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 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 PetscCall(TSGetDM(ts,&da)); 162 PetscCall(DMDAGetCorners(da,&mstart,0,0,&xm,0,0)); 163 PetscCall(DMDAGetInfo(da,PETSC_IGNORE,&M,0,0,0,0,0,0,0,0,0,0,0)); 164 h = 1.0/M; 165 mend = mstart + xm; 166 /* 167 Get a pointer to vector data. 168 - For default PETSc vectors, VecGetArray() returns a pointer to 169 the data array. Otherwise, the routine is implementation dependent. 170 - You MUST call VecRestoreArray() when you no longer need access to 171 the array. 172 - Note that the Fortran interface to VecGetArray() differs from the 173 C version. See the users manual for details. 174 */ 175 PetscCall(DMDAVecGetArray(da,U,&u)); 176 177 /* 178 We initialize the solution array by simply writing the solution 179 directly into the array locations. Alternatively, we could use 180 VecSetValues() or VecSetValuesLocal(). 181 */ 182 for (i=mstart; i<mend; i++) u[i] = PetscSinScalar(PETSC_PI*i*6.*h) + 3.*PetscSinScalar(PETSC_PI*i*2.*h); 183 184 /* 185 Restore vector 186 */ 187 PetscCall(DMDAVecRestoreArray(da,U,&u)); 188 return 0; 189 } 190 /* --------------------------------------------------------------------- */ 191 /* 192 Solution - Computes the exact solution at a given time. 193 194 Input Parameters: 195 t - current time 196 solution - vector in which exact solution will be computed 197 appctx - user-defined application context 198 199 Output Parameter: 200 solution - vector with the newly computed exact solution 201 */ 202 PetscErrorCode Solution(TS ts,PetscReal t,Vec U,AppCtx *appctx) 203 { 204 PetscScalar *u,ex1,ex2,sc1,sc2,h; 205 PetscInt i,mstart,mend,xm,M; 206 DM da; 207 208 PetscCall(TSGetDM(ts,&da)); 209 PetscCall(DMDAGetCorners(da,&mstart,0,0,&xm,0,0)); 210 PetscCall(DMDAGetInfo(da,PETSC_IGNORE,&M,0,0,0,0,0,0,0,0,0,0,0)); 211 h = 1.0/M; 212 mend = mstart + xm; 213 /* 214 Get a pointer to vector data. 215 */ 216 PetscCall(DMDAVecGetArray(da,U,&u)); 217 218 /* 219 Simply write the solution directly into the array locations. 220 Alternatively, we culd use VecSetValues() or VecSetValuesLocal(). 221 */ 222 ex1 = PetscExpScalar(-36.*PETSC_PI*PETSC_PI*appctx->d*t); 223 ex2 = PetscExpScalar(-4.*PETSC_PI*PETSC_PI*appctx->d*t); 224 sc1 = PETSC_PI*6.*h; sc2 = PETSC_PI*2.*h; 225 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; 226 227 /* 228 Restore vector 229 */ 230 PetscCall(DMDAVecRestoreArray(da,U,&u)); 231 return 0; 232 } 233 234 /* --------------------------------------------------------------------- */ 235 /* 236 RHSMatrixHeat - User-provided routine to compute the right-hand-side 237 matrix for the heat equation. 238 239 Input Parameters: 240 ts - the TS context 241 t - current time 242 global_in - global input vector 243 dummy - optional user-defined context, as set by TSetRHSJacobian() 244 245 Output Parameters: 246 AA - Jacobian matrix 247 BB - optionally different preconditioning matrix 248 str - flag indicating matrix structure 249 250 Notes: 251 Recall that MatSetValues() uses 0-based row and column numbers 252 in Fortran as well as in C. 253 */ 254 PetscErrorCode RHSMatrixHeat(TS ts,PetscReal t,Vec U,Mat AA,Mat BB,void *ctx) 255 { 256 Mat A = AA; /* Jacobian matrix */ 257 AppCtx *appctx = (AppCtx*)ctx; /* user-defined application context */ 258 PetscInt mstart, mend; 259 PetscInt i,idx[3],M,xm; 260 PetscScalar v[3],h; 261 DM da; 262 263 PetscCall(TSGetDM(ts,&da)); 264 PetscCall(DMDAGetInfo(da,0,&M,0,0,0,0,0,0,0,0,0,0,0)); 265 PetscCall(DMDAGetCorners(da,&mstart,0,0,&xm,0,0)); 266 h = 1.0/M; 267 mend = mstart + xm; 268 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 269 Compute entries for the locally owned part of the matrix 270 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 271 /* 272 Set matrix rows corresponding to boundary data 273 */ 274 275 /* diffusion */ 276 v[0] = appctx->d/(h*h); 277 v[1] = -2.0*appctx->d/(h*h); 278 v[2] = appctx->d/(h*h); 279 if (!mstart) { 280 idx[0] = M-1; idx[1] = 0; idx[2] = 1; 281 PetscCall(MatSetValues(A,1,&mstart,3,idx,v,INSERT_VALUES)); 282 mstart++; 283 } 284 285 if (mend == M) { 286 mend--; 287 idx[0] = M-2; idx[1] = M-1; idx[2] = 0; 288 PetscCall(MatSetValues(A,1,&mend,3,idx,v,INSERT_VALUES)); 289 } 290 291 /* 292 Set matrix rows corresponding to interior data. We construct the 293 matrix one row at a time. 294 */ 295 for (i=mstart; i<mend; i++) { 296 idx[0] = i-1; idx[1] = i; idx[2] = i+1; 297 PetscCall(MatSetValues(A,1,&i,3,idx,v,INSERT_VALUES)); 298 } 299 PetscCall(MatAssemblyBegin(A,MAT_FLUSH_ASSEMBLY)); 300 PetscCall(MatAssemblyEnd(A,MAT_FLUSH_ASSEMBLY)); 301 302 PetscCall(DMDAGetCorners(da,&mstart,0,0,&xm,0,0)); 303 mend = mstart + xm; 304 if (!appctx->upwind) { 305 /* advection -- centered differencing */ 306 v[0] = -.5*appctx->a/(h); 307 v[1] = .5*appctx->a/(h); 308 if (!mstart) { 309 idx[0] = M-1; idx[1] = 1; 310 PetscCall(MatSetValues(A,1,&mstart,2,idx,v,ADD_VALUES)); 311 mstart++; 312 } 313 314 if (mend == M) { 315 mend--; 316 idx[0] = M-2; idx[1] = 0; 317 PetscCall(MatSetValues(A,1,&mend,2,idx,v,ADD_VALUES)); 318 } 319 320 for (i=mstart; i<mend; i++) { 321 idx[0] = i-1; idx[1] = i+1; 322 PetscCall(MatSetValues(A,1,&i,2,idx,v,ADD_VALUES)); 323 } 324 } else { 325 /* advection -- upwinding */ 326 v[0] = -appctx->a/(h); 327 v[1] = appctx->a/(h); 328 if (!mstart) { 329 idx[0] = 0; idx[1] = 1; 330 PetscCall(MatSetValues(A,1,&mstart,2,idx,v,ADD_VALUES)); 331 mstart++; 332 } 333 334 if (mend == M) { 335 mend--; 336 idx[0] = M-1; idx[1] = 0; 337 PetscCall(MatSetValues(A,1,&mend,2,idx,v,ADD_VALUES)); 338 } 339 340 for (i=mstart; i<mend; i++) { 341 idx[0] = i; idx[1] = i+1; 342 PetscCall(MatSetValues(A,1,&i,2,idx,v,ADD_VALUES)); 343 } 344 } 345 346 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 347 Complete the matrix assembly process and set some options 348 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 349 /* 350 Assemble matrix, using the 2-step process: 351 MatAssemblyBegin(), MatAssemblyEnd() 352 Computations can be done while messages are in transition 353 by placing code between these two statements. 354 */ 355 PetscCall(MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY)); 356 PetscCall(MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY)); 357 358 /* 359 Set and option to indicate that we will never add a new nonzero location 360 to the matrix. If we do, it will generate an error. 361 */ 362 PetscCall(MatSetOption(A,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE)); 363 return 0; 364 } 365 366 /*TEST 367 368 test: 369 args: -pc_type mg -da_refine 2 -ts_view -ts_monitor -ts_max_time .3 -mg_levels_ksp_max_it 3 370 requires: double 371 filter: grep -v "total number of" 372 373 test: 374 suffix: 2 375 args: -pc_type mg -da_refine 2 -ts_view -ts_monitor_draw_solution -ts_monitor -ts_max_time .3 -mg_levels_ksp_max_it 3 376 requires: x 377 output_file: output/ex3_1.out 378 requires: double 379 filter: grep -v "total number of" 380 381 TEST*/ 382