xref: /petsc/src/ts/tutorials/extchemfield.c (revision d0609ced746bc51b019815ca91d747429db24893)

static const char help[] = "Integrate chemistry using TChem.\n";

#include <petscts.h>
#include <petscdmda.h>

#if defined(PETSC_HAVE_TCHEM)
#if defined(MAX)
#undef MAX
#endif
#if defined(MIN)
#undef MIN
#endif
#  include <TC_params.h>
#  include <TC_interface.h>
#else
#  error TChem is required for this example.  Reconfigure PETSc using --download-tchem.
#endif
/*

    This is an extension of extchem.c to solve the reaction equations independently in each cell of a one dimensional field

    Obtain the three files into this directory

       curl http://combustion.berkeley.edu/gri_mech/version30/files30/grimech30.dat > chem.inp
       curl http://combustion.berkeley.edu/gri_mech/version30/files30/thermo30.dat > therm.dat
       cp $PETSC_DIR/$PETSC_ARCH/externalpackages/tchem/data/periodictable.dat .

    Run with
     ./extchemfield  -ts_arkimex_fully_implicit -ts_max_snes_failures -1 -ts_adapt_monitor -ts_adapt_dt_max 1e-4 -ts_arkimex_type 4 -ts_max_time .005

     Options for visualizing the solution:
        Watch certain variables in each cell evolve with time
        -draw_solution 1 -ts_monitor_lg_solution_variables Temp,H2,O2,H2O,CH4,CO,CO2,C2H2,N2 -lg_use_markers false  -draw_pause -2

        Watch certain variables in all cells evolve with time
        -da_refine 4 -ts_monitor_draw_solution -draw_fields_by_name Temp,H2 -draw_vec_mark_points  -draw_pause -2

        Keep the initial temperature distribution as one monitors the current temperature distribution
        -ts_monitor_draw_solution_initial -draw_bounds .9,1.7 -draw_fields_by_name Temp

        Save the images in a .gif (movie) file
        -draw_save -draw_save_single_file

        Compute the sensitivies of the solution of the first temperature on the initial conditions
        -ts_adjoint_solve  -ts_dt 1.e-5 -ts_type cn -ts_adjoint_view_solution draw

        Turn off diffusion
        -diffusion no

        Turn off reactions
        -reactions no

    The solution for component i = 0 is the temperature.

    The solution, i > 0, is the mass fraction, massf[i], of species i, i.e. mass of species i/ total mass of all species

    The mole fraction molef[i], i > 0, is the number of moles of a species/ total number of moles of all species
        Define M[i] = mass per mole of species i then
        molef[i] = massf[i]/(M[i]*(sum_j massf[j]/M[j]))

    FormMoleFraction(User,massf,molef) converts the mass fraction solution of each species to the mole fraction of each species.

*/
typedef struct _User *User;
struct _User {
  PetscReal pressure;
  int       Nspec;
  int       Nreac;
  PetscReal Tini,dx;
  PetscReal diffus;
  DM        dm;
  PetscBool diffusion,reactions;
  double    *tchemwork;
  double    *Jdense;        /* Dense array workspace where Tchem computes the Jacobian */
  PetscInt  *rows;
};

static PetscErrorCode MonitorCell(TS,User,PetscInt);
static PetscErrorCode FormRHSFunction(TS,PetscReal,Vec,Vec,void*);
static PetscErrorCode FormRHSJacobian(TS,PetscReal,Vec,Mat,Mat,void*);
static PetscErrorCode FormInitialSolution(TS,Vec,void*);

#define PetscCallTC(ierr) do {PetscCheck(!ierr,PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in TChem library, return code %d",ierr);} while (0)

int main(int argc,char **argv)
{
  TS                ts;         /* time integrator */
  TSAdapt           adapt;
  Vec               X;          /* solution vector */
  Mat               J;          /* Jacobian matrix */
  PetscInt          steps,ncells,xs,xm,i;
  PetscReal         ftime,dt;
  char              chemfile[PETSC_MAX_PATH_LEN] = "chem.inp",thermofile[PETSC_MAX_PATH_LEN] = "therm.dat";
  struct _User      user;
  TSConvergedReason reason;
  PetscBool         showsolutions = PETSC_FALSE;
  char              **snames,*names;
  Vec               lambda;     /* used with TSAdjoint for sensitivities */

  PetscCall(PetscInitialize(&argc,&argv,(char*)0,help));
  PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"Chemistry solver options","");
  PetscCall(PetscOptionsString("-chem","CHEMKIN input file","",chemfile,chemfile,sizeof(chemfile),NULL));
  PetscCall(PetscOptionsString("-thermo","NASA thermo input file","",thermofile,thermofile,sizeof(thermofile),NULL));
  user.pressure = 1.01325e5;    /* Pascal */
  PetscCall(PetscOptionsReal("-pressure","Pressure of reaction [Pa]","",user.pressure,&user.pressure,NULL));
  user.Tini   = 1550;
  PetscCall(PetscOptionsReal("-Tini","Initial temperature [K]","",user.Tini,&user.Tini,NULL));
  user.diffus = 100;
  PetscCall(PetscOptionsReal("-diffus","Diffusion constant","",user.diffus,&user.diffus,NULL));
  PetscCall(PetscOptionsBool("-draw_solution","Plot the solution for each cell","",showsolutions,&showsolutions,NULL));
  user.diffusion = PETSC_TRUE;
  PetscCall(PetscOptionsBool("-diffusion","Have diffusion","",user.diffusion,&user.diffusion,NULL));
  user.reactions = PETSC_TRUE;
  PetscCall(PetscOptionsBool("-reactions","Have reactions","",user.reactions,&user.reactions,NULL));
  PetscOptionsEnd();

  PetscCallTC(TC_initChem(chemfile, thermofile, 0, 1.0));
  user.Nspec = TC_getNspec();
  user.Nreac = TC_getNreac();

  PetscCall(DMDACreate1d(PETSC_COMM_WORLD,DM_BOUNDARY_PERIODIC,10,user.Nspec+1,1,NULL,&user.dm));
  PetscCall(DMSetFromOptions(user.dm));
  PetscCall(DMSetUp(user.dm));
  PetscCall(DMDAGetInfo(user.dm,NULL,&ncells,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL));
  user.dx = 1.0/ncells;  /* Set the coordinates of the cell centers; note final ghost cell is at x coordinate 1.0 */
  PetscCall(DMDASetUniformCoordinates(user.dm,0.0,1.0,0.0,1.0,0.0,1.0));

  /* set the names of each field in the DMDA based on the species name */
  PetscCall(PetscMalloc1((user.Nspec+1)*LENGTHOFSPECNAME,&names));
  PetscCall(PetscStrcpy(names,"Temp"));
  TC_getSnames(user.Nspec,names+LENGTHOFSPECNAME);
  PetscCall(PetscMalloc1((user.Nspec+2),&snames));
  for (i=0; i<user.Nspec+1; i++) snames[i] = names+i*LENGTHOFSPECNAME;
  snames[user.Nspec+1] = NULL;
  PetscCall(DMDASetFieldNames(user.dm,(const char * const *)snames));
  PetscCall(PetscFree(snames));
  PetscCall(PetscFree(names));

  PetscCall(DMCreateMatrix(user.dm,&J));
  PetscCall(DMCreateGlobalVector(user.dm,&X));

  PetscCall(PetscMalloc3(user.Nspec+1,&user.tchemwork,PetscSqr(user.Nspec+1),&user.Jdense,user.Nspec+1,&user.rows));

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Create timestepping solver context
     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  PetscCall(TSCreate(PETSC_COMM_WORLD,&ts));
  PetscCall(TSSetDM(ts,user.dm));
  PetscCall(TSSetType(ts,TSARKIMEX));
  PetscCall(TSARKIMEXSetFullyImplicit(ts,PETSC_TRUE));
  PetscCall(TSARKIMEXSetType(ts,TSARKIMEX4));
  PetscCall(TSSetRHSFunction(ts,NULL,FormRHSFunction,&user));
  PetscCall(TSSetRHSJacobian(ts,J,J,FormRHSJacobian,&user));

  ftime = 1.0;
  PetscCall(TSSetMaxTime(ts,ftime));
  PetscCall(TSSetExactFinalTime(ts,TS_EXACTFINALTIME_STEPOVER));

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Set initial conditions
   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  PetscCall(FormInitialSolution(ts,X,&user));
  PetscCall(TSSetSolution(ts,X));
  dt   = 1e-10;                 /* Initial time step */
  PetscCall(TSSetTimeStep(ts,dt));
  PetscCall(TSGetAdapt(ts,&adapt));
  PetscCall(TSAdaptSetStepLimits(adapt,1e-12,1e-4)); /* Also available with -ts_adapt_dt_min/-ts_adapt_dt_max */
  PetscCall(TSSetMaxSNESFailures(ts,-1));            /* Retry step an unlimited number of times */

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Pass information to graphical monitoring routine
   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  if (showsolutions) {
    PetscCall(DMDAGetCorners(user.dm,&xs,NULL,NULL,&xm,NULL,NULL));
    for (i=xs;i<xs+xm;i++) {
      PetscCall(MonitorCell(ts,&user,i));
    }
  }

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Set runtime options
   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  PetscCall(TSSetFromOptions(ts));

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Set final conditions for sensitivities
   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  PetscCall(DMCreateGlobalVector(user.dm,&lambda));
  PetscCall(TSSetCostGradients(ts,1,&lambda,NULL));
  PetscCall(VecSetValue(lambda,0,1.0,INSERT_VALUES));
  PetscCall(VecAssemblyBegin(lambda));
  PetscCall(VecAssemblyEnd(lambda));

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Solve ODE
     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  PetscCall(TSSolve(ts,X));
  PetscCall(TSGetSolveTime(ts,&ftime));
  PetscCall(TSGetStepNumber(ts,&steps));
  PetscCall(TSGetConvergedReason(ts,&reason));
  PetscCall(PetscPrintf(PETSC_COMM_WORLD,"%s at time %g after %D steps\n",TSConvergedReasons[reason],(double)ftime,steps));

  {
    Vec                max;
    const char * const *names;
    PetscInt           i;
    const PetscReal    *bmax;

    PetscCall(TSMonitorEnvelopeGetBounds(ts,&max,NULL));
    if (max) {
      PetscCall(TSMonitorLGGetVariableNames(ts,&names));
      if (names) {
        PetscCall(VecGetArrayRead(max,&bmax));
        PetscCall(PetscPrintf(PETSC_COMM_SELF,"Species - maximum mass fraction\n"));
        for (i=1; i<user.Nspec; i++) {
          if (bmax[i] > .01) PetscCall(PetscPrintf(PETSC_COMM_SELF,"%s %g\n",names[i],bmax[i]));
        }
        PetscCall(VecRestoreArrayRead(max,&bmax));
      }
    }
  }

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Free work space.
   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  TC_reset();
  PetscCall(DMDestroy(&user.dm));
  PetscCall(MatDestroy(&J));
  PetscCall(VecDestroy(&X));
  PetscCall(VecDestroy(&lambda));
  PetscCall(TSDestroy(&ts));
  PetscCall(PetscFree3(user.tchemwork,user.Jdense,user.rows));
  PetscCall(PetscFinalize());
  return 0;
}

/*
   Applies the second order centered difference diffusion operator on a one dimensional periodic domain
*/
static PetscErrorCode FormDiffusionFunction(TS ts,PetscReal t,Vec X,Vec F,void *ptr)
{
  User              user = (User)ptr;
  PetscScalar       **f;
  const PetscScalar **x;
  DM                dm;
  PetscInt          i,xs,xm,j,dof;
  Vec               Xlocal;
  PetscReal         idx;

  PetscFunctionBeginUser;
  PetscCall(TSGetDM(ts,&dm));
  PetscCall(DMDAGetInfo(dm,NULL,NULL,NULL,NULL,NULL,NULL,NULL,&dof,NULL,NULL,NULL,NULL,NULL));
  PetscCall(DMGetLocalVector(dm,&Xlocal));
  PetscCall(DMGlobalToLocalBegin(dm,X,INSERT_VALUES,Xlocal));
  PetscCall(DMGlobalToLocalEnd(dm,X,INSERT_VALUES,Xlocal));
  PetscCall(DMDAVecGetArrayDOFRead(dm,Xlocal,&x));
  PetscCall(DMDAVecGetArrayDOF(dm,F,&f));
  PetscCall(DMDAGetCorners(dm,&xs,NULL,NULL,&xm,NULL,NULL));

  idx = 1.0*user->diffus/user->dx;
  for (i=xs; i<xs+xm; i++) {
    for (j=0; j<dof; j++) {
      f[i][j] += idx*(x[i+1][j] - 2.0*x[i][j] + x[i-1][j]);
    }
  }
  PetscCall(DMDAVecRestoreArrayDOFRead(dm,Xlocal,&x));
  PetscCall(DMDAVecRestoreArrayDOF(dm,F,&f));
  PetscCall(DMRestoreLocalVector(dm,&Xlocal));
  PetscFunctionReturn(0);
}

/*
   Produces the second order centered difference diffusion operator on a one dimensional periodic domain
*/
static PetscErrorCode FormDiffusionJacobian(TS ts,PetscReal t,Vec X,Mat Amat,Mat Pmat,void *ptr)
{
  User              user = (User)ptr;
  DM                dm;
  PetscInt          i,xs,xm,j,dof;
  PetscReal         idx,values[3];
  MatStencil        row,col[3];

  PetscFunctionBeginUser;
  PetscCall(TSGetDM(ts,&dm));
  PetscCall(DMDAGetInfo(dm,NULL,NULL,NULL,NULL,NULL,NULL,NULL,&dof,NULL,NULL,NULL,NULL,NULL));
  PetscCall(DMDAGetCorners(dm,&xs,NULL,NULL,&xm,NULL,NULL));

  idx = 1.0*user->diffus/user->dx;
  values[0] = idx;
  values[1] = -2.0*idx;
  values[2] = idx;
  for (i=xs; i<xs+xm; i++) {
    for (j=0; j<dof; j++) {
      row.i = i;      row.c = j;
      col[0].i = i-1; col[0].c = j;
      col[1].i = i;   col[1].c = j;
      col[2].i = i+1; col[2].c = j;
      PetscCall(MatSetValuesStencil(Pmat,1,&row,3,col,values,ADD_VALUES));
    }
  }
  PetscCall(MatAssemblyBegin(Pmat,MAT_FINAL_ASSEMBLY));
  PetscCall(MatAssemblyEnd(Pmat,MAT_FINAL_ASSEMBLY));
  PetscFunctionReturn(0);
}

static PetscErrorCode FormRHSFunction(TS ts,PetscReal t,Vec X,Vec F,void *ptr)
{
  User              user = (User)ptr;
  PetscScalar       **f;
  const PetscScalar **x;
  DM                dm;
  PetscInt          i,xs,xm;

  PetscFunctionBeginUser;
  if (user->reactions) {
    PetscCall(TSGetDM(ts,&dm));
    PetscCall(DMDAVecGetArrayDOFRead(dm,X,&x));
    PetscCall(DMDAVecGetArrayDOF(dm,F,&f));
    PetscCall(DMDAGetCorners(dm,&xs,NULL,NULL,&xm,NULL,NULL));

    for (i=xs; i<xs+xm; i++) {
      PetscCall(PetscArraycpy(user->tchemwork,x[i],user->Nspec+1));
      user->tchemwork[0] *= user->Tini; /* Dimensionalize */
      PetscCallTC(TC_getSrc(user->tchemwork,user->Nspec+1,f[i]));
      f[i][0] /= user->Tini;           /* Non-dimensionalize */
    }

    PetscCall(DMDAVecRestoreArrayDOFRead(dm,X,&x));
    PetscCall(DMDAVecRestoreArrayDOF(dm,F,&f));
  } else {
    PetscCall(VecZeroEntries(F));
  }
  if (user->diffusion) {
    PetscCall(FormDiffusionFunction(ts,t,X,F,ptr));
  }
  PetscFunctionReturn(0);
}

static PetscErrorCode FormRHSJacobian(TS ts,PetscReal t,Vec X,Mat Amat,Mat Pmat,void *ptr)
{
  User              user = (User)ptr;
  const PetscScalar **x;
  PetscInt          M = user->Nspec+1,i,j,xs,xm;
  DM                dm;

  PetscFunctionBeginUser;
  if (user->reactions) {
    PetscCall(TSGetDM(ts,&dm));
    PetscCall(MatZeroEntries(Pmat));
    PetscCall(MatSetOption(Pmat,MAT_ROW_ORIENTED,PETSC_FALSE));
    PetscCall(MatSetOption(Pmat,MAT_IGNORE_ZERO_ENTRIES,PETSC_TRUE));
    PetscCall(DMDAVecGetArrayDOFRead(dm,X,&x));
    PetscCall(DMDAGetCorners(dm,&xs,NULL,NULL,&xm,NULL,NULL));

    for (i=xs; i<xs+xm; i++) {
      PetscCall(PetscArraycpy(user->tchemwork,x[i],user->Nspec+1));
      user->tchemwork[0] *= user->Tini;  /* Dimensionalize temperature (first row) because that is what Tchem wants */
      PetscCall(TC_getJacTYN(user->tchemwork,user->Nspec,user->Jdense,1));

      for (j=0; j<M; j++) user->Jdense[j + 0*M] /= user->Tini; /* Non-dimensionalize first column */
      for (j=0; j<M; j++) user->Jdense[0 + j*M] /= user->Tini; /* Non-dimensionalize first row */
      for (j=0; j<M; j++) user->rows[j] = i*M+j;
      PetscCall(MatSetValues(Pmat,M,user->rows,M,user->rows,user->Jdense,INSERT_VALUES));
    }
    PetscCall(DMDAVecRestoreArrayDOFRead(dm,X,&x));
    PetscCall(MatAssemblyBegin(Pmat,MAT_FINAL_ASSEMBLY));
    PetscCall(MatAssemblyEnd(Pmat,MAT_FINAL_ASSEMBLY));
  } else {
    PetscCall(MatZeroEntries(Pmat));
  }
  if (user->diffusion) {
    PetscCall(FormDiffusionJacobian(ts,t,X,Amat,Pmat,ptr));
  }
  if (Amat != Pmat) {
    PetscCall(MatAssemblyBegin(Amat,MAT_FINAL_ASSEMBLY));
    PetscCall(MatAssemblyEnd(Amat,MAT_FINAL_ASSEMBLY));
  }
  PetscFunctionReturn(0);
}

PetscErrorCode FormInitialSolution(TS ts,Vec X,void *ctx)
{
  PetscScalar    **x,*xc;
  struct {const char *name; PetscReal massfrac;} initial[] = {
    {"CH4", 0.0948178320887},
    {"O2", 0.189635664177},
    {"N2", 0.706766236705},
    {"AR", 0.00878026702874}
  };
  PetscInt       i,j,xs,xm;
  DM             dm;

  PetscFunctionBeginUser;
  PetscCall(VecZeroEntries(X));
  PetscCall(TSGetDM(ts,&dm));
  PetscCall(DMDAGetCorners(dm,&xs,NULL,NULL,&xm,NULL,NULL));

  PetscCall(DMDAGetCoordinateArray(dm,&xc));
  PetscCall(DMDAVecGetArrayDOF(dm,X,&x));
  for (i=xs; i<xs+xm; i++) {
    x[i][0] = 1.0 + .05*PetscSinScalar(2.*PETSC_PI*xc[i]);  /* Non-dimensionalized by user->Tini */
    for (j=0; j<PETSC_STATIC_ARRAY_LENGTH(initial); j++) {
      int ispec = TC_getSpos(initial[j].name, strlen(initial[j].name));
      PetscCheck(ispec >= 0,PETSC_COMM_SELF,PETSC_ERR_USER,"Could not find species %s",initial[j].name);
      PetscCall(PetscPrintf(PETSC_COMM_SELF,"Species %d: %s %g\n",j,initial[j].name,initial[j].massfrac));
      x[i][1+ispec] = initial[j].massfrac;
    }
  }
  PetscCall(DMDAVecRestoreArrayDOF(dm,X,&x));
  PetscCall(DMDARestoreCoordinateArray(dm,&xc));
  PetscFunctionReturn(0);
}

/*
    Routines for displaying the solutions
*/
typedef struct {
  PetscInt cell;
  User     user;
} UserLGCtx;

static PetscErrorCode FormMoleFraction(UserLGCtx *ctx,Vec massf,Vec *molef)
{
  User              user = ctx->user;
  PetscReal         *M,tM=0;
  PetscInt          i,n = user->Nspec+1;
  PetscScalar       *mof;
  const PetscScalar **maf;

  PetscFunctionBegin;
  PetscCall(VecCreateSeq(PETSC_COMM_SELF,n,molef));
  PetscCall(PetscMalloc1(user->Nspec,&M));
  TC_getSmass(user->Nspec, M);
  PetscCall(DMDAVecGetArrayDOFRead(user->dm,massf,&maf));
  PetscCall(VecGetArray(*molef,&mof));
  mof[0] = maf[ctx->cell][0]; /* copy over temperature */
  for (i=1; i<n; i++) tM += maf[ctx->cell][i]/M[i-1];
  for (i=1; i<n; i++) {
    mof[i] = maf[ctx->cell][i]/(M[i-1]*tM);
  }
  PetscCall(DMDAVecRestoreArrayDOFRead(user->dm,massf,&maf));
  PetscCall(VecRestoreArray(*molef,&mof));
  PetscCall(PetscFree(M));
  PetscFunctionReturn(0);
}

static PetscErrorCode MonitorCellDestroy(UserLGCtx *uctx)
{
  PetscFunctionBegin;
  PetscCall(PetscFree(uctx));
  PetscFunctionReturn(0);
}

/*
   Use TSMonitorLG to monitor the reactions in a particular cell
*/
static PetscErrorCode MonitorCell(TS ts,User user,PetscInt cell)
{
  TSMonitorLGCtx ctx;
  char           **snames;
  UserLGCtx      *uctx;
  char           label[128];
  PetscReal      temp,*xc;
  PetscMPIInt    rank;

  PetscFunctionBegin;
  PetscCall(DMDAGetCoordinateArray(user->dm,&xc));
  temp = 1.0 + .05*PetscSinScalar(2.*PETSC_PI*xc[cell]);  /* Non-dimensionalized by user->Tini */
  PetscCall(DMDARestoreCoordinateArray(user->dm,&xc));
  PetscCallMPI(MPI_Comm_rank(PETSC_COMM_WORLD,&rank));
  PetscCall(PetscSNPrintf(label,sizeof(label),"Initial Temperature %g Cell %d Rank %d",(double)user->Tini*temp,(int)cell,rank));
  PetscCall(TSMonitorLGCtxCreate(PETSC_COMM_SELF,NULL,label,PETSC_DECIDE,PETSC_DECIDE,600,400,1,&ctx));
  PetscCall(DMDAGetFieldNames(user->dm,(const char * const **)&snames));
  PetscCall(TSMonitorLGCtxSetVariableNames(ctx,(const char * const *)snames));
  PetscCall(PetscNew(&uctx));
  uctx->cell = cell;
  uctx->user = user;
  PetscCall(TSMonitorLGCtxSetTransform(ctx,(PetscErrorCode (*)(void*,Vec,Vec*))FormMoleFraction,(PetscErrorCode (*)(void*))MonitorCellDestroy,uctx));
  PetscCall(TSMonitorSet(ts,TSMonitorLGSolution,ctx,(PetscErrorCode (*)(void**))TSMonitorLGCtxDestroy));
  PetscFunctionReturn(0);
}