/*
Laplacian in 2D. Modeled by the partial differential equation

   div  grad u = f,  0 < x,y < 1,

with forcing function

   f = e^{-(1 - x)^2/\nu} e^{-(1 - y)^2/\nu}

with pure Neumann boundary conditions

The functions are cell-centered

This uses multigrid to solve the linear system

       Contributed by Andrei Draganescu <aidraga@sandia.gov>

Note the nice multigrid convergence despite the fact it is only using
piecewise constant interpolation/restriction. This is because cell-centered multigrid
does not need the same rule:

    polynomial degree(interpolation) + polynomial degree(restriction) + 2 > degree of PDE

that vertex based multigrid needs.
*/

static char help[] = "Solves 2D inhomogeneous Laplacian using multigrid.\n\n";

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

extern PetscErrorCode ComputeMatrix(KSP, Mat, Mat, void *);
extern PetscErrorCode ComputeRHS(KSP, Vec, void *);

typedef enum {
  DIRICHLET,
  NEUMANN
} BCType;

typedef struct {
  PetscScalar nu;
  BCType      bcType;
} UserContext;

int main(int argc, char **argv)
{
  KSP         ksp;
  DM          da;
  UserContext user;
  const char *bcTypes[2] = {"dirichlet", "neumann"};
  PetscInt    bc;

  PetscFunctionBeginUser;
  PetscCall(PetscInitialize(&argc, &argv, NULL, help));
  PetscCall(KSPCreate(PETSC_COMM_WORLD, &ksp));
  PetscCall(DMDACreate2d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE, DMDA_STENCIL_STAR, 2, 2, PETSC_DECIDE, PETSC_DECIDE, 1, 1, 0, 0, &da));
  PetscCall(DMDASetInterpolationType(da, DMDA_Q0));
  PetscCall(DMSetFromOptions(da));
  PetscCall(DMSetUp(da));

  PetscCall(KSPSetDM(ksp, da));

  PetscOptionsBegin(PETSC_COMM_WORLD, "", "Options for the inhomogeneous Poisson equation", "DM");
  user.nu = 0.1;
  PetscCall(PetscOptionsScalar("-nu", "The width of the Gaussian source", "ex29.c", 0.1, &user.nu, NULL));
  bc = (PetscInt)NEUMANN;
  PetscCall(PetscOptionsEList("-bc_type", "Type of boundary condition", "ex29.c", bcTypes, 2, bcTypes[0], &bc, NULL));
  user.bcType = (BCType)bc;
  PetscOptionsEnd();

  PetscCall(KSPSetComputeRHS(ksp, ComputeRHS, &user));
  PetscCall(KSPSetComputeOperators(ksp, ComputeMatrix, &user));
  PetscCall(KSPSetFromOptions(ksp));
  PetscCall(KSPSetUp(ksp));
  PetscCall(KSPSolve(ksp, NULL, NULL));
  PetscCall(KSPDestroy(&ksp));
  PetscCall(DMDestroy(&da));
  PetscCall(PetscFinalize());
  return 0;
}

PetscErrorCode ComputeRHS(KSP ksp, Vec b, void *ctx)
{
  UserContext  *user = (UserContext *)ctx;
  PetscInt      i, j, mx, my, xm, ym, xs, ys;
  PetscScalar   Hx, Hy;
  PetscScalar **array;
  DM            da;

  PetscFunctionBeginUser;
  PetscCall(KSPGetDM(ksp, &da));
  PetscCall(DMDAGetInfo(da, 0, &mx, &my, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0));
  Hx = 1.0 / (PetscReal)mx;
  Hy = 1.0 / (PetscReal)my;
  PetscCall(DMDAGetCorners(da, &xs, &ys, 0, &xm, &ym, 0));
  PetscCall(DMDAVecGetArray(da, b, &array));
  for (j = ys; j < ys + ym; j++) {
    for (i = xs; i < xs + xm; i++) array[j][i] = PetscExpScalar(-(((PetscReal)i + 0.5) * Hx) * (((PetscReal)i + 0.5) * Hx) / user->nu) * PetscExpScalar(-(((PetscReal)j + 0.5) * Hy) * (((PetscReal)j + 0.5) * Hy) / user->nu) * Hx * Hy;
  }
  PetscCall(DMDAVecRestoreArray(da, b, &array));
  PetscCall(VecAssemblyBegin(b));
  PetscCall(VecAssemblyEnd(b));

  /* force right-hand side to be consistent for singular matrix */
  /* note this is really a hack, normally the model would provide you with a consistent right handside */
  if (user->bcType == NEUMANN) {
    MatNullSpace nullspace;

    PetscCall(MatNullSpaceCreate(PETSC_COMM_WORLD, PETSC_TRUE, 0, 0, &nullspace));
    PetscCall(MatNullSpaceRemove(nullspace, b));
    PetscCall(MatNullSpaceDestroy(&nullspace));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode ComputeMatrix(KSP ksp, Mat J, Mat jac, void *ctx)
{
  UserContext *user = (UserContext *)ctx;
  PetscInt     i, j, mx, my, xm, ym, xs, ys, num, numi, numj;
  PetscScalar  v[5], Hx, Hy, HydHx, HxdHy;
  MatStencil   row, col[5];
  DM           da;

  PetscFunctionBeginUser;
  PetscCall(KSPGetDM(ksp, &da));
  PetscCall(DMDAGetInfo(da, 0, &mx, &my, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0));
  Hx    = 1.0 / (PetscReal)mx;
  Hy    = 1.0 / (PetscReal)my;
  HxdHy = Hx / Hy;
  HydHx = Hy / Hx;
  PetscCall(DMDAGetCorners(da, &xs, &ys, 0, &xm, &ym, 0));
  for (j = ys; j < ys + ym; j++) {
    for (i = xs; i < xs + xm; i++) {
      row.i = i;
      row.j = j;
      if (i == 0 || j == 0 || i == mx - 1 || j == my - 1) {
        if (user->bcType == DIRICHLET) {
          v[0] = 2.0 * (HxdHy + HydHx);
          PetscCall(MatSetValuesStencil(jac, 1, &row, 1, &row, v, INSERT_VALUES));
          SETERRQ(PETSC_COMM_WORLD, PETSC_ERR_SUP, "Dirichlet boundary conditions not supported !");
        } else if (user->bcType == NEUMANN) {
          num  = 0;
          numi = 0;
          numj = 0;
          if (j != 0) {
            v[num]     = -HxdHy;
            col[num].i = i;
            col[num].j = j - 1;
            num++;
            numj++;
          }
          if (i != 0) {
            v[num]     = -HydHx;
            col[num].i = i - 1;
            col[num].j = j;
            num++;
            numi++;
          }
          if (i != mx - 1) {
            v[num]     = -HydHx;
            col[num].i = i + 1;
            col[num].j = j;
            num++;
            numi++;
          }
          if (j != my - 1) {
            v[num]     = -HxdHy;
            col[num].i = i;
            col[num].j = j + 1;
            num++;
            numj++;
          }
          v[num]     = (PetscReal)numj * HxdHy + (PetscReal)numi * HydHx;
          col[num].i = i;
          col[num].j = j;
          num++;
          PetscCall(MatSetValuesStencil(jac, 1, &row, num, col, v, INSERT_VALUES));
        }
      } else {
        v[0]     = -HxdHy;
        col[0].i = i;
        col[0].j = j - 1;
        v[1]     = -HydHx;
        col[1].i = i - 1;
        col[1].j = j;
        v[2]     = 2.0 * (HxdHy + HydHx);
        col[2].i = i;
        col[2].j = j;
        v[3]     = -HydHx;
        col[3].i = i + 1;
        col[3].j = j;
        v[4]     = -HxdHy;
        col[4].i = i;
        col[4].j = j + 1;
        PetscCall(MatSetValuesStencil(jac, 1, &row, 5, col, v, INSERT_VALUES));
      }
    }
  }
  PetscCall(MatAssemblyBegin(jac, MAT_FINAL_ASSEMBLY));
  PetscCall(MatAssemblyEnd(jac, MAT_FINAL_ASSEMBLY));
  if (user->bcType == NEUMANN) {
    MatNullSpace nullspace;

    PetscCall(MatNullSpaceCreate(PETSC_COMM_WORLD, PETSC_TRUE, 0, 0, &nullspace));
    PetscCall(MatSetNullSpace(J, nullspace));
    PetscCall(MatNullSpaceDestroy(&nullspace));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*TEST

   test:
     suffix: 2
     requires: !single
     args: -pc_type mg -pc_mg_levels 5 -ksp_monitor_true_residual -ksp_rtol 1.e-10 -ksp_type cg -mg_levels_pc_type sor -mg_levels_ksp_type richardson -mg_levels_ksp_max_it 2 -mg_coarse_pc_type svd -da_refine 5

   test:
     suffix: 3
     requires: !single
     args: -pc_type mg -pc_mg_levels 2 -ksp_monitor_true_residual -ksp_rtol 1.e-10 -ksp_type cg -mg_levels_pc_type sor -mg_levels_ksp_type richardson -mg_levels_ksp_max_it 2 -mg_coarse_pc_type svd -da_refine 5

   test:
     suffix: 4
     requires: !single
     args: -pc_type mg -pc_mg_levels 2 -ksp_monitor_true_residual -ksp_rtol 1.e-10 -ksp_type cg -mg_levels_pc_type sor -mg_levels_ksp_type richardson -mg_levels_ksp_max_it 2 -mg_coarse_pc_type svd -da_refine 4

TEST*/
