Actual source code: rk.c
petsc-3.4.5 2014-06-29
1: /*
2: * Code for Timestepping with Runge Kutta
3: *
4: * Written by
5: * Asbjorn Hoiland Aarrestad
6: * asbjorn@aarrestad.com
7: * http://asbjorn.aarrestad.com/
8: *
9: */
10: #include <petsc-private/tsimpl.h> /*I "petscts.h" I*/
11: #include <time.h>
13: typedef struct {
14: Vec y1,y2; /* work wectors for the two rk permuations */
15: PetscInt nok,nnok; /* counters for ok and not ok steps */
16: PetscReal maxerror; /* variable to tell the maxerror allowed */
17: PetscReal ferror; /* variable to tell (global maxerror)/(total time) */
18: PetscReal tolerance; /* initial value set for maxerror by user */
19: Vec tmp,tmp_y,*k; /* two temp vectors and the k vectors for rk */
20: PetscScalar a[7][6]; /* rk scalars */
21: PetscScalar b1[7],b2[7]; /* rk scalars */
22: PetscReal c[7]; /* rk scalars */
23: PetscInt p,s; /* variables to tell the size of the runge-kutta solver */
24: } TS_RK;
28: PetscErrorCode TSRKSetTolerance_RK(TS ts,PetscReal aabs)
29: {
30: TS_RK *rk = (TS_RK*)ts->data;
33: rk->tolerance = aabs;
34: return(0);
35: }
39: /*@
40: TSRKSetTolerance - Sets the total error the RK explicit time integrators
41: will allow over the given time interval.
43: Logically Collective on TS
45: Input parameters:
46: + ts - the time-step context
47: - aabs - the absolute tolerance
49: Level: intermediate
51: .keywords: RK, tolerance
53: .seealso: TSSundialsSetTolerance()
55: @*/
56: PetscErrorCode TSRKSetTolerance(TS ts,PetscReal aabs)
57: {
62: PetscTryMethod(ts,"TSRKSetTolerance_C",(TS,PetscReal),(ts,aabs));
63: return(0);
64: }
69: static PetscErrorCode TSSetUp_RK(TS ts)
70: {
71: TS_RK *rk = (TS_RK*)ts->data;
75: rk->nok = 0;
76: rk->nnok = 0;
77: rk->maxerror = rk->tolerance;
79: /* fixing maxerror: global vs local */
80: rk->ferror = rk->maxerror / (ts->max_time - ts->ptime);
82: /* 34.0/45.0 gives double precision division */
83: /* defining variables needed for Runge-Kutta computing */
84: /* when changing below, please remember to change a, b1, b2 and c above! */
85: /* Found in table on page 171: Dormand-Prince 5(4) */
87: /* are these right? */
88: rk->p=6;
89: rk->s=7;
91: rk->a[1][0]=1.0/5.0;
92: rk->a[2][0]=3.0/40.0;
93: rk->a[2][1]=9.0/40.0;
94: rk->a[3][0]=44.0/45.0;
95: rk->a[3][1]=-56.0/15.0;
96: rk->a[3][2]=32.0/9.0;
97: rk->a[4][0]=19372.0/6561.0;
98: rk->a[4][1]=-25360.0/2187.0;
99: rk->a[4][2]=64448.0/6561.0;
100: rk->a[4][3]=-212.0/729.0;
101: rk->a[5][0]=9017.0/3168.0;
102: rk->a[5][1]=-355.0/33.0;
103: rk->a[5][2]=46732.0/5247.0;
104: rk->a[5][3]=49.0/176.0;
105: rk->a[5][4]=-5103.0/18656.0;
106: rk->a[6][0]=35.0/384.0;
107: rk->a[6][1]=0.0;
108: rk->a[6][2]=500.0/1113.0;
109: rk->a[6][3]=125.0/192.0;
110: rk->a[6][4]=-2187.0/6784.0;
111: rk->a[6][5]=11.0/84.0;
114: rk->c[0]=0.0;
115: rk->c[1]=1.0/5.0;
116: rk->c[2]=3.0/10.0;
117: rk->c[3]=4.0/5.0;
118: rk->c[4]=8.0/9.0;
119: rk->c[5]=1.0;
120: rk->c[6]=1.0;
122: rk->b1[0]=35.0/384.0;
123: rk->b1[1]=0.0;
124: rk->b1[2]=500.0/1113.0;
125: rk->b1[3]=125.0/192.0;
126: rk->b1[4]=-2187.0/6784.0;
127: rk->b1[5]=11.0/84.0;
128: rk->b1[6]=0.0;
130: rk->b2[0]=5179.0/57600.0;
131: rk->b2[1]=0.0;
132: rk->b2[2]=7571.0/16695.0;
133: rk->b2[3]=393.0/640.0;
134: rk->b2[4]=-92097.0/339200.0;
135: rk->b2[5]=187.0/2100.0;
136: rk->b2[6]=1.0/40.0;
139: /* Found in table on page 170: Fehlberg 4(5) */
140: /*
141: rk->p=5;
142: rk->s=6;
144: rk->a[1][0]=1.0/4.0;
145: rk->a[2][0]=3.0/32.0;
146: rk->a[2][1]=9.0/32.0;
147: rk->a[3][0]=1932.0/2197.0;
148: rk->a[3][1]=-7200.0/2197.0;
149: rk->a[3][2]=7296.0/2197.0;
150: rk->a[4][0]=439.0/216.0;
151: rk->a[4][1]=-8.0;
152: rk->a[4][2]=3680.0/513.0;
153: rk->a[4][3]=-845.0/4104.0;
154: rk->a[5][0]=-8.0/27.0;
155: rk->a[5][1]=2.0;
156: rk->a[5][2]=-3544.0/2565.0;
157: rk->a[5][3]=1859.0/4104.0;
158: rk->a[5][4]=-11.0/40.0;
160: rk->c[0]=0.0;
161: rk->c[1]=1.0/4.0;
162: rk->c[2]=3.0/8.0;
163: rk->c[3]=12.0/13.0;
164: rk->c[4]=1.0;
165: rk->c[5]=1.0/2.0;
167: rk->b1[0]=25.0/216.0;
168: rk->b1[1]=0.0;
169: rk->b1[2]=1408.0/2565.0;
170: rk->b1[3]=2197.0/4104.0;
171: rk->b1[4]=-1.0/5.0;
172: rk->b1[5]=0.0;
174: rk->b2[0]=16.0/135.0;
175: rk->b2[1]=0.0;
176: rk->b2[2]=6656.0/12825.0;
177: rk->b2[3]=28561.0/56430.0;
178: rk->b2[4]=-9.0/50.0;
179: rk->b2[5]=2.0/55.0;
180: */
181: /* Found in table on page 169: Merson 4("5") */
182: /*
183: rk->p=4;
184: rk->s=5;
185: rk->a[1][0] = 1.0/3.0;
186: rk->a[2][0] = 1.0/6.0;
187: rk->a[2][1] = 1.0/6.0;
188: rk->a[3][0] = 1.0/8.0;
189: rk->a[3][1] = 0.0;
190: rk->a[3][2] = 3.0/8.0;
191: rk->a[4][0] = 1.0/2.0;
192: rk->a[4][1] = 0.0;
193: rk->a[4][2] = -3.0/2.0;
194: rk->a[4][3] = 2.0;
196: rk->c[0] = 0.0;
197: rk->c[1] = 1.0/3.0;
198: rk->c[2] = 1.0/3.0;
199: rk->c[3] = 0.5;
200: rk->c[4] = 1.0;
202: rk->b1[0] = 1.0/2.0;
203: rk->b1[1] = 0.0;
204: rk->b1[2] = -3.0/2.0;
205: rk->b1[3] = 2.0;
206: rk->b1[4] = 0.0;
208: rk->b2[0] = 1.0/6.0;
209: rk->b2[1] = 0.0;
210: rk->b2[2] = 0.0;
211: rk->b2[3] = 2.0/3.0;
212: rk->b2[4] = 1.0/6.0;
213: */
215: /* making b2 -> e=b1-b2 */
216: /*
217: for (i=0;i<rk->s;i++) {
218: rk->b2[i] = (rk->b1[i]) - (rk->b2[i]);
219: }
220: */
221: rk->b2[0]=71.0/57600.0;
222: rk->b2[1]=0.0;
223: rk->b2[2]=-71.0/16695.0;
224: rk->b2[3]=71.0/1920.0;
225: rk->b2[4]=-17253.0/339200.0;
226: rk->b2[5]=22.0/525.0;
227: rk->b2[6]=-1.0/40.0;
229: /* initializing vectors */
230: VecDuplicate(ts->vec_sol,&rk->y1);
231: VecDuplicate(ts->vec_sol,&rk->y2);
232: VecDuplicate(rk->y1,&rk->tmp);
233: VecDuplicate(rk->y1,&rk->tmp_y);
234: VecDuplicateVecs(rk->y1,rk->s,&rk->k);
235: return(0);
236: }
238: /*------------------------------------------------------------*/
241: PetscErrorCode TSRKqs(TS ts,PetscReal t,PetscReal h)
242: {
243: TS_RK *rk = (TS_RK*)ts->data;
245: PetscInt j,l;
246: PetscReal tmp_t = t;
247: PetscScalar hh = h;
250: /* k[0]=0 */
251: VecSet(rk->k[0],0.0);
253: /* k[0] = derivs(t,y1) */
254: TSComputeRHSFunction(ts,t,rk->y1,rk->k[0]);
255: /* looping over runge-kutta variables */
256: /* building the k - array of vectors */
257: for (j = 1; j < rk->s; j++) {
259: /* rk->tmp = 0 */
260: VecSet(rk->tmp,0.0);
262: for (l=0; l<j; l++) {
263: /* tmp += a(j,l)*k[l] */
264: VecAXPY(rk->tmp,rk->a[j][l],rk->k[l]);
265: }
267: /* VecView(rk->tmp,PETSC_VIEWER_STDOUT_WORLD); */
269: /* k[j] = derivs(t+c(j)*h,y1+h*tmp,k(j)) */
270: /* I need the following helpers:
271: PetscScalar tmp_t=t+c(j)*h
272: Vec tmp_y=h*tmp+y1
273: */
275: tmp_t = t + rk->c[j] * h;
277: /* tmp_y = h * tmp + y1 */
278: VecWAXPY(rk->tmp_y,hh,rk->tmp,rk->y1);
280: /* rk->k[j]=0 */
281: VecSet(rk->k[j],0.0);
282: TSComputeRHSFunction(ts,tmp_t,rk->tmp_y,rk->k[j]);
283: }
285: /* tmp=0 and tmp_y=0 */
286: VecSet(rk->tmp,0.0);
287: VecSet(rk->tmp_y,0.0);
289: for (j = 0; j < rk->s; j++) {
290: /* tmp=b1[j]*k[j]+tmp */
291: VecAXPY(rk->tmp,rk->b1[j],rk->k[j]);
292: /* tmp_y=b2[j]*k[j]+tmp_y */
293: VecAXPY(rk->tmp_y,rk->b2[j],rk->k[j]);
294: }
296: /* y2 = hh * tmp_y */
297: VecSet(rk->y2,0.0);
298: VecAXPY(rk->y2,hh,rk->tmp_y);
299: /* y1 = hh*tmp + y1 */
300: VecAXPY(rk->y1,hh,rk->tmp);
301: /* Finding difference between y1 and y2 */
302: return(0);
303: }
307: static PetscErrorCode TSSolve_RK(TS ts)
308: {
309: TS_RK *rk = (TS_RK*)ts->data;
310: PetscReal norm=0.0,dt_fac=0.0,fac = 0.0 /*,ttmp=0.0*/;
311: PetscInt i;
315: VecCopy(ts->vec_sol,rk->y1);
317: /* while loop to get from start to stop */
318: for (i = 0; i < ts->max_steps; i++) {
319: TSPreStep(ts); /* Note that this is called once per STEP, not once per STAGE. */
321: /* calling rkqs */
322: /*
323: -- input
324: ts - pointer to ts
325: ts->ptime - current time
326: ts->time_step - try this timestep
327: y1 - solution for this step
329: --output
330: y1 - suggested solution
331: y2 - check solution (runge - kutta second permutation)
332: */
333: TSRKqs(ts,ts->ptime,ts->time_step);
334: /* counting steps */
335: ts->steps++;
336: /* checking for maxerror */
337: /* comparing difference to maxerror */
338: VecNorm(rk->y2,NORM_2,&norm);
339: /* modifying maxerror to satisfy this timestep */
340: rk->maxerror = rk->ferror * ts->time_step;
341: /* PetscPrintf(PETSC_COMM_WORLD,"norm err: %f maxerror: %f dt: %f",norm,rk->maxerror,ts->time_step); */
343: /* handling ok and not ok */
344: if (norm < rk->maxerror) {
345: /* if ok: */
346: VecCopy(rk->y1,ts->vec_sol); /* saves the suggested solution to current solution */
347: ts->ptime += ts->time_step; /* storing the new current time */
348: rk->nok++;
349: fac=5.0;
350: /* trying to save the vector */
351: TSPostStep(ts);
352: TSMonitor(ts,ts->steps,ts->ptime,ts->vec_sol);
353: if (ts->ptime >= ts->max_time) break;
354: } else {
355: /* if not OK */
356: rk->nnok++;
357: fac =1.0;
358: ierr=VecCopy(ts->vec_sol,rk->y1); /* restores old solution */
359: }
361: /*Computing next stepsize. See page 167 in Solving ODE 1
362: *
363: * h_new = h * min(facmax , max(facmin , fac * (tol/err)^(1/(p+1))))
364: * facmax set above
365: * facmin
366: */
367: dt_fac = exp(log((rk->maxerror) / norm) / ((rk->p) + 1)) * 0.9;
369: if (dt_fac > fac) dt_fac = fac;
370:
372: /* computing new ts->time_step */
373: ts->time_step = ts->time_step * dt_fac;
375: if (ts->ptime+ts->time_step > ts->max_time) ts->time_step = ts->max_time - ts->ptime;
377: if (ts->time_step < 1e-14) {
378: PetscPrintf(PETSC_COMM_WORLD,"Very small steps: %f\n",ts->time_step);
379: ts->time_step = 1e-14;
380: }
382: /* trying to purify h */
383: /* (did not give any visible result) */
384: /* ttmp = ts->ptime + ts->time_step;
385: ts->time_step = ttmp - ts->ptime; */
387: }
389: ierr=VecCopy(rk->y1,ts->vec_sol);
390: return(0);
391: }
393: /*------------------------------------------------------------*/
396: static PetscErrorCode TSReset_RK(TS ts)
397: {
398: TS_RK *rk = (TS_RK*)ts->data;
402: VecDestroy(&rk->y1);
403: VecDestroy(&rk->y2);
404: VecDestroy(&rk->tmp);
405: VecDestroy(&rk->tmp_y);
406: if (rk->k) {VecDestroyVecs(rk->s,&rk->k);}
407: return(0);
408: }
412: static PetscErrorCode TSDestroy_RK(TS ts)
413: {
417: TSReset_RK(ts);
418: PetscFree(ts->data);
419: PetscObjectComposeFunction((PetscObject)ts,"TSRKSetTolerance_C",NULL);
420: return(0);
421: }
422: /*------------------------------------------------------------*/
426: static PetscErrorCode TSSetFromOptions_RK(TS ts)
427: {
428: TS_RK *rk = (TS_RK*)ts->data;
432: PetscOptionsHead("RK ODE solver options");
433: PetscOptionsReal("-ts_rk_tol","Tolerance for convergence","TSRKSetTolerance",rk->tolerance,&rk->tolerance,NULL);
434: PetscOptionsTail();
435: return(0);
436: }
440: static PetscErrorCode TSView_RK(TS ts,PetscViewer viewer)
441: {
442: TS_RK *rk = (TS_RK*)ts->data;
443: PetscBool iascii;
447: PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);
448: if (iascii) {
449: PetscViewerASCIIPrintf(viewer,"number of ok steps: %D\n",rk->nok);
450: PetscViewerASCIIPrintf(viewer,"number of rejected steps: %D\n",rk->nnok);
451: }
452: return(0);
453: }
455: /* ------------------------------------------------------------ */
456: /*MC
457: TSRK - ODE solver using the explicit Runge-Kutta methods
459: Options Database:
460: . -ts_rk_tol <tol> Tolerance for convergence
462: Contributed by: Asbjorn Hoiland Aarrestad, asbjorn@aarrestad.com, http://asbjorn.aarrestad.com/
464: Level: beginner
466: .seealso: TSCreate(), TS, TSSetType(), TSEULER, TSRKSetTolerance()
468: M*/
472: PETSC_EXTERN PetscErrorCode TSCreate_RK(TS ts)
473: {
474: TS_RK *rk;
478: ts->ops->setup = TSSetUp_RK;
479: ts->ops->solve = TSSolve_RK;
480: ts->ops->destroy = TSDestroy_RK;
481: ts->ops->setfromoptions = TSSetFromOptions_RK;
482: ts->ops->view = TSView_RK;
484: PetscNewLog(ts,TS_RK,&rk);
485: ts->data = (void*)rk;
487: PetscObjectComposeFunction((PetscObject)ts,"TSRKSetTolerance_C",TSRKSetTolerance_RK);
488: return(0);
489: }