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->numberadjs,&rk->VecDeltaLam);CHKERRQ(ierr); 489 if(ts->vecs_sensip) { 490 ierr = VecDuplicateVecs(ts->vecs_sensip[0],s*ts->numberadjs,&rk->VecDeltaMu);CHKERRQ(ierr); 491 } 492 ierr = VecDuplicateVecs(ts->vecs_sensi[0],ts->numberadjs,&rk->VecSensiTemp);CHKERRQ(ierr); 493 PetscFunctionReturn(0); 494 } 495 496 #undef __FUNCT__ 497 #define __FUNCT__ "TSStepAdj_RK" 498 static PetscErrorCode TSStepAdj_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; 509 510 PetscFunctionBegin; 511 t = ts->ptime; 512 rk->status = TS_STEP_INCOMPLETE; 513 PetscReal h = ts->time_step; 514 ierr = TSPreStep(ts);CHKERRQ(ierr); 515 for (i=s-1; i>=0; i--) { 516 Mat J,Jp; 517 rk->stage_time = t + h*(1.0-c[i]); 518 for (nadj=0; nadj<ts->numberadjs; nadj++) { 519 ierr = VecCopy(ts->vecs_sensi[nadj],VecSensiTemp[nadj]);CHKERRQ(ierr); 520 ierr = VecScale(VecSensiTemp[nadj],-h*b[i]); 521 for (j=i+1; j<s; j++) { 522 ierr = VecAXPY(VecSensiTemp[nadj],-h*A[j*s+i],VecDeltaLam[nadj*s+j]); 523 } 524 } 525 /* Stage values of lambda */ 526 ierr = TSGetRHSJacobian(ts,&J,&Jp,NULL,NULL);CHKERRQ(ierr); 527 ierr = TSComputeRHSJacobian(ts,rk->stage_time,Y[i],J,Jp);CHKERRQ(ierr); 528 for (nadj=0; nadj<ts->numberadjs; nadj++) { 529 ierr = MatMultTranspose(J,VecSensiTemp[nadj],VecDeltaLam[nadj*s+i]);CHKERRQ(ierr); 530 } 531 532 /* Stage values of mu */ 533 if(ts->vecs_sensip) { 534 ierr = TSAdjointComputeRHSJacobianP(ts,rk->stage_time,Y[i],ts->Jacp);CHKERRQ(ierr); 535 for (nadj=0; nadj<ts->numberadjs; nadj++) { 536 ierr = MatMultTranspose(ts->Jacp,VecSensiTemp[nadj],VecDeltaMu[nadj*s+i]);CHKERRQ(ierr); 537 } 538 } 539 } 540 541 for (j=0; j<s; j++) w[j] = 1.0; 542 for (nadj=0; nadj<ts->numberadjs; nadj++) { 543 ierr = VecMAXPY(ts->vecs_sensi[nadj],s,w,&VecDeltaLam[nadj*s]);CHKERRQ(ierr); 544 if(ts->vecs_sensip) { 545 ierr = VecMAXPY(ts->vecs_sensip[nadj],s,w,&VecDeltaMu[nadj*s]);CHKERRQ(ierr); 546 } 547 } 548 ts->ptime += ts->time_step; 549 ts->steps++; 550 rk->status = TS_STEP_COMPLETE; 551 ierr = PetscObjectComposedDataSetReal((PetscObject)ts->vecs_sensi,explicit_stage_time_id,ts->ptime);CHKERRQ(ierr); 552 if(ts->vecs_sensip) { 553 ierr = PetscObjectComposedDataSetReal((PetscObject)ts->vecs_sensip,explicit_stage_time_id,ts->ptime);CHKERRQ(ierr); 554 } 555 PetscFunctionReturn(0); 556 } 557 558 #undef __FUNCT__ 559 #define __FUNCT__ "TSInterpolate_RK" 560 static PetscErrorCode TSInterpolate_RK(TS ts,PetscReal itime,Vec X) 561 { 562 TS_RK *rk = (TS_RK*)ts->data; 563 PetscInt s = rk->tableau->s,pinterp = rk->tableau->pinterp,i,j; 564 PetscReal h; 565 PetscReal tt,t; 566 PetscScalar *b; 567 const PetscReal *B = rk->tableau->binterp; 568 PetscErrorCode ierr; 569 570 PetscFunctionBegin; 571 if (!B) SETERRQ1(PetscObjectComm((PetscObject)ts),PETSC_ERR_SUP,"TSRK %s does not have an interpolation formula",rk->tableau->name); 572 switch (rk->status) { 573 case TS_STEP_INCOMPLETE: 574 case TS_STEP_PENDING: 575 h = ts->time_step; 576 t = (itime - ts->ptime)/h; 577 break; 578 case TS_STEP_COMPLETE: 579 h = ts->time_step_prev; 580 t = (itime - ts->ptime)/h + 1; /* In the interval [0,1] */ 581 break; 582 default: SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_PLIB,"Invalid TSStepStatus"); 583 } 584 ierr = PetscMalloc1(s,&b);CHKERRQ(ierr); 585 for (i=0; i<s; i++) b[i] = 0; 586 for (j=0,tt=t; j<pinterp; j++,tt*=t) { 587 for (i=0; i<s; i++) { 588 b[i] += h * B[i*pinterp+j] * tt; 589 } 590 } 591 ierr = VecCopy(rk->Y[0],X);CHKERRQ(ierr); 592 ierr = VecMAXPY(X,s,b,rk->YdotRHS);CHKERRQ(ierr); 593 ierr = PetscFree(b);CHKERRQ(ierr); 594 PetscFunctionReturn(0); 595 } 596 597 /*------------------------------------------------------------*/ 598 #undef __FUNCT__ 599 #define __FUNCT__ "TSReset_RK" 600 static PetscErrorCode TSReset_RK(TS ts) 601 { 602 TS_RK *rk = (TS_RK*)ts->data; 603 PetscInt s; 604 PetscErrorCode ierr; 605 606 PetscFunctionBegin; 607 if (!rk->tableau) PetscFunctionReturn(0); 608 s = rk->tableau->s; 609 ierr = VecDestroyVecs(s,&rk->Y);CHKERRQ(ierr); 610 ierr = VecDestroyVecs(s,&rk->YdotRHS);CHKERRQ(ierr); 611 if(ts->reverse_mode) { 612 ierr = VecDestroyVecs(s*ts->numberadjs,&rk->VecDeltaLam);CHKERRQ(ierr); 613 if(rk->VecDeltaMu) { 614 ierr = VecDestroyVecs(s*ts->numberadjs,&rk->VecDeltaMu);CHKERRQ(ierr); 615 } 616 ierr = VecDestroyVecs(ts->numberadjs,&rk->VecSensiTemp);CHKERRQ(ierr); 617 } 618 ierr = PetscFree(rk->work);CHKERRQ(ierr); 619 PetscFunctionReturn(0); 620 } 621 622 #undef __FUNCT__ 623 #define __FUNCT__ "TSDestroy_RK" 624 static PetscErrorCode TSDestroy_RK(TS ts) 625 { 626 PetscErrorCode ierr; 627 628 PetscFunctionBegin; 629 ierr = TSReset_RK(ts);CHKERRQ(ierr); 630 ierr = PetscFree(ts->data);CHKERRQ(ierr); 631 ierr = PetscObjectComposeFunction((PetscObject)ts,"TSRKGetType_C",NULL);CHKERRQ(ierr); 632 ierr = PetscObjectComposeFunction((PetscObject)ts,"TSRKSetType_C",NULL);CHKERRQ(ierr); 633 PetscFunctionReturn(0); 634 } 635 636 637 #undef __FUNCT__ 638 #define __FUNCT__ "DMCoarsenHook_TSRK" 639 static PetscErrorCode DMCoarsenHook_TSRK(DM fine,DM coarse,void *ctx) 640 { 641 PetscFunctionBegin; 642 PetscFunctionReturn(0); 643 } 644 645 #undef __FUNCT__ 646 #define __FUNCT__ "DMRestrictHook_TSRK" 647 static PetscErrorCode DMRestrictHook_TSRK(DM fine,Mat restrct,Vec rscale,Mat inject,DM coarse,void *ctx) 648 { 649 PetscFunctionBegin; 650 PetscFunctionReturn(0); 651 } 652 653 654 #undef __FUNCT__ 655 #define __FUNCT__ "DMSubDomainHook_TSRK" 656 static PetscErrorCode DMSubDomainHook_TSRK(DM dm,DM subdm,void *ctx) 657 { 658 PetscFunctionBegin; 659 PetscFunctionReturn(0); 660 } 661 662 #undef __FUNCT__ 663 #define __FUNCT__ "DMSubDomainRestrictHook_TSRK" 664 static PetscErrorCode DMSubDomainRestrictHook_TSRK(DM dm,VecScatter gscat,VecScatter lscat,DM subdm,void *ctx) 665 { 666 667 PetscFunctionBegin; 668 PetscFunctionReturn(0); 669 } 670 /* 671 #undef __FUNCT__ 672 #define __FUNCT__ "RKSetAdjCoe" 673 static PetscErrorCode RKSetAdjCoe(RKTableau tab) 674 { 675 PetscReal *A,*b; 676 PetscInt s,i,j; 677 PetscErrorCode ierr; 678 679 PetscFunctionBegin; 680 s = tab->s; 681 ierr = PetscMalloc2(s*s,&A,s,&b);CHKERRQ(ierr); 682 683 for (i=0; i<s; i++) 684 for (j=0; j<s; j++) { 685 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]; 686 ierr = PetscPrintf(PETSC_COMM_WORLD,"Coefficients: A[%D][%D]=%.6f\n",i,j,A[i*s+j]);CHKERRQ(ierr); 687 } 688 689 for (i=0; i<s; i++) b[i] = (tab->b[s-1-i]==0)? 0: -tab->b[s-1-i]; 690 691 ierr = PetscMemcpy(tab->A,A,s*s*sizeof(A[0]));CHKERRQ(ierr); 692 ierr = PetscMemcpy(tab->b,b,s*sizeof(b[0]));CHKERRQ(ierr); 693 ierr = PetscFree2(A,b);CHKERRQ(ierr); 694 PetscFunctionReturn(0); 695 } 696 */ 697 #undef __FUNCT__ 698 #define __FUNCT__ "TSSetUp_RK" 699 static PetscErrorCode TSSetUp_RK(TS ts) 700 { 701 TS_RK *rk = (TS_RK*)ts->data; 702 RKTableau tab; 703 PetscInt s; 704 PetscErrorCode ierr; 705 DM dm; 706 707 PetscFunctionBegin; 708 if (!rk->tableau) { 709 ierr = TSRKSetType(ts,TSRKDefault);CHKERRQ(ierr); 710 } 711 tab = rk->tableau; 712 s = tab->s; 713 ierr = VecDuplicateVecs(ts->vec_sol,s,&rk->Y);CHKERRQ(ierr); 714 ierr = VecDuplicateVecs(ts->vec_sol,s,&rk->YdotRHS);CHKERRQ(ierr); 715 ierr = PetscMalloc1(s,&rk->work);CHKERRQ(ierr); 716 ierr = TSGetDM(ts,&dm);CHKERRQ(ierr); 717 if (dm) { 718 ierr = DMCoarsenHookAdd(dm,DMCoarsenHook_TSRK,DMRestrictHook_TSRK,ts);CHKERRQ(ierr); 719 ierr = DMSubDomainHookAdd(dm,DMSubDomainHook_TSRK,DMSubDomainRestrictHook_TSRK,ts);CHKERRQ(ierr); 720 } 721 PetscFunctionReturn(0); 722 } 723 724 725 /*------------------------------------------------------------*/ 726 727 #undef __FUNCT__ 728 #define __FUNCT__ "TSSetFromOptions_RK" 729 static PetscErrorCode TSSetFromOptions_RK(PetscOptions *PetscOptionsObject,TS ts) 730 { 731 PetscErrorCode ierr; 732 char rktype[256]; 733 734 PetscFunctionBegin; 735 ierr = PetscOptionsHead(PetscOptionsObject,"RK ODE solver options");CHKERRQ(ierr); 736 { 737 RKTableauLink link; 738 PetscInt count,choice; 739 PetscBool flg; 740 const char **namelist; 741 ierr = PetscStrncpy(rktype,TSRKDefault,sizeof(rktype));CHKERRQ(ierr); 742 for (link=RKTableauList,count=0; link; link=link->next,count++) ; 743 ierr = PetscMalloc1(count,&namelist);CHKERRQ(ierr); 744 for (link=RKTableauList,count=0; link; link=link->next,count++) namelist[count] = link->tab.name; 745 ierr = PetscOptionsEList("-ts_rk_type","Family of RK method","TSRKSetType",(const char*const*)namelist,count,rktype,&choice,&flg);CHKERRQ(ierr); 746 ierr = TSRKSetType(ts,flg ? namelist[choice] : rktype);CHKERRQ(ierr); 747 ierr = PetscFree(namelist);CHKERRQ(ierr); 748 } 749 ierr = PetscOptionsTail();CHKERRQ(ierr); 750 PetscFunctionReturn(0); 751 } 752 753 #undef __FUNCT__ 754 #define __FUNCT__ "PetscFormatRealArray" 755 static PetscErrorCode PetscFormatRealArray(char buf[],size_t len,const char *fmt,PetscInt n,const PetscReal x[]) 756 { 757 PetscErrorCode ierr; 758 PetscInt i; 759 size_t left,count; 760 char *p; 761 762 PetscFunctionBegin; 763 for (i=0,p=buf,left=len; i<n; i++) { 764 ierr = PetscSNPrintfCount(p,left,fmt,&count,x[i]);CHKERRQ(ierr); 765 if (count >= left) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Insufficient space in buffer"); 766 left -= count; 767 p += count; 768 *p++ = ' '; 769 } 770 p[i ? 0 : -1] = 0; 771 PetscFunctionReturn(0); 772 } 773 774 #undef __FUNCT__ 775 #define __FUNCT__ "TSView_RK" 776 static PetscErrorCode TSView_RK(TS ts,PetscViewer viewer) 777 { 778 TS_RK *rk = (TS_RK*)ts->data; 779 RKTableau tab = rk->tableau; 780 PetscBool iascii; 781 PetscErrorCode ierr; 782 TSAdapt adapt; 783 784 PetscFunctionBegin; 785 ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);CHKERRQ(ierr); 786 if (iascii) { 787 TSRKType rktype; 788 char buf[512]; 789 ierr = TSRKGetType(ts,&rktype);CHKERRQ(ierr); 790 ierr = PetscViewerASCIIPrintf(viewer," RK %s\n",rktype);CHKERRQ(ierr); 791 ierr = PetscFormatRealArray(buf,sizeof(buf),"% 8.6f",tab->s,tab->c);CHKERRQ(ierr); 792 ierr = PetscViewerASCIIPrintf(viewer," Abscissa c = %s\n",buf);CHKERRQ(ierr); 793 ierr = PetscViewerASCIIPrintf(viewer,"FSAL: %s\n",tab->FSAL ? "yes" : "no");CHKERRQ(ierr); 794 } 795 ierr = TSGetAdapt(ts,&adapt);CHKERRQ(ierr); 796 ierr = TSAdaptView(adapt,viewer);CHKERRQ(ierr); 797 PetscFunctionReturn(0); 798 } 799 800 #undef __FUNCT__ 801 #define __FUNCT__ "TSLoad_RK" 802 static PetscErrorCode TSLoad_RK(TS ts,PetscViewer viewer) 803 { 804 PetscErrorCode ierr; 805 TSAdapt tsadapt; 806 807 PetscFunctionBegin; 808 ierr = TSGetAdapt(ts,&tsadapt);CHKERRQ(ierr); 809 ierr = TSAdaptLoad(tsadapt,viewer);CHKERRQ(ierr); 810 PetscFunctionReturn(0); 811 } 812 813 #undef __FUNCT__ 814 #define __FUNCT__ "TSRKSetType" 815 /*@C 816 TSRKSetType - Set the type of RK scheme 817 818 Logically collective 819 820 Input Parameter: 821 + ts - timestepping context 822 - rktype - type of RK-scheme 823 824 Level: intermediate 825 826 .seealso: TSRKGetType(), TSRK, TSRK2, TSRK3, TSRKPRSSP2, TSRK4, TSRK5 827 @*/ 828 PetscErrorCode TSRKSetType(TS ts,TSRKType rktype) 829 { 830 PetscErrorCode ierr; 831 832 PetscFunctionBegin; 833 PetscValidHeaderSpecific(ts,TS_CLASSID,1); 834 ierr = PetscTryMethod(ts,"TSRKSetType_C",(TS,TSRKType),(ts,rktype));CHKERRQ(ierr); 835 PetscFunctionReturn(0); 836 } 837 838 #undef __FUNCT__ 839 #define __FUNCT__ "TSRKGetType" 840 /*@C 841 TSRKGetType - Get the type of RK scheme 842 843 Logically collective 844 845 Input Parameter: 846 . ts - timestepping context 847 848 Output Parameter: 849 . rktype - type of RK-scheme 850 851 Level: intermediate 852 853 .seealso: TSRKGetType() 854 @*/ 855 PetscErrorCode TSRKGetType(TS ts,TSRKType *rktype) 856 { 857 PetscErrorCode ierr; 858 859 PetscFunctionBegin; 860 PetscValidHeaderSpecific(ts,TS_CLASSID,1); 861 ierr = PetscUseMethod(ts,"TSRKGetType_C",(TS,TSRKType*),(ts,rktype));CHKERRQ(ierr); 862 PetscFunctionReturn(0); 863 } 864 865 #undef __FUNCT__ 866 #define __FUNCT__ "TSRKGetType_RK" 867 PetscErrorCode TSRKGetType_RK(TS ts,TSRKType *rktype) 868 { 869 TS_RK *rk = (TS_RK*)ts->data; 870 PetscErrorCode ierr; 871 872 PetscFunctionBegin; 873 if (!rk->tableau) { 874 ierr = TSRKSetType(ts,TSRKDefault);CHKERRQ(ierr); 875 } 876 *rktype = rk->tableau->name; 877 PetscFunctionReturn(0); 878 } 879 #undef __FUNCT__ 880 #define __FUNCT__ "TSRKSetType_RK" 881 PetscErrorCode TSRKSetType_RK(TS ts,TSRKType rktype) 882 { 883 TS_RK *rk = (TS_RK*)ts->data; 884 PetscErrorCode ierr; 885 PetscBool match; 886 RKTableauLink link; 887 888 PetscFunctionBegin; 889 if (rk->tableau) { 890 ierr = PetscStrcmp(rk->tableau->name,rktype,&match);CHKERRQ(ierr); 891 if (match) PetscFunctionReturn(0); 892 } 893 for (link = RKTableauList; link; link=link->next) { 894 ierr = PetscStrcmp(link->tab.name,rktype,&match);CHKERRQ(ierr); 895 if (match) { 896 ierr = TSReset_RK(ts);CHKERRQ(ierr); 897 rk->tableau = &link->tab; 898 PetscFunctionReturn(0); 899 } 900 } 901 SETERRQ1(PetscObjectComm((PetscObject)ts),PETSC_ERR_ARG_UNKNOWN_TYPE,"Could not find '%s'",rktype); 902 PetscFunctionReturn(0); 903 } 904 905 #undef __FUNCT__ 906 #define __FUNCT__ "TSGetStages_RK" 907 static PetscErrorCode TSGetStages_RK(TS ts,PetscInt *ns,Vec **Y) 908 { 909 TS_RK *rk = (TS_RK*)ts->data; 910 911 PetscFunctionBegin; 912 *ns = rk->tableau->s; 913 if(Y) *Y = rk->Y; 914 PetscFunctionReturn(0); 915 } 916 917 918 /* ------------------------------------------------------------ */ 919 /*MC 920 TSRK - ODE and DAE solver using Runge-Kutta schemes 921 922 The user should provide the right hand side of the equation 923 using TSSetRHSFunction(). 924 925 Notes: 926 The default is TSRK3, it can be changed with TSRKSetType() or -ts_rk_type 927 928 Level: beginner 929 930 .seealso: TSCreate(), TS, TSSetType(), TSRKSetType(), TSRKGetType(), TSRKSetFullyImplicit(), TSRK2D, TTSRK2E, TSRK3, 931 TSRK4, TSRK5, TSRKPRSSP2, TSRKBPR3, TSRKType, TSRKRegister() 932 933 M*/ 934 #undef __FUNCT__ 935 #define __FUNCT__ "TSCreate_RK" 936 PETSC_EXTERN PetscErrorCode TSCreate_RK(TS ts) 937 { 938 TS_RK *th; 939 PetscErrorCode ierr; 940 941 PetscFunctionBegin; 942 #if !defined(PETSC_USE_DYNAMIC_LIBRARIES) 943 ierr = TSRKInitializePackage();CHKERRQ(ierr); 944 #endif 945 946 ts->ops->reset = TSReset_RK; 947 ts->ops->destroy = TSDestroy_RK; 948 ts->ops->view = TSView_RK; 949 ts->ops->load = TSLoad_RK; 950 ts->ops->setup = TSSetUp_RK; 951 ts->ops->setupadj = TSAdjointSetUp_RK; 952 ts->ops->step = TSStep_RK; 953 ts->ops->interpolate = TSInterpolate_RK; 954 ts->ops->evaluatestep = TSEvaluateStep_RK; 955 ts->ops->setfromoptions = TSSetFromOptions_RK; 956 ts->ops->getstages = TSGetStages_RK; 957 ts->ops->stepadj = TSStepAdj_RK; 958 959 ierr = PetscNewLog(ts,&th);CHKERRQ(ierr); 960 ts->data = (void*)th; 961 962 ierr = PetscObjectComposeFunction((PetscObject)ts,"TSRKGetType_C",TSRKGetType_RK);CHKERRQ(ierr); 963 ierr = PetscObjectComposeFunction((PetscObject)ts,"TSRKSetType_C",TSRKSetType_RK);CHKERRQ(ierr); 964 PetscFunctionReturn(0); 965 } 966