1 /*$Id: rk.c,v 0.1 2003/03/21 Asbjorn Hoiland Aarrestad$*/ 2 /* 3 Code for Timestepping with Runge Kutta 4 5 Contributed by: Asbj�rn H�iland Aarrestad" <asbjorn@aarrestad.com> 6 */ 7 #include "src/ts/tsimpl.h" /*I "petscts.h" I*/ 8 9 typedef struct { 10 Vec y1,y2; /* work wectors for the two rk permuations */ 11 int nok,nnok; /* counters for ok and not ok steps */ 12 PetscReal maxerror; /* variable to tell the maxerror allowed */ 13 PetscReal ferror; /* variable to tell (global maxerror)/(total time) */ 14 Vec tmp,tmp_y,*k; /* two temp vectors and the k vectors for rk */ 15 PetscScalar a[7][6]; /* rk scalars */ 16 PetscScalar b1[7],b2[7]; /* rk scalars */ 17 PetscReal c[7]; /* rk scalars */ 18 int p,s; /* variables to tell the size of the runge-kutta solver */ 19 } TS_Rk; 20 21 22 23 #undef __FUNCT__ 24 #define __FUNCT__ "TSSetUp_Rk" 25 static int TSSetUp_Rk(TS ts) 26 { 27 TS_Rk *rk = (TS_Rk*)ts->data; 28 int i,j,ierr; 29 30 PetscFunctionBegin; 31 rk->nok = 0; 32 rk->nnok = 0; 33 rk->maxerror = ts->time_step; 34 35 /* fixing maxerror: global vs local */ 36 rk->ferror = rk->maxerror / (ts->max_time - ts->ptime); 37 38 /* 34.0/45.0 gives double precision division */ 39 /* defining variables needed for Runge-Kutta computing */ 40 /* when changing below, please remember to change a, b1, b2 and c above! */ 41 /* Found in table on page 171: Dormand-Prince 5(4) */ 42 43 /* are these right? */ 44 rk->p=6; 45 rk->s=7; 46 47 rk->a[1][0]=1.0/5.0; 48 rk->a[2][0]=3.0/40.0; 49 rk->a[2][1]=9.0/40.0; 50 rk->a[3][0]=44.0/45.0; 51 rk->a[3][1]=-56.0/15.0; 52 rk->a[3][2]=32.0/9.0; 53 rk->a[4][0]=19372.0/6561.0; 54 rk->a[4][1]=-25360.0/2187.0; 55 rk->a[4][2]=64448.0/6561.0; 56 rk->a[4][3]=-212.0/729.0; 57 rk->a[5][0]=9017.0/3168.0; 58 rk->a[5][1]=-355.0/33.0; 59 rk->a[5][2]=46732.0/5247.0; 60 rk->a[5][3]=49.0/176.0; 61 rk->a[5][4]=-5103.0/18656.0; 62 rk->a[6][0]=35.0/384.0; 63 rk->a[6][1]=0.0; 64 rk->a[6][2]=500.0/1113.0; 65 rk->a[6][3]=125.0/192.0; 66 rk->a[6][4]=-2187.0/6784.0; 67 rk->a[6][5]=11.0/84.0; 68 69 70 rk->c[0]=0.0; 71 rk->c[1]=1.0/5.0; 72 rk->c[2]=3.0/10.0; 73 rk->c[3]=4.0/5.0; 74 rk->c[4]=8.0/9.0; 75 rk->c[5]=1.0; 76 rk->c[6]=1.0; 77 78 rk->b1[0]=35.0/384.0; 79 rk->b1[1]=0.0; 80 rk->b1[2]=500.0/1113.0; 81 rk->b1[3]=125.0/192.0; 82 rk->b1[4]=-2187.0/6784.0; 83 rk->b1[5]=11.0/84.0; 84 rk->b1[6]=0.0; 85 86 rk->b2[0]=5179.0/57600.0; 87 rk->b2[1]=0.0; 88 rk->b2[2]=7571.0/16695.0; 89 rk->b2[3]=393.0/640.0; 90 rk->b2[4]=-92097.0/339200.0; 91 rk->b2[5]=187.0/2100.0; 92 rk->b2[6]=1.0/40.0; 93 94 95 /* Found in table on page 170: Fehlberg 4(5) */ 96 /* 97 rk->p=5; 98 rk->s=6; 99 100 rk->a[1][0]=1.0/4.0; 101 rk->a[2][0]=3.0/32.0; 102 rk->a[2][1]=9.0/32.0; 103 rk->a[3][0]=1932.0/2197.0; 104 rk->a[3][1]=-7200.0/2197.0; 105 rk->a[3][2]=7296.0/2197.0; 106 rk->a[4][0]=439.0/216.0; 107 rk->a[4][1]=-8.0; 108 rk->a[4][2]=3680.0/513.0; 109 rk->a[4][3]=-845.0/4104.0; 110 rk->a[5][0]=-8.0/27.0; 111 rk->a[5][1]=2.0; 112 rk->a[5][2]=-3544.0/2565.0; 113 rk->a[5][3]=1859.0/4104.0; 114 rk->a[5][4]=-11.0/40.0; 115 116 rk->c[0]=0.0; 117 rk->c[1]=1.0/4.0; 118 rk->c[2]=3.0/8.0; 119 rk->c[3]=12.0/13.0; 120 rk->c[4]=1.0; 121 rk->c[5]=1.0/2.0; 122 123 rk->b1[0]=25.0/216.0; 124 rk->b1[1]=0.0; 125 rk->b1[2]=1408.0/2565.0; 126 rk->b1[3]=2197.0/4104.0; 127 rk->b1[4]=-1.0/5.0; 128 rk->b1[5]=0.0; 129 130 rk->b2[0]=16.0/135.0; 131 rk->b2[1]=0.0; 132 rk->b2[2]=6656.0/12825.0; 133 rk->b2[3]=28561.0/56430.0; 134 rk->b2[4]=-9.0/50.0; 135 rk->b2[5]=2.0/55.0; 136 */ 137 /* Found in table on page 169: Merson 4("5") */ 138 /* 139 rk->p=4; 140 rk->s=5; 141 rk->a[1][0] = 1.0/3.0; 142 rk->a[2][0] = 1.0/6.0; 143 rk->a[2][1] = 1.0/6.0; 144 rk->a[3][0] = 1.0/8.0; 145 rk->a[3][1] = 0.0; 146 rk->a[3][2] = 3.0/8.0; 147 rk->a[4][0] = 1.0/2.0; 148 rk->a[4][1] = 0.0; 149 rk->a[4][2] = -3.0/2.0; 150 rk->a[4][3] = 2.0; 151 152 rk->c[0] = 0.0; 153 rk->c[1] = 1.0/3.0; 154 rk->c[2] = 1.0/3.0; 155 rk->c[3] = 0.5; 156 rk->c[4] = 1.0; 157 158 rk->b1[0] = 1.0/2.0; 159 rk->b1[1] = 0.0; 160 rk->b1[2] = -3.0/2.0; 161 rk->b1[3] = 2.0; 162 rk->b1[4] = 0.0; 163 164 rk->b2[0] = 1.0/6.0; 165 rk->b2[1] = 0.0; 166 rk->b2[2] = 0.0; 167 rk->b2[3] = 2.0/3.0; 168 rk->b2[4] = 1.0/6.0; 169 */ 170 171 /* making b2 -> e=b1-b2 */ 172 /* 173 for(i=0;i<rk->s;i++){ 174 rk->b2[i] = rk->b1[i] - rk->b2[i]; 175 ierr = PetscPrintf(PETSC_COMM_WORLD,"%f \n",rk->b2[i]);CHKERRQ(ierr); 176 } 177 */ 178 /* initializing vectors */ 179 ierr = VecDuplicate(ts->vec_sol,&rk->y1);CHKERRQ(ierr); 180 ierr = VecDuplicate(ts->vec_sol,&rk->y2);CHKERRQ(ierr); 181 ierr = VecDuplicate(rk->y1,&rk->tmp);CHKERRQ(ierr); 182 ierr = VecDuplicate(rk->y1,&rk->tmp_y);CHKERRQ(ierr); 183 ierr = VecDuplicateVecs(rk->y1,rk->s,&rk->k);CHKERRQ(ierr); 184 185 PetscFunctionReturn(0); 186 } 187 188 #undef __FUNCT__ 189 #define __FUNCT__ "TSStep_Rk" 190 static int TSStep_Rk(TS ts,int *steps,PetscReal *ptime) 191 { 192 TS_Rk *rk = (TS_Rk*)ts->data; 193 int ierr,i,max_steps = ts->max_steps,dill=0; 194 PetscReal dt = 0.001; /* fixed first step guess */ 195 PetscReal norm=0.0,dt_fac=0.0,fac = 0.0,ttmp=0.0; 196 PetscScalar men = -1.0; 197 PetscViewer view; 198 199 ierr = PetscViewerASCIIOpen(PETSC_COMM_WORLD,"out/ch.m",&view);CHKERRQ(ierr); 200 ierr = PetscViewerSetFormat(view,PETSC_VIEWER_ASCII_MATLAB);CHKERRQ(ierr); 201 202 PetscFunctionBegin; 203 204 ierr=VecCopy(ts->vec_sol,rk->y1);CHKERRQ(ierr); 205 *steps = -ts->steps; 206 /* trying to save the vector */ 207 ierr = VecView(rk->y1,view);CHKERRQ(ierr); 208 ierr = TSMonitor(ts,ts->steps,ts->ptime,ts->vec_sol);CHKERRQ(ierr); 209 /* while loop to get from start to stop */ 210 while (ts->ptime < ts->max_time){ 211 /* calling rkqs */ 212 /* 213 -- input 214 ts - pointer to ts 215 ts->ptime - current time 216 dt - try this timestep 217 y1 - solution for this step 218 219 --output 220 y1 - suggested solution 221 y2 - check solution (runge - kutta second permutation) 222 */ 223 ierr = TSRkqs(ts,ts->ptime,dt);CHKERRQ(ierr); 224 /* checking for maxerror */ 225 /* Finding difference between y1 and y2 */ 226 ierr = VecAYPX(&men,rk->y1,rk->y2);CHKERRQ(ierr); /* y2=y1+(-1*y2)*/ 227 228 /* comparing difference to maxerror */ 229 /* CHECK THE NEXT LINE!!!!!!!!! */ 230 ierr = VecNorm(rk->y2,NORM_2,&norm);CHKERRQ(ierr); 231 /* modifying maxerror to satisfy this timestep */ 232 rk->maxerror = rk->ferror * dt; 233 /* ierr = PetscPrintf(PETSC_COMM_WORLD,"norm err: %f maxerror: %f dt: %f",norm,rk->maxerror,dt);CHKERRQ(ierr); */ 234 235 /* handling ok and not ok */ 236 if(norm < rk->maxerror){ 237 /* if ok: */ 238 ierr=VecCopy(rk->y1,ts->vec_sol);CHKERRQ(ierr); /* saves the suggested solution to current solution */ 239 ts->ptime += dt; /* storing the new current time */ 240 rk->nok++; 241 fac=5.0; 242 /* trying to save the vector */ 243 ierr = VecView(rk->y1,view);CHKERRQ(ierr); 244 /* calling monitor */ 245 ierr = TSMonitor(ts,ts->steps,ts->ptime,ts->vec_sol);CHKERRQ(ierr); 246 }else{ 247 /* if not OK */ 248 rk->nnok++; 249 fac=1.0; 250 ierr=VecCopy(ts->vec_sol,rk->y1);CHKERRQ(ierr); /* restores old solution */ 251 } 252 253 /*Computing next stepsize. See page 167 in Solving ODE 1 254 * 255 * h_new = h * min( facmax , max( facmin , fac * (tol/err)^(1/(p+1)) ) ) 256 * facmax set above 257 * facmin 258 */ 259 260 261 262 dt_fac = exp(log((rk->maxerror) / norm) / ((rk->p) + 1) ) * 0.9 ; 263 264 if(dt_fac > fac){ 265 ierr = PetscPrintf(PETSC_COMM_WORLD,"changing fac %f\n",fac); 266 dt_fac = fac; 267 } 268 269 /* computing new dt */ 270 dt = dt * dt_fac; 271 272 if(ts->ptime+dt > ts->max_time){ 273 dt = ts->max_time - ts->ptime; 274 } 275 276 if(dt < 1e-12){ 277 ierr = PetscPrintf(PETSC_COMM_WORLD,"Very small steps: %f\n",dt);CHKERRQ(ierr); 278 dt = 1e-12; 279 } 280 281 /* trying to purify h */ 282 /* (did not give any visible result) */ 283 ttmp = ts->ptime + dt; 284 dt = ttmp - ts->ptime; 285 286 /* counting steps */ 287 ts->steps++; 288 } 289 290 ierr=VecCopy(rk->y1,ts->vec_sol);CHKERRQ(ierr); 291 *steps += ts->steps; 292 *ptime = ts->ptime; 293 294 PetscFunctionReturn(0); 295 } 296 /*------------------------------------------------------------*/ 297 #undef __FUNCT__ 298 #define __FUNCT__ "TSRkqs" 299 int TSRkqs(TS ts,PetscReal t,PetscReal h) 300 { 301 TS_Rk *rk = (TS_Rk*)ts->data; 302 int ierr; 303 PetscReal tmp_t=t; 304 PetscScalar null=0.0,tt=t,hh=h; 305 306 /* printf("h: %f, hh: %f",h,hh); */ 307 308 PetscFunctionBegin; 309 310 /* k[0]=0 */ 311 ierr = VecSet(&null,rk->k[0]);CHKERRQ(ierr); 312 313 /* k[0] = derivs(t,y1) */ 314 ierr = TSComputeRHSFunction(ts,t,rk->y1,rk->k[0]);CHKERRQ(ierr); 315 /* looping over runge-kutta variables */ 316 /* building the k - array of vectors */ 317 for(int j = 1 ; j < rk->s ; j++){ 318 319 /* rk->tmp = 0 */ 320 ierr = VecSet(&null,rk->tmp);CHKERRQ(ierr); 321 322 for(int l=0;l<j-1;l++){ 323 /* tmp += a(j,l)*k[l] */ 324 ierr = VecAXPY(&rk->a[j][l],rk->k[l],rk->tmp);CHKERRQ(ierr); 325 } 326 327 /* k[j] = derivs(t+c(j)*h,y1+h*tmp,k(j)) */ 328 /* I need the following helpers: 329 PetscScalar tmp_t=t+c(j)*h 330 Vec tmp_y=h*tmp+y1 331 */ 332 333 tmp_t = t + rk->c[j] * h; 334 335 /* tmp_y = h * tmp + y1 */ 336 ierr = VecWAXPY(&hh,rk->tmp,rk->y1,rk->tmp_y);CHKERRQ(ierr); 337 338 /* rk->k[j]=0 */ 339 ierr = VecSet(&null,rk->k[j]);CHKERRQ(ierr); 340 ierr = TSComputeRHSFunction(ts,tmp_t,rk->tmp_y,rk->k[j]);CHKERRQ(ierr); 341 } 342 343 /* tmp=0 and tmp_y=0 */ 344 ierr = VecSet(&null,rk->tmp);CHKERRQ(ierr); 345 ierr = VecSet(&null,rk->tmp_y);CHKERRQ(ierr); 346 347 for(int j = 0 ; j < rk->s ; j++){ 348 /* tmp=b1[j]*k[j]+tmp */ 349 ierr = VecAXPY(&rk->b1[j],rk->k[j],rk->tmp);CHKERRQ(ierr); 350 /* tmp_y=b2[j]*k[j]+tmp_y */ 351 ierr = VecAXPY(&rk->b2[j],rk->k[j],rk->tmp_y);CHKERRQ(ierr); 352 } 353 354 355 /* y2 = hh*tmp_y + y1 */ 356 ierr = VecWAXPY(&hh,rk->tmp_y,rk->y1,rk->y2);CHKERRQ(ierr); 357 /* ierr = VecAXPY(&hh,rk->tmp_y,rk->y2);CHKERRQ(ierr);*/ 358 /* y1 = hh*tmp + y1 */ 359 ierr = VecAXPY(&hh,rk->tmp,rk->y1);CHKERRQ(ierr); 360 361 PetscFunctionReturn(0); 362 } 363 364 /*------------------------------------------------------------*/ 365 #undef __FUNCT__ 366 #define __FUNCT__ "TSDestroy_Rk" 367 static int TSDestroy_Rk(TS ts) 368 { 369 TS_Rk *rk = (TS_Rk*)ts->data; 370 int i,ierr; 371 372 /* REMEMBER TO DESTROY ALL */ 373 374 PetscFunctionBegin; 375 if (rk->y1) {ierr = VecDestroy(rk->y1);CHKERRQ(ierr);} 376 if (rk->y2) {ierr = VecDestroy(rk->y2);CHKERRQ(ierr);} 377 if (rk->tmp) {ierr = VecDestroy(rk->tmp);CHKERRQ(ierr);} 378 if (rk->tmp_y) {ierr = VecDestroy(rk->tmp_y);CHKERRQ(ierr);} 379 for(i=0;i<rk->s;i++){ 380 if (rk->k[i]) {ierr = VecDestroy(rk->k[i]);CHKERRQ(ierr);} 381 } 382 ierr = PetscFree(rk);CHKERRQ(ierr); 383 PetscFunctionReturn(0); 384 } 385 /*------------------------------------------------------------*/ 386 387 #undef __FUNCT__ 388 #define __FUNCT__ "TSSetFromOptions_Rk" 389 static int TSSetFromOptions_Rk(TS ts) 390 { 391 PetscFunctionBegin; 392 PetscFunctionReturn(0); 393 } 394 395 #undef __FUNCT__ 396 #define __FUNCT__ "TSView_Rk" 397 static int TSView_Rk(TS ts,PetscViewer viewer) 398 { 399 TS_Rk *rk = (TS_Rk*)ts->data; 400 int ierr; 401 PetscFunctionBegin; 402 ierr = PetscPrintf(PETSC_COMM_WORLD," number of ok steps: %d\n",rk->nok);CHKERRQ(ierr); 403 ierr = PetscPrintf(PETSC_COMM_WORLD," mumber of rejected steps: %d\n",rk->nnok);CHKERRQ(ierr); 404 PetscFunctionReturn(0); 405 } 406 407 /* ------------------------------------------------------------ */ 408 EXTERN_C_BEGIN 409 #undef __FUNCT__ 410 #define __FUNCT__ "TSCreate_Rk" 411 int TSCreate_Rk(TS ts) 412 { 413 TS_Rk *rk; 414 int ierr; 415 416 PetscFunctionBegin; 417 ts->ops->setup = TSSetUp_Rk; 418 ts->ops->step = TSStep_Rk; 419 ts->ops->destroy = TSDestroy_Rk; 420 ts->ops->setfromoptions = TSSetFromOptions_Rk; 421 ts->ops->view = TSView_Rk; 422 423 ierr = PetscNew(TS_Rk,&rk);CHKERRQ(ierr); 424 PetscLogObjectMemory(ts,sizeof(TS_Rk)); 425 ts->data = (void*)rk; 426 427 PetscFunctionReturn(0); 428 } 429 EXTERN_C_END 430 431 432 433 434