1 2 static char help[] ="Solves a time-dependent nonlinear PDE with lower and upper bounds on the interior grid points. Uses implicit\n\ 3 timestepping. Runtime options include:\n\ 4 -M <xg>, where <xg> = number of grid points\n\ 5 -debug : Activate debugging printouts\n\ 6 -nox : Deactivate x-window graphics\n\ 7 -ul : lower bound\n\ 8 -uh : upper bound\n\n"; 9 10 /* 11 Concepts: TS^time-dependent nonlinear problems 12 Concepts: TS^Variational inequality nonlinear solver 13 Processors: n 14 */ 15 16 /* ------------------------------------------------------------------------ 17 18 This is a variation of ex2.c to solve the PDE 19 20 u * u_xx 21 u_t = --------- 22 2*(t+1)^2 23 24 with box constraints on the interior grid points 25 ul <= u(t,x) <= uh with x != 0,1 26 on the domain 0 <= x <= 1, with boundary conditions 27 u(t,0) = t + 1, u(t,1) = 2*t + 2, 28 and initial condition 29 u(0,x) = 1 + x*x. 30 31 The exact solution is: 32 u(t,x) = (1 + x*x) * (1 + t) 33 34 We use by default the backward Euler method. 35 36 ------------------------------------------------------------------------- */ 37 38 /* 39 Include "petscts.h" to use the PETSc timestepping routines. Note that 40 this file automatically includes "petscsys.h" and other lower-level 41 PETSc include files. 42 43 Include the "petscdmda.h" to allow us to use the distributed array data 44 structures to manage the parallel grid. 45 */ 46 #include <petscts.h> 47 #include <petscdm.h> 48 #include <petscdmda.h> 49 #include <petscdraw.h> 50 51 /* 52 User-defined application context - contains data needed by the 53 application-provided callback routines. 54 */ 55 typedef struct { 56 MPI_Comm comm; /* communicator */ 57 DM da; /* distributed array data structure */ 58 Vec localwork; /* local ghosted work vector */ 59 Vec u_local; /* local ghosted approximate solution vector */ 60 Vec solution; /* global exact solution vector */ 61 PetscInt m; /* total number of grid points */ 62 PetscReal h; /* mesh width: h = 1/(m-1) */ 63 PetscBool debug; /* flag (1 indicates activation of debugging printouts) */ 64 } AppCtx; 65 66 /* 67 User-defined routines, provided below. 68 */ 69 extern PetscErrorCode InitialConditions(Vec,AppCtx*); 70 extern PetscErrorCode RHSFunction(TS,PetscReal,Vec,Vec,void*); 71 extern PetscErrorCode RHSJacobian(TS,PetscReal,Vec,Mat,Mat,void*); 72 extern PetscErrorCode Monitor(TS,PetscInt,PetscReal,Vec,void*); 73 extern PetscErrorCode ExactSolution(PetscReal,Vec,AppCtx*); 74 extern PetscErrorCode SetBounds(Vec,Vec,PetscScalar,PetscScalar,AppCtx*); 75 76 int main(int argc,char **argv) 77 { 78 AppCtx appctx; /* user-defined application context */ 79 TS ts; /* timestepping context */ 80 Mat A; /* Jacobian matrix data structure */ 81 Vec u; /* approximate solution vector */ 82 Vec r; /* residual vector */ 83 PetscInt time_steps_max = 1000; /* default max timesteps */ 84 PetscErrorCode ierr; 85 PetscReal dt; 86 PetscReal time_total_max = 100.0; /* default max total time */ 87 Vec xl,xu; /* Lower and upper bounds on variables */ 88 PetscScalar ul=0.0,uh = 3.0; 89 PetscBool mymonitor; 90 PetscReal bounds[] = {1.0, 3.3}; 91 92 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 93 Initialize program and set problem parameters 94 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 95 96 ierr = PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr; 97 CHKERRQ(PetscViewerDrawSetBounds(PETSC_VIEWER_DRAW_(PETSC_COMM_WORLD),1,bounds)); 98 99 appctx.comm = PETSC_COMM_WORLD; 100 appctx.m = 60; 101 CHKERRQ(PetscOptionsGetInt(NULL,NULL,"-M",&appctx.m,NULL)); 102 CHKERRQ(PetscOptionsGetScalar(NULL,NULL,"-ul",&ul,NULL)); 103 CHKERRQ(PetscOptionsGetScalar(NULL,NULL,"-uh",&uh,NULL)); 104 CHKERRQ(PetscOptionsHasName(NULL,NULL,"-debug",&appctx.debug)); 105 CHKERRQ(PetscOptionsHasName(NULL,NULL,"-mymonitor",&mymonitor)); 106 appctx.h = 1.0/(appctx.m-1.0); 107 108 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 109 Create vector data structures 110 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 111 112 /* 113 Create distributed array (DMDA) to manage parallel grid and vectors 114 and to set up the ghost point communication pattern. There are M 115 total grid values spread equally among all the processors. 116 */ 117 CHKERRQ(DMDACreate1d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,appctx.m,1,1,NULL,&appctx.da)); 118 CHKERRQ(DMSetFromOptions(appctx.da)); 119 CHKERRQ(DMSetUp(appctx.da)); 120 121 /* 122 Extract global and local vectors from DMDA; we use these to store the 123 approximate solution. Then duplicate these for remaining vectors that 124 have the same types. 125 */ 126 CHKERRQ(DMCreateGlobalVector(appctx.da,&u)); 127 CHKERRQ(DMCreateLocalVector(appctx.da,&appctx.u_local)); 128 129 /* 130 Create local work vector for use in evaluating right-hand-side function; 131 create global work vector for storing exact solution. 132 */ 133 CHKERRQ(VecDuplicate(appctx.u_local,&appctx.localwork)); 134 CHKERRQ(VecDuplicate(u,&appctx.solution)); 135 136 /* Create residual vector */ 137 CHKERRQ(VecDuplicate(u,&r)); 138 /* Create lower and upper bound vectors */ 139 CHKERRQ(VecDuplicate(u,&xl)); 140 CHKERRQ(VecDuplicate(u,&xu)); 141 CHKERRQ(SetBounds(xl,xu,ul,uh,&appctx)); 142 143 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 144 Create timestepping solver context; set callback routine for 145 right-hand-side function evaluation. 146 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 147 148 CHKERRQ(TSCreate(PETSC_COMM_WORLD,&ts)); 149 CHKERRQ(TSSetProblemType(ts,TS_NONLINEAR)); 150 CHKERRQ(TSSetRHSFunction(ts,r,RHSFunction,&appctx)); 151 152 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 153 Set optional user-defined monitoring routine 154 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 155 156 if (mymonitor) { 157 CHKERRQ(TSMonitorSet(ts,Monitor,&appctx,NULL)); 158 } 159 160 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 161 For nonlinear problems, the user can provide a Jacobian evaluation 162 routine (or use a finite differencing approximation). 163 164 Create matrix data structure; set Jacobian evaluation routine. 165 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 166 167 CHKERRQ(MatCreate(PETSC_COMM_WORLD,&A)); 168 CHKERRQ(MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,appctx.m,appctx.m)); 169 CHKERRQ(MatSetFromOptions(A)); 170 CHKERRQ(MatSetUp(A)); 171 CHKERRQ(TSSetRHSJacobian(ts,A,A,RHSJacobian,&appctx)); 172 173 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 174 Set solution vector and initial timestep 175 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 176 177 dt = appctx.h/2.0; 178 CHKERRQ(TSSetTimeStep(ts,dt)); 179 180 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 181 Customize timestepping solver: 182 - Set the solution method to be the Backward Euler method. 183 - Set timestepping duration info 184 Then set runtime options, which can override these defaults. 185 For example, 186 -ts_max_steps <maxsteps> -ts_max_time <maxtime> 187 to override the defaults set by TSSetMaxSteps()/TSSetMaxTime(). 188 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 189 190 CHKERRQ(TSSetType(ts,TSBEULER)); 191 CHKERRQ(TSSetMaxSteps(ts,time_steps_max)); 192 CHKERRQ(TSSetMaxTime(ts,time_total_max)); 193 CHKERRQ(TSSetExactFinalTime(ts,TS_EXACTFINALTIME_STEPOVER)); 194 /* Set lower and upper bound on the solution vector for each time step */ 195 CHKERRQ(TSVISetVariableBounds(ts,xl,xu)); 196 CHKERRQ(TSSetFromOptions(ts)); 197 198 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 199 Solve the problem 200 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 201 202 /* 203 Evaluate initial conditions 204 */ 205 CHKERRQ(InitialConditions(u,&appctx)); 206 207 /* 208 Run the timestepping solver 209 */ 210 CHKERRQ(TSSolve(ts,u)); 211 212 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 213 Free work space. All PETSc objects should be destroyed when they 214 are no longer needed. 215 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 216 217 CHKERRQ(VecDestroy(&r)); 218 CHKERRQ(VecDestroy(&xl)); 219 CHKERRQ(VecDestroy(&xu)); 220 CHKERRQ(TSDestroy(&ts)); 221 CHKERRQ(VecDestroy(&u)); 222 CHKERRQ(MatDestroy(&A)); 223 CHKERRQ(DMDestroy(&appctx.da)); 224 CHKERRQ(VecDestroy(&appctx.localwork)); 225 CHKERRQ(VecDestroy(&appctx.solution)); 226 CHKERRQ(VecDestroy(&appctx.u_local)); 227 228 /* 229 Always call PetscFinalize() before exiting a program. This routine 230 - finalizes the PETSc libraries as well as MPI 231 - provides summary and diagnostic information if certain runtime 232 options are chosen (e.g., -log_view). 233 */ 234 ierr = PetscFinalize(); 235 return ierr; 236 } 237 /* --------------------------------------------------------------------- */ 238 /* 239 InitialConditions - Computes the solution at the initial time. 240 241 Input Parameters: 242 u - uninitialized solution vector (global) 243 appctx - user-defined application context 244 245 Output Parameter: 246 u - vector with solution at initial time (global) 247 */ 248 PetscErrorCode InitialConditions(Vec u,AppCtx *appctx) 249 { 250 PetscScalar *u_localptr,h = appctx->h,x; 251 PetscInt i,mybase,myend; 252 253 /* 254 Determine starting point of each processor's range of 255 grid values. 256 */ 257 CHKERRQ(VecGetOwnershipRange(u,&mybase,&myend)); 258 259 /* 260 Get a pointer to vector data. 261 - For default PETSc vectors, VecGetArray() returns a pointer to 262 the data array. Otherwise, the routine is implementation dependent. 263 - You MUST call VecRestoreArray() when you no longer need access to 264 the array. 265 - Note that the Fortran interface to VecGetArray() differs from the 266 C version. See the users manual for details. 267 */ 268 CHKERRQ(VecGetArray(u,&u_localptr)); 269 270 /* 271 We initialize the solution array by simply writing the solution 272 directly into the array locations. Alternatively, we could use 273 VecSetValues() or VecSetValuesLocal(). 274 */ 275 for (i=mybase; i<myend; i++) { 276 x = h*(PetscReal)i; /* current location in global grid */ 277 u_localptr[i-mybase] = 1.0 + x*x; 278 } 279 280 /* 281 Restore vector 282 */ 283 CHKERRQ(VecRestoreArray(u,&u_localptr)); 284 285 /* 286 Print debugging information if desired 287 */ 288 if (appctx->debug) { 289 CHKERRQ(PetscPrintf(appctx->comm,"initial guess vector\n")); 290 CHKERRQ(VecView(u,PETSC_VIEWER_STDOUT_WORLD)); 291 } 292 293 return 0; 294 } 295 296 /* --------------------------------------------------------------------- */ 297 /* 298 SetBounds - Sets the lower and uper bounds on the interior points 299 300 Input parameters: 301 xl - vector of lower bounds 302 xu - vector of upper bounds 303 ul - constant lower bound for all variables 304 uh - constant upper bound for all variables 305 appctx - Application context 306 */ 307 PetscErrorCode SetBounds(Vec xl, Vec xu, PetscScalar ul, PetscScalar uh,AppCtx *appctx) 308 { 309 PetscScalar *l,*u; 310 PetscMPIInt rank,size; 311 PetscInt localsize; 312 313 PetscFunctionBeginUser; 314 CHKERRQ(VecSet(xl,ul)); 315 CHKERRQ(VecSet(xu,uh)); 316 CHKERRQ(VecGetLocalSize(xl,&localsize)); 317 CHKERRQ(VecGetArray(xl,&l)); 318 CHKERRQ(VecGetArray(xu,&u)); 319 320 CHKERRMPI(MPI_Comm_rank(appctx->comm,&rank)); 321 CHKERRMPI(MPI_Comm_size(appctx->comm,&size)); 322 if (rank == 0) { 323 l[0] = -PETSC_INFINITY; 324 u[0] = PETSC_INFINITY; 325 } 326 if (rank == size-1) { 327 l[localsize-1] = -PETSC_INFINITY; 328 u[localsize-1] = PETSC_INFINITY; 329 } 330 CHKERRQ(VecRestoreArray(xl,&l)); 331 CHKERRQ(VecRestoreArray(xu,&u)); 332 PetscFunctionReturn(0); 333 } 334 335 /* --------------------------------------------------------------------- */ 336 /* 337 ExactSolution - Computes the exact solution at a given time. 338 339 Input Parameters: 340 t - current time 341 solution - vector in which exact solution will be computed 342 appctx - user-defined application context 343 344 Output Parameter: 345 solution - vector with the newly computed exact solution 346 */ 347 PetscErrorCode ExactSolution(PetscReal t,Vec solution,AppCtx *appctx) 348 { 349 PetscScalar *s_localptr,h = appctx->h,x; 350 PetscInt i,mybase,myend; 351 352 /* 353 Determine starting and ending points of each processor's 354 range of grid values 355 */ 356 CHKERRQ(VecGetOwnershipRange(solution,&mybase,&myend)); 357 358 /* 359 Get a pointer to vector data. 360 */ 361 CHKERRQ(VecGetArray(solution,&s_localptr)); 362 363 /* 364 Simply write the solution directly into the array locations. 365 Alternatively, we could use VecSetValues() or VecSetValuesLocal(). 366 */ 367 for (i=mybase; i<myend; i++) { 368 x = h*(PetscReal)i; 369 s_localptr[i-mybase] = (t + 1.0)*(1.0 + x*x); 370 } 371 372 /* 373 Restore vector 374 */ 375 CHKERRQ(VecRestoreArray(solution,&s_localptr)); 376 return 0; 377 } 378 /* --------------------------------------------------------------------- */ 379 /* 380 Monitor - User-provided routine to monitor the solution computed at 381 each timestep. This example plots the solution and computes the 382 error in two different norms. 383 384 Input Parameters: 385 ts - the timestep context 386 step - the count of the current step (with 0 meaning the 387 initial condition) 388 time - the current time 389 u - the solution at this timestep 390 ctx - the user-provided context for this monitoring routine. 391 In this case we use the application context which contains 392 information about the problem size, workspace and the exact 393 solution. 394 */ 395 PetscErrorCode Monitor(TS ts,PetscInt step,PetscReal time,Vec u,void *ctx) 396 { 397 AppCtx *appctx = (AppCtx*) ctx; /* user-defined application context */ 398 PetscReal en2,en2s,enmax; 399 PetscDraw draw; 400 401 /* 402 We use the default X windows viewer 403 PETSC_VIEWER_DRAW_(appctx->comm) 404 that is associated with the current communicator. This saves 405 the effort of calling PetscViewerDrawOpen() to create the window. 406 Note that if we wished to plot several items in separate windows we 407 would create each viewer with PetscViewerDrawOpen() and store them in 408 the application context, appctx. 409 410 PetscReal buffering makes graphics look better. 411 */ 412 CHKERRQ(PetscViewerDrawGetDraw(PETSC_VIEWER_DRAW_(appctx->comm),0,&draw)); 413 CHKERRQ(PetscDrawSetDoubleBuffer(draw)); 414 CHKERRQ(VecView(u,PETSC_VIEWER_DRAW_(appctx->comm))); 415 416 /* 417 Compute the exact solution at this timestep 418 */ 419 CHKERRQ(ExactSolution(time,appctx->solution,appctx)); 420 421 /* 422 Print debugging information if desired 423 */ 424 if (appctx->debug) { 425 CHKERRQ(PetscPrintf(appctx->comm,"Computed solution vector\n")); 426 CHKERRQ(VecView(u,PETSC_VIEWER_STDOUT_WORLD)); 427 CHKERRQ(PetscPrintf(appctx->comm,"Exact solution vector\n")); 428 CHKERRQ(VecView(appctx->solution,PETSC_VIEWER_STDOUT_WORLD)); 429 } 430 431 /* 432 Compute the 2-norm and max-norm of the error 433 */ 434 CHKERRQ(VecAXPY(appctx->solution,-1.0,u)); 435 CHKERRQ(VecNorm(appctx->solution,NORM_2,&en2)); 436 en2s = PetscSqrtReal(appctx->h)*en2; /* scale the 2-norm by the grid spacing */ 437 CHKERRQ(VecNorm(appctx->solution,NORM_MAX,&enmax)); 438 439 /* 440 PetscPrintf() causes only the first processor in this 441 communicator to print the timestep information. 442 */ 443 CHKERRQ(PetscPrintf(appctx->comm,"Timestep %D: time = %g,2-norm error = %g, max norm error = %g\n",step,(double)time,(double)en2s,(double)enmax)); 444 445 /* 446 Print debugging information if desired 447 */ 448 /* if (appctx->debug) { 449 CHKERRQ(PetscPrintf(appctx->comm,"Error vector\n")); 450 CHKERRQ(VecView(appctx->solution,PETSC_VIEWER_STDOUT_WORLD)); 451 } */ 452 return 0; 453 } 454 /* --------------------------------------------------------------------- */ 455 /* 456 RHSFunction - User-provided routine that evalues the right-hand-side 457 function of the ODE. This routine is set in the main program by 458 calling TSSetRHSFunction(). We compute: 459 global_out = F(global_in) 460 461 Input Parameters: 462 ts - timesteping context 463 t - current time 464 global_in - vector containing the current iterate 465 ctx - (optional) user-provided context for function evaluation. 466 In this case we use the appctx defined above. 467 468 Output Parameter: 469 global_out - vector containing the newly evaluated function 470 */ 471 PetscErrorCode RHSFunction(TS ts,PetscReal t,Vec global_in,Vec global_out,void *ctx) 472 { 473 AppCtx *appctx = (AppCtx*) ctx; /* user-defined application context */ 474 DM da = appctx->da; /* distributed array */ 475 Vec local_in = appctx->u_local; /* local ghosted input vector */ 476 Vec localwork = appctx->localwork; /* local ghosted work vector */ 477 PetscInt i,localsize; 478 PetscMPIInt rank,size; 479 PetscScalar *copyptr,sc; 480 const PetscScalar *localptr; 481 482 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 483 Get ready for local function computations 484 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 485 /* 486 Scatter ghost points to local vector, using the 2-step process 487 DMGlobalToLocalBegin(), DMGlobalToLocalEnd(). 488 By placing code between these two statements, computations can be 489 done while messages are in transition. 490 */ 491 CHKERRQ(DMGlobalToLocalBegin(da,global_in,INSERT_VALUES,local_in)); 492 CHKERRQ(DMGlobalToLocalEnd(da,global_in,INSERT_VALUES,local_in)); 493 494 /* 495 Access directly the values in our local INPUT work array 496 */ 497 CHKERRQ(VecGetArrayRead(local_in,&localptr)); 498 499 /* 500 Access directly the values in our local OUTPUT work array 501 */ 502 CHKERRQ(VecGetArray(localwork,©ptr)); 503 504 sc = 1.0/(appctx->h*appctx->h*2.0*(1.0+t)*(1.0+t)); 505 506 /* 507 Evaluate our function on the nodes owned by this processor 508 */ 509 CHKERRQ(VecGetLocalSize(local_in,&localsize)); 510 511 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 512 Compute entries for the locally owned part 513 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 514 515 /* 516 Handle boundary conditions: This is done by using the boundary condition 517 u(t,boundary) = g(t,boundary) 518 for some function g. Now take the derivative with respect to t to obtain 519 u_{t}(t,boundary) = g_{t}(t,boundary) 520 521 In our case, u(t,0) = t + 1, so that u_{t}(t,0) = 1 522 and u(t,1) = 2t+ 2, so that u_{t}(t,1) = 2 523 */ 524 CHKERRMPI(MPI_Comm_rank(appctx->comm,&rank)); 525 CHKERRMPI(MPI_Comm_size(appctx->comm,&size)); 526 if (rank == 0) copyptr[0] = 1.0; 527 if (rank == size-1) copyptr[localsize-1] = (t < .5) ? 2.0 : 0.0; 528 529 /* 530 Handle the interior nodes where the PDE is replace by finite 531 difference operators. 532 */ 533 for (i=1; i<localsize-1; i++) copyptr[i] = localptr[i] * sc * (localptr[i+1] + localptr[i-1] - 2.0*localptr[i]); 534 535 /* 536 Restore vectors 537 */ 538 CHKERRQ(VecRestoreArrayRead(local_in,&localptr)); 539 CHKERRQ(VecRestoreArray(localwork,©ptr)); 540 541 /* 542 Insert values from the local OUTPUT vector into the global 543 output vector 544 */ 545 CHKERRQ(DMLocalToGlobalBegin(da,localwork,INSERT_VALUES,global_out)); 546 CHKERRQ(DMLocalToGlobalEnd(da,localwork,INSERT_VALUES,global_out)); 547 548 /* Print debugging information if desired */ 549 /* if (appctx->debug) { 550 CHKERRQ(PetscPrintf(appctx->comm,"RHS function vector\n")); 551 CHKERRQ(VecView(global_out,PETSC_VIEWER_STDOUT_WORLD)); 552 } */ 553 554 return 0; 555 } 556 /* --------------------------------------------------------------------- */ 557 /* 558 RHSJacobian - User-provided routine to compute the Jacobian of 559 the nonlinear right-hand-side function of the ODE. 560 561 Input Parameters: 562 ts - the TS context 563 t - current time 564 global_in - global input vector 565 dummy - optional user-defined context, as set by TSetRHSJacobian() 566 567 Output Parameters: 568 AA - Jacobian matrix 569 BB - optionally different preconditioning matrix 570 str - flag indicating matrix structure 571 572 Notes: 573 RHSJacobian computes entries for the locally owned part of the Jacobian. 574 - Currently, all PETSc parallel matrix formats are partitioned by 575 contiguous chunks of rows across the processors. 576 - Each processor needs to insert only elements that it owns 577 locally (but any non-local elements will be sent to the 578 appropriate processor during matrix assembly). 579 - Always specify global row and columns of matrix entries when 580 using MatSetValues(). 581 - Here, we set all entries for a particular row at once. 582 - Note that MatSetValues() uses 0-based row and column numbers 583 in Fortran as well as in C. 584 */ 585 PetscErrorCode RHSJacobian(TS ts,PetscReal t,Vec global_in,Mat AA,Mat B,void *ctx) 586 { 587 AppCtx *appctx = (AppCtx*)ctx; /* user-defined application context */ 588 Vec local_in = appctx->u_local; /* local ghosted input vector */ 589 DM da = appctx->da; /* distributed array */ 590 PetscScalar v[3],sc; 591 const PetscScalar *localptr; 592 PetscInt i,mstart,mend,mstarts,mends,idx[3],is; 593 594 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 595 Get ready for local Jacobian computations 596 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 597 /* 598 Scatter ghost points to local vector, using the 2-step process 599 DMGlobalToLocalBegin(), DMGlobalToLocalEnd(). 600 By placing code between these two statements, computations can be 601 done while messages are in transition. 602 */ 603 CHKERRQ(DMGlobalToLocalBegin(da,global_in,INSERT_VALUES,local_in)); 604 CHKERRQ(DMGlobalToLocalEnd(da,global_in,INSERT_VALUES,local_in)); 605 606 /* 607 Get pointer to vector data 608 */ 609 CHKERRQ(VecGetArrayRead(local_in,&localptr)); 610 611 /* 612 Get starting and ending locally owned rows of the matrix 613 */ 614 CHKERRQ(MatGetOwnershipRange(B,&mstarts,&mends)); 615 mstart = mstarts; mend = mends; 616 617 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 618 Compute entries for the locally owned part of the Jacobian. 619 - Currently, all PETSc parallel matrix formats are partitioned by 620 contiguous chunks of rows across the processors. 621 - Each processor needs to insert only elements that it owns 622 locally (but any non-local elements will be sent to the 623 appropriate processor during matrix assembly). 624 - Here, we set all entries for a particular row at once. 625 - We can set matrix entries either using either 626 MatSetValuesLocal() or MatSetValues(). 627 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 628 629 /* 630 Set matrix rows corresponding to boundary data 631 */ 632 if (mstart == 0) { 633 v[0] = 0.0; 634 CHKERRQ(MatSetValues(B,1,&mstart,1,&mstart,v,INSERT_VALUES)); 635 mstart++; 636 } 637 if (mend == appctx->m) { 638 mend--; 639 v[0] = 0.0; 640 CHKERRQ(MatSetValues(B,1,&mend,1,&mend,v,INSERT_VALUES)); 641 } 642 643 /* 644 Set matrix rows corresponding to interior data. We construct the 645 matrix one row at a time. 646 */ 647 sc = 1.0/(appctx->h*appctx->h*2.0*(1.0+t)*(1.0+t)); 648 for (i=mstart; i<mend; i++) { 649 idx[0] = i-1; idx[1] = i; idx[2] = i+1; 650 is = i - mstart + 1; 651 v[0] = sc*localptr[is]; 652 v[1] = sc*(localptr[is+1] + localptr[is-1] - 4.0*localptr[is]); 653 v[2] = sc*localptr[is]; 654 CHKERRQ(MatSetValues(B,1,&i,3,idx,v,INSERT_VALUES)); 655 } 656 657 /* 658 Restore vector 659 */ 660 CHKERRQ(VecRestoreArrayRead(local_in,&localptr)); 661 662 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 663 Complete the matrix assembly process and set some options 664 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 665 /* 666 Assemble matrix, using the 2-step process: 667 MatAssemblyBegin(), MatAssemblyEnd() 668 Computations can be done while messages are in transition 669 by placing code between these two statements. 670 */ 671 CHKERRQ(MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY)); 672 CHKERRQ(MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY)); 673 674 /* 675 Set and option to indicate that we will never add a new nonzero location 676 to the matrix. If we do, it will generate an error. 677 */ 678 CHKERRQ(MatSetOption(B,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE)); 679 680 return 0; 681 } 682 683 /*TEST 684 685 test: 686 args: -snes_type vinewtonrsls -ts_type glee -mymonitor -ts_max_steps 10 -nox 687 requires: !single 688 689 TEST*/ 690