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 "src/ts/tsimpl.h" /*I "petscts.h" I*/ 11 #include "time.h" 12 13 typedef struct { 14 Vec y1,y2; /* work wectors for the two rk permuations */ 15 int 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 int p,s; /* variables to tell the size of the runge-kutta solver */ 24 clock_t start,end; /* variables to mesure cpu time */ 25 } TS_Rk; 26 27 EXTERN_C_BEGIN 28 #undef __FUNCT__ 29 #define __FUNCT__ "TSRKSetTolerance_RK" 30 PetscErrorCode TSRKSetTolerance_RK(TS ts,PetscReal aabs) 31 { 32 TS_Rk *rk = (TS_Rk*)ts->data; 33 34 PetscFunctionBegin; 35 rk->tolerance = aabs; 36 PetscFunctionReturn(0); 37 } 38 EXTERN_C_END 39 40 #undef __FUNCT__ 41 #define __FUNCT__ "TSRKSetTolerance" 42 /*@ 43 TSRKSetTolerance - Sets the total error the RK explicit time integrators 44 will allow over the given time interval. 45 46 Collective on TS 47 48 Input parameters: 49 + ts - the time-step context 50 - aabs - the absolute tolerance 51 52 Level: intermediate 53 54 .keywords: RK, tolerance 55 56 .seealso: TSPVodeSetTolerance() 57 58 @*/ 59 PetscErrorCode TSRKSetTolerance(TS ts,PetscReal aabs) 60 { 61 PetscErrorCode ierr,(*f)(TS,PetscReal); 62 63 PetscFunctionBegin; 64 ierr = PetscObjectQueryFunction((PetscObject)ts,"TSRKSetTolerance_C",(void (**)(void))&f);CHKERRQ(ierr); 65 if (f) { 66 ierr = (*f)(ts,aabs);CHKERRQ(ierr); 67 } 68 PetscFunctionReturn(0); 69 } 70 71 72 #undef __FUNCT__ 73 #define __FUNCT__ "TSSetUp_Rk" 74 static int TSSetUp_Rk(TS ts) 75 { 76 TS_Rk *rk = (TS_Rk*)ts->data; 77 int ierr; 78 79 PetscFunctionBegin; 80 rk->nok = 0; 81 rk->nnok = 0; 82 rk->maxerror = rk->tolerance; 83 84 /* fixing maxerror: global vs local */ 85 rk->ferror = rk->maxerror / (ts->max_time - ts->ptime); 86 87 /* 34.0/45.0 gives double precision division */ 88 /* defining variables needed for Runge-Kutta computing */ 89 /* when changing below, please remember to change a, b1, b2 and c above! */ 90 /* Found in table on page 171: Dormand-Prince 5(4) */ 91 92 /* are these right? */ 93 rk->p=6; 94 rk->s=7; 95 96 rk->a[1][0]=1.0/5.0; 97 rk->a[2][0]=3.0/40.0; 98 rk->a[2][1]=9.0/40.0; 99 rk->a[3][0]=44.0/45.0; 100 rk->a[3][1]=-56.0/15.0; 101 rk->a[3][2]=32.0/9.0; 102 rk->a[4][0]=19372.0/6561.0; 103 rk->a[4][1]=-25360.0/2187.0; 104 rk->a[4][2]=64448.0/6561.0; 105 rk->a[4][3]=-212.0/729.0; 106 rk->a[5][0]=9017.0/3168.0; 107 rk->a[5][1]=-355.0/33.0; 108 rk->a[5][2]=46732.0/5247.0; 109 rk->a[5][3]=49.0/176.0; 110 rk->a[5][4]=-5103.0/18656.0; 111 rk->a[6][0]=35.0/384.0; 112 rk->a[6][1]=0.0; 113 rk->a[6][2]=500.0/1113.0; 114 rk->a[6][3]=125.0/192.0; 115 rk->a[6][4]=-2187.0/6784.0; 116 rk->a[6][5]=11.0/84.0; 117 118 119 rk->c[0]=0.0; 120 rk->c[1]=1.0/5.0; 121 rk->c[2]=3.0/10.0; 122 rk->c[3]=4.0/5.0; 123 rk->c[4]=8.0/9.0; 124 rk->c[5]=1.0; 125 rk->c[6]=1.0; 126 127 rk->b1[0]=35.0/384.0; 128 rk->b1[1]=0.0; 129 rk->b1[2]=500.0/1113.0; 130 rk->b1[3]=125.0/192.0; 131 rk->b1[4]=-2187.0/6784.0; 132 rk->b1[5]=11.0/84.0; 133 rk->b1[6]=0.0; 134 135 rk->b2[0]=5179.0/57600.0; 136 rk->b2[1]=0.0; 137 rk->b2[2]=7571.0/16695.0; 138 rk->b2[3]=393.0/640.0; 139 rk->b2[4]=-92097.0/339200.0; 140 rk->b2[5]=187.0/2100.0; 141 rk->b2[6]=1.0/40.0; 142 143 144 /* Found in table on page 170: Fehlberg 4(5) */ 145 /* 146 rk->p=5; 147 rk->s=6; 148 149 rk->a[1][0]=1.0/4.0; 150 rk->a[2][0]=3.0/32.0; 151 rk->a[2][1]=9.0/32.0; 152 rk->a[3][0]=1932.0/2197.0; 153 rk->a[3][1]=-7200.0/2197.0; 154 rk->a[3][2]=7296.0/2197.0; 155 rk->a[4][0]=439.0/216.0; 156 rk->a[4][1]=-8.0; 157 rk->a[4][2]=3680.0/513.0; 158 rk->a[4][3]=-845.0/4104.0; 159 rk->a[5][0]=-8.0/27.0; 160 rk->a[5][1]=2.0; 161 rk->a[5][2]=-3544.0/2565.0; 162 rk->a[5][3]=1859.0/4104.0; 163 rk->a[5][4]=-11.0/40.0; 164 165 rk->c[0]=0.0; 166 rk->c[1]=1.0/4.0; 167 rk->c[2]=3.0/8.0; 168 rk->c[3]=12.0/13.0; 169 rk->c[4]=1.0; 170 rk->c[5]=1.0/2.0; 171 172 rk->b1[0]=25.0/216.0; 173 rk->b1[1]=0.0; 174 rk->b1[2]=1408.0/2565.0; 175 rk->b1[3]=2197.0/4104.0; 176 rk->b1[4]=-1.0/5.0; 177 rk->b1[5]=0.0; 178 179 rk->b2[0]=16.0/135.0; 180 rk->b2[1]=0.0; 181 rk->b2[2]=6656.0/12825.0; 182 rk->b2[3]=28561.0/56430.0; 183 rk->b2[4]=-9.0/50.0; 184 rk->b2[5]=2.0/55.0; 185 */ 186 /* Found in table on page 169: Merson 4("5") */ 187 /* 188 rk->p=4; 189 rk->s=5; 190 rk->a[1][0] = 1.0/3.0; 191 rk->a[2][0] = 1.0/6.0; 192 rk->a[2][1] = 1.0/6.0; 193 rk->a[3][0] = 1.0/8.0; 194 rk->a[3][1] = 0.0; 195 rk->a[3][2] = 3.0/8.0; 196 rk->a[4][0] = 1.0/2.0; 197 rk->a[4][1] = 0.0; 198 rk->a[4][2] = -3.0/2.0; 199 rk->a[4][3] = 2.0; 200 201 rk->c[0] = 0.0; 202 rk->c[1] = 1.0/3.0; 203 rk->c[2] = 1.0/3.0; 204 rk->c[3] = 0.5; 205 rk->c[4] = 1.0; 206 207 rk->b1[0] = 1.0/2.0; 208 rk->b1[1] = 0.0; 209 rk->b1[2] = -3.0/2.0; 210 rk->b1[3] = 2.0; 211 rk->b1[4] = 0.0; 212 213 rk->b2[0] = 1.0/6.0; 214 rk->b2[1] = 0.0; 215 rk->b2[2] = 0.0; 216 rk->b2[3] = 2.0/3.0; 217 rk->b2[4] = 1.0/6.0; 218 */ 219 220 /* making b2 -> e=b1-b2 */ 221 /* 222 for(i=0;i<rk->s;i++){ 223 rk->b2[i] = (rk->b1[i]) - (rk->b2[i]); 224 } 225 */ 226 rk->b2[0]=71.0/57600.0; 227 rk->b2[1]=0.0; 228 rk->b2[2]=-71.0/16695.0; 229 rk->b2[3]=71.0/1920.0; 230 rk->b2[4]=-17253.0/339200.0; 231 rk->b2[5]=22.0/525.0; 232 rk->b2[6]=-1.0/40.0; 233 234 /* initializing vectors */ 235 ierr = VecDuplicate(ts->vec_sol,&rk->y1);CHKERRQ(ierr); 236 ierr = VecDuplicate(ts->vec_sol,&rk->y2);CHKERRQ(ierr); 237 ierr = VecDuplicate(rk->y1,&rk->tmp);CHKERRQ(ierr); 238 ierr = VecDuplicate(rk->y1,&rk->tmp_y);CHKERRQ(ierr); 239 ierr = VecDuplicateVecs(rk->y1,rk->s,&rk->k);CHKERRQ(ierr); 240 241 PetscFunctionReturn(0); 242 } 243 244 /*------------------------------------------------------------*/ 245 #undef __FUNCT__ 246 #define __FUNCT__ "TSRkqs" 247 PetscErrorCode TSRkqs(TS ts,PetscReal t,PetscReal h) 248 { 249 TS_Rk *rk = (TS_Rk*)ts->data; 250 int ierr,j,l; 251 PetscReal tmp_t=t; 252 PetscScalar null=0.0,hh=h; 253 254 /* printf("h: %f, hh: %f",h,hh); */ 255 256 PetscFunctionBegin; 257 258 /* k[0]=0 */ 259 ierr = VecSet(&null,rk->k[0]);CHKERRQ(ierr); 260 261 /* k[0] = derivs(t,y1) */ 262 ierr = TSComputeRHSFunction(ts,t,rk->y1,rk->k[0]);CHKERRQ(ierr); 263 /* looping over runge-kutta variables */ 264 /* building the k - array of vectors */ 265 for(j = 1 ; j < rk->s ; j++){ 266 267 /* rk->tmp = 0 */ 268 ierr = VecSet(&null,rk->tmp);CHKERRQ(ierr); 269 270 for(l=0;l<j;l++){ 271 /* tmp += a(j,l)*k[l] */ 272 /* ierr = PetscPrintf(PETSC_COMM_WORLD,"a(%i,%i)=%f \n",j,l,rk->a[j][l]);CHKERRQ(ierr); */ 273 ierr = VecAXPY(&rk->a[j][l],rk->k[l],rk->tmp);CHKERRQ(ierr); 274 } 275 276 /* ierr = VecView(rk->tmp,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr); */ 277 278 /* k[j] = derivs(t+c(j)*h,y1+h*tmp,k(j)) */ 279 /* I need the following helpers: 280 PetscScalar tmp_t=t+c(j)*h 281 Vec tmp_y=h*tmp+y1 282 */ 283 284 tmp_t = t + rk->c[j] * h; 285 286 /* tmp_y = h * tmp + y1 */ 287 ierr = VecWAXPY(&hh,rk->tmp,rk->y1,rk->tmp_y);CHKERRQ(ierr); 288 289 /* rk->k[j]=0 */ 290 ierr = VecSet(&null,rk->k[j]);CHKERRQ(ierr); 291 ierr = TSComputeRHSFunction(ts,tmp_t,rk->tmp_y,rk->k[j]);CHKERRQ(ierr); 292 } 293 294 /* tmp=0 and tmp_y=0 */ 295 ierr = VecSet(&null,rk->tmp);CHKERRQ(ierr); 296 ierr = VecSet(&null,rk->tmp_y);CHKERRQ(ierr); 297 298 for(j = 0 ; j < rk->s ; j++){ 299 /* tmp=b1[j]*k[j]+tmp */ 300 ierr = VecAXPY(&rk->b1[j],rk->k[j],rk->tmp);CHKERRQ(ierr); 301 /* tmp_y=b2[j]*k[j]+tmp_y */ 302 ierr = VecAXPY(&rk->b2[j],rk->k[j],rk->tmp_y);CHKERRQ(ierr); 303 } 304 305 /* y2 = hh * tmp_y */ 306 ierr = VecSet(&null,rk->y2);CHKERRQ(ierr); 307 ierr = VecAXPY(&hh,rk->tmp_y,rk->y2);CHKERRQ(ierr); 308 /* y1 = hh*tmp + y1 */ 309 ierr = VecAXPY(&hh,rk->tmp,rk->y1);CHKERRQ(ierr); 310 /* Finding difference between y1 and y2 */ 311 312 PetscFunctionReturn(0); 313 } 314 315 #undef __FUNCT__ 316 #define __FUNCT__ "TSStep_Rk" 317 static int TSStep_Rk(TS ts,int *steps,PetscReal *ptime) 318 { 319 TS_Rk *rk = (TS_Rk*)ts->data; 320 int ierr; 321 PetscReal dt = 0.001; /* fixed first step guess */ 322 PetscReal norm=0.0,dt_fac=0.0,fac = 0.0/*,ttmp=0.0*/; 323 324 PetscFunctionBegin; 325 rk->start=clock(); 326 ierr=VecCopy(ts->vec_sol,rk->y1);CHKERRQ(ierr); 327 *steps = -ts->steps; 328 /* trying to save the vector */ 329 ierr = TSMonitor(ts,ts->steps,ts->ptime,ts->vec_sol);CHKERRQ(ierr); 330 /* while loop to get from start to stop */ 331 while (ts->ptime < ts->max_time){ 332 /* calling rkqs */ 333 /* 334 -- input 335 ts - pointer to ts 336 ts->ptime - current time 337 dt - try this timestep 338 y1 - solution for this step 339 340 --output 341 y1 - suggested solution 342 y2 - check solution (runge - kutta second permutation) 343 */ 344 ierr = TSRkqs(ts,ts->ptime,dt);CHKERRQ(ierr); 345 /* checking for maxerror */ 346 /* comparing difference to maxerror */ 347 ierr = VecNorm(rk->y2,NORM_2,&norm);CHKERRQ(ierr); 348 /* modifying maxerror to satisfy this timestep */ 349 rk->maxerror = rk->ferror * dt; 350 /* ierr = PetscPrintf(PETSC_COMM_WORLD,"norm err: %f maxerror: %f dt: %f",norm,rk->maxerror,dt);CHKERRQ(ierr); */ 351 352 /* handling ok and not ok */ 353 if(norm < rk->maxerror){ 354 /* if ok: */ 355 ierr=VecCopy(rk->y1,ts->vec_sol);CHKERRQ(ierr); /* saves the suggested solution to current solution */ 356 ts->ptime += dt; /* storing the new current time */ 357 rk->nok++; 358 fac=5.0; 359 /* trying to save the vector */ 360 /* calling monitor */ 361 ierr = TSMonitor(ts,ts->steps,ts->ptime,ts->vec_sol);CHKERRQ(ierr); 362 }else{ 363 /* if not OK */ 364 rk->nnok++; 365 fac=1.0; 366 ierr=VecCopy(ts->vec_sol,rk->y1);CHKERRQ(ierr); /* restores old solution */ 367 } 368 369 /*Computing next stepsize. See page 167 in Solving ODE 1 370 * 371 * h_new = h * min( facmax , max( facmin , fac * (tol/err)^(1/(p+1)) ) ) 372 * facmax set above 373 * facmin 374 */ 375 dt_fac = exp(log((rk->maxerror) / norm) / ((rk->p) + 1) ) * 0.9 ; 376 377 if(dt_fac > fac){ 378 /*ierr = PetscPrintf(PETSC_COMM_WORLD,"changing fac %f\n",fac);*/ 379 dt_fac = fac; 380 } 381 382 /* computing new dt */ 383 dt = dt * dt_fac; 384 385 if(ts->ptime+dt > ts->max_time){ 386 dt = ts->max_time - ts->ptime; 387 } 388 389 if(dt < 1e-14){ 390 ierr = PetscPrintf(PETSC_COMM_WORLD,"Very small steps: %f\n",dt);CHKERRQ(ierr); 391 dt = 1e-14; 392 } 393 394 /* trying to purify h */ 395 /* (did not give any visible result) */ 396 /* ttmp = ts->ptime + dt; 397 dt = ttmp - ts->ptime; */ 398 399 /* counting steps */ 400 ts->steps++; 401 } 402 403 ierr=VecCopy(rk->y1,ts->vec_sol);CHKERRQ(ierr); 404 *steps += ts->steps; 405 *ptime = ts->ptime; 406 rk->end=clock(); 407 PetscFunctionReturn(0); 408 } 409 410 /*------------------------------------------------------------*/ 411 #undef __FUNCT__ 412 #define __FUNCT__ "TSDestroy_Rk" 413 static int TSDestroy_Rk(TS ts) 414 { 415 TS_Rk *rk = (TS_Rk*)ts->data; 416 int i,ierr; 417 418 /* REMEMBER TO DESTROY ALL */ 419 420 PetscFunctionBegin; 421 if (rk->y1) {ierr = VecDestroy(rk->y1);CHKERRQ(ierr);} 422 if (rk->y2) {ierr = VecDestroy(rk->y2);CHKERRQ(ierr);} 423 if (rk->tmp) {ierr = VecDestroy(rk->tmp);CHKERRQ(ierr);} 424 if (rk->tmp_y) {ierr = VecDestroy(rk->tmp_y);CHKERRQ(ierr);} 425 for(i=0;i<rk->s;i++){ 426 if (rk->k[i]) {ierr = VecDestroy(rk->k[i]);CHKERRQ(ierr);} 427 } 428 ierr = PetscFree(rk);CHKERRQ(ierr); 429 PetscFunctionReturn(0); 430 } 431 /*------------------------------------------------------------*/ 432 433 #undef __FUNCT__ 434 #define __FUNCT__ "TSSetFromOptions_Rk" 435 static int TSSetFromOptions_Rk(TS ts) 436 { 437 TS_Rk *rk = (TS_Rk*)ts->data; 438 PetscErrorCode ierr; 439 440 PetscFunctionBegin; 441 ierr = PetscOptionsHead("RK ODE solver options");CHKERRQ(ierr); 442 ierr = PetscOptionsReal("-ts_rk_tol","Tolerance for convergence","TSRKSetTolerance",rk->tolerance,&rk->tolerance,PETSC_NULL);CHKERRQ(ierr); 443 ierr = PetscOptionsTail();CHKERRQ(ierr); 444 PetscFunctionReturn(0); 445 } 446 447 #undef __FUNCT__ 448 #define __FUNCT__ "TSView_Rk" 449 static int TSView_Rk(TS ts,PetscViewer viewer) 450 { 451 TS_Rk *rk = (TS_Rk*)ts->data; 452 PetscErrorCode ierr; 453 /*double elapsed;*/ 454 455 PetscFunctionBegin; 456 ierr = PetscPrintf(PETSC_COMM_WORLD," number of ok steps: %d\n",rk->nok);CHKERRQ(ierr); 457 ierr = PetscPrintf(PETSC_COMM_WORLD," number of rejected steps: %d\n",rk->nnok);CHKERRQ(ierr); 458 /* elapsed = ((double) (rk->end - rk->start)) / CLOCKS_PER_SEC; 459 460 ierr = PetscPrintf(PETSC_COMM_WORLD," CPU time used (in seconds): %f\n",elapsed);CHKERRQ(ierr); */ 461 PetscFunctionReturn(0); 462 } 463 464 /* ------------------------------------------------------------ */ 465 /*MC 466 TS_RK - ODE solver using the explicit Runge-Kutta methods 467 468 Options Database: 469 . -ts_rk_tol <tol> Tolerance for convergence 470 471 Contributed by: Asbjorn Hoiland Aarrestad, asbjorn@aarrestad.com, http://asbjorn.aarrestad.com/ 472 473 Level: beginner 474 475 .seealso: TSCreate(), TS, TSSetType(), TS_EULER, TSRKSetTolerance() 476 477 M*/ 478 479 EXTERN_C_BEGIN 480 #undef __FUNCT__ 481 #define __FUNCT__ "TSCreate_Rk" 482 PetscErrorCode TSCreate_Rk(TS ts) 483 { 484 TS_Rk *rk; 485 PetscErrorCode ierr; 486 487 PetscFunctionBegin; 488 ts->ops->setup = TSSetUp_Rk; 489 ts->ops->step = TSStep_Rk; 490 ts->ops->destroy = TSDestroy_Rk; 491 ts->ops->setfromoptions = TSSetFromOptions_Rk; 492 ts->ops->view = TSView_Rk; 493 494 ierr = PetscNew(TS_Rk,&rk);CHKERRQ(ierr); 495 PetscLogObjectMemory(ts,sizeof(TS_Rk)); 496 ts->data = (void*)rk; 497 498 ierr = PetscObjectComposeFunctionDynamic((PetscObject)ts,"TSRKSetTolerance_C","TSRKSetTolerance_RK", 499 TSRKSetTolerance_RK);CHKERRQ(ierr); 500 501 PetscFunctionReturn(0); 502 } 503 EXTERN_C_END 504 505 506 507 508