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 PetscErrorCode ierr; 55 PetscReal dt; 56 DM da; 57 PetscInt M; 58 59 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 60 Initialize program and set problem parameters 61 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 62 63 ierr = PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr; 64 appctx.a = 1.0; 65 appctx.d = 0.0; 66 ierr = PetscOptionsGetScalar(NULL,NULL,"-a",&appctx.a,NULL);CHKERRQ(ierr); 67 ierr = PetscOptionsGetScalar(NULL,NULL,"-d",&appctx.d,NULL);CHKERRQ(ierr); 68 appctx.upwind = PETSC_TRUE; 69 ierr = PetscOptionsGetBool(NULL,NULL,"-upwind",&appctx.upwind,NULL);CHKERRQ(ierr); 70 71 ierr = DMDACreate1d(PETSC_COMM_WORLD,DM_BOUNDARY_PERIODIC, 60, 1, 1,NULL,&da);CHKERRQ(ierr); 72 ierr = DMSetFromOptions(da);CHKERRQ(ierr); 73 ierr = DMSetUp(da);CHKERRQ(ierr); 74 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 75 Create vector data structures 76 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 77 78 /* 79 Create vector data structures for approximate and exact solutions 80 */ 81 ierr = DMCreateGlobalVector(da,&U);CHKERRQ(ierr); 82 83 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 84 Create timestepping solver context 85 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 86 87 ierr = TSCreate(PETSC_COMM_WORLD,&ts);CHKERRQ(ierr); 88 ierr = TSSetDM(ts,da);CHKERRQ(ierr); 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 ierr = TSSetRHSFunction(ts,NULL,TSComputeRHSFunctionLinear,&appctx);CHKERRQ(ierr); 96 ierr = TSSetRHSJacobian(ts,NULL,NULL,RHSMatrixHeat,&appctx);CHKERRQ(ierr); 97 ierr = TSSetSolutionFunction(ts,(PetscErrorCode (*)(TS,PetscReal,Vec,void*))Solution,&appctx);CHKERRQ(ierr); 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 ierr = DMDAGetInfo(da,PETSC_IGNORE,&M,0,0,0,0,0,0,0,0,0,0,0);CHKERRQ(ierr); 109 dt = .48/(M*M); 110 ierr = TSSetTimeStep(ts,dt);CHKERRQ(ierr); 111 ierr = TSSetMaxSteps(ts,1000);CHKERRQ(ierr); 112 ierr = TSSetMaxTime(ts,100.0);CHKERRQ(ierr); 113 ierr = TSSetExactFinalTime(ts,TS_EXACTFINALTIME_STEPOVER);CHKERRQ(ierr); 114 ierr = TSSetType(ts,TSARKIMEX);CHKERRQ(ierr); 115 ierr = TSSetFromOptions(ts);CHKERRQ(ierr); 116 117 /* 118 Evaluate initial conditions 119 */ 120 ierr = InitialConditions(ts,U,&appctx);CHKERRQ(ierr); 121 122 /* 123 Run the timestepping solver 124 */ 125 ierr = TSSolve(ts,U);CHKERRQ(ierr); 126 127 128 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 129 Free work space. All PETSc objects should be destroyed when they 130 are no longer needed. 131 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 132 133 ierr = TSDestroy(&ts);CHKERRQ(ierr); 134 ierr = VecDestroy(&U);CHKERRQ(ierr); 135 ierr = DMDestroy(&da);CHKERRQ(ierr); 136 137 /* 138 Always call PetscFinalize() before exiting a program. This routine 139 - finalizes the PETSc libraries as well as MPI 140 - provides summary and diagnostic information if certain runtime 141 options are chosen (e.g., -log_view). 142 */ 143 ierr = PetscFinalize(); 144 return ierr; 145 } 146 /* --------------------------------------------------------------------- */ 147 /* 148 InitialConditions - Computes the solution at the initial time. 149 150 Input Parameter: 151 u - uninitialized solution vector (global) 152 appctx - user-defined application context 153 154 Output Parameter: 155 u - vector with solution at initial time (global) 156 */ 157 PetscErrorCode InitialConditions(TS ts,Vec U,AppCtx *appctx) 158 { 159 PetscScalar *u,h; 160 PetscErrorCode ierr; 161 PetscInt i,mstart,mend,xm,M; 162 DM da; 163 164 ierr = TSGetDM(ts,&da);CHKERRQ(ierr); 165 ierr = DMDAGetCorners(da,&mstart,0,0,&xm,0,0);CHKERRQ(ierr); 166 ierr = DMDAGetInfo(da,PETSC_IGNORE,&M,0,0,0,0,0,0,0,0,0,0,0);CHKERRQ(ierr); 167 h = 1.0/M; 168 mend = mstart + xm; 169 /* 170 Get a pointer to vector data. 171 - For default PETSc vectors, VecGetArray() returns a pointer to 172 the data array. Otherwise, the routine is implementation dependent. 173 - You MUST call VecRestoreArray() when you no longer need access to 174 the array. 175 - Note that the Fortran interface to VecGetArray() differs from the 176 C version. See the users manual for details. 177 */ 178 ierr = DMDAVecGetArray(da,U,&u);CHKERRQ(ierr); 179 180 /* 181 We initialize the solution array by simply writing the solution 182 directly into the array locations. Alternatively, we could use 183 VecSetValues() or VecSetValuesLocal(). 184 */ 185 for (i=mstart; i<mend; i++) u[i] = PetscSinScalar(PETSC_PI*i*6.*h) + 3.*PetscSinScalar(PETSC_PI*i*2.*h); 186 187 /* 188 Restore vector 189 */ 190 ierr = DMDAVecRestoreArray(da,U,&u);CHKERRQ(ierr); 191 return 0; 192 } 193 /* --------------------------------------------------------------------- */ 194 /* 195 Solution - Computes the exact solution at a given time. 196 197 Input Parameters: 198 t - current time 199 solution - vector in which exact solution will be computed 200 appctx - user-defined application context 201 202 Output Parameter: 203 solution - vector with the newly computed exact solution 204 */ 205 PetscErrorCode Solution(TS ts,PetscReal t,Vec U,AppCtx *appctx) 206 { 207 PetscScalar *u,ex1,ex2,sc1,sc2,h; 208 PetscErrorCode ierr; 209 PetscInt i,mstart,mend,xm,M; 210 DM da; 211 212 ierr = TSGetDM(ts,&da);CHKERRQ(ierr); 213 ierr = DMDAGetCorners(da,&mstart,0,0,&xm,0,0);CHKERRQ(ierr); 214 ierr = DMDAGetInfo(da,PETSC_IGNORE,&M,0,0,0,0,0,0,0,0,0,0,0);CHKERRQ(ierr); 215 h = 1.0/M; 216 mend = mstart + xm; 217 /* 218 Get a pointer to vector data. 219 */ 220 ierr = DMDAVecGetArray(da,U,&u);CHKERRQ(ierr); 221 222 /* 223 Simply write the solution directly into the array locations. 224 Alternatively, we culd use VecSetValues() or VecSetValuesLocal(). 225 */ 226 ex1 = PetscExpScalar(-36.*PETSC_PI*PETSC_PI*appctx->d*t); 227 ex2 = PetscExpScalar(-4.*PETSC_PI*PETSC_PI*appctx->d*t); 228 sc1 = PETSC_PI*6.*h; 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 ierr = DMDAVecRestoreArray(da,U,&u);CHKERRQ(ierr); 235 return 0; 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 PetscErrorCode ierr; 264 PetscInt i,idx[3],M,xm; 265 PetscScalar v[3],h; 266 DM da; 267 268 ierr = TSGetDM(ts,&da);CHKERRQ(ierr); 269 ierr = DMDAGetInfo(da,0,&M,0,0,0,0,0,0,0,0,0,0,0);CHKERRQ(ierr); 270 ierr = DMDAGetCorners(da,&mstart,0,0,&xm,0,0);CHKERRQ(ierr); 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; idx[1] = 0; idx[2] = 1; 286 ierr = MatSetValues(A,1,&mstart,3,idx,v,INSERT_VALUES);CHKERRQ(ierr); 287 mstart++; 288 } 289 290 if (mend == M) { 291 mend--; 292 idx[0] = M-2; idx[1] = M-1; idx[2] = 0; 293 ierr = MatSetValues(A,1,&mend,3,idx,v,INSERT_VALUES);CHKERRQ(ierr); 294 } 295 296 /* 297 Set matrix rows corresponding to interior data. We construct the 298 matrix one row at a time. 299 */ 300 for (i=mstart; i<mend; i++) { 301 idx[0] = i-1; idx[1] = i; idx[2] = i+1; 302 ierr = MatSetValues(A,1,&i,3,idx,v,INSERT_VALUES);CHKERRQ(ierr); 303 } 304 ierr = MatAssemblyBegin(A,MAT_FLUSH_ASSEMBLY);CHKERRQ(ierr); 305 ierr = MatAssemblyEnd(A,MAT_FLUSH_ASSEMBLY);CHKERRQ(ierr); 306 307 ierr = DMDAGetCorners(da,&mstart,0,0,&xm,0,0);CHKERRQ(ierr); 308 mend = mstart + xm; 309 if (!appctx->upwind) { 310 /* advection -- centered differencing */ 311 v[0] = -.5*appctx->a/(h); 312 v[1] = .5*appctx->a/(h); 313 if (!mstart) { 314 idx[0] = M-1; idx[1] = 1; 315 ierr = MatSetValues(A,1,&mstart,2,idx,v,ADD_VALUES);CHKERRQ(ierr); 316 mstart++; 317 } 318 319 if (mend == M) { 320 mend--; 321 idx[0] = M-2; idx[1] = 0; 322 ierr = MatSetValues(A,1,&mend,2,idx,v,ADD_VALUES);CHKERRQ(ierr); 323 } 324 325 for (i=mstart; i<mend; i++) { 326 idx[0] = i-1; idx[1] = i+1; 327 ierr = MatSetValues(A,1,&i,2,idx,v,ADD_VALUES);CHKERRQ(ierr); 328 } 329 } else { 330 /* advection -- upwinding */ 331 v[0] = -appctx->a/(h); 332 v[1] = appctx->a/(h); 333 if (!mstart) { 334 idx[0] = 0; idx[1] = 1; 335 ierr = MatSetValues(A,1,&mstart,2,idx,v,ADD_VALUES);CHKERRQ(ierr); 336 mstart++; 337 } 338 339 if (mend == M) { 340 mend--; 341 idx[0] = M-1; idx[1] = 0; 342 ierr = MatSetValues(A,1,&mend,2,idx,v,ADD_VALUES);CHKERRQ(ierr); 343 } 344 345 for (i=mstart; i<mend; i++) { 346 idx[0] = i; idx[1] = i+1; 347 ierr = MatSetValues(A,1,&i,2,idx,v,ADD_VALUES);CHKERRQ(ierr); 348 } 349 } 350 351 352 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 353 Complete the matrix assembly process and set some options 354 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 355 /* 356 Assemble matrix, using the 2-step process: 357 MatAssemblyBegin(), MatAssemblyEnd() 358 Computations can be done while messages are in transition 359 by placing code between these two statements. 360 */ 361 ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 362 ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 363 364 /* 365 Set and option to indicate that we will never add a new nonzero location 366 to the matrix. If we do, it will generate an error. 367 */ 368 ierr = MatSetOption(A,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr); 369 return 0; 370 } 371 372 373 /*TEST 374 375 test: 376 args: -pc_type mg -da_refine 2 -ts_view -ts_monitor -ts_max_time .3 -mg_levels_ksp_max_it 3 377 requires: double 378 379 test: 380 suffix: 2 381 args: -pc_type mg -da_refine 2 -ts_view -ts_monitor_draw_solution -ts_monitor -ts_max_time .3 -mg_levels_ksp_max_it 3 382 requires: x 383 output_file: output/ex3_1.out 384 requires: double 385 386 TEST*/ 387