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; sc2 = PETSC_PI*2.*h; 226 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; 227 228 /* 229 Restore vector 230 */ 231 PetscCall(DMDAVecRestoreArray(da,U,&u)); 232 return 0; 233 } 234 235 /* --------------------------------------------------------------------- */ 236 /* 237 RHSMatrixHeat - User-provided routine to compute the right-hand-side 238 matrix for the heat equation. 239 240 Input Parameters: 241 ts - the TS context 242 t - current time 243 global_in - global input vector 244 dummy - optional user-defined context, as set by TSetRHSJacobian() 245 246 Output Parameters: 247 AA - Jacobian matrix 248 BB - optionally different preconditioning matrix 249 str - flag indicating matrix structure 250 251 Notes: 252 Recall that MatSetValues() uses 0-based row and column numbers 253 in Fortran as well as in C. 254 */ 255 PetscErrorCode RHSMatrixHeat(TS ts,PetscReal t,Vec U,Mat AA,Mat BB,void *ctx) 256 { 257 Mat A = AA; /* Jacobian matrix */ 258 AppCtx *appctx = (AppCtx*)ctx; /* user-defined application context */ 259 PetscInt mstart, mend; 260 PetscInt i,idx[3],M,xm; 261 PetscScalar v[3],h; 262 DM da; 263 264 PetscCall(TSGetDM(ts,&da)); 265 PetscCall(DMDAGetInfo(da,0,&M,0,0,0,0,0,0,0,0,0,0,0)); 266 PetscCall(DMDAGetCorners(da,&mstart,0,0,&xm,0,0)); 267 h = 1.0/M; 268 mend = mstart + xm; 269 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 270 Compute entries for the locally owned part of the matrix 271 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 272 /* 273 Set matrix rows corresponding to boundary data 274 */ 275 276 /* diffusion */ 277 v[0] = appctx->d/(h*h); 278 v[1] = -2.0*appctx->d/(h*h); 279 v[2] = appctx->d/(h*h); 280 if (!mstart) { 281 idx[0] = M-1; idx[1] = 0; idx[2] = 1; 282 PetscCall(MatSetValues(A,1,&mstart,3,idx,v,INSERT_VALUES)); 283 mstart++; 284 } 285 286 if (mend == M) { 287 mend--; 288 idx[0] = M-2; idx[1] = M-1; idx[2] = 0; 289 PetscCall(MatSetValues(A,1,&mend,3,idx,v,INSERT_VALUES)); 290 } 291 292 /* 293 Set matrix rows corresponding to interior data. We construct the 294 matrix one row at a time. 295 */ 296 for (i=mstart; i<mend; i++) { 297 idx[0] = i-1; idx[1] = i; idx[2] = i+1; 298 PetscCall(MatSetValues(A,1,&i,3,idx,v,INSERT_VALUES)); 299 } 300 PetscCall(MatAssemblyBegin(A,MAT_FLUSH_ASSEMBLY)); 301 PetscCall(MatAssemblyEnd(A,MAT_FLUSH_ASSEMBLY)); 302 303 PetscCall(DMDAGetCorners(da,&mstart,0,0,&xm,0,0)); 304 mend = mstart + xm; 305 if (!appctx->upwind) { 306 /* advection -- centered differencing */ 307 v[0] = -.5*appctx->a/(h); 308 v[1] = .5*appctx->a/(h); 309 if (!mstart) { 310 idx[0] = M-1; idx[1] = 1; 311 PetscCall(MatSetValues(A,1,&mstart,2,idx,v,ADD_VALUES)); 312 mstart++; 313 } 314 315 if (mend == M) { 316 mend--; 317 idx[0] = M-2; idx[1] = 0; 318 PetscCall(MatSetValues(A,1,&mend,2,idx,v,ADD_VALUES)); 319 } 320 321 for (i=mstart; i<mend; i++) { 322 idx[0] = i-1; idx[1] = i+1; 323 PetscCall(MatSetValues(A,1,&i,2,idx,v,ADD_VALUES)); 324 } 325 } else { 326 /* advection -- upwinding */ 327 v[0] = -appctx->a/(h); 328 v[1] = appctx->a/(h); 329 if (!mstart) { 330 idx[0] = 0; idx[1] = 1; 331 PetscCall(MatSetValues(A,1,&mstart,2,idx,v,ADD_VALUES)); 332 mstart++; 333 } 334 335 if (mend == M) { 336 mend--; 337 idx[0] = M-1; idx[1] = 0; 338 PetscCall(MatSetValues(A,1,&mend,2,idx,v,ADD_VALUES)); 339 } 340 341 for (i=mstart; i<mend; i++) { 342 idx[0] = i; idx[1] = i+1; 343 PetscCall(MatSetValues(A,1,&i,2,idx,v,ADD_VALUES)); 344 } 345 } 346 347 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 348 Complete the matrix assembly process and set some options 349 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 350 /* 351 Assemble matrix, using the 2-step process: 352 MatAssemblyBegin(), MatAssemblyEnd() 353 Computations can be done while messages are in transition 354 by placing code between these two statements. 355 */ 356 PetscCall(MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY)); 357 PetscCall(MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY)); 358 359 /* 360 Set and option to indicate that we will never add a new nonzero location 361 to the matrix. If we do, it will generate an error. 362 */ 363 PetscCall(MatSetOption(A,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE)); 364 return 0; 365 } 366 367 /*TEST 368 369 test: 370 args: -pc_type mg -da_refine 2 -ts_view -ts_monitor -ts_max_time .3 -mg_levels_ksp_max_it 3 371 requires: double 372 filter: grep -v "total number of" 373 374 test: 375 suffix: 2 376 args: -pc_type mg -da_refine 2 -ts_view -ts_monitor_draw_solution -ts_monitor -ts_max_time .3 -mg_levels_ksp_max_it 3 377 requires: x 378 output_file: output/ex3_1.out 379 requires: double 380 filter: grep -v "total number of" 381 382 TEST*/ 383