static const char help[] ="Minimum surface problem in 2D.\n\
Uses 2-dimensional distributed arrays.\n\
\n\
  Solves the linear systems via multilevel methods \n\
\n\n";

/*

    This example models the partial differential equation

         - Div((1 + ||GRAD T||^2)^(1/2) (GRAD T)) = 0.

    in the unit square, which is uniformly discretized in each of x and
    y in this simple encoding.  The degrees of freedom are vertex centered

    A finite difference approximation with the usual 5-point stencil
    is used to discretize the boundary value problem to obtain a
    nonlinear system of equations.

*/

#include <petscsnes.h>
#include <petscdm.h>
#include <petscdmda.h>

extern PetscErrorCode FormFunctionLocal(DMDALocalInfo*,PetscScalar**,PetscScalar**,void*);

int main(int argc,char **argv)
{
  SNES           snes;
  PetscInt       its,lits;
  PetscReal      litspit;
  DM             da;

  PetscCall(PetscInitialize(&argc,&argv,NULL,help));
  /*
      Set the DMDA (grid structure) for the grids.
  */
  PetscCall(DMDACreate2d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE,DMDA_STENCIL_STAR,5,5,PETSC_DECIDE,PETSC_DECIDE,1,1,0,0,&da));
  PetscCall(DMSetFromOptions(da));
  PetscCall(DMSetUp(da));
  PetscCall(DMDASNESSetFunctionLocal(da,INSERT_VALUES,(PetscErrorCode (*)(DMDALocalInfo*,void*,void*,void*))FormFunctionLocal,NULL));
  PetscCall(SNESCreate(PETSC_COMM_WORLD,&snes));
  PetscCall(SNESSetDM(snes,da));
  PetscCall(DMDestroy(&da));

  PetscCall(SNESSetFromOptions(snes));

  PetscCall(SNESSolve(snes,0,0));
  PetscCall(SNESGetIterationNumber(snes,&its));
  PetscCall(SNESGetLinearSolveIterations(snes,&lits));
  litspit = ((PetscReal)lits)/((PetscReal)its);
  PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Number of SNES iterations = %D\n",its));
  PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Number of Linear iterations = %D\n",lits));
  PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Average Linear its / SNES = %e\n",(double)litspit));

  PetscCall(SNESDestroy(&snes));
  PetscCall(PetscFinalize());
  return 0;
}

PetscErrorCode FormFunctionLocal(DMDALocalInfo *info,PetscScalar **t,PetscScalar **f,void *ptr)
{
  PetscInt    i,j;
  PetscScalar hx,hy;
  PetscScalar gradup,graddown,gradleft,gradright,gradx,grady;
  PetscScalar coeffup,coeffdown,coeffleft,coeffright;

  PetscFunctionBeginUser;
  hx = 1.0/(PetscReal)(info->mx-1);  hy    = 1.0/(PetscReal)(info->my-1);

  /* Evaluate function */
  for (j=info->ys; j<info->ys+info->ym; j++) {
    for (i=info->xs; i<info->xs+info->xm; i++) {

      if (i == 0 || i == info->mx-1 || j == 0 || j == info->my-1) {
        f[j][i] = t[j][i] - (1.0 - (2.0*hx*(PetscReal)i - 1.0)*(2.0*hx*(PetscReal)i - 1.0));
      } else {

        gradup    = (t[j+1][i] - t[j][i])/hy;
        graddown  = (t[j][i] - t[j-1][i])/hy;
        gradright = (t[j][i+1] - t[j][i])/hx;
        gradleft  = (t[j][i] - t[j][i-1])/hx;

        gradx = .5*(t[j][i+1] - t[j][i-1])/hx;
        grady = .5*(t[j+1][i] - t[j-1][i])/hy;

        coeffup   = 1.0/PetscSqrtScalar(1.0 + gradup*gradup + gradx*gradx);
        coeffdown = 1.0/PetscSqrtScalar(1.0 + graddown*graddown + gradx*gradx);

        coeffleft  = 1.0/PetscSqrtScalar(1.0 + gradleft*gradleft + grady*grady);
        coeffright = 1.0/PetscSqrtScalar(1.0 + gradright*gradright + grady*grady);

        f[j][i] = (coeffup*gradup - coeffdown*graddown)*hx + (coeffright*gradright - coeffleft*gradleft)*hy;
      }

    }
  }
  PetscFunctionReturn(0);
}

/*TEST

   test:
      args: -pc_type mg -da_refine 1 -ksp_type fgmres

   test:
      suffix: 2
      nsize: 2
      args: -pc_type mg -da_refine 1 -ksp_type fgmres

   test:
      suffix: 3
      nsize: 2
      args: -pc_type mg -da_refine 1 -ksp_type fgmres -snes_type newtontrdc -snes_trdc_use_cauchy false

   test:
      suffix: 4
      nsize: 2
      args: -pc_type mg -da_refine 1 -ksp_type fgmres -snes_type newtontrdc
      filter: sed -e "s/SNES iterations = 1[1-3]/SNES iterations = 13/g" |sed -e "s/Linear iterations = 2[8-9]/Linear iterations = 29/g" |sed -e "s/Linear iterations = 3[0-1]/Linear iterations = 29/g"

TEST*/