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