1 static char help[] = "Solves 1D heat equation with FEM formulation.\n\ 2 Input arguments are\n\ 3 -useAlhs: solve Alhs*U' = (Arhs*U + g) \n\ 4 otherwise, solve U' = inv(Alhs)*(Arhs*U + g) \n\n"; 5 6 /*-------------------------------------------------------------------------- 7 Solves 1D heat equation U_t = U_xx with FEM formulation: 8 Alhs*U' = rhs (= Arhs*U + g) 9 We thank Chris Cox <clcox@clemson.edu> for contributing the original code 10 ----------------------------------------------------------------------------*/ 11 12 #include <petscksp.h> 13 #include <petscts.h> 14 15 /* special variable - max size of all arrays */ 16 #define num_z 10 17 18 /* 19 User-defined application context - contains data needed by the 20 application-provided call-back routines. 21 */ 22 typedef struct { 23 Mat Amat; /* left hand side matrix */ 24 Vec ksp_rhs, ksp_sol; /* working vectors for formulating inv(Alhs)*(Arhs*U+g) */ 25 int max_probsz; /* max size of the problem */ 26 PetscBool useAlhs; /* flag (1 indicates solving Alhs*U' = Arhs*U+g */ 27 int nz; /* total number of grid points */ 28 PetscInt m; /* total number of interio grid points */ 29 Vec solution; /* global exact ts solution vector */ 30 PetscScalar *z; /* array of grid points */ 31 PetscBool debug; /* flag (1 indicates activation of debugging printouts) */ 32 } AppCtx; 33 34 extern PetscScalar exact(PetscScalar, PetscReal); 35 extern PetscErrorCode Monitor(TS, PetscInt, PetscReal, Vec, void *); 36 extern PetscErrorCode Petsc_KSPSolve(AppCtx *); 37 extern PetscScalar bspl(PetscScalar *, PetscScalar, PetscInt, PetscInt, PetscInt[][2], PetscInt); 38 extern PetscErrorCode femBg(PetscScalar[][3], PetscScalar *, PetscInt, PetscScalar *, PetscReal); 39 extern PetscErrorCode femA(AppCtx *, PetscInt, PetscScalar *); 40 extern PetscErrorCode rhs(AppCtx *, PetscScalar *, PetscInt, PetscScalar *, PetscReal); 41 extern PetscErrorCode RHSfunction(TS, PetscReal, Vec, Vec, void *); 42 43 int main(int argc, char **argv) 44 { 45 PetscInt i, m, nz, steps, max_steps, k, nphase = 1; 46 PetscScalar zInitial, zFinal, val, *z; 47 PetscReal stepsz[4], T, ftime; 48 TS ts; 49 SNES snes; 50 Mat Jmat; 51 AppCtx appctx; /* user-defined application context */ 52 Vec init_sol; /* ts solution vector */ 53 PetscMPIInt size; 54 55 PetscFunctionBeginUser; 56 PetscCall(PetscInitialize(&argc, &argv, (char *)0, help)); 57 PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD, &size)); 58 PetscCheck(size == 1, PETSC_COMM_SELF, PETSC_ERR_WRONG_MPI_SIZE, "This is a uniprocessor example only"); 59 60 /* initializations */ 61 zInitial = 0.0; 62 zFinal = 1.0; 63 nz = num_z; 64 m = nz - 2; 65 appctx.nz = nz; 66 max_steps = (PetscInt)10000; 67 68 appctx.m = m; 69 appctx.max_probsz = nz; 70 appctx.debug = PETSC_FALSE; 71 appctx.useAlhs = PETSC_FALSE; 72 73 PetscOptionsBegin(PETSC_COMM_WORLD, NULL, "", ""); 74 PetscCall(PetscOptionsName("-debug", NULL, NULL, &appctx.debug)); 75 PetscCall(PetscOptionsName("-useAlhs", NULL, NULL, &appctx.useAlhs)); 76 PetscCall(PetscOptionsRangeInt("-nphase", NULL, NULL, nphase, &nphase, NULL, 1, 3)); 77 PetscOptionsEnd(); 78 T = 0.014 / nphase; 79 80 /* create vector to hold ts solution */ 81 /*-----------------------------------*/ 82 PetscCall(VecCreate(PETSC_COMM_WORLD, &init_sol)); 83 PetscCall(VecSetSizes(init_sol, PETSC_DECIDE, m)); 84 PetscCall(VecSetFromOptions(init_sol)); 85 86 /* create vector to hold true ts soln for comparison */ 87 PetscCall(VecDuplicate(init_sol, &appctx.solution)); 88 89 /* create LHS matrix Amat */ 90 /*------------------------*/ 91 PetscCall(MatCreateSeqAIJ(PETSC_COMM_WORLD, m, m, 3, NULL, &appctx.Amat)); 92 PetscCall(MatSetFromOptions(appctx.Amat)); 93 PetscCall(MatSetUp(appctx.Amat)); 94 /* set space grid points - interio points only! */ 95 PetscCall(PetscMalloc1(nz + 1, &z)); 96 for (i = 0; i < nz; i++) z[i] = (i) * ((zFinal - zInitial) / (nz - 1)); 97 appctx.z = z; 98 PetscCall(femA(&appctx, nz, z)); 99 100 /* create the jacobian matrix */ 101 /*----------------------------*/ 102 PetscCall(MatCreate(PETSC_COMM_WORLD, &Jmat)); 103 PetscCall(MatSetSizes(Jmat, PETSC_DECIDE, PETSC_DECIDE, m, m)); 104 PetscCall(MatSetFromOptions(Jmat)); 105 PetscCall(MatSetUp(Jmat)); 106 107 /* create working vectors for formulating rhs=inv(Alhs)*(Arhs*U + g) */ 108 PetscCall(VecDuplicate(init_sol, &appctx.ksp_rhs)); 109 PetscCall(VecDuplicate(init_sol, &appctx.ksp_sol)); 110 111 /* set initial guess */ 112 /*-------------------*/ 113 for (i = 0; i < nz - 2; i++) { 114 val = exact(z[i + 1], 0.0); 115 PetscCall(VecSetValue(init_sol, i, (PetscScalar)val, INSERT_VALUES)); 116 } 117 PetscCall(VecAssemblyBegin(init_sol)); 118 PetscCall(VecAssemblyEnd(init_sol)); 119 120 /*create a time-stepping context and set the problem type */ 121 /*--------------------------------------------------------*/ 122 PetscCall(TSCreate(PETSC_COMM_WORLD, &ts)); 123 PetscCall(TSSetProblemType(ts, TS_NONLINEAR)); 124 125 /* set time-step method */ 126 PetscCall(TSSetType(ts, TSCN)); 127 128 /* Set optional user-defined monitoring routine */ 129 PetscCall(TSMonitorSet(ts, Monitor, &appctx, NULL)); 130 /* set the right hand side of U_t = RHSfunction(U,t) */ 131 PetscCall(TSSetRHSFunction(ts, NULL, (PetscErrorCode(*)(TS, PetscScalar, Vec, Vec, void *))RHSfunction, &appctx)); 132 133 if (appctx.useAlhs) { 134 /* set the left hand side matrix of Amat*U_t = rhs(U,t) */ 135 136 /* Note: this approach is incompatible with the finite differenced Jacobian set below because we can't restore the 137 * Alhs matrix without making a copy. Either finite difference the entire thing or use analytic Jacobians in both 138 * places. 139 */ 140 PetscCall(TSSetIFunction(ts, NULL, TSComputeIFunctionLinear, &appctx)); 141 PetscCall(TSSetIJacobian(ts, appctx.Amat, appctx.Amat, TSComputeIJacobianConstant, &appctx)); 142 } 143 144 /* use petsc to compute the jacobian by finite differences */ 145 PetscCall(TSGetSNES(ts, &snes)); 146 PetscCall(SNESSetJacobian(snes, Jmat, Jmat, SNESComputeJacobianDefault, NULL)); 147 148 /* get the command line options if there are any and set them */ 149 PetscCall(TSSetFromOptions(ts)); 150 151 #if defined(PETSC_HAVE_SUNDIALS2) 152 { 153 TSType type; 154 PetscBool sundialstype = PETSC_FALSE; 155 PetscCall(TSGetType(ts, &type)); 156 PetscCall(PetscObjectTypeCompare((PetscObject)ts, TSSUNDIALS, &sundialstype)); 157 PetscCheck(!sundialstype || !appctx.useAlhs, PETSC_COMM_SELF, PETSC_ERR_SUP, "Cannot use Alhs formulation for TSSUNDIALS type"); 158 } 159 #endif 160 /* Sets the initial solution */ 161 PetscCall(TSSetSolution(ts, init_sol)); 162 163 stepsz[0] = 1.0 / (2.0 * (nz - 1) * (nz - 1)); /* (mesh_size)^2/2.0 */ 164 ftime = 0.0; 165 for (k = 0; k < nphase; k++) { 166 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))); 167 PetscCall(TSSetTime(ts, ftime)); 168 PetscCall(TSSetTimeStep(ts, stepsz[k])); 169 PetscCall(TSSetMaxSteps(ts, max_steps)); 170 PetscCall(TSSetMaxTime(ts, (k + 1) * T)); 171 PetscCall(TSSetExactFinalTime(ts, TS_EXACTFINALTIME_STEPOVER)); 172 173 /* loop over time steps */ 174 /*----------------------*/ 175 PetscCall(TSSolve(ts, init_sol)); 176 PetscCall(TSGetSolveTime(ts, &ftime)); 177 PetscCall(TSGetStepNumber(ts, &steps)); 178 stepsz[k + 1] = stepsz[k] * 1.5; /* change step size for the next phase */ 179 } 180 181 /* free space */ 182 PetscCall(TSDestroy(&ts)); 183 PetscCall(MatDestroy(&appctx.Amat)); 184 PetscCall(MatDestroy(&Jmat)); 185 PetscCall(VecDestroy(&appctx.ksp_rhs)); 186 PetscCall(VecDestroy(&appctx.ksp_sol)); 187 PetscCall(VecDestroy(&init_sol)); 188 PetscCall(VecDestroy(&appctx.solution)); 189 PetscCall(PetscFree(z)); 190 191 PetscCall(PetscFinalize()); 192 return 0; 193 } 194 195 /*------------------------------------------------------------------------ 196 Set exact solution 197 u(z,t) = sin(6*PI*z)*exp(-36.*PI*PI*t) + 3.*sin(2*PI*z)*exp(-4.*PI*PI*t) 198 --------------------------------------------------------------------------*/ 199 PetscScalar exact(PetscScalar z, PetscReal t) 200 { 201 PetscScalar val, ex1, ex2; 202 203 ex1 = PetscExpReal(-36. * PETSC_PI * PETSC_PI * t); 204 ex2 = PetscExpReal(-4. * PETSC_PI * PETSC_PI * t); 205 val = PetscSinScalar(6 * PETSC_PI * z) * ex1 + 3. * PetscSinScalar(2 * PETSC_PI * z) * ex2; 206 return val; 207 } 208 209 /* 210 Monitor - User-provided routine to monitor the solution computed at 211 each timestep. This example plots the solution and computes the 212 error in two different norms. 213 214 Input Parameters: 215 ts - the timestep context 216 step - the count of the current step (with 0 meaning the 217 initial condition) 218 time - the current time 219 u - the solution at this timestep 220 ctx - the user-provided context for this monitoring routine. 221 In this case we use the application context which contains 222 information about the problem size, workspace and the exact 223 solution. 224 */ 225 PetscErrorCode Monitor(TS ts, PetscInt step, PetscReal time, Vec u, void *ctx) 226 { 227 AppCtx *appctx = (AppCtx *)ctx; 228 PetscInt i, m = appctx->m; 229 PetscReal norm_2, norm_max, h = 1.0 / (m + 1); 230 PetscScalar *u_exact; 231 232 PetscFunctionBeginUser; 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 PetscFunctionReturn(PETSC_SUCCESS); 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 PetscFunctionBeginUser; 274 /*create the ksp context and set the operators,that is, associate the system matrix with it*/ 275 PetscCall(KSPCreate(PETSC_COMM_WORLD, &ksp)); 276 PetscCall(KSPSetOperators(ksp, obj->Amat, obj->Amat)); 277 278 /*get the preconditioner context, set its type and the tolerances*/ 279 PetscCall(KSPGetPC(ksp, &pc)); 280 PetscCall(PCSetType(pc, PCLU)); 281 PetscCall(KSPSetTolerances(ksp, 1.e-7, PETSC_DEFAULT, PETSC_DEFAULT, PETSC_DEFAULT)); 282 283 /*get the command line options if there are any and set them*/ 284 PetscCall(KSPSetFromOptions(ksp)); 285 286 /*get the linear system (ksp) solve*/ 287 PetscCall(KSPSolve(ksp, obj->ksp_rhs, obj->ksp_sol)); 288 289 PetscCall(KSPDestroy(&ksp)); 290 PetscFunctionReturn(PETSC_SUCCESS); 291 } 292 293 /*********************************************************************** 294 Function to return value of basis function or derivative of basis function. 295 *********************************************************************** 296 297 Arguments: 298 x = array of xpoints or nodal values 299 xx = point at which the basis function is to be 300 evaluated. 301 il = interval containing xx. 302 iq = indicates which of the two basis functions in 303 interval intrvl should be used 304 nll = array containing the endpoints of each interval. 305 id = If id ~= 2, the value of the basis function 306 is calculated; if id = 2, the value of the 307 derivative of the basis function is returned. 308 ***********************************************************************/ 309 310 PetscScalar bspl(PetscScalar *x, PetscScalar xx, PetscInt il, PetscInt iq, PetscInt nll[][2], PetscInt id) 311 { 312 PetscScalar x1, x2, bfcn; 313 PetscInt i1, i2, iq1, iq2; 314 315 /* Determine which basis function in interval intrvl is to be used in */ 316 iq1 = iq; 317 if (iq1 == 0) iq2 = 1; 318 else iq2 = 0; 319 320 /* Determine endpoint of the interval intrvl */ 321 i1 = nll[il][iq1]; 322 i2 = nll[il][iq2]; 323 324 /* Determine nodal values at the endpoints of the interval intrvl */ 325 x1 = x[i1]; 326 x2 = x[i2]; 327 328 /* Evaluate basis function */ 329 if (id == 2) bfcn = (1.0) / (x1 - x2); 330 else bfcn = (xx - x2) / (x1 - x2); 331 return bfcn; 332 } 333 334 /*--------------------------------------------------------- 335 Function called by rhs function to get B and g 336 ---------------------------------------------------------*/ 337 PetscErrorCode femBg(PetscScalar btri[][3], PetscScalar *f, PetscInt nz, PetscScalar *z, PetscReal t) 338 { 339 PetscInt i, j, jj, il, ip, ipp, ipq, iq, iquad, iqq; 340 PetscInt nli[num_z][2], indx[num_z]; 341 PetscScalar dd, dl, zip, zipq, zz, b_z, bb_z, bij; 342 PetscScalar zquad[num_z][3], dlen[num_z], qdwt[3]; 343 344 PetscFunctionBeginUser; 345 /* initializing everything - btri and f are initialized in rhs.c */ 346 for (i = 0; i < nz; i++) { 347 nli[i][0] = 0; 348 nli[i][1] = 0; 349 indx[i] = 0; 350 zquad[i][0] = 0.0; 351 zquad[i][1] = 0.0; 352 zquad[i][2] = 0.0; 353 dlen[i] = 0.0; 354 } /*end for (i)*/ 355 356 /* quadrature weights */ 357 qdwt[0] = 1.0 / 6.0; 358 qdwt[1] = 4.0 / 6.0; 359 qdwt[2] = 1.0 / 6.0; 360 361 /* 1st and last nodes have Dirichlet boundary condition - 362 set indices there to -1 */ 363 364 for (i = 0; i < nz - 1; i++) indx[i] = i - 1; 365 indx[nz - 1] = -1; 366 367 ipq = 0; 368 for (il = 0; il < nz - 1; il++) { 369 ip = ipq; 370 ipq = ip + 1; 371 zip = z[ip]; 372 zipq = z[ipq]; 373 dl = zipq - zip; 374 zquad[il][0] = zip; 375 zquad[il][1] = (0.5) * (zip + zipq); 376 zquad[il][2] = zipq; 377 dlen[il] = PetscAbsScalar(dl); 378 nli[il][0] = ip; 379 nli[il][1] = ipq; 380 } 381 382 for (il = 0; il < nz - 1; il++) { 383 for (iquad = 0; iquad < 3; iquad++) { 384 dd = (dlen[il]) * (qdwt[iquad]); 385 zz = zquad[il][iquad]; 386 387 for (iq = 0; iq < 2; iq++) { 388 ip = nli[il][iq]; 389 b_z = bspl(z, zz, il, iq, nli, 2); 390 i = indx[ip]; 391 392 if (i > -1) { 393 for (iqq = 0; iqq < 2; iqq++) { 394 ipp = nli[il][iqq]; 395 bb_z = bspl(z, zz, il, iqq, nli, 2); 396 j = indx[ipp]; 397 bij = -b_z * bb_z; 398 399 if (j > -1) { 400 jj = 1 + j - i; 401 btri[i][jj] += bij * dd; 402 } else { 403 f[i] += bij * dd * exact(z[ipp], t); 404 /* f[i] += 0.0; */ 405 /* if (il==0 && j==-1) { */ 406 /* f[i] += bij*dd*exact(zz,t); */ 407 /* }*/ /*end if*/ 408 } /*end else*/ 409 } /*end for (iqq)*/ 410 } /*end if (i>0)*/ 411 } /*end for (iq)*/ 412 } /*end for (iquad)*/ 413 } /*end for (il)*/ 414 PetscFunctionReturn(PETSC_SUCCESS); 415 } 416 417 PetscErrorCode femA(AppCtx *obj, PetscInt nz, PetscScalar *z) 418 { 419 PetscInt i, j, il, ip, ipp, ipq, iq, iquad, iqq; 420 PetscInt nli[num_z][2], indx[num_z]; 421 PetscScalar dd, dl, zip, zipq, zz, bb, bbb, aij; 422 PetscScalar rquad[num_z][3], dlen[num_z], qdwt[3], add_term; 423 424 PetscFunctionBeginUser; 425 /* initializing everything */ 426 for (i = 0; i < nz; i++) { 427 nli[i][0] = 0; 428 nli[i][1] = 0; 429 indx[i] = 0; 430 rquad[i][0] = 0.0; 431 rquad[i][1] = 0.0; 432 rquad[i][2] = 0.0; 433 dlen[i] = 0.0; 434 } /*end for (i)*/ 435 436 /* quadrature weights */ 437 qdwt[0] = 1.0 / 6.0; 438 qdwt[1] = 4.0 / 6.0; 439 qdwt[2] = 1.0 / 6.0; 440 441 /* 1st and last nodes have Dirichlet boundary condition - 442 set indices there to -1 */ 443 444 for (i = 0; i < nz - 1; i++) indx[i] = i - 1; 445 indx[nz - 1] = -1; 446 447 ipq = 0; 448 449 for (il = 0; il < nz - 1; il++) { 450 ip = ipq; 451 ipq = ip + 1; 452 zip = z[ip]; 453 zipq = z[ipq]; 454 dl = zipq - zip; 455 rquad[il][0] = zip; 456 rquad[il][1] = (0.5) * (zip + zipq); 457 rquad[il][2] = zipq; 458 dlen[il] = PetscAbsScalar(dl); 459 nli[il][0] = ip; 460 nli[il][1] = ipq; 461 } /*end for (il)*/ 462 463 for (il = 0; il < nz - 1; il++) { 464 for (iquad = 0; iquad < 3; iquad++) { 465 dd = (dlen[il]) * (qdwt[iquad]); 466 zz = rquad[il][iquad]; 467 468 for (iq = 0; iq < 2; iq++) { 469 ip = nli[il][iq]; 470 bb = bspl(z, zz, il, iq, nli, 1); 471 i = indx[ip]; 472 if (i > -1) { 473 for (iqq = 0; iqq < 2; iqq++) { 474 ipp = nli[il][iqq]; 475 bbb = bspl(z, zz, il, iqq, nli, 1); 476 j = indx[ipp]; 477 aij = bb * bbb; 478 if (j > -1) { 479 add_term = aij * dd; 480 PetscCall(MatSetValue(obj->Amat, i, j, add_term, ADD_VALUES)); 481 } /*endif*/ 482 } /*end for (iqq)*/ 483 } /*end if (i>0)*/ 484 } /*end for (iq)*/ 485 } /*end for (iquad)*/ 486 } /*end for (il)*/ 487 PetscCall(MatAssemblyBegin(obj->Amat, MAT_FINAL_ASSEMBLY)); 488 PetscCall(MatAssemblyEnd(obj->Amat, MAT_FINAL_ASSEMBLY)); 489 PetscFunctionReturn(PETSC_SUCCESS); 490 } 491 492 /*--------------------------------------------------------- 493 Function to fill the rhs vector with 494 By + g values **** 495 ---------------------------------------------------------*/ 496 PetscErrorCode rhs(AppCtx *obj, PetscScalar *y, PetscInt nz, PetscScalar *z, PetscReal t) 497 { 498 PetscInt i, j, js, je, jj; 499 PetscScalar val, g[num_z], btri[num_z][3], add_term; 500 501 PetscFunctionBeginUser; 502 for (i = 0; i < nz - 2; i++) { 503 for (j = 0; j <= 2; j++) btri[i][j] = 0.0; 504 g[i] = 0.0; 505 } 506 507 /* call femBg to set the tri-diagonal b matrix and vector g */ 508 PetscCall(femBg(btri, g, nz, z, t)); 509 510 /* setting the entries of the right hand side vector */ 511 for (i = 0; i < nz - 2; i++) { 512 val = 0.0; 513 js = 0; 514 if (i == 0) js = 1; 515 je = 2; 516 if (i == nz - 2) je = 1; 517 518 for (jj = js; jj <= je; jj++) { 519 j = i + jj - 1; 520 val += (btri[i][jj]) * (y[j]); 521 } 522 add_term = val + g[i]; 523 PetscCall(VecSetValue(obj->ksp_rhs, (PetscInt)i, (PetscScalar)add_term, INSERT_VALUES)); 524 } 525 PetscCall(VecAssemblyBegin(obj->ksp_rhs)); 526 PetscCall(VecAssemblyEnd(obj->ksp_rhs)); 527 PetscFunctionReturn(PETSC_SUCCESS); 528 } 529 530 /*%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 531 %% Function to form the right hand side of the time-stepping problem. %% 532 %% -------------------------------------------------------------------------------------------%% 533 if (useAlhs): 534 globalout = By+g 535 else if (!useAlhs): 536 globalout = f(y,t)=Ainv(By+g), 537 in which the ksp solver to transform the problem A*ydot=By+g 538 to the problem ydot=f(y,t)=inv(A)*(By+g) 539 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%*/ 540 541 PetscErrorCode RHSfunction(TS ts, PetscReal t, Vec globalin, Vec globalout, void *ctx) 542 { 543 AppCtx *obj = (AppCtx *)ctx; 544 PetscScalar soln[num_z]; 545 const PetscScalar *soln_ptr; 546 PetscInt i, nz = obj->nz; 547 PetscReal time; 548 549 PetscFunctionBeginUser; 550 /* get the previous solution to compute updated system */ 551 PetscCall(VecGetArrayRead(globalin, &soln_ptr)); 552 for (i = 0; i < num_z - 2; i++) soln[i] = soln_ptr[i]; 553 PetscCall(VecRestoreArrayRead(globalin, &soln_ptr)); 554 soln[num_z - 1] = 0.0; 555 soln[num_z - 2] = 0.0; 556 557 /* clear out the matrix and rhs for ksp to keep things straight */ 558 PetscCall(VecSet(obj->ksp_rhs, (PetscScalar)0.0)); 559 560 time = t; 561 /* get the updated system */ 562 PetscCall(rhs(obj, soln, nz, obj->z, time)); /* setup of the By+g rhs */ 563 564 /* do a ksp solve to get the rhs for the ts problem */ 565 if (obj->useAlhs) { 566 /* ksp_sol = ksp_rhs */ 567 PetscCall(VecCopy(obj->ksp_rhs, globalout)); 568 } else { 569 /* ksp_sol = inv(Amat)*ksp_rhs */ 570 PetscCall(Petsc_KSPSolve(obj)); 571 PetscCall(VecCopy(obj->ksp_sol, globalout)); 572 } 573 PetscFunctionReturn(PETSC_SUCCESS); 574 } 575 576 /*TEST 577 578 build: 579 requires: !complex 580 581 test: 582 suffix: euler 583 output_file: output/ex3.out 584 585 test: 586 suffix: 2 587 args: -useAlhs 588 output_file: output/ex3.out 589 TODO: Broken because SNESComputeJacobianDefault is incompatible with TSComputeIJacobianConstant 590 591 TEST*/ 592