1 /*$Id: rk.c,v 0.1 2003/06/03 Asbjorn Hoiland Aarrestad$*/ 2 /* 3 * Code for Timestepping with Runge Kutta 4 * 5 * Written by 6 * Asbjorn Hoiland Aarrestad 7 * asbjorn@aarrestad.com 8 * http://asbjorn.aarrestad.com/ 9 * 10 */ 11 #include "src/ts/tsimpl.h" /*I "petscts.h" I*/ 12 #include "time.h" 13 14 typedef struct { 15 Vec y1,y2; /* work wectors for the two rk permuations */ 16 int nok,nnok; /* counters for ok and not ok steps */ 17 PetscReal maxerror; /* variable to tell the maxerror allowed */ 18 PetscReal ferror; /* variable to tell (global maxerror)/(total time) */ 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 28 29 #undef __FUNCT__ 30 #define __FUNCT__ "TSSetUp_Rk" 31 static int TSSetUp_Rk(TS ts) 32 { 33 TS_Rk *rk = (TS_Rk*)ts->data; 34 int ierr; 35 36 PetscFunctionBegin; 37 rk->nok = 0; 38 rk->nnok = 0; 39 rk->maxerror = ts->time_step; 40 41 /* fixing maxerror: global vs local */ 42 rk->ferror = rk->maxerror / (ts->max_time - ts->ptime); 43 44 /* 34.0/45.0 gives double precision division */ 45 /* defining variables needed for Runge-Kutta computing */ 46 /* when changing below, please remember to change a, b1, b2 and c above! */ 47 /* Found in table on page 171: Dormand-Prince 5(4) */ 48 49 /* are these right? */ 50 rk->p=6; 51 rk->s=7; 52 53 rk->a[1][0]=1.0/5.0; 54 rk->a[2][0]=3.0/40.0; 55 rk->a[2][1]=9.0/40.0; 56 rk->a[3][0]=44.0/45.0; 57 rk->a[3][1]=-56.0/15.0; 58 rk->a[3][2]=32.0/9.0; 59 rk->a[4][0]=19372.0/6561.0; 60 rk->a[4][1]=-25360.0/2187.0; 61 rk->a[4][2]=64448.0/6561.0; 62 rk->a[4][3]=-212.0/729.0; 63 rk->a[5][0]=9017.0/3168.0; 64 rk->a[5][1]=-355.0/33.0; 65 rk->a[5][2]=46732.0/5247.0; 66 rk->a[5][3]=49.0/176.0; 67 rk->a[5][4]=-5103.0/18656.0; 68 rk->a[6][0]=35.0/384.0; 69 rk->a[6][1]=0.0; 70 rk->a[6][2]=500.0/1113.0; 71 rk->a[6][3]=125.0/192.0; 72 rk->a[6][4]=-2187.0/6784.0; 73 rk->a[6][5]=11.0/84.0; 74 75 76 rk->c[0]=0.0; 77 rk->c[1]=1.0/5.0; 78 rk->c[2]=3.0/10.0; 79 rk->c[3]=4.0/5.0; 80 rk->c[4]=8.0/9.0; 81 rk->c[5]=1.0; 82 rk->c[6]=1.0; 83 84 rk->b1[0]=35.0/384.0; 85 rk->b1[1]=0.0; 86 rk->b1[2]=500.0/1113.0; 87 rk->b1[3]=125.0/192.0; 88 rk->b1[4]=-2187.0/6784.0; 89 rk->b1[5]=11.0/84.0; 90 rk->b1[6]=0.0; 91 92 rk->b2[0]=5179.0/57600.0; 93 rk->b2[1]=0.0; 94 rk->b2[2]=7571.0/16695.0; 95 rk->b2[3]=393.0/640.0; 96 rk->b2[4]=-92097.0/339200.0; 97 rk->b2[5]=187.0/2100.0; 98 rk->b2[6]=1.0/40.0; 99 100 101 /* Found in table on page 170: Fehlberg 4(5) */ 102 /* 103 rk->p=5; 104 rk->s=6; 105 106 rk->a[1][0]=1.0/4.0; 107 rk->a[2][0]=3.0/32.0; 108 rk->a[2][1]=9.0/32.0; 109 rk->a[3][0]=1932.0/2197.0; 110 rk->a[3][1]=-7200.0/2197.0; 111 rk->a[3][2]=7296.0/2197.0; 112 rk->a[4][0]=439.0/216.0; 113 rk->a[4][1]=-8.0; 114 rk->a[4][2]=3680.0/513.0; 115 rk->a[4][3]=-845.0/4104.0; 116 rk->a[5][0]=-8.0/27.0; 117 rk->a[5][1]=2.0; 118 rk->a[5][2]=-3544.0/2565.0; 119 rk->a[5][3]=1859.0/4104.0; 120 rk->a[5][4]=-11.0/40.0; 121 122 rk->c[0]=0.0; 123 rk->c[1]=1.0/4.0; 124 rk->c[2]=3.0/8.0; 125 rk->c[3]=12.0/13.0; 126 rk->c[4]=1.0; 127 rk->c[5]=1.0/2.0; 128 129 rk->b1[0]=25.0/216.0; 130 rk->b1[1]=0.0; 131 rk->b1[2]=1408.0/2565.0; 132 rk->b1[3]=2197.0/4104.0; 133 rk->b1[4]=-1.0/5.0; 134 rk->b1[5]=0.0; 135 136 rk->b2[0]=16.0/135.0; 137 rk->b2[1]=0.0; 138 rk->b2[2]=6656.0/12825.0; 139 rk->b2[3]=28561.0/56430.0; 140 rk->b2[4]=-9.0/50.0; 141 rk->b2[5]=2.0/55.0; 142 */ 143 /* Found in table on page 169: Merson 4("5") */ 144 /* 145 rk->p=4; 146 rk->s=5; 147 rk->a[1][0] = 1.0/3.0; 148 rk->a[2][0] = 1.0/6.0; 149 rk->a[2][1] = 1.0/6.0; 150 rk->a[3][0] = 1.0/8.0; 151 rk->a[3][1] = 0.0; 152 rk->a[3][2] = 3.0/8.0; 153 rk->a[4][0] = 1.0/2.0; 154 rk->a[4][1] = 0.0; 155 rk->a[4][2] = -3.0/2.0; 156 rk->a[4][3] = 2.0; 157 158 rk->c[0] = 0.0; 159 rk->c[1] = 1.0/3.0; 160 rk->c[2] = 1.0/3.0; 161 rk->c[3] = 0.5; 162 rk->c[4] = 1.0; 163 164 rk->b1[0] = 1.0/2.0; 165 rk->b1[1] = 0.0; 166 rk->b1[2] = -3.0/2.0; 167 rk->b1[3] = 2.0; 168 rk->b1[4] = 0.0; 169 170 rk->b2[0] = 1.0/6.0; 171 rk->b2[1] = 0.0; 172 rk->b2[2] = 0.0; 173 rk->b2[3] = 2.0/3.0; 174 rk->b2[4] = 1.0/6.0; 175 */ 176 177 /* making b2 -> e=b1-b2 */ 178 /* 179 for(i=0;i<rk->s;i++){ 180 rk->b2[i] = (rk->b1[i]) - (rk->b2[i]); 181 } 182 */ 183 rk->b2[0]=71.0/57600.0; 184 rk->b2[1]=0.0; 185 rk->b2[2]=-71.0/16695.0; 186 rk->b2[3]=71.0/1920.0; 187 rk->b2[4]=-17253.0/339200.0; 188 rk->b2[5]=22.0/525.0; 189 rk->b2[6]=-1.0/40.0; 190 191 /* initializing vectors */ 192 ierr = VecDuplicate(ts->vec_sol,&rk->y1);CHKERRQ(ierr); 193 ierr = VecDuplicate(ts->vec_sol,&rk->y2);CHKERRQ(ierr); 194 ierr = VecDuplicate(rk->y1,&rk->tmp);CHKERRQ(ierr); 195 ierr = VecDuplicate(rk->y1,&rk->tmp_y);CHKERRQ(ierr); 196 ierr = VecDuplicateVecs(rk->y1,rk->s,&rk->k);CHKERRQ(ierr); 197 198 PetscFunctionReturn(0); 199 } 200 201 #undef __FUNCT__ 202 #define __FUNCT__ "TSStep_Rk" 203 static int TSStep_Rk(TS ts,int *steps,PetscReal *ptime) 204 { 205 TS_Rk *rk = (TS_Rk*)ts->data; 206 int ierr; 207 PetscReal dt = 0.001; /* fixed first step guess */ 208 PetscReal norm=0.0,dt_fac=0.0,fac = 0.0,ttmp=0.0; 209 210 PetscFunctionBegin; 211 rk->start=clock(); 212 ierr=VecCopy(ts->vec_sol,rk->y1);CHKERRQ(ierr); 213 *steps = -ts->steps; 214 /* trying to save the vector */ 215 ierr = TSMonitor(ts,ts->steps,ts->ptime,ts->vec_sol);CHKERRQ(ierr); 216 /* while loop to get from start to stop */ 217 while (ts->ptime < ts->max_time){ 218 /* calling rkqs */ 219 /* 220 -- input 221 ts - pointer to ts 222 ts->ptime - current time 223 dt - try this timestep 224 y1 - solution for this step 225 226 --output 227 y1 - suggested solution 228 y2 - check solution (runge - kutta second permutation) 229 */ 230 ierr = TSRkqs(ts,ts->ptime,dt);CHKERRQ(ierr); 231 /* checking for maxerror */ 232 /* comparing difference to maxerror */ 233 ierr = VecNorm(rk->y2,NORM_2,&norm);CHKERRQ(ierr); 234 /* modifying maxerror to satisfy this timestep */ 235 rk->maxerror = rk->ferror * dt; 236 /* ierr = PetscPrintf(PETSC_COMM_WORLD,"norm err: %f maxerror: %f dt: %f",norm,rk->maxerror,dt);CHKERRQ(ierr); */ 237 238 /* handling ok and not ok */ 239 if(norm < rk->maxerror){ 240 /* if ok: */ 241 ierr=VecCopy(rk->y1,ts->vec_sol);CHKERRQ(ierr); /* saves the suggested solution to current solution */ 242 ts->ptime += dt; /* storing the new current time */ 243 rk->nok++; 244 fac=5.0; 245 /* trying to save the vector */ 246 /* calling monitor */ 247 ierr = TSMonitor(ts,ts->steps,ts->ptime,ts->vec_sol);CHKERRQ(ierr); 248 }else{ 249 /* if not OK */ 250 rk->nnok++; 251 fac=1.0; 252 ierr=VecCopy(ts->vec_sol,rk->y1);CHKERRQ(ierr); /* restores old solution */ 253 } 254 255 /*Computing next stepsize. See page 167 in Solving ODE 1 256 * 257 * h_new = h * min( facmax , max( facmin , fac * (tol/err)^(1/(p+1)) ) ) 258 * facmax set above 259 * facmin 260 */ 261 dt_fac = exp(log((rk->maxerror) / norm) / ((rk->p) + 1) ) * 0.9 ; 262 263 if(dt_fac > fac){ 264 /*ierr = PetscPrintf(PETSC_COMM_WORLD,"changing fac %f\n",fac);*/ 265 dt_fac = fac; 266 } 267 268 /* computing new dt */ 269 dt = dt * dt_fac; 270 271 if(ts->ptime+dt > ts->max_time){ 272 dt = ts->max_time - ts->ptime; 273 } 274 275 if(dt < 1e-14){ 276 ierr = PetscPrintf(PETSC_COMM_WORLD,"Very small steps: %f\n",dt);CHKERRQ(ierr); 277 dt = 1e-14; 278 } 279 280 /* trying to purify h */ 281 /* (did not give any visible result) */ 282 /* ttmp = ts->ptime + dt; 283 dt = ttmp - ts->ptime; */ 284 285 /* counting steps */ 286 ts->steps++; 287 } 288 289 ierr=VecCopy(rk->y1,ts->vec_sol);CHKERRQ(ierr); 290 *steps += ts->steps; 291 *ptime = ts->ptime; 292 rk->end=clock(); 293 PetscFunctionReturn(0); 294 } 295 /*------------------------------------------------------------*/ 296 #undef __FUNCT__ 297 #define __FUNCT__ "TSRkqs" 298 int TSRkqs(TS ts,PetscReal t,PetscReal h) 299 { 300 TS_Rk *rk = (TS_Rk*)ts->data; 301 int ierr,j,l; 302 PetscReal tmp_t=t; 303 PetscScalar null=0.0,hh=h; 304 305 /* printf("h: %f, hh: %f",h,hh); */ 306 307 PetscFunctionBegin; 308 309 /* k[0]=0 */ 310 ierr = VecSet(&null,rk->k[0]);CHKERRQ(ierr); 311 312 /* k[0] = derivs(t,y1) */ 313 ierr = TSComputeRHSFunction(ts,t,rk->y1,rk->k[0]);CHKERRQ(ierr); 314 /* looping over runge-kutta variables */ 315 /* building the k - array of vectors */ 316 for(j = 1 ; j < rk->s ; j++){ 317 318 /* rk->tmp = 0 */ 319 ierr = VecSet(&null,rk->tmp);CHKERRQ(ierr); 320 321 for(l=0;l<j;l++){ 322 /* tmp += a(j,l)*k[l] */ 323 /* ierr = PetscPrintf(PETSC_COMM_WORLD,"a(%i,%i)=%f \n",j,l,rk->a[j][l]);CHKERRQ(ierr); */ 324 ierr = VecAXPY(&rk->a[j][l],rk->k[l],rk->tmp);CHKERRQ(ierr); 325 } 326 327 /* ierr = VecView(rk->tmp,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr); */ 328 329 /* k[j] = derivs(t+c(j)*h,y1+h*tmp,k(j)) */ 330 /* I need the following helpers: 331 PetscScalar tmp_t=t+c(j)*h 332 Vec tmp_y=h*tmp+y1 333 */ 334 335 tmp_t = t + rk->c[j] * h; 336 337 /* tmp_y = h * tmp + y1 */ 338 ierr = VecWAXPY(&hh,rk->tmp,rk->y1,rk->tmp_y);CHKERRQ(ierr); 339 340 /* rk->k[j]=0 */ 341 ierr = VecSet(&null,rk->k[j]);CHKERRQ(ierr); 342 ierr = TSComputeRHSFunction(ts,tmp_t,rk->tmp_y,rk->k[j]);CHKERRQ(ierr); 343 } 344 345 /* tmp=0 and tmp_y=0 */ 346 ierr = VecSet(&null,rk->tmp);CHKERRQ(ierr); 347 ierr = VecSet(&null,rk->tmp_y);CHKERRQ(ierr); 348 349 for(j = 0 ; j < rk->s ; j++){ 350 /* tmp=b1[j]*k[j]+tmp */ 351 ierr = VecAXPY(&rk->b1[j],rk->k[j],rk->tmp);CHKERRQ(ierr); 352 /* tmp_y=b2[j]*k[j]+tmp_y */ 353 ierr = VecAXPY(&rk->b2[j],rk->k[j],rk->tmp_y);CHKERRQ(ierr); 354 } 355 356 /* y2 = hh * tmp_y */ 357 ierr = VecSet(&null,rk->y2);CHKERRQ(ierr); 358 ierr = VecAXPY(&hh,rk->tmp_y,rk->y2);CHKERRQ(ierr); 359 /* y1 = hh*tmp + y1 */ 360 ierr = VecAXPY(&hh,rk->tmp,rk->y1);CHKERRQ(ierr); 361 /* Finding difference between y1 and y2 */ 362 363 PetscFunctionReturn(0); 364 } 365 366 /*------------------------------------------------------------*/ 367 #undef __FUNCT__ 368 #define __FUNCT__ "TSDestroy_Rk" 369 static int TSDestroy_Rk(TS ts) 370 { 371 TS_Rk *rk = (TS_Rk*)ts->data; 372 int i,ierr; 373 374 /* REMEMBER TO DESTROY ALL */ 375 376 PetscFunctionBegin; 377 if (rk->y1) {ierr = VecDestroy(rk->y1);CHKERRQ(ierr);} 378 if (rk->y2) {ierr = VecDestroy(rk->y2);CHKERRQ(ierr);} 379 if (rk->tmp) {ierr = VecDestroy(rk->tmp);CHKERRQ(ierr);} 380 if (rk->tmp_y) {ierr = VecDestroy(rk->tmp_y);CHKERRQ(ierr);} 381 for(i=0;i<rk->s;i++){ 382 if (rk->k[i]) {ierr = VecDestroy(rk->k[i]);CHKERRQ(ierr);} 383 } 384 ierr = PetscFree(rk);CHKERRQ(ierr); 385 PetscFunctionReturn(0); 386 } 387 /*------------------------------------------------------------*/ 388 389 #undef __FUNCT__ 390 #define __FUNCT__ "TSSetFromOptions_Rk" 391 static int TSSetFromOptions_Rk(TS ts) 392 { 393 PetscFunctionBegin; 394 PetscFunctionReturn(0); 395 } 396 397 #undef __FUNCT__ 398 #define __FUNCT__ "TSView_Rk" 399 static int TSView_Rk(TS ts,PetscViewer viewer) 400 { 401 TS_Rk *rk = (TS_Rk*)ts->data; 402 int ierr; 403 double elapsed; 404 405 PetscFunctionBegin; 406 ierr = PetscPrintf(PETSC_COMM_WORLD," number of ok steps: %d\n",rk->nok);CHKERRQ(ierr); 407 ierr = PetscPrintf(PETSC_COMM_WORLD," number of rejected steps: %d\n",rk->nnok);CHKERRQ(ierr); 408 /* elapsed = ((double) (rk->end - rk->start)) / CLOCKS_PER_SEC; 409 410 ierr = PetscPrintf(PETSC_COMM_WORLD," CPU time used (in seconds): %f\n",elapsed);CHKERRQ(ierr); */ 411 PetscFunctionReturn(0); 412 } 413 414 /* ------------------------------------------------------------ */ 415 EXTERN_C_BEGIN 416 #undef __FUNCT__ 417 #define __FUNCT__ "TSCreate_Rk" 418 int TSCreate_Rk(TS ts) 419 { 420 TS_Rk *rk; 421 int ierr; 422 423 PetscFunctionBegin; 424 ts->ops->setup = TSSetUp_Rk; 425 ts->ops->step = TSStep_Rk; 426 ts->ops->destroy = TSDestroy_Rk; 427 ts->ops->setfromoptions = TSSetFromOptions_Rk; 428 ts->ops->view = TSView_Rk; 429 430 ierr = PetscNew(TS_Rk,&rk);CHKERRQ(ierr); 431 PetscLogObjectMemory(ts,sizeof(TS_Rk)); 432 ts->data = (void*)rk; 433 434 PetscFunctionReturn(0); 435 } 436 EXTERN_C_END 437 438 439 440 441