1 static char help[] = "Model Equations for Advection-Diffusion\n"; 2 3 /* 4 Page 9, Section 1.2 Model Equations for Advection-Diffusion 5 6 u_t = a u_x + d u_xx 7 8 The initial conditions used here different then in the book. 9 10 */ 11 12 /* 13 Helpful runtime linear solver options: 14 -pc_type mg -da_refine 2 -snes_monitor -ksp_monitor -ts_view (geometric multigrid with three levels) 15 16 */ 17 18 /* 19 Include "petscts.h" so that we can use TS solvers. Note that this file 20 automatically includes: 21 petscsys.h - base PETSc routines petscvec.h - vectors 22 petscmat.h - matrices 23 petscis.h - index sets petscksp.h - Krylov subspace methods 24 petscviewer.h - viewers petscpc.h - preconditioners 25 petscksp.h - linear solvers petscsnes.h - nonlinear solvers 26 */ 27 28 #include <petscts.h> 29 #include <petscdm.h> 30 #include <petscdmda.h> 31 32 /* 33 User-defined application context - contains data needed by the 34 application-provided call-back routines. 35 */ 36 typedef struct { 37 PetscScalar a, d; /* advection and diffusion strength */ 38 PetscBool upwind; 39 } AppCtx; 40 41 /* 42 User-defined routines 43 */ 44 extern PetscErrorCode InitialConditions(TS, Vec, AppCtx *); 45 extern PetscErrorCode RHSMatrixHeat(TS, PetscReal, Vec, Mat, Mat, void *); 46 extern PetscErrorCode Solution(TS, PetscReal, Vec, AppCtx *); 47 48 int main(int argc, char **argv) 49 { 50 AppCtx appctx; /* user-defined application context */ 51 TS ts; /* timestepping context */ 52 Vec U; /* approximate solution vector */ 53 PetscReal dt; 54 DM da; 55 PetscInt M; 56 57 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 58 Initialize program and set problem parameters 59 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 60 61 PetscFunctionBeginUser; 62 PetscCall(PetscInitialize(&argc, &argv, (char *)0, help)); 63 appctx.a = 1.0; 64 appctx.d = 0.0; 65 PetscCall(PetscOptionsGetScalar(NULL, NULL, "-a", &appctx.a, NULL)); 66 PetscCall(PetscOptionsGetScalar(NULL, NULL, "-d", &appctx.d, NULL)); 67 appctx.upwind = PETSC_TRUE; 68 PetscCall(PetscOptionsGetBool(NULL, NULL, "-upwind", &appctx.upwind, NULL)); 69 70 PetscCall(DMDACreate1d(PETSC_COMM_WORLD, DM_BOUNDARY_PERIODIC, 60, 1, 1, NULL, &da)); 71 PetscCall(DMSetFromOptions(da)); 72 PetscCall(DMSetUp(da)); 73 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 74 Create vector data structures 75 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 76 77 /* 78 Create vector data structures for approximate and exact solutions 79 */ 80 PetscCall(DMCreateGlobalVector(da, &U)); 81 82 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 83 Create timestepping solver context 84 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 85 86 PetscCall(TSCreate(PETSC_COMM_WORLD, &ts)); 87 PetscCall(TSSetDM(ts, da)); 88 89 /* 90 For linear problems with a time-dependent f(U,t) in the equation 91 u_t = f(u,t), the user provides the discretized right-hand-side 92 as a time-dependent matrix. 93 */ 94 PetscCall(TSSetRHSFunction(ts, NULL, TSComputeRHSFunctionLinear, &appctx)); 95 PetscCall(TSSetRHSJacobian(ts, NULL, NULL, RHSMatrixHeat, &appctx)); 96 PetscCall(TSSetSolutionFunction(ts, (PetscErrorCode(*)(TS, PetscReal, Vec, void *))Solution, &appctx)); 97 98 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 99 Customize timestepping solver: 100 - Set timestepping duration info 101 Then set runtime options, which can override these defaults. 102 For example, 103 -ts_max_steps <maxsteps> -ts_max_time <maxtime> 104 to override the defaults set by TSSetMaxSteps()/TSSetMaxTime(). 105 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 106 107 PetscCall(DMDAGetInfo(da, PETSC_IGNORE, &M, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)); 108 dt = .48 / (M * M); 109 PetscCall(TSSetTimeStep(ts, dt)); 110 PetscCall(TSSetMaxSteps(ts, 1000)); 111 PetscCall(TSSetMaxTime(ts, 100.0)); 112 PetscCall(TSSetExactFinalTime(ts, TS_EXACTFINALTIME_STEPOVER)); 113 PetscCall(TSSetType(ts, TSARKIMEX)); 114 PetscCall(TSSetFromOptions(ts)); 115 116 /* 117 Evaluate initial conditions 118 */ 119 PetscCall(InitialConditions(ts, U, &appctx)); 120 121 /* 122 Run the timestepping solver 123 */ 124 PetscCall(TSSolve(ts, U)); 125 126 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 127 Free work space. All PETSc objects should be destroyed when they 128 are no longer needed. 129 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 130 131 PetscCall(TSDestroy(&ts)); 132 PetscCall(VecDestroy(&U)); 133 PetscCall(DMDestroy(&da)); 134 135 /* 136 Always call PetscFinalize() before exiting a program. This routine 137 - finalizes the PETSc libraries as well as MPI 138 - provides summary and diagnostic information if certain runtime 139 options are chosen (e.g., -log_view). 140 */ 141 PetscCall(PetscFinalize()); 142 return 0; 143 } 144 /* --------------------------------------------------------------------- */ 145 /* 146 InitialConditions - Computes the solution at the initial time. 147 148 Input Parameter: 149 u - uninitialized solution vector (global) 150 appctx - user-defined application context 151 152 Output Parameter: 153 u - vector with solution at initial time (global) 154 */ 155 PetscErrorCode InitialConditions(TS ts, Vec U, AppCtx *appctx) 156 { 157 PetscScalar *u, h; 158 PetscInt i, mstart, mend, xm, M; 159 DM da; 160 161 PetscFunctionBeginUser; 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 PetscFunctionReturn(PETSC_SUCCESS); 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 PetscFunctionBeginUser; 210 PetscCall(TSGetDM(ts, &da)); 211 PetscCall(DMDAGetCorners(da, &mstart, 0, 0, &xm, 0, 0)); 212 PetscCall(DMDAGetInfo(da, PETSC_IGNORE, &M, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)); 213 h = 1.0 / M; 214 mend = mstart + xm; 215 /* 216 Get a pointer to vector data. 217 */ 218 PetscCall(DMDAVecGetArray(da, U, &u)); 219 220 /* 221 Simply write the solution directly into the array locations. 222 Alternatively, we culd use VecSetValues() or VecSetValuesLocal(). 223 */ 224 ex1 = PetscExpScalar(-36. * PETSC_PI * PETSC_PI * appctx->d * t); 225 ex2 = PetscExpScalar(-4. * PETSC_PI * PETSC_PI * appctx->d * t); 226 sc1 = PETSC_PI * 6. * h; 227 sc2 = PETSC_PI * 2. * h; 228 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; 229 230 /* 231 Restore vector 232 */ 233 PetscCall(DMDAVecRestoreArray(da, U, &u)); 234 PetscFunctionReturn(PETSC_SUCCESS); 235 } 236 237 /* --------------------------------------------------------------------- */ 238 /* 239 RHSMatrixHeat - User-provided routine to compute the right-hand-side 240 matrix for the heat equation. 241 242 Input Parameters: 243 ts - the TS context 244 t - current time 245 global_in - global input vector 246 dummy - optional user-defined context, as set by TSetRHSJacobian() 247 248 Output Parameters: 249 AA - Jacobian matrix 250 BB - optionally different preconditioning matrix 251 str - flag indicating matrix structure 252 253 Notes: 254 Recall that MatSetValues() uses 0-based row and column numbers 255 in Fortran as well as in C. 256 */ 257 PetscErrorCode RHSMatrixHeat(TS ts, PetscReal t, Vec U, Mat AA, Mat BB, void *ctx) 258 { 259 Mat A = AA; /* Jacobian matrix */ 260 AppCtx *appctx = (AppCtx *)ctx; /* user-defined application context */ 261 PetscInt mstart, mend; 262 PetscInt i, idx[3], M, xm; 263 PetscScalar v[3], h; 264 DM da; 265 266 PetscFunctionBeginUser; 267 PetscCall(TSGetDM(ts, &da)); 268 PetscCall(DMDAGetInfo(da, 0, &M, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)); 269 PetscCall(DMDAGetCorners(da, &mstart, 0, 0, &xm, 0, 0)); 270 h = 1.0 / M; 271 mend = mstart + xm; 272 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 273 Compute entries for the locally owned part of the matrix 274 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 275 /* 276 Set matrix rows corresponding to boundary data 277 */ 278 279 /* diffusion */ 280 v[0] = appctx->d / (h * h); 281 v[1] = -2.0 * appctx->d / (h * h); 282 v[2] = appctx->d / (h * h); 283 if (!mstart) { 284 idx[0] = M - 1; 285 idx[1] = 0; 286 idx[2] = 1; 287 PetscCall(MatSetValues(A, 1, &mstart, 3, idx, v, INSERT_VALUES)); 288 mstart++; 289 } 290 291 if (mend == M) { 292 mend--; 293 idx[0] = M - 2; 294 idx[1] = M - 1; 295 idx[2] = 0; 296 PetscCall(MatSetValues(A, 1, &mend, 3, idx, v, INSERT_VALUES)); 297 } 298 299 /* 300 Set matrix rows corresponding to interior data. We construct the 301 matrix one row at a time. 302 */ 303 for (i = mstart; i < mend; i++) { 304 idx[0] = i - 1; 305 idx[1] = i; 306 idx[2] = i + 1; 307 PetscCall(MatSetValues(A, 1, &i, 3, idx, v, INSERT_VALUES)); 308 } 309 PetscCall(MatAssemblyBegin(A, MAT_FLUSH_ASSEMBLY)); 310 PetscCall(MatAssemblyEnd(A, MAT_FLUSH_ASSEMBLY)); 311 312 PetscCall(DMDAGetCorners(da, &mstart, 0, 0, &xm, 0, 0)); 313 mend = mstart + xm; 314 if (!appctx->upwind) { 315 /* advection -- centered differencing */ 316 v[0] = -.5 * appctx->a / (h); 317 v[1] = .5 * appctx->a / (h); 318 if (!mstart) { 319 idx[0] = M - 1; 320 idx[1] = 1; 321 PetscCall(MatSetValues(A, 1, &mstart, 2, idx, v, ADD_VALUES)); 322 mstart++; 323 } 324 325 if (mend == M) { 326 mend--; 327 idx[0] = M - 2; 328 idx[1] = 0; 329 PetscCall(MatSetValues(A, 1, &mend, 2, idx, v, ADD_VALUES)); 330 } 331 332 for (i = mstart; i < mend; i++) { 333 idx[0] = i - 1; 334 idx[1] = i + 1; 335 PetscCall(MatSetValues(A, 1, &i, 2, idx, v, ADD_VALUES)); 336 } 337 } else { 338 /* advection -- upwinding */ 339 v[0] = -appctx->a / (h); 340 v[1] = appctx->a / (h); 341 if (!mstart) { 342 idx[0] = 0; 343 idx[1] = 1; 344 PetscCall(MatSetValues(A, 1, &mstart, 2, idx, v, ADD_VALUES)); 345 mstart++; 346 } 347 348 if (mend == M) { 349 mend--; 350 idx[0] = M - 1; 351 idx[1] = 0; 352 PetscCall(MatSetValues(A, 1, &mend, 2, idx, v, ADD_VALUES)); 353 } 354 355 for (i = mstart; i < mend; i++) { 356 idx[0] = i; 357 idx[1] = i + 1; 358 PetscCall(MatSetValues(A, 1, &i, 2, idx, v, ADD_VALUES)); 359 } 360 } 361 362 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 363 Complete the matrix assembly process and set some options 364 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 365 /* 366 Assemble matrix, using the 2-step process: 367 MatAssemblyBegin(), MatAssemblyEnd() 368 Computations can be done while messages are in transition 369 by placing code between these two statements. 370 */ 371 PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY)); 372 PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY)); 373 374 /* 375 Set and option to indicate that we will never add a new nonzero location 376 to the matrix. If we do, it will generate an error. 377 */ 378 PetscCall(MatSetOption(A, MAT_NEW_NONZERO_LOCATION_ERR, PETSC_TRUE)); 379 PetscFunctionReturn(PETSC_SUCCESS); 380 } 381 382 /*TEST 383 384 test: 385 args: -pc_type mg -da_refine 2 -ts_view -ts_monitor -ts_max_time .3 -mg_levels_ksp_max_it 3 386 requires: double 387 filter: grep -v "total number of" 388 389 test: 390 suffix: 2 391 args: -pc_type mg -da_refine 2 -ts_view -ts_monitor_draw_solution -ts_monitor -ts_max_time .3 -mg_levels_ksp_max_it 3 392 requires: x 393 output_file: output/ex3_1.out 394 requires: double 395 filter: grep -v "total number of" 396 397 TEST*/ 398