1 2 static char help[] = "Solves 1D heat equation with FEM formulation.\n\ 3 Input arguments are\n\ 4 -useAlhs: solve Alhs*U' = (Arhs*U + g) \n\ 5 otherwise, solve U' = inv(Alhs)*(Arhs*U + g) \n\n"; 6 7 /*-------------------------------------------------------------------------- 8 Solves 1D heat equation U_t = U_xx with FEM formulation: 9 Alhs*U' = rhs (= Arhs*U + g) 10 We thank Chris Cox <clcox@clemson.edu> for contributing the original code 11 ----------------------------------------------------------------------------*/ 12 13 #include <petscksp.h> 14 #include <petscts.h> 15 16 /* special variable - max size of all arrays */ 17 #define num_z 10 18 19 /* 20 User-defined application context - contains data needed by the 21 application-provided call-back routines. 22 */ 23 typedef struct { 24 Mat Amat; /* left hand side matrix */ 25 Vec ksp_rhs,ksp_sol; /* working vectors for formulating inv(Alhs)*(Arhs*U+g) */ 26 int max_probsz; /* max size of the problem */ 27 PetscBool useAlhs; /* flag (1 indicates solving Alhs*U' = Arhs*U+g */ 28 int nz; /* total number of grid points */ 29 PetscInt m; /* total number of interio grid points */ 30 Vec solution; /* global exact ts solution vector */ 31 PetscScalar *z; /* array of grid points */ 32 PetscBool debug; /* flag (1 indicates activation of debugging printouts) */ 33 } AppCtx; 34 35 extern PetscScalar exact(PetscScalar,PetscReal); 36 extern PetscErrorCode Monitor(TS,PetscInt,PetscReal,Vec,void*); 37 extern PetscErrorCode Petsc_KSPSolve(AppCtx*); 38 extern PetscScalar bspl(PetscScalar*,PetscScalar,PetscInt,PetscInt,PetscInt[][2],PetscInt); 39 extern PetscErrorCode femBg(PetscScalar[][3],PetscScalar*,PetscInt,PetscScalar*,PetscReal); 40 extern PetscErrorCode femA(AppCtx*,PetscInt,PetscScalar*); 41 extern PetscErrorCode rhs(AppCtx*,PetscScalar*, PetscInt, PetscScalar*,PetscReal); 42 extern PetscErrorCode RHSfunction(TS,PetscReal,Vec,Vec,void*); 43 44 int main(int argc,char **argv) 45 { 46 PetscInt i,m,nz,steps,max_steps,k,nphase=1; 47 PetscScalar zInitial,zFinal,val,*z; 48 PetscReal stepsz[4],T,ftime; 49 TS ts; 50 SNES snes; 51 Mat Jmat; 52 AppCtx appctx; /* user-defined application context */ 53 Vec init_sol; /* ts solution vector */ 54 PetscMPIInt size; 55 56 PetscFunctionBeginUser; 57 PetscCall(PetscInitialize(&argc,&argv,(char*)0,help)); 58 PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD,&size)); 59 PetscCheck(size == 1,PETSC_COMM_SELF,PETSC_ERR_WRONG_MPI_SIZE,"This is a uniprocessor example only"); 60 61 /* initializations */ 62 zInitial = 0.0; 63 zFinal = 1.0; 64 nz = num_z; 65 m = nz-2; 66 appctx.nz = nz; 67 max_steps = (PetscInt)10000; 68 69 appctx.m = m; 70 appctx.max_probsz = nz; 71 appctx.debug = PETSC_FALSE; 72 appctx.useAlhs = PETSC_FALSE; 73 74 PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"",""); 75 PetscCall(PetscOptionsName("-debug",NULL,NULL,&appctx.debug)); 76 PetscCall(PetscOptionsName("-useAlhs",NULL,NULL,&appctx.useAlhs)); 77 PetscCall(PetscOptionsRangeInt("-nphase",NULL,NULL,nphase,&nphase,NULL,1,3)); 78 PetscOptionsEnd(); 79 T = 0.014/nphase; 80 81 /* create vector to hold ts solution */ 82 /*-----------------------------------*/ 83 PetscCall(VecCreate(PETSC_COMM_WORLD, &init_sol)); 84 PetscCall(VecSetSizes(init_sol, PETSC_DECIDE, m)); 85 PetscCall(VecSetFromOptions(init_sol)); 86 87 /* create vector to hold true ts soln for comparison */ 88 PetscCall(VecDuplicate(init_sol, &appctx.solution)); 89 90 /* create LHS matrix Amat */ 91 /*------------------------*/ 92 PetscCall(MatCreateSeqAIJ(PETSC_COMM_WORLD, m, m, 3, NULL, &appctx.Amat)); 93 PetscCall(MatSetFromOptions(appctx.Amat)); 94 PetscCall(MatSetUp(appctx.Amat)); 95 /* set space grid points - interio points only! */ 96 PetscCall(PetscMalloc1(nz+1,&z)); 97 for (i=0; i<nz; i++) z[i]=(i)*((zFinal-zInitial)/(nz-1)); 98 appctx.z = z; 99 femA(&appctx,nz,z); 100 101 /* create the jacobian matrix */ 102 /*----------------------------*/ 103 PetscCall(MatCreate(PETSC_COMM_WORLD, &Jmat)); 104 PetscCall(MatSetSizes(Jmat,PETSC_DECIDE,PETSC_DECIDE,m,m)); 105 PetscCall(MatSetFromOptions(Jmat)); 106 PetscCall(MatSetUp(Jmat)); 107 108 /* create working vectors for formulating rhs=inv(Alhs)*(Arhs*U + g) */ 109 PetscCall(VecDuplicate(init_sol,&appctx.ksp_rhs)); 110 PetscCall(VecDuplicate(init_sol,&appctx.ksp_sol)); 111 112 /* set initial guess */ 113 /*-------------------*/ 114 for (i=0; i<nz-2; i++) { 115 val = exact(z[i+1], 0.0); 116 PetscCall(VecSetValue(init_sol,i,(PetscScalar)val,INSERT_VALUES)); 117 } 118 PetscCall(VecAssemblyBegin(init_sol)); 119 PetscCall(VecAssemblyEnd(init_sol)); 120 121 /*create a time-stepping context and set the problem type */ 122 /*--------------------------------------------------------*/ 123 PetscCall(TSCreate(PETSC_COMM_WORLD, &ts)); 124 PetscCall(TSSetProblemType(ts,TS_NONLINEAR)); 125 126 /* set time-step method */ 127 PetscCall(TSSetType(ts,TSCN)); 128 129 /* Set optional user-defined monitoring routine */ 130 PetscCall(TSMonitorSet(ts,Monitor,&appctx,NULL)); 131 /* set the right hand side of U_t = RHSfunction(U,t) */ 132 PetscCall(TSSetRHSFunction(ts,NULL,(PetscErrorCode (*)(TS,PetscScalar,Vec,Vec,void*))RHSfunction,&appctx)); 133 134 if (appctx.useAlhs) { 135 /* set the left hand side matrix of Amat*U_t = rhs(U,t) */ 136 137 /* Note: this approach is incompatible with the finite differenced Jacobian set below because we can't restore the 138 * Alhs matrix without making a copy. Either finite difference the entire thing or use analytic Jacobians in both 139 * places. 140 */ 141 PetscCall(TSSetIFunction(ts,NULL,TSComputeIFunctionLinear,&appctx)); 142 PetscCall(TSSetIJacobian(ts,appctx.Amat,appctx.Amat,TSComputeIJacobianConstant,&appctx)); 143 } 144 145 /* use petsc to compute the jacobian by finite differences */ 146 PetscCall(TSGetSNES(ts,&snes)); 147 PetscCall(SNESSetJacobian(snes,Jmat,Jmat,SNESComputeJacobianDefault,NULL)); 148 149 /* get the command line options if there are any and set them */ 150 PetscCall(TSSetFromOptions(ts)); 151 152 #if defined(PETSC_HAVE_SUNDIALS2) 153 { 154 TSType type; 155 PetscBool sundialstype=PETSC_FALSE; 156 PetscCall(TSGetType(ts,&type)); 157 PetscCall(PetscObjectTypeCompare((PetscObject)ts,TSSUNDIALS,&sundialstype)); 158 PetscCheck(!sundialstype || !appctx.useAlhs,PETSC_COMM_SELF,PETSC_ERR_SUP,"Cannot use Alhs formulation for TSSUNDIALS type"); 159 } 160 #endif 161 /* Sets the initial solution */ 162 PetscCall(TSSetSolution(ts,init_sol)); 163 164 stepsz[0] = 1.0/(2.0*(nz-1)*(nz-1)); /* (mesh_size)^2/2.0 */ 165 ftime = 0.0; 166 for (k=0; k<nphase; k++) { 167 if (nphase > 1) PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Phase %" PetscInt_FMT " initial time %g, stepsz %g, duration: %g\n",k,(double)ftime,(double)stepsz[k],(double)((k+1)*T))); 168 PetscCall(TSSetTime(ts,ftime)); 169 PetscCall(TSSetTimeStep(ts,stepsz[k])); 170 PetscCall(TSSetMaxSteps(ts,max_steps)); 171 PetscCall(TSSetMaxTime(ts,(k+1)*T)); 172 PetscCall(TSSetExactFinalTime(ts,TS_EXACTFINALTIME_STEPOVER)); 173 174 /* loop over time steps */ 175 /*----------------------*/ 176 PetscCall(TSSolve(ts,init_sol)); 177 PetscCall(TSGetSolveTime(ts,&ftime)); 178 PetscCall(TSGetStepNumber(ts,&steps)); 179 stepsz[k+1] = stepsz[k]*1.5; /* change step size for the next phase */ 180 } 181 182 /* free space */ 183 PetscCall(TSDestroy(&ts)); 184 PetscCall(MatDestroy(&appctx.Amat)); 185 PetscCall(MatDestroy(&Jmat)); 186 PetscCall(VecDestroy(&appctx.ksp_rhs)); 187 PetscCall(VecDestroy(&appctx.ksp_sol)); 188 PetscCall(VecDestroy(&init_sol)); 189 PetscCall(VecDestroy(&appctx.solution)); 190 PetscCall(PetscFree(z)); 191 192 PetscCall(PetscFinalize()); 193 return 0; 194 } 195 196 /*------------------------------------------------------------------------ 197 Set exact solution 198 u(z,t) = sin(6*PI*z)*exp(-36.*PI*PI*t) + 3.*sin(2*PI*z)*exp(-4.*PI*PI*t) 199 --------------------------------------------------------------------------*/ 200 PetscScalar exact(PetscScalar z,PetscReal t) 201 { 202 PetscScalar val, ex1, ex2; 203 204 ex1 = PetscExpReal(-36.*PETSC_PI*PETSC_PI*t); 205 ex2 = PetscExpReal(-4.*PETSC_PI*PETSC_PI*t); 206 val = PetscSinScalar(6*PETSC_PI*z)*ex1 + 3.*PetscSinScalar(2*PETSC_PI*z)*ex2; 207 return val; 208 } 209 210 /* 211 Monitor - User-provided routine to monitor the solution computed at 212 each timestep. This example plots the solution and computes the 213 error in two different norms. 214 215 Input Parameters: 216 ts - the timestep context 217 step - the count of the current step (with 0 meaning the 218 initial condition) 219 time - the current time 220 u - the solution at this timestep 221 ctx - the user-provided context for this monitoring routine. 222 In this case we use the application context which contains 223 information about the problem size, workspace and the exact 224 solution. 225 */ 226 PetscErrorCode Monitor(TS ts,PetscInt step,PetscReal time,Vec u,void *ctx) 227 { 228 AppCtx *appctx = (AppCtx*)ctx; 229 PetscInt i,m=appctx->m; 230 PetscReal norm_2,norm_max,h=1.0/(m+1); 231 PetscScalar *u_exact; 232 233 /* Compute the exact solution */ 234 PetscCall(VecGetArrayWrite(appctx->solution,&u_exact)); 235 for (i=0; i<m; i++) u_exact[i] = exact(appctx->z[i+1],time); 236 PetscCall(VecRestoreArrayWrite(appctx->solution,&u_exact)); 237 238 /* Print debugging information if desired */ 239 if (appctx->debug) { 240 PetscCall(PetscPrintf(PETSC_COMM_SELF,"Computed solution vector at time %g\n",(double)time)); 241 PetscCall(VecView(u,PETSC_VIEWER_STDOUT_SELF)); 242 PetscCall(PetscPrintf(PETSC_COMM_SELF,"Exact solution vector\n")); 243 PetscCall(VecView(appctx->solution,PETSC_VIEWER_STDOUT_SELF)); 244 } 245 246 /* Compute the 2-norm and max-norm of the error */ 247 PetscCall(VecAXPY(appctx->solution,-1.0,u)); 248 PetscCall(VecNorm(appctx->solution,NORM_2,&norm_2)); 249 250 norm_2 = PetscSqrtReal(h)*norm_2; 251 PetscCall(VecNorm(appctx->solution,NORM_MAX,&norm_max)); 252 PetscCall(PetscPrintf(PETSC_COMM_SELF,"Timestep %" PetscInt_FMT ": time = %g, 2-norm error = %6.4f, max norm error = %6.4f\n",step,(double)time,(double)norm_2,(double)norm_max)); 253 254 /* 255 Print debugging information if desired 256 */ 257 if (appctx->debug) { 258 PetscCall(PetscPrintf(PETSC_COMM_SELF,"Error vector\n")); 259 PetscCall(VecView(appctx->solution,PETSC_VIEWER_STDOUT_SELF)); 260 } 261 return 0; 262 } 263 264 /*%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 265 Function to solve a linear system using KSP 266 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%*/ 267 268 PetscErrorCode Petsc_KSPSolve(AppCtx *obj) 269 { 270 KSP ksp; 271 PC pc; 272 273 /*create the ksp context and set the operators,that is, associate the system matrix with it*/ 274 PetscCall(KSPCreate(PETSC_COMM_WORLD,&ksp)); 275 PetscCall(KSPSetOperators(ksp,obj->Amat,obj->Amat)); 276 277 /*get the preconditioner context, set its type and the tolerances*/ 278 PetscCall(KSPGetPC(ksp,&pc)); 279 PetscCall(PCSetType(pc,PCLU)); 280 PetscCall(KSPSetTolerances(ksp,1.e-7,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT)); 281 282 /*get the command line options if there are any and set them*/ 283 PetscCall(KSPSetFromOptions(ksp)); 284 285 /*get the linear system (ksp) solve*/ 286 PetscCall(KSPSolve(ksp,obj->ksp_rhs,obj->ksp_sol)); 287 288 PetscCall(KSPDestroy(&ksp)); 289 return 0; 290 } 291 292 /*********************************************************************** 293 Function to return value of basis function or derivative of basis function. 294 *********************************************************************** 295 296 Arguments: 297 x = array of xpoints or nodal values 298 xx = point at which the basis function is to be 299 evaluated. 300 il = interval containing xx. 301 iq = indicates which of the two basis functions in 302 interval intrvl should be used 303 nll = array containing the endpoints of each interval. 304 id = If id ~= 2, the value of the basis function 305 is calculated; if id = 2, the value of the 306 derivative of the basis function is returned. 307 ***********************************************************************/ 308 309 PetscScalar bspl(PetscScalar *x, PetscScalar xx,PetscInt il,PetscInt iq,PetscInt nll[][2],PetscInt id) 310 { 311 PetscScalar x1,x2,bfcn; 312 PetscInt i1,i2,iq1,iq2; 313 314 /* Determine which basis function in interval intrvl is to be used in */ 315 iq1 = iq; 316 if (iq1==0) iq2 = 1; 317 else iq2 = 0; 318 319 /* Determine endpoint of the interval intrvl */ 320 i1=nll[il][iq1]; 321 i2=nll[il][iq2]; 322 323 /* Determine nodal values at the endpoints of the interval intrvl */ 324 x1=x[i1]; 325 x2=x[i2]; 326 327 /* Evaluate basis function */ 328 if (id == 2) bfcn=(1.0)/(x1-x2); 329 else bfcn=(xx-x2)/(x1-x2); 330 return bfcn; 331 } 332 333 /*--------------------------------------------------------- 334 Function called by rhs function to get B and g 335 ---------------------------------------------------------*/ 336 PetscErrorCode femBg(PetscScalar btri[][3],PetscScalar *f,PetscInt nz,PetscScalar *z, PetscReal t) 337 { 338 PetscInt i,j,jj,il,ip,ipp,ipq,iq,iquad,iqq; 339 PetscInt nli[num_z][2],indx[num_z]; 340 PetscScalar dd,dl,zip,zipq,zz,b_z,bb_z,bij; 341 PetscScalar zquad[num_z][3],dlen[num_z],qdwt[3]; 342 343 /* initializing everything - btri and f are initialized in rhs.c */ 344 for (i=0; i < nz; i++) { 345 nli[i][0] = 0; 346 nli[i][1] = 0; 347 indx[i] = 0; 348 zquad[i][0] = 0.0; 349 zquad[i][1] = 0.0; 350 zquad[i][2] = 0.0; 351 dlen[i] = 0.0; 352 } /*end for (i)*/ 353 354 /* quadrature weights */ 355 qdwt[0] = 1.0/6.0; 356 qdwt[1] = 4.0/6.0; 357 qdwt[2] = 1.0/6.0; 358 359 /* 1st and last nodes have Dirichlet boundary condition - 360 set indices there to -1 */ 361 362 for (i=0; i < nz-1; i++) indx[i] = i-1; 363 indx[nz-1] = -1; 364 365 ipq = 0; 366 for (il=0; il < nz-1; il++) { 367 ip = ipq; 368 ipq = ip+1; 369 zip = z[ip]; 370 zipq = z[ipq]; 371 dl = zipq-zip; 372 zquad[il][0] = zip; 373 zquad[il][1] = (0.5)*(zip+zipq); 374 zquad[il][2] = zipq; 375 dlen[il] = PetscAbsScalar(dl); 376 nli[il][0] = ip; 377 nli[il][1] = ipq; 378 } 379 380 for (il=0; il < nz-1; il++) { 381 for (iquad=0; iquad < 3; iquad++) { 382 dd = (dlen[il])*(qdwt[iquad]); 383 zz = zquad[il][iquad]; 384 385 for (iq=0; iq < 2; iq++) { 386 ip = nli[il][iq]; 387 b_z = bspl(z,zz,il,iq,nli,2); 388 i = indx[ip]; 389 390 if (i > -1) { 391 for (iqq=0; iqq < 2; iqq++) { 392 ipp = nli[il][iqq]; 393 bb_z = bspl(z,zz,il,iqq,nli,2); 394 j = indx[ipp]; 395 bij = -b_z*bb_z; 396 397 if (j > -1) { 398 jj = 1+j-i; 399 btri[i][jj] += bij*dd; 400 } else { 401 f[i] += bij*dd*exact(z[ipp], t); 402 /* f[i] += 0.0; */ 403 /* if (il==0 && j==-1) { */ 404 /* f[i] += bij*dd*exact(zz,t); */ 405 /* }*/ /*end if*/ 406 } /*end else*/ 407 } /*end for (iqq)*/ 408 } /*end if (i>0)*/ 409 } /*end for (iq)*/ 410 } /*end for (iquad)*/ 411 } /*end for (il)*/ 412 return 0; 413 } 414 415 PetscErrorCode femA(AppCtx *obj,PetscInt nz,PetscScalar *z) 416 { 417 PetscInt i,j,il,ip,ipp,ipq,iq,iquad,iqq; 418 PetscInt nli[num_z][2],indx[num_z]; 419 PetscScalar dd,dl,zip,zipq,zz,bb,bbb,aij; 420 PetscScalar rquad[num_z][3],dlen[num_z],qdwt[3],add_term; 421 422 /* initializing everything */ 423 for (i=0; i < nz; i++) { 424 nli[i][0] = 0; 425 nli[i][1] = 0; 426 indx[i] = 0; 427 rquad[i][0] = 0.0; 428 rquad[i][1] = 0.0; 429 rquad[i][2] = 0.0; 430 dlen[i] = 0.0; 431 } /*end for (i)*/ 432 433 /* quadrature weights */ 434 qdwt[0] = 1.0/6.0; 435 qdwt[1] = 4.0/6.0; 436 qdwt[2] = 1.0/6.0; 437 438 /* 1st and last nodes have Dirichlet boundary condition - 439 set indices there to -1 */ 440 441 for (i=0; i < nz-1; i++) indx[i]=i-1; 442 indx[nz-1]=-1; 443 444 ipq = 0; 445 446 for (il=0; il < nz-1; il++) { 447 ip = ipq; 448 ipq = ip+1; 449 zip = z[ip]; 450 zipq = z[ipq]; 451 dl = zipq-zip; 452 rquad[il][0] = zip; 453 rquad[il][1] = (0.5)*(zip+zipq); 454 rquad[il][2] = zipq; 455 dlen[il] = PetscAbsScalar(dl); 456 nli[il][0] = ip; 457 nli[il][1] = ipq; 458 } /*end for (il)*/ 459 460 for (il=0; il < nz-1; il++) { 461 for (iquad=0; iquad < 3; iquad++) { 462 dd = (dlen[il])*(qdwt[iquad]); 463 zz = rquad[il][iquad]; 464 465 for (iq=0; iq < 2; iq++) { 466 ip = nli[il][iq]; 467 bb = bspl(z,zz,il,iq,nli,1); 468 i = indx[ip]; 469 if (i > -1) { 470 for (iqq=0; iqq < 2; iqq++) { 471 ipp = nli[il][iqq]; 472 bbb = bspl(z,zz,il,iqq,nli,1); 473 j = indx[ipp]; 474 aij = bb*bbb; 475 if (j > -1) { 476 add_term = aij*dd; 477 PetscCall(MatSetValue(obj->Amat,i,j,add_term,ADD_VALUES)); 478 }/*endif*/ 479 } /*end for (iqq)*/ 480 } /*end if (i>0)*/ 481 } /*end for (iq)*/ 482 } /*end for (iquad)*/ 483 } /*end for (il)*/ 484 PetscCall(MatAssemblyBegin(obj->Amat,MAT_FINAL_ASSEMBLY)); 485 PetscCall(MatAssemblyEnd(obj->Amat,MAT_FINAL_ASSEMBLY)); 486 return 0; 487 } 488 489 /*--------------------------------------------------------- 490 Function to fill the rhs vector with 491 By + g values **** 492 ---------------------------------------------------------*/ 493 PetscErrorCode rhs(AppCtx *obj,PetscScalar *y, PetscInt nz, PetscScalar *z, PetscReal t) 494 { 495 PetscInt i,j,js,je,jj; 496 PetscScalar val,g[num_z],btri[num_z][3],add_term; 497 498 for (i=0; i < nz-2; i++) { 499 for (j=0; j <= 2; j++) btri[i][j]=0.0; 500 g[i] = 0.0; 501 } 502 503 /* call femBg to set the tri-diagonal b matrix and vector g */ 504 femBg(btri,g,nz,z,t); 505 506 /* setting the entries of the right hand side vector */ 507 for (i=0; i < nz-2; i++) { 508 val = 0.0; 509 js = 0; 510 if (i == 0) js = 1; 511 je = 2; 512 if (i == nz-2) je = 1; 513 514 for (jj=js; jj <= je; jj++) { 515 j = i+jj-1; 516 val += (btri[i][jj])*(y[j]); 517 } 518 add_term = val + g[i]; 519 PetscCall(VecSetValue(obj->ksp_rhs,(PetscInt)i,(PetscScalar)add_term,INSERT_VALUES)); 520 } 521 PetscCall(VecAssemblyBegin(obj->ksp_rhs)); 522 PetscCall(VecAssemblyEnd(obj->ksp_rhs)); 523 return 0; 524 } 525 526 /*%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 527 %% Function to form the right hand side of the time-stepping problem. %% 528 %% -------------------------------------------------------------------------------------------%% 529 if (useAlhs): 530 globalout = By+g 531 else if (!useAlhs): 532 globalout = f(y,t)=Ainv(By+g), 533 in which the ksp solver to transform the problem A*ydot=By+g 534 to the problem ydot=f(y,t)=inv(A)*(By+g) 535 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%*/ 536 537 PetscErrorCode RHSfunction(TS ts,PetscReal t,Vec globalin,Vec globalout,void *ctx) 538 { 539 AppCtx *obj = (AppCtx*)ctx; 540 PetscScalar soln[num_z]; 541 const PetscScalar *soln_ptr; 542 PetscInt i,nz=obj->nz; 543 PetscReal time; 544 545 /* get the previous solution to compute updated system */ 546 PetscCall(VecGetArrayRead(globalin,&soln_ptr)); 547 for (i=0; i < num_z-2; i++) soln[i] = soln_ptr[i]; 548 PetscCall(VecRestoreArrayRead(globalin,&soln_ptr)); 549 soln[num_z-1] = 0.0; 550 soln[num_z-2] = 0.0; 551 552 /* clear out the matrix and rhs for ksp to keep things straight */ 553 PetscCall(VecSet(obj->ksp_rhs,(PetscScalar)0.0)); 554 555 time = t; 556 /* get the updated system */ 557 rhs(obj,soln,nz,obj->z,time); /* setup of the By+g rhs */ 558 559 /* do a ksp solve to get the rhs for the ts problem */ 560 if (obj->useAlhs) { 561 /* ksp_sol = ksp_rhs */ 562 PetscCall(VecCopy(obj->ksp_rhs,globalout)); 563 } else { 564 /* ksp_sol = inv(Amat)*ksp_rhs */ 565 PetscCall(Petsc_KSPSolve(obj)); 566 PetscCall(VecCopy(obj->ksp_sol,globalout)); 567 } 568 return 0; 569 } 570 571 /*TEST 572 573 build: 574 requires: !complex 575 576 test: 577 suffix: euler 578 output_file: output/ex3.out 579 580 test: 581 suffix: 2 582 args: -useAlhs 583 output_file: output/ex3.out 584 TODO: Broken because SNESComputeJacobianDefault is incompatible with TSComputeIJacobianConstant 585 586 TEST*/ 587