Actual source code: rosw.c
petsc-3.4.5 2014-06-29
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> /*I "petscts.h" I*/
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 VecSolPrev; /* Work vector holding the solution from the previous step (used for interpolation)*/
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: 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: 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: 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: 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: References:
114: Rang and Angermann, New Rosenbrock-W methods of order 3 for partial differential algebraic equations of index 1, 2005.
116: Level: intermediate
118: .seealso: 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: References:
129: Rang and Angermann, New Rosenbrock-W methods of order 3 for partial differential algebraic equations of index 1, 2005.
131: Level: intermediate
133: .seealso: 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: References:
144: Sandu et al, Benchmarking stiff ODE solvers for atmospheric chemistry problems II, Rosenbrock solvers, 1997.
146: Level: intermediate
148: .seealso: 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: References:
162: Sandu et al, Benchmarking stiff ODE solvers for atmospheric chemistry problems II, Rosenbrock solvers, 1997.
164: Level: intermediate
166: .seealso: 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: References:
177: Emil Constantinescu
179: Level: intermediate
181: .seealso: 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: References:
192: Emil Constantinescu
194: Level: intermediate
196: .seealso: 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: References:
207: Emil Constantinescu
209: Level: intermediate
211: .seealso: 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: References:
224: Kaps and Rentrop, Generalized Runge-Kutta methods of order four with stepsize control for stiff ordinary differential equations, 1979.
226: Hairer and Wanner, Solving Ordinary Differential Equations II, Section 4 Table 7.2.
228: Hairer's code ros4.f
230: Level: intermediate
232: .seealso: TSROSW, TSROSWSHAMP4, TSROSWVELDD4, TSROSW4L
233: M*/
235: /*MC
236: TSROSWSHAMP4 - four stage, fourth order Rosenbrock (not W) method from Shampine
238: By default, the Jacobian is only recomputed once per step.
240: A-stable, |R(infty)| = 1/3.
242: This method does not provide a dense output formula.
244: References:
245: 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: Level: intermediate
253: .seealso: TSROSW, TSROSWGRK4T, TSROSWVELDD4, TSROSW4L
254: M*/
256: /*MC
257: TSROSWVELDD4 - four stage, fourth order Rosenbrock (not W) method from van Veldhuizen
259: By default, the Jacobian is only recomputed once per step.
261: A(89.5 degrees)-stable, |R(infty)| = 0.24.
263: This method does not provide a dense output formula.
265: References:
266: van Veldhuizen, D-stability and Kaps-Rentrop methods, 1984.
268: Hairer and Wanner, Solving Ordinary Differential Equations II, Section 4 Table 7.2.
270: Hairer's code ros4.f
272: Level: intermediate
274: .seealso: TSROSW, TSROSWGRK4T, TSROSWSHAMP4, TSROSW4L
275: M*/
277: /*MC
278: TSROSW4L - four stage, fourth order Rosenbrock (not W) method
280: By default, the Jacobian is only recomputed once per step.
282: A-stable and L-stable
284: This method does not provide a dense output formula.
286: References:
287: Hairer and Wanner, Solving Ordinary Differential Equations II, Section 4 Table 7.2.
289: Hairer's code ros4.f
291: Level: intermediate
293: .seealso: TSROSW, TSROSWGRK4T, TSROSWSHAMP4, TSROSW4L
294: M*/
298: /*@C
299: TSRosWRegisterAll - Registers all of the additive Runge-Kutta implicit-explicit methods in TSRosW
301: Not Collective, but should be called by all processes which will need the schemes to be registered
303: Level: advanced
305: .keywords: TS, TSRosW, register, all
307: .seealso: TSRosWRegisterDestroy()
308: @*/
309: PetscErrorCode TSRosWRegisterAll(void)
310: {
314: if (TSRosWRegisterAllCalled) return(0);
315: TSRosWRegisterAllCalled = PETSC_TRUE;
317: {
318: const PetscReal A = 0;
319: const PetscReal Gamma = 1;
320: const PetscReal b = 1;
321: const PetscReal binterpt=1;
323: TSRosWRegister(TSROSWTHETA1,1,1,&A,&Gamma,&b,NULL,1,&binterpt);
324: }
326: {
327: const PetscReal A = 0;
328: const PetscReal Gamma = 0.5;
329: const PetscReal b = 1;
330: const PetscReal binterpt=1;
332: TSRosWRegister(TSROSWTHETA2,2,1,&A,&Gamma,&b,NULL,1,&binterpt);
333: }
335: {
336: /*const PetscReal g = 1. + 1./PetscSqrtReal(2.0); Direct evaluation: 1.707106781186547524401. Used for setting up arrays of values known at compile time below. */
337: const PetscReal
338: A[2][2] = {{0,0}, {1.,0}},
339: Gamma[2][2] = {{1.707106781186547524401,0}, {-2.*1.707106781186547524401,1.707106781186547524401}},
340: b[2] = {0.5,0.5},
341: b1[2] = {1.0,0.0};
342: PetscReal binterpt[2][2];
343: binterpt[0][0] = 1.707106781186547524401 - 1.0;
344: binterpt[1][0] = 2.0 - 1.707106781186547524401;
345: binterpt[0][1] = 1.707106781186547524401 - 1.5;
346: binterpt[1][1] = 1.5 - 1.707106781186547524401;
348: TSRosWRegister(TSROSW2P,2,2,&A[0][0],&Gamma[0][0],b,b1,2,&binterpt[0][0]);
349: }
350: {
351: /*const PetscReal g = 1. - 1./PetscSqrtReal(2.0); Direct evaluation: 0.2928932188134524755992. Used for setting up arrays of values known at compile time below. */
352: const PetscReal
353: A[2][2] = {{0,0}, {1.,0}},
354: Gamma[2][2] = {{0.2928932188134524755992,0}, {-2.*0.2928932188134524755992,0.2928932188134524755992}},
355: b[2] = {0.5,0.5},
356: b1[2] = {1.0,0.0};
357: PetscReal binterpt[2][2];
358: binterpt[0][0] = 0.2928932188134524755992 - 1.0;
359: binterpt[1][0] = 2.0 - 0.2928932188134524755992;
360: binterpt[0][1] = 0.2928932188134524755992 - 1.5;
361: binterpt[1][1] = 1.5 - 0.2928932188134524755992;
363: TSRosWRegister(TSROSW2M,2,2,&A[0][0],&Gamma[0][0],b,b1,2,&binterpt[0][0]);
364: }
365: {
366: /*const PetscReal g = 7.8867513459481287e-01; Directly written in-place below */
367: PetscReal binterpt[3][2];
368: const PetscReal
369: A[3][3] = {{0,0,0},
370: {1.5773502691896257e+00,0,0},
371: {0.5,0,0}},
372: Gamma[3][3] = {{7.8867513459481287e-01,0,0},
373: {-1.5773502691896257e+00,7.8867513459481287e-01,0},
374: {-6.7075317547305480e-01,-1.7075317547305482e-01,7.8867513459481287e-01}},
375: b[3] = {1.0566243270259355e-01,4.9038105676657971e-02,8.4529946162074843e-01},
376: b2[3] = {-1.7863279495408180e-01,1./3.,8.4529946162074843e-01};
378: binterpt[0][0] = -0.8094010767585034;
379: binterpt[1][0] = -0.5;
380: binterpt[2][0] = 2.3094010767585034;
381: binterpt[0][1] = 0.9641016151377548;
382: binterpt[1][1] = 0.5;
383: binterpt[2][1] = -1.4641016151377548;
385: TSRosWRegister(TSROSWRA3PW,3,3,&A[0][0],&Gamma[0][0],b,b2,2,&binterpt[0][0]);
386: }
387: {
388: PetscReal binterpt[4][3];
389: /*const PetscReal g = 4.3586652150845900e-01; Directly written in-place below */
390: const PetscReal
391: A[4][4] = {{0,0,0,0},
392: {8.7173304301691801e-01,0,0,0},
393: {8.4457060015369423e-01,-1.1299064236484185e-01,0,0},
394: {0,0,1.,0}},
395: Gamma[4][4] = {{4.3586652150845900e-01,0,0,0},
396: {-8.7173304301691801e-01,4.3586652150845900e-01,0,0},
397: {-9.0338057013044082e-01,5.4180672388095326e-02,4.3586652150845900e-01,0},
398: {2.4212380706095346e-01,-1.2232505839045147e+00,5.4526025533510214e-01,4.3586652150845900e-01}},
399: b[4] = {2.4212380706095346e-01,-1.2232505839045147e+00,1.5452602553351020e+00,4.3586652150845900e-01},
400: b2[4] = {3.7810903145819369e-01,-9.6042292212423178e-02,5.0000000000000000e-01,2.1793326075422950e-01};
402: binterpt[0][0]=1.0564298455794094;
403: binterpt[1][0]=2.296429974281067;
404: binterpt[2][0]=-1.307599564525376;
405: binterpt[3][0]=-1.045260255335102;
406: binterpt[0][1]=-1.3864882699759573;
407: binterpt[1][1]=-8.262611700275677;
408: binterpt[2][1]=7.250979895056055;
409: binterpt[3][1]=2.398120075195581;
410: binterpt[0][2]=0.5721822314575016;
411: binterpt[1][2]=4.742931142090097;
412: binterpt[2][2]=-4.398120075195578;
413: binterpt[3][2]=-0.9169932983520199;
415: TSRosWRegister(TSROSWRA34PW2,3,4,&A[0][0],&Gamma[0][0],b,b2,3,&binterpt[0][0]);
416: }
417: {
418: /* const PetscReal g = 0.5; Directly written in-place below */
419: const PetscReal
420: A[4][4] = {{0,0,0,0},
421: {0,0,0,0},
422: {1.,0,0,0},
423: {0.75,-0.25,0.5,0}},
424: Gamma[4][4] = {{0.5,0,0,0},
425: {1.,0.5,0,0},
426: {-0.25,-0.25,0.5,0},
427: {1./12,1./12,-2./3,0.5}},
428: b[4] = {5./6,-1./6,-1./6,0.5},
429: b2[4] = {0.75,-0.25,0.5,0};
431: TSRosWRegister(TSROSWRODAS3,3,4,&A[0][0],&Gamma[0][0],b,b2,0,NULL);
432: }
433: {
434: /*const PetscReal g = 0.43586652150845899941601945119356; Directly written in-place below */
435: const PetscReal
436: A[3][3] = {{0,0,0},
437: {0.43586652150845899941601945119356,0,0},
438: {0.43586652150845899941601945119356,0,0}},
439: Gamma[3][3] = {{0.43586652150845899941601945119356,0,0},
440: {-0.19294655696029095575009695436041,0.43586652150845899941601945119356,0},
441: {0,1.74927148125794685173529749738960,0.43586652150845899941601945119356}},
442: b[3] = {-0.75457412385404315829818998646589,1.94100407061964420292840123379419,-0.18642994676560104463021124732829},
443: b2[3] = {-1.53358745784149585370766523913002,2.81745131148625772213931745457622,-0.28386385364476186843165221544619};
445: PetscReal binterpt[3][2];
446: binterpt[0][0] = 3.793692883777660870425141387941;
447: binterpt[1][0] = -2.918692883777660870425141387941;
448: binterpt[2][0] = 0.125;
449: binterpt[0][1] = -0.725741064379812106687651020584;
450: binterpt[1][1] = 0.559074397713145440020984353917;
451: binterpt[2][1] = 0.16666666666666666666666666666667;
453: TSRosWRegister(TSROSWSANDU3,3,3,&A[0][0],&Gamma[0][0],b,b2,2,&binterpt[0][0]);
454: }
455: {
456: /*const PetscReal s3 = PetscSqrtReal(3.),g = (3.0+s3)/6.0;
457: * Direct evaluation: s3 = 1.732050807568877293527;
458: * g = 0.7886751345948128822546;
459: * Values are directly inserted below to ensure availability at compile time (compiler warnings otherwise...) */
460: const PetscReal
461: A[3][3] = {{0,0,0},
462: {1,0,0},
463: {0.25,0.25,0}},
464: Gamma[3][3] = {{0,0,0},
465: {(-3.0-1.732050807568877293527)/6.0,0.7886751345948128822546,0},
466: {(-3.0-1.732050807568877293527)/24.0,(-3.0-1.732050807568877293527)/8.0,0.7886751345948128822546}},
467: b[3] = {1./6.,1./6.,2./3.},
468: b2[3] = {1./4.,1./4.,1./2.};
469: PetscReal binterpt[3][2];
471: binterpt[0][0]=0.089316397477040902157517886164709;
472: binterpt[1][0]=-0.91068360252295909784248211383529;
473: binterpt[2][0]=1.8213672050459181956849642276706;
474: binterpt[0][1]=0.077350269189625764509148780501957;
475: binterpt[1][1]=1.077350269189625764509148780502;
476: binterpt[2][1]=-1.1547005383792515290182975610039;
478: TSRosWRegister(TSROSWASSP3P3S1C,3,3,&A[0][0],&Gamma[0][0],b,b2,2,&binterpt[0][0]);
479: }
481: {
482: const PetscReal
483: A[4][4] = {{0,0,0,0},
484: {1./2.,0,0,0},
485: {1./2.,1./2.,0,0},
486: {1./6.,1./6.,1./6.,0}},
487: Gamma[4][4] = {{1./2.,0,0,0},
488: {0.0,1./4.,0,0},
489: {-2.,-2./3.,2./3.,0},
490: {1./2.,5./36.,-2./9,0}},
491: b[4] = {1./6.,1./6.,1./6.,1./2.},
492: b2[4] = {1./8.,3./4.,1./8.,0};
493: PetscReal binterpt[4][3];
495: binterpt[0][0]=6.25;
496: binterpt[1][0]=-30.25;
497: binterpt[2][0]=1.75;
498: binterpt[3][0]=23.25;
499: binterpt[0][1]=-9.75;
500: binterpt[1][1]=58.75;
501: binterpt[2][1]=-3.25;
502: binterpt[3][1]=-45.75;
503: binterpt[0][2]=3.6666666666666666666666666666667;
504: binterpt[1][2]=-28.333333333333333333333333333333;
505: binterpt[2][2]=1.6666666666666666666666666666667;
506: binterpt[3][2]=23.;
508: TSRosWRegister(TSROSWLASSP3P4S2C,3,4,&A[0][0],&Gamma[0][0],b,b2,3,&binterpt[0][0]);
509: }
511: {
512: const PetscReal
513: A[4][4] = {{0,0,0,0},
514: {1./2.,0,0,0},
515: {1./2.,1./2.,0,0},
516: {1./6.,1./6.,1./6.,0}},
517: Gamma[4][4] = {{1./2.,0,0,0},
518: {0.0,3./4.,0,0},
519: {-2./3.,-23./9.,2./9.,0},
520: {1./18.,65./108.,-2./27,0}},
521: b[4] = {1./6.,1./6.,1./6.,1./2.},
522: b2[4] = {3./16.,10./16.,3./16.,0};
523: PetscReal binterpt[4][3];
525: binterpt[0][0]=1.6911764705882352941176470588235;
526: binterpt[1][0]=3.6813725490196078431372549019608;
527: binterpt[2][0]=0.23039215686274509803921568627451;
528: binterpt[3][0]=-4.6029411764705882352941176470588;
529: binterpt[0][1]=-0.95588235294117647058823529411765;
530: binterpt[1][1]=-6.2401960784313725490196078431373;
531: binterpt[2][1]=-0.31862745098039215686274509803922;
532: binterpt[3][1]=7.5147058823529411764705882352941;
533: binterpt[0][2]=-0.56862745098039215686274509803922;
534: binterpt[1][2]=2.7254901960784313725490196078431;
535: binterpt[2][2]=0.25490196078431372549019607843137;
536: binterpt[3][2]=-2.4117647058823529411764705882353;
538: TSRosWRegister(TSROSWLLSSP3P4S2C,3,4,&A[0][0],&Gamma[0][0],b,b2,3,&binterpt[0][0]);
539: }
541: {
542: PetscReal A[4][4],Gamma[4][4],b[4],b2[4];
543: PetscReal binterpt[4][3];
545: Gamma[0][0]=0.4358665215084589994160194475295062513822671686978816;
546: Gamma[0][1]=0; Gamma[0][2]=0; Gamma[0][3]=0;
547: Gamma[1][0]=-1.997527830934941248426324674704153457289527280554476;
548: Gamma[1][1]=0.4358665215084589994160194475295062513822671686978816;
549: Gamma[1][2]=0; Gamma[1][3]=0;
550: Gamma[2][0]=-1.007948511795029620852002345345404191008352770119903;
551: Gamma[2][1]=-0.004648958462629345562774289390054679806993396798458131;
552: Gamma[2][2]=0.4358665215084589994160194475295062513822671686978816;
553: Gamma[2][3]=0;
554: Gamma[3][0]=-0.6685429734233467180451604600279552604364311322650783;
555: Gamma[3][1]=0.6056625986449338476089525334450053439525178740492984;
556: Gamma[3][2]=-0.9717899277217721234705114616271378792182450260943198;
557: Gamma[3][3]=0;
559: A[0][0]=0; A[0][1]=0; A[0][2]=0; A[0][3]=0;
560: A[1][0]=0.8717330430169179988320388950590125027645343373957631;
561: A[1][1]=0; A[1][2]=0; A[1][3]=0;
562: A[2][0]=0.5275890119763004115618079766722914408876108660811028;
563: A[2][1]=0.07241098802369958843819203208518599088698057726988732;
564: A[2][2]=0; A[2][3]=0;
565: A[3][0]=0.3990960076760701320627260685975778145384666450351314;
566: A[3][1]=-0.4375576546135194437228463747348862825846903771419953;
567: A[3][2]=1.038461646937449311660120300601880176655352737312713;
568: A[3][3]=0;
570: b[0]=0.1876410243467238251612921333138006734899663569186926;
571: b[1]=-0.5952974735769549480478230473706443582188442040780541;
572: b[2]=0.9717899277217721234705114616271378792182450260943198;
573: b[3]=0.4358665215084589994160194475295062513822671686978816;
575: b2[0]=0.2147402862233891404862383521089097657790734483804460;
576: b2[1]=-0.4851622638849390928209050538171743017757490232519684;
577: b2[2]=0.8687250025203875511662123688667549217531982787600080;
578: b2[3]=0.4016969751411624011684543450940068201770721128357014;
580: binterpt[0][0]=2.2565812720167954547104627844105;
581: binterpt[1][0]=1.349166413351089573796243820819;
582: binterpt[2][0]=-2.4695174540533503758652847586647;
583: binterpt[3][0]=-0.13623023131453465264142184656474;
584: binterpt[0][1]=-3.0826699111559187902922463354557;
585: binterpt[1][1]=-2.4689115685996042534544925650515;
586: binterpt[2][1]=5.7428279814696677152129332773553;
587: binterpt[3][1]=-0.19124650171414467146619437684812;
588: binterpt[0][2]=1.0137296634858471607430756831148;
589: binterpt[1][2]=0.52444768167155973161042570784064;
590: binterpt[2][2]=-2.3015205996945452158771370439586;
591: binterpt[3][2]=0.76334325453713832352363565300308;
593: TSRosWRegister(TSROSWARK3,3,4,&A[0][0],&Gamma[0][0],b,b2,3,&binterpt[0][0]);
594: }
595: TSRosWRegisterRos4(TSROSWGRK4T,0.231,PETSC_DEFAULT,PETSC_DEFAULT,0,-0.1282612945269037e+01);
596: TSRosWRegisterRos4(TSROSWSHAMP4,0.5,PETSC_DEFAULT,PETSC_DEFAULT,0,125./108.);
597: TSRosWRegisterRos4(TSROSWVELDD4,0.22570811482256823492,PETSC_DEFAULT,PETSC_DEFAULT,0,-1.355958941201148);
598: TSRosWRegisterRos4(TSROSW4L,0.57282,PETSC_DEFAULT,PETSC_DEFAULT,0,-1.093502252409163);
599: return(0);
600: }
606: /*@C
607: TSRosWRegisterDestroy - Frees the list of schemes that were registered by TSRosWRegister().
609: Not Collective
611: Level: advanced
613: .keywords: TSRosW, register, destroy
614: .seealso: TSRosWRegister(), TSRosWRegisterAll()
615: @*/
616: PetscErrorCode TSRosWRegisterDestroy(void)
617: {
618: PetscErrorCode ierr;
619: RosWTableauLink link;
622: while ((link = RosWTableauList)) {
623: RosWTableau t = &link->tab;
624: RosWTableauList = link->next;
625: PetscFree5(t->A,t->Gamma,t->b,t->ASum,t->GammaSum);
626: PetscFree5(t->At,t->bt,t->GammaInv,t->GammaZeroDiag,t->GammaExplicitCorr);
627: PetscFree2(t->bembed,t->bembedt);
628: PetscFree(t->binterpt);
629: PetscFree(t->name);
630: PetscFree(link);
631: }
632: TSRosWRegisterAllCalled = PETSC_FALSE;
633: return(0);
634: }
638: /*@C
639: TSRosWInitializePackage - This function initializes everything in the TSRosW package. It is called
640: from PetscDLLibraryRegister() when using dynamic libraries, and on the first call to TSCreate_RosW()
641: when using static libraries.
643: Level: developer
645: .keywords: TS, TSRosW, initialize, package
646: .seealso: PetscInitialize()
647: @*/
648: PetscErrorCode TSRosWInitializePackage(void)
649: {
653: if (TSRosWPackageInitialized) return(0);
654: TSRosWPackageInitialized = PETSC_TRUE;
655: TSRosWRegisterAll();
656: PetscRegisterFinalize(TSRosWFinalizePackage);
657: return(0);
658: }
662: /*@C
663: TSRosWFinalizePackage - This function destroys everything in the TSRosW package. It is
664: called from PetscFinalize().
666: Level: developer
668: .keywords: Petsc, destroy, package
669: .seealso: PetscFinalize()
670: @*/
671: PetscErrorCode TSRosWFinalizePackage(void)
672: {
676: TSRosWPackageInitialized = PETSC_FALSE;
677: TSRosWRegisterDestroy();
678: return(0);
679: }
683: /*@C
684: TSRosWRegister - register a Rosenbrock W scheme by providing the entries in the Butcher tableau and optionally embedded approximations and interpolation
686: Not Collective, but the same schemes should be registered on all processes on which they will be used
688: Input Parameters:
689: + name - identifier for method
690: . order - approximation order of method
691: . s - number of stages, this is the dimension of the matrices below
692: . A - Table of propagated stage coefficients (dimension s*s, row-major), strictly lower triangular
693: . Gamma - Table of coefficients in implicit stage equations (dimension s*s, row-major), lower triangular with nonzero diagonal
694: . b - Step completion table (dimension s)
695: . bembed - Step completion table for a scheme of order one less (dimension s, NULL if no embedded scheme is available)
696: . pinterp - Order of the interpolation scheme, equal to the number of columns of binterpt
697: - binterpt - Coefficients of the interpolation formula (dimension s*pinterp)
699: Notes:
700: Several Rosenbrock W methods are provided, this function is only needed to create new methods.
702: Level: advanced
704: .keywords: TS, register
706: .seealso: TSRosW
707: @*/
708: PetscErrorCode TSRosWRegister(TSRosWType name,PetscInt order,PetscInt s,const PetscReal A[],const PetscReal Gamma[],const PetscReal b[],const PetscReal bembed[],
709: PetscInt pinterp,const PetscReal binterpt[])
710: {
711: PetscErrorCode ierr;
712: RosWTableauLink link;
713: RosWTableau t;
714: PetscInt i,j,k;
715: PetscScalar *GammaInv;
724: PetscMalloc(sizeof(*link),&link);
725: PetscMemzero(link,sizeof(*link));
726: t = &link->tab;
727: PetscStrallocpy(name,&t->name);
728: t->order = order;
729: t->s = s;
730: PetscMalloc5(s*s,PetscReal,&t->A,s*s,PetscReal,&t->Gamma,s,PetscReal,&t->b,s,PetscReal,&t->ASum,s,PetscReal,&t->GammaSum);
731: PetscMalloc5(s*s,PetscReal,&t->At,s,PetscReal,&t->bt,s*s,PetscReal,&t->GammaInv,s,PetscBool,&t->GammaZeroDiag,s*s,PetscReal,&t->GammaExplicitCorr);
732: PetscMemcpy(t->A,A,s*s*sizeof(A[0]));
733: PetscMemcpy(t->Gamma,Gamma,s*s*sizeof(Gamma[0]));
734: PetscMemcpy(t->GammaExplicitCorr,Gamma,s*s*sizeof(Gamma[0]));
735: PetscMemcpy(t->b,b,s*sizeof(b[0]));
736: if (bembed) {
737: PetscMalloc2(s,PetscReal,&t->bembed,s,PetscReal,&t->bembedt);
738: PetscMemcpy(t->bembed,bembed,s*sizeof(bembed[0]));
739: }
740: for (i=0; i<s; i++) {
741: t->ASum[i] = 0;
742: t->GammaSum[i] = 0;
743: for (j=0; j<s; j++) {
744: t->ASum[i] += A[i*s+j];
745: t->GammaSum[i] += Gamma[i*s+j];
746: }
747: }
748: PetscMalloc(s*s*sizeof(PetscScalar),&GammaInv); /* Need to use Scalar for inverse, then convert back to Real */
749: for (i=0; i<s*s; i++) GammaInv[i] = Gamma[i];
750: for (i=0; i<s; i++) {
751: if (Gamma[i*s+i] == 0.0) {
752: GammaInv[i*s+i] = 1.0;
753: t->GammaZeroDiag[i] = PETSC_TRUE;
754: } else {
755: t->GammaZeroDiag[i] = PETSC_FALSE;
756: }
757: }
759: switch (s) {
760: case 1: GammaInv[0] = 1./GammaInv[0]; break;
761: case 2: PetscKernel_A_gets_inverse_A_2(GammaInv,0); break;
762: case 3: PetscKernel_A_gets_inverse_A_3(GammaInv,0); break;
763: case 4: PetscKernel_A_gets_inverse_A_4(GammaInv,0); break;
764: case 5: {
765: PetscInt ipvt5[5];
766: MatScalar work5[5*5];
767: PetscKernel_A_gets_inverse_A_5(GammaInv,ipvt5,work5,0); break;
768: }
769: case 6: PetscKernel_A_gets_inverse_A_6(GammaInv,0); break;
770: case 7: PetscKernel_A_gets_inverse_A_7(GammaInv,0); break;
771: default: SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Not implemented for %D stages",s);
772: }
773: for (i=0; i<s*s; i++) t->GammaInv[i] = PetscRealPart(GammaInv[i]);
774: PetscFree(GammaInv);
776: for (i=0; i<s; i++) {
777: for (k=0; k<i+1; k++) {
778: t->GammaExplicitCorr[i*s+k]=(t->GammaExplicitCorr[i*s+k])*(t->GammaInv[k*s+k]);
779: for (j=k+1; j<i+1; j++) {
780: t->GammaExplicitCorr[i*s+k]+=(t->GammaExplicitCorr[i*s+j])*(t->GammaInv[j*s+k]);
781: }
782: }
783: }
785: for (i=0; i<s; i++) {
786: for (j=0; j<s; j++) {
787: t->At[i*s+j] = 0;
788: for (k=0; k<s; k++) {
789: t->At[i*s+j] += t->A[i*s+k] * t->GammaInv[k*s+j];
790: }
791: }
792: t->bt[i] = 0;
793: for (j=0; j<s; j++) {
794: t->bt[i] += t->b[j] * t->GammaInv[j*s+i];
795: }
796: if (bembed) {
797: t->bembedt[i] = 0;
798: for (j=0; j<s; j++) {
799: t->bembedt[i] += t->bembed[j] * t->GammaInv[j*s+i];
800: }
801: }
802: }
803: t->ccfl = 1.0; /* Fix this */
805: t->pinterp = pinterp;
806: PetscMalloc(s*pinterp*sizeof(binterpt[0]),&t->binterpt);
807: PetscMemcpy(t->binterpt,binterpt,s*pinterp*sizeof(binterpt[0]));
808: link->next = RosWTableauList;
809: RosWTableauList = link;
810: return(0);
811: }
815: /*@C
816: TSRosWRegisterRos4 - register a fourth order Rosenbrock scheme by providing paramter choices
818: Not Collective, but the same schemes should be registered on all processes on which they will be used
820: Input Parameters:
821: + name - identifier for method
822: . gamma - leading coefficient (diagonal entry)
823: . a2 - design parameter, see Table 7.2 of Hairer&Wanner
824: . a3 - design parameter or PETSC_DEFAULT to satisfy one of the order five conditions (Eq 7.22)
825: . b3 - design parameter, see Table 7.2 of Hairer&Wanner
826: . beta43 - design parameter or PETSC_DEFAULT to use Equation 7.21 of Hairer&Wanner
827: . e4 - design parameter for embedded method, see coefficient E4 in ros4.f code from Hairer
829: Notes:
830: This routine encodes the design of fourth order Rosenbrock methods as described in Hairer and Wanner volume 2.
831: It is used here to implement several methods from the book and can be used to experiment with new methods.
832: It was written this way instead of by copying coefficients in order to provide better than double precision satisfaction of the order conditions.
834: Level: developer
836: .keywords: TS, register
838: .seealso: TSRosW, TSRosWRegister()
839: @*/
840: PetscErrorCode TSRosWRegisterRos4(TSRosWType name,PetscReal gamma,PetscReal a2,PetscReal a3,PetscReal b3,PetscReal e4)
841: {
843: /* Declare numeric constants so they can be quad precision without being truncated at double */
844: const PetscReal one = 1,two = 2,three = 3,four = 4,five = 5,six = 6,eight = 8,twelve = 12,twenty = 20,twentyfour = 24,
845: p32 = one/six - gamma + gamma*gamma,
846: p42 = one/eight - gamma/three,
847: p43 = one/twelve - gamma/three,
848: p44 = one/twentyfour - gamma/two + three/two*gamma*gamma - gamma*gamma*gamma,
849: p56 = one/twenty - gamma/four;
850: PetscReal a4,a32,a42,a43,b1,b2,b4,beta2p,beta3p,beta4p,beta32,beta42,beta43,beta32beta2p,beta4jbetajp;
851: PetscReal A[4][4],Gamma[4][4],b[4],bm[4];
852: PetscScalar M[3][3],rhs[3];
855: /* Step 1: choose Gamma (input) */
856: /* Step 2: choose a2,a3,a4; b1,b2,b3,b4 to satisfy order conditions */
857: if (a3 == PETSC_DEFAULT) a3 = (one/five - a2/four)/(one/four - a2/three); /* Eq 7.22 */
858: a4 = a3; /* consequence of 7.20 */
860: /* Solve order conditions 7.15a, 7.15c, 7.15e */
861: M[0][0] = one; M[0][1] = one; M[0][2] = one; /* 7.15a */
862: M[1][0] = 0.0; M[1][1] = a2*a2; M[1][2] = a4*a4; /* 7.15c */
863: M[2][0] = 0.0; M[2][1] = a2*a2*a2; M[2][2] = a4*a4*a4; /* 7.15e */
864: rhs[0] = one - b3;
865: rhs[1] = one/three - a3*a3*b3;
866: rhs[2] = one/four - a3*a3*a3*b3;
867: PetscKernel_A_gets_inverse_A_3(&M[0][0],0);
868: b1 = PetscRealPart(M[0][0]*rhs[0] + M[0][1]*rhs[1] + M[0][2]*rhs[2]);
869: b2 = PetscRealPart(M[1][0]*rhs[0] + M[1][1]*rhs[1] + M[1][2]*rhs[2]);
870: b4 = PetscRealPart(M[2][0]*rhs[0] + M[2][1]*rhs[1] + M[2][2]*rhs[2]);
872: /* Step 3 */
873: beta43 = (p56 - a2*p43) / (b4*a3*a3*(a3 - a2)); /* 7.21 */
874: beta32beta2p = p44 / (b4*beta43); /* 7.15h */
875: beta4jbetajp = (p32 - b3*beta32beta2p) / b4;
876: M[0][0] = b2; M[0][1] = b3; M[0][2] = b4;
877: M[1][0] = a4*a4*beta32beta2p-a3*a3*beta4jbetajp; M[1][1] = a2*a2*beta4jbetajp; M[1][2] = -a2*a2*beta32beta2p;
878: M[2][0] = b4*beta43*a3*a3-p43; M[2][1] = -b4*beta43*a2*a2; M[2][2] = 0;
879: rhs[0] = one/two - gamma; rhs[1] = 0; rhs[2] = -a2*a2*p32;
880: PetscKernel_A_gets_inverse_A_3(&M[0][0],0);
881: beta2p = PetscRealPart(M[0][0]*rhs[0] + M[0][1]*rhs[1] + M[0][2]*rhs[2]);
882: beta3p = PetscRealPart(M[1][0]*rhs[0] + M[1][1]*rhs[1] + M[1][2]*rhs[2]);
883: beta4p = PetscRealPart(M[2][0]*rhs[0] + M[2][1]*rhs[1] + M[2][2]*rhs[2]);
885: /* Step 4: back-substitute */
886: beta32 = beta32beta2p / beta2p;
887: beta42 = (beta4jbetajp - beta43*beta3p) / beta2p;
889: /* Step 5: 7.15f and 7.20, then 7.16 */
890: a43 = 0;
891: a32 = p42 / (b3*a3*beta2p + b4*a4*beta2p);
892: a42 = a32;
894: A[0][0] = 0; A[0][1] = 0; A[0][2] = 0; A[0][3] = 0;
895: A[1][0] = a2; A[1][1] = 0; A[1][2] = 0; A[1][3] = 0;
896: A[2][0] = a3-a32; A[2][1] = a32; A[2][2] = 0; A[2][3] = 0;
897: A[3][0] = a4-a43-a42; A[3][1] = a42; A[3][2] = a43; A[3][3] = 0;
898: Gamma[0][0] = gamma; Gamma[0][1] = 0; Gamma[0][2] = 0; Gamma[0][3] = 0;
899: Gamma[1][0] = beta2p-A[1][0]; Gamma[1][1] = gamma; Gamma[1][2] = 0; Gamma[1][3] = 0;
900: Gamma[2][0] = beta3p-beta32-A[2][0]; Gamma[2][1] = beta32-A[2][1]; Gamma[2][2] = gamma; Gamma[2][3] = 0;
901: Gamma[3][0] = beta4p-beta42-beta43-A[3][0]; Gamma[3][1] = beta42-A[3][1]; Gamma[3][2] = beta43-A[3][2]; Gamma[3][3] = gamma;
902: b[0] = b1; b[1] = b2; b[2] = b3; b[3] = b4;
904: /* Construct embedded formula using given e4. We are solving Equation 7.18. */
905: bm[3] = b[3] - e4*gamma; /* using definition of E4 */
906: bm[2] = (p32 - beta4jbetajp*bm[3]) / (beta32*beta2p); /* fourth row of 7.18 */
907: bm[1] = (one/two - gamma - beta3p*bm[2] - beta4p*bm[3]) / beta2p; /* second row */
908: bm[0] = one - bm[1] - bm[2] - bm[3]; /* first row */
910: {
911: const PetscReal misfit = a2*a2*bm[1] + a3*a3*bm[2] + a4*a4*bm[3] - one/three;
912: if (PetscAbs(misfit) > PETSC_SMALL) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Assumptions violated, could not construct a third order embedded method");
913: }
914: TSRosWRegister(name,4,4,&A[0][0],&Gamma[0][0],b,bm,0,NULL);
915: return(0);
916: }
920: /*
921: The step completion formula is
923: x1 = x0 + b^T Y
925: where Y is the multi-vector of stages corrections. This function can be called before or after ts->vec_sol has been
926: updated. Suppose we have a completion formula b and an embedded formula be of different order. We can write
928: x1e = x0 + be^T Y
929: = x1 - b^T Y + be^T Y
930: = x1 + (be - b)^T Y
932: so we can evaluate the method of different order even after the step has been optimistically completed.
933: */
934: static PetscErrorCode TSEvaluateStep_RosW(TS ts,PetscInt order,Vec U,PetscBool *done)
935: {
936: TS_RosW *ros = (TS_RosW*)ts->data;
937: RosWTableau tab = ros->tableau;
938: PetscScalar *w = ros->work;
939: PetscInt i;
943: if (order == tab->order) {
944: if (ros->status == TS_STEP_INCOMPLETE) { /* Use standard completion formula */
945: VecCopy(ts->vec_sol,U);
946: for (i=0; i<tab->s; i++) w[i] = tab->bt[i];
947: VecMAXPY(U,tab->s,w,ros->Y);
948: } else {VecCopy(ts->vec_sol,U);}
949: if (done) *done = PETSC_TRUE;
950: return(0);
951: } else if (order == tab->order-1) {
952: if (!tab->bembedt) goto unavailable;
953: if (ros->status == TS_STEP_INCOMPLETE) { /* Use embedded completion formula */
954: VecCopy(ts->vec_sol,U);
955: for (i=0; i<tab->s; i++) w[i] = tab->bembedt[i];
956: VecMAXPY(U,tab->s,w,ros->Y);
957: } else { /* Use rollback-and-recomplete formula (bembedt - bt) */
958: for (i=0; i<tab->s; i++) w[i] = tab->bembedt[i] - tab->bt[i];
959: VecCopy(ts->vec_sol,U);
960: VecMAXPY(U,tab->s,w,ros->Y);
961: }
962: if (done) *done = PETSC_TRUE;
963: return(0);
964: }
965: unavailable:
966: if (done) *done = PETSC_FALSE;
967: else SETERRQ3(PetscObjectComm((PetscObject)ts),PETSC_ERR_SUP,"Rosenbrock-W '%s' of order %D cannot evaluate step at order %D",tab->name,tab->order,order);
968: return(0);
969: }
973: static PetscErrorCode TSStep_RosW(TS ts)
974: {
975: TS_RosW *ros = (TS_RosW*)ts->data;
976: RosWTableau tab = ros->tableau;
977: const PetscInt s = tab->s;
978: const PetscReal *At = tab->At,*Gamma = tab->Gamma,*ASum = tab->ASum,*GammaInv = tab->GammaInv;
979: const PetscReal *GammaExplicitCorr = tab->GammaExplicitCorr;
980: const PetscBool *GammaZeroDiag = tab->GammaZeroDiag;
981: PetscScalar *w = ros->work;
982: Vec *Y = ros->Y,Ydot = ros->Ydot,Zdot = ros->Zdot,Zstage = ros->Zstage;
983: SNES snes;
984: TSAdapt adapt;
985: PetscInt i,j,its,lits,reject,next_scheme;
986: PetscReal next_time_step;
987: PetscBool accept;
988: PetscErrorCode ierr;
989: MatStructure str;
992: TSGetSNES(ts,&snes);
993: next_time_step = ts->time_step;
994: accept = PETSC_TRUE;
995: ros->status = TS_STEP_INCOMPLETE;
997: for (reject=0; reject<ts->max_reject && !ts->reason; reject++,ts->reject++) {
998: const PetscReal h = ts->time_step;
999: TSPreStep(ts);
1000: VecCopy(ts->vec_sol,ros->VecSolPrev); /*move this at the end*/
1001: for (i=0; i<s; i++) {
1002: ros->stage_time = ts->ptime + h*ASum[i];
1003: TSPreStage(ts,ros->stage_time);
1004: if (GammaZeroDiag[i]) {
1005: ros->stage_explicit = PETSC_TRUE;
1006: ros->scoeff = 1.;
1007: } else {
1008: ros->stage_explicit = PETSC_FALSE;
1009: ros->scoeff = 1./Gamma[i*s+i];
1010: }
1012: VecCopy(ts->vec_sol,Zstage);
1013: for (j=0; j<i; j++) w[j] = At[i*s+j];
1014: VecMAXPY(Zstage,i,w,Y);
1016: for (j=0; j<i; j++) w[j] = 1./h * GammaInv[i*s+j];
1017: VecZeroEntries(Zdot);
1018: VecMAXPY(Zdot,i,w,Y);
1020: /* Initial guess taken from last stage */
1021: VecZeroEntries(Y[i]);
1023: if (!ros->stage_explicit) {
1024: if (!ros->recompute_jacobian && !i) {
1025: SNESSetLagJacobian(snes,-2); /* Recompute the Jacobian on this solve, but not again */
1026: }
1027: SNESSolve(snes,NULL,Y[i]);
1028: SNESGetIterationNumber(snes,&its);
1029: SNESGetLinearSolveIterations(snes,&lits);
1030: ts->snes_its += its; ts->ksp_its += lits;
1031: TSGetAdapt(ts,&adapt);
1032: TSAdaptCheckStage(adapt,ts,&accept);
1033: if (!accept) goto reject_step;
1034: } else {
1035: Mat J,Jp;
1036: VecZeroEntries(Ydot); /* Evaluate Y[i]=G(t,Ydot=0,Zstage) */
1037: TSComputeIFunction(ts,ros->stage_time,Zstage,Ydot,Y[i],PETSC_FALSE);
1038: VecScale(Y[i],-1.0);
1039: VecAXPY(Y[i],-1.0,Zdot); /*Y[i]=F(Zstage)-Zdot[=GammaInv*Y]*/
1041: VecZeroEntries(Zstage); /* Zstage = GammaExplicitCorr[i,j] * Y[j] */
1042: for (j=0; j<i; j++) w[j] = GammaExplicitCorr[i*s+j];
1043: VecMAXPY(Zstage,i,w,Y);
1044: /*Y[i] += Y[i] + Jac*Zstage[=Jac*GammaExplicitCorr[i,j] * Y[j]] */
1045: str = SAME_NONZERO_PATTERN;
1046: TSGetIJacobian(ts,&J,&Jp,NULL,NULL);
1047: TSComputeIJacobian(ts,ros->stage_time,ts->vec_sol,Ydot,0,&J,&Jp,&str,PETSC_FALSE);
1048: MatMult(J,Zstage,Zdot);
1050: VecAXPY(Y[i],-1.0,Zdot);
1051: VecScale(Y[i],h);
1052: ts->ksp_its += 1;
1053: }
1054: }
1055: TSEvaluateStep(ts,tab->order,ts->vec_sol,NULL);
1056: ros->status = TS_STEP_PENDING;
1058: /* Register only the current method as a candidate because we're not supporting multiple candidates yet. */
1059: TSGetAdapt(ts,&adapt);
1060: TSAdaptCandidatesClear(adapt);
1061: TSAdaptCandidateAdd(adapt,tab->name,tab->order,1,tab->ccfl,1.*tab->s,PETSC_TRUE);
1062: TSAdaptChoose(adapt,ts,ts->time_step,&next_scheme,&next_time_step,&accept);
1063: if (accept) {
1064: /* ignore next_scheme for now */
1065: ts->ptime += ts->time_step;
1066: ts->time_step = next_time_step;
1067: ts->steps++;
1068: ros->status = TS_STEP_COMPLETE;
1069: break;
1070: } else { /* Roll back the current step */
1071: for (i=0; i<s; i++) w[i] = -tab->bt[i];
1072: VecMAXPY(ts->vec_sol,s,w,Y);
1073: ts->time_step = next_time_step;
1074: ros->status = TS_STEP_INCOMPLETE;
1075: }
1076: reject_step: continue;
1077: }
1078: if (ros->status != TS_STEP_COMPLETE && !ts->reason) ts->reason = TS_DIVERGED_STEP_REJECTED;
1079: return(0);
1080: }
1084: static PetscErrorCode TSInterpolate_RosW(TS ts,PetscReal itime,Vec U)
1085: {
1086: TS_RosW *ros = (TS_RosW*)ts->data;
1087: PetscInt s = ros->tableau->s,pinterp = ros->tableau->pinterp,i,j;
1088: PetscReal h;
1089: PetscReal tt,t;
1090: PetscScalar *bt;
1091: const PetscReal *Bt = ros->tableau->binterpt;
1092: PetscErrorCode ierr;
1093: const PetscReal *GammaInv = ros->tableau->GammaInv;
1094: PetscScalar *w = ros->work;
1095: Vec *Y = ros->Y;
1098: if (!Bt) SETERRQ1(PetscObjectComm((PetscObject)ts),PETSC_ERR_SUP,"TSRosW %s does not have an interpolation formula",ros->tableau->name);
1100: switch (ros->status) {
1101: case TS_STEP_INCOMPLETE:
1102: case TS_STEP_PENDING:
1103: h = ts->time_step;
1104: t = (itime - ts->ptime)/h;
1105: break;
1106: case TS_STEP_COMPLETE:
1107: h = ts->time_step_prev;
1108: t = (itime - ts->ptime)/h + 1; /* In the interval [0,1] */
1109: break;
1110: default: SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_PLIB,"Invalid TSStepStatus");
1111: }
1112: PetscMalloc(s*sizeof(bt[0]),&bt);
1113: for (i=0; i<s; i++) bt[i] = 0;
1114: for (j=0,tt=t; j<pinterp; j++,tt*=t) {
1115: for (i=0; i<s; i++) {
1116: bt[i] += Bt[i*pinterp+j] * tt;
1117: }
1118: }
1120: /* y(t+tt*h) = y(t) + Sum bt(tt) * GammaInv * Ydot */
1121: /*U<-0*/
1122: VecZeroEntries(U);
1124: /*U<- Sum bt_i * GammaInv(i,1:i) * Y(1:i) */
1125: for (j=0; j<s; j++) w[j]=0;
1126: for (j=0; j<s; j++) {
1127: for (i=j; i<s; i++) {
1128: w[j] += bt[i]*GammaInv[i*s+j];
1129: }
1130: }
1131: VecMAXPY(U,i,w,Y);
1133: /*X<-y(t) + X*/
1134: VecAXPY(U,1.0,ros->VecSolPrev);
1136: PetscFree(bt);
1137: return(0);
1138: }
1140: /*------------------------------------------------------------*/
1143: static PetscErrorCode TSReset_RosW(TS ts)
1144: {
1145: TS_RosW *ros = (TS_RosW*)ts->data;
1146: PetscInt s;
1150: if (!ros->tableau) return(0);
1151: s = ros->tableau->s;
1152: VecDestroyVecs(s,&ros->Y);
1153: VecDestroy(&ros->Ydot);
1154: VecDestroy(&ros->Ystage);
1155: VecDestroy(&ros->Zdot);
1156: VecDestroy(&ros->Zstage);
1157: VecDestroy(&ros->VecSolPrev);
1158: PetscFree(ros->work);
1159: return(0);
1160: }
1164: static PetscErrorCode TSDestroy_RosW(TS ts)
1165: {
1169: TSReset_RosW(ts);
1170: PetscFree(ts->data);
1171: PetscObjectComposeFunction((PetscObject)ts,"TSRosWGetType_C",NULL);
1172: PetscObjectComposeFunction((PetscObject)ts,"TSRosWSetType_C",NULL);
1173: PetscObjectComposeFunction((PetscObject)ts,"TSRosWSetRecomputeJacobian_C",NULL);
1174: return(0);
1175: }
1180: static PetscErrorCode TSRosWGetVecs(TS ts,DM dm,Vec *Ydot,Vec *Zdot,Vec *Ystage,Vec *Zstage)
1181: {
1182: TS_RosW *rw = (TS_RosW*)ts->data;
1186: if (Ydot) {
1187: if (dm && dm != ts->dm) {
1188: DMGetNamedGlobalVector(dm,"TSRosW_Ydot",Ydot);
1189: } else *Ydot = rw->Ydot;
1190: }
1191: if (Zdot) {
1192: if (dm && dm != ts->dm) {
1193: DMGetNamedGlobalVector(dm,"TSRosW_Zdot",Zdot);
1194: } else *Zdot = rw->Zdot;
1195: }
1196: if (Ystage) {
1197: if (dm && dm != ts->dm) {
1198: DMGetNamedGlobalVector(dm,"TSRosW_Ystage",Ystage);
1199: } else *Ystage = rw->Ystage;
1200: }
1201: if (Zstage) {
1202: if (dm && dm != ts->dm) {
1203: DMGetNamedGlobalVector(dm,"TSRosW_Zstage",Zstage);
1204: } else *Zstage = rw->Zstage;
1205: }
1206: return(0);
1207: }
1212: static PetscErrorCode TSRosWRestoreVecs(TS ts,DM dm,Vec *Ydot,Vec *Zdot, Vec *Ystage, Vec *Zstage)
1213: {
1217: if (Ydot) {
1218: if (dm && dm != ts->dm) {
1219: DMRestoreNamedGlobalVector(dm,"TSRosW_Ydot",Ydot);
1220: }
1221: }
1222: if (Zdot) {
1223: if (dm && dm != ts->dm) {
1224: DMRestoreNamedGlobalVector(dm,"TSRosW_Zdot",Zdot);
1225: }
1226: }
1227: if (Ystage) {
1228: if (dm && dm != ts->dm) {
1229: DMRestoreNamedGlobalVector(dm,"TSRosW_Ystage",Ystage);
1230: }
1231: }
1232: if (Zstage) {
1233: if (dm && dm != ts->dm) {
1234: DMRestoreNamedGlobalVector(dm,"TSRosW_Zstage",Zstage);
1235: }
1236: }
1237: return(0);
1238: }
1242: static PetscErrorCode DMCoarsenHook_TSRosW(DM fine,DM coarse,void *ctx)
1243: {
1245: return(0);
1246: }
1250: static PetscErrorCode DMRestrictHook_TSRosW(DM fine,Mat restrct,Vec rscale,Mat inject,DM coarse,void *ctx)
1251: {
1252: TS ts = (TS)ctx;
1254: Vec Ydot,Zdot,Ystage,Zstage;
1255: Vec Ydotc,Zdotc,Ystagec,Zstagec;
1258: TSRosWGetVecs(ts,fine,&Ydot,&Ystage,&Zdot,&Zstage);
1259: TSRosWGetVecs(ts,coarse,&Ydotc,&Ystagec,&Zdotc,&Zstagec);
1260: MatRestrict(restrct,Ydot,Ydotc);
1261: VecPointwiseMult(Ydotc,rscale,Ydotc);
1262: MatRestrict(restrct,Ystage,Ystagec);
1263: VecPointwiseMult(Ystagec,rscale,Ystagec);
1264: MatRestrict(restrct,Zdot,Zdotc);
1265: VecPointwiseMult(Zdotc,rscale,Zdotc);
1266: MatRestrict(restrct,Zstage,Zstagec);
1267: VecPointwiseMult(Zstagec,rscale,Zstagec);
1268: TSRosWRestoreVecs(ts,fine,&Ydot,&Ystage,&Zdot,&Zstage);
1269: TSRosWRestoreVecs(ts,coarse,&Ydotc,&Ystagec,&Zdotc,&Zstagec);
1270: return(0);
1271: }
1276: static PetscErrorCode DMSubDomainHook_TSRosW(DM fine,DM coarse,void *ctx)
1277: {
1279: return(0);
1280: }
1284: static PetscErrorCode DMSubDomainRestrictHook_TSRosW(DM dm,VecScatter gscat,VecScatter lscat,DM subdm,void *ctx)
1285: {
1286: TS ts = (TS)ctx;
1288: Vec Ydot,Zdot,Ystage,Zstage;
1289: Vec Ydots,Zdots,Ystages,Zstages;
1292: TSRosWGetVecs(ts,dm,&Ydot,&Ystage,&Zdot,&Zstage);
1293: TSRosWGetVecs(ts,subdm,&Ydots,&Ystages,&Zdots,&Zstages);
1295: VecScatterBegin(gscat,Ydot,Ydots,INSERT_VALUES,SCATTER_FORWARD);
1296: VecScatterEnd(gscat,Ydot,Ydots,INSERT_VALUES,SCATTER_FORWARD);
1298: VecScatterBegin(gscat,Ystage,Ystages,INSERT_VALUES,SCATTER_FORWARD);
1299: VecScatterEnd(gscat,Ystage,Ystages,INSERT_VALUES,SCATTER_FORWARD);
1301: VecScatterBegin(gscat,Zdot,Zdots,INSERT_VALUES,SCATTER_FORWARD);
1302: VecScatterEnd(gscat,Zdot,Zdots,INSERT_VALUES,SCATTER_FORWARD);
1304: VecScatterBegin(gscat,Zstage,Zstages,INSERT_VALUES,SCATTER_FORWARD);
1305: VecScatterEnd(gscat,Zstage,Zstages,INSERT_VALUES,SCATTER_FORWARD);
1307: TSRosWRestoreVecs(ts,dm,&Ydot,&Ystage,&Zdot,&Zstage);
1308: TSRosWRestoreVecs(ts,subdm,&Ydots,&Ystages,&Zdots,&Zstages);
1309: return(0);
1310: }
1312: /*
1313: This defines the nonlinear equation that is to be solved with SNES
1314: G(U) = F[t0+Theta*dt, U, (U-U0)*shift] = 0
1315: */
1318: static PetscErrorCode SNESTSFormFunction_RosW(SNES snes,Vec U,Vec F,TS ts)
1319: {
1320: TS_RosW *ros = (TS_RosW*)ts->data;
1322: Vec Ydot,Zdot,Ystage,Zstage;
1323: PetscReal shift = ros->scoeff / ts->time_step;
1324: DM dm,dmsave;
1327: SNESGetDM(snes,&dm);
1328: TSRosWGetVecs(ts,dm,&Ydot,&Zdot,&Ystage,&Zstage);
1329: VecWAXPY(Ydot,shift,U,Zdot); /* Ydot = shift*U + Zdot */
1330: VecWAXPY(Ystage,1.0,U,Zstage); /* Ystage = U + Zstage */
1331: dmsave = ts->dm;
1332: ts->dm = dm;
1333: TSComputeIFunction(ts,ros->stage_time,Ystage,Ydot,F,PETSC_FALSE);
1334: ts->dm = dmsave;
1335: TSRosWRestoreVecs(ts,dm,&Ydot,&Zdot,&Ystage,&Zstage);
1336: return(0);
1337: }
1341: static PetscErrorCode SNESTSFormJacobian_RosW(SNES snes,Vec U,Mat *A,Mat *B,MatStructure *str,TS ts)
1342: {
1343: TS_RosW *ros = (TS_RosW*)ts->data;
1344: Vec Ydot,Zdot,Ystage,Zstage;
1345: PetscReal shift = ros->scoeff / ts->time_step;
1347: DM dm,dmsave;
1350: /* ros->Ydot and ros->Ystage have already been computed in SNESTSFormFunction_RosW (SNES guarantees this) */
1351: SNESGetDM(snes,&dm);
1352: TSRosWGetVecs(ts,dm,&Ydot,&Zdot,&Ystage,&Zstage);
1353: dmsave = ts->dm;
1354: ts->dm = dm;
1355: TSComputeIJacobian(ts,ros->stage_time,Ystage,Ydot,shift,A,B,str,PETSC_TRUE);
1356: ts->dm = dmsave;
1357: TSRosWRestoreVecs(ts,dm,&Ydot,&Zdot,&Ystage,&Zstage);
1358: return(0);
1359: }
1363: static PetscErrorCode TSSetUp_RosW(TS ts)
1364: {
1365: TS_RosW *ros = (TS_RosW*)ts->data;
1366: RosWTableau tab = ros->tableau;
1367: PetscInt s = tab->s;
1369: DM dm;
1372: if (!ros->tableau) {
1373: TSRosWSetType(ts,TSRosWDefault);
1374: }
1375: VecDuplicateVecs(ts->vec_sol,s,&ros->Y);
1376: VecDuplicate(ts->vec_sol,&ros->Ydot);
1377: VecDuplicate(ts->vec_sol,&ros->Ystage);
1378: VecDuplicate(ts->vec_sol,&ros->Zdot);
1379: VecDuplicate(ts->vec_sol,&ros->Zstage);
1380: VecDuplicate(ts->vec_sol,&ros->VecSolPrev);
1381: PetscMalloc(s*sizeof(ros->work[0]),&ros->work);
1382: TSGetDM(ts,&dm);
1383: if (dm) {
1384: DMCoarsenHookAdd(dm,DMCoarsenHook_TSRosW,DMRestrictHook_TSRosW,ts);
1385: DMSubDomainHookAdd(dm,DMSubDomainHook_TSRosW,DMSubDomainRestrictHook_TSRosW,ts);
1386: }
1387: return(0);
1388: }
1389: /*------------------------------------------------------------*/
1393: static PetscErrorCode TSSetFromOptions_RosW(TS ts)
1394: {
1395: TS_RosW *ros = (TS_RosW*)ts->data;
1397: char rostype[256];
1400: PetscOptionsHead("RosW ODE solver options");
1401: {
1402: RosWTableauLink link;
1403: PetscInt count,choice;
1404: PetscBool flg;
1405: const char **namelist;
1406: SNES snes;
1408: PetscStrncpy(rostype,TSRosWDefault,sizeof(rostype));
1409: for (link=RosWTableauList,count=0; link; link=link->next,count++) ;
1410: PetscMalloc(count*sizeof(char*),&namelist);
1411: for (link=RosWTableauList,count=0; link; link=link->next,count++) namelist[count] = link->tab.name;
1412: PetscOptionsEList("-ts_rosw_type","Family of Rosenbrock-W method","TSRosWSetType",(const char*const*)namelist,count,rostype,&choice,&flg);
1413: TSRosWSetType(ts,flg ? namelist[choice] : rostype);
1414: PetscFree(namelist);
1416: PetscOptionsBool("-ts_rosw_recompute_jacobian","Recompute the Jacobian at each stage","TSRosWSetRecomputeJacobian",ros->recompute_jacobian,&ros->recompute_jacobian,NULL);
1418: /* Rosenbrock methods are linearly implicit, so set that unless the user has specifically asked for something else */
1419: TSGetSNES(ts,&snes);
1420: if (!((PetscObject)snes)->type_name) {
1421: SNESSetType(snes,SNESKSPONLY);
1422: }
1423: SNESSetFromOptions(snes);
1424: }
1425: PetscOptionsTail();
1426: return(0);
1427: }
1431: static PetscErrorCode PetscFormatRealArray(char buf[],size_t len,const char *fmt,PetscInt n,const PetscReal x[])
1432: {
1434: PetscInt i;
1435: size_t left,count;
1436: char *p;
1439: for (i=0,p=buf,left=len; i<n; i++) {
1440: PetscSNPrintfCount(p,left,fmt,&count,x[i]);
1441: if (count >= left) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Insufficient space in buffer");
1442: left -= count;
1443: p += count;
1444: *p++ = ' ';
1445: }
1446: p[i ? 0 : -1] = 0;
1447: return(0);
1448: }
1452: static PetscErrorCode TSView_RosW(TS ts,PetscViewer viewer)
1453: {
1454: TS_RosW *ros = (TS_RosW*)ts->data;
1455: RosWTableau tab = ros->tableau;
1456: PetscBool iascii;
1458: TSAdapt adapt;
1461: PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);
1462: if (iascii) {
1463: TSRosWType rostype;
1464: PetscInt i;
1465: PetscReal abscissa[512];
1466: char buf[512];
1467: TSRosWGetType(ts,&rostype);
1468: PetscViewerASCIIPrintf(viewer," Rosenbrock-W %s\n",rostype);
1469: PetscFormatRealArray(buf,sizeof(buf),"% 8.6f",tab->s,tab->ASum);
1470: PetscViewerASCIIPrintf(viewer," Abscissa of A = %s\n",buf);
1471: for (i=0; i<tab->s; i++) abscissa[i] = tab->ASum[i] + tab->Gamma[i];
1472: PetscFormatRealArray(buf,sizeof(buf),"% 8.6f",tab->s,abscissa);
1473: PetscViewerASCIIPrintf(viewer," Abscissa of A+Gamma = %s\n",buf);
1474: }
1475: TSGetAdapt(ts,&adapt);
1476: TSAdaptView(adapt,viewer);
1477: SNESView(ts->snes,viewer);
1478: return(0);
1479: }
1483: /*@C
1484: TSRosWSetType - Set the type of Rosenbrock-W scheme
1486: Logically collective
1488: Input Parameter:
1489: + ts - timestepping context
1490: - rostype - type of Rosenbrock-W scheme
1492: Level: beginner
1494: .seealso: TSRosWGetType(), TSROSW, TSROSW2M, TSROSW2P, TSROSWRA3PW, TSROSWRA34PW2, TSROSWRODAS3, TSROSWSANDU3, TSROSWASSP3P3S1C, TSROSWLASSP3P4S2C, TSROSWLLSSP3P4S2C, TSROSWARK3
1495: @*/
1496: PetscErrorCode TSRosWSetType(TS ts,TSRosWType rostype)
1497: {
1502: PetscTryMethod(ts,"TSRosWSetType_C",(TS,TSRosWType),(ts,rostype));
1503: return(0);
1504: }
1508: /*@C
1509: TSRosWGetType - Get the type of Rosenbrock-W scheme
1511: Logically collective
1513: Input Parameter:
1514: . ts - timestepping context
1516: Output Parameter:
1517: . rostype - type of Rosenbrock-W scheme
1519: Level: intermediate
1521: .seealso: TSRosWGetType()
1522: @*/
1523: PetscErrorCode TSRosWGetType(TS ts,TSRosWType *rostype)
1524: {
1529: PetscUseMethod(ts,"TSRosWGetType_C",(TS,TSRosWType*),(ts,rostype));
1530: return(0);
1531: }
1535: /*@C
1536: TSRosWSetRecomputeJacobian - Set whether to recompute the Jacobian at each stage. The default is to update the Jacobian once per step.
1538: Logically collective
1540: Input Parameter:
1541: + ts - timestepping context
1542: - flg - PETSC_TRUE to recompute the Jacobian at each stage
1544: Level: intermediate
1546: .seealso: TSRosWGetType()
1547: @*/
1548: PetscErrorCode TSRosWSetRecomputeJacobian(TS ts,PetscBool flg)
1549: {
1554: PetscTryMethod(ts,"TSRosWSetRecomputeJacobian_C",(TS,PetscBool),(ts,flg));
1555: return(0);
1556: }
1560: PetscErrorCode TSRosWGetType_RosW(TS ts,TSRosWType *rostype)
1561: {
1562: TS_RosW *ros = (TS_RosW*)ts->data;
1566: if (!ros->tableau) {TSRosWSetType(ts,TSRosWDefault);}
1567: *rostype = ros->tableau->name;
1568: return(0);
1569: }
1573: PetscErrorCode TSRosWSetType_RosW(TS ts,TSRosWType rostype)
1574: {
1575: TS_RosW *ros = (TS_RosW*)ts->data;
1576: PetscErrorCode ierr;
1577: PetscBool match;
1578: RosWTableauLink link;
1581: if (ros->tableau) {
1582: PetscStrcmp(ros->tableau->name,rostype,&match);
1583: if (match) return(0);
1584: }
1585: for (link = RosWTableauList; link; link=link->next) {
1586: PetscStrcmp(link->tab.name,rostype,&match);
1587: if (match) {
1588: TSReset_RosW(ts);
1589: ros->tableau = &link->tab;
1590: return(0);
1591: }
1592: }
1593: SETERRQ1(PetscObjectComm((PetscObject)ts),PETSC_ERR_ARG_UNKNOWN_TYPE,"Could not find '%s'",rostype);
1594: return(0);
1595: }
1599: PetscErrorCode TSRosWSetRecomputeJacobian_RosW(TS ts,PetscBool flg)
1600: {
1601: TS_RosW *ros = (TS_RosW*)ts->data;
1604: ros->recompute_jacobian = flg;
1605: return(0);
1606: }
1609: /* ------------------------------------------------------------ */
1610: /*MC
1611: TSROSW - ODE solver using Rosenbrock-W schemes
1613: These methods are intended for problems with well-separated time scales, especially when a slow scale is strongly
1614: nonlinear such that it is expensive to solve with a fully implicit method. The user should provide the stiff part
1615: of the equation using TSSetIFunction() and the non-stiff part with TSSetRHSFunction().
1617: Notes:
1618: This method currently only works with autonomous ODE and DAE.
1620: Developer notes:
1621: Rosenbrock-W methods are typically specified for autonomous ODE
1623: $ udot = f(u)
1625: by the stage equations
1627: $ k_i = h f(u_0 + sum_j alpha_ij k_j) + h J sum_j gamma_ij k_j
1629: and step completion formula
1631: $ u_1 = u_0 + sum_j b_j k_j
1633: with step size h and coefficients alpha_ij, gamma_ij, and b_i. Implementing the method in this form would require f(u)
1634: and the Jacobian J to be available, in addition to the shifted matrix I - h gamma_ii J. Following Hairer and Wanner,
1635: we define new variables for the stage equations
1637: $ y_i = gamma_ij k_j
1639: The k_j can be recovered because Gamma is invertible. Let C be the lower triangular part of Gamma^{-1} and define
1641: $ A = Alpha Gamma^{-1}, bt^T = b^T Gamma^{-i}
1643: to rewrite the method as
1645: $ [M/(h gamma_ii) - J] y_i = f(u_0 + sum_j a_ij y_j) + M sum_j (c_ij/h) y_j
1646: $ u_1 = u_0 + sum_j bt_j y_j
1648: where we have introduced the mass matrix M. Continue by defining
1650: $ ydot_i = 1/(h gamma_ii) y_i - sum_j (c_ij/h) y_j
1652: or, more compactly in tensor notation
1654: $ Ydot = 1/h (Gamma^{-1} \otimes I) Y .
1656: Note that Gamma^{-1} is lower triangular. With this definition of Ydot in terms of known quantities and the current
1657: stage y_i, the stage equations reduce to performing one Newton step (typically with a lagged Jacobian) on the
1658: equation
1660: $ g(u_0 + sum_j a_ij y_j + y_i, ydot_i) = 0
1662: with initial guess y_i = 0.
1664: Level: beginner
1666: .seealso: TSCreate(), TS, TSSetType(), TSRosWSetType(), TSRosWRegister(), TSROSW2M, TSROSW2P, TSROSWRA3PW, TSROSWRA34PW2, TSROSWRODAS3,
1667: TSROSWSANDU3, TSROSWASSP3P3S1C, TSROSWLASSP3P4S2C, TSROSWLLSSP3P4S2C, TSROSWGRK4T, TSROSWSHAMP4, TSROSWVELDD4, TSROSW4L
1668: M*/
1671: PETSC_EXTERN PetscErrorCode TSCreate_RosW(TS ts)
1672: {
1673: TS_RosW *ros;
1677: #if !defined(PETSC_USE_DYNAMIC_LIBRARIES)
1678: TSRosWInitializePackage();
1679: #endif
1681: ts->ops->reset = TSReset_RosW;
1682: ts->ops->destroy = TSDestroy_RosW;
1683: ts->ops->view = TSView_RosW;
1684: ts->ops->setup = TSSetUp_RosW;
1685: ts->ops->step = TSStep_RosW;
1686: ts->ops->interpolate = TSInterpolate_RosW;
1687: ts->ops->evaluatestep = TSEvaluateStep_RosW;
1688: ts->ops->setfromoptions = TSSetFromOptions_RosW;
1689: ts->ops->snesfunction = SNESTSFormFunction_RosW;
1690: ts->ops->snesjacobian = SNESTSFormJacobian_RosW;
1692: PetscNewLog(ts,TS_RosW,&ros);
1693: ts->data = (void*)ros;
1695: PetscObjectComposeFunction((PetscObject)ts,"TSRosWGetType_C",TSRosWGetType_RosW);
1696: PetscObjectComposeFunction((PetscObject)ts,"TSRosWSetType_C",TSRosWSetType_RosW);
1697: PetscObjectComposeFunction((PetscObject)ts,"TSRosWSetRecomputeJacobian_C",TSRosWSetRecomputeJacobian_RosW);
1698: return(0);
1699: }