Ejemplo n.º 1
0
/*
   Sets up a monitor that will display He as a function of space and cluster size for each time step
*/
PetscErrorCode MyMonitorSetUp(TS ts)
{
  DM             da;
  PetscErrorCode ierr;
  PetscInt       xi,xs,xm,*idx,M,xj,cnt = 0,dof = 3*N + N*N;
  const PetscInt *lx;
  Vec            C;
  MyMonitorCtx   *ctx;
  PetscBool      flg;
  IS             is;
  char           ycoor[32];
  PetscReal      valuebounds[4]  = {0, 1.2, 0, 1.2};

  PetscFunctionBeginUser;
  ierr = PetscOptionsHasName(PETSC_NULL,"-mymonitor",&flg);CHKERRQ(ierr);
  if (!flg) PetscFunctionReturn(0);

  ierr = TSGetDM(ts,&da);CHKERRQ(ierr);
  ierr = PetscNew(MyMonitorCtx,&ctx);CHKERRQ(ierr);
  ierr = PetscViewerDrawOpen(((PetscObject)da)->comm,PETSC_NULL,"",PETSC_DECIDE,PETSC_DECIDE,600,400,&ctx->viewer);CHKERRQ(ierr);

  ierr = DMDAGetCorners(da,&xs,PETSC_NULL,PETSC_NULL,&xm,PETSC_NULL,PETSC_NULL);CHKERRQ(ierr);
  ierr = DMDAGetInfo(da,PETSC_IGNORE,&M,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);CHKERRQ(ierr);
  ierr = DMDAGetOwnershipRanges(da,&lx,PETSC_NULL,PETSC_NULL);CHKERRQ(ierr);
  ierr = DMDACreate2d(((PetscObject)da)->comm,DMDA_BOUNDARY_NONE,DMDA_BOUNDARY_NONE,DMDA_STENCIL_STAR,M,N,PETSC_DETERMINE,1,2,1,lx,PETSC_NULL,&ctx->da);CHKERRQ(ierr);
  ierr = DMDASetFieldName(ctx->da,0,"He");CHKERRQ(ierr);
  ierr = DMDASetFieldName(ctx->da,1,"V");CHKERRQ(ierr);
  ierr = DMDASetCoordinateName(ctx->da,0,"X coordinate direction");CHKERRQ(ierr);
  ierr = PetscSNPrintf(ycoor,32,"%D ... Cluster size ... 1",N);CHKERRQ(ierr);
  ierr = DMDASetCoordinateName(ctx->da,1,ycoor);CHKERRQ(ierr);

  ierr = DMCreateGlobalVector(ctx->da,&ctx->He);CHKERRQ(ierr);
  ierr = PetscMalloc(2*N*xm*sizeof(PetscInt),&idx);CHKERRQ(ierr);
  cnt  = 0;
  for (xj=0; xj<N; xj++) {
    for (xi=xs; xi<xs+xm; xi++) {
      idx[cnt++] = dof*xi + xj;
      idx[cnt++] = dof*xi + xj + N;
    }
  }
  ierr = ISCreateGeneral(((PetscObject)ts)->comm,2*N*xm,idx,PETSC_OWN_POINTER,&is);CHKERRQ(ierr);
  ierr = TSGetSolution(ts,&C);CHKERRQ(ierr);
  ierr = VecScatterCreate(C,is,ctx->He,PETSC_NULL,&ctx->scatter);CHKERRQ(ierr);
  ierr = ISDestroy(&is);CHKERRQ(ierr);

  /* sets the bounds on the contour plot values so the colors mean the same thing for different timesteps */
  ierr = PetscViewerDrawSetBounds(ctx->viewer,2,valuebounds);CHKERRQ(ierr);

  ierr = TSMonitorSet(ts,MyMonitorMonitor,ctx,MyMonitorDestroy);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}
Ejemplo n.º 2
0
PetscErrorCode PetscViewerSetFromOptions_Draw(PetscOptionItems *PetscOptionsObject,PetscViewer v)
{
  PetscErrorCode ierr;
  PetscReal      bounds[16];
  PetscInt       nbounds = 16;
  PetscBool      flg;

  PetscFunctionBegin;
  ierr = PetscOptionsHead(PetscOptionsObject,"Draw PetscViewer Options");CHKERRQ(ierr);
  ierr = PetscOptionsRealArray("-draw_bounds","Bounds to put on plots axis","PetscViewerDrawSetBounds",bounds,&nbounds,&flg);CHKERRQ(ierr);
  if (flg) {
    ierr = PetscViewerDrawSetBounds(v,nbounds/2,bounds);CHKERRQ(ierr);
  }
  ierr = PetscOptionsTail();CHKERRQ(ierr);
  PetscFunctionReturn(0);
}
Ejemplo n.º 3
0
void PETSC_STDCALL  petscviewerdrawsetbounds_(PetscViewer viewer,PetscInt *nbounds, PetscReal *bounds, int *__ierr ){
*__ierr = PetscViewerDrawSetBounds(
	(PetscViewer)PetscToPointer((viewer) ),*nbounds,bounds);
}
Ejemplo n.º 4
0
Archivo: ex5.c Proyecto: ZJLi2013/petsc
int main(int argc,char **argv)
{
  PetscErrorCode ierr;
  int            time;           /* amount of loops */
  struct in      put;
  PetscScalar    rh;             /* relative humidity */
  PetscScalar    x;              /* memory varialbe for relative humidity calculation */
  PetscScalar    deep_grnd_temp; /* temperature of ground under top soil surface layer */
  PetscScalar    emma;           /* absorption-emission constant for air */
  PetscScalar    pressure1 = 101300; /* surface pressure */
  PetscScalar    mixratio;       /* mixing ratio */
  PetscScalar    airtemp;        /* temperature of air near boundary layer inversion */
  PetscScalar    dewtemp;        /* dew point temperature */
  PetscScalar    sfctemp;        /* temperature at surface */
  PetscScalar    pwat;           /* total column precipitable water */
  PetscScalar    cloudTemp;      /* temperature at base of cloud */
  AppCtx         user;           /*  user-defined work context */
  MonitorCtx     usermonitor;    /* user-defined monitor context */
  PetscMPIInt    rank,size;
  TS             ts;
  SNES           snes;
  DM             da;
  Vec            T,rhs;          /* solution vector */
  Mat            J;              /* Jacobian matrix */
  PetscReal      ftime,dt;
  PetscInt       steps,dof = 5;
  PetscBool      use_coloring  = PETSC_TRUE;
  MatFDColoring  matfdcoloring = 0;
  PetscBool      monitor_off = PETSC_FALSE;

  PetscInitialize(&argc,&argv,(char*)0,help);
  ierr = MPI_Comm_size(PETSC_COMM_WORLD,&size);CHKERRQ(ierr);
  ierr = MPI_Comm_rank(PETSC_COMM_WORLD,&rank);CHKERRQ(ierr);

  /* Inputs */
  readinput(&put);

  sfctemp   = put.Ts;
  dewtemp   = put.Td;
  cloudTemp = put.Tc;
  airtemp   = put.Ta;
  pwat      = put.pwt;

  if (!rank) PetscPrintf(PETSC_COMM_SELF,"Initial Temperature = %g\n",sfctemp); /* input surface temperature */

  deep_grnd_temp = sfctemp - 10;   /* set underlying ground layer temperature */
  emma           = emission(pwat); /* accounts for radiative effects of water vapor */

  /* Converts from Fahrenheit to Celsuis */
  sfctemp        = fahr_to_cel(sfctemp);
  airtemp        = fahr_to_cel(airtemp);
  dewtemp        = fahr_to_cel(dewtemp);
  cloudTemp      = fahr_to_cel(cloudTemp);
  deep_grnd_temp = fahr_to_cel(deep_grnd_temp);

  /* Converts from Celsius to Kelvin */
  sfctemp        += 273;
  airtemp        += 273;
  dewtemp        += 273;
  cloudTemp      += 273;
  deep_grnd_temp += 273;

  /* Calculates initial relative humidity */
  x        = calcmixingr(dewtemp,pressure1);
  mixratio = calcmixingr(sfctemp,pressure1);
  rh       = (x/mixratio)*100;

  if (!rank) printf("Initial RH = %.1f percent\n\n",rh);   /* prints initial relative humidity */

  time = 3600*put.time;                         /* sets amount of timesteps to run model */

  /* Configure PETSc TS solver */
  /*------------------------------------------*/

  /* Create grid */
  ierr = DMDACreate2d(PETSC_COMM_WORLD,DMDA_BOUNDARY_PERIODIC,DMDA_BOUNDARY_PERIODIC,DMDA_STENCIL_STAR,-20,-20,
                      PETSC_DECIDE,PETSC_DECIDE,dof,1,NULL,NULL,&da);CHKERRQ(ierr);
  ierr = DMDASetUniformCoordinates(da, 0.0, 1.0, 0.0, 1.0, 0.0, 1.0);CHKERRQ(ierr);

  /* Define output window for each variable of interest */
  ierr = DMDASetFieldName(da,0,"Ts");CHKERRQ(ierr);
  ierr = DMDASetFieldName(da,1,"Ta");CHKERRQ(ierr);
  ierr = DMDASetFieldName(da,2,"u");CHKERRQ(ierr);
  ierr = DMDASetFieldName(da,3,"v");CHKERRQ(ierr);
  ierr = DMDASetFieldName(da,4,"p");CHKERRQ(ierr);

  /* set values for appctx */
  user.da             = da;
  user.Ts             = sfctemp;
  user.fract          = put.fr;          /* fraction of sky covered by clouds */
  user.dewtemp        = dewtemp;         /* dew point temperature (mositure in air) */
  user.csoil          = 2000000;         /* heat constant for layer */
  user.dzlay          = 0.08;            /* thickness of top soil layer */
  user.emma           = emma;            /* emission parameter */
  user.wind           = put.wnd;         /* wind spped */
  user.pressure1      = pressure1;       /* sea level pressure */
  user.airtemp        = airtemp;         /* temperature of air near boundar layer inversion */
  user.Tc             = cloudTemp;       /* temperature at base of lowest cloud layer */
  user.init           = put.init;        /* user chosen initiation scenario */
  user.lat            = 70*0.0174532;    /* converts latitude degrees to latitude in radians */
  user.deep_grnd_temp = deep_grnd_temp;  /* temp in lowest ground layer */

  /* set values for MonitorCtx */
  usermonitor.drawcontours = PETSC_FALSE;
  ierr = PetscOptionsHasName(NULL,"-drawcontours",&usermonitor.drawcontours);CHKERRQ(ierr);
  if (usermonitor.drawcontours) {
    PetscReal bounds[] = {1000.0,-1000.,  -1000.,-1000.,  1000.,-1000.,  1000.,-1000.,  1000,-1000, 100700,100800};
    ierr = PetscViewerDrawOpen(PETSC_COMM_WORLD,0,0,0,0,300,300,&usermonitor.drawviewer);CHKERRQ(ierr);
    ierr = PetscViewerDrawSetBounds(usermonitor.drawviewer,dof,bounds);CHKERRQ(ierr);
  }
  usermonitor.interval = 1;
  ierr = PetscOptionsGetInt(NULL,"-monitor_interval",&usermonitor.interval,NULL);CHKERRQ(ierr);

  /*  - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Extract global vectors from DA;
   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  ierr = DMCreateGlobalVector(da,&T);CHKERRQ(ierr);
  ierr = VecDuplicate(T,&rhs);CHKERRQ(ierr); /* r: vector to put the computed right hand side */

  ierr = TSCreate(PETSC_COMM_WORLD,&ts);CHKERRQ(ierr);
  ierr = TSSetProblemType(ts,TS_NONLINEAR);CHKERRQ(ierr);
  ierr = TSSetType(ts,TSBEULER);CHKERRQ(ierr);
  ierr = TSSetRHSFunction(ts,rhs,RhsFunc,&user);CHKERRQ(ierr);

  /* Set Jacobian evaluation routine - use coloring to compute finite difference Jacobian efficiently */
  ierr = DMSetMatType(da,MATAIJ);CHKERRQ(ierr);
  ierr = DMCreateMatrix(da,&J);CHKERRQ(ierr);
  ierr = TSGetSNES(ts,&snes);CHKERRQ(ierr);
  if (use_coloring) {
    ISColoring iscoloring;
    ierr = DMCreateColoring(da,IS_COLORING_GLOBAL,&iscoloring);CHKERRQ(ierr);
    ierr = MatFDColoringCreate(J,iscoloring,&matfdcoloring);CHKERRQ(ierr);
    ierr = MatFDColoringSetFromOptions(matfdcoloring);CHKERRQ(ierr);
    ierr = MatFDColoringSetUp(J,iscoloring,matfdcoloring);CHKERRQ(ierr);
    ierr = ISColoringDestroy(&iscoloring);CHKERRQ(ierr);
    ierr = MatFDColoringSetFunction(matfdcoloring,(PetscErrorCode (*)(void))SNESTSFormFunction,ts);CHKERRQ(ierr);
    ierr = SNESSetJacobian(snes,J,J,SNESComputeJacobianDefaultColor,matfdcoloring);CHKERRQ(ierr);
  } else {
    ierr = SNESSetJacobian(snes,J,J,SNESComputeJacobianDefault,NULL);CHKERRQ(ierr);
  }

  /* Define what to print for ts_monitor option */
  ierr = PetscOptionsHasName(NULL,"-monitor_off",&monitor_off);CHKERRQ(ierr);
  if (!monitor_off) {
    ierr = TSMonitorSet(ts,Monitor,&usermonitor,NULL);CHKERRQ(ierr);
  }
  ierr  = FormInitialSolution(da,T,&user);CHKERRQ(ierr);
  dt    = TIMESTEP; /* initial time step */
  ftime = TIMESTEP*time;
  if (!rank) printf("time %d, ftime %g hour, TIMESTEP %g\n",time,ftime/3600,dt);

  ierr = TSSetInitialTimeStep(ts,0.0,dt);CHKERRQ(ierr);
  ierr = TSSetDuration(ts,time,ftime);CHKERRQ(ierr);
  ierr = TSSetSolution(ts,T);CHKERRQ(ierr);
  ierr = TSSetDM(ts,da);CHKERRQ(ierr);

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Set runtime options
   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  ierr = TSSetFromOptions(ts);CHKERRQ(ierr);

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Solve nonlinear system
     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  ierr = TSSolve(ts,T);CHKERRQ(ierr);
  ierr = TSGetSolveTime(ts,&ftime);CHKERRQ(ierr);
  ierr = TSGetTimeStepNumber(ts,&steps);CHKERRQ(ierr);
  if (!rank) PetscPrintf(PETSC_COMM_WORLD,"Solution T after %g hours %d steps\n",ftime/3600,steps);


  if (matfdcoloring) {ierr = MatFDColoringDestroy(&matfdcoloring);CHKERRQ(ierr);}
  if (usermonitor.drawcontours) {
    ierr = PetscViewerDestroy(&usermonitor.drawviewer);CHKERRQ(ierr);
  }
  ierr = MatDestroy(&J);CHKERRQ(ierr);
  ierr = VecDestroy(&T);CHKERRQ(ierr);
  ierr = VecDestroy(&rhs);CHKERRQ(ierr);
  ierr = TSDestroy(&ts);CHKERRQ(ierr);
  ierr = DMDestroy(&da);CHKERRQ(ierr);

  PetscFinalize();
  return 0;
}
Ejemplo n.º 5
0
/*
    This routine is not parallel
*/
PetscErrorCode  MyMonitor(TS ts,PetscInt step,PetscReal time,Vec U,void *ptr)
{
  UserCtx            *ctx = (UserCtx*)ptr;
  PetscDrawLG        lg;
  PetscErrorCode     ierr;
  PetscScalar        *u;
  PetscInt           Mx,i,xs,xm,cnt;
  PetscReal          x,y,hx,pause,sx,len,max,xx[2],yy[2];
  PetscDraw          draw;
  Vec                localU;
  DM                 da;
  int                colors[] = {PETSC_DRAW_YELLOW,PETSC_DRAW_RED,PETSC_DRAW_BLUE};
  const char*const   legend[] = {"-kappa (\\grad u,\\grad u)","(1 - u^2)^2"};
  PetscDrawAxis      axis;
  PetscDrawViewPorts *ports;
  PetscReal          vbounds[] = {-1.1,1.1};

  PetscFunctionBegin;
  ierr = PetscViewerDrawSetBounds(PETSC_VIEWER_DRAW_(PETSC_COMM_WORLD),1,vbounds);CHKERRQ(ierr);
  ierr = PetscViewerDrawResize(PETSC_VIEWER_DRAW_(PETSC_COMM_WORLD),1200,800);CHKERRQ(ierr);
  ierr = TSGetDM(ts,&da);CHKERRQ(ierr);
  ierr = DMGetLocalVector(da,&localU);CHKERRQ(ierr);
  ierr = DMDAGetInfo(da,PETSC_IGNORE,&Mx,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);CHKERRQ(ierr);
  ierr = DMDAGetCorners(da,&xs,NULL,NULL,&xm,NULL,NULL);CHKERRQ(ierr);
  hx   = 1.0/(PetscReal)Mx; sx = 1.0/(hx*hx);
  ierr = DMGlobalToLocalBegin(da,U,INSERT_VALUES,localU);CHKERRQ(ierr);
  ierr = DMGlobalToLocalEnd(da,U,INSERT_VALUES,localU);CHKERRQ(ierr);
  ierr = DMDAVecGetArrayRead(da,localU,&u);CHKERRQ(ierr);

  ierr = PetscViewerDrawGetDrawLG(PETSC_VIEWER_DRAW_(PETSC_COMM_WORLD),1,&lg);CHKERRQ(ierr);
  ierr = PetscDrawLGGetDraw(lg,&draw);CHKERRQ(ierr);
  ierr = PetscDrawCheckResizedWindow(draw);CHKERRQ(ierr);
  if (!ctx->ports) {
    ierr = PetscDrawViewPortsCreateRect(draw,1,3,&ctx->ports);CHKERRQ(ierr);
  }
  ports = ctx->ports;
  ierr  = PetscDrawLGGetAxis(lg,&axis);CHKERRQ(ierr);
  ierr  = PetscDrawLGReset(lg);CHKERRQ(ierr);

  xx[0] = 0.0; xx[1] = 1.0; cnt = 2;
  ierr  = PetscOptionsGetRealArray(NULL,NULL,"-zoom",xx,&cnt,NULL);CHKERRQ(ierr);
  xs    = xx[0]/hx; xm = (xx[1] - xx[0])/hx;

  /*
      Plot the  energies
  */
  ierr = PetscDrawLGSetDimension(lg,1 + (ctx->allencahn ? 1 : 0));CHKERRQ(ierr);
  ierr = PetscDrawLGSetColors(lg,colors+1);CHKERRQ(ierr);
  ierr = PetscDrawViewPortsSet(ports,2);CHKERRQ(ierr);
  x    = hx*xs;
  for (i=xs; i<xs+xm; i++) {
    xx[0] = xx[1] = x;
    yy[0] = PetscRealPart(.25*ctx->kappa*(u[i-1] - u[i+1])*(u[i-1] - u[i+1])*sx);
    if (ctx->allencahn) yy[1] = .25*PetscRealPart((1. - u[i]*u[i])*(1. - u[i]*u[i]));
    ierr = PetscDrawLGAddPoint(lg,xx,yy);CHKERRQ(ierr);
    x   += hx;
  }
  ierr = PetscDrawGetPause(draw,&pause);CHKERRQ(ierr);
  ierr = PetscDrawSetPause(draw,0.0);CHKERRQ(ierr);
  ierr = PetscDrawAxisSetLabels(axis,"Energy","","");CHKERRQ(ierr);
  ierr = PetscDrawLGSetLegend(lg,legend);CHKERRQ(ierr);
  ierr = PetscDrawLGDraw(lg);CHKERRQ(ierr);

  /*
      Plot the  forces
  */
  ierr = PetscDrawViewPortsSet(ports,1);CHKERRQ(ierr);
  ierr = PetscDrawLGReset(lg);CHKERRQ(ierr);
  x    = xs*hx;;
  max  = 0.;
  for (i=xs; i<xs+xm; i++) {
    xx[0] = xx[1] = x;
    yy[0] = PetscRealPart(ctx->kappa*(u[i-1] + u[i+1] - 2.0*u[i])*sx);
    max   = PetscMax(max,PetscAbs(yy[0]));
    if (ctx->allencahn) {
      yy[1] = PetscRealPart(u[i] - u[i]*u[i]*u[i]);
      max   = PetscMax(max,PetscAbs(yy[1]));
    }
    ierr = PetscDrawLGAddPoint(lg,xx,yy);CHKERRQ(ierr);
    x   += hx;
  }
  ierr = PetscDrawAxisSetLabels(axis,"Right hand side","","");CHKERRQ(ierr);
  ierr = PetscDrawLGSetLegend(lg,NULL);CHKERRQ(ierr);
  ierr = PetscDrawLGDraw(lg);CHKERRQ(ierr);

  /*
        Plot the solution
  */
  ierr = PetscDrawLGSetDimension(lg,1);CHKERRQ(ierr);
  ierr = PetscDrawViewPortsSet(ports,0);CHKERRQ(ierr);
  ierr = PetscDrawLGReset(lg);CHKERRQ(ierr);
  x    = hx*xs;
  ierr = PetscDrawLGSetLimits(lg,x,x+(xm-1)*hx,-1.1,1.1);CHKERRQ(ierr);
  ierr = PetscDrawLGSetColors(lg,colors);CHKERRQ(ierr);
  for (i=xs; i<xs+xm; i++) {
    xx[0] = x;
    yy[0] = PetscRealPart(u[i]);
    ierr  = PetscDrawLGAddPoint(lg,xx,yy);CHKERRQ(ierr);
    x    += hx;
  }
  ierr = PetscDrawAxisSetLabels(axis,"Solution","","");CHKERRQ(ierr);
  ierr = PetscDrawLGDraw(lg);CHKERRQ(ierr);

  /*
      Print the  forces as arrows on the solution
  */
  x   = hx*xs;
  cnt = xm/60;
  cnt = (!cnt) ? 1 : cnt;

  for (i=xs; i<xs+xm; i += cnt) {
    y    = PetscRealPart(u[i]);
    len  = .5*PetscRealPart(ctx->kappa*(u[i-1] + u[i+1] - 2.0*u[i])*sx)/max;
    ierr = PetscDrawArrow(draw,x,y,x,y+len,PETSC_DRAW_RED);CHKERRQ(ierr);
    if (ctx->allencahn) {
      len  = .5*PetscRealPart(u[i] - u[i]*u[i]*u[i])/max;
      ierr = PetscDrawArrow(draw,x,y,x,y+len,PETSC_DRAW_BLUE);CHKERRQ(ierr);
    }
    x += cnt*hx;
  }
  ierr = DMDAVecRestoreArrayRead(da,localU,&x);CHKERRQ(ierr);
  ierr = DMRestoreLocalVector(da,&localU);CHKERRQ(ierr);
  ierr = PetscDrawStringSetSize(draw,.2,.2);CHKERRQ(ierr);
  ierr = PetscDrawFlush(draw);CHKERRQ(ierr);
  ierr = PetscDrawSetPause(draw,pause);CHKERRQ(ierr);
  ierr = PetscDrawPause(draw);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}
Ejemplo n.º 6
0
int main(int argc,char **argv)
{
  TS             ts;                           /* nonlinear solver */
  Vec            x,r;                          /* solution, residual vectors */
  Mat            J;                            /* Jacobian matrix */
  PetscInt       steps,Mx,maxsteps = 10000000;
  PetscErrorCode ierr;
  DM             da;
  MatFDColoring  matfdcoloring;
  ISColoring     iscoloring;
  PetscReal      dt;
  PetscReal      vbounds[] = {-100000,100000,-1.1,1.1};
  PetscBool      wait;
  Vec            ul,uh;
  SNES           snes;
  UserCtx        ctx;

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Initialize program
     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  ierr = PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
  ctx.kappa       = 1.0;
  ierr            = PetscOptionsGetReal(NULL,"-kappa",&ctx.kappa,NULL);CHKERRQ(ierr);
  ctx.cahnhillard = PETSC_FALSE;
  ierr            = PetscOptionsGetBool(NULL,NULL,"-cahn-hillard",&ctx.cahnhillard,NULL);CHKERRQ(ierr);
  ierr            = PetscViewerDrawSetBounds(PETSC_VIEWER_DRAW_(PETSC_COMM_WORLD),2,vbounds);CHKERRQ(ierr);
  ierr            = PetscViewerDrawResize(PETSC_VIEWER_DRAW_(PETSC_COMM_WORLD),600,600);CHKERRQ(ierr);
  ctx.energy      = 1;
  /* ierr = PetscOptionsGetInt(NULL,NULL,"-energy",&ctx.energy,NULL);CHKERRQ(ierr); */
  ierr        = PetscOptionsGetInt(NULL,NULL,"-energy",&ctx.energy,NULL);CHKERRQ(ierr);
  ctx.tol     = 1.0e-8;
  ierr        = PetscOptionsGetReal(NULL,"-tol",&ctx.tol,NULL);CHKERRQ(ierr);
  ctx.theta   = .001;
  ctx.theta_c = 1.0;
  ierr        = PetscOptionsGetReal(NULL,"-theta",&ctx.theta,NULL);CHKERRQ(ierr);
  ierr        = PetscOptionsGetReal(NULL,"-theta_c",&ctx.theta_c,NULL);CHKERRQ(ierr);

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Create distributed array (DMDA) to manage parallel grid and vectors
  - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  ierr = DMDACreate1d(PETSC_COMM_WORLD, DM_BOUNDARY_PERIODIC, -10,2,2,NULL,&da);CHKERRQ(ierr);
  ierr = DMSetFromOptions(da);CHKERRQ(ierr);
  ierr = DMSetUp(da);CHKERRQ(ierr);
  ierr = DMDASetFieldName(da,0,"Biharmonic heat equation: w = -kappa*u_xx");CHKERRQ(ierr);
  ierr = DMDASetFieldName(da,1,"Biharmonic heat equation: u");CHKERRQ(ierr);
  ierr = DMDAGetInfo(da,0,&Mx,0,0,0,0,0,0,0,0,0,0,0);CHKERRQ(ierr);
  dt   = 1.0/(10.*ctx.kappa*Mx*Mx*Mx*Mx);

  /*  - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Extract global vectors from DMDA; then duplicate for remaining
     vectors that are the same types
   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  ierr = DMCreateGlobalVector(da,&x);CHKERRQ(ierr);
  ierr = VecDuplicate(x,&r);CHKERRQ(ierr);

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Create timestepping solver context
     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  ierr = TSCreate(PETSC_COMM_WORLD,&ts);CHKERRQ(ierr);
  ierr = TSSetDM(ts,da);CHKERRQ(ierr);
  ierr = TSSetProblemType(ts,TS_NONLINEAR);CHKERRQ(ierr);
  ierr = TSSetIFunction(ts,NULL,FormFunction,&ctx);CHKERRQ(ierr);
  ierr = TSSetDuration(ts,maxsteps,.02);CHKERRQ(ierr);
  ierr = TSSetExactFinalTime(ts,TS_EXACTFINALTIME_STEPOVER);CHKERRQ(ierr);

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Create matrix data structure; set Jacobian evaluation routine

<     Set Jacobian matrix data structure and default Jacobian evaluation
     routine. User can override with:
     -snes_mf : matrix-free Newton-Krylov method with no preconditioning
                (unless user explicitly sets preconditioner)
     -snes_mf_operator : form preconditioning matrix as set by the user,
                         but use matrix-free approx for Jacobian-vector
                         products within Newton-Krylov method

     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  ierr = TSGetSNES(ts,&snes);CHKERRQ(ierr);
  ierr = DMCreateColoring(da,IS_COLORING_GLOBAL,&iscoloring);CHKERRQ(ierr);
  ierr = DMSetMatType(da,MATAIJ);CHKERRQ(ierr);
  ierr = DMCreateMatrix(da,&J);CHKERRQ(ierr);
  ierr = MatFDColoringCreate(J,iscoloring,&matfdcoloring);CHKERRQ(ierr);
  ierr = ISColoringDestroy(&iscoloring);CHKERRQ(ierr);
  ierr = MatFDColoringSetFunction(matfdcoloring,(PetscErrorCode (*)(void))SNESTSFormFunction,ts);CHKERRQ(ierr);
  ierr = MatFDColoringSetFromOptions(matfdcoloring);CHKERRQ(ierr);
  ierr = MatFDColoringSetUp(J,iscoloring,matfdcoloring);CHKERRQ(ierr);
  ierr = SNESSetJacobian(snes,J,J,SNESComputeJacobianDefaultColor,matfdcoloring);CHKERRQ(ierr);

  {
    ierr = VecDuplicate(x,&ul);CHKERRQ(ierr);
    ierr = VecDuplicate(x,&uh);CHKERRQ(ierr);
    ierr = VecStrideSet(ul,0,PETSC_NINFINITY);CHKERRQ(ierr);
    ierr = VecStrideSet(ul,1,-1.0);CHKERRQ(ierr);
    ierr = VecStrideSet(uh,0,PETSC_INFINITY);CHKERRQ(ierr);
    ierr = VecStrideSet(uh,1,1.0);CHKERRQ(ierr);
    ierr = TSVISetVariableBounds(ts,ul,uh);CHKERRQ(ierr);
  }

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Customize nonlinear solver
   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  ierr = TSSetType(ts,TSBEULER);CHKERRQ(ierr);

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Set initial conditions
   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  ierr = FormInitialSolution(da,x,ctx.kappa);CHKERRQ(ierr);
  ierr = TSSetInitialTimeStep(ts,0.0,dt);CHKERRQ(ierr);
  ierr = TSSetSolution(ts,x);CHKERRQ(ierr);

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Set runtime options
   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  ierr = TSSetFromOptions(ts);CHKERRQ(ierr);

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Solve nonlinear system
     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  ierr = TSSolve(ts,x);CHKERRQ(ierr);
  wait = PETSC_FALSE;
  ierr = PetscOptionsGetBool(NULL,NULL,"-wait",&wait,NULL);CHKERRQ(ierr);
  if (wait) {
    ierr = PetscSleep(-1);CHKERRQ(ierr);
  }
  ierr = TSGetTimeStepNumber(ts,&steps);CHKERRQ(ierr);

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Free work space.  All PETSc objects should be destroyed when they
     are no longer needed.
   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  {
    ierr = VecDestroy(&ul);CHKERRQ(ierr);
    ierr = VecDestroy(&uh);CHKERRQ(ierr);
  }
  ierr = MatDestroy(&J);CHKERRQ(ierr);
  ierr = MatFDColoringDestroy(&matfdcoloring);CHKERRQ(ierr);
  ierr = VecDestroy(&x);CHKERRQ(ierr);
  ierr = VecDestroy(&r);CHKERRQ(ierr);
  ierr = TSDestroy(&ts);CHKERRQ(ierr);
  ierr = DMDestroy(&da);CHKERRQ(ierr);

  ierr = PetscFinalize();
  PetscFunctionReturn(0);
}