Actual source code: ex35.cxx

      1: static const char help[] = "Time-dependent Brusselator reaction-diffusion PDE in 1d. Demonstrates IMEX methods and uses MOAB.\n";
      2: /*
      3:    u_t - alpha u_xx = A + u^2 v - (B+1) u
      4:    v_t - alpha v_xx = B u - u^2 v
      5:    0 < x < 1;
      6:    A = 1, B = 3, alpha = 1/50

      8:    Initial conditions:
      9:    u(x,0) = 1 + sin(2 pi x)
     10:    v(x,0) = 3

     12:    Boundary conditions:
     13:    u(0,t) = u(1,t) = 1
     14:    v(0,t) = v(1,t) = 3
     15: */

     17: // PETSc includes:
     18: #include <petscts.h>
     19: #include <petscdmmoab.h>

     21: typedef struct {
     22:   PetscScalar u,v;
     23: } Field;

     25: struct pUserCtx {
     26:   PetscReal A,B;        /* Reaction coefficients */
     27:   PetscReal alpha;      /* Diffusion coefficient */
     28:   Field leftbc;         /* Dirichlet boundary conditions at left boundary */
     29:   Field rightbc;        /* Dirichlet boundary conditions at right boundary */
     30:   PetscInt  n,npts;       /* Number of mesh points */
     31:   PetscInt  ntsteps;    /* Number of time steps */
     32:   PetscInt nvars;       /* Number of variables in the equation system */
     33:   PetscBool io;
     34: };
     35: typedef pUserCtx* UserCtx;

     37: PetscErrorCode Initialize_AppContext(UserCtx *puser)
     38: {
     39:   UserCtx           user;
     40:   PetscErrorCode    ierr;

     43:   PetscNew(&user);

     45:   PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"Advection-reaction options","ex35.cxx");
     46:   {
     47:     user->nvars  = 2;
     48:     user->A      = 1;
     49:     user->B      = 3;
     50:     user->alpha  = 0.02;
     51:     user->leftbc.u  = 1;
     52:     user->rightbc.u = 1;
     53:     user->leftbc.v  = 3;
     54:     user->rightbc.v = 3;
     55:     user->n      = 10;
     56:     user->ntsteps = 10000;
     57:     user->io = PETSC_FALSE;
     58:     PetscOptionsReal("-A","Reaction rate","ex35.cxx",user->A,&user->A,NULL);
     59:     PetscOptionsReal("-B","Reaction rate","ex35.cxx",user->B,&user->B,NULL);
     60:     PetscOptionsReal("-alpha","Diffusion coefficient","ex35.cxx",user->alpha,&user->alpha,NULL);
     61:     PetscOptionsScalar("-uleft","Dirichlet boundary condition","ex35.cxx",user->leftbc.u,&user->leftbc.u,NULL);
     62:     PetscOptionsScalar("-uright","Dirichlet boundary condition","ex35.cxx",user->rightbc.u,&user->rightbc.u,NULL);
     63:     PetscOptionsScalar("-vleft","Dirichlet boundary condition","ex35.cxx",user->leftbc.v,&user->leftbc.v,NULL);
     64:     PetscOptionsScalar("-vright","Dirichlet boundary condition","ex35.cxx",user->rightbc.v,&user->rightbc.v,NULL);
     65:     PetscOptionsInt("-n","Number of 1-D elements","ex35.cxx",user->n,&user->n,NULL);
     66:     PetscOptionsInt("-ndt","Number of time steps","ex35.cxx",user->ntsteps,&user->ntsteps,NULL);
     67:     PetscOptionsBool("-io","Write the mesh and solution output to a file.","ex35.cxx",user->io,&user->io,NULL);
     68:     user->npts   = user->n+1;
     69:   }
     70:   PetscOptionsEnd();

     72:   *puser = user;
     73:   return(0);
     74: }

     76: PetscErrorCode Destroy_AppContext(UserCtx *user)
     77: {

     81:   PetscFree(*user);
     82:   return(0);
     83: }

     85: static PetscErrorCode FormInitialSolution(TS,Vec,void*);
     86: static PetscErrorCode FormRHSFunction(TS,PetscReal,Vec,Vec,void*);
     87: static PetscErrorCode FormIFunction(TS,PetscReal,Vec,Vec,Vec,void*);
     88: static PetscErrorCode FormIJacobian(TS,PetscReal,Vec,Vec,PetscReal,Mat,Mat,void*);

     90: /****************
     91:  *              *
     92:  *     MAIN     *
     93:  *              *
     94:  ****************/
     95: int main(int argc,char **argv)
     96: {
     97:   TS                ts;         /* nonlinear solver */
     98:   Vec               X;          /* solution, residual vectors */
     99:   Mat               J;          /* Jacobian matrix */
    100:   PetscInt          steps,mx;
    101:   PetscErrorCode    ierr;
    102:   PetscReal         hx,dt,ftime;
    103:   UserCtx           user;       /* user-defined work context */
    104:   TSConvergedReason reason;

    106:   DM                dm;
    107:   const char        *fields[2] = {"U","V"};

    109:   PetscInitialize(&argc,&argv,(char *)0,help);if (ierr) return ierr;

    111:   /* Initialize the user context struct */
    112:   Initialize_AppContext(&user);

    114:   /* Fill in the user defined work context: */
    115:   DMMoabCreateBoxMesh(PETSC_COMM_WORLD, 1, PETSC_FALSE, NULL, user->n, 1, &dm);
    116:   DMMoabSetFieldNames(dm, user->nvars, fields);
    117:   DMMoabSetBlockSize(dm, user->nvars);
    118:   DMSetFromOptions(dm);

    120:   /* SetUp the data structures for DMMOAB */
    121:   DMSetUp(dm);

    123:   /*  Create timestepping solver context */
    124:   TSCreate(PETSC_COMM_WORLD,&ts);
    125:   TSSetDM(ts, dm);
    126:   TSSetType(ts,TSARKIMEX);
    127:   TSSetEquationType(ts,TS_EQ_DAE_IMPLICIT_INDEX1);
    128:   DMSetMatType(dm,MATBAIJ);
    129:   DMCreateMatrix(dm,&J);

    131:   TSSetRHSFunction(ts,NULL,FormRHSFunction,user);
    132:   TSSetIFunction(ts,NULL,FormIFunction,user);
    133:   TSSetIJacobian(ts,J,J,FormIJacobian,user);

    135:   ftime = 10.0;
    136:   TSSetMaxSteps(ts,user->ntsteps);
    137:   TSSetMaxTime(ts,ftime);
    138:   TSSetExactFinalTime(ts,TS_EXACTFINALTIME_STEPOVER);

    140:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    141:      Create the solution vector and set the initial conditions
    142:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    143:   DMCreateGlobalVector(dm, &X);

    145:   FormInitialSolution(ts,X,user);
    146:   TSSetSolution(ts,X);
    147:   VecGetSize(X,&mx);
    148:   hx = 1.0/(PetscReal)(mx/2-1);
    149:   dt = 0.4 * PetscSqr(hx) / user->alpha; /* Diffusive stability limit */
    150:   TSSetTimeStep(ts,dt);

    152:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    153:      Set runtime options
    154:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    155:   TSSetFromOptions(ts);

    157:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    158:      Solve nonlinear system
    159:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    160:   TSSolve(ts,X);
    161:   TSGetSolveTime(ts,&ftime);
    162:   TSGetStepNumber(ts,&steps);
    163:   TSGetConvergedReason(ts,&reason);
    164:   PetscPrintf(PETSC_COMM_WORLD,"%s at time %g after %D steps\n",TSConvergedReasons[reason],ftime,steps);

    166:   if (user->io) {
    167:     /* Print the numerical solution to screen and then dump to file */
    168:     VecView(X,PETSC_VIEWER_STDOUT_WORLD);

    170:     /* Write out the solution along with the mesh */
    171:     DMMoabSetGlobalFieldVector(dm, X);
    172: #ifdef MOAB_HAVE_HDF5
    173:     DMMoabOutput(dm, "ex35.h5m", "");
    174: #else
    175:     /* MOAB does not support true parallel writers that aren't HDF5 based
    176:        And so if you are using VTK as the output format in parallel,
    177:        the data could be jumbled due to the order in which the processors
    178:        write out their parts of the mesh and solution tags
    179:     */
    180:     DMMoabOutput(dm, "ex35.vtk", "");
    181: #endif
    182:   }

    184:   /* Free work space.
    185:      Free all PETSc related resources: */
    186:   MatDestroy(&J);
    187:   VecDestroy(&X);
    188:   TSDestroy(&ts);
    189:   DMDestroy(&dm);

    191:   /* Free all MOAB related resources: */
    192:   Destroy_AppContext(&user);
    193:   PetscFinalize();
    194:   return ierr;
    195: }

    198: /*
    199:   IJacobian - Compute IJacobian = dF/dU + a dF/dUdot
    200: */
    201: PetscErrorCode FormIJacobian(TS ts,PetscReal t,Vec X,Vec Xdot,PetscReal a,Mat J,Mat Jpre,void *ptr)
    202: {
    203:   UserCtx             user = (UserCtx)ptr;
    204:   PetscErrorCode      ierr;
    205:   PetscInt            dof;
    206:   PetscReal           hx;
    207:   DM                  dm;
    208:   const moab::Range   *vlocal;
    209:   PetscBool           vonboundary;

    212:   TSGetDM(ts, &dm);

    214:   /* get the essential MOAB mesh related quantities needed for FEM assembly */
    215:   DMMoabGetLocalVertices(dm, &vlocal, NULL);

    217:   /* compute local element sizes - structured grid */
    218:   hx = 1.0/user->n;

    220:   /* Compute function over the locally owned part of the grid
    221:      Assemble the operator by looping over edges and computing
    222:      contribution for each vertex dof                         */
    223:   for (moab::Range::iterator iter = vlocal->begin(); iter != vlocal->end(); iter++) {
    224:     const moab::EntityHandle vhandle = *iter;

    226:     DMMoabGetDofsBlocked(dm, 1, &vhandle, &dof);

    228:     /* check if vertex is on the boundary */
    229:     DMMoabIsEntityOnBoundary(dm,vhandle,&vonboundary);

    231:     if (vonboundary) {
    232:       const PetscScalar bcvals[2][2] = {{hx,0},{0,hx}};
    233:       MatSetValuesBlocked(Jpre,1,&dof,1,&dof,&bcvals[0][0],INSERT_VALUES);
    234:     }
    235:     else {
    236:       const PetscInt    row           = dof,col[] = {dof-1,dof,dof+1};
    237:       const PetscScalar dxxL          = -user->alpha/hx,dxx0 = 2.*user->alpha/hx,dxxR = -user->alpha/hx;
    238:       const PetscScalar vals[2][3][2] = {{{dxxL,0},{a *hx+dxx0,0},{dxxR,0}},
    239:                                          {{0,dxxL},{0,a*hx+dxx0},{0,dxxR}}};
    240:       MatSetValuesBlocked(Jpre,1,&row,3,col,&vals[0][0][0],INSERT_VALUES);
    241:     }
    242:   }

    244:   MatAssemblyBegin(Jpre,MAT_FINAL_ASSEMBLY);
    245:   MatAssemblyEnd(Jpre,MAT_FINAL_ASSEMBLY);
    246:   if (J != Jpre) {
    247:     MatAssemblyBegin(J,MAT_FINAL_ASSEMBLY);
    248:     MatAssemblyEnd(J,MAT_FINAL_ASSEMBLY);
    249:   }
    250:   return(0);
    251: }

    254: static PetscErrorCode FormRHSFunction(TS ts,PetscReal t,Vec X,Vec F,void *ptr)
    255: {
    256:   UserCtx           user = (UserCtx)ptr;
    257:   DM                dm;
    258:   PetscReal         hx;
    259:   const Field       *x;
    260:   Field             *f;
    261:   PetscInt          dof;
    262:   const moab::Range *ownedvtx;
    263:   PetscErrorCode    ierr;

    266:   hx = 1.0/user->n;
    267:   TSGetDM(ts,&dm);

    269:   /* Get pointers to vector data */
    270:   VecSet(F,0.0);

    272:   DMMoabVecGetArrayRead(dm, X, &x);
    273:   DMMoabVecGetArray(dm, F, &f);

    275:   DMMoabGetLocalVertices(dm, &ownedvtx, NULL);

    277:   /* Compute function over the locally owned part of the grid */
    278:   for (moab::Range::iterator iter = ownedvtx->begin(); iter != ownedvtx->end(); iter++) {
    279:     const moab::EntityHandle vhandle = *iter;
    280:     DMMoabGetDofsBlockedLocal(dm, 1, &vhandle, &dof);

    282:     PetscScalar u = x[dof].u,v = x[dof].v;
    283:     f[dof].u = hx*(user->A + u*u*v - (user->B+1)*u);
    284:     f[dof].v = hx*(user->B*u - u*u*v);
    285:   }

    287:   /* Restore vectors */
    288:   DMMoabVecRestoreArrayRead(dm, X, &x);
    289:   DMMoabVecRestoreArray(dm, F, &f);
    290:   return(0);
    291: }

    294: static PetscErrorCode FormIFunction(TS ts,PetscReal t,Vec X,Vec Xdot,Vec F,void *ctx)
    295: {
    296:   UserCtx         user = (UserCtx)ctx;
    297:   DM              dm;
    298:   Field           *x,*xdot,*f;
    299:   PetscReal       hx;
    300:   Vec             Xloc;
    301:   PetscErrorCode  ierr;
    302:   PetscInt        i,bcindx;
    303:   PetscBool       elem_on_boundary;
    304:   const moab::Range   *vlocal;

    307:   hx = 1.0/user->n;
    308:   TSGetDM(ts, &dm);

    310:   /* get the essential MOAB mesh related quantities needed for FEM assembly */
    311:   DMMoabGetLocalVertices(dm, &vlocal, NULL);

    313:   /* reset the residual vector */
    314:   VecSet(F,0.0);

    316:   DMGetLocalVector(dm,&Xloc);
    317:   DMGlobalToLocalBegin(dm,X,INSERT_VALUES,Xloc);
    318:   DMGlobalToLocalEnd(dm,X,INSERT_VALUES,Xloc);

    320:   /* get the local representation of the arrays from Vectors */
    321:   DMMoabVecGetArrayRead(dm, Xloc, &x);
    322:   DMMoabVecGetArrayRead(dm, Xdot, &xdot);
    323:   DMMoabVecGetArray(dm, F, &f);

    325:   /* loop over local elements */
    326:   for (moab::Range::iterator iter = vlocal->begin(); iter != vlocal->end(); iter++) {
    327:     const moab::EntityHandle vhandle = *iter;

    329:     DMMoabGetDofsBlockedLocal(dm,1,&vhandle,&i);

    331:     /* check if vertex is on the boundary */
    332:     DMMoabIsEntityOnBoundary(dm,vhandle,&elem_on_boundary);

    334:     if (elem_on_boundary) {
    335:       DMMoabGetDofsBlocked(dm, 1, &vhandle, &bcindx);
    336:       if (bcindx == 0) {  /* Apply left BC */
    337:         f[i].u = hx * (x[i].u - user->leftbc.u);
    338:         f[i].v = hx * (x[i].v - user->leftbc.v);
    339:       } else {       /* Apply right BC */
    340:         f[i].u = hx * (x[i].u - user->rightbc.u);
    341:         f[i].v = hx * (x[i].v - user->rightbc.v);
    342:       }
    343:     }
    344:     else {
    345:       f[i].u = hx * xdot[i].u - user->alpha * (x[i-1].u - 2.*x[i].u + x[i+1].u) / hx;
    346:       f[i].v = hx * xdot[i].v - user->alpha * (x[i-1].v - 2.*x[i].v + x[i+1].v) / hx;
    347:     }
    348:   }

    350:   /* Restore data */
    351:   DMMoabVecRestoreArrayRead(dm, Xloc, &x);
    352:   DMMoabVecRestoreArrayRead(dm, Xdot, &xdot);
    353:   DMMoabVecRestoreArray(dm, F, &f);
    354:   DMRestoreLocalVector(dm, &Xloc);
    355:   return(0);
    356: }

    359: PetscErrorCode FormInitialSolution(TS ts,Vec X,void *ctx)
    360: {
    361:   UserCtx           user = (UserCtx)ctx;
    362:   PetscReal         vpos[3];
    363:   DM                dm;
    364:   Field             *x;
    365:   PetscErrorCode    ierr;
    366:   const moab::Range *vowned;
    367:   PetscInt          dof;
    368:   moab::Range::iterator iter;

    371:   TSGetDM(ts, &dm);

    373:   /* get the essential MOAB mesh related quantities needed for FEM assembly */
    374:   DMMoabGetLocalVertices(dm, &vowned, NULL);

    376:   VecSet(X, 0.0);

    378:   /* Get pointers to vector data */
    379:   DMMoabVecGetArray(dm, X, &x);

    381:   /* Compute function over the locally owned part of the grid */
    382:   for (moab::Range::iterator iter = vowned->begin(); iter != vowned->end(); iter++) {
    383:     const moab::EntityHandle vhandle = *iter;
    384:     DMMoabGetDofsBlockedLocal(dm, 1, &vhandle, &dof);

    386:     /* compute the mid-point of the element and use a 1-point lumped quadrature */
    387:     DMMoabGetVertexCoordinates(dm,1,&vhandle,vpos);

    389:     PetscReal xi = vpos[0];
    390:     x[dof].u = user->leftbc.u*(1.-xi) + user->rightbc.u*xi + PetscSinReal(2.*PETSC_PI*xi);
    391:     x[dof].v = user->leftbc.v*(1.-xi) + user->rightbc.v*xi;
    392:   }

    394:   /* Restore vectors */
    395:   DMMoabVecRestoreArray(dm, X, &x);
    396:   return(0);
    397: }

    399: /*TEST

    401:     build:
    402:       requires: moab

    404:     test:
    405:       args: -n 20 -ts_type rosw -ts_rosw_type 2p -ts_dt 5e-2 -ts_adapt_type none

    407:     test:
    408:       suffix: 2
    409:       nsize: 2
    410:       args: -n 50 -ts_type glee -ts_adapt_type none -ts_dt 0.1 -io
    411:       TODO:

    413: TEST*/