Actual source code: alpha.c
petsc-3.6.4 2016-04-12
1: /*
2: Code for timestepping with implicit generalized-\alpha method
3: for first order systems.
4: */
5: #include <petsc/private/tsimpl.h> /*I "petscts.h" I*/
7: typedef PetscErrorCode (*TSAlphaAdaptFunction)(TS,PetscReal,Vec,Vec,PetscReal*,PetscBool*,void*);
9: typedef struct {
10: Vec X0,Xa,X1;
11: Vec V0,Va,V1;
12: Vec R,E;
13: PetscReal Alpha_m;
14: PetscReal Alpha_f;
15: PetscReal Gamma;
16: PetscReal stage_time;
17: PetscReal shift;
19: TSAlphaAdaptFunction adapt;
20: void *adaptctx;
21: PetscReal rtol;
22: PetscReal atol;
23: PetscReal rho;
24: PetscReal scale_min;
25: PetscReal scale_max;
26: PetscReal dt_min;
27: PetscReal dt_max;
28: } TS_Alpha;
32: static PetscErrorCode TSStep_Alpha(TS ts)
33: {
34: TS_Alpha *th = (TS_Alpha*)ts->data;
35: PetscInt its,lits,reject;
36: PetscReal next_time_step;
37: SNESConvergedReason snesreason = SNES_CONVERGED_ITERATING;
38: PetscErrorCode ierr;
41: if (ts->steps == 0) {
42: VecSet(th->V0,0.0);
43: } else {
44: VecCopy(th->V1,th->V0);
45: }
46: VecCopy(ts->vec_sol,th->X0);
47: next_time_step = ts->time_step;
48: for (reject=0; reject<ts->max_reject; reject++,ts->reject++) {
49: ts->time_step = next_time_step;
50: th->stage_time = ts->ptime + th->Alpha_f*ts->time_step;
51: th->shift = th->Alpha_m/(th->Alpha_f*th->Gamma*ts->time_step);
52: TSPreStep(ts);
53: TSPreStage(ts,th->stage_time);
54: /* predictor */
55: VecCopy(th->X0,th->X1);
56: /* solve R(X,V) = 0 */
57: SNESSolve(ts->snes,NULL,th->X1);
58: /* V1 = (1-1/Gamma)*V0 + 1/(Gamma*dT)*(X1-X0) */
59: VecWAXPY(th->V1,-1,th->X0,th->X1);
60: VecAXPBY(th->V1,1-1/th->Gamma,1/(th->Gamma*ts->time_step),th->V0);
61: TSPostStage(ts,th->stage_time,0,&(th->V1));
62: /* nonlinear solve convergence */
63: SNESGetConvergedReason(ts->snes,&snesreason);
64: if (snesreason < 0 && !th->adapt) break;
65: SNESGetIterationNumber(ts->snes,&its);
66: SNESGetLinearSolveIterations(ts->snes,&lits);
67: ts->snes_its += its; ts->ksp_its += lits;
68: PetscInfo3(ts,"step=%D, nonlinear solve iterations=%D, linear solve iterations=%D\n",ts->steps,its,lits);
69: /* time step adaptativity */
70: if (!th->adapt) break;
71: else {
72: PetscReal t1 = ts->ptime + ts->time_step;
73: PetscBool stepok = (reject==0) ? PETSC_TRUE : PETSC_FALSE;
74: th->adapt(ts,t1,th->X1,th->V1,&next_time_step,&stepok,th->adaptctx);
75: PetscInfo5(ts,"Step %D (t=%g,dt=%g) %s, next dt=%g\n",ts->steps,(double)ts->ptime,(double)ts->time_step,stepok?"accepted":"rejected",(double)next_time_step);
76: if (stepok) break;
77: }
78: }
79: if (snesreason < 0 && ts->max_snes_failures > 0 && ++ts->num_snes_failures >= ts->max_snes_failures) {
80: ts->reason = TS_DIVERGED_NONLINEAR_SOLVE;
81: PetscInfo2(ts,"Step=%D, nonlinear solve solve failures %D greater than current TS allowed, stopping solve\n",ts->steps,ts->num_snes_failures);
82: return(0);
83: }
84: if (reject >= ts->max_reject) {
85: ts->reason = TS_DIVERGED_STEP_REJECTED;
86: PetscInfo2(ts,"Step=%D, step rejections %D greater than current TS allowed, stopping solve\n",ts->steps,reject);
87: return(0);
88: }
89: VecCopy(th->X1,ts->vec_sol);
90: ts->ptime += ts->time_step;
91: ts->time_step = next_time_step;
92: ts->steps++;
93: return(0);
94: }
98: static PetscErrorCode TSInterpolate_Alpha(TS ts,PetscReal t,Vec X)
99: {
100: TS_Alpha *th = (TS_Alpha*)ts->data;
101: PetscReal dt = t - ts->ptime;
105: VecCopy(ts->vec_sol,X);
106: VecAXPY(X,th->Gamma*dt,th->V1);
107: VecAXPY(X,(1-th->Gamma)*dt,th->V0);
108: return(0);
109: }
111: /*------------------------------------------------------------*/
114: static PetscErrorCode TSReset_Alpha(TS ts)
115: {
116: TS_Alpha *th = (TS_Alpha*)ts->data;
120: VecDestroy(&th->X0);
121: VecDestroy(&th->Xa);
122: VecDestroy(&th->X1);
123: VecDestroy(&th->V0);
124: VecDestroy(&th->Va);
125: VecDestroy(&th->V1);
126: VecDestroy(&th->E);
127: return(0);
128: }
132: static PetscErrorCode TSDestroy_Alpha(TS ts)
133: {
137: TSReset_Alpha(ts);
138: PetscFree(ts->data);
140: PetscObjectComposeFunction((PetscObject)ts,"TSAlphaSetRadius_C",NULL);
141: PetscObjectComposeFunction((PetscObject)ts,"TSAlphaSetParams_C",NULL);
142: PetscObjectComposeFunction((PetscObject)ts,"TSAlphaGetParams_C",NULL);
143: PetscObjectComposeFunction((PetscObject)ts,"TSAlphaSetAdapt_C",NULL);
144: return(0);
145: }
149: static PetscErrorCode SNESTSFormFunction_Alpha(SNES snes,Vec x,Vec y,TS ts)
150: {
151: TS_Alpha *th = (TS_Alpha*)ts->data;
152: Vec X0 = th->X0, V0 = th->V0;
153: Vec X1 = x, V1 = th->V1, R = y;
157: /* V1 = (1-1/Gamma)*V0 + 1/(Gamma*dT)*(X1-X0) */
158: VecWAXPY(V1,-1,X0,X1);
159: VecAXPBY(V1,1-1/th->Gamma,1/(th->Gamma*ts->time_step),V0);
160: /* Xa = X0 + Alpha_f*(X1-X0) */
161: VecWAXPY(th->Xa,-1,X0,X1);
162: VecAYPX(th->Xa,th->Alpha_f,X0);
163: /* Va = V0 + Alpha_m*(V1-V0) */
164: VecWAXPY(th->Va,-1,V0,V1);
165: VecAYPX(th->Va,th->Alpha_m,V0);
166: /* F = Function(ta,Xa,Va) */
167: TSComputeIFunction(ts,th->stage_time,th->Xa,th->Va,R,PETSC_FALSE);
168: VecScale(R,1/th->Alpha_f);
169: return(0);
170: }
174: static PetscErrorCode SNESTSFormJacobian_Alpha(SNES snes,Vec x,Mat A,Mat B,TS ts)
175: {
176: TS_Alpha *th = (TS_Alpha*)ts->data;
180: /* A,B = Jacobian(ta,Xa,Va) */
181: TSComputeIJacobian(ts,th->stage_time,th->Xa,th->Va,th->shift,A,B,PETSC_FALSE);
182: return(0);
183: }
187: static PetscErrorCode TSSetUp_Alpha(TS ts)
188: {
189: TS_Alpha *th = (TS_Alpha*)ts->data;
193: VecDuplicate(ts->vec_sol,&th->X0);
194: VecDuplicate(ts->vec_sol,&th->Xa);
195: VecDuplicate(ts->vec_sol,&th->X1);
196: VecDuplicate(ts->vec_sol,&th->V0);
197: VecDuplicate(ts->vec_sol,&th->Va);
198: VecDuplicate(ts->vec_sol,&th->V1);
199: return(0);
200: }
204: static PetscErrorCode TSSetFromOptions_Alpha(PetscOptions *PetscOptionsObject,TS ts)
205: {
206: TS_Alpha *th = (TS_Alpha*)ts->data;
210: PetscOptionsHead(PetscOptionsObject,"Alpha ODE solver options");
211: {
212: PetscBool flag, adapt = PETSC_FALSE;
213: PetscReal radius = 1.0;
214: PetscOptionsReal("-ts_alpha_radius","spectral radius","TSAlphaSetRadius",radius,&radius,&flag);
215: if (flag) { TSAlphaSetRadius(ts,radius); }
216: PetscOptionsReal("-ts_alpha_alpha_m","algoritmic parameter alpha_m","TSAlphaSetParams",th->Alpha_m,&th->Alpha_m,NULL);
217: PetscOptionsReal("-ts_alpha_alpha_f","algoritmic parameter alpha_f","TSAlphaSetParams",th->Alpha_f,&th->Alpha_f,NULL);
218: PetscOptionsReal("-ts_alpha_gamma","algoritmic parameter gamma","TSAlphaSetParams",th->Gamma,&th->Gamma,NULL);
219: TSAlphaSetParams(ts,th->Alpha_m,th->Alpha_f,th->Gamma);
221: PetscOptionsBool("-ts_alpha_adapt","default time step adaptativity","TSAlphaSetAdapt",adapt,&adapt,&flag);
222: if (flag) { TSAlphaSetAdapt(ts,adapt ? TSAlphaAdaptDefault : NULL,NULL); }
223: PetscOptionsReal("-ts_alpha_adapt_rtol","relative tolerance for dt adaptativity","",th->rtol,&th->rtol,NULL);
224: PetscOptionsReal("-ts_alpha_adapt_atol","absolute tolerance for dt adaptativity","",th->atol,&th->atol,NULL);
225: PetscOptionsReal("-ts_alpha_adapt_min","minimum dt scale","",th->scale_min,&th->scale_min,NULL);
226: PetscOptionsReal("-ts_alpha_adapt_max","maximum dt scale","",th->scale_max,&th->scale_max,NULL);
227: PetscOptionsReal("-ts_alpha_adapt_dt_min","minimum dt","",th->dt_min,&th->dt_min,NULL);
228: PetscOptionsReal("-ts_alpha_adapt_dt_max","maximum dt","",th->dt_max,&th->dt_max,NULL);
229: }
230: PetscOptionsTail();
231: return(0);
232: }
236: static PetscErrorCode TSView_Alpha(TS ts,PetscViewer viewer)
237: {
238: TS_Alpha *th = (TS_Alpha*)ts->data;
239: PetscBool iascii;
243: PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);
244: if (iascii) {
245: PetscViewerASCIIPrintf(viewer," Alpha_m=%g, Alpha_f=%g, Gamma=%g\n",(double)th->Alpha_m,(double)th->Alpha_f,(double)th->Gamma);
246: }
247: SNESView(ts->snes,viewer);
248: return(0);
249: }
251: /*------------------------------------------------------------*/
255: PetscErrorCode TSAlphaSetRadius_Alpha(TS ts,PetscReal radius)
256: {
257: TS_Alpha *th = (TS_Alpha*)ts->data;
260: if (radius < 0 || radius > 1) SETERRQ1(PetscObjectComm((PetscObject)ts),PETSC_ERR_ARG_OUTOFRANGE,"Radius %g not in range [0,1]",(double)radius);
261: th->Alpha_m = 0.5*(3-radius)/(1+radius);
262: th->Alpha_f = 1/(1+radius);
263: th->Gamma = 0.5 + th->Alpha_m - th->Alpha_f;
264: return(0);
265: }
269: PetscErrorCode TSAlphaSetParams_Alpha(TS ts,PetscReal alpha_m,PetscReal alpha_f,PetscReal gamma)
270: {
271: TS_Alpha *th = (TS_Alpha*)ts->data;
274: th->Alpha_m = alpha_m;
275: th->Alpha_f = alpha_f;
276: th->Gamma = gamma;
277: return(0);
278: }
282: PetscErrorCode TSAlphaGetParams_Alpha(TS ts,PetscReal *alpha_m,PetscReal *alpha_f,PetscReal *gamma)
283: {
284: TS_Alpha *th = (TS_Alpha*)ts->data;
287: if (alpha_m) *alpha_m = th->Alpha_m;
288: if (alpha_f) *alpha_f = th->Alpha_f;
289: if (gamma) *gamma = th->Gamma;
290: return(0);
291: }
295: PetscErrorCode TSAlphaSetAdapt_Alpha(TS ts,TSAlphaAdaptFunction adapt,void *ctx)
296: {
297: TS_Alpha *th = (TS_Alpha*)ts->data;
300: th->adapt = adapt;
301: th->adaptctx = ctx;
302: return(0);
303: }
305: /* ------------------------------------------------------------ */
306: /*MC
307: TSALPHA - DAE solver using the implicit Generalized-Alpha method
309: Level: beginner
311: References:
312: K.E. Jansen, C.H. Whiting, G.M. Hulber, "A generalized-alpha
313: method for integrating the filtered Navier-Stokes equations with a
314: stabilized finite element method", Computer Methods in Applied
315: Mechanics and Engineering, 190, 305-319, 2000.
316: DOI: 10.1016/S0045-7825(00)00203-6.
318: J. Chung, G.M.Hubert. "A Time Integration Algorithm for Structural
319: Dynamics with Improved Numerical Dissipation: The Generalized-alpha
320: Method" ASME Journal of Applied Mechanics, 60, 371:375, 1993.
322: .seealso: TSCreate(), TS, TSSetType()
324: M*/
327: PETSC_EXTERN PetscErrorCode TSCreate_Alpha(TS ts)
328: {
329: TS_Alpha *th;
333: ts->ops->reset = TSReset_Alpha;
334: ts->ops->destroy = TSDestroy_Alpha;
335: ts->ops->view = TSView_Alpha;
336: ts->ops->setup = TSSetUp_Alpha;
337: ts->ops->step = TSStep_Alpha;
338: ts->ops->interpolate = TSInterpolate_Alpha;
339: ts->ops->setfromoptions = TSSetFromOptions_Alpha;
340: ts->ops->snesfunction = SNESTSFormFunction_Alpha;
341: ts->ops->snesjacobian = SNESTSFormJacobian_Alpha;
343: PetscNewLog(ts,&th);
344: ts->data = (void*)th;
346: th->Alpha_m = 0.5;
347: th->Alpha_f = 0.5;
348: th->Gamma = 0.5;
350: th->rtol = 1e-3;
351: th->atol = 1e-3;
352: th->rho = 0.9;
353: th->scale_min = 0.1;
354: th->scale_max = 5.0;
355: th->dt_min = 0.0;
356: th->dt_max = PETSC_MAX_REAL;
358: PetscObjectComposeFunction((PetscObject)ts,"TSAlphaSetAdapt_C",TSAlphaSetAdapt_Alpha);
359: PetscObjectComposeFunction((PetscObject)ts,"TSAlphaSetRadius_C",TSAlphaSetRadius_Alpha);
360: PetscObjectComposeFunction((PetscObject)ts,"TSAlphaSetParams_C",TSAlphaSetParams_Alpha);
361: PetscObjectComposeFunction((PetscObject)ts,"TSAlphaGetParams_C",TSAlphaGetParams_Alpha);
362: return(0);
363: }
367: /*@C
368: TSAlphaSetAdapt - sets the time step adaptativity and acceptance test routine
370: This function allows to accept/reject a step and select the
371: next time step to use.
373: Not Collective
375: Input Parameter:
376: + ts - timestepping context
377: . adapt - user-defined adapt routine
378: - ctx - [optional] user-defined context for private data for the
379: adapt routine (may be NULL)
381: Calling sequence of adapt:
382: $ adapt (TS ts,PetscReal t,Vec X,Vec Xdot,
383: $ PetscReal *next_dt,PetscBool *accepted,void *ctx);
385: Level: intermediate
387: @*/
388: PetscErrorCode TSAlphaSetAdapt(TS ts,TSAlphaAdaptFunction adapt,void *ctx)
389: {
394: PetscTryMethod(ts,"TSAlphaSetAdapt_C",(TS,TSAlphaAdaptFunction,void*),(ts,adapt,ctx));
395: return(0);
396: }
400: PetscErrorCode TSAlphaAdaptDefault(TS ts,PetscReal t,Vec X,Vec Xdot, PetscReal *nextdt,PetscBool *ok,void *ctx)
401: {
402: TS_Alpha *th;
403: SNESConvergedReason snesreason;
404: PetscReal dt,normX,normE,Emax,scale;
405: PetscErrorCode ierr;
409: #if PETSC_USE_DEBUG
410: {
411: PetscBool match;
412: PetscObjectTypeCompare((PetscObject)ts,TSALPHA,&match);
413: if (!match) SETERRQ(PetscObjectComm((PetscObject)ts),1,"Only for TSALPHA");
414: }
415: #endif
416: th = (TS_Alpha*)ts->data;
418: SNESGetConvergedReason(ts->snes,&snesreason);
419: if (snesreason < 0) {
420: *ok = PETSC_FALSE;
421: *nextdt *= th->scale_min;
422: goto finally;
423: }
425: /* first-order aproximation to the local error */
426: /* E = (X0 + dt*Xdot) - X */
427: TSGetTimeStep(ts,&dt);
428: if (!th->E) {VecDuplicate(th->X0,&th->E);}
429: VecWAXPY(th->E,dt,Xdot,th->X0);
430: VecAXPY(th->E,-1,X);
431: VecNorm(th->E,NORM_2,&normE);
432: /* compute maximum allowable error */
433: VecNorm(X,NORM_2,&normX);
434: if (normX == 0) {VecNorm(th->X0,NORM_2,&normX);}
435: Emax = th->rtol * normX + th->atol;
436: /* compute next time step */
437: if (normE > 0) {
438: scale = th->rho * PetscRealPart(PetscSqrtScalar((PetscScalar)(Emax/normE)));
439: scale = PetscMax(scale,th->scale_min);
440: scale = PetscMin(scale,th->scale_max);
441: if (!(*ok)) scale = PetscMin(1.0,scale);
442: *nextdt *= scale;
443: }
444: /* accept or reject step */
445: if (normE <= Emax) *ok = PETSC_TRUE;
446: else *ok = PETSC_FALSE;
448: finally:
449: *nextdt = PetscMax(*nextdt,th->dt_min);
450: *nextdt = PetscMin(*nextdt,th->dt_max);
451: return(0);
452: }
456: /*@
457: TSAlphaSetRadius - sets the desired spectral radius of the method
458: (i.e. high-frequency numerical damping)
460: Logically Collective on TS
462: The algorithmic parameters \alpha_m and \alpha_f of the
463: generalized-\alpha method can be computed in terms of a specified
464: spectral radius \rho in [0,1] for infinite time step in order to
465: control high-frequency numerical damping:
466: alpha_m = 0.5*(3-\rho)/(1+\rho)
467: alpha_f = 1/(1+\rho)
469: Input Parameter:
470: + ts - timestepping context
471: - radius - the desired spectral radius
473: Options Database:
474: . -ts_alpha_radius <radius>
476: Level: intermediate
478: .seealso: TSAlphaSetParams(), TSAlphaGetParams()
479: @*/
480: PetscErrorCode TSAlphaSetRadius(TS ts,PetscReal radius)
481: {
486: PetscTryMethod(ts,"TSAlphaSetRadius_C",(TS,PetscReal),(ts,radius));
487: return(0);
488: }
492: /*@
493: TSAlphaSetParams - sets the algorithmic parameters for TSALPHA
495: Not Collective
497: Second-order accuracy can be obtained so long as:
498: \gamma = 0.5 + alpha_m - alpha_f
500: Unconditional stability requires:
501: \alpha_m >= \alpha_f >= 0.5
503: Backward Euler method is recovered when:
504: \alpha_m = \alpha_f = gamma = 1
507: Input Parameter:
508: + ts - timestepping context
509: . \alpha_m - algorithmic paramenter
510: . \alpha_f - algorithmic paramenter
511: - \gamma - algorithmic paramenter
513: Options Database:
514: + -ts_alpha_alpha_m <alpha_m>
515: . -ts_alpha_alpha_f <alpha_f>
516: - -ts_alpha_gamma <gamma>
518: Note:
519: Use of this function is normally only required to hack TSALPHA to
520: use a modified integration scheme. Users should call
521: TSAlphaSetRadius() to set the desired spectral radius of the methods
522: (i.e. high-frequency damping) in order so select optimal values for
523: these parameters.
525: Level: advanced
527: .seealso: TSAlphaSetRadius(), TSAlphaGetParams()
528: @*/
529: PetscErrorCode TSAlphaSetParams(TS ts,PetscReal alpha_m,PetscReal alpha_f,PetscReal gamma)
530: {
535: PetscTryMethod(ts,"TSAlphaSetParams_C",(TS,PetscReal,PetscReal,PetscReal),(ts,alpha_m,alpha_f,gamma));
536: return(0);
537: }
541: /*@
542: TSAlphaGetParams - gets the algorithmic parameters for TSALPHA
544: Not Collective
546: Input Parameter:
547: + ts - timestepping context
548: . \alpha_m - algorithmic parameter
549: . \alpha_f - algorithmic parameter
550: - \gamma - algorithmic parameter
552: Note:
553: Use of this function is normally only required to hack TSALPHA to
554: use a modified integration scheme. Users should call
555: TSAlphaSetRadius() to set the high-frequency damping (i.e. spectral
556: radius of the method) in order so select optimal values for these
557: parameters.
559: Level: advanced
561: .seealso: TSAlphaSetRadius(), TSAlphaSetParams()
562: @*/
563: PetscErrorCode TSAlphaGetParams(TS ts,PetscReal *alpha_m,PetscReal *alpha_f,PetscReal *gamma)
564: {
572: PetscUseMethod(ts,"TSAlphaGetParams_C",(TS,PetscReal*,PetscReal*,PetscReal*),(ts,alpha_m,alpha_f,gamma));
573: return(0);
574: }