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 ierr = VecDestroyVecs(s*ts->numberadjs,&rk->VecDeltaLam);CHKERRQ(ierr); 612 ierr = VecDestroyVecs(s*ts->numberadjs,&rk->VecDeltaMu);CHKERRQ(ierr); 613 ierr = VecDestroyVecs(ts->numberadjs,&rk->VecSensiTemp);CHKERRQ(ierr); 614 ierr = PetscFree(rk->work);CHKERRQ(ierr); 615 PetscFunctionReturn(0); 616 } 617 618 #undef __FUNCT__ 619 #define __FUNCT__ "TSDestroy_RK" 620 static PetscErrorCode TSDestroy_RK(TS ts) 621 { 622 PetscErrorCode ierr; 623 624 PetscFunctionBegin; 625 ierr = TSReset_RK(ts);CHKERRQ(ierr); 626 ierr = PetscFree(ts->data);CHKERRQ(ierr); 627 ierr = PetscObjectComposeFunction((PetscObject)ts,"TSRKGetType_C",NULL);CHKERRQ(ierr); 628 ierr = PetscObjectComposeFunction((PetscObject)ts,"TSRKSetType_C",NULL);CHKERRQ(ierr); 629 PetscFunctionReturn(0); 630 } 631 632 633 #undef __FUNCT__ 634 #define __FUNCT__ "DMCoarsenHook_TSRK" 635 static PetscErrorCode DMCoarsenHook_TSRK(DM fine,DM coarse,void *ctx) 636 { 637 PetscFunctionBegin; 638 PetscFunctionReturn(0); 639 } 640 641 #undef __FUNCT__ 642 #define __FUNCT__ "DMRestrictHook_TSRK" 643 static PetscErrorCode DMRestrictHook_TSRK(DM fine,Mat restrct,Vec rscale,Mat inject,DM coarse,void *ctx) 644 { 645 PetscFunctionBegin; 646 PetscFunctionReturn(0); 647 } 648 649 650 #undef __FUNCT__ 651 #define __FUNCT__ "DMSubDomainHook_TSRK" 652 static PetscErrorCode DMSubDomainHook_TSRK(DM dm,DM subdm,void *ctx) 653 { 654 PetscFunctionBegin; 655 PetscFunctionReturn(0); 656 } 657 658 #undef __FUNCT__ 659 #define __FUNCT__ "DMSubDomainRestrictHook_TSRK" 660 static PetscErrorCode DMSubDomainRestrictHook_TSRK(DM dm,VecScatter gscat,VecScatter lscat,DM subdm,void *ctx) 661 { 662 663 PetscFunctionBegin; 664 PetscFunctionReturn(0); 665 } 666 /* 667 #undef __FUNCT__ 668 #define __FUNCT__ "RKSetAdjCoe" 669 static PetscErrorCode RKSetAdjCoe(RKTableau tab) 670 { 671 PetscReal *A,*b; 672 PetscInt s,i,j; 673 PetscErrorCode ierr; 674 675 PetscFunctionBegin; 676 s = tab->s; 677 ierr = PetscMalloc2(s*s,&A,s,&b);CHKERRQ(ierr); 678 679 for (i=0; i<s; i++) 680 for (j=0; j<s; j++) { 681 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]; 682 ierr = PetscPrintf(PETSC_COMM_WORLD,"Coefficients: A[%D][%D]=%.6f\n",i,j,A[i*s+j]);CHKERRQ(ierr); 683 } 684 685 for (i=0; i<s; i++) b[i] = (tab->b[s-1-i]==0)? 0: -tab->b[s-1-i]; 686 687 ierr = PetscMemcpy(tab->A,A,s*s*sizeof(A[0]));CHKERRQ(ierr); 688 ierr = PetscMemcpy(tab->b,b,s*sizeof(b[0]));CHKERRQ(ierr); 689 ierr = PetscFree2(A,b);CHKERRQ(ierr); 690 PetscFunctionReturn(0); 691 } 692 */ 693 #undef __FUNCT__ 694 #define __FUNCT__ "TSSetUp_RK" 695 static PetscErrorCode TSSetUp_RK(TS ts) 696 { 697 TS_RK *rk = (TS_RK*)ts->data; 698 RKTableau tab; 699 PetscInt s; 700 PetscErrorCode ierr; 701 DM dm; 702 703 PetscFunctionBegin; 704 if (!rk->tableau) { 705 ierr = TSRKSetType(ts,TSRKDefault);CHKERRQ(ierr); 706 } 707 tab = rk->tableau; 708 s = tab->s; 709 ierr = VecDuplicateVecs(ts->vec_sol,s,&rk->Y);CHKERRQ(ierr); 710 ierr = VecDuplicateVecs(ts->vec_sol,s,&rk->YdotRHS);CHKERRQ(ierr); 711 ierr = PetscMalloc1(s,&rk->work);CHKERRQ(ierr); 712 ierr = TSGetDM(ts,&dm);CHKERRQ(ierr); 713 if (dm) { 714 ierr = DMCoarsenHookAdd(dm,DMCoarsenHook_TSRK,DMRestrictHook_TSRK,ts);CHKERRQ(ierr); 715 ierr = DMSubDomainHookAdd(dm,DMSubDomainHook_TSRK,DMSubDomainRestrictHook_TSRK,ts);CHKERRQ(ierr); 716 } 717 PetscFunctionReturn(0); 718 } 719 720 721 /*------------------------------------------------------------*/ 722 723 #undef __FUNCT__ 724 #define __FUNCT__ "TSSetFromOptions_RK" 725 static PetscErrorCode TSSetFromOptions_RK(PetscOptions *PetscOptionsObject,TS ts) 726 { 727 PetscErrorCode ierr; 728 char rktype[256]; 729 730 PetscFunctionBegin; 731 ierr = PetscOptionsHead(PetscOptionsObject,"RK ODE solver options");CHKERRQ(ierr); 732 { 733 RKTableauLink link; 734 PetscInt count,choice; 735 PetscBool flg; 736 const char **namelist; 737 ierr = PetscStrncpy(rktype,TSRKDefault,sizeof(rktype));CHKERRQ(ierr); 738 for (link=RKTableauList,count=0; link; link=link->next,count++) ; 739 ierr = PetscMalloc1(count,&namelist);CHKERRQ(ierr); 740 for (link=RKTableauList,count=0; link; link=link->next,count++) namelist[count] = link->tab.name; 741 ierr = PetscOptionsEList("-ts_rk_type","Family of RK method","TSRKSetType",(const char*const*)namelist,count,rktype,&choice,&flg);CHKERRQ(ierr); 742 ierr = TSRKSetType(ts,flg ? namelist[choice] : rktype);CHKERRQ(ierr); 743 ierr = PetscFree(namelist);CHKERRQ(ierr); 744 } 745 ierr = PetscOptionsTail();CHKERRQ(ierr); 746 PetscFunctionReturn(0); 747 } 748 749 #undef __FUNCT__ 750 #define __FUNCT__ "PetscFormatRealArray" 751 static PetscErrorCode PetscFormatRealArray(char buf[],size_t len,const char *fmt,PetscInt n,const PetscReal x[]) 752 { 753 PetscErrorCode ierr; 754 PetscInt i; 755 size_t left,count; 756 char *p; 757 758 PetscFunctionBegin; 759 for (i=0,p=buf,left=len; i<n; i++) { 760 ierr = PetscSNPrintfCount(p,left,fmt,&count,x[i]);CHKERRQ(ierr); 761 if (count >= left) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Insufficient space in buffer"); 762 left -= count; 763 p += count; 764 *p++ = ' '; 765 } 766 p[i ? 0 : -1] = 0; 767 PetscFunctionReturn(0); 768 } 769 770 #undef __FUNCT__ 771 #define __FUNCT__ "TSView_RK" 772 static PetscErrorCode TSView_RK(TS ts,PetscViewer viewer) 773 { 774 TS_RK *rk = (TS_RK*)ts->data; 775 RKTableau tab = rk->tableau; 776 PetscBool iascii; 777 PetscErrorCode ierr; 778 TSAdapt adapt; 779 780 PetscFunctionBegin; 781 ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);CHKERRQ(ierr); 782 if (iascii) { 783 TSRKType rktype; 784 char buf[512]; 785 ierr = TSRKGetType(ts,&rktype);CHKERRQ(ierr); 786 ierr = PetscViewerASCIIPrintf(viewer," RK %s\n",rktype);CHKERRQ(ierr); 787 ierr = PetscFormatRealArray(buf,sizeof(buf),"% 8.6f",tab->s,tab->c);CHKERRQ(ierr); 788 ierr = PetscViewerASCIIPrintf(viewer," Abscissa c = %s\n",buf);CHKERRQ(ierr); 789 ierr = PetscViewerASCIIPrintf(viewer,"FSAL: %s\n",tab->FSAL ? "yes" : "no");CHKERRQ(ierr); 790 } 791 ierr = TSGetAdapt(ts,&adapt);CHKERRQ(ierr); 792 ierr = TSAdaptView(adapt,viewer);CHKERRQ(ierr); 793 PetscFunctionReturn(0); 794 } 795 796 #undef __FUNCT__ 797 #define __FUNCT__ "TSLoad_RK" 798 static PetscErrorCode TSLoad_RK(TS ts,PetscViewer viewer) 799 { 800 PetscErrorCode ierr; 801 TSAdapt tsadapt; 802 803 PetscFunctionBegin; 804 ierr = TSGetAdapt(ts,&tsadapt);CHKERRQ(ierr); 805 ierr = TSAdaptLoad(tsadapt,viewer);CHKERRQ(ierr); 806 PetscFunctionReturn(0); 807 } 808 809 #undef __FUNCT__ 810 #define __FUNCT__ "TSRKSetType" 811 /*@C 812 TSRKSetType - Set the type of RK scheme 813 814 Logically collective 815 816 Input Parameter: 817 + ts - timestepping context 818 - rktype - type of RK-scheme 819 820 Level: intermediate 821 822 .seealso: TSRKGetType(), TSRK, TSRK2, TSRK3, TSRKPRSSP2, TSRK4, TSRK5 823 @*/ 824 PetscErrorCode TSRKSetType(TS ts,TSRKType rktype) 825 { 826 PetscErrorCode ierr; 827 828 PetscFunctionBegin; 829 PetscValidHeaderSpecific(ts,TS_CLASSID,1); 830 ierr = PetscTryMethod(ts,"TSRKSetType_C",(TS,TSRKType),(ts,rktype));CHKERRQ(ierr); 831 PetscFunctionReturn(0); 832 } 833 834 #undef __FUNCT__ 835 #define __FUNCT__ "TSRKGetType" 836 /*@C 837 TSRKGetType - Get the type of RK scheme 838 839 Logically collective 840 841 Input Parameter: 842 . ts - timestepping context 843 844 Output Parameter: 845 . rktype - type of RK-scheme 846 847 Level: intermediate 848 849 .seealso: TSRKGetType() 850 @*/ 851 PetscErrorCode TSRKGetType(TS ts,TSRKType *rktype) 852 { 853 PetscErrorCode ierr; 854 855 PetscFunctionBegin; 856 PetscValidHeaderSpecific(ts,TS_CLASSID,1); 857 ierr = PetscUseMethod(ts,"TSRKGetType_C",(TS,TSRKType*),(ts,rktype));CHKERRQ(ierr); 858 PetscFunctionReturn(0); 859 } 860 861 #undef __FUNCT__ 862 #define __FUNCT__ "TSRKGetType_RK" 863 PetscErrorCode TSRKGetType_RK(TS ts,TSRKType *rktype) 864 { 865 TS_RK *rk = (TS_RK*)ts->data; 866 PetscErrorCode ierr; 867 868 PetscFunctionBegin; 869 if (!rk->tableau) { 870 ierr = TSRKSetType(ts,TSRKDefault);CHKERRQ(ierr); 871 } 872 *rktype = rk->tableau->name; 873 PetscFunctionReturn(0); 874 } 875 #undef __FUNCT__ 876 #define __FUNCT__ "TSRKSetType_RK" 877 PetscErrorCode TSRKSetType_RK(TS ts,TSRKType rktype) 878 { 879 TS_RK *rk = (TS_RK*)ts->data; 880 PetscErrorCode ierr; 881 PetscBool match; 882 RKTableauLink link; 883 884 PetscFunctionBegin; 885 if (rk->tableau) { 886 ierr = PetscStrcmp(rk->tableau->name,rktype,&match);CHKERRQ(ierr); 887 if (match) PetscFunctionReturn(0); 888 } 889 for (link = RKTableauList; link; link=link->next) { 890 ierr = PetscStrcmp(link->tab.name,rktype,&match);CHKERRQ(ierr); 891 if (match) { 892 ierr = TSReset_RK(ts);CHKERRQ(ierr); 893 rk->tableau = &link->tab; 894 PetscFunctionReturn(0); 895 } 896 } 897 SETERRQ1(PetscObjectComm((PetscObject)ts),PETSC_ERR_ARG_UNKNOWN_TYPE,"Could not find '%s'",rktype); 898 PetscFunctionReturn(0); 899 } 900 901 #undef __FUNCT__ 902 #define __FUNCT__ "TSGetStages_RK" 903 static PetscErrorCode TSGetStages_RK(TS ts,PetscInt *ns,Vec **Y) 904 { 905 TS_RK *rk = (TS_RK*)ts->data; 906 907 PetscFunctionBegin; 908 *ns = rk->tableau->s; 909 if(Y) *Y = rk->Y; 910 PetscFunctionReturn(0); 911 } 912 913 914 /* ------------------------------------------------------------ */ 915 /*MC 916 TSRK - ODE and DAE solver using Runge-Kutta schemes 917 918 The user should provide the right hand side of the equation 919 using TSSetRHSFunction(). 920 921 Notes: 922 The default is TSRK3, it can be changed with TSRKSetType() or -ts_rk_type 923 924 Level: beginner 925 926 .seealso: TSCreate(), TS, TSSetType(), TSRKSetType(), TSRKGetType(), TSRKSetFullyImplicit(), TSRK2D, TTSRK2E, TSRK3, 927 TSRK4, TSRK5, TSRKPRSSP2, TSRKBPR3, TSRKType, TSRKRegister() 928 929 M*/ 930 #undef __FUNCT__ 931 #define __FUNCT__ "TSCreate_RK" 932 PETSC_EXTERN PetscErrorCode TSCreate_RK(TS ts) 933 { 934 TS_RK *th; 935 PetscErrorCode ierr; 936 937 PetscFunctionBegin; 938 #if !defined(PETSC_USE_DYNAMIC_LIBRARIES) 939 ierr = TSRKInitializePackage();CHKERRQ(ierr); 940 #endif 941 942 ts->ops->reset = TSReset_RK; 943 ts->ops->destroy = TSDestroy_RK; 944 ts->ops->view = TSView_RK; 945 ts->ops->load = TSLoad_RK; 946 ts->ops->setup = TSSetUp_RK; 947 ts->ops->setupadj = TSAdjointSetUp_RK; 948 ts->ops->step = TSStep_RK; 949 ts->ops->interpolate = TSInterpolate_RK; 950 ts->ops->evaluatestep = TSEvaluateStep_RK; 951 ts->ops->setfromoptions = TSSetFromOptions_RK; 952 ts->ops->getstages = TSGetStages_RK; 953 ts->ops->stepadj = TSStepAdj_RK; 954 955 ierr = PetscNewLog(ts,&th);CHKERRQ(ierr); 956 ts->data = (void*)th; 957 958 ierr = PetscObjectComposeFunction((PetscObject)ts,"TSRKGetType_C",TSRKGetType_RK);CHKERRQ(ierr); 959 ierr = PetscObjectComposeFunction((PetscObject)ts,"TSRKSetType_C",TSRKSetType_RK);CHKERRQ(ierr); 960 PetscFunctionReturn(0); 961 } 962