static char help[] = "Poisson Problem with a split domain.\n\
We solve the Poisson problem in two halves of a domain.\n\
In one half, we include an additional field.\n\n\n";

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

typedef struct {
  PetscInt dummy;
} AppCtx;

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

static PetscErrorCode quad_p(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nc, PetscScalar *u, void *ctx)
{
  u[0] = 2.0;
  return 0;
}

static void f0_quad_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[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[])
{
  PetscInt d;
  for (d = 0; d < dim; ++d) f0[0] += 2.0;
}

static void f0_quad_p(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[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[])
{
  f0[0] = u[uOff[1]] - 2.0;
}

static 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[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f1[])
{
  PetscInt d;
  for (d = 0; d < dim; ++d) f1[d] = u_x[d];
}

static 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[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g3[])
{
  PetscInt d;
  for (d = 0; d < dim; ++d) g3[d*dim+d] = 1.0;
}

static void g0_pp(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[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g0[])
{
  g0[0] = 1.0;
}

static PetscErrorCode DivideDomain(DM dm, AppCtx *user)
{
  DMLabel        top, bottom;
  PetscReal      low[3], high[3], midy;
  PetscInt       cStart, cEnd, c;
  PetscErrorCode ierr;

  PetscFunctionBeginUser;
  ierr = DMCreateLabel(dm, "top");CHKERRQ(ierr);
  ierr = DMCreateLabel(dm, "bottom");CHKERRQ(ierr);
  ierr = DMGetLabel(dm, "top", &top);CHKERRQ(ierr);
  ierr = DMGetLabel(dm, "bottom", &bottom);CHKERRQ(ierr);
  ierr = DMGetBoundingBox(dm, low, high);CHKERRQ(ierr);
  midy = 0.5*(high[1] - low[1]);
  ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
  for (c = cStart; c < cEnd; ++c) {
    PetscReal centroid[3];

    ierr = DMPlexComputeCellGeometryFVM(dm, c, NULL, centroid, NULL);CHKERRQ(ierr);
    if (centroid[1] > midy) {ierr = DMLabelSetValue(top, c, 1);CHKERRQ(ierr);}
    else                    {ierr = DMLabelSetValue(bottom, c, 1);CHKERRQ(ierr);}
  }
  ierr = DMPlexLabelComplete(dm, top);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

static PetscErrorCode CreateMesh(MPI_Comm comm, AppCtx *user, DM *dm)
{
  PetscErrorCode ierr;

  PetscFunctionBeginUser;
  ierr = DMCreate(comm, dm);CHKERRQ(ierr);
  ierr = DMSetType(*dm, DMPLEX);CHKERRQ(ierr);
  ierr = DMSetFromOptions(*dm);CHKERRQ(ierr);
  ierr = DivideDomain(*dm, user);CHKERRQ(ierr);
  ierr = DMSetApplicationContext(*dm, user);CHKERRQ(ierr);
  ierr = DMViewFromOptions(*dm, NULL, "-dm_view");CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

static PetscErrorCode SetupPrimalProblem(DM dm, AppCtx *user)
{
  PetscDS        ds;
  PetscWeakForm  wf;
  DMLabel        label;
  const PetscInt id = 1;
  PetscErrorCode ierr;

  PetscFunctionBeginUser;
  ierr = DMGetRegionNumDS(dm, 0, &label, NULL, &ds);CHKERRQ(ierr);
  ierr = PetscDSGetWeakForm(ds, &wf);CHKERRQ(ierr);
  ierr = PetscWeakFormSetIndexResidual(wf, label, 1, 0, 0, 0, f0_quad_u, 0, f1_u);CHKERRQ(ierr);
  ierr = PetscWeakFormSetIndexJacobian(wf, label, 1, 0, 0, 0, 0, NULL, 0, NULL, 0, NULL, 0, g3_uu);CHKERRQ(ierr);
  ierr = PetscDSSetExactSolution(ds, 0, quad_u, user);CHKERRQ(ierr);
  ierr = DMGetRegionNumDS(dm, 1, &label, NULL, &ds);CHKERRQ(ierr);
  ierr = PetscDSGetWeakForm(ds, &wf);CHKERRQ(ierr);
  ierr = PetscWeakFormSetIndexResidual(wf, label, 1, 0, 0, 0, f0_quad_u, 0, f1_u);CHKERRQ(ierr);
  ierr = PetscWeakFormSetIndexJacobian(wf, label, 1, 0, 0, 0, 0, NULL, 0, NULL, 0, NULL, 0, g3_uu);CHKERRQ(ierr);
  ierr = PetscWeakFormSetIndexResidual(wf, label, 1, 1, 0, 0, f0_quad_p, 0, NULL);CHKERRQ(ierr);
  ierr = PetscWeakFormSetIndexJacobian(wf, label, 1, 1, 1, 0, 0, g0_pp, 0, NULL, 0, NULL, 0, NULL);CHKERRQ(ierr);
  ierr = PetscDSSetExactSolution(ds, 0, quad_u, user);CHKERRQ(ierr);
  ierr = PetscDSSetExactSolution(ds, 1, quad_p, user);CHKERRQ(ierr);
  ierr = DMGetLabel(dm, "marker", &label);CHKERRQ(ierr);
  ierr = DMAddBoundary(dm, DM_BC_ESSENTIAL, "wall", label, 1, &id, 0, 0, NULL, (void (*)(void)) quad_u, NULL, user, NULL);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

static PetscErrorCode SetupDiscretization(DM dm, const char name[], PetscErrorCode (*setup)(DM, AppCtx *), AppCtx *user)
{
  DM              cdm = dm;
  DMLabel         top;
  PetscFE         fe, feTop;
  PetscQuadrature q;
  PetscInt        dim;
  PetscBool       simplex;
  const char     *nameTop = "pressure";
  char            prefix[PETSC_MAX_PATH_LEN];
  PetscErrorCode  ierr;

  PetscFunctionBeginUser;
  ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
  ierr = DMPlexIsSimplex(dm, &simplex);CHKERRQ(ierr);
  ierr = PetscSNPrintf(prefix, PETSC_MAX_PATH_LEN, "%s_", name);CHKERRQ(ierr);
  ierr = PetscFECreateDefault(PetscObjectComm((PetscObject) dm), dim, 1, simplex, name ? prefix : NULL, -1, &fe);CHKERRQ(ierr);
  ierr = PetscObjectSetName((PetscObject) fe, name);CHKERRQ(ierr);
  ierr = DMSetField(dm, 0, NULL, (PetscObject) fe);CHKERRQ(ierr);
  ierr = PetscFEGetQuadrature(fe, &q);CHKERRQ(ierr);
  ierr = PetscFEDestroy(&fe);CHKERRQ(ierr);
  ierr = DMGetLabel(dm, "top", &top);CHKERRQ(ierr);
  ierr = PetscSNPrintf(prefix, PETSC_MAX_PATH_LEN, "%s_top_", nameTop);CHKERRQ(ierr);
  ierr = PetscFECreateDefault(PetscObjectComm((PetscObject) dm), dim, 1, simplex, name ? prefix : NULL, -1, &feTop);CHKERRQ(ierr);
  ierr = PetscObjectSetName((PetscObject) feTop, nameTop);CHKERRQ(ierr);
  ierr = PetscFESetQuadrature(feTop, q);CHKERRQ(ierr);
  ierr = DMSetField(dm, 1, top, (PetscObject) feTop);CHKERRQ(ierr);
  ierr = PetscFEDestroy(&feTop);CHKERRQ(ierr);
  ierr = DMCreateDS(dm);CHKERRQ(ierr);
  ierr = (*setup)(dm, user);CHKERRQ(ierr);
  while (cdm) {
    ierr = DMCopyDisc(dm,cdm);CHKERRQ(ierr);
    ierr = DMGetCoarseDM(cdm, &cdm);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}

int main(int argc, char **argv)
{
  DM             dm;   /* Problem specification */
  SNES           snes; /* Nonlinear solver */
  Vec            u;    /* Solutions */
  AppCtx         user; /* User-defined work context */
  PetscErrorCode ierr;

  ierr = PetscInitialize(&argc, &argv, NULL,help);if (ierr) return ierr;
  /* Primal system */
  ierr = SNESCreate(PETSC_COMM_WORLD, &snes);CHKERRQ(ierr);
  ierr = CreateMesh(PETSC_COMM_WORLD, &user, &dm);CHKERRQ(ierr);
  ierr = SNESSetDM(snes, dm);CHKERRQ(ierr);
  ierr = SetupDiscretization(dm, "potential", SetupPrimalProblem, &user);CHKERRQ(ierr);
  ierr = DMCreateGlobalVector(dm, &u);CHKERRQ(ierr);
  ierr = VecSet(u, 0.0);CHKERRQ(ierr);
  ierr = PetscObjectSetName((PetscObject) u, "solution");CHKERRQ(ierr);
  ierr = DMPlexSetSNESLocalFEM(dm, &user, &user, &user);CHKERRQ(ierr);
  ierr = SNESSetFromOptions(snes);CHKERRQ(ierr);
  ierr = DMSNESCheckFromOptions(snes, u);CHKERRQ(ierr);
  ierr = SNESSolve(snes, NULL, u);CHKERRQ(ierr);
  ierr = SNESGetSolution(snes, &u);CHKERRQ(ierr);
  ierr = VecViewFromOptions(u, NULL, "-sol_view");CHKERRQ(ierr);
  /* Cleanup */
  ierr = VecDestroy(&u);CHKERRQ(ierr);
  ierr = SNESDestroy(&snes);CHKERRQ(ierr);
  ierr = DMDestroy(&dm);CHKERRQ(ierr);
  ierr = PetscFinalize();
  return ierr;
}

/*TEST

  test:
    suffix: 2d_p1_0
    requires: triangle
    args: -potential_petscspace_degree 2 -pressure_top_petscspace_degree 0 -dm_refine 0 -dmsnes_check

  test:
    suffix: 2d_p1_1
    requires: triangle
    args: -potential_petscspace_degree 1 -pressure_top_petscspace_degree 0 -dm_refine 0 -convest_num_refine 3 -snes_convergence_estimate

TEST*/