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 PetscFunctionBeginUser; 163 PetscCall(TSGetDM(ts, &da)); 164 PetscCall(DMDAGetCorners(da, &mstart, 0, 0, &xm, 0, 0)); 165 PetscCall(DMDAGetInfo(da, PETSC_IGNORE, &M, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)); 166 h = 1.0 / M; 167 mend = mstart + xm; 168 /* 169 Get a pointer to vector data. 170 - For default PETSc vectors, VecGetArray() returns a pointer to 171 the data array. Otherwise, the routine is implementation dependent. 172 - You MUST call VecRestoreArray() when you no longer need access to 173 the array. 174 - Note that the Fortran interface to VecGetArray() differs from the 175 C version. See the users manual for details. 176 */ 177 PetscCall(DMDAVecGetArray(da, U, &u)); 178 179 /* 180 We initialize the solution array by simply writing the solution 181 directly into the array locations. Alternatively, we could use 182 VecSetValues() or VecSetValuesLocal(). 183 */ 184 for (i = mstart; i < mend; i++) u[i] = PetscSinScalar(PETSC_PI * i * 6. * h) + 3. * PetscSinScalar(PETSC_PI * i * 2. * h); 185 186 /* 187 Restore vector 188 */ 189 PetscCall(DMDAVecRestoreArray(da, U, &u)); 190 PetscFunctionReturn(PETSC_SUCCESS); 191 } 192 /* --------------------------------------------------------------------- */ 193 /* 194 Solution - Computes the exact solution at a given time. 195 196 Input Parameters: 197 t - current time 198 solution - vector in which exact solution will be computed 199 appctx - user-defined application context 200 201 Output Parameter: 202 solution - vector with the newly computed exact solution 203 */ 204 PetscErrorCode Solution(TS ts, PetscReal t, Vec U, AppCtx *appctx) 205 { 206 PetscScalar *u, ex1, ex2, sc1, sc2, h; 207 PetscInt i, mstart, mend, xm, M; 208 DM da; 209 210 PetscFunctionBeginUser; 211 PetscCall(TSGetDM(ts, &da)); 212 PetscCall(DMDAGetCorners(da, &mstart, 0, 0, &xm, 0, 0)); 213 PetscCall(DMDAGetInfo(da, PETSC_IGNORE, &M, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)); 214 h = 1.0 / M; 215 mend = mstart + xm; 216 /* 217 Get a pointer to vector data. 218 */ 219 PetscCall(DMDAVecGetArray(da, U, &u)); 220 221 /* 222 Simply write the solution directly into the array locations. 223 Alternatively, we culd use VecSetValues() or VecSetValuesLocal(). 224 */ 225 ex1 = PetscExpScalar(-36. * PETSC_PI * PETSC_PI * appctx->d * t); 226 ex2 = PetscExpScalar(-4. * PETSC_PI * PETSC_PI * appctx->d * t); 227 sc1 = PETSC_PI * 6. * h; 228 sc2 = PETSC_PI * 2. * h; 229 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; 230 231 /* 232 Restore vector 233 */ 234 PetscCall(DMDAVecRestoreArray(da, U, &u)); 235 PetscFunctionReturn(PETSC_SUCCESS); 236 } 237 238 /* --------------------------------------------------------------------- */ 239 /* 240 RHSMatrixHeat - User-provided routine to compute the right-hand-side 241 matrix for the heat equation. 242 243 Input Parameters: 244 ts - the TS context 245 t - current time 246 global_in - global input vector 247 dummy - optional user-defined context, as set by TSetRHSJacobian() 248 249 Output Parameters: 250 AA - Jacobian matrix 251 BB - optionally different preconditioning matrix 252 str - flag indicating matrix structure 253 254 Notes: 255 Recall that MatSetValues() uses 0-based row and column numbers 256 in Fortran as well as in C. 257 */ 258 PetscErrorCode RHSMatrixHeat(TS ts, PetscReal t, Vec U, Mat AA, Mat BB, void *ctx) 259 { 260 Mat A = AA; /* Jacobian matrix */ 261 AppCtx *appctx = (AppCtx *)ctx; /* user-defined application context */ 262 PetscInt mstart, mend; 263 PetscInt i, idx[3], M, xm; 264 PetscScalar v[3], h; 265 DM da; 266 267 PetscFunctionBeginUser; 268 PetscCall(TSGetDM(ts, &da)); 269 PetscCall(DMDAGetInfo(da, 0, &M, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)); 270 PetscCall(DMDAGetCorners(da, &mstart, 0, 0, &xm, 0, 0)); 271 h = 1.0 / M; 272 mend = mstart + xm; 273 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 274 Compute entries for the locally owned part of the matrix 275 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 276 /* 277 Set matrix rows corresponding to boundary data 278 */ 279 280 /* diffusion */ 281 v[0] = appctx->d / (h * h); 282 v[1] = -2.0 * appctx->d / (h * h); 283 v[2] = appctx->d / (h * h); 284 if (!mstart) { 285 idx[0] = M - 1; 286 idx[1] = 0; 287 idx[2] = 1; 288 PetscCall(MatSetValues(A, 1, &mstart, 3, idx, v, INSERT_VALUES)); 289 mstart++; 290 } 291 292 if (mend == M) { 293 mend--; 294 idx[0] = M - 2; 295 idx[1] = M - 1; 296 idx[2] = 0; 297 PetscCall(MatSetValues(A, 1, &mend, 3, idx, v, INSERT_VALUES)); 298 } 299 300 /* 301 Set matrix rows corresponding to interior data. We construct the 302 matrix one row at a time. 303 */ 304 for (i = mstart; i < mend; i++) { 305 idx[0] = i - 1; 306 idx[1] = i; 307 idx[2] = i + 1; 308 PetscCall(MatSetValues(A, 1, &i, 3, idx, v, INSERT_VALUES)); 309 } 310 PetscCall(MatAssemblyBegin(A, MAT_FLUSH_ASSEMBLY)); 311 PetscCall(MatAssemblyEnd(A, MAT_FLUSH_ASSEMBLY)); 312 313 PetscCall(DMDAGetCorners(da, &mstart, 0, 0, &xm, 0, 0)); 314 mend = mstart + xm; 315 if (!appctx->upwind) { 316 /* advection -- centered differencing */ 317 v[0] = -.5 * appctx->a / (h); 318 v[1] = .5 * appctx->a / (h); 319 if (!mstart) { 320 idx[0] = M - 1; 321 idx[1] = 1; 322 PetscCall(MatSetValues(A, 1, &mstart, 2, idx, v, ADD_VALUES)); 323 mstart++; 324 } 325 326 if (mend == M) { 327 mend--; 328 idx[0] = M - 2; 329 idx[1] = 0; 330 PetscCall(MatSetValues(A, 1, &mend, 2, idx, v, ADD_VALUES)); 331 } 332 333 for (i = mstart; i < mend; i++) { 334 idx[0] = i - 1; 335 idx[1] = i + 1; 336 PetscCall(MatSetValues(A, 1, &i, 2, idx, v, ADD_VALUES)); 337 } 338 } else { 339 /* advection -- upwinding */ 340 v[0] = -appctx->a / (h); 341 v[1] = appctx->a / (h); 342 if (!mstart) { 343 idx[0] = 0; 344 idx[1] = 1; 345 PetscCall(MatSetValues(A, 1, &mstart, 2, idx, v, ADD_VALUES)); 346 mstart++; 347 } 348 349 if (mend == M) { 350 mend--; 351 idx[0] = M - 1; 352 idx[1] = 0; 353 PetscCall(MatSetValues(A, 1, &mend, 2, idx, v, ADD_VALUES)); 354 } 355 356 for (i = mstart; i < mend; i++) { 357 idx[0] = i; 358 idx[1] = i + 1; 359 PetscCall(MatSetValues(A, 1, &i, 2, idx, v, ADD_VALUES)); 360 } 361 } 362 363 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 364 Complete the matrix assembly process and set some options 365 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 366 /* 367 Assemble matrix, using the 2-step process: 368 MatAssemblyBegin(), MatAssemblyEnd() 369 Computations can be done while messages are in transition 370 by placing code between these two statements. 371 */ 372 PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY)); 373 PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY)); 374 375 /* 376 Set and option to indicate that we will never add a new nonzero location 377 to the matrix. If we do, it will generate an error. 378 */ 379 PetscCall(MatSetOption(A, MAT_NEW_NONZERO_LOCATION_ERR, PETSC_TRUE)); 380 PetscFunctionReturn(PETSC_SUCCESS); 381 } 382 383 /*TEST 384 385 test: 386 args: -pc_type mg -da_refine 2 -ts_view -ts_monitor -ts_max_time .3 -mg_levels_ksp_max_it 3 387 requires: double 388 filter: grep -v "total number of" 389 390 test: 391 suffix: 2 392 args: -pc_type mg -da_refine 2 -ts_view -ts_monitor_draw_solution -ts_monitor -ts_max_time .3 -mg_levels_ksp_max_it 3 393 requires: x 394 output_file: output/ex3_1.out 395 requires: double 396 filter: grep -v "total number of" 397 398 TEST*/ 399