1 2 static char help[] = "Model Equations for Advection-Diffusion\n"; 3 4 /* 5 Page 9, Section 1.2 Model Equations for Advection-Diffusion 6 7 u_t = a u_x + d u_xx 8 9 The initial conditions used here different then in the book. 10 11 */ 12 13 /* 14 Helpful runtime linear solver options: 15 -pc_type mg -da_refine 2 -snes_monitor -ksp_monitor -ts_view (geometric multigrid with three levels) 16 17 */ 18 19 /* 20 Include "petscts.h" so that we can use TS solvers. Note that this file 21 automatically includes: 22 petscsys.h - base PETSc routines petscvec.h - vectors 23 petscmat.h - matrices 24 petscis.h - index sets petscksp.h - Krylov subspace methods 25 petscviewer.h - viewers petscpc.h - preconditioners 26 petscksp.h - linear solvers petscsnes.h - nonlinear solvers 27 */ 28 29 #include <petscts.h> 30 #include <petscdm.h> 31 #include <petscdmda.h> 32 33 /* 34 User-defined application context - contains data needed by the 35 application-provided call-back routines. 36 */ 37 typedef struct { 38 PetscScalar a, d; /* advection and diffusion strength */ 39 PetscBool upwind; 40 } AppCtx; 41 42 /* 43 User-defined routines 44 */ 45 extern PetscErrorCode InitialConditions(TS, Vec, AppCtx *); 46 extern PetscErrorCode RHSMatrixHeat(TS, PetscReal, Vec, Mat, Mat, void *); 47 extern PetscErrorCode Solution(TS, PetscReal, Vec, AppCtx *); 48 49 int main(int argc, char **argv) 50 { 51 AppCtx appctx; /* user-defined application context */ 52 TS ts; /* timestepping context */ 53 Vec U; /* approximate solution vector */ 54 PetscReal dt; 55 DM da; 56 PetscInt M; 57 58 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 59 Initialize program and set problem parameters 60 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 61 62 PetscFunctionBeginUser; 63 PetscCall(PetscInitialize(&argc, &argv, (char *)0, help)); 64 appctx.a = 1.0; 65 appctx.d = 0.0; 66 PetscCall(PetscOptionsGetScalar(NULL, NULL, "-a", &appctx.a, NULL)); 67 PetscCall(PetscOptionsGetScalar(NULL, NULL, "-d", &appctx.d, NULL)); 68 appctx.upwind = PETSC_TRUE; 69 PetscCall(PetscOptionsGetBool(NULL, NULL, "-upwind", &appctx.upwind, NULL)); 70 71 PetscCall(DMDACreate1d(PETSC_COMM_WORLD, DM_BOUNDARY_PERIODIC, 60, 1, 1, NULL, &da)); 72 PetscCall(DMSetFromOptions(da)); 73 PetscCall(DMSetUp(da)); 74 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 75 Create vector data structures 76 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 77 78 /* 79 Create vector data structures for approximate and exact solutions 80 */ 81 PetscCall(DMCreateGlobalVector(da, &U)); 82 83 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 84 Create timestepping solver context 85 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 86 87 PetscCall(TSCreate(PETSC_COMM_WORLD, &ts)); 88 PetscCall(TSSetDM(ts, da)); 89 90 /* 91 For linear problems with a time-dependent f(U,t) in the equation 92 u_t = f(u,t), the user provides the discretized right-hand-side 93 as a time-dependent matrix. 94 */ 95 PetscCall(TSSetRHSFunction(ts, NULL, TSComputeRHSFunctionLinear, &appctx)); 96 PetscCall(TSSetRHSJacobian(ts, NULL, NULL, RHSMatrixHeat, &appctx)); 97 PetscCall(TSSetSolutionFunction(ts, (PetscErrorCode(*)(TS, PetscReal, Vec, void *))Solution, &appctx)); 98 99 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 100 Customize timestepping solver: 101 - Set timestepping duration info 102 Then set runtime options, which can override these defaults. 103 For example, 104 -ts_max_steps <maxsteps> -ts_max_time <maxtime> 105 to override the defaults set by TSSetMaxSteps()/TSSetMaxTime(). 106 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 107 108 PetscCall(DMDAGetInfo(da, PETSC_IGNORE, &M, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)); 109 dt = .48 / (M * M); 110 PetscCall(TSSetTimeStep(ts, dt)); 111 PetscCall(TSSetMaxSteps(ts, 1000)); 112 PetscCall(TSSetMaxTime(ts, 100.0)); 113 PetscCall(TSSetExactFinalTime(ts, TS_EXACTFINALTIME_STEPOVER)); 114 PetscCall(TSSetType(ts, TSARKIMEX)); 115 PetscCall(TSSetFromOptions(ts)); 116 117 /* 118 Evaluate initial conditions 119 */ 120 PetscCall(InitialConditions(ts, U, &appctx)); 121 122 /* 123 Run the timestepping solver 124 */ 125 PetscCall(TSSolve(ts, U)); 126 127 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 128 Free work space. All PETSc objects should be destroyed when they 129 are no longer needed. 130 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 131 132 PetscCall(TSDestroy(&ts)); 133 PetscCall(VecDestroy(&U)); 134 PetscCall(DMDestroy(&da)); 135 136 /* 137 Always call PetscFinalize() before exiting a program. This routine 138 - finalizes the PETSc libraries as well as MPI 139 - provides summary and diagnostic information if certain runtime 140 options are chosen (e.g., -log_view). 141 */ 142 PetscCall(PetscFinalize()); 143 return 0; 144 } 145 /* --------------------------------------------------------------------- */ 146 /* 147 InitialConditions - Computes the solution at the initial time. 148 149 Input Parameter: 150 u - uninitialized solution vector (global) 151 appctx - user-defined application context 152 153 Output Parameter: 154 u - vector with solution at initial time (global) 155 */ 156 PetscErrorCode InitialConditions(TS ts, Vec U, AppCtx *appctx) 157 { 158 PetscScalar *u, h; 159 PetscInt i, mstart, mend, xm, M; 160 DM da; 161 162 PetscCall(TSGetDM(ts, &da)); 163 PetscCall(DMDAGetCorners(da, &mstart, 0, 0, &xm, 0, 0)); 164 PetscCall(DMDAGetInfo(da, PETSC_IGNORE, &M, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)); 165 h = 1.0 / M; 166 mend = mstart + xm; 167 /* 168 Get a pointer to vector data. 169 - For default PETSc vectors, VecGetArray() returns a pointer to 170 the data array. Otherwise, the routine is implementation dependent. 171 - You MUST call VecRestoreArray() when you no longer need access to 172 the array. 173 - Note that the Fortran interface to VecGetArray() differs from the 174 C version. See the users manual for details. 175 */ 176 PetscCall(DMDAVecGetArray(da, U, &u)); 177 178 /* 179 We initialize the solution array by simply writing the solution 180 directly into the array locations. Alternatively, we could use 181 VecSetValues() or VecSetValuesLocal(). 182 */ 183 for (i = mstart; i < mend; i++) u[i] = PetscSinScalar(PETSC_PI * i * 6. * h) + 3. * PetscSinScalar(PETSC_PI * i * 2. * h); 184 185 /* 186 Restore vector 187 */ 188 PetscCall(DMDAVecRestoreArray(da, U, &u)); 189 return 0; 190 } 191 /* --------------------------------------------------------------------- */ 192 /* 193 Solution - Computes the exact solution at a given time. 194 195 Input Parameters: 196 t - current time 197 solution - vector in which exact solution will be computed 198 appctx - user-defined application context 199 200 Output Parameter: 201 solution - vector with the newly computed exact solution 202 */ 203 PetscErrorCode Solution(TS ts, PetscReal t, Vec U, AppCtx *appctx) 204 { 205 PetscScalar *u, ex1, ex2, sc1, sc2, h; 206 PetscInt i, mstart, mend, xm, M; 207 DM da; 208 209 PetscCall(TSGetDM(ts, &da)); 210 PetscCall(DMDAGetCorners(da, &mstart, 0, 0, &xm, 0, 0)); 211 PetscCall(DMDAGetInfo(da, PETSC_IGNORE, &M, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)); 212 h = 1.0 / M; 213 mend = mstart + xm; 214 /* 215 Get a pointer to vector data. 216 */ 217 PetscCall(DMDAVecGetArray(da, U, &u)); 218 219 /* 220 Simply write the solution directly into the array locations. 221 Alternatively, we culd use VecSetValues() or VecSetValuesLocal(). 222 */ 223 ex1 = PetscExpScalar(-36. * PETSC_PI * PETSC_PI * appctx->d * t); 224 ex2 = PetscExpScalar(-4. * PETSC_PI * PETSC_PI * appctx->d * t); 225 sc1 = PETSC_PI * 6. * h; 226 sc2 = PETSC_PI * 2. * h; 227 for (i = mstart; i < mend; i++) u[i] = PetscSinScalar(sc1 * (PetscReal)i + appctx->a * PETSC_PI * 6. * t) * ex1 + 3. * PetscSinScalar(sc2 * (PetscReal)i + appctx->a * PETSC_PI * 2. * t) * ex2; 228 229 /* 230 Restore vector 231 */ 232 PetscCall(DMDAVecRestoreArray(da, U, &u)); 233 return 0; 234 } 235 236 /* --------------------------------------------------------------------- */ 237 /* 238 RHSMatrixHeat - User-provided routine to compute the right-hand-side 239 matrix for the heat equation. 240 241 Input Parameters: 242 ts - the TS context 243 t - current time 244 global_in - global input vector 245 dummy - optional user-defined context, as set by TSetRHSJacobian() 246 247 Output Parameters: 248 AA - Jacobian matrix 249 BB - optionally different preconditioning matrix 250 str - flag indicating matrix structure 251 252 Notes: 253 Recall that MatSetValues() uses 0-based row and column numbers 254 in Fortran as well as in C. 255 */ 256 PetscErrorCode RHSMatrixHeat(TS ts, PetscReal t, Vec U, Mat AA, Mat BB, void *ctx) 257 { 258 Mat A = AA; /* Jacobian matrix */ 259 AppCtx *appctx = (AppCtx *)ctx; /* user-defined application context */ 260 PetscInt mstart, mend; 261 PetscInt i, idx[3], M, xm; 262 PetscScalar v[3], h; 263 DM da; 264 265 PetscCall(TSGetDM(ts, &da)); 266 PetscCall(DMDAGetInfo(da, 0, &M, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)); 267 PetscCall(DMDAGetCorners(da, &mstart, 0, 0, &xm, 0, 0)); 268 h = 1.0 / M; 269 mend = mstart + xm; 270 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 271 Compute entries for the locally owned part of the matrix 272 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 273 /* 274 Set matrix rows corresponding to boundary data 275 */ 276 277 /* diffusion */ 278 v[0] = appctx->d / (h * h); 279 v[1] = -2.0 * appctx->d / (h * h); 280 v[2] = appctx->d / (h * h); 281 if (!mstart) { 282 idx[0] = M - 1; 283 idx[1] = 0; 284 idx[2] = 1; 285 PetscCall(MatSetValues(A, 1, &mstart, 3, idx, v, INSERT_VALUES)); 286 mstart++; 287 } 288 289 if (mend == M) { 290 mend--; 291 idx[0] = M - 2; 292 idx[1] = M - 1; 293 idx[2] = 0; 294 PetscCall(MatSetValues(A, 1, &mend, 3, idx, v, INSERT_VALUES)); 295 } 296 297 /* 298 Set matrix rows corresponding to interior data. We construct the 299 matrix one row at a time. 300 */ 301 for (i = mstart; i < mend; i++) { 302 idx[0] = i - 1; 303 idx[1] = i; 304 idx[2] = i + 1; 305 PetscCall(MatSetValues(A, 1, &i, 3, idx, v, INSERT_VALUES)); 306 } 307 PetscCall(MatAssemblyBegin(A, MAT_FLUSH_ASSEMBLY)); 308 PetscCall(MatAssemblyEnd(A, MAT_FLUSH_ASSEMBLY)); 309 310 PetscCall(DMDAGetCorners(da, &mstart, 0, 0, &xm, 0, 0)); 311 mend = mstart + xm; 312 if (!appctx->upwind) { 313 /* advection -- centered differencing */ 314 v[0] = -.5 * appctx->a / (h); 315 v[1] = .5 * appctx->a / (h); 316 if (!mstart) { 317 idx[0] = M - 1; 318 idx[1] = 1; 319 PetscCall(MatSetValues(A, 1, &mstart, 2, idx, v, ADD_VALUES)); 320 mstart++; 321 } 322 323 if (mend == M) { 324 mend--; 325 idx[0] = M - 2; 326 idx[1] = 0; 327 PetscCall(MatSetValues(A, 1, &mend, 2, idx, v, ADD_VALUES)); 328 } 329 330 for (i = mstart; i < mend; i++) { 331 idx[0] = i - 1; 332 idx[1] = i + 1; 333 PetscCall(MatSetValues(A, 1, &i, 2, idx, v, ADD_VALUES)); 334 } 335 } else { 336 /* advection -- upwinding */ 337 v[0] = -appctx->a / (h); 338 v[1] = appctx->a / (h); 339 if (!mstart) { 340 idx[0] = 0; 341 idx[1] = 1; 342 PetscCall(MatSetValues(A, 1, &mstart, 2, idx, v, ADD_VALUES)); 343 mstart++; 344 } 345 346 if (mend == M) { 347 mend--; 348 idx[0] = M - 1; 349 idx[1] = 0; 350 PetscCall(MatSetValues(A, 1, &mend, 2, idx, v, ADD_VALUES)); 351 } 352 353 for (i = mstart; i < mend; i++) { 354 idx[0] = i; 355 idx[1] = i + 1; 356 PetscCall(MatSetValues(A, 1, &i, 2, idx, v, ADD_VALUES)); 357 } 358 } 359 360 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 361 Complete the matrix assembly process and set some options 362 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 363 /* 364 Assemble matrix, using the 2-step process: 365 MatAssemblyBegin(), MatAssemblyEnd() 366 Computations can be done while messages are in transition 367 by placing code between these two statements. 368 */ 369 PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY)); 370 PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY)); 371 372 /* 373 Set and option to indicate that we will never add a new nonzero location 374 to the matrix. If we do, it will generate an error. 375 */ 376 PetscCall(MatSetOption(A, MAT_NEW_NONZERO_LOCATION_ERR, PETSC_TRUE)); 377 return 0; 378 } 379 380 /*TEST 381 382 test: 383 args: -pc_type mg -da_refine 2 -ts_view -ts_monitor -ts_max_time .3 -mg_levels_ksp_max_it 3 384 requires: double 385 filter: grep -v "total number of" 386 387 test: 388 suffix: 2 389 args: -pc_type mg -da_refine 2 -ts_view -ts_monitor_draw_solution -ts_monitor -ts_max_time .3 -mg_levels_ksp_max_it 3 390 requires: x 391 output_file: output/ex3_1.out 392 requires: double 393 filter: grep -v "total number of" 394 395 TEST*/ 396