Actual source code: ex3.c

      3: static char help[] ="Model Equations for Advection-Diffusion\n";

      5: /*
      6:     Page 9, Section 1.2 Model Equations for Advection-Diffusion

      8:           u_t = a u_x + d u_xx

     10:    The initial conditions used here different then in the book.

     12: */

     14: /*
     15:      Helpful runtime linear solver options:
     16:            -pc_type mg -da_refine 2 -snes_monitor -ksp_monitor -ts_view   (geometric multigrid with three levels)

     18: */

     20: /*
     21:    Include "petscts.h" so that we can use TS solvers.  Note that this file
     22:    automatically includes:
     23:      petscsys.h       - base PETSc routines   petscvec.h  - vectors
     24:      petscmat.h  - matrices
     25:      petscis.h     - index sets            petscksp.h  - Krylov subspace methods
     26:      petscviewer.h - viewers               petscpc.h   - preconditioners
     27:      petscksp.h   - linear solvers        petscsnes.h - nonlinear solvers
     28: */

     30: #include <petscts.h>
     31: #include <petscdm.h>
     32: #include <petscdmda.h>

     34: /*
     35:    User-defined application context - contains data needed by the
     36:    application-provided call-back routines.
     37: */
     38: typedef struct {
     39:   PetscScalar a,d;   /* advection and diffusion strength */
     40:   PetscBool   upwind;
     41: } AppCtx;

     43: /*
     44:    User-defined routines
     45: */
     46: extern PetscErrorCode InitialConditions(TS,Vec,AppCtx*);
     47: extern PetscErrorCode RHSMatrixHeat(TS,PetscReal,Vec,Mat,Mat,void*);
     48: extern PetscErrorCode Solution(TS,PetscReal,Vec,AppCtx*);

     50: int main(int argc,char **argv)
     51: {
     52:   AppCtx         appctx;                 /* user-defined application context */
     53:   TS             ts;                     /* timestepping context */
     54:   Vec            U;                      /* approximate solution vector */
     56:   PetscReal      dt;
     57:   DM             da;
     58:   PetscInt       M;

     60:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     61:      Initialize program and set problem parameters
     62:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     64:   PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
     65:   appctx.a      = 1.0;
     66:   appctx.d      = 0.0;
     67:   PetscOptionsGetScalar(NULL,NULL,"-a",&appctx.a,NULL);
     68:   PetscOptionsGetScalar(NULL,NULL,"-d",&appctx.d,NULL);
     69:   appctx.upwind = PETSC_TRUE;
     70:   PetscOptionsGetBool(NULL,NULL,"-upwind",&appctx.upwind,NULL);

     72:   DMDACreate1d(PETSC_COMM_WORLD,DM_BOUNDARY_PERIODIC, 60, 1, 1,NULL,&da);
     73:   DMSetFromOptions(da);
     74:   DMSetUp(da);
     75:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     76:      Create vector data structures
     77:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     79:   /*
     80:      Create vector data structures for approximate and exact solutions
     81:   */
     82:   DMCreateGlobalVector(da,&U);

     84:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     85:      Create timestepping solver context
     86:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     88:   TSCreate(PETSC_COMM_WORLD,&ts);
     89:   TSSetDM(ts,da);

     91:   /*
     92:       For linear problems with a time-dependent f(U,t) in the equation
     93:      u_t = f(u,t), the user provides the discretized right-hand-side
     94:       as a time-dependent matrix.
     95:   */
     96:   TSSetRHSFunction(ts,NULL,TSComputeRHSFunctionLinear,&appctx);
     97:   TSSetRHSJacobian(ts,NULL,NULL,RHSMatrixHeat,&appctx);
     98:   TSSetSolutionFunction(ts,(PetscErrorCode (*)(TS,PetscReal,Vec,void*))Solution,&appctx);

    100:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    101:      Customize timestepping solver:
    102:        - Set timestepping duration info
    103:      Then set runtime options, which can override these defaults.
    104:      For example,
    105:           -ts_max_steps <maxsteps> -ts_max_time <maxtime>
    106:      to override the defaults set by TSSetMaxSteps()/TSSetMaxTime().
    107:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    109:   DMDAGetInfo(da,PETSC_IGNORE,&M,0,0,0,0,0,0,0,0,0,0,0);
    110:   dt   = .48/(M*M);
    111:   TSSetTimeStep(ts,dt);
    112:   TSSetMaxSteps(ts,1000);
    113:   TSSetMaxTime(ts,100.0);
    114:   TSSetExactFinalTime(ts,TS_EXACTFINALTIME_STEPOVER);
    115:   TSSetType(ts,TSARKIMEX);
    116:   TSSetFromOptions(ts);

    118:   /*
    119:      Evaluate initial conditions
    120:   */
    121:   InitialConditions(ts,U,&appctx);

    123:   /*
    124:      Run the timestepping solver
    125:   */
    126:   TSSolve(ts,U);

    129:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    130:      Free work space.  All PETSc objects should be destroyed when they
    131:      are no longer needed.
    132:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    134:   TSDestroy(&ts);
    135:   VecDestroy(&U);
    136:   DMDestroy(&da);

    138:   /*
    139:      Always call PetscFinalize() before exiting a program.  This routine
    140:        - finalizes the PETSc libraries as well as MPI
    141:        - provides summary and diagnostic information if certain runtime
    142:          options are chosen (e.g., -log_view).
    143:   */
    144:   PetscFinalize();
    145:   return ierr;
    146: }
    147: /* --------------------------------------------------------------------- */
    148: /*
    149:    InitialConditions - Computes the solution at the initial time.

    151:    Input Parameter:
    152:    u - uninitialized solution vector (global)
    153:    appctx - user-defined application context

    155:    Output Parameter:
    156:    u - vector with solution at initial time (global)
    157: */
    158: PetscErrorCode InitialConditions(TS ts,Vec U,AppCtx *appctx)
    159: {
    160:   PetscScalar    *u,h;
    162:   PetscInt       i,mstart,mend,xm,M;
    163:   DM             da;

    165:   TSGetDM(ts,&da);
    166:   DMDAGetCorners(da,&mstart,0,0,&xm,0,0);
    167:   DMDAGetInfo(da,PETSC_IGNORE,&M,0,0,0,0,0,0,0,0,0,0,0);
    168:   h    = 1.0/M;
    169:   mend = mstart + xm;
    170:   /*
    171:     Get a pointer to vector data.
    172:     - For default PETSc vectors, VecGetArray() returns a pointer to
    173:       the data array.  Otherwise, the routine is implementation dependent.
    174:     - You MUST call VecRestoreArray() when you no longer need access to
    175:       the array.
    176:     - Note that the Fortran interface to VecGetArray() differs from the
    177:       C version.  See the users manual for details.
    178:   */
    179:   DMDAVecGetArray(da,U,&u);

    181:   /*
    182:      We initialize the solution array by simply writing the solution
    183:      directly into the array locations.  Alternatively, we could use
    184:      VecSetValues() or VecSetValuesLocal().
    185:   */
    186:   for (i=mstart; i<mend; i++) u[i] = PetscSinScalar(PETSC_PI*i*6.*h) + 3.*PetscSinScalar(PETSC_PI*i*2.*h);

    188:   /*
    189:      Restore vector
    190:   */
    191:   DMDAVecRestoreArray(da,U,&u);
    192:   return 0;
    193: }
    194: /* --------------------------------------------------------------------- */
    195: /*
    196:    Solution - Computes the exact solution at a given time.

    198:    Input Parameters:
    199:    t - current time
    200:    solution - vector in which exact solution will be computed
    201:    appctx - user-defined application context

    203:    Output Parameter:
    204:    solution - vector with the newly computed exact solution
    205: */
    206: PetscErrorCode Solution(TS ts,PetscReal t,Vec U,AppCtx *appctx)
    207: {
    208:   PetscScalar    *u,ex1,ex2,sc1,sc2,h;
    210:   PetscInt       i,mstart,mend,xm,M;
    211:   DM             da;

    213:   TSGetDM(ts,&da);
    214:   DMDAGetCorners(da,&mstart,0,0,&xm,0,0);
    215:   DMDAGetInfo(da,PETSC_IGNORE,&M,0,0,0,0,0,0,0,0,0,0,0);
    216:   h    = 1.0/M;
    217:   mend = mstart + xm;
    218:   /*
    219:      Get a pointer to vector data.
    220:   */
    221:   DMDAVecGetArray(da,U,&u);

    223:   /*
    224:      Simply write the solution directly into the array locations.
    225:      Alternatively, we culd use VecSetValues() or VecSetValuesLocal().
    226:   */
    227:   ex1 = PetscExpScalar(-36.*PETSC_PI*PETSC_PI*appctx->d*t);
    228:   ex2 = PetscExpScalar(-4.*PETSC_PI*PETSC_PI*appctx->d*t);
    229:   sc1 = PETSC_PI*6.*h;                 sc2 = PETSC_PI*2.*h;
    230:   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;

    232:   /*
    233:      Restore vector
    234:   */
    235:   DMDAVecRestoreArray(da,U,&u);
    236:   return 0;
    237: }

    239: /* --------------------------------------------------------------------- */
    240: /*
    241:    RHSMatrixHeat - User-provided routine to compute the right-hand-side
    242:    matrix for the heat equation.

    244:    Input Parameters:
    245:    ts - the TS context
    246:    t - current time
    247:    global_in - global input vector
    248:    dummy - optional user-defined context, as set by TSetRHSJacobian()

    250:    Output Parameters:
    251:    AA - Jacobian matrix
    252:    BB - optionally different preconditioning matrix
    253:    str - flag indicating matrix structure

    255:    Notes:
    256:    Recall that MatSetValues() uses 0-based row and column numbers
    257:    in Fortran as well as in C.
    258: */
    259: PetscErrorCode RHSMatrixHeat(TS ts,PetscReal t,Vec U,Mat AA,Mat BB,void *ctx)
    260: {
    261:   Mat            A       = AA;                /* Jacobian matrix */
    262:   AppCtx         *appctx = (AppCtx*)ctx;     /* user-defined application context */
    263:   PetscInt       mstart, mend;
    265:   PetscInt       i,idx[3],M,xm;
    266:   PetscScalar    v[3],h;
    267:   DM             da;

    269:   TSGetDM(ts,&da);
    270:   DMDAGetInfo(da,0,&M,0,0,0,0,0,0,0,0,0,0,0);
    271:   DMDAGetCorners(da,&mstart,0,0,&xm,0,0);
    272:   h    = 1.0/M;
    273:   mend = mstart + xm;
    274:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    275:      Compute entries for the locally owned part of the matrix
    276:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    277:   /*
    278:      Set matrix rows corresponding to boundary data
    279:   */

    281:   /* diffusion */
    282:   v[0] = appctx->d/(h*h);
    283:   v[1] = -2.0*appctx->d/(h*h);
    284:   v[2] = appctx->d/(h*h);
    285:   if (!mstart) {
    286:     idx[0] = M-1; idx[1] = 0; idx[2] = 1;
    287:     MatSetValues(A,1,&mstart,3,idx,v,INSERT_VALUES);
    288:     mstart++;
    289:   }

    291:   if (mend == M) {
    292:     mend--;
    293:     idx[0] = M-2; idx[1] = M-1; idx[2] = 0;
    294:     MatSetValues(A,1,&mend,3,idx,v,INSERT_VALUES);
    295:   }

    297:   /*
    298:      Set matrix rows corresponding to interior data.  We construct the
    299:      matrix one row at a time.
    300:   */
    301:   for (i=mstart; i<mend; i++) {
    302:     idx[0] = i-1; idx[1] = i; idx[2] = i+1;
    303:     MatSetValues(A,1,&i,3,idx,v,INSERT_VALUES);
    304:   }
    305:   MatAssemblyBegin(A,MAT_FLUSH_ASSEMBLY);
    306:   MatAssemblyEnd(A,MAT_FLUSH_ASSEMBLY);

    308:   DMDAGetCorners(da,&mstart,0,0,&xm,0,0);
    309:   mend = mstart + xm;
    310:   if (!appctx->upwind) {
    311:     /* advection -- centered differencing */
    312:     v[0] = -.5*appctx->a/(h);
    313:     v[1] = .5*appctx->a/(h);
    314:     if (!mstart) {
    315:       idx[0] = M-1; idx[1] = 1;
    316:       MatSetValues(A,1,&mstart,2,idx,v,ADD_VALUES);
    317:       mstart++;
    318:     }

    320:     if (mend == M) {
    321:       mend--;
    322:       idx[0] = M-2; idx[1] = 0;
    323:       MatSetValues(A,1,&mend,2,idx,v,ADD_VALUES);
    324:     }

    326:     for (i=mstart; i<mend; i++) {
    327:       idx[0] = i-1; idx[1] = i+1;
    328:       MatSetValues(A,1,&i,2,idx,v,ADD_VALUES);
    329:     }
    330:   } else {
    331:     /* advection -- upwinding */
    332:     v[0] = -appctx->a/(h);
    333:     v[1] = appctx->a/(h);
    334:     if (!mstart) {
    335:       idx[0] = 0; idx[1] = 1;
    336:       MatSetValues(A,1,&mstart,2,idx,v,ADD_VALUES);
    337:       mstart++;
    338:     }

    340:     if (mend == M) {
    341:       mend--;
    342:       idx[0] = M-1; idx[1] = 0;
    343:       MatSetValues(A,1,&mend,2,idx,v,ADD_VALUES);
    344:     }

    346:     for (i=mstart; i<mend; i++) {
    347:       idx[0] = i; idx[1] = i+1;
    348:       MatSetValues(A,1,&i,2,idx,v,ADD_VALUES);
    349:     }
    350:   }

    353:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    354:      Complete the matrix assembly process and set some options
    355:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    356:   /*
    357:      Assemble matrix, using the 2-step process:
    358:        MatAssemblyBegin(), MatAssemblyEnd()
    359:      Computations can be done while messages are in transition
    360:      by placing code between these two statements.
    361:   */
    362:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
    363:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);

    365:   /*
    366:      Set and option to indicate that we will never add a new nonzero location
    367:      to the matrix. If we do, it will generate an error.
    368:   */
    369:   MatSetOption(A,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);
    370:   return 0;
    371: }

    374: /*TEST

    376:    test:
    377:       args: -pc_type mg -da_refine 2  -ts_view  -ts_monitor -ts_max_time .3 -mg_levels_ksp_max_it 3
    378:       requires: double
    379:       filter: grep -v "total number of"

    381:    test:
    382:       suffix: 2
    383:       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
    384:       requires: x
    385:       output_file: output/ex3_1.out
    386:       requires: double
    387:       filter: grep -v "total number of"

    389: TEST*/