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__ "TSAdjointSetUp_RK" 477 static PetscErrorCode TSAdjointSetUp_RK(TS ts) 478 { 479 TS_RK *rk = (TS_RK*)ts->data; 480 RKTableau tab; 481 PetscInt s; 482 PetscErrorCode ierr; 483 484 PetscFunctionBegin; 485 if (ts->adjointsetupcalled++) PetscFunctionReturn(0); 486 tab = rk->tableau; 487 s = tab->s; 488 ierr = VecDuplicateVecs(ts->vecs_sensi[0],s*ts->numcost,&rk->VecDeltaLam);CHKERRQ(ierr); 489 if(ts->vecs_sensip) { 490 ierr = VecDuplicateVecs(ts->vecs_sensip[0],s*ts->numcost,&rk->VecDeltaMu);CHKERRQ(ierr); 491 } 492 ierr = VecDuplicateVecs(ts->vecs_sensi[0],ts->numcost,&rk->VecSensiTemp);CHKERRQ(ierr); 493 PetscFunctionReturn(0); 494 } 495 496 #undef __FUNCT__ 497 #define __FUNCT__ "TSAdjointStep_RK" 498 static PetscErrorCode TSAdjointStep_RK(TS ts) 499 { 500 TS_RK *rk = (TS_RK*)ts->data; 501 RKTableau tab = rk->tableau; 502 const PetscInt s = tab->s; 503 const PetscReal *A = tab->A,*b = tab->b,*c = tab->c; 504 PetscScalar *w = rk->work; 505 Vec *Y = rk->Y,*VecDeltaLam = rk->VecDeltaLam,*VecDeltaMu = rk->VecDeltaMu,*VecSensiTemp = rk->VecSensiTemp; 506 PetscInt i,j,nadj; 507 PetscReal t; 508 PetscErrorCode ierr; 509 PetscReal h = ts->time_step; 510 Mat J,Jp; 511 512 PetscFunctionBegin; 513 t = ts->ptime; 514 rk->status = TS_STEP_INCOMPLETE; 515 h = ts->time_step; 516 ierr = TSPreStep(ts);CHKERRQ(ierr); 517 for (i=s-1; i>=0; i--) { 518 rk->stage_time = t + h*(1.0-c[i]); 519 for (nadj=0; nadj<ts->numcost; nadj++) { 520 ierr = VecCopy(ts->vecs_sensi[nadj],VecSensiTemp[nadj]);CHKERRQ(ierr); 521 ierr = VecScale(VecSensiTemp[nadj],-h*b[i]); 522 for (j=i+1; j<s; j++) { 523 ierr = VecAXPY(VecSensiTemp[nadj],-h*A[j*s+i],VecDeltaLam[nadj*s+j]); 524 } 525 } 526 /* Stage values of lambda */ 527 ierr = TSGetRHSJacobian(ts,&J,&Jp,NULL,NULL);CHKERRQ(ierr); 528 ierr = TSComputeRHSJacobian(ts,rk->stage_time,Y[i],J,Jp);CHKERRQ(ierr); 529 for (nadj=0; nadj<ts->numcost; nadj++) { 530 ierr = MatMultTranspose(J,VecSensiTemp[nadj],VecDeltaLam[nadj*s+i]);CHKERRQ(ierr); 531 } 532 533 /* Stage values of mu */ 534 if(ts->vecs_sensip) { 535 ierr = TSAdjointComputeRHSJacobian(ts,rk->stage_time,Y[i],ts->Jacp);CHKERRQ(ierr); 536 for (nadj=0; nadj<ts->numcost; nadj++) { 537 ierr = MatMultTranspose(ts->Jacp,VecSensiTemp[nadj],VecDeltaMu[nadj*s+i]);CHKERRQ(ierr); 538 } 539 } 540 } 541 542 for (j=0; j<s; j++) w[j] = 1.0; 543 for (nadj=0; nadj<ts->numcost; nadj++) { 544 ierr = VecMAXPY(ts->vecs_sensi[nadj],s,w,&VecDeltaLam[nadj*s]);CHKERRQ(ierr); 545 if(ts->vecs_sensip) { 546 ierr = VecMAXPY(ts->vecs_sensip[nadj],s,w,&VecDeltaMu[nadj*s]);CHKERRQ(ierr); 547 } 548 } 549 ts->ptime += ts->time_step; 550 ts->steps++; 551 rk->status = TS_STEP_COMPLETE; 552 PetscFunctionReturn(0); 553 } 554 555 #undef __FUNCT__ 556 #define __FUNCT__ "TSInterpolate_RK" 557 static PetscErrorCode TSInterpolate_RK(TS ts,PetscReal itime,Vec X) 558 { 559 TS_RK *rk = (TS_RK*)ts->data; 560 PetscInt s = rk->tableau->s,pinterp = rk->tableau->pinterp,i,j; 561 PetscReal h; 562 PetscReal tt,t; 563 PetscScalar *b; 564 const PetscReal *B = rk->tableau->binterp; 565 PetscErrorCode ierr; 566 567 PetscFunctionBegin; 568 if (!B) SETERRQ1(PetscObjectComm((PetscObject)ts),PETSC_ERR_SUP,"TSRK %s does not have an interpolation formula",rk->tableau->name); 569 switch (rk->status) { 570 case TS_STEP_INCOMPLETE: 571 case TS_STEP_PENDING: 572 h = ts->time_step; 573 t = (itime - ts->ptime)/h; 574 break; 575 case TS_STEP_COMPLETE: 576 h = ts->time_step_prev; 577 t = (itime - ts->ptime)/h + 1; /* In the interval [0,1] */ 578 break; 579 default: SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_PLIB,"Invalid TSStepStatus"); 580 } 581 ierr = PetscMalloc1(s,&b);CHKERRQ(ierr); 582 for (i=0; i<s; i++) b[i] = 0; 583 for (j=0,tt=t; j<pinterp; j++,tt*=t) { 584 for (i=0; i<s; i++) { 585 b[i] += h * B[i*pinterp+j] * tt; 586 } 587 } 588 ierr = VecCopy(rk->Y[0],X);CHKERRQ(ierr); 589 ierr = VecMAXPY(X,s,b,rk->YdotRHS);CHKERRQ(ierr); 590 ierr = PetscFree(b);CHKERRQ(ierr); 591 PetscFunctionReturn(0); 592 } 593 594 /*------------------------------------------------------------*/ 595 #undef __FUNCT__ 596 #define __FUNCT__ "TSReset_RK" 597 static PetscErrorCode TSReset_RK(TS ts) 598 { 599 TS_RK *rk = (TS_RK*)ts->data; 600 PetscInt s; 601 PetscErrorCode ierr; 602 603 PetscFunctionBegin; 604 if (!rk->tableau) PetscFunctionReturn(0); 605 s = rk->tableau->s; 606 ierr = VecDestroyVecs(s,&rk->Y);CHKERRQ(ierr); 607 ierr = VecDestroyVecs(s,&rk->YdotRHS);CHKERRQ(ierr); 608 ierr = VecDestroyVecs(s*ts->numcost,&rk->VecDeltaLam);CHKERRQ(ierr); 609 ierr = VecDestroyVecs(s*ts->numcost,&rk->VecDeltaMu);CHKERRQ(ierr); 610 ierr = VecDestroyVecs(ts->numcost,&rk->VecSensiTemp);CHKERRQ(ierr); 611 ierr = PetscFree(rk->work);CHKERRQ(ierr); 612 PetscFunctionReturn(0); 613 } 614 615 #undef __FUNCT__ 616 #define __FUNCT__ "TSDestroy_RK" 617 static PetscErrorCode TSDestroy_RK(TS ts) 618 { 619 PetscErrorCode ierr; 620 621 PetscFunctionBegin; 622 ierr = TSReset_RK(ts);CHKERRQ(ierr); 623 ierr = PetscFree(ts->data);CHKERRQ(ierr); 624 ierr = PetscObjectComposeFunction((PetscObject)ts,"TSRKGetType_C",NULL);CHKERRQ(ierr); 625 ierr = PetscObjectComposeFunction((PetscObject)ts,"TSRKSetType_C",NULL);CHKERRQ(ierr); 626 PetscFunctionReturn(0); 627 } 628 629 630 #undef __FUNCT__ 631 #define __FUNCT__ "DMCoarsenHook_TSRK" 632 static PetscErrorCode DMCoarsenHook_TSRK(DM fine,DM coarse,void *ctx) 633 { 634 PetscFunctionBegin; 635 PetscFunctionReturn(0); 636 } 637 638 #undef __FUNCT__ 639 #define __FUNCT__ "DMRestrictHook_TSRK" 640 static PetscErrorCode DMRestrictHook_TSRK(DM fine,Mat restrct,Vec rscale,Mat inject,DM coarse,void *ctx) 641 { 642 PetscFunctionBegin; 643 PetscFunctionReturn(0); 644 } 645 646 647 #undef __FUNCT__ 648 #define __FUNCT__ "DMSubDomainHook_TSRK" 649 static PetscErrorCode DMSubDomainHook_TSRK(DM dm,DM subdm,void *ctx) 650 { 651 PetscFunctionBegin; 652 PetscFunctionReturn(0); 653 } 654 655 #undef __FUNCT__ 656 #define __FUNCT__ "DMSubDomainRestrictHook_TSRK" 657 static PetscErrorCode DMSubDomainRestrictHook_TSRK(DM dm,VecScatter gscat,VecScatter lscat,DM subdm,void *ctx) 658 { 659 660 PetscFunctionBegin; 661 PetscFunctionReturn(0); 662 } 663 /* 664 #undef __FUNCT__ 665 #define __FUNCT__ "RKSetAdjCoe" 666 static PetscErrorCode RKSetAdjCoe(RKTableau tab) 667 { 668 PetscReal *A,*b; 669 PetscInt s,i,j; 670 PetscErrorCode ierr; 671 672 PetscFunctionBegin; 673 s = tab->s; 674 ierr = PetscMalloc2(s*s,&A,s,&b);CHKERRQ(ierr); 675 676 for (i=0; i<s; i++) 677 for (j=0; j<s; j++) { 678 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]; 679 ierr = PetscPrintf(PETSC_COMM_WORLD,"Coefficients: A[%D][%D]=%.6f\n",i,j,A[i*s+j]);CHKERRQ(ierr); 680 } 681 682 for (i=0; i<s; i++) b[i] = (tab->b[s-1-i]==0)? 0: -tab->b[s-1-i]; 683 684 ierr = PetscMemcpy(tab->A,A,s*s*sizeof(A[0]));CHKERRQ(ierr); 685 ierr = PetscMemcpy(tab->b,b,s*sizeof(b[0]));CHKERRQ(ierr); 686 ierr = PetscFree2(A,b);CHKERRQ(ierr); 687 PetscFunctionReturn(0); 688 } 689 */ 690 #undef __FUNCT__ 691 #define __FUNCT__ "TSSetUp_RK" 692 static PetscErrorCode TSSetUp_RK(TS ts) 693 { 694 TS_RK *rk = (TS_RK*)ts->data; 695 RKTableau tab; 696 PetscInt s; 697 PetscErrorCode ierr; 698 DM dm; 699 700 PetscFunctionBegin; 701 if (!rk->tableau) { 702 ierr = TSRKSetType(ts,TSRKDefault);CHKERRQ(ierr); 703 } 704 tab = rk->tableau; 705 s = tab->s; 706 ierr = VecDuplicateVecs(ts->vec_sol,s,&rk->Y);CHKERRQ(ierr); 707 ierr = VecDuplicateVecs(ts->vec_sol,s,&rk->YdotRHS);CHKERRQ(ierr); 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 /*------------------------------------------------------------*/ 719 720 #undef __FUNCT__ 721 #define __FUNCT__ "TSSetFromOptions_RK" 722 static PetscErrorCode TSSetFromOptions_RK(PetscOptions *PetscOptionsObject,TS ts) 723 { 724 PetscErrorCode ierr; 725 char rktype[256]; 726 727 PetscFunctionBegin; 728 ierr = PetscOptionsHead(PetscOptionsObject,"RK ODE solver options");CHKERRQ(ierr); 729 { 730 RKTableauLink link; 731 PetscInt count,choice; 732 PetscBool flg; 733 const char **namelist; 734 ierr = PetscStrncpy(rktype,TSRKDefault,sizeof(rktype));CHKERRQ(ierr); 735 for (link=RKTableauList,count=0; link; link=link->next,count++) ; 736 ierr = PetscMalloc1(count,&namelist);CHKERRQ(ierr); 737 for (link=RKTableauList,count=0; link; link=link->next,count++) namelist[count] = link->tab.name; 738 ierr = PetscOptionsEList("-ts_rk_type","Family of RK method","TSRKSetType",(const char*const*)namelist,count,rktype,&choice,&flg);CHKERRQ(ierr); 739 ierr = TSRKSetType(ts,flg ? namelist[choice] : rktype);CHKERRQ(ierr); 740 ierr = PetscFree(namelist);CHKERRQ(ierr); 741 } 742 ierr = PetscOptionsTail();CHKERRQ(ierr); 743 PetscFunctionReturn(0); 744 } 745 746 #undef __FUNCT__ 747 #define __FUNCT__ "PetscFormatRealArray" 748 static PetscErrorCode PetscFormatRealArray(char buf[],size_t len,const char *fmt,PetscInt n,const PetscReal x[]) 749 { 750 PetscErrorCode ierr; 751 PetscInt i; 752 size_t left,count; 753 char *p; 754 755 PetscFunctionBegin; 756 for (i=0,p=buf,left=len; i<n; i++) { 757 ierr = PetscSNPrintfCount(p,left,fmt,&count,x[i]);CHKERRQ(ierr); 758 if (count >= left) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Insufficient space in buffer"); 759 left -= count; 760 p += count; 761 *p++ = ' '; 762 } 763 p[i ? 0 : -1] = 0; 764 PetscFunctionReturn(0); 765 } 766 767 #undef __FUNCT__ 768 #define __FUNCT__ "TSView_RK" 769 static PetscErrorCode TSView_RK(TS ts,PetscViewer viewer) 770 { 771 TS_RK *rk = (TS_RK*)ts->data; 772 RKTableau tab = rk->tableau; 773 PetscBool iascii; 774 PetscErrorCode ierr; 775 TSAdapt adapt; 776 777 PetscFunctionBegin; 778 ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);CHKERRQ(ierr); 779 if (iascii) { 780 TSRKType rktype; 781 char buf[512]; 782 ierr = TSRKGetType(ts,&rktype);CHKERRQ(ierr); 783 ierr = PetscViewerASCIIPrintf(viewer," RK %s\n",rktype);CHKERRQ(ierr); 784 ierr = PetscFormatRealArray(buf,sizeof(buf),"% 8.6f",tab->s,tab->c);CHKERRQ(ierr); 785 ierr = PetscViewerASCIIPrintf(viewer," Abscissa c = %s\n",buf);CHKERRQ(ierr); 786 ierr = PetscViewerASCIIPrintf(viewer,"FSAL: %s\n",tab->FSAL ? "yes" : "no");CHKERRQ(ierr); 787 } 788 ierr = TSGetAdapt(ts,&adapt);CHKERRQ(ierr); 789 ierr = TSAdaptView(adapt,viewer);CHKERRQ(ierr); 790 PetscFunctionReturn(0); 791 } 792 793 #undef __FUNCT__ 794 #define __FUNCT__ "TSLoad_RK" 795 static PetscErrorCode TSLoad_RK(TS ts,PetscViewer viewer) 796 { 797 PetscErrorCode ierr; 798 TSAdapt tsadapt; 799 800 PetscFunctionBegin; 801 ierr = TSGetAdapt(ts,&tsadapt);CHKERRQ(ierr); 802 ierr = TSAdaptLoad(tsadapt,viewer);CHKERRQ(ierr); 803 PetscFunctionReturn(0); 804 } 805 806 #undef __FUNCT__ 807 #define __FUNCT__ "TSRKSetType" 808 /*@C 809 TSRKSetType - Set the type of RK scheme 810 811 Logically collective 812 813 Input Parameter: 814 + ts - timestepping context 815 - rktype - type of RK-scheme 816 817 Level: intermediate 818 819 .seealso: TSRKGetType(), TSRK, TSRK2, TSRK3, TSRKPRSSP2, TSRK4, TSRK5 820 @*/ 821 PetscErrorCode TSRKSetType(TS ts,TSRKType rktype) 822 { 823 PetscErrorCode ierr; 824 825 PetscFunctionBegin; 826 PetscValidHeaderSpecific(ts,TS_CLASSID,1); 827 ierr = PetscTryMethod(ts,"TSRKSetType_C",(TS,TSRKType),(ts,rktype));CHKERRQ(ierr); 828 PetscFunctionReturn(0); 829 } 830 831 #undef __FUNCT__ 832 #define __FUNCT__ "TSRKGetType" 833 /*@C 834 TSRKGetType - Get the type of RK scheme 835 836 Logically collective 837 838 Input Parameter: 839 . ts - timestepping context 840 841 Output Parameter: 842 . rktype - type of RK-scheme 843 844 Level: intermediate 845 846 .seealso: TSRKGetType() 847 @*/ 848 PetscErrorCode TSRKGetType(TS ts,TSRKType *rktype) 849 { 850 PetscErrorCode ierr; 851 852 PetscFunctionBegin; 853 PetscValidHeaderSpecific(ts,TS_CLASSID,1); 854 ierr = PetscUseMethod(ts,"TSRKGetType_C",(TS,TSRKType*),(ts,rktype));CHKERRQ(ierr); 855 PetscFunctionReturn(0); 856 } 857 858 #undef __FUNCT__ 859 #define __FUNCT__ "TSRKGetType_RK" 860 PetscErrorCode TSRKGetType_RK(TS ts,TSRKType *rktype) 861 { 862 TS_RK *rk = (TS_RK*)ts->data; 863 PetscErrorCode ierr; 864 865 PetscFunctionBegin; 866 if (!rk->tableau) { 867 ierr = TSRKSetType(ts,TSRKDefault);CHKERRQ(ierr); 868 } 869 *rktype = rk->tableau->name; 870 PetscFunctionReturn(0); 871 } 872 #undef __FUNCT__ 873 #define __FUNCT__ "TSRKSetType_RK" 874 PetscErrorCode TSRKSetType_RK(TS ts,TSRKType rktype) 875 { 876 TS_RK *rk = (TS_RK*)ts->data; 877 PetscErrorCode ierr; 878 PetscBool match; 879 RKTableauLink link; 880 881 PetscFunctionBegin; 882 if (rk->tableau) { 883 ierr = PetscStrcmp(rk->tableau->name,rktype,&match);CHKERRQ(ierr); 884 if (match) PetscFunctionReturn(0); 885 } 886 for (link = RKTableauList; link; link=link->next) { 887 ierr = PetscStrcmp(link->tab.name,rktype,&match);CHKERRQ(ierr); 888 if (match) { 889 ierr = TSReset_RK(ts);CHKERRQ(ierr); 890 rk->tableau = &link->tab; 891 PetscFunctionReturn(0); 892 } 893 } 894 SETERRQ1(PetscObjectComm((PetscObject)ts),PETSC_ERR_ARG_UNKNOWN_TYPE,"Could not find '%s'",rktype); 895 PetscFunctionReturn(0); 896 } 897 898 #undef __FUNCT__ 899 #define __FUNCT__ "TSGetStages_RK" 900 static PetscErrorCode TSGetStages_RK(TS ts,PetscInt *ns,Vec **Y) 901 { 902 TS_RK *rk = (TS_RK*)ts->data; 903 904 PetscFunctionBegin; 905 *ns = rk->tableau->s; 906 if(Y) *Y = rk->Y; 907 PetscFunctionReturn(0); 908 } 909 910 911 /* ------------------------------------------------------------ */ 912 /*MC 913 TSRK - ODE and DAE solver using Runge-Kutta schemes 914 915 The user should provide the right hand side of the equation 916 using TSSetRHSFunction(). 917 918 Notes: 919 The default is TSRK3, it can be changed with TSRKSetType() or -ts_rk_type 920 921 Level: beginner 922 923 .seealso: TSCreate(), TS, TSSetType(), TSRKSetType(), TSRKGetType(), TSRKSetFullyImplicit(), TSRK2D, TTSRK2E, TSRK3, 924 TSRK4, TSRK5, TSRKPRSSP2, TSRKBPR3, TSRKType, TSRKRegister() 925 926 M*/ 927 #undef __FUNCT__ 928 #define __FUNCT__ "TSCreate_RK" 929 PETSC_EXTERN PetscErrorCode TSCreate_RK(TS ts) 930 { 931 TS_RK *th; 932 PetscErrorCode ierr; 933 934 PetscFunctionBegin; 935 #if !defined(PETSC_USE_DYNAMIC_LIBRARIES) 936 ierr = TSRKInitializePackage();CHKERRQ(ierr); 937 #endif 938 939 ts->ops->reset = TSReset_RK; 940 ts->ops->destroy = TSDestroy_RK; 941 ts->ops->view = TSView_RK; 942 ts->ops->load = TSLoad_RK; 943 ts->ops->setup = TSSetUp_RK; 944 ts->ops->adjointsetup = TSAdjointSetUp_RK; 945 ts->ops->step = TSStep_RK; 946 ts->ops->interpolate = TSInterpolate_RK; 947 ts->ops->evaluatestep = TSEvaluateStep_RK; 948 ts->ops->setfromoptions = TSSetFromOptions_RK; 949 ts->ops->getstages = TSGetStages_RK; 950 ts->ops->adjointstep = TSAdjointStep_RK; 951 952 ierr = PetscNewLog(ts,&th);CHKERRQ(ierr); 953 ts->data = (void*)th; 954 955 ierr = PetscObjectComposeFunction((PetscObject)ts,"TSRKGetType_C",TSRKGetType_RK);CHKERRQ(ierr); 956 ierr = PetscObjectComposeFunction((PetscObject)ts,"TSRKSetType_C",TSRKSetType_RK);CHKERRQ(ierr); 957 PetscFunctionReturn(0); 958 } 959