;
434: PetscCall(TSRosWRegister(TSROSWSANDU3, 3, 3, &A[0][0], &Gamma[0][0], b, b2, 2, &binterpt[0][0]));
435: }
436: {
437: /*const PetscReal s3 = PetscSqrtReal(3.),g = (3.0+s3)/6.0;
438: * Direct evaluation: s3 = 1.732050807568877293527;
439: * g = 0.7886751345948128822546;
440: * Values are directly inserted below to ensure availability at compile time (compiler warnings otherwise...) */
441: const PetscReal A[3][3] = {
442: {0, 0, 0},
443: {1, 0, 0},
444: {0.25, 0.25, 0}
445: };
446: const PetscReal Gamma[3][3] = {
447: {0, 0, 0 },
448: {(-3.0 - 1.732050807568877293527) / 6.0, 0.7886751345948128822546, 0 },
449: {(-3.0 - 1.732050807568877293527) / 24.0, (-3.0 - 1.732050807568877293527) / 8.0, 0.7886751345948128822546}
450: };
451: const PetscReal b[3] = {1. / 6., 1. / 6., 2. / 3.};
452: const PetscReal b2[3] = {1. / 4., 1. / 4., 1. / 2.};
453: PetscReal binterpt[3][2];
455: binterpt[0][0] = 0.089316397477040902157517886164709;
456: binterpt[1][0] = -0.91068360252295909784248211383529;
457: binterpt[2][0] = 1.8213672050459181956849642276706;
458: binterpt[0][1] = 0.077350269189625764509148780501957;
459: binterpt[1][1] = 1.077350269189625764509148780502;
460: binterpt[2][1] = -1.1547005383792515290182975610039;
462: PetscCall(TSRosWRegister(TSROSWASSP3P3S1C, 3, 3, &A[0][0], &Gamma[0][0], b, b2, 2, &binterpt[0][0]));
463: }
465: {
466: const PetscReal A[4][4] = {
467: {0, 0, 0, 0},
468: {1. / 2., 0, 0, 0},
469: {1. / 2., 1. / 2., 0, 0},
470: {1. / 6., 1. / 6., 1. / 6., 0}
471: };
472: const PetscReal Gamma[4][4] = {
473: {1. / 2., 0, 0, 0},
474: {0.0, 1. / 4., 0, 0},
475: {-2., -2. / 3., 2. / 3., 0},
476: {1. / 2., 5. / 36., -2. / 9, 0}
477: };
478: const PetscReal b[4] = {1. / 6., 1. / 6., 1. / 6., 1. / 2.};
479: const PetscReal b2[4] = {1. / 8., 3. / 4., 1. / 8., 0};
480: PetscReal binterpt[4][3];
482: binterpt[0][0] = 6.25;
483: binterpt[1][0] = -30.25;
484: binterpt[2][0] = 1.75;
485: binterpt[3][0] = 23.25;
486: binterpt[0][1] = -9.75;
487: binterpt[1][1] = 58.75;
488: binterpt[2][1] = -3.25;
489: binterpt[3][1] = -45.75;
490: binterpt[0][2] = 3.6666666666666666666666666666667;
491: binterpt[1][2] = -28.333333333333333333333333333333;
492: binterpt[2][2] = 1.6666666666666666666666666666667;
493: binterpt[3][2] = 23.;
495: PetscCall(TSRosWRegister(TSROSWLASSP3P4S2C, 3, 4, &A[0][0], &Gamma[0][0], b, b2, 3, &binterpt[0][0]));
496: }
498: {
499: const PetscReal A[4][4] = {
500: {0, 0, 0, 0},
501: {1. / 2., 0, 0, 0},
502: {1. / 2., 1. / 2., 0, 0},
503: {1. / 6., 1. / 6., 1. / 6., 0}
504: };
505: const PetscReal Gamma[4][4] = {
506: {1. / 2., 0, 0, 0},
507: {0.0, 3. / 4., 0, 0},
508: {-2. / 3., -23. / 9., 2. / 9., 0},
509: {1. / 18., 65. / 108., -2. / 27, 0}
510: };
511: const PetscReal b[4] = {1. / 6., 1. / 6., 1. / 6., 1. / 2.};
512: const PetscReal b2[4] = {3. / 16., 10. / 16., 3. / 16., 0};
513: PetscReal binterpt[4][3];
515: binterpt[0][0] = 1.6911764705882352941176470588235;
516: binterpt[1][0] = 3.6813725490196078431372549019608;
517: binterpt[2][0] = 0.23039215686274509803921568627451;
518: binterpt[3][0] = -4.6029411764705882352941176470588;
519: binterpt[0][1] = -0.95588235294117647058823529411765;
520: binterpt[1][1] = -6.2401960784313725490196078431373;
521: binterpt[2][1] = -0.31862745098039215686274509803922;
522: binterpt[3][1] = 7.5147058823529411764705882352941;
523: binterpt[0][2] = -0.56862745098039215686274509803922;
524: binterpt[1][2] = 2.7254901960784313725490196078431;
525: binterpt[2][2] = 0.25490196078431372549019607843137;
526: binterpt[3][2] = -2.4117647058823529411764705882353;
528: PetscCall(TSRosWRegister(TSROSWLLSSP3P4S2C, 3, 4, &A[0][0], &Gamma[0][0], b, b2, 3, &binterpt[0][0]));
529: }
531: {
532: PetscReal A[4][4], Gamma[4][4], b[4], b2[4];
533: PetscReal binterpt[4][3];
535: Gamma[0][0] = 0.4358665215084589994160194475295062513822671686978816;
536: Gamma[0][1] = 0;
537: Gamma[0][2] = 0;
538: Gamma[0][3] = 0;
539: Gamma[1][0] = -1.997527830934941248426324674704153457289527280554476;
540: Gamma[1][1] = 0.4358665215084589994160194475295062513822671686978816;
541: Gamma[1][2] = 0;
542: Gamma[1][3] = 0;
543: Gamma[2][0] = -1.007948511795029620852002345345404191008352770119903;
544: Gamma[2][1] = -0.004648958462629345562774289390054679806993396798458131;
545: Gamma[2][2] = 0.4358665215084589994160194475295062513822671686978816;
546: Gamma[2][3] = 0;
547: Gamma[3][0] = -0.6685429734233467180451604600279552604364311322650783;
548: Gamma[3][1] = 0.6056625986449338476089525334450053439525178740492984;
549: Gamma[3][2] = -0.9717899277217721234705114616271378792182450260943198;
550: Gamma[3][3] = 0;
552: A[0][0] = 0;
553: A[0][1] = 0;
554: A[0][2] = 0;
555: A[0][3] = 0;
556: A[1][0] = 0.8717330430169179988320388950590125027645343373957631;
557: A[1][1] = 0;
558: A[1][2] = 0;
559: A[1][3] = 0;
560: A[2][0] = 0.5275890119763004115618079766722914408876108660811028;
561: A[2][1] = 0.07241098802369958843819203208518599088698057726988732;
562: A[2][2] = 0;
563: A[2][3] = 0;
564: A[3][0] = 0.3990960076760701320627260685975778145384666450351314;
565: A[3][1] = -0.4375576546135194437228463747348862825846903771419953;
566: A[3][2] = 1.038461646937449311660120300601880176655352737312713;
567: A[3][3] = 0;
569: b[0] = 0.1876410243467238251612921333138006734899663569186926;
570: b[1] = -0.5952974735769549480478230473706443582188442040780541;
571: b[2] = 0.9717899277217721234705114616271378792182450260943198;
572: b[3] = 0.4358665215084589994160194475295062513822671686978816;
574: b2[0] = 0.2147402862233891404862383521089097657790734483804460;
575: b2[1] = -0.4851622638849390928209050538171743017757490232519684;
576: b2[2] = 0.8687250025203875511662123688667549217531982787600080;
577: b2[3] = 0.4016969751411624011684543450940068201770721128357014;
579: binterpt[0][0] = 2.2565812720167954547104627844105;
580: binterpt[1][0] = 1.349166413351089573796243820819;
581: binterpt[2][0] = -2.4695174540533503758652847586647;
582: binterpt[3][0] = -0.13623023131453465264142184656474;
583: binterpt[0][1] = -3.0826699111559187902922463354557;
584: binterpt[1][1] = -2.4689115685996042534544925650515;
585: binterpt[2][1] = 5.7428279814696677152129332773553;
586: binterpt[3][1] = -0.19124650171414467146619437684812;
587: binterpt[0][2] = 1.0137296634858471607430756831148;
588: binterpt[1][2] = 0.52444768167155973161042570784064;
589: binterpt[2][2] = -2.3015205996945452158771370439586;
590: binterpt[3][2] = 0.76334325453713832352363565300308;
592: PetscCall(TSRosWRegister(TSROSWARK3, 3, 4, &A[0][0], &Gamma[0][0], b, b2, 3, &binterpt[0][0]));
593: }
594: PetscCall(TSRosWRegisterRos4(TSROSWGRK4T, 0.231, PETSC_DEFAULT, PETSC_DEFAULT, 0, -0.1282612945269037e+01));
595: PetscCall(TSRosWRegisterRos4(TSROSWSHAMP4, 0.5, PETSC_DEFAULT, PETSC_DEFAULT, 0, 125. / 108.));
596: PetscCall(TSRosWRegisterRos4(TSROSWVELDD4, 0.22570811482256823492, PETSC_DEFAULT, PETSC_DEFAULT, 0, -1.355958941201148));
597: PetscCall(TSRosWRegisterRos4(TSROSW4L, 0.57282, PETSC_DEFAULT, PETSC_DEFAULT, 0, -1.093502252409163));
598: PetscFunctionReturn(PETSC_SUCCESS);
599: }
601: /*@C
602: TSRosWRegisterDestroy - Frees the list of schemes that were registered by `TSRosWRegister()`.
604: Not Collective
606: Level: advanced
608: .seealso: [](ch_ts), `TSRosWRegister()`, `TSRosWRegisterAll()`
609: @*/
610: PetscErrorCode TSRosWRegisterDestroy(void)
611: {
612: RosWTableauLink link;
614: PetscFunctionBegin;
615: while ((link = RosWTableauList)) {
616: RosWTableau t = &link->tab;
617: RosWTableauList = link->next;
618: PetscCall(PetscFree5(t->A, t->Gamma, t->b, t->ASum, t->GammaSum));
619: PetscCall(PetscFree5(t->At, t->bt, t->GammaInv, t->GammaZeroDiag, t->GammaExplicitCorr));
620: PetscCall(PetscFree2(t->bembed, t->bembedt));
621: PetscCall(PetscFree(t->binterpt));
622: PetscCall(PetscFree(t->name));
623: PetscCall(PetscFree(link));
624: }
625: TSRosWRegisterAllCalled = PETSC_FALSE;
626: PetscFunctionReturn(PETSC_SUCCESS);
627: }
629: /*@C
630: TSRosWInitializePackage - This function initializes everything in the `TSROSW` package. It is called
631: from `TSInitializePackage()`.
633: Level: developer
635: .seealso: [](ch_ts), `TSROSW`, `PetscInitialize()`, `TSRosWFinalizePackage()`
636: @*/
637: PetscErrorCode TSRosWInitializePackage(void)
638: {
639: PetscFunctionBegin;
640: if (TSRosWPackageInitialized) PetscFunctionReturn(PETSC_SUCCESS);
641: TSRosWPackageInitialized = PETSC_TRUE;
642: PetscCall(TSRosWRegisterAll());
643: PetscCall(PetscRegisterFinalize(TSRosWFinalizePackage));
644: PetscFunctionReturn(PETSC_SUCCESS);
645: }
647: /*@C
648: TSRosWFinalizePackage - This function destroys everything in the `TSROSW` package. It is
649: called from `PetscFinalize()`.
651: Level: developer
653: .seealso: [](ch_ts), `TSROSW`, `PetscFinalize()`, `TSRosWInitializePackage()`
654: @*/
655: PetscErrorCode TSRosWFinalizePackage(void)
656: {
657: PetscFunctionBegin;
658: TSRosWPackageInitialized = PETSC_FALSE;
659: PetscCall(TSRosWRegisterDestroy());
660: PetscFunctionReturn(PETSC_SUCCESS);
661: }
663: /*@C
664: TSRosWRegister - register a `TSROSW`, Rosenbrock W scheme by providing the entries in the Butcher tableau and optionally embedded approximations and interpolation
666: Not Collective, but the same schemes should be registered on all processes on which they will be used
668: Input Parameters:
669: + name - identifier for method
670: . order - approximation order of method
671: . s - number of stages, this is the dimension of the matrices below
672: . A - Table of propagated stage coefficients (dimension s*s, row-major), strictly lower triangular
673: . Gamma - Table of coefficients in implicit stage equations (dimension s*s, row-major), lower triangular with nonzero diagonal
674: . b - Step completion table (dimension s)
675: . bembed - Step completion table for a scheme of order one less (dimension s, NULL if no embedded scheme is available)
676: . pinterp - Order of the interpolation scheme, equal to the number of columns of binterpt
677: - binterpt - Coefficients of the interpolation formula (dimension s*pinterp)
679: Level: advanced
681: Note:
682: Several Rosenbrock W methods are provided, this function is only needed to create new methods.
684: .seealso: [](ch_ts), `TSROSW`
685: @*/
686: 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[])
687: {
688: RosWTableauLink link;
689: RosWTableau t;
690: PetscInt i, j, k;
691: PetscScalar *GammaInv;
693: PetscFunctionBegin;
694: PetscAssertPointer(name, 1);
695: PetscAssertPointer(A, 4);
696: PetscAssertPointer(Gamma, 5);
697: PetscAssertPointer(b, 6);
698: if (bembed) PetscAssertPointer(bembed, 7);
700: PetscCall(TSRosWInitializePackage());
701: PetscCall(PetscNew(&link));
702: t = &link->tab;
703: PetscCall(PetscStrallocpy(name, &t->name));
704: t->order = order;
705: t->s = s;
706: PetscCall(PetscMalloc5(s * s, &t->A, s * s, &t->Gamma, s, &t->b, s, &t->ASum, s, &t->GammaSum));
707: PetscCall(PetscMalloc5(s * s, &t->At, s, &t->bt, s * s, &t->GammaInv, s, &t->GammaZeroDiag, s * s, &t->GammaExplicitCorr));
708: PetscCall(PetscArraycpy(t->A, A, s * s));
709: PetscCall(PetscArraycpy(t->Gamma, Gamma, s * s));
710: PetscCall(PetscArraycpy(t->GammaExplicitCorr, Gamma, s * s));
711: PetscCall(PetscArraycpy(t->b, b, s));
712: if (bembed) {
713: PetscCall(PetscMalloc2(s, &t->bembed, s, &t->bembedt));
714: PetscCall(PetscArraycpy(t->bembed, bembed, s));
715: }
716: for (i = 0; i < s; i++) {
717: t->ASum[i] = 0;
718: t->GammaSum[i] = 0;
719: for (j = 0; j < s; j++) {
720: t->ASum[i] += A[i * s + j];
721: t->GammaSum[i] += Gamma[i * s + j];
722: }
723: }
724: PetscCall(PetscMalloc1(s * s, &GammaInv)); /* Need to use Scalar for inverse, then convert back to Real */
725: for (i = 0; i < s * s; i++) GammaInv[i] = Gamma[i];
726: for (i = 0; i < s; i++) {
727: if (Gamma[i * s + i] == 0.0) {
728: GammaInv[i * s + i] = 1.0;
729: t->GammaZeroDiag[i] = PETSC_TRUE;
730: } else {
731: t->GammaZeroDiag[i] = PETSC_FALSE;
732: }
733: }
735: switch (s) {
736: case 1:
737: GammaInv[0] = 1. / GammaInv[0];
738: break;
739: case 2:
740: PetscCall(PetscKernel_A_gets_inverse_A_2(GammaInv, 0, PETSC_FALSE, NULL));
741: break;
742: case 3:
743: PetscCall(PetscKernel_A_gets_inverse_A_3(GammaInv, 0, PETSC_FALSE, NULL));
744: break;
745: case 4:
746: PetscCall(PetscKernel_A_gets_inverse_A_4(GammaInv, 0, PETSC_FALSE, NULL));
747: break;
748: case 5: {
749: PetscInt ipvt5[5];
750: MatScalar work5[5 * 5];
751: PetscCall(PetscKernel_A_gets_inverse_A_5(GammaInv, ipvt5, work5, 0, PETSC_FALSE, NULL));
752: break;
753: }
754: case 6:
755: PetscCall(PetscKernel_A_gets_inverse_A_6(GammaInv, 0, PETSC_FALSE, NULL));
756: break;
757: case 7:
758: PetscCall(PetscKernel_A_gets_inverse_A_7(GammaInv, 0, PETSC_FALSE, NULL));
759: break;
760: default:
761: SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "Not implemented for %" PetscInt_FMT " stages", s);
762: }
763: for (i = 0; i < s * s; i++) t->GammaInv[i] = PetscRealPart(GammaInv[i]);
764: PetscCall(PetscFree(GammaInv));
766: for (i = 0; i < s; i++) {
767: for (k = 0; k < i + 1; k++) {
768: t->GammaExplicitCorr[i * s + k] = (t->GammaExplicitCorr[i * s + k]) * (t->GammaInv[k * s + k]);
769: for (j = k + 1; j < i + 1; j++) t->GammaExplicitCorr[i * s + k] += (t->GammaExplicitCorr[i * s + j]) * (t->GammaInv[j * s + k]);
770: }
771: }
773: for (i = 0; i < s; i++) {
774: for (j = 0; j < s; j++) {
775: t->At[i * s + j] = 0;
776: for (k = 0; k < s; k++) t->At[i * s + j] += t->A[i * s + k] * t->GammaInv[k * s + j];
777: }
778: t->bt[i] = 0;
779: for (j = 0; j < s; j++) t->bt[i] += t->b[j] * t->GammaInv[j * s + i];
780: if (bembed) {
781: t->bembedt[i] = 0;
782: for (j = 0; j < s; j++) t->bembedt[i] += t->bembed[j] * t->GammaInv[j * s + i];
783: }
784: }
785: t->ccfl = 1.0; /* Fix this */
787: t->pinterp = pinterp;
788: PetscCall(PetscMalloc1(s * pinterp, &t->binterpt));
789: PetscCall(PetscArraycpy(t->binterpt, binterpt, s * pinterp));
790: link->next = RosWTableauList;
791: RosWTableauList = link;
792: PetscFunctionReturn(PETSC_SUCCESS);
793: }
795: /*@C
796: TSRosWRegisterRos4 - register a fourth order Rosenbrock scheme by providing parameter choices
798: Not Collective, but the same schemes should be registered on all processes on which they will be used
800: Input Parameters:
801: + name - identifier for method
802: . gamma - leading coefficient (diagonal entry)
803: . a2 - design parameter, see Table 7.2 of Hairer&Wanner
804: . a3 - design parameter or PETSC_DEFAULT to satisfy one of the order five conditions (Eq 7.22)
805: . b3 - design parameter, see Table 7.2 of Hairer&Wanner
806: - e4 - design parameter for embedded method, see coefficient E4 in ros4.f code from Hairer
808: Level: developer
810: Notes:
811: This routine encodes the design of fourth order Rosenbrock methods as described in Hairer and Wanner volume 2.
812: It is used here to implement several methods from the book and can be used to experiment with new methods.
813: It was written this way instead of by copying coefficients in order to provide better than double precision satisfaction of the order conditions.
815: .seealso: [](ch_ts), `TSRosW`, `TSRosWRegister()`
816: @*/
817: PetscErrorCode TSRosWRegisterRos4(TSRosWType name, PetscReal gamma, PetscReal a2, PetscReal a3, PetscReal b3, PetscReal e4)
818: {
819: /* Declare numeric constants so they can be quad precision without being truncated at double */
820: 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;
821: PetscReal a4, a32, a42, a43, b1, b2, b4, beta2p, beta3p, beta4p, beta32, beta42, beta43, beta32beta2p, beta4jbetajp;
822: PetscReal A[4][4], Gamma[4][4], b[4], bm[4];
823: PetscScalar M[3][3], rhs[3];
825: PetscFunctionBegin;
826: /* Step 1: choose Gamma (input) */
827: /* Step 2: choose a2,a3,a4; b1,b2,b3,b4 to satisfy order conditions */
828: if (a3 == (PetscReal)PETSC_DEFAULT) a3 = (one / five - a2 / four) / (one / four - a2 / three); /* Eq 7.22 */
829: a4 = a3; /* consequence of 7.20 */
831: /* Solve order conditions 7.15a, 7.15c, 7.15e */
832: M[0][0] = one;
833: M[0][1] = one;
834: M[0][2] = one; /* 7.15a */
835: M[1][0] = 0.0;
836: M[1][1] = a2 * a2;
837: M[1][2] = a4 * a4; /* 7.15c */
838: M[2][0] = 0.0;
839: M[2][1] = a2 * a2 * a2;
840: M[2][2] = a4 * a4 * a4; /* 7.15e */
841: rhs[0] = one - b3;
842: rhs[1] = one / three - a3 * a3 * b3;
843: rhs[2] = one / four - a3 * a3 * a3 * b3;
844: PetscCall(PetscKernel_A_gets_inverse_A_3(&M[0][0], 0, PETSC_FALSE, NULL));
845: b1 = PetscRealPart(M[0][0] * rhs[0] + M[0][1] * rhs[1] + M[0][2] * rhs[2]);
846: b2 = PetscRealPart(M[1][0] * rhs[0] + M[1][1] * rhs[1] + M[1][2] * rhs[2]);
847: b4 = PetscRealPart(M[2][0] * rhs[0] + M[2][1] * rhs[1] + M[2][2] * rhs[2]);
849: /* Step 3 */
850: beta43 = (p56 - a2 * p43) / (b4 * a3 * a3 * (a3 - a2)); /* 7.21 */
851: beta32beta2p = p44 / (b4 * beta43); /* 7.15h */
852: beta4jbetajp = (p32 - b3 * beta32beta2p) / b4;
853: M[0][0] = b2;
854: M[0][1] = b3;
855: M[0][2] = b4;
856: M[1][0] = a4 * a4 * beta32beta2p - a3 * a3 * beta4jbetajp;
857: M[1][1] = a2 * a2 * beta4jbetajp;
858: M[1][2] = -a2 * a2 * beta32beta2p;
859: M[2][0] = b4 * beta43 * a3 * a3 - p43;
860: M[2][1] = -b4 * beta43 * a2 * a2;
861: M[2][2] = 0;
862: rhs[0] = one / two - gamma;
863: rhs[1] = 0;
864: rhs[2] = -a2 * a2 * p32;
865: PetscCall(PetscKernel_A_gets_inverse_A_3(&M[0][0], 0, PETSC_FALSE, NULL));
866: beta2p = PetscRealPart(M[0][0] * rhs[0] + M[0][1] * rhs[1] + M[0][2] * rhs[2]);
867: beta3p = PetscRealPart(M[1][0] * rhs[0] + M[1][1] * rhs[1] + M[1][2] * rhs[2]);
868: beta4p = PetscRealPart(M[2][0] * rhs[0] + M[2][1] * rhs[1] + M[2][2] * rhs[2]);
870: /* Step 4: back-substitute */
871: beta32 = beta32beta2p / beta2p;
872: beta42 = (beta4jbetajp - beta43 * beta3p) / beta2p;
874: /* Step 5: 7.15f and 7.20, then 7.16 */
875: a43 = 0;
876: a32 = p42 / (b3 * a3 * beta2p + b4 * a4 * beta2p);
877: a42 = a32;
879: A[0][0] = 0;
880: A[0][1] = 0;
881: A[0][2] = 0;
882: A[0][3] = 0;
883: A[1][0] = a2;
884: A[1][1] = 0;
885: A[1][2] = 0;
886: A[1][3] = 0;
887: A[2][0] = a3 - a32;
888: A[2][1] = a32;
889: A[2][2] = 0;
890: A[2][3] = 0;
891: A[3][0] = a4 - a43 - a42;
892: A[3][1] = a42;
893: A[3][2] = a43;
894: A[3][3] = 0;
895: Gamma[0][0] = gamma;
896: Gamma[0][1] = 0;
897: Gamma[0][2] = 0;
898: Gamma[0][3] = 0;
899: Gamma[1][0] = beta2p - A[1][0];
900: Gamma[1][1] = gamma;
901: Gamma[1][2] = 0;
902: Gamma[1][3] = 0;
903: Gamma[2][0] = beta3p - beta32 - A[2][0];
904: Gamma[2][1] = beta32 - A[2][1];
905: Gamma[2][2] = gamma;
906: Gamma[2][3] = 0;
907: Gamma[3][0] = beta4p - beta42 - beta43 - A[3][0];
908: Gamma[3][1] = beta42 - A[3][1];
909: Gamma[3][2] = beta43 - A[3][2];
910: Gamma[3][3] = gamma;
911: b[0] = b1;
912: b[1] = b2;
913: b[2] = b3;
914: b[3] = b4;
916: /* Construct embedded formula using given e4. We are solving Equation 7.18. */
917: bm[3] = b[3] - e4 * gamma; /* using definition of E4 */
918: bm[2] = (p32 - beta4jbetajp * bm[3]) / (beta32 * beta2p); /* fourth row of 7.18 */
919: bm[1] = (one / two - gamma - beta3p * bm[2] - beta4p * bm[3]) / beta2p; /* second row */
920: bm[0] = one - bm[1] - bm[2] - bm[3]; /* first row */
922: {
923: const PetscReal misfit = a2 * a2 * bm[1] + a3 * a3 * bm[2] + a4 * a4 * bm[3] - one / three;
924: PetscCheck(PetscAbs(misfit) <= PETSC_SMALL, PETSC_COMM_SELF, PETSC_ERR_SUP, "Assumptions violated, could not construct a third order embedded method");
925: }
926: PetscCall(TSRosWRegister(name, 4, 4, &A[0][0], &Gamma[0][0], b, bm, 0, NULL));
927: PetscFunctionReturn(PETSC_SUCCESS);
928: }
930: /*
931: The step completion formula is
933: x1 = x0 + b^T Y
935: where Y is the multi-vector of stages corrections. This function can be called before or after ts->vec_sol has been
936: updated. Suppose we have a completion formula b and an embedded formula be of different order. We can write
938: x1e = x0 + be^T Y
939: = x1 - b^T Y + be^T Y
940: = x1 + (be - b)^T Y
942: so we can evaluate the method of different order even after the step has been optimistically completed.
943: */
944: static PetscErrorCode TSEvaluateStep_RosW(TS ts, PetscInt order, Vec U, PetscBool *done)
945: {
946: TS_RosW *ros = (TS_RosW *)ts->data;
947: RosWTableau tab = ros->tableau;
948: PetscScalar *w = ros->work;
949: PetscInt i;
951: PetscFunctionBegin;
952: if (order == tab->order) {
953: if (ros->status == TS_STEP_INCOMPLETE) { /* Use standard completion formula */
954: PetscCall(VecCopy(ts->vec_sol, U));
955: for (i = 0; i < tab->s; i++) w[i] = tab->bt[i];
956: PetscCall(VecMAXPY(U, tab->s, w, ros->Y));
957: } else PetscCall(VecCopy(ts->vec_sol, U));
958: if (done) *done = PETSC_TRUE;
959: PetscFunctionReturn(PETSC_SUCCESS);
960: } else if (order == tab->order - 1) {
961: if (!tab->bembedt) goto unavailable;
962: if (ros->status == TS_STEP_INCOMPLETE) { /* Use embedded completion formula */
963: PetscCall(VecCopy(ts->vec_sol, U));
964: for (i = 0; i < tab->s; i++) w[i] = tab->bembedt[i];
965: PetscCall(VecMAXPY(U, tab->s, w, ros->Y));
966: } else { /* Use rollback-and-recomplete formula (bembedt - bt) */
967: for (i = 0; i < tab->s; i++) w[i] = tab->bembedt[i] - tab->bt[i];
968: PetscCall(VecCopy(ts->vec_sol, U));
969: PetscCall(VecMAXPY(U, tab->s, w, ros->Y));
970: }
971: if (done) *done = PETSC_TRUE;
972: PetscFunctionReturn(PETSC_SUCCESS);
973: }
974: unavailable:
975: if (done) *done = PETSC_FALSE;
976: else
977: 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,
978: tab->order, order);
979: PetscFunctionReturn(PETSC_SUCCESS);
980: }
982: static PetscErrorCode TSRollBack_RosW(TS ts)
983: {
984: TS_RosW *ros = (TS_RosW *)ts->data;
986: PetscFunctionBegin;
987: PetscCall(VecCopy(ros->vec_sol_prev, ts->vec_sol));
988: PetscFunctionReturn(PETSC_SUCCESS);
989: }
991: static PetscErrorCode TSStep_RosW(TS ts)
992: {
993: TS_RosW *ros = (TS_RosW *)ts->data;
994: RosWTableau tab = ros->tableau;
995: const PetscInt s = tab->s;
996: const PetscReal *At = tab->At, *Gamma = tab->Gamma, *ASum = tab->ASum, *GammaInv = tab->GammaInv;
997: const PetscReal *GammaExplicitCorr = tab->GammaExplicitCorr;
998: const PetscBool *GammaZeroDiag = tab->GammaZeroDiag;
999: PetscScalar *w = ros->work;
1000: Vec *Y = ros->Y, Ydot = ros->Ydot, Zdot = ros->Zdot, Zstage = ros->Zstage;
1001: SNES snes;
1002: TSAdapt adapt;
1003: PetscInt i, j, its, lits;
1004: PetscInt rejections = 0;
1005: PetscBool stageok, accept = PETSC_TRUE;
1006: PetscReal next_time_step = ts->time_step;
1007: PetscInt lag;
1009: PetscFunctionBegin;
1010: if (!ts->steprollback) PetscCall(VecCopy(ts->vec_sol, ros->vec_sol_prev));
1012: ros->status = TS_STEP_INCOMPLETE;
1013: while (!ts->reason && ros->status != TS_STEP_COMPLETE) {
1014: const PetscReal h = ts->time_step;
1015: for (i = 0; i < s; i++) {
1016: ros->stage_time = ts->ptime + h * ASum[i];
1017: PetscCall(TSPreStage(ts, ros->stage_time));
1018: if (GammaZeroDiag[i]) {
1019: ros->stage_explicit = PETSC_TRUE;
1020: ros->scoeff = 1.;
1021: } else {
1022: ros->stage_explicit = PETSC_FALSE;
1023: ros->scoeff = 1. / Gamma[i * s + i];
1024: }
1026: PetscCall(VecCopy(ts->vec_sol, Zstage));
1027: for (j = 0; j < i; j++) w[j] = At[i * s + j];
1028: PetscCall(VecMAXPY(Zstage, i, w, Y));
1030: for (j = 0; j < i; j++) w[j] = 1. / h * GammaInv[i * s + j];
1031: PetscCall(VecZeroEntries(Zdot));
1032: PetscCall(VecMAXPY(Zdot, i, w, Y));
1034: /* Initial guess taken from last stage */
1035: PetscCall(VecZeroEntries(Y[i]));
1037: if (!ros->stage_explicit) {
1038: PetscCall(TSGetSNES(ts, &snes));
1039: if (!ros->recompute_jacobian && !i) {
1040: PetscCall(SNESGetLagJacobian(snes, &lag));
1041: if (lag == 1) { /* use did not set a nontrivial lag, so lag over all stages */
1042: PetscCall(SNESSetLagJacobian(snes, -2)); /* Recompute the Jacobian on this solve, but not again for the rest of the stages */
1043: }
1044: }
1045: PetscCall(SNESSolve(snes, NULL, Y[i]));
1046: 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 */ }
1047: PetscCall(SNESGetIterationNumber(snes, &its));
1048: PetscCall(SNESGetLinearSolveIterations(snes, &lits));
1049: ts->snes_its += its;
1050: ts->ksp_its += lits;
1051: } else {
1052: Mat J, Jp;
1053: PetscCall(VecZeroEntries(Ydot)); /* Evaluate Y[i]=G(t,Ydot=0,Zstage) */
1054: PetscCall(TSComputeIFunction(ts, ros->stage_time, Zstage, Ydot, Y[i], PETSC_FALSE));
1055: PetscCall(VecScale(Y[i], -1.0));
1056: PetscCall(VecAXPY(Y[i], -1.0, Zdot)); /*Y[i] = F(Zstage)-Zdot[=GammaInv*Y]*/
1058: PetscCall(VecZeroEntries(Zstage)); /* Zstage = GammaExplicitCorr[i,j] * Y[j] */
1059: for (j = 0; j < i; j++) w[j] = GammaExplicitCorr[i * s + j];
1060: PetscCall(VecMAXPY(Zstage, i, w, Y));
1062: /* Y[i] = Y[i] + Jac*Zstage[=Jac*GammaExplicitCorr[i,j] * Y[j]] */
1063: PetscCall(TSGetIJacobian(ts, &J, &Jp, NULL, NULL));
1064: PetscCall(TSComputeIJacobian(ts, ros->stage_time, ts->vec_sol, Ydot, 0, J, Jp, PETSC_FALSE));
1065: PetscCall(MatMult(J, Zstage, Zdot));
1066: PetscCall(VecAXPY(Y[i], -1.0, Zdot));
1067: ts->ksp_its += 1;
1069: PetscCall(VecScale(Y[i], h));
1070: }
1071: PetscCall(TSPostStage(ts, ros->stage_time, i, Y));
1072: PetscCall(TSGetAdapt(ts, &adapt));
1073: PetscCall(TSAdaptCheckStage(adapt, ts, ros->stage_time, Y[i], &stageok));
1074: if (!stageok) goto reject_step;
1075: }
1077: ros->status = TS_STEP_INCOMPLETE;
1078: PetscCall(TSEvaluateStep_RosW(ts, tab->order, ts->vec_sol, NULL));
1079: ros->status = TS_STEP_PENDING;
1080: PetscCall(TSGetAdapt(ts, &adapt));
1081: PetscCall(TSAdaptCandidatesClear(adapt));
1082: PetscCall(TSAdaptCandidateAdd(adapt, tab->name, tab->order, 1, tab->ccfl, (PetscReal)tab->s, PETSC_TRUE));
1083: PetscCall(TSAdaptChoose(adapt, ts, ts->time_step, NULL, &next_time_step, &accept));
1084: ros->status = accept ? TS_STEP_COMPLETE : TS_STEP_INCOMPLETE;
1085: if (!accept) { /* Roll back the current step */
1086: PetscCall(TSRollBack_RosW(ts));
1087: ts->time_step = next_time_step;
1088: goto reject_step;
1089: }
1091: ts->ptime += ts->time_step;
1092: ts->time_step = next_time_step;
1093: break;
1095: reject_step:
1096: ts->reject++;
1097: accept = PETSC_FALSE;
1098: if (!ts->reason && ++rejections > ts->max_reject && ts->max_reject >= 0) {
1099: ts->reason = TS_DIVERGED_STEP_REJECTED;
1100: PetscCall(PetscInfo(ts, "Step=%" PetscInt_FMT ", step rejections %" PetscInt_FMT " greater than current TS allowed, stopping solve\n", ts->steps, rejections));
1101: }
1102: }
1103: PetscFunctionReturn(PETSC_SUCCESS);
1104: }
1106: static PetscErrorCode TSInterpolate_RosW(TS ts, PetscReal itime, Vec U)
1107: {
1108: TS_RosW *ros = (TS_RosW *)ts->data;
1109: PetscInt s = ros->tableau->s, pinterp = ros->tableau->pinterp, i, j;
1110: PetscReal h;
1111: PetscReal tt, t;
1112: PetscScalar *bt;
1113: const PetscReal *Bt = ros->tableau->binterpt;
1114: const PetscReal *GammaInv = ros->tableau->GammaInv;
1115: PetscScalar *w = ros->work;
1116: Vec *Y = ros->Y;
1118: PetscFunctionBegin;
1119: PetscCheck(Bt, PetscObjectComm((PetscObject)ts), PETSC_ERR_SUP, "TSRosW %s does not have an interpolation formula", ros->tableau->name);
1121: switch (ros->status) {
1122: case TS_STEP_INCOMPLETE:
1123: case TS_STEP_PENDING:
1124: h = ts->time_step;
1125: t = (itime - ts->ptime) / h;
1126: break;
1127: case TS_STEP_COMPLETE:
1128: h = ts->ptime - ts->ptime_prev;
1129: t = (itime - ts->ptime) / h + 1; /* In the interval [0,1] */
1130: break;
1131: default:
1132: SETERRQ(PetscObjectComm((PetscObject)ts), PETSC_ERR_PLIB, "Invalid TSStepStatus");
1133: }
1134: PetscCall(PetscMalloc1(s, &bt));
1135: for (i = 0; i < s; i++) bt[i] = 0;
1136: for (j = 0, tt = t; j < pinterp; j++, tt *= t) {
1137: for (i = 0; i < s; i++) bt[i] += Bt[i * pinterp + j] * tt;
1138: }
1140: /* y(t+tt*h) = y(t) + Sum bt(tt) * GammaInv * Ydot */
1141: /* U <- 0*/
1142: PetscCall(VecZeroEntries(U));
1143: /* U <- Sum bt_i * GammaInv(i,1:i) * Y(1:i) */
1144: for (j = 0; j < s; j++) w[j] = 0;
1145: for (j = 0; j < s; j++) {
1146: for (i = j; i < s; i++) w[j] += bt[i] * GammaInv[i * s + j];
1147: }
1148: PetscCall(VecMAXPY(U, i, w, Y));
1149: /* U <- y(t) + U */
1150: PetscCall(VecAXPY(U, 1, ros->vec_sol_prev));
1152: PetscCall(PetscFree(bt));
1153: PetscFunctionReturn(PETSC_SUCCESS);
1154: }
1156: /*------------------------------------------------------------*/
1158: static PetscErrorCode TSRosWTableauReset(TS ts)
1159: {
1160: TS_RosW *ros = (TS_RosW *)ts->data;
1161: RosWTableau tab = ros->tableau;
1163: PetscFunctionBegin;
1164: if (!tab) PetscFunctionReturn(PETSC_SUCCESS);
1165: PetscCall(VecDestroyVecs(tab->s, &ros->Y));
1166: PetscCall(PetscFree(ros->work));
1167: PetscFunctionReturn(PETSC_SUCCESS);
1168: }
1170: static PetscErrorCode TSReset_RosW(TS ts)
1171: {
1172: TS_RosW *ros = (TS_RosW *)ts->data;
1174: PetscFunctionBegin;
1175: PetscCall(TSRosWTableauReset(ts));
1176: PetscCall(VecDestroy(&ros->Ydot));
1177: PetscCall(VecDestroy(&ros->Ystage));
1178: PetscCall(VecDestroy(&ros->Zdot));
1179: PetscCall(VecDestroy(&ros->Zstage));
1180: PetscCall(VecDestroy(&ros->vec_sol_prev));
1181: PetscFunctionReturn(PETSC_SUCCESS);
1182: }
1184: static PetscErrorCode TSRosWGetVecs(TS ts, DM dm, Vec *Ydot, Vec *Zdot, Vec *Ystage, Vec *Zstage)
1185: {
1186: TS_RosW *rw = (TS_RosW *)ts->data;
1188: PetscFunctionBegin;
1189: if (Ydot) {
1190: if (dm && dm != ts->dm) {
1191: PetscCall(DMGetNamedGlobalVector(dm, "TSRosW_Ydot", Ydot));
1192: } else *Ydot = rw->Ydot;
1193: }
1194: if (Zdot) {
1195: if (dm && dm != ts->dm) {
1196: PetscCall(DMGetNamedGlobalVector(dm, "TSRosW_Zdot", Zdot));
1197: } else *Zdot = rw->Zdot;
1198: }
1199: if (Ystage) {
1200: if (dm && dm != ts->dm) {
1201: PetscCall(DMGetNamedGlobalVector(dm, "TSRosW_Ystage", Ystage));
1202: } else *Ystage = rw->Ystage;
1203: }
1204: if (Zstage) {
1205: if (dm && dm != ts->dm) {
1206: PetscCall(DMGetNamedGlobalVector(dm, "TSRosW_Zstage", Zstage));
1207: } else *Zstage = rw->Zstage;
1208: }
1209: PetscFunctionReturn(PETSC_SUCCESS);
1210: }
1212: static PetscErrorCode TSRosWRestoreVecs(TS ts, DM dm, Vec *Ydot, Vec *Zdot, Vec *Ystage, Vec *Zstage)
1213: {
1214: PetscFunctionBegin;
1215: if (Ydot) {
1216: if (dm && dm != ts->dm) PetscCall(DMRestoreNamedGlobalVector(dm, "TSRosW_Ydot", Ydot));
1217: }
1218: if (Zdot) {
1219: if (dm && dm != ts->dm) PetscCall(DMRestoreNamedGlobalVector(dm, "TSRosW_Zdot", Zdot));
1220: }
1221: if (Ystage) {
1222: if (dm && dm != ts->dm) PetscCall(DMRestoreNamedGlobalVector(dm, "TSRosW_Ystage", Ystage));
1223: }
1224: if (Zstage) {
1225: if (dm && dm != ts->dm) PetscCall(DMRestoreNamedGlobalVector(dm, "TSRosW_Zstage", Zstage));
1226: }
1227: PetscFunctionReturn(PETSC_SUCCESS);
1228: }
1230: static PetscErrorCode DMCoarsenHook_TSRosW(DM fine, DM coarse, void *ctx)
1231: {
1232: PetscFunctionBegin;
1233: PetscFunctionReturn(PETSC_SUCCESS);
1234: }
1236: static PetscErrorCode DMRestrictHook_TSRosW(DM fine, Mat restrct, Vec rscale, Mat inject, DM coarse, void *ctx)
1237: {
1238: TS ts = (TS)ctx;
1239: Vec Ydot, Zdot, Ystage, Zstage;
1240: Vec Ydotc, Zdotc, Ystagec, Zstagec;
1242: PetscFunctionBegin;
1243: PetscCall(TSRosWGetVecs(ts, fine, &Ydot, &Ystage, &Zdot, &Zstage));
1244: PetscCall(TSRosWGetVecs(ts, coarse, &Ydotc, &Ystagec, &Zdotc, &Zstagec));
1245: PetscCall(MatRestrict(restrct, Ydot, Ydotc));
1246: PetscCall(VecPointwiseMult(Ydotc, rscale, Ydotc));
1247: PetscCall(MatRestrict(restrct, Ystage, Ystagec));
1248: PetscCall(VecPointwiseMult(Ystagec, rscale, Ystagec));
1249: PetscCall(MatRestrict(restrct, Zdot, Zdotc));
1250: PetscCall(VecPointwiseMult(Zdotc, rscale, Zdotc));
1251: PetscCall(MatRestrict(restrct, Zstage, Zstagec));
1252: PetscCall(VecPointwiseMult(Zstagec, rscale, Zstagec));
1253: PetscCall(TSRosWRestoreVecs(ts, fine, &Ydot, &Ystage, &Zdot, &Zstage));
1254: PetscCall(TSRosWRestoreVecs(ts, coarse, &Ydotc, &Ystagec, &Zdotc, &Zstagec));
1255: PetscFunctionReturn(PETSC_SUCCESS);
1256: }
1258: static PetscErrorCode DMSubDomainHook_TSRosW(DM fine, DM coarse, void *ctx)
1259: {
1260: PetscFunctionBegin;
1261: PetscFunctionReturn(PETSC_SUCCESS);
1262: }
1264: static PetscErrorCode DMSubDomainRestrictHook_TSRosW(DM dm, VecScatter gscat, VecScatter lscat, DM subdm, void *ctx)
1265: {
1266: TS ts = (TS)ctx;
1267: Vec Ydot, Zdot, Ystage, Zstage;
1268: Vec Ydots, Zdots, Ystages, Zstages;
1270: PetscFunctionBegin;
1271: PetscCall(TSRosWGetVecs(ts, dm, &Ydot, &Ystage, &Zdot, &Zstage));
1272: PetscCall(TSRosWGetVecs(ts, subdm, &Ydots, &Ystages, &Zdots, &Zstages));
1274: PetscCall(VecScatterBegin(gscat, Ydot, Ydots, INSERT_VALUES, SCATTER_FORWARD));
1275: PetscCall(VecScatterEnd(gscat, Ydot, Ydots, INSERT_VALUES, SCATTER_FORWARD));
1277: PetscCall(VecScatterBegin(gscat, Ystage, Ystages, INSERT_VALUES, SCATTER_FORWARD));
1278: PetscCall(VecScatterEnd(gscat, Ystage, Ystages, INSERT_VALUES, SCATTER_FORWARD));
1280: PetscCall(VecScatterBegin(gscat, Zdot, Zdots, INSERT_VALUES, SCATTER_FORWARD));
1281: PetscCall(VecScatterEnd(gscat, Zdot, Zdots, INSERT_VALUES, SCATTER_FORWARD));
1283: PetscCall(VecScatterBegin(gscat, Zstage, Zstages, INSERT_VALUES, SCATTER_FORWARD));
1284: PetscCall(VecScatterEnd(gscat, Zstage, Zstages, INSERT_VALUES, SCATTER_FORWARD));
1286: PetscCall(TSRosWRestoreVecs(ts, dm, &Ydot, &Ystage, &Zdot, &Zstage));
1287: PetscCall(TSRosWRestoreVecs(ts, subdm, &Ydots, &Ystages, &Zdots, &Zstages));
1288: PetscFunctionReturn(PETSC_SUCCESS);
1289: }
1291: /*
1292: This defines the nonlinear equation that is to be solved with SNES
1293: G(U) = F[t0+Theta*dt, U, (U-U0)*shift] = 0
1294: */
1295: static PetscErrorCode SNESTSFormFunction_RosW(SNES snes, Vec U, Vec F, TS ts)
1296: {
1297: TS_RosW *ros = (TS_RosW *)ts->data;
1298: Vec Ydot, Zdot, Ystage, Zstage;
1299: PetscReal shift = ros->scoeff / ts->time_step;
1300: DM dm, dmsave;
1302: PetscFunctionBegin;
1303: PetscCall(SNESGetDM(snes, &dm));
1304: PetscCall(TSRosWGetVecs(ts, dm, &Ydot, &Zdot, &Ystage, &Zstage));
1305: PetscCall(VecWAXPY(Ydot, shift, U, Zdot)); /* Ydot = shift*U + Zdot */
1306: PetscCall(VecWAXPY(Ystage, 1.0, U, Zstage)); /* Ystage = U + Zstage */
1307: dmsave = ts->dm;
1308: ts->dm = dm;
1309: PetscCall(TSComputeIFunction(ts, ros->stage_time, Ystage, Ydot, F, PETSC_FALSE));
1310: ts->dm = dmsave;
1311: PetscCall(TSRosWRestoreVecs(ts, dm, &Ydot, &Zdot, &Ystage, &Zstage));
1312: PetscFunctionReturn(PETSC_SUCCESS);
1313: }
1315: static PetscErrorCode SNESTSFormJacobian_RosW(SNES snes, Vec U, Mat A, Mat B, TS ts)
1316: {
1317: TS_RosW *ros = (TS_RosW *)ts->data;
1318: Vec Ydot, Zdot, Ystage, Zstage;
1319: PetscReal shift = ros->scoeff / ts->time_step;
1320: DM dm, dmsave;
1322: PetscFunctionBegin;
1323: /* ros->Ydot and ros->Ystage have already been computed in SNESTSFormFunction_RosW (SNES guarantees this) */
1324: PetscCall(SNESGetDM(snes, &dm));
1325: PetscCall(TSRosWGetVecs(ts, dm, &Ydot, &Zdot, &Ystage, &Zstage));
1326: dmsave = ts->dm;
1327: ts->dm = dm;
1328: PetscCall(TSComputeIJacobian(ts, ros->stage_time, Ystage, Ydot, shift, A, B, PETSC_TRUE));
1329: ts->dm = dmsave;
1330: PetscCall(TSRosWRestoreVecs(ts, dm, &Ydot, &Zdot, &Ystage, &Zstage));
1331: PetscFunctionReturn(PETSC_SUCCESS);
1332: }
1334: static PetscErrorCode TSRosWTableauSetUp(TS ts)
1335: {
1336: TS_RosW *ros = (TS_RosW *)ts->data;
1337: RosWTableau tab = ros->tableau;
1339: PetscFunctionBegin;
1340: PetscCall(VecDuplicateVecs(ts->vec_sol, tab->s, &ros->Y));
1341: PetscCall(PetscMalloc1(tab->s, &ros->work));
1342: PetscFunctionReturn(PETSC_SUCCESS);
1343: }
1345: static PetscErrorCode TSSetUp_RosW(TS ts)
1346: {
1347: TS_RosW *ros = (TS_RosW *)ts->data;
1348: DM dm;
1349: SNES snes;
1350: TSRHSJacobian rhsjacobian;
1352: PetscFunctionBegin;
1353: PetscCall(TSRosWTableauSetUp(ts));
1354: PetscCall(VecDuplicate(ts->vec_sol, &ros->Ydot));
1355: PetscCall(VecDuplicate(ts->vec_sol, &ros->Ystage));
1356: PetscCall(VecDuplicate(ts->vec_sol, &ros->Zdot));
1357: PetscCall(VecDuplicate(ts->vec_sol, &ros->Zstage));
1358: PetscCall(VecDuplicate(ts->vec_sol, &ros->vec_sol_prev));
1359: PetscCall(TSGetDM(ts, &dm));
1360: PetscCall(DMCoarsenHookAdd(dm, DMCoarsenHook_TSRosW, DMRestrictHook_TSRosW, ts));
1361: PetscCall(DMSubDomainHookAdd(dm, DMSubDomainHook_TSRosW, DMSubDomainRestrictHook_TSRosW, ts));
1362: /* Rosenbrock methods are linearly implicit, so set that unless the user has specifically asked for something else */
1363: PetscCall(TSGetSNES(ts, &snes));
1364: if (!((PetscObject)snes)->type_name) PetscCall(SNESSetType(snes, SNESKSPONLY));
1365: PetscCall(DMTSGetRHSJacobian(dm, &rhsjacobian, NULL));
1366: if (rhsjacobian == TSComputeRHSJacobianConstant) {
1367: Mat Amat, Pmat;
1369: /* Set the SNES matrix to be different from the RHS matrix because there is no way to reconstruct shift*M-J */
1370: PetscCall(SNESGetJacobian(snes, &Amat, &Pmat, NULL, NULL));
1371: if (Amat && Amat == ts->Arhs) {
1372: if (Amat == Pmat) {
1373: PetscCall(MatDuplicate(ts->Arhs, MAT_COPY_VALUES, &Amat));
1374: PetscCall(SNESSetJacobian(snes, Amat, Amat, NULL, NULL));
1375: } else {
1376: PetscCall(MatDuplicate(ts->Arhs, MAT_COPY_VALUES, &Amat));
1377: PetscCall(SNESSetJacobian(snes, Amat, NULL, NULL, NULL));
1378: if (Pmat && Pmat == ts->Brhs) {
1379: PetscCall(MatDuplicate(ts->Brhs, MAT_COPY_VALUES, &Pmat));
1380: PetscCall(SNESSetJacobian(snes, NULL, Pmat, NULL, NULL));
1381: PetscCall(MatDestroy(&Pmat));
1382: }
1383: }
1384: PetscCall(MatDestroy(&Amat));
1385: }
1386: }
1387: PetscFunctionReturn(PETSC_SUCCESS);
1388: }
1389: /*------------------------------------------------------------*/
1391: static PetscErrorCode TSSetFromOptions_RosW(TS ts, PetscOptionItems *PetscOptionsObject)
1392: {
1393: TS_RosW *ros = (TS_RosW *)ts->data;
1394: SNES snes;
1396: PetscFunctionBegin;
1397: PetscOptionsHeadBegin(PetscOptionsObject, "RosW ODE solver options");
1398: {
1399: RosWTableauLink link;
1400: PetscInt count, choice;
1401: PetscBool flg;
1402: const char **namelist;
1404: for (link = RosWTableauList, count = 0; link; link = link->next, count++)
1405: ;
1406: PetscCall(PetscMalloc1(count, (char ***)&namelist));
1407: for (link = RosWTableauList, count = 0; link; link = link->next, count++) namelist[count] = link->tab.name;
1408: PetscCall(PetscOptionsEList("-ts_rosw_type", "Family of Rosenbrock-W method", "TSRosWSetType", (const char *const *)namelist, count, ros->tableau->name, &choice, &flg));
1409: if (flg) PetscCall(TSRosWSetType(ts, namelist[choice]));
1410: PetscCall(PetscFree(namelist));
1412: PetscCall(PetscOptionsBool("-ts_rosw_recompute_jacobian", "Recompute the Jacobian at each stage", "TSRosWSetRecomputeJacobian", ros->recompute_jacobian, &ros->recompute_jacobian, NULL));
1413: }
1414: PetscOptionsHeadEnd();
1415: /* Rosenbrock methods are linearly implicit, so set that unless the user has specifically asked for something else */
1416: PetscCall(TSGetSNES(ts, &snes));
1417: if (!((PetscObject)snes)->type_name) PetscCall(SNESSetType(snes, SNESKSPONLY));
1418: PetscFunctionReturn(PETSC_SUCCESS);
1419: }
1421: static PetscErrorCode TSView_RosW(TS ts, PetscViewer viewer)
1422: {
1423: TS_RosW *ros = (TS_RosW *)ts->data;
1424: PetscBool iascii;
1426: PetscFunctionBegin;
1427: PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &iascii));
1428: if (iascii) {
1429: RosWTableau tab = ros->tableau;
1430: TSRosWType rostype;
1431: char buf[512];
1432: PetscInt i;
1433: PetscReal abscissa[512];
1434: PetscCall(TSRosWGetType(ts, &rostype));
1435: PetscCall(PetscViewerASCIIPrintf(viewer, " Rosenbrock-W %s\n", rostype));
1436: PetscCall(PetscFormatRealArray(buf, sizeof(buf), "% 8.6f", tab->s, tab->ASum));
1437: PetscCall(PetscViewerASCIIPrintf(viewer, " Abscissa of A = %s\n", buf));
1438: for (i = 0; i < tab->s; i++) abscissa[i] = tab->ASum[i] + tab->Gamma[i];
1439: PetscCall(PetscFormatRealArray(buf, sizeof(buf), "% 8.6f", tab->s, abscissa));
1440: PetscCall(PetscViewerASCIIPrintf(viewer, " Abscissa of A+Gamma = %s\n", buf));
1441: }
1442: PetscFunctionReturn(PETSC_SUCCESS);
1443: }
1445: static PetscErrorCode TSLoad_RosW(TS ts, PetscViewer viewer)
1446: {
1447: SNES snes;
1448: TSAdapt adapt;
1450: PetscFunctionBegin;
1451: PetscCall(TSGetAdapt(ts, &adapt));
1452: PetscCall(TSAdaptLoad(adapt, viewer));
1453: PetscCall(TSGetSNES(ts, &snes));
1454: PetscCall(SNESLoad(snes, viewer));
1455: /* function and Jacobian context for SNES when used with TS is always ts object */
1456: PetscCall(SNESSetFunction(snes, NULL, NULL, ts));
1457: PetscCall(SNESSetJacobian(snes, NULL, NULL, NULL, ts));
1458: PetscFunctionReturn(PETSC_SUCCESS);
1459: }
1461: /*@C
1462: TSRosWSetType - Set the type of Rosenbrock-W, `TSROSW`, scheme
1464: Logically Collective
1466: Input Parameters:
1467: + ts - timestepping context
1468: - roswtype - type of Rosenbrock-W scheme
1470: Level: beginner
1472: .seealso: [](ch_ts), `TSRosWGetType()`, `TSROSW`, `TSROSW2M`, `TSROSW2P`, `TSROSWRA3PW`, `TSROSWRA34PW2`, `TSROSWRODAS3`, `TSROSWSANDU3`, `TSROSWASSP3P3S1C`, `TSROSWLASSP3P4S2C`, `TSROSWLLSSP3P4S2C`, `TSROSWARK3`
1473: @*/
1474: PetscErrorCode TSRosWSetType(TS ts, TSRosWType roswtype)
1475: {
1476: PetscFunctionBegin;
1478: PetscAssertPointer(roswtype, 2);
1479: PetscTryMethod(ts, "TSRosWSetType_C", (TS, TSRosWType), (ts, roswtype));
1480: PetscFunctionReturn(PETSC_SUCCESS);
1481: }
1483: /*@C
1484: TSRosWGetType - Get the type of Rosenbrock-W scheme
1486: Logically Collective
1488: Input Parameter:
1489: . ts - timestepping context
1491: Output Parameter:
1492: . rostype - type of Rosenbrock-W scheme
1494: Level: intermediate
1496: .seealso: [](ch_ts), `TSRosWType`, `TSRosWSetType()`
1497: @*/
1498: PetscErrorCode TSRosWGetType(TS ts, TSRosWType *rostype)
1499: {
1500: PetscFunctionBegin;
1502: PetscUseMethod(ts, "TSRosWGetType_C", (TS, TSRosWType *), (ts, rostype));
1503: PetscFunctionReturn(PETSC_SUCCESS);
1504: }
1506: /*@C
1507: TSRosWSetRecomputeJacobian - Set whether to recompute the Jacobian at each stage. The default is to update the Jacobian once per step.
1509: Logically Collective
1511: Input Parameters:
1512: + ts - timestepping context
1513: - flg - `PETSC_TRUE` to recompute the Jacobian at each stage
1515: Level: intermediate
1517: .seealso: [](ch_ts), `TSRosWType`, `TSRosWGetType()`
1518: @*/
1519: PetscErrorCode TSRosWSetRecomputeJacobian(TS ts, PetscBool flg)
1520: {
1521: PetscFunctionBegin;
1523: PetscTryMethod(ts, "TSRosWSetRecomputeJacobian_C", (TS, PetscBool), (ts, flg));
1524: PetscFunctionReturn(PETSC_SUCCESS);
1525: }
1527: static PetscErrorCode TSRosWGetType_RosW(TS ts, TSRosWType *rostype)
1528: {
1529: TS_RosW *ros = (TS_RosW *)ts->data;
1531: PetscFunctionBegin;
1532: *rostype = ros->tableau->name;
1533: PetscFunctionReturn(PETSC_SUCCESS);
1534: }
1536: static PetscErrorCode TSRosWSetType_RosW(TS ts, TSRosWType rostype)
1537: {
1538: TS_RosW *ros = (TS_RosW *)ts->data;
1539: PetscBool match;
1540: RosWTableauLink link;
1542: PetscFunctionBegin;
1543: if (ros->tableau) {
1544: PetscCall(PetscStrcmp(ros->tableau->name, rostype, &match));
1545: if (match) PetscFunctionReturn(PETSC_SUCCESS);
1546: }
1547: for (link = RosWTableauList; link; link = link->next) {
1548: PetscCall(PetscStrcmp(link->tab.name, rostype, &match));
1549: if (match) {
1550: if (ts->setupcalled) PetscCall(TSRosWTableauReset(ts));
1551: ros->tableau = &link->tab;
1552: if (ts->setupcalled) PetscCall(TSRosWTableauSetUp(ts));
1553: ts->default_adapt_type = ros->tableau->bembed ? TSADAPTBASIC : TSADAPTNONE;
1554: PetscFunctionReturn(PETSC_SUCCESS);
1555: }
1556: }
1557: SETERRQ(PetscObjectComm((PetscObject)ts), PETSC_ERR_ARG_UNKNOWN_TYPE, "Could not find '%s'", rostype);
1558: }
1560: static PetscErrorCode TSRosWSetRecomputeJacobian_RosW(TS ts, PetscBool flg)
1561: {
1562: TS_RosW *ros = (TS_RosW *)ts->data;
1564: PetscFunctionBegin;
1565: ros->recompute_jacobian = flg;
1566: PetscFunctionReturn(PETSC_SUCCESS);
1567: }
1569: static PetscErrorCode TSDestroy_RosW(TS ts)
1570: {
1571: PetscFunctionBegin;
1572: PetscCall(TSReset_RosW(ts));
1573: if (ts->dm) {
1574: PetscCall(DMCoarsenHookRemove(ts->dm, DMCoarsenHook_TSRosW, DMRestrictHook_TSRosW, ts));
1575: PetscCall(DMSubDomainHookRemove(ts->dm, DMSubDomainHook_TSRosW, DMSubDomainRestrictHook_TSRosW, ts));
1576: }
1577: PetscCall(PetscFree(ts->data));
1578: PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSRosWGetType_C", NULL));
1579: PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSRosWSetType_C", NULL));
1580: PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSRosWSetRecomputeJacobian_C", NULL));
1581: PetscFunctionReturn(PETSC_SUCCESS);
1582: }
1584: /* ------------------------------------------------------------ */
1585: /*MC
1586: TSROSW - ODE solver using Rosenbrock-W schemes
1588: These methods are intended for problems with well-separated time scales, especially when a slow scale is strongly
1589: nonlinear such that it is expensive to solve with a fully implicit method. The user should provide the stiff part
1590: of the equation using `TSSetIFunction()` and the non-stiff part with `TSSetRHSFunction()`.
1592: Level: beginner
1594: Notes:
1595: This method currently only works with autonomous ODE and DAE.
1597: Consider trying `TSARKIMEX` if the stiff part is strongly nonlinear.
1599: 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
1601: Developer Notes:
1602: Rosenbrock-W methods are typically specified for autonomous ODE
1604: $ udot = f(u)
1606: by the stage equations
1608: $ k_i = h f(u_0 + sum_j alpha_ij k_j) + h J sum_j gamma_ij k_j
1610: and step completion formula
1612: $ u_1 = u_0 + sum_j b_j k_j
1614: with step size h and coefficients alpha_ij, gamma_ij, and b_i. Implementing the method in this form would require f(u)
1615: and the Jacobian J to be available, in addition to the shifted matrix I - h gamma_ii J. Following Hairer and Wanner,
1616: we define new variables for the stage equations
1618: $ y_i = gamma_ij k_j
1620: The k_j can be recovered because Gamma is invertible. Let C be the lower triangular part of Gamma^{-1} and define
1622: $ A = Alpha Gamma^{-1}, bt^T = b^T Gamma^{-1}
1624: to rewrite the method as
1626: .vb
1627: [M/(h gamma_ii) - J] y_i = f(u_0 + sum_j a_ij y_j) + M sum_j (c_ij/h) y_j
1628: u_1 = u_0 + sum_j bt_j y_j
1629: .ve
1631: where we have introduced the mass matrix M. Continue by defining
1633: $ ydot_i = 1/(h gamma_ii) y_i - sum_j (c_ij/h) y_j
1635: or, more compactly in tensor notation
1637: $ Ydot = 1/h (Gamma^{-1} \otimes I) Y .
1639: Note that Gamma^{-1} is lower triangular. With this definition of Ydot in terms of known quantities and the current
1640: stage y_i, the stage equations reduce to performing one Newton step (typically with a lagged Jacobian) on the
1641: equation
1643: $ g(u_0 + sum_j a_ij y_j + y_i, ydot_i) = 0
1645: with initial guess y_i = 0.
1647: .seealso: [](ch_ts), `TSCreate()`, `TS`, `TSSetType()`, `TSRosWSetType()`, `TSRosWRegister()`, `TSROSWTHETA1`, `TSROSWTHETA2`, `TSROSW2M`, `TSROSW2P`, `TSROSWRA3PW`, `TSROSWRA34PW2`, `TSROSWRODAS3`,
1648: `TSROSWSANDU3`, `TSROSWASSP3P3S1C`, `TSROSWLASSP3P4S2C`, `TSROSWLLSSP3P4S2C`, `TSROSWGRK4T`, `TSROSWSHAMP4`, `TSROSWVELDD4`, `TSROSW4L`, `TSType`
1649: M*/
1650: PETSC_EXTERN PetscErrorCode TSCreate_RosW(TS ts)
1651: {
1652: TS_RosW *ros;
1654: PetscFunctionBegin;
1655: PetscCall(TSRosWInitializePackage());
1657: ts->ops->reset = TSReset_RosW;
1658: ts->ops->destroy = TSDestroy_RosW;
1659: ts->ops->view = TSView_RosW;
1660: ts->ops->load = TSLoad_RosW;
1661: ts->ops->setup = TSSetUp_RosW;
1662: ts->ops->step = TSStep_RosW;
1663: ts->ops->interpolate = TSInterpolate_RosW;
1664: ts->ops->evaluatestep = TSEvaluateStep_RosW;
1665: ts->ops->rollback = TSRollBack_RosW;
1666: ts->ops->setfromoptions = TSSetFromOptions_RosW;
1667: ts->ops->snesfunction = SNESTSFormFunction_RosW;
1668: ts->ops->snesjacobian = SNESTSFormJacobian_RosW;
1670: ts->usessnes = PETSC_TRUE;
1672: PetscCall(PetscNew(&ros));
1673: ts->data = (void *)ros;
1675: PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSRosWGetType_C", TSRosWGetType_RosW));
1676: PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSRosWSetType_C", TSRosWSetType_RosW));
1677: PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSRosWSetRecomputeJacobian_C", TSRosWSetRecomputeJacobian_RosW));
1679: PetscCall(TSRosWSetType(ts, TSRosWDefault));
1680: PetscFunctionReturn(PETSC_SUCCESS);
1681: }