#include <petscdmplex.h>
#include <petscsnes.h>
#include <petscds.h>
#include <petscviewerhdf5.h>

typedef struct {
  PetscInt      debug;             /* The debugging level */
  PetscBool     jacobianMF;        /* Whether to calculate the Jacobian action on the fly */
  PetscLogEvent createMeshEvent;
  PetscBool     showInitial, showSolution, restart, check;
  /* Domain and mesh definition */
  PetscInt      dim;               /* The topological mesh dimension */
  char          filename[2048];    /* The optional ExodusII file */
  PetscBool     interpolate;       /* Generate intermediate mesh elements */
  PetscReal     refinementLimit;   /* The largest allowable cell volume */
  PetscBool     viewHierarchy;     /* Whether to view the hierarchy */
  /* Problem definition */
  PetscFE       fe;
  PetscErrorCode (**exactFuncs)(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *u, void *ctx);
  /* Solver */
  PC            pcmg;              /* This is needed for error monitoring */
} AppCtx;

PetscErrorCode zero(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *u, void *ctx)
{
  u[0] = 0.0;
  return 0;
}

/*
  In 2D for Dirichlet conditions, we use exact solution:

  u = x^2 + y^2
  f = 4

  so that

  -\Delta u + f = -4 + 4 = 0

*/
PetscErrorCode quadratic_u_2d(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *u, void *ctx)
{
  *u = x[0]*x[0] + x[1]*x[1];
  return 0;
}

void f0_u(PetscInt dim, PetscInt Nf, PetscInt NfAux,
          const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
          const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
          PetscReal t, const PetscReal x[], PetscScalar f0[])
{
  f0[0] = 4.0;
}

void f0_bd_u(PetscInt dim, PetscInt Nf, PetscInt NfAux,
             const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
             const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
             PetscReal t, const PetscReal x[], const PetscReal n[], PetscScalar f0[])
{
  PetscInt d;
  for (d = 0, f0[0] = 0.0; d < dim; ++d) f0[0] += -n[d]*2.0*x[d];
}

void f0_bd_zero(PetscInt dim, PetscInt Nf, PetscInt NfAux,
                const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
                const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
                PetscReal t, const PetscReal x[], const PetscReal n[], PetscScalar f0[])
{
  f0[0] = 0.0;
}

void f1_bd_zero(PetscInt dim, PetscInt Nf, PetscInt NfAux,
                const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
                const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
                PetscReal t, const PetscReal x[], const PetscReal n[], PetscScalar f1[])
{
  PetscInt comp;
  for (comp = 0; comp < dim; ++comp) f1[comp] = 0.0;
}

/* gradU[comp*dim+d] = {u_x, u_y} or {u_x, u_y, u_z} */
void f1_u(PetscInt dim, PetscInt Nf, PetscInt NfAux,
          const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
          const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
          PetscReal t, const PetscReal x[], PetscScalar f1[])
{
  PetscInt d;
  for (d = 0; d < dim; ++d) f1[d] = u_x[d];
}

/* < \nabla v, \nabla u + {\nabla u}^T >
   This just gives \nabla u, give the perdiagonal for the transpose */
void g3_uu(PetscInt dim, PetscInt Nf, PetscInt NfAux,
           const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
           const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
           PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscScalar g3[])
{
  PetscInt d;
  for (d = 0; d < dim; ++d) g3[d*dim+d] = 1.0;
}

/*
  In 2D for Dirichlet conditions with a variable coefficient, we use exact solution:

  u  = x^2 + y^2
  f  = 6 (x + y)
  nu = (x + y)

  so that

  -\div \nu \grad u + f = -6 (x + y) + 6 (x + y) = 0
*/
PetscErrorCode nu_2d(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *u, void *ctx)
{
  *u = x[0] + x[1];
  return 0;
}

void f0_analytic_u(PetscInt dim, PetscInt Nf, PetscInt NfAux,
                   const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
                   const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
                   PetscReal t, const PetscReal x[], PetscScalar f0[])
{
  f0[0] = 6.0*(x[0] + x[1]);
}

/* gradU[comp*dim+d] = {u_x, u_y} or {u_x, u_y, u_z} */
void f1_analytic_u(PetscInt dim, PetscInt Nf, PetscInt NfAux,
                   const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
                   const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
                   PetscReal t, const PetscReal x[], PetscScalar f1[])
{
  PetscInt d;
  for (d = 0; d < dim; ++d) f1[d] = (x[0] + x[1])*u_x[d];
}

void f1_field_u(PetscInt dim, PetscInt Nf, PetscInt NfAux,
                const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
                const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
                PetscReal t, const PetscReal x[], PetscScalar f1[])
{
  PetscInt d;
  for (d = 0; d < dim; ++d) f1[d] = a[0]*u_x[d];
}

/* < \nabla v, \nabla u + {\nabla u}^T >
   This just gives \nabla u, give the perdiagonal for the transpose */
void g3_analytic_uu(PetscInt dim, PetscInt Nf, PetscInt NfAux,
                    const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
                    const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
                    PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscScalar g3[])
{
  PetscInt d;
  for (d = 0; d < dim; ++d) g3[d*dim+d] = x[0] + x[1];
}

void g3_field_uu(PetscInt dim, PetscInt Nf, PetscInt NfAux,
                 const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
                 const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
                 PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscScalar g3[])
{
  PetscInt d;
  for (d = 0; d < dim; ++d) g3[d*dim+d] = a[0];
}

/*
  In 2D for Dirichlet conditions with a nonlinear coefficient (p-Laplacian with p = 4), we use exact solution:

  u  = x^2 + y^2
  f  = 16 (x^2 + y^2)
  nu = 1/2 |grad u|^2

  so that

  -\div \nu \grad u + f = -16 (x^2 + y^2) + 16 (x^2 + y^2) = 0
*/
void f0_analytic_nonlinear_u(PetscInt dim, PetscInt Nf, PetscInt NfAux,
                             const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
                             const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
                             PetscReal t, const PetscReal x[], PetscScalar f0[])
{
  f0[0] = 16.0*(x[0]*x[0] + x[1]*x[1]);
}

/* gradU[comp*dim+d] = {u_x, u_y} or {u_x, u_y, u_z} */
void f1_analytic_nonlinear_u(PetscInt dim, PetscInt Nf, PetscInt NfAux,
                             const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
                             const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
                             PetscReal t, const PetscReal x[], PetscScalar f1[])
{
  PetscScalar nu = 0.0;
  PetscInt    d;
  for (d = 0; d < dim; ++d) nu += u_x[d]*u_x[d];
  for (d = 0; d < dim; ++d) f1[d] = 0.5*nu*u_x[d];
}

/*
  grad (u + eps w) - grad u = eps grad w

  1/2 |grad (u + eps w)|^2 grad (u + eps w) - 1/2 |grad u|^2 grad u
  = 1/2 (|grad u|^2 + 2 eps <grad u,grad w>) (grad u + eps grad w) - 1/2 |grad u|^2 grad u
  = 1/2 (eps |grad u|^2 grad w + 2 eps <grad u,grad w> grad u)
  = eps (1/2 |grad u|^2 grad w + grad u <grad u,grad w>)
*/
void g3_analytic_nonlinear_uu(PetscInt dim, PetscInt Nf, PetscInt NfAux,
                              const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
                              const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
                              PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscScalar g3[])
{
  PetscScalar nu = 0.0;
  PetscInt    d, e;
  for (d = 0; d < dim; ++d) nu += u_x[d]*u_x[d];
  for (d = 0; d < dim; ++d) {
    g3[d*dim+d] = 0.5*nu;
    for (e = 0; e < dim; ++e) {
      g3[d*dim+e] += u_x[d]*u_x[e];
    }
  }
}

/*
  In 3D for Dirichlet conditions we use exact solution:

  u = 2/3 (x^2 + y^2 + z^2)
  f = 4

  so that

  -\Delta u + f = -2/3 * 6 + 4 = 0
*/
PetscErrorCode quadratic_u_3d(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *u, void *ctx)
{
  *u = 2.0*(x[0]*x[0] + x[1]*x[1] + x[2]*x[2])/3.0;
  return 0;
}

#undef __FUNCT__
#define __FUNCT__ "ProcessOptions"
PetscErrorCode ProcessOptions(MPI_Comm comm, AppCtx *options)
{
  PetscBool      flg;
  PetscErrorCode ierr;

  PetscFunctionBeginUser;
  options->debug               = 0;
  options->dim                 = 2;
  options->filename[0]         = '\0';
  options->interpolate         = PETSC_FALSE;
  options->refinementLimit     = 0.0;
  options->jacobianMF          = PETSC_FALSE;
  options->showInitial         = PETSC_FALSE;
  options->showSolution        = PETSC_FALSE;
  options->restart             = PETSC_FALSE;
  options->check               = PETSC_FALSE;
  options->viewHierarchy       = PETSC_FALSE;

  ierr = PetscOptionsBegin(comm, "", "Poisson Problem Options", "DMPLEX");CHKERRQ(ierr);
  ierr = PetscOptionsInt("-debug", "The debugging level", "ex12.c", options->debug, &options->debug, NULL);CHKERRQ(ierr);
  ierr = PetscOptionsInt("-dim", "The topological mesh dimension", "ex12.c", options->dim, &options->dim, NULL);CHKERRQ(ierr);
  ierr = PetscOptionsString("-f", "Exodus.II filename to read", "ex12.c", options->filename, options->filename, sizeof(options->filename), &flg);CHKERRQ(ierr);
#if !defined(PETSC_HAVE_EXODUSII)
  if (flg) SETERRQ(comm, PETSC_ERR_ARG_WRONG, "This option requires ExodusII support. Reconfigure using --download-exodusii");
#endif
  ierr = PetscOptionsBool("-interpolate", "Generate intermediate mesh elements", "ex12.c", options->interpolate, &options->interpolate, NULL);CHKERRQ(ierr);
  ierr = PetscOptionsReal("-refinement_limit", "The largest allowable cell volume", "ex12.c", options->refinementLimit, &options->refinementLimit, NULL);CHKERRQ(ierr);
  ierr = PetscOptionsBool("-jacobian_mf", "Calculate the action of the Jacobian on the fly", "ex12.c", options->jacobianMF, &options->jacobianMF, NULL);CHKERRQ(ierr);
  ierr = PetscOptionsBool("-show_initial", "Output the initial guess for verification", "ex12.c", options->showInitial, &options->showInitial, NULL);CHKERRQ(ierr);
  ierr = PetscOptionsBool("-show_solution", "Output the solution for verification", "ex12.c", options->showSolution, &options->showSolution, NULL);CHKERRQ(ierr);
  ierr = PetscOptionsBool("-restart", "Read in the mesh and solution from a file", "ex12.c", options->restart, &options->restart, NULL);CHKERRQ(ierr);
  ierr = PetscOptionsBool("-check", "Compare with default integration routines", "ex12.c", options->check, &options->check, NULL);CHKERRQ(ierr);
  ierr = PetscOptionsBool("-dm_view_hierarchy", "View the coarsened hierarchy", "ex12.c", options->viewHierarchy, &options->viewHierarchy, NULL);CHKERRQ(ierr);
  ierr = PetscOptionsEnd();
  ierr = PetscLogEventRegister("CreateMesh", DM_CLASSID, &options->createMeshEvent);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "CreateMesh"
PetscErrorCode CreateMesh(MPI_Comm comm, AppCtx *user, DM *dm)
{
  PetscInt       dim             = user->dim;
  const char    *filename        = user->filename;
  PetscBool      interpolate     = user->interpolate;
  PetscReal      refinementLimit = user->refinementLimit;
  size_t         len;
  PetscErrorCode ierr;

  PetscFunctionBeginUser;
  ierr = PetscLogEventBegin(user->createMeshEvent,0,0,0,0);CHKERRQ(ierr);
  ierr = PetscStrlen(filename, &len);CHKERRQ(ierr);
  if (!len) {
    ierr = DMPlexCreateBoxMesh(comm, dim, interpolate, dm);CHKERRQ(ierr);
    ierr = PetscObjectSetName((PetscObject) *dm, "Mesh");CHKERRQ(ierr);
  } else {
    ierr = DMPlexCreateFromFile(comm, filename, interpolate, dm);CHKERRQ(ierr);
    ierr = DMPlexSetRefinementUniform(*dm, PETSC_FALSE);CHKERRQ(ierr);
  }
  {
    DM refinedMesh     = NULL;
    DM distributedMesh = NULL;

    /* Refine mesh using a volume constraint */
    ierr = DMPlexSetRefinementLimit(*dm, refinementLimit);CHKERRQ(ierr);
    ierr = DMRefine(*dm, comm, &refinedMesh);CHKERRQ(ierr);
    if (refinedMesh) {
      const char *name;

      ierr = PetscObjectGetName((PetscObject) *dm,         &name);CHKERRQ(ierr);
      ierr = PetscObjectSetName((PetscObject) refinedMesh,  name);CHKERRQ(ierr);
      ierr = DMDestroy(dm);CHKERRQ(ierr);
      *dm  = refinedMesh;
    }
    /* Distribute mesh over processes */
    ierr = DMPlexDistribute(*dm, 0, NULL, &distributedMesh);CHKERRQ(ierr);
    if (distributedMesh) {
      ierr = DMDestroy(dm);CHKERRQ(ierr);
      *dm  = distributedMesh;
    }
  }
  ierr = DMSetFromOptions(*dm);CHKERRQ(ierr);
  /* Must have boundary marker for Dirichlet conditions */
  {
    DM cdm = *dm;

    while (cdm) {
      PetscBool hasBdLabel;

      ierr = DMHasLabel(cdm, "marker", &hasBdLabel);CHKERRQ(ierr);
      if (!hasBdLabel) {
        DMLabel label;

        ierr = DMCreateLabel(cdm, "marker");CHKERRQ(ierr);
        ierr = DMGetLabel(cdm, "marker", &label);CHKERRQ(ierr);
        ierr = DMPlexMarkBoundaryFaces(cdm, label);CHKERRQ(ierr);
        ierr = DMPlexLabelComplete(cdm, label);CHKERRQ(ierr);
      }
      ierr = DMPlexGetCoarseDM(cdm, &cdm);CHKERRQ(ierr);
    }
  }

  ierr = DMViewFromOptions(*dm, NULL, "-dm_view");CHKERRQ(ierr);
  if (user->viewHierarchy) {
    DM       cdm = *dm;
    PetscInt i   = 0;
    char     buf[256];

    while (cdm) {ierr = DMPlexGetCoarseDM(cdm, &cdm);CHKERRQ(ierr); ++i;}
    cdm = *dm;
    while (cdm) {
      PetscViewer viewer;

      --i;
      ierr = PetscSNPrintf(buf, 256, "ex12-%d.h5", i);CHKERRQ(ierr);
      ierr = PetscViewerHDF5Open(comm, buf, FILE_MODE_WRITE, &viewer);CHKERRQ(ierr);
      ierr = DMView(cdm, viewer);CHKERRQ(ierr);
      ierr = PetscViewerDestroy(&viewer);CHKERRQ(ierr);
      ierr = DMPlexGetCoarseDM(cdm, &cdm);CHKERRQ(ierr);
    }
  }
  ierr = PetscLogEventEnd(user->createMeshEvent,0,0,0,0);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "SetupProblem"
PetscErrorCode SetupProblem(DM dm, AppCtx *user)
{
  PetscDS        prob;
  PetscErrorCode ierr;

  PetscFunctionBeginUser;
  ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
  ierr = PetscDSSetResidual(prob, 0, f0_u, f1_u);CHKERRQ(ierr);
  ierr = PetscDSSetJacobian(prob, 0, 0, NULL, NULL, NULL, g3_uu);CHKERRQ(ierr);
  switch (user->dim) {
  case 2:
    user->exactFuncs[0] = quadratic_u_2d;
    break;
  case 3:
    user->exactFuncs[0] = quadratic_u_3d;
    break;
  default:
    SETERRQ1(PETSC_COMM_WORLD, PETSC_ERR_ARG_OUTOFRANGE, "Invalid dimension %d", user->dim);
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "SetupDiscretization"
PetscErrorCode SetupDiscretization(DM dm, AppCtx *user)
{
  DM             cdm   = dm;
  const PetscInt dim   = user->dim;
  const PetscInt id    = 1;
  PetscDS        prob;
  PetscErrorCode ierr;

  PetscFunctionBeginUser;
  /* Create finite element */
  ierr = PetscFECreateDefault(dm, dim, 1, PETSC_TRUE, NULL, -1, &user->fe);CHKERRQ(ierr);
  ierr = PetscObjectSetName((PetscObject) user->fe, "potential");CHKERRQ(ierr);
  /* Set discretization and boundary conditions for each mesh */
  while (cdm) {
    ierr = DMGetDS(cdm, &prob);CHKERRQ(ierr);
    ierr = PetscDSSetDiscretization(prob, 0, (PetscObject) user->fe);CHKERRQ(ierr);
    ierr = SetupProblem(cdm, user);CHKERRQ(ierr);
    ierr = DMPlexAddBoundary(cdm, PETSC_TRUE, "wall", "marker", 0, 0, NULL, (void (*)()) user->exactFuncs[0], 1, &id, user);CHKERRQ(ierr);
    ierr = DMPlexGetCoarseDM(cdm, &cdm);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}

void mass_kernel(PetscInt dim, PetscInt Nf, PetscInt NfAux,
           const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
           const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
           PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscScalar g0[])
{
  PetscInt d, e;
  for (d = 0, e = 0; d < dim; d++, e+=dim+1) {
    g0[e] = 1.;
  }
}

#undef __FUNCT__
#define __FUNCT__ "main"
int main(int argc, char **argv)
{
  DM             dm;          /* Problem specification */
  SNES           snes;        /* nonlinear solver */
  Vec            u,r;         /* solution, residual vectors */
  Mat            A,J;         /* Jacobian matrix */
  AppCtx         user;        /* user-defined work context */
  PetscInt       its;         /* iterations for convergence */
  PetscReal      error = 0.0; /* L_2 error in the solution */
  PetscErrorCode ierr;

  ierr = PetscInitialize(&argc, &argv, NULL, NULL);CHKERRQ(ierr);
  ierr = ProcessOptions(PETSC_COMM_WORLD, &user);CHKERRQ(ierr);
  ierr = SNESCreate(PETSC_COMM_WORLD, &snes);CHKERRQ(ierr);
  ierr = CreateMesh(PETSC_COMM_WORLD, &user, &dm);CHKERRQ(ierr);
  ierr = SNESSetDM(snes, dm);CHKERRQ(ierr);
  ierr = DMSetApplicationContext(dm, &user);CHKERRQ(ierr);

  ierr = PetscMalloc(1 * sizeof(void (*)(const PetscReal[], PetscScalar *, void *)), &user.exactFuncs);CHKERRQ(ierr);
  ierr = SetupDiscretization(dm, &user);CHKERRQ(ierr);

  ierr = DMCreateGlobalVector(dm, &u);CHKERRQ(ierr);
  ierr = PetscObjectSetName((PetscObject) u, "potential");CHKERRQ(ierr);
  ierr = VecDuplicate(u, &r);CHKERRQ(ierr);

  ierr = DMSetMatType(dm,MATAIJ);CHKERRQ(ierr);
  ierr = DMCreateMatrix(dm, &J);CHKERRQ(ierr);
  A = J;

  Vec local;
  DMGetLocalVector(dm, &local);
  DMPlexSNESComputeJacobianFEM(dm,local,A,A,NULL);
  MatViewFromOptions(A, NULL, "-view_A");
  
  DM dm_mass;
  PetscDS ds_mass;
  Mat M;
  
  /* DMClone(dm, &dm_mass); */
  DMGetDS(dm, &ds_mass);
  PetscDSSetJacobian(ds_mass, 0, 0, mass_kernel, NULL, NULL, NULL);
  PetscDSSetDiscretization(ds_mass, 0, (PetscObject) user.fe);
  /* DMSetMatType(dm_mass, MATAIJ); */
  DMCreateMatrix(dm, &M);
  DMPlexSNESComputeJacobianFEM(dm, local, M, M, NULL);

  MatViewFromOptions(M, NULL, "-view_M");

  ierr = DMSNESSetFunctionLocal(dm,  (PetscErrorCode (*)(DM,Vec,Vec,void*)) DMPlexSNESComputeResidualFEM, &user);CHKERRQ(ierr);
  ierr = DMSNESSetJacobianLocal(dm,  (PetscErrorCode (*)(DM,Vec,Mat,Mat,void*)) DMPlexSNESComputeJacobianFEM, &user);CHKERRQ(ierr);
  ierr = SNESSetJacobian(snes, A, J, NULL, NULL);CHKERRQ(ierr);

  ierr = SNESSetFromOptions(snes);CHKERRQ(ierr);

  ierr = DMPlexProjectFunction(dm, 0.0, user.exactFuncs, NULL, INSERT_ALL_VALUES, u);CHKERRQ(ierr);
  PetscErrorCode (*initialGuess[1])(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar u[], void *ctx) = {zero};

  ierr = DMPlexProjectFunction(dm, 0.0, initialGuess, NULL, INSERT_VALUES, u);CHKERRQ(ierr);
  ierr = SNESSolve(snes, NULL, u);CHKERRQ(ierr);
  ierr = SNESGetIterationNumber(snes, &its);CHKERRQ(ierr);
  ierr = PetscPrintf(PETSC_COMM_WORLD, "Number of SNES iterations = %D\n", its);CHKERRQ(ierr);
  ierr = DMPlexComputeL2Diff(dm, 0.0, user.exactFuncs, NULL, u, &error);CHKERRQ(ierr);
  if (error < 1.0e-11) {ierr = PetscPrintf(PETSC_COMM_WORLD, "L_2 Error: < 1.0e-11\n");CHKERRQ(ierr);}
  else                 {ierr = PetscPrintf(PETSC_COMM_WORLD, "L_2 Error: %g\n", error);CHKERRQ(ierr);}    

  ierr = PetscFinalize();
  return 0;
}