1 /* 2 Code for time stepping with the Runge-Kutta method 3 4 Notes: 5 The general system is written as 6 7 Udot = F(t,U) 8 9 */ 10 #include <petsc-private/tsimpl.h> /*I "petscts.h" I*/ 11 #include <petscdm.h> 12 13 static TSRKType TSRKDefault = TSRK3BS; 14 static PetscBool TSRKRegisterAllCalled; 15 static PetscBool TSRKPackageInitialized; 16 static PetscInt explicit_stage_time_id; 17 18 typedef struct _RKTableau *RKTableau; 19 struct _RKTableau { 20 char *name; 21 PetscInt order; /* Classical approximation order of the method i */ 22 PetscInt s; /* Number of stages */ 23 PetscBool FSAL; /* flag to indicate if tableau is FSAL */ 24 PetscInt pinterp; /* Interpolation order */ 25 PetscReal *A,*b,*c; /* Tableau */ 26 PetscReal *bembed; /* Embedded formula of order one less (order-1) */ 27 PetscReal *binterp; /* Dense output formula */ 28 PetscReal ccfl; /* Placeholder for CFL coefficient relative to forward Euler */ 29 }; 30 typedef struct _RKTableauLink *RKTableauLink; 31 struct _RKTableauLink { 32 struct _RKTableau tab; 33 RKTableauLink next; 34 }; 35 static RKTableauLink RKTableauList; 36 37 typedef struct { 38 RKTableau tableau; 39 Vec *Y; /* States computed during the step */ 40 Vec *YdotRHS; /* Function evaluations for the non-stiff part */ 41 Vec *VecDeltaLam; /* Increment of the adjoint sensitivity w.r.t IC at stage*/ 42 Vec *VecDeltaMu; /* Increment of the adjoint sensitivity w.r.t P at stage*/ 43 Vec *VecSensiTemp; /* Vector to be timed with Jacobian transpose*/ 44 PetscScalar *work; /* Scalar work */ 45 PetscReal stage_time; 46 TSStepStatus status; 47 } TS_RK; 48 49 /*MC 50 TSRK1 - First order forward Euler scheme. 51 52 This method has one stage. 53 54 Level: advanced 55 56 .seealso: TSRK 57 M*/ 58 /*MC 59 TSRK2A - Second order RK scheme. 60 61 This method has two stages. 62 63 Level: advanced 64 65 .seealso: TSRK 66 M*/ 67 /*MC 68 TSRK3 - Third order RK scheme. 69 70 This method has three stages. 71 72 Level: advanced 73 74 .seealso: TSRK 75 M*/ 76 /*MC 77 TSRK3BS - Third order RK scheme of Bogacki-Shampine with 2nd order embedded method. 78 79 This method has four stages. 80 81 Level: advanced 82 83 .seealso: TSRK 84 M*/ 85 /*MC 86 TSRK4 - Fourth order RK scheme. 87 88 This is the classical Runge-Kutta method with four stages. 89 90 Level: advanced 91 92 .seealso: TSRK 93 M*/ 94 /*MC 95 TSRK5F - Fifth order Fehlberg RK scheme with a 4th order embedded method. 96 97 This method has six stages. 98 99 Level: advanced 100 101 .seealso: TSRK 102 M*/ 103 /*MC 104 TSRK5DP - Fifth order Dormand-Prince RK scheme with the 4th order embedded method. 105 106 This method has seven stages. 107 108 Level: advanced 109 110 .seealso: TSRK 111 M*/ 112 113 #undef __FUNCT__ 114 #define __FUNCT__ "TSRKRegisterAll" 115 /*@C 116 TSRKRegisterAll - Registers all of the Runge-Kutta explicit methods in TSRK 117 118 Not Collective, but should be called by all processes which will need the schemes to be registered 119 120 Level: advanced 121 122 .keywords: TS, TSRK, register, all 123 124 .seealso: TSRKRegisterDestroy() 125 @*/ 126 PetscErrorCode TSRKRegisterAll(void) 127 { 128 PetscErrorCode ierr; 129 130 PetscFunctionBegin; 131 if (TSRKRegisterAllCalled) PetscFunctionReturn(0); 132 TSRKRegisterAllCalled = PETSC_TRUE; 133 134 { 135 const PetscReal 136 A[1][1] = {{0.0}}, 137 b[1] = {1.0}; 138 ierr = TSRKRegister(TSRK1FE,1,1,&A[0][0],b,NULL,NULL,1,b);CHKERRQ(ierr); 139 } 140 { 141 const PetscReal 142 A[2][2] = {{0.0,0.0}, 143 {1.0,0.0}}, 144 b[2] = {0.5,0.5}, 145 bembed[2] = {1.0,0}; 146 ierr = TSRKRegister(TSRK2A,2,2,&A[0][0],b,NULL,bembed,2,b);CHKERRQ(ierr); 147 } 148 { 149 const PetscReal 150 A[3][3] = {{0,0,0}, 151 {2.0/3.0,0,0}, 152 {-1.0/3.0,1.0,0}}, 153 b[3] = {0.25,0.5,0.25}; 154 ierr = TSRKRegister(TSRK3,3,3,&A[0][0],b,NULL,NULL,3,b);CHKERRQ(ierr); 155 } 156 { 157 const PetscReal 158 A[4][4] = {{0,0,0,0}, 159 {1.0/2.0,0,0,0}, 160 {0,3.0/4.0,0,0}, 161 {2.0/9.0,1.0/3.0,4.0/9.0,0}}, 162 b[4] = {2.0/9.0,1.0/3.0,4.0/9.0,0}, 163 bembed[4] = {7.0/24.0,1.0/4.0,1.0/3.0,1.0/8.0}; 164 ierr = TSRKRegister(TSRK3BS,3,4,&A[0][0],b,NULL,bembed,3,b);CHKERRQ(ierr); 165 } 166 { 167 const PetscReal 168 A[4][4] = {{0,0,0,0}, 169 {0.5,0,0,0}, 170 {0,0.5,0,0}, 171 {0,0,1.0,0}}, 172 b[4] = {1.0/6.0,1.0/3.0,1.0/3.0,1.0/6.0}; 173 ierr = TSRKRegister(TSRK4,4,4,&A[0][0],b,NULL,NULL,4,b);CHKERRQ(ierr); 174 } 175 { 176 const PetscReal 177 A[6][6] = {{0,0,0,0,0,0}, 178 {0.25,0,0,0,0,0}, 179 {3.0/32.0,9.0/32.0,0,0,0,0}, 180 {1932.0/2197.0,-7200.0/2197.0,7296.0/2197.0,0,0,0}, 181 {439.0/216.0,-8.0,3680.0/513.0,-845.0/4104.0,0,0}, 182 {-8.0/27.0,2.0,-3544.0/2565.0,1859.0/4104.0,-11.0/40.0,0}}, 183 b[6] = {16.0/135.0,0,6656.0/12825.0,28561.0/56430.0,-9.0/50.0,2.0/55.0}, 184 bembed[6] = {25.0/216.0,0,1408.0/2565.0,2197.0/4104.0,-1.0/5.0,0}; 185 ierr = TSRKRegister(TSRK5F,5,6,&A[0][0],b,NULL,bembed,5,b);CHKERRQ(ierr); 186 } 187 { 188 const PetscReal 189 A[7][7] = {{0,0,0,0,0,0,0}, 190 {1.0/5.0,0,0,0,0,0,0}, 191 {3.0/40.0,9.0/40.0,0,0,0,0,0}, 192 {44.0/45.0,-56.0/15.0,32.0/9.0,0,0,0,0}, 193 {19372.0/6561.0,-25360.0/2187.0,64448.0/6561.0,-212.0/729.0,0,0,0}, 194 {9017.0/3168.0,-355.0/33.0,46732.0/5247.0,49.0/176.0,-5103.0/18656.0,0,0}, 195 {35.0/384.0,0,500.0/1113.0,125.0/192.0,-2187.0/6784.0,11.0/84.0,0}}, 196 b[7] = {35.0/384.0,0,500.0/1113.0,125.0/192.0,-2187.0/6784.0,11.0/84.0,0}, 197 bembed[7] = {5179.0/57600.0,0,7571.0/16695.0,393.0/640.0,-92097.0/339200.0,187.0/2100.0,1.0/40.0}; 198 ierr = TSRKRegister(TSRK5DP,5,7,&A[0][0],b,NULL,bembed,5,b);CHKERRQ(ierr); 199 } 200 PetscFunctionReturn(0); 201 } 202 203 #undef __FUNCT__ 204 #define __FUNCT__ "TSRKRegisterDestroy" 205 /*@C 206 TSRKRegisterDestroy - Frees the list of schemes that were registered by TSRKRegister(). 207 208 Not Collective 209 210 Level: advanced 211 212 .keywords: TSRK, register, destroy 213 .seealso: TSRKRegister(), TSRKRegisterAll() 214 @*/ 215 PetscErrorCode TSRKRegisterDestroy(void) 216 { 217 PetscErrorCode ierr; 218 RKTableauLink link; 219 220 PetscFunctionBegin; 221 while ((link = RKTableauList)) { 222 RKTableau t = &link->tab; 223 RKTableauList = link->next; 224 ierr = PetscFree3(t->A,t->b,t->c); CHKERRQ(ierr); 225 ierr = PetscFree (t->bembed); CHKERRQ(ierr); 226 ierr = PetscFree (t->binterp); CHKERRQ(ierr); 227 ierr = PetscFree (t->name); CHKERRQ(ierr); 228 ierr = PetscFree (link); CHKERRQ(ierr); 229 } 230 TSRKRegisterAllCalled = PETSC_FALSE; 231 PetscFunctionReturn(0); 232 } 233 234 #undef __FUNCT__ 235 #define __FUNCT__ "TSRKInitializePackage" 236 /*@C 237 TSRKInitializePackage - This function initializes everything in the TSRK package. It is called 238 from PetscDLLibraryRegister() when using dynamic libraries, and on the first call to TSCreate_RK() 239 when using static libraries. 240 241 Level: developer 242 243 .keywords: TS, TSRK, initialize, package 244 .seealso: PetscInitialize() 245 @*/ 246 PetscErrorCode TSRKInitializePackage(void) 247 { 248 PetscErrorCode ierr; 249 250 PetscFunctionBegin; 251 if (TSRKPackageInitialized) PetscFunctionReturn(0); 252 TSRKPackageInitialized = PETSC_TRUE; 253 ierr = TSRKRegisterAll();CHKERRQ(ierr); 254 ierr = PetscObjectComposedDataRegister(&explicit_stage_time_id);CHKERRQ(ierr); 255 ierr = PetscRegisterFinalize(TSRKFinalizePackage);CHKERRQ(ierr); 256 PetscFunctionReturn(0); 257 } 258 259 #undef __FUNCT__ 260 #define __FUNCT__ "TSRKFinalizePackage" 261 /*@C 262 TSRKFinalizePackage - This function destroys everything in the TSRK package. It is 263 called from PetscFinalize(). 264 265 Level: developer 266 267 .keywords: Petsc, destroy, package 268 .seealso: PetscFinalize() 269 @*/ 270 PetscErrorCode TSRKFinalizePackage(void) 271 { 272 PetscErrorCode ierr; 273 274 PetscFunctionBegin; 275 TSRKPackageInitialized = PETSC_FALSE; 276 ierr = TSRKRegisterDestroy();CHKERRQ(ierr); 277 PetscFunctionReturn(0); 278 } 279 280 #undef __FUNCT__ 281 #define __FUNCT__ "TSRKRegister" 282 /*@C 283 TSRKRegister - register an RK scheme by providing the entries in the Butcher tableau and optionally embedded approximations and interpolation 284 285 Not Collective, but the same schemes should be registered on all processes on which they will be used 286 287 Input Parameters: 288 + name - identifier for method 289 . order - approximation order of method 290 . s - number of stages, this is the dimension of the matrices below 291 . A - stage coefficients (dimension s*s, row-major) 292 . b - step completion table (dimension s; NULL to use last row of A) 293 . c - abscissa (dimension s; NULL to use row sums of A) 294 . bembed - completion table for embedded method (dimension s; NULL if not available) 295 . pinterp - Order of the interpolation scheme, equal to the number of columns of binterp 296 - binterp - Coefficients of the interpolation formula (dimension s*pinterp; NULL to reuse binterpt) 297 298 Notes: 299 Several RK methods are provided, this function is only needed to create new methods. 300 301 Level: advanced 302 303 .keywords: TS, register 304 305 .seealso: TSRK 306 @*/ 307 PetscErrorCode TSRKRegister(TSRKType name,PetscInt order,PetscInt s, 308 const PetscReal A[],const PetscReal b[],const PetscReal c[], 309 const PetscReal bembed[], 310 PetscInt pinterp,const PetscReal binterp[]) 311 { 312 PetscErrorCode ierr; 313 RKTableauLink link; 314 RKTableau t; 315 PetscInt i,j; 316 317 PetscFunctionBegin; 318 ierr = PetscMalloc(sizeof(*link),&link);CHKERRQ(ierr); 319 ierr = PetscMemzero(link,sizeof(*link));CHKERRQ(ierr); 320 t = &link->tab; 321 ierr = PetscStrallocpy(name,&t->name);CHKERRQ(ierr); 322 t->order = order; 323 t->s = s; 324 ierr = PetscMalloc3(s*s,&t->A,s,&t->b,s,&t->c);CHKERRQ(ierr); 325 ierr = PetscMemcpy(t->A,A,s*s*sizeof(A[0]));CHKERRQ(ierr); 326 if (b) { ierr = PetscMemcpy(t->b,b,s*sizeof(b[0]));CHKERRQ(ierr); } 327 else for (i=0; i<s; i++) t->b[i] = A[(s-1)*s+i]; 328 if (c) { ierr = PetscMemcpy(t->c,c,s*sizeof(c[0]));CHKERRQ(ierr); } 329 else for (i=0; i<s; i++) for (j=0,t->c[i]=0; j<s; j++) t->c[i] += A[i*s+j]; 330 t->FSAL = PETSC_TRUE; 331 for (i=0; i<s; i++) if (t->A[(s-1)*s+i] != t->b[i]) t->FSAL = PETSC_FALSE; 332 if (bembed) { 333 ierr = PetscMalloc1(s,&t->bembed);CHKERRQ(ierr); 334 ierr = PetscMemcpy(t->bembed,bembed,s*sizeof(bembed[0]));CHKERRQ(ierr); 335 } 336 337 t->pinterp = pinterp; 338 ierr = PetscMalloc1(s*pinterp,&t->binterp);CHKERRQ(ierr); 339 ierr = PetscMemcpy(t->binterp,binterp,s*pinterp*sizeof(binterp[0]));CHKERRQ(ierr); 340 link->next = RKTableauList; 341 RKTableauList = link; 342 PetscFunctionReturn(0); 343 } 344 345 #undef __FUNCT__ 346 #define __FUNCT__ "TSEvaluateStep_RK" 347 /* 348 The step completion formula is 349 350 x1 = x0 + h b^T YdotRHS 351 352 This function can be called before or after ts->vec_sol has been updated. 353 Suppose we have a completion formula (b) and an embedded formula (be) of different order. 354 We can write 355 356 x1e = x0 + h be^T YdotRHS 357 = x1 - h b^T YdotRHS + h be^T YdotRHS 358 = x1 + h (be - b)^T YdotRHS 359 360 so we can evaluate the method with different order even after the step has been optimistically completed. 361 */ 362 static PetscErrorCode TSEvaluateStep_RK(TS ts,PetscInt order,Vec X,PetscBool *done) 363 { 364 TS_RK *rk = (TS_RK*)ts->data; 365 RKTableau tab = rk->tableau; 366 PetscScalar *w = rk->work; 367 PetscReal h; 368 PetscInt s = tab->s,j; 369 PetscErrorCode ierr; 370 371 PetscFunctionBegin; 372 switch (rk->status) { 373 case TS_STEP_INCOMPLETE: 374 case TS_STEP_PENDING: 375 h = ts->time_step; break; 376 case TS_STEP_COMPLETE: 377 h = ts->time_step_prev; break; 378 default: SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_PLIB,"Invalid TSStepStatus"); 379 } 380 if (order == tab->order) { 381 if (rk->status == TS_STEP_INCOMPLETE) { 382 ierr = VecCopy(ts->vec_sol,X);CHKERRQ(ierr); 383 for (j=0; j<s; j++) w[j] = h*tab->b[j]; 384 ierr = VecMAXPY(X,s,w,rk->YdotRHS);CHKERRQ(ierr); 385 } else {ierr = VecCopy(ts->vec_sol,X);CHKERRQ(ierr);} 386 PetscFunctionReturn(0); 387 } else if (order == tab->order-1) { 388 if (!tab->bembed) goto unavailable; 389 if (rk->status == TS_STEP_INCOMPLETE) { /* Complete with the embedded method (be) */ 390 ierr = VecCopy(ts->vec_sol,X);CHKERRQ(ierr); 391 for (j=0; j<s; j++) w[j] = h*tab->bembed[j]; 392 ierr = VecMAXPY(X,s,w,rk->YdotRHS);CHKERRQ(ierr); 393 } else { /* Rollback and re-complete using (be-b) */ 394 ierr = VecCopy(ts->vec_sol,X);CHKERRQ(ierr); 395 for (j=0; j<s; j++) w[j] = h*(tab->bembed[j] - tab->b[j]); 396 ierr = VecMAXPY(X,s,w,rk->YdotRHS);CHKERRQ(ierr); 397 } 398 if (done) *done = PETSC_TRUE; 399 PetscFunctionReturn(0); 400 } 401 unavailable: 402 if (done) *done = PETSC_FALSE; 403 else SETERRQ3(PetscObjectComm((PetscObject)ts),PETSC_ERR_SUP,"RK '%s' of order %D cannot evaluate step at order %D",tab->name,tab->order,order); 404 PetscFunctionReturn(0); 405 } 406 407 #undef __FUNCT__ 408 #define __FUNCT__ "TSStep_RK" 409 static PetscErrorCode TSStep_RK(TS ts) 410 { 411 TS_RK *rk = (TS_RK*)ts->data; 412 RKTableau tab = rk->tableau; 413 const PetscInt s = tab->s; 414 const PetscReal *A = tab->A,*b = tab->b,*c = tab->c; 415 PetscScalar *w = rk->work; 416 Vec *Y = rk->Y,*YdotRHS = rk->YdotRHS; 417 TSAdapt adapt; 418 PetscInt i,j,reject,next_scheme; 419 PetscReal next_time_step; 420 PetscReal t; 421 PetscBool accept; 422 PetscErrorCode ierr; 423 424 PetscFunctionBegin; 425 426 next_time_step = ts->time_step; 427 t = ts->ptime; 428 accept = PETSC_TRUE; 429 rk->status = TS_STEP_INCOMPLETE; 430 431 432 for (reject=0; reject<ts->max_reject && !ts->reason; reject++,ts->reject++) { 433 PetscReal h = ts->time_step; 434 ierr = TSPreStep(ts);CHKERRQ(ierr); 435 for (i=0; i<s; i++) { 436 rk->stage_time = t + h*c[i]; 437 ierr = TSPreStage(ts,rk->stage_time); CHKERRQ(ierr); 438 ierr = VecCopy(ts->vec_sol,Y[i]);CHKERRQ(ierr); 439 for (j=0; j<i; j++) w[j] = h*A[i*s+j]; 440 ierr = VecMAXPY(Y[i],i,w,YdotRHS);CHKERRQ(ierr); 441 ierr = TSPostStage(ts,rk->stage_time,i,Y); CHKERRQ(ierr); 442 ierr = TSGetAdapt(ts,&adapt);CHKERRQ(ierr); 443 ierr = TSAdaptCheckStage(adapt,ts,&accept);CHKERRQ(ierr); 444 if (!accept) goto reject_step; 445 ierr = TSComputeRHSFunction(ts,t+h*c[i],Y[i],YdotRHS[i]);CHKERRQ(ierr); 446 } 447 ierr = TSEvaluateStep(ts,tab->order,ts->vec_sol,NULL);CHKERRQ(ierr); 448 rk->status = TS_STEP_PENDING; 449 450 /* Register only the current method as a candidate because we're not supporting multiple candidates yet. */ 451 ierr = TSGetAdapt(ts,&adapt);CHKERRQ(ierr); 452 ierr = TSAdaptCandidatesClear(adapt);CHKERRQ(ierr); 453 ierr = TSAdaptCandidateAdd(adapt,tab->name,tab->order,1,tab->ccfl,1.*tab->s,PETSC_TRUE);CHKERRQ(ierr); 454 ierr = TSAdaptChoose(adapt,ts,ts->time_step,&next_scheme,&next_time_step,&accept);CHKERRQ(ierr); 455 if (accept) { 456 /* ignore next_scheme for now */ 457 ts->ptime += ts->time_step; 458 ts->time_step = next_time_step; 459 ts->steps++; 460 rk->status = TS_STEP_COMPLETE; 461 ierr = PetscObjectComposedDataSetReal((PetscObject)ts->vec_sol,explicit_stage_time_id,ts->ptime);CHKERRQ(ierr); 462 break; 463 } else { /* Roll back the current step */ 464 for (j=0; j<s; j++) w[j] = -h*b[j]; 465 ierr = VecMAXPY(ts->vec_sol,s,w,rk->YdotRHS);CHKERRQ(ierr); 466 ts->time_step = next_time_step; 467 rk->status = TS_STEP_INCOMPLETE; 468 } 469 reject_step: continue; 470 } 471 if (rk->status != TS_STEP_COMPLETE && !ts->reason) ts->reason = TS_DIVERGED_STEP_REJECTED; 472 PetscFunctionReturn(0); 473 } 474 475 #undef __FUNCT__ 476 #define __FUNCT__ "TSStepAdj_RK" 477 static PetscErrorCode TSStepAdj_RK(TS ts) 478 { 479 TS_RK *rk = (TS_RK*)ts->data; 480 RKTableau tab = rk->tableau; 481 const PetscInt s = tab->s; 482 const PetscReal *A = tab->A,*b = tab->b,*c = tab->c; 483 PetscScalar *w = rk->work; 484 Vec *Y = rk->Y,*VecDeltaLam = rk->VecDeltaLam,*VecDeltaMu = rk->VecDeltaMu,*VecSensiTemp = rk->VecSensiTemp; 485 PetscInt i,j,nadj; 486 PetscReal t; 487 PetscErrorCode ierr; 488 489 PetscFunctionBegin; 490 491 /*ierr = TSStep_RK(ts);CHKERRQ(ierr); // reuse TSStep */ 492 493 t = ts->ptime; 494 rk->status = TS_STEP_INCOMPLETE; 495 PetscReal h = ts->time_step; 496 ierr = TSPreStep(ts);CHKERRQ(ierr); 497 for (i=s-1; i>=0; i--) { 498 Mat J,Jp; 499 rk->stage_time = t + h*(1.0-c[i]); 500 for (nadj=0; nadj<ts->numberadjs; nadj++) { 501 ierr = VecCopy(ts->vecs_sensi[nadj],VecSensiTemp[nadj]);CHKERRQ(ierr); 502 ierr = VecScale(VecSensiTemp[nadj],-h*b[i]); 503 for (j=i+1; j<s; j++) { 504 ierr = VecAXPY(VecSensiTemp[nadj],-h*A[j*s+i],VecDeltaLam[nadj*s+j]); 505 } 506 } 507 /* Stage values of lambda */ 508 ierr = TSGetRHSJacobian(ts,&J,&Jp,NULL,NULL);CHKERRQ(ierr); 509 ierr = TSComputeRHSJacobian(ts,rk->stage_time,Y[i],J,Jp);CHKERRQ(ierr); 510 for (nadj=0; nadj<ts->numberadjs; nadj++) { 511 ierr = MatMultTranspose(J,VecSensiTemp[nadj],VecDeltaLam[nadj*s+i]);CHKERRQ(ierr); 512 } 513 514 /* Stage values of mu */ 515 if(ts->vecs_sensip) { 516 ierr = TSRHSJacobianP(ts,rk->stage_time,Y[i],ts->Jacp);CHKERRQ(ierr); 517 for (nadj=0; nadj<ts->numberadjs; nadj++) { 518 ierr = MatMultTranspose(ts->Jacp,VecSensiTemp[nadj],VecDeltaMu[nadj*s+i]);CHKERRQ(ierr); 519 } 520 } 521 } 522 523 for (j=0; j<s; j++) w[j] = 1.0; 524 for (nadj=0; nadj<ts->numberadjs; nadj++) { 525 ierr = VecMAXPY(ts->vecs_sensi[nadj],s,w,&VecDeltaLam[nadj*s]);CHKERRQ(ierr); 526 if(ts->vecs_sensip) { 527 ierr = VecMAXPY(ts->vecs_sensip[nadj],s,w,&VecDeltaMu[nadj*s]);CHKERRQ(ierr); 528 } 529 } 530 ts->ptime += ts->time_step; 531 ts->steps++; 532 rk->status = TS_STEP_COMPLETE; 533 ierr = PetscObjectComposedDataSetReal((PetscObject)ts->vecs_sensi,explicit_stage_time_id,ts->ptime);CHKERRQ(ierr); 534 if(ts->vecs_sensip) { 535 ierr = PetscObjectComposedDataSetReal((PetscObject)ts->vecs_sensip,explicit_stage_time_id,ts->ptime);CHKERRQ(ierr); 536 } 537 PetscFunctionReturn(0); 538 } 539 540 #undef __FUNCT__ 541 #define __FUNCT__ "TSInterpolate_RK" 542 static PetscErrorCode TSInterpolate_RK(TS ts,PetscReal itime,Vec X) 543 { 544 TS_RK *rk = (TS_RK*)ts->data; 545 PetscInt s = rk->tableau->s,pinterp = rk->tableau->pinterp,i,j; 546 PetscReal h; 547 PetscReal tt,t; 548 PetscScalar *b; 549 const PetscReal *B = rk->tableau->binterp; 550 PetscErrorCode ierr; 551 552 PetscFunctionBegin; 553 if (!B) SETERRQ1(PetscObjectComm((PetscObject)ts),PETSC_ERR_SUP,"TSRK %s does not have an interpolation formula",rk->tableau->name); 554 switch (rk->status) { 555 case TS_STEP_INCOMPLETE: 556 case TS_STEP_PENDING: 557 h = ts->time_step; 558 t = (itime - ts->ptime)/h; 559 break; 560 case TS_STEP_COMPLETE: 561 h = ts->time_step_prev; 562 t = (itime - ts->ptime)/h + 1; /* In the interval [0,1] */ 563 break; 564 default: SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_PLIB,"Invalid TSStepStatus"); 565 } 566 ierr = PetscMalloc1(s,&b);CHKERRQ(ierr); 567 for (i=0; i<s; i++) b[i] = 0; 568 for (j=0,tt=t; j<pinterp; j++,tt*=t) { 569 for (i=0; i<s; i++) { 570 b[i] += h * B[i*pinterp+j] * tt; 571 } 572 } 573 ierr = VecCopy(rk->Y[0],X);CHKERRQ(ierr); 574 ierr = VecMAXPY(X,s,b,rk->YdotRHS);CHKERRQ(ierr); 575 ierr = PetscFree(b);CHKERRQ(ierr); 576 PetscFunctionReturn(0); 577 } 578 579 /*------------------------------------------------------------*/ 580 #undef __FUNCT__ 581 #define __FUNCT__ "TSReset_RK" 582 static PetscErrorCode TSReset_RK(TS ts) 583 { 584 TS_RK *rk = (TS_RK*)ts->data; 585 PetscInt s; 586 PetscErrorCode ierr; 587 588 PetscFunctionBegin; 589 if (!rk->tableau) PetscFunctionReturn(0); 590 s = rk->tableau->s; 591 ierr = VecDestroyVecs(s,&rk->Y);CHKERRQ(ierr); 592 ierr = VecDestroyVecs(s,&rk->YdotRHS);CHKERRQ(ierr); 593 if(ts->reverse_mode) { 594 ierr = VecDestroyVecs(s*ts->numberadjs,&rk->VecDeltaLam);CHKERRQ(ierr); 595 if(rk->VecDeltaMu) { 596 ierr = VecDestroyVecs(s*ts->numberadjs,&rk->VecDeltaMu);CHKERRQ(ierr); 597 } 598 ierr = VecDestroyVecs(ts->numberadjs,&rk->VecSensiTemp);CHKERRQ(ierr); 599 } 600 ierr = PetscFree(rk->work);CHKERRQ(ierr); 601 PetscFunctionReturn(0); 602 } 603 604 #undef __FUNCT__ 605 #define __FUNCT__ "TSDestroy_RK" 606 static PetscErrorCode TSDestroy_RK(TS ts) 607 { 608 PetscErrorCode ierr; 609 610 PetscFunctionBegin; 611 ierr = TSReset_RK(ts);CHKERRQ(ierr); 612 ierr = PetscFree(ts->data);CHKERRQ(ierr); 613 ierr = PetscObjectComposeFunction((PetscObject)ts,"TSRKGetType_C",NULL);CHKERRQ(ierr); 614 ierr = PetscObjectComposeFunction((PetscObject)ts,"TSRKSetType_C",NULL);CHKERRQ(ierr); 615 PetscFunctionReturn(0); 616 } 617 618 619 #undef __FUNCT__ 620 #define __FUNCT__ "DMCoarsenHook_TSRK" 621 static PetscErrorCode DMCoarsenHook_TSRK(DM fine,DM coarse,void *ctx) 622 { 623 PetscFunctionBegin; 624 PetscFunctionReturn(0); 625 } 626 627 #undef __FUNCT__ 628 #define __FUNCT__ "DMRestrictHook_TSRK" 629 static PetscErrorCode DMRestrictHook_TSRK(DM fine,Mat restrct,Vec rscale,Mat inject,DM coarse,void *ctx) 630 { 631 PetscFunctionBegin; 632 PetscFunctionReturn(0); 633 } 634 635 636 #undef __FUNCT__ 637 #define __FUNCT__ "DMSubDomainHook_TSRK" 638 static PetscErrorCode DMSubDomainHook_TSRK(DM dm,DM subdm,void *ctx) 639 { 640 PetscFunctionBegin; 641 PetscFunctionReturn(0); 642 } 643 644 #undef __FUNCT__ 645 #define __FUNCT__ "DMSubDomainRestrictHook_TSRK" 646 static PetscErrorCode DMSubDomainRestrictHook_TSRK(DM dm,VecScatter gscat,VecScatter lscat,DM subdm,void *ctx) 647 { 648 649 PetscFunctionBegin; 650 PetscFunctionReturn(0); 651 } 652 /* 653 #undef __FUNCT__ 654 #define __FUNCT__ "RKSetAdjCoe" 655 static PetscErrorCode RKSetAdjCoe(RKTableau tab) 656 { 657 PetscReal *A,*b; 658 PetscInt s,i,j; 659 PetscErrorCode ierr; 660 661 PetscFunctionBegin; 662 s = tab->s; 663 ierr = PetscMalloc2(s*s,&A,s,&b);CHKERRQ(ierr); 664 665 for (i=0; i<s; i++) 666 for (j=0; j<s; j++) { 667 A[i*s+j] = (tab->b[s-1-i]==0) ? 0: -tab->A[s-1-i+(s-1-j)*s] * tab->b[s-1-j] / tab->b[s-1-i]; 668 ierr = PetscPrintf(PETSC_COMM_WORLD,"Coefficients: A[%D][%D]=%.6f\n",i,j,A[i*s+j]);CHKERRQ(ierr); 669 } 670 671 for (i=0; i<s; i++) b[i] = (tab->b[s-1-i]==0)? 0: -tab->b[s-1-i]; 672 673 ierr = PetscMemcpy(tab->A,A,s*s*sizeof(A[0]));CHKERRQ(ierr); 674 ierr = PetscMemcpy(tab->b,b,s*sizeof(b[0]));CHKERRQ(ierr); 675 ierr = PetscFree2(A,b);CHKERRQ(ierr); 676 PetscFunctionReturn(0); 677 } 678 */ 679 #undef __FUNCT__ 680 #define __FUNCT__ "TSSetUp_RK" 681 static PetscErrorCode TSSetUp_RK(TS ts) 682 { 683 TS_RK *rk = (TS_RK*)ts->data; 684 RKTableau tab; 685 PetscInt s; 686 PetscErrorCode ierr; 687 DM dm; 688 689 PetscFunctionBegin; 690 if (!rk->tableau) { 691 ierr = TSRKSetType(ts,TSRKDefault);CHKERRQ(ierr); 692 } 693 tab = rk->tableau; 694 s = tab->s; 695 /* old */ 696 /*if (ts->reverse_mode) { 697 ierr = RKSetAdjCoe(tab);CHKERRQ(ierr); 698 }*/ 699 ierr = VecDuplicateVecs(ts->vec_sol,s,&rk->Y);CHKERRQ(ierr); 700 ierr = VecDuplicateVecs(ts->vec_sol,s,&rk->YdotRHS);CHKERRQ(ierr); 701 if (ts->reverse_mode) { 702 ierr = VecDuplicateVecs(ts->vecs_sensi[0],s*ts->numberadjs,&rk->VecDeltaLam);CHKERRQ(ierr); 703 if(ts->vecs_sensip) { 704 ierr = VecDuplicateVecs(ts->vecs_sensip[0],s*ts->numberadjs,&rk->VecDeltaMu);CHKERRQ(ierr); 705 } 706 ierr = VecDuplicateVecs(ts->vecs_sensi[0],ts->numberadjs,&rk->VecSensiTemp);CHKERRQ(ierr); 707 } 708 ierr = PetscMalloc1(s,&rk->work);CHKERRQ(ierr); 709 ierr = TSGetDM(ts,&dm);CHKERRQ(ierr); 710 if (dm) { 711 ierr = DMCoarsenHookAdd(dm,DMCoarsenHook_TSRK,DMRestrictHook_TSRK,ts);CHKERRQ(ierr); 712 ierr = DMSubDomainHookAdd(dm,DMSubDomainHook_TSRK,DMSubDomainRestrictHook_TSRK,ts);CHKERRQ(ierr); 713 } 714 PetscFunctionReturn(0); 715 } 716 717 /*------------------------------------------------------------*/ 718 719 #undef __FUNCT__ 720 #define __FUNCT__ "TSSetFromOptions_RK" 721 static PetscErrorCode TSSetFromOptions_RK(PetscOptions *PetscOptionsObject,TS ts) 722 { 723 PetscErrorCode ierr; 724 char rktype[256]; 725 726 PetscFunctionBegin; 727 ierr = PetscOptionsHead(PetscOptionsObject,"RK ODE solver options");CHKERRQ(ierr); 728 { 729 RKTableauLink link; 730 PetscInt count,choice; 731 PetscBool flg; 732 const char **namelist; 733 ierr = PetscStrncpy(rktype,TSRKDefault,sizeof(rktype));CHKERRQ(ierr); 734 for (link=RKTableauList,count=0; link; link=link->next,count++) ; 735 ierr = PetscMalloc1(count,&namelist);CHKERRQ(ierr); 736 for (link=RKTableauList,count=0; link; link=link->next,count++) namelist[count] = link->tab.name; 737 ierr = PetscOptionsEList("-ts_rk_type","Family of RK method","TSRKSetType",(const char*const*)namelist,count,rktype,&choice,&flg);CHKERRQ(ierr); 738 ierr = TSRKSetType(ts,flg ? namelist[choice] : rktype);CHKERRQ(ierr); 739 ierr = PetscFree(namelist);CHKERRQ(ierr); 740 } 741 ierr = PetscOptionsTail();CHKERRQ(ierr); 742 PetscFunctionReturn(0); 743 } 744 745 #undef __FUNCT__ 746 #define __FUNCT__ "PetscFormatRealArray" 747 static PetscErrorCode PetscFormatRealArray(char buf[],size_t len,const char *fmt,PetscInt n,const PetscReal x[]) 748 { 749 PetscErrorCode ierr; 750 PetscInt i; 751 size_t left,count; 752 char *p; 753 754 PetscFunctionBegin; 755 for (i=0,p=buf,left=len; i<n; i++) { 756 ierr = PetscSNPrintfCount(p,left,fmt,&count,x[i]);CHKERRQ(ierr); 757 if (count >= left) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Insufficient space in buffer"); 758 left -= count; 759 p += count; 760 *p++ = ' '; 761 } 762 p[i ? 0 : -1] = 0; 763 PetscFunctionReturn(0); 764 } 765 766 #undef __FUNCT__ 767 #define __FUNCT__ "TSView_RK" 768 static PetscErrorCode TSView_RK(TS ts,PetscViewer viewer) 769 { 770 TS_RK *rk = (TS_RK*)ts->data; 771 RKTableau tab = rk->tableau; 772 PetscBool iascii; 773 PetscErrorCode ierr; 774 TSAdapt adapt; 775 776 PetscFunctionBegin; 777 ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);CHKERRQ(ierr); 778 if (iascii) { 779 TSRKType rktype; 780 char buf[512]; 781 ierr = TSRKGetType(ts,&rktype);CHKERRQ(ierr); 782 ierr = PetscViewerASCIIPrintf(viewer," RK %s\n",rktype);CHKERRQ(ierr); 783 ierr = PetscFormatRealArray(buf,sizeof(buf),"% 8.6f",tab->s,tab->c);CHKERRQ(ierr); 784 ierr = PetscViewerASCIIPrintf(viewer," Abscissa c = %s\n",buf);CHKERRQ(ierr); 785 ierr = PetscViewerASCIIPrintf(viewer,"FSAL: %s\n",tab->FSAL ? "yes" : "no");CHKERRQ(ierr); 786 } 787 ierr = TSGetAdapt(ts,&adapt);CHKERRQ(ierr); 788 ierr = TSAdaptView(adapt,viewer);CHKERRQ(ierr); 789 PetscFunctionReturn(0); 790 } 791 792 #undef __FUNCT__ 793 #define __FUNCT__ "TSLoad_RK" 794 static PetscErrorCode TSLoad_RK(TS ts,PetscViewer viewer) 795 { 796 PetscErrorCode ierr; 797 TSAdapt tsadapt; 798 799 PetscFunctionBegin; 800 ierr = TSGetAdapt(ts,&tsadapt);CHKERRQ(ierr); 801 ierr = TSAdaptLoad(tsadapt,viewer);CHKERRQ(ierr); 802 PetscFunctionReturn(0); 803 } 804 805 #undef __FUNCT__ 806 #define __FUNCT__ "TSRKSetType" 807 /*@C 808 TSRKSetType - Set the type of RK scheme 809 810 Logically collective 811 812 Input Parameter: 813 + ts - timestepping context 814 - rktype - type of RK-scheme 815 816 Level: intermediate 817 818 .seealso: TSRKGetType(), TSRK, TSRK2, TSRK3, TSRKPRSSP2, TSRK4, TSRK5 819 @*/ 820 PetscErrorCode TSRKSetType(TS ts,TSRKType rktype) 821 { 822 PetscErrorCode ierr; 823 824 PetscFunctionBegin; 825 PetscValidHeaderSpecific(ts,TS_CLASSID,1); 826 ierr = PetscTryMethod(ts,"TSRKSetType_C",(TS,TSRKType),(ts,rktype));CHKERRQ(ierr); 827 PetscFunctionReturn(0); 828 } 829 830 #undef __FUNCT__ 831 #define __FUNCT__ "TSRKGetType" 832 /*@C 833 TSRKGetType - Get the type of RK scheme 834 835 Logically collective 836 837 Input Parameter: 838 . ts - timestepping context 839 840 Output Parameter: 841 . rktype - type of RK-scheme 842 843 Level: intermediate 844 845 .seealso: TSRKGetType() 846 @*/ 847 PetscErrorCode TSRKGetType(TS ts,TSRKType *rktype) 848 { 849 PetscErrorCode ierr; 850 851 PetscFunctionBegin; 852 PetscValidHeaderSpecific(ts,TS_CLASSID,1); 853 ierr = PetscUseMethod(ts,"TSRKGetType_C",(TS,TSRKType*),(ts,rktype));CHKERRQ(ierr); 854 PetscFunctionReturn(0); 855 } 856 857 #undef __FUNCT__ 858 #define __FUNCT__ "TSRKGetType_RK" 859 PetscErrorCode TSRKGetType_RK(TS ts,TSRKType *rktype) 860 { 861 TS_RK *rk = (TS_RK*)ts->data; 862 PetscErrorCode ierr; 863 864 PetscFunctionBegin; 865 if (!rk->tableau) { 866 ierr = TSRKSetType(ts,TSRKDefault);CHKERRQ(ierr); 867 } 868 *rktype = rk->tableau->name; 869 PetscFunctionReturn(0); 870 } 871 #undef __FUNCT__ 872 #define __FUNCT__ "TSRKSetType_RK" 873 PetscErrorCode TSRKSetType_RK(TS ts,TSRKType rktype) 874 { 875 TS_RK *rk = (TS_RK*)ts->data; 876 PetscErrorCode ierr; 877 PetscBool match; 878 RKTableauLink link; 879 880 PetscFunctionBegin; 881 if (rk->tableau) { 882 ierr = PetscStrcmp(rk->tableau->name,rktype,&match);CHKERRQ(ierr); 883 if (match) PetscFunctionReturn(0); 884 } 885 for (link = RKTableauList; link; link=link->next) { 886 ierr = PetscStrcmp(link->tab.name,rktype,&match);CHKERRQ(ierr); 887 if (match) { 888 ierr = TSReset_RK(ts);CHKERRQ(ierr); 889 rk->tableau = &link->tab; 890 PetscFunctionReturn(0); 891 } 892 } 893 SETERRQ1(PetscObjectComm((PetscObject)ts),PETSC_ERR_ARG_UNKNOWN_TYPE,"Could not find '%s'",rktype); 894 PetscFunctionReturn(0); 895 } 896 897 #undef __FUNCT__ 898 #define __FUNCT__ "TSGetStages_RK" 899 static PetscErrorCode TSGetStages_RK(TS ts,PetscInt *ns,Vec **Y) 900 { 901 TS_RK *rk = (TS_RK*)ts->data; 902 903 PetscFunctionBegin; 904 *ns = rk->tableau->s; 905 if(Y) *Y = rk->Y; 906 PetscFunctionReturn(0); 907 } 908 909 910 /* ------------------------------------------------------------ */ 911 /*MC 912 TSRK - ODE and DAE solver using Runge-Kutta schemes 913 914 The user should provide the right hand side of the equation 915 using TSSetRHSFunction(). 916 917 Notes: 918 The default is TSRK3, it can be changed with TSRKSetType() or -ts_rk_type 919 920 Level: beginner 921 922 .seealso: TSCreate(), TS, TSSetType(), TSRKSetType(), TSRKGetType(), TSRKSetFullyImplicit(), TSRK2D, TTSRK2E, TSRK3, 923 TSRK4, TSRK5, TSRKPRSSP2, TSRKBPR3, TSRKType, TSRKRegister() 924 925 M*/ 926 #undef __FUNCT__ 927 #define __FUNCT__ "TSCreate_RK" 928 PETSC_EXTERN PetscErrorCode TSCreate_RK(TS ts) 929 { 930 TS_RK *th; 931 PetscErrorCode ierr; 932 933 PetscFunctionBegin; 934 #if !defined(PETSC_USE_DYNAMIC_LIBRARIES) 935 ierr = TSRKInitializePackage();CHKERRQ(ierr); 936 #endif 937 938 ts->ops->reset = TSReset_RK; 939 ts->ops->destroy = TSDestroy_RK; 940 ts->ops->view = TSView_RK; 941 ts->ops->load = TSLoad_RK; 942 ts->ops->setup = TSSetUp_RK; 943 ts->ops->step = TSStep_RK; 944 ts->ops->interpolate = TSInterpolate_RK; 945 ts->ops->evaluatestep = TSEvaluateStep_RK; 946 ts->ops->setfromoptions = TSSetFromOptions_RK; 947 ts->ops->getstages = TSGetStages_RK; 948 ts->ops->stepadj = TSStepAdj_RK; 949 950 ierr = PetscNewLog(ts,&th);CHKERRQ(ierr); 951 ts->data = (void*)th; 952 953 ierr = PetscObjectComposeFunction((PetscObject)ts,"TSRKGetType_C",TSRKGetType_RK);CHKERRQ(ierr); 954 ierr = PetscObjectComposeFunction((PetscObject)ts,"TSRKSetType_C",TSRKSetType_RK);CHKERRQ(ierr); 955 PetscFunctionReturn(0); 956 } 957