update_coarse Subroutine

  subroutine update_coarse(mg, lvl)
    type(mg_t), intent(inout) :: mg
    !< Tree containing full grid
    integer, intent(in)       :: lvl
    !< Update coarse values at lvl-1
    integer                   :: i, id, nc, nc_c

    nc   = mg%box_size_lvl(lvl)
    nc_c = mg%box_size_lvl(lvl-1)

    ! Compute residual
    do i = 1, size(mg%lvls(lvl)%my_ids)
       id = mg%lvls(lvl)%my_ids(i)
       call residual_box(mg, id, nc)
    end do

    ! Restrict phi and the residual
    call mg_restrict_lvl(mg, mg_iphi, lvl)
    call mg_restrict_lvl(mg, mg_ires, lvl)

    call mg_fill_ghost_cells_lvl(mg, lvl-1, mg_iphi)

    ! Set rhs_c = laplacian(phi_c) + restrict(res) where it is refined, and
    ! store current coarse phi in old.
    do i = 1, size(mg%lvls(lvl-1)%my_parents)
       id = mg%lvls(lvl-1)%my_parents(i)

       ! Set rhs = L phi
       call mg%box_op(mg, id, nc_c, mg_irhs)

       ! Add the fine grid residual to rhs
       mg%boxes(id)%cc(1:nc_c, 1:nc_c, mg_irhs) = mg%boxes(id)%cc(1:nc_c,&
           1:nc_c, mg_irhs) + mg%boxes(id)%cc(1:nc_c, 1:nc_c, mg_ires)

       ! Story a copy of phi
       mg%boxes(id)%cc(:, :, mg_iold) = mg%boxes(id)%cc(:, :, mg_iphi)
    end do
  end subroutine update_coarse