mesh.f90

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module mesh
  use num_types, only : rp, dp, i8
  use point, only : point_t
  use element, only : element_t
  use hex, only : hex_t, neko_hex_neds, neko_hex_nfcs, &
       neko_hex_npts
  use quad, only : quad_t, neko_quad_neds, neko_quad_npts
  use utils, only : neko_error, neko_warning, nonlinear_index
  use mask, only : mask_t
  use stack, only : stack_i4_t, stack_i8_t, stack_i4t4_t, stack_i4t2_t
  use tuple, only : tuple_i4_t, tuple4_i4_t
  use htable, only : htable_t, htable_i8_t, htable_i4_t, htable_i4t4_t,&
       htable_i4t2_t, htable_iter_i4t2_t, htable_iter_i4t4_t
  use datadist, only : linear_dist_t
  use distdata, only : distdata_t
  use comm, only : pe_size, pe_rank, neko_comm
  use facet_zone, only : facet_zone_t, facet_zone_periodic_t
  use math, only : abscmp, sort
  use crystal_router, only : crystal_router_transfer, crystal_router_pack
  use mpi_f08, only : mpi_integer, mpi_max, mpi_sum, mpi_in_place, &
       mpi_allreduce, mpi_exscan, mpi_request, mpi_status, mpi_wait, &
       mpi_issend, mpi_irecv, mpi_status_ignore, mpi_integer8, &
       mpi_get_count
  use uset, only : uset_i8_t
  use curve, only : curve_t
  use logger, only : log_size
  use, intrinsic :: iso_fortran_env, only: error_unit
  implicit none
  private
 
  integer, public, parameter :: neko_msh_max_zlbls = 20
  integer, public, parameter :: neko_msh_max_zlbl_len = 40
 
  type, private :: mesh_element_t
     class(element_t), allocatable :: e
  end type mesh_element_t
 
  type, public :: mesh_t
     integer :: nelv
     integer :: npts
     integer :: gdim
     integer :: mpts
     integer :: mfcs
     integer :: meds
 
     integer :: glb_nelv
     integer :: glb_mpts
     integer :: glb_mfcs
     integer :: glb_meds
 
     integer :: offset_el
     integer :: max_pts_id
 
     type(point_t), allocatable :: points(:)
     type(mesh_element_t), allocatable :: elements(:)
     logical, allocatable :: dfrmd_el(:)
 
     type(htable_i4_t) :: htp
     type(htable_i4t4_t) :: htf
     type(htable_i4t2_t) :: hte
     type(htable_i4_t) :: htel
 
 
     integer, allocatable :: facet_neigh(:,:)
 
     class(htable_t), allocatable :: facet_map
     type(stack_i4_t), allocatable :: point_neigh(:)
 
     type(distdata_t) :: ddata
     logical, allocatable :: neigh(:)
     integer, allocatable :: neigh_order(:)
 
     integer(2), allocatable :: facet_type(:,:)
 
     type(facet_zone_t), allocatable :: labeled_zones(:)
     type(facet_zone_periodic_t) :: periodic
     type(curve_t) :: curve
 
     logical :: lconn = .false. 
     logical :: ldist = .false. 
     logical :: lnumr = .false. 
     logical :: lgenc = .true. 
 
     logical :: is_submesh = .false. 
 
     procedure(mesh_deform), pass(msh), pointer :: apply_deform => null()
   contains
     procedure, private, pass(this) :: init_nelv => mesh_init_nelv
     procedure, private, pass(this) :: init_dist => mesh_init_dist
     procedure, private, pass(this) :: add_quad => mesh_add_quad
     procedure, private, pass(this) :: add_hex => mesh_add_hex
     procedure, private, pass(this) :: add_edge => mesh_add_edge
     procedure, private, pass(this) :: add_face => mesh_add_face
     procedure, private, pass(this) :: add_point => mesh_add_point
     procedure, private, pass(this) :: get_local_point => mesh_get_local_point
     procedure, private, pass(this) :: get_local_edge => mesh_get_local_edge
     procedure, private, pass(this) :: get_local_facet => mesh_get_local_facet
     procedure, private, pass(this) :: get_global_edge => mesh_get_global_edge
     procedure, private, pass(this) :: get_global_facet => mesh_get_global_facet
     procedure, private, pass(this) :: is_shared_point => mesh_is_shared_point
     procedure, private, pass(this) :: is_shared_edge => mesh_is_shared_edge
     procedure, private, pass(this) :: is_shared_facet => mesh_is_shared_facet
     procedure, pass(this) :: free => mesh_free
     procedure, pass(this) :: finalize => mesh_finalize
     procedure, pass(this) :: mark_periodic_facet => mesh_mark_periodic_facet
     procedure, pass(this) :: mark_labeled_facet => mesh_mark_labeled_facet
     procedure, pass(this) :: mark_curve_element => mesh_mark_curve_element
     procedure, pass(this) :: apply_periodic_facet => mesh_apply_periodic_facet
     procedure, pass(this) :: all_deformed => mesh_all_deformed
     procedure, pass(this) :: get_facet_ids => mesh_get_facet_ids
     procedure, pass(this) :: reset_periodic_ids => mesh_reset_periodic_ids
     procedure, pass(this) :: create_periodic_ids => mesh_create_periodic_ids
     procedure, pass(this) :: generate_conn => mesh_generate_conn
     procedure, pass(this) :: have_point_glb_idx => mesh_have_point_glb_idx
     procedure, pass(this) :: subset_by_mask => mesh_subset_by_mask
 
     procedure, pass(this) :: check_right_handedness => &
          mesh_check_right_handedness
     generic :: init => init_nelv, init_dist
     generic :: add_element => add_quad, add_hex
     generic :: get_local => get_local_point, get_local_edge, get_local_facet
     generic :: get_global => get_global_edge, get_global_facet
     generic :: is_shared => is_shared_point, is_shared_edge, is_shared_facet
  end type mesh_t
 
  abstract interface
     subroutine mesh_deform(msh, x, y, z, lx, ly, lz)
       import mesh_t
       import rp
       class(mesh_t) :: msh
       integer, intent(in) :: lx, ly, lz
       real(kind=rp), intent(inout) :: x(lx, ly, lz, msh%nelv)
       real(kind=rp), intent(inout) :: y(lx, ly, lz, msh%nelv)
       real(kind=rp), intent(inout) :: z(lx, ly, lz, msh%nelv)
     end subroutine mesh_deform
  end interface
 
  public :: mesh_deform, parallelepiped_signed_volume
 
 
contains
 
  subroutine mesh_init_nelv(this, gdim, nelv)
    class(mesh_t), intent(inout) :: this
    integer, intent(in) :: gdim
    integer, intent(in) :: nelv
    integer :: ierr
    character(len=LOG_SIZE) :: log_buf
 
    call this%free()
 
    this%nelv = nelv
    this%gdim = gdim
 
    if (this%nelv < 1) then
       write(log_buf, '(A,I0,A)') 'MPI rank ', pe_rank, ' has zero elements'
       call neko_warning(log_buf)
    end if
 
    call mpi_allreduce(this%nelv, this%glb_nelv, 1, &
         mpi_integer, mpi_sum, neko_comm, ierr)
 
    this%offset_el = 0
    call mpi_exscan(this%nelv, this%offset_el, 1, &
         mpi_integer, mpi_sum, neko_comm, ierr)
 
    call mesh_init_common(this)
 
  end subroutine mesh_init_nelv
 
  subroutine mesh_init_dist(this, gdim, dist)
    class(mesh_t), intent(inout) :: this
    integer, intent(in) :: gdim
    type(linear_dist_t), intent(in) :: dist
    character(len=LOG_SIZE) :: log_buf
 
    call this%free()
 
    this%nelv = dist%num_local()
    if (this%nelv < 1) then
       write(log_buf, '(A,I0,A)') 'MPI rank ', pe_rank, ' has zero elements'
       call neko_warning(log_buf)
    end if
    this%glb_nelv = dist%num_global()
    this%offset_el = dist%start_idx()
    this%gdim = gdim
 
    call mesh_init_common(this)
 
  end subroutine mesh_init_dist
 
  subroutine mesh_init_common(this)
    type(mesh_t), intent(inout) :: this
    integer :: i
    type(tuple_i4_t) :: facet_data
 
    this%max_pts_id = 0
 
    allocate(this%elements(this%nelv))
    allocate(this%dfrmd_el(this%nelv))
    if (this%gdim .eq. 3) then
       do i = 1, this%nelv
          allocate(hex_t::this%elements(i)%e)
       end do
       this%npts = neko_hex_npts
       if (this%lgenc) then
          allocate(htable_i4t4_t::this%facet_map)
          select type (fmp => this%facet_map)
          type is(htable_i4t4_t)
             call fmp%init(this%nelv, facet_data)
          end select
 
          allocate(this%facet_neigh(neko_hex_nfcs, this%nelv))
 
          call this%htf%init(this%nelv * neko_hex_nfcs, i)
          call this%hte%init(this%nelv * neko_hex_neds, i)
       end if
    else if (this%gdim .eq. 2) then
       do i = 1, this%nelv
          allocate(quad_t::this%elements(i)%e)
       end do
       this%npts = neko_quad_npts
       if (this%lgenc) then
          allocate(htable_i4t2_t::this%facet_map)
          select type (fmp => this%facet_map)
          type is(htable_i4t2_t)
             call fmp%init(this%nelv, facet_data)
          end select
 
          allocate(this%facet_neigh(neko_quad_neds, this%nelv))
 
          call this%hte%init(this%nelv * neko_quad_neds, i)
       end if
    else
       call neko_error("Invalid dimension")
    end if
 
    allocate(this%points(this%npts*this%nelv))
 
    if (this%lgenc) then
       ! Temporary workaround to avoid long vacations with Cray Fortran
       if (allocated(this%point_neigh)) then
          deallocate(this%point_neigh)
       end if
       allocate(this%point_neigh(this%gdim*this%npts*this%nelv))
       do i = 1, this%gdim*this%npts*this%nelv
          call this%point_neigh(i)%init(size=4)
       end do
    end if
 
    allocate(this%facet_type(2 * this%gdim, this%nelv))
    this%facet_type = 0
 
    call this%htp%init(this%npts*this%nelv, i)
    call this%htel%init(this%nelv, i)
 
    call this%periodic%init(this%nelv)
 
    allocate(this%labeled_zones(neko_msh_max_zlbls))
    do i = 1, neko_msh_max_zlbls
       call this%labeled_zones(i)%init(this%nelv)
    end do
 
    call this%curve%init(this%nelv)
 
    call this%ddata%init()
 
    allocate(this%neigh(0:pe_size-1))
    this%neigh = .false.
 
    this%mpts = 0
    this%mfcs = 0
    this%meds = 0
 
  end subroutine mesh_init_common
 
  subroutine mesh_free(this)
    class(mesh_t), intent(inout) :: this
    integer :: i
 
    call this%htp%free()
    call this%htf%free()
    call this%hte%free()
    call this%htel%free()
    call this%ddata%free()
    call this%curve%free()
 
    if (allocated(this%dfrmd_el)) then
       deallocate(this%dfrmd_el)
    end if
 
    if (allocated(this%elements)) then
       do i = 1, this%nelv
          call this%elements(i)%e%free()
          deallocate(this%elements(i)%e)
       end do
       deallocate(this%elements)
    end if
 
    if (allocated(this%facet_map)) then
       select type (fmp => this%facet_map)
       type is(htable_i4t2_t)
          call fmp%free()
       type is(htable_i4t4_t)
          call fmp%free()
       end select
       deallocate(this%facet_map)
    end if
 
    if (allocated(this%facet_neigh)) then
       deallocate(this%facet_neigh)
    end if
 
    if (allocated(this%point_neigh)) then
       do i = 1, this%gdim * this%npts * this%nelv
          call this%point_neigh(i)%free()
       end do
       ! This causes Cray Fortran to take a long vacation
       !deallocate(this%point_neigh)
    end if
 
    if (allocated(this%facet_type)) then
       deallocate(this%facet_type)
    end if
    if (allocated(this%labeled_zones)) then
       do i = 1, neko_msh_max_zlbls
          call this%labeled_zones(i)%free()
       end do
       deallocate(this%labeled_zones)
    end if
 
    if (allocated(this%neigh)) then
       deallocate(this%neigh)
    end if
 
    if (allocated(this%neigh_order)) then
       deallocate(this%neigh_order)
    end if
 
    if (allocated(this%points)) then
       deallocate(this%points)
    end if
 
    call this%periodic%free()
    this%lconn = .false.
    this%lnumr = .false.
    this%ldist = .false.
    this%lgenc = .true.
 
  end subroutine mesh_free
 
  subroutine mesh_finalize(this)
    class(mesh_t), target, intent(inout) :: this
    integer :: i
 
    call mesh_generate_flags(this)
    call mesh_generate_conn(this)
 
    call this%periodic%finalize()
    do i = 1, neko_msh_max_zlbls
       call this%labeled_zones(i)%finalize()
    end do
    call this%curve%finalize()
 
    ! Due to a bug, right handedness check disabled for the time being.
    !call this%check_right_handedness()
 
  end subroutine mesh_finalize
 
  subroutine mesh_generate_flags(this)
    type(mesh_t), intent(inout) :: this
    real(kind=dp) :: u(3), v(3), w(3), temp
    integer :: e
 
    do e = 1, this%nelv
       if (this%gdim .eq. 2) then
          this%dfrmd_el(e) = .false.
          u = this%elements(e)%e%pts(2)%p%x - this%elements(e)%e%pts(1)%p%x
          v = this%elements(e)%e%pts(3)%p%x - this%elements(e)%e%pts(1)%p%x
          temp = u(1)*v(1) + u(2)*v(2)
          if(.not. abscmp(temp, 0d0)) this%dfrmd_el(e) = .true.
       else
          this%dfrmd_el(e) = .false.
          u = this%elements(e)%e%pts(2)%p%x - this%elements(e)%e%pts(1)%p%x
          v = this%elements(e)%e%pts(3)%p%x - this%elements(e)%e%pts(1)%p%x
          w = this%elements(e)%e%pts(5)%p%x - this%elements(e)%e%pts(1)%p%x
          temp = u(1)*v(1) + u(2)*v(2) + u(3)*v(3)
          if(.not. abscmp(temp, 0d0)) this%dfrmd_el(e) = .true.
          temp = u(1)*w(1) + u(2)*w(2) + u(3)*w(3)
          if(.not. abscmp(temp, 0d0)) this%dfrmd_el(e) = .true.
          u = this%elements(e)%e%pts(7)%p%x - this%elements(e)%e%pts(8)%p%x
          v = this%elements(e)%e%pts(6)%p%x - this%elements(e)%e%pts(8)%p%x
          w = this%elements(e)%e%pts(4)%p%x - this%elements(e)%e%pts(8)%p%x
          temp = u(1)*v(1) + u(2)*v(2) + u(3)*v(3)
          if(.not. abscmp(temp, 0d0)) this%dfrmd_el(e) = .true.
          temp = u(1)*w(1) + u(2)*w(2) + u(3)*w(3)
          if(.not. abscmp(temp, 0d0)) this%dfrmd_el(e) = .true.
       end if
    end do
  end subroutine mesh_generate_flags
 
  subroutine mesh_all_deformed(this)
    class(mesh_t), intent(inout) :: this
    this%dfrmd_el = .true.
  end subroutine mesh_all_deformed
 
  subroutine mesh_generate_conn(this)
    class(mesh_t), target, intent(inout) :: this
    type(tuple_i4_t) :: edge
    type(tuple4_i4_t) :: face, face_comp
    type(tuple_i4_t) :: facet_data
    type(stack_i4_t) :: neigh_order
    class(element_t), pointer :: ep
    type(tuple_i4_t) :: e
    type(tuple4_i4_t) :: f
    integer :: p_local_idx
    integer :: el, id
    integer :: i, j, k, ierr, el_glb_idx, n_sides, n_nodes, src, dst
 
    if (this%lconn) return
 
    if (.not. this%lgenc) return
 
    !If we generate connectivity, we do that here.
    do el = 1, this%nelv
       ep => this%elements(el)%e
       select type(ep)
       type is (hex_t)
          do i = 1, neko_hex_npts
             !Only for getting the id
             call this%add_point(ep%pts(i)%p, id)
             p_local_idx = this%get_local(this%points(id))
             !should stack have inout on what we push? would be neat with in
             id = ep%id()
             call this%point_neigh(p_local_idx)%push(id)
          end do
          do i = 1, neko_hex_nfcs
             call ep%facet_id(f, i)
             call this%add_face(f)
          end do
 
          do i = 1, neko_hex_neds
             call ep%edge_id(e, i)
             call this%add_edge(e)
          end do
       type is (quad_t)
          do i = 1, neko_quad_npts
             !Only for getting the id
             call this%add_point(ep%pts(i)%p, id)
             p_local_idx = this%get_local(this%points(id))
             !should stack have inout on what we push? would be neat with in
             id = ep%id()
             call this%point_neigh(p_local_idx)%push(id)
          end do
 
          do i = 1, neko_quad_neds
             call ep%facet_id(e, i)
             call this%add_edge(e)
          end do
       end select
    end do
 
 
    if (this%gdim .eq. 2) then
       n_sides = 4
       n_nodes = 2
    else
       n_sides = 6
       n_nodes = 4
    end if
 
    ! Compute global number of unique points
    call mpi_allreduce(this%max_pts_id, this%glb_mpts, 1, &
         mpi_integer, mpi_max, neko_comm, ierr)
 
    !
    ! Find all (local) boundaries
    !
 
    select type (fmp => this%facet_map)
    type is(htable_i4t2_t)
       do k = 1, 2
          do i = 1, this%nelv
             el_glb_idx = i + this%offset_el
             do j = 1, n_sides
                call this%elements(i)%e%facet_id(edge, j)
 
                ! Assume that all facets are on the exterior
                facet_data%x = [0, 0]
 
                !check it this face has shown up earlier
                if (fmp%get(edge, facet_data) .eq. 0) then
                   !if element is already recognized on face
                   if (facet_data%x(1) .eq. el_glb_idx ) then
                      this%facet_neigh(j, i) = facet_data%x(2)
                   else if( facet_data%x(2) .eq. el_glb_idx) then
                      this%facet_neigh(j, i) = facet_data%x(1)
                      !if this is the second element, arrange so low id is first
                   else if(facet_data%x(1) .gt. el_glb_idx) then
                      facet_data%x(2) = facet_data%x(1)
                      facet_data%x(1) = el_glb_idx
                      this%facet_neigh(j, i) = facet_data%x(2)
                      call fmp%set(edge, facet_data)
                   else if(facet_data%x(1) .lt. el_glb_idx) then
                      facet_data%x(2) = el_glb_idx
                      this%facet_neigh(j, i) = facet_data%x(1)
                      call fmp%set(edge, facet_data)
                   end if
                else
                   facet_data%x(1) = el_glb_idx
                   this%facet_neigh(j, i) = facet_data%x(2)
                   call fmp%set(edge, facet_data)
                end if
             end do
          end do
       end do
    type is(htable_i4t4_t)
 
       do k = 1, 2
          do i = 1, this%nelv
             el_glb_idx = i + this%offset_el
             do j = 1, n_sides
                call this%elements(i)%e%facet_id(face, j)
 
                facet_data%x = (/ 0, 0/)
 
                !check it this face has shown up earlier
                if (fmp%get(face, facet_data) .eq. 0) then
                   !if element is already recognized on face
                   if (facet_data%x(1) .eq. el_glb_idx ) then
                      this%facet_neigh(j, i) = facet_data%x(2)
                      call this%elements(i)%e%facet_id(face_comp, &
                           j + (2*mod(j, 2) - 1))
                      if (face_comp .eq. face) then
                         facet_data%x(2) = el_glb_idx
                         this%facet_neigh(j, i) = facet_data%x(1)
                         call fmp%set(face, facet_data)
                      end if
                   else if( facet_data%x(2) .eq. el_glb_idx) then
                      this%facet_neigh(j, i) = facet_data%x(1)
                      !if this is the second element, arrange so low id is first
                   else if(facet_data%x(1) .gt. el_glb_idx) then
                      facet_data%x(2) = facet_data%x(1)
                      facet_data%x(1) = el_glb_idx
                      this%facet_neigh(j, i) = facet_data%x(2)
                      call fmp%set(face, facet_data)
                   else if(facet_data%x(1) .lt. el_glb_idx) then
                      facet_data%x(2) = el_glb_idx
                      this%facet_neigh(j, i) = facet_data%x(1)
                      call fmp%set(face, facet_data)
                   end if
                else
                   facet_data%x(1) = el_glb_idx
                   this%facet_neigh(j, i) = 0
                   call fmp%set(face, facet_data)
                end if
             end do
          end do
       end do
    class default
       call neko_error('Invalid facet map')
    end select
 
 
    !
    ! Find all external (between PEs) boundaries
    !
    if (pe_size .gt. 1) then
 
       call mesh_generate_external_point_conn(this)
 
       !
       ! Generate neighbour exchange order
       !
       call neigh_order%init(pe_size)
 
       do i = 1, pe_size - 1
          src = modulo(pe_rank - i + pe_size, pe_size)
          dst = modulo(pe_rank + i, pe_size)
          if (this%neigh(src) .or. this%neigh(dst)) then
             j = i ! adhere to standards...
             call neigh_order%push(j)
          end if
       end do
 
       allocate(this%neigh_order(neigh_order%size()))
       select type(order => neigh_order%data)
       type is (integer)
          do i = 1, neigh_order%size()
             this%neigh_order(i) = order(i)
          end do
       end select
       call neigh_order%free()
 
       call mesh_generate_external_facet_conn(this)
    else
       allocate(this%neigh_order(1))
       this%neigh_order = 1
    end if
 
    !
    ! Find all internal/extenral edge connections
    ! (Note it needs to be called after external point connections has
    ! been established)
    !
    if (this%gdim .eq. 3) then
       call mesh_generate_edge_conn(this)
    end if
 
 
    call mesh_generate_facet_numbering(this)
 
    this%lconn = .true.
 
  end subroutine mesh_generate_conn
 
  subroutine mesh_generate_external_facet_conn(this)
    type(mesh_t), intent(inout) :: this
    type(tuple_i4_t) :: edge, edge2
    type(tuple4_i4_t) :: face, face2
    type(tuple_i4_t) :: facet_data
    type(stack_i4_t) :: buffer
    type(mpi_status) :: status
    type(mpi_request) :: send_req, recv_req
    integer, allocatable :: recv_buffer(:)
    integer :: i, j, k, el_glb_idx, n_sides, n_nodes, facet, element, l
    integer :: max_recv, ierr, src, dst, n_recv, recv_side, neigh_el
 
 
    if (this%gdim .eq. 2) then
       n_sides = 4
       n_nodes = 2
    else
       n_sides = 6
       n_nodes = 4
    end if
 
    call buffer%init()
 
    ! Build send buffers containing
    ! [el_glb_idx, side number, facet_id (global ids of points)]
    do i = 1, this%nelv
       el_glb_idx = i + this%offset_el
       do j = 1, n_sides
          facet = j ! Adhere to standards...
          if (this%facet_neigh(j, i) .eq. 0) then
             if (n_nodes .eq. 2) then
                call this%elements(i)%e%facet_id(edge, j)
                call buffer%push(el_glb_idx)
                call buffer%push(facet)
                do k = 1, n_nodes
                   call buffer%push(edge%x(k))
                end do
             else
                call this%elements(i)%e%facet_id(face, j)
                call buffer%push(el_glb_idx)
                call buffer%push(facet)
                do k = 1, n_nodes
                   call buffer%push(face%x(k))
                end do
             end if
          end if
       end do
    end do
 
 
    call mpi_allreduce(buffer%size(), max_recv, 1, &
         mpi_integer, mpi_max, neko_comm, ierr)
 
    allocate(recv_buffer(max_recv))
 
    do i = 1, size(this%neigh_order)
       src = modulo(pe_rank - this%neigh_order(i) + pe_size, pe_size)
       dst = modulo(pe_rank + this%neigh_order(i), pe_size)
 
       if (this%neigh(src)) then
          call mpi_irecv(recv_buffer, max_recv, mpi_integer, &
               src, 0, neko_comm, recv_req, ierr)
       end if
 
       if (this%neigh(dst)) then
          ! Synchronous send so the buffer is never eager-buffered as an
          ! unexpected message, which exhausts the MPI internal buffer pool
          ! (SIGBUS) under flat MPI at high rank counts. Deadlock-safe: the
          ! matching recv is pre-posted at the top of the peer's iteration.
          call mpi_issend(buffer%array(), buffer%size(), mpi_integer, &
               dst, 0, neko_comm, send_req, ierr)
       end if
 
       if (this%neigh(src)) then
          call mpi_wait(recv_req, status, ierr)
          call mpi_get_count(status, mpi_integer, n_recv, ierr)
 
          select type (fmp => this%facet_map)
          type is(htable_i4t2_t)
             do j = 1, n_recv, n_nodes + 2
                neigh_el = recv_buffer(j)
                recv_side = recv_buffer(j+1)
 
                edge = (/ recv_buffer(j+2), recv_buffer(j+3) /)
 
                facet_data = (/ 0, 0 /)
                !Check if the face is present on this PE
                if (fmp%get(edge, facet_data) .eq. 0) then
                   element = facet_data%x(1) - this%offset_el
                   !Check which side is connected
                   do l = 1, n_sides
                      call this%elements(element)%e%facet_id(edge2, l)
                      if(edge2 .eq. edge) then
                         facet = l
                         exit
                      end if
                   end do
                   this%facet_neigh(facet, element) = -neigh_el
                   facet_data%x(2) = -neigh_el
 
                   !  Update facet map
                   call fmp%set(edge, facet_data)
 
                   call this%ddata%set_shared_el_facet(element, facet)
 
                   if (this%hte%get(edge, facet) .eq. 0) then
                      call this%ddata%set_shared_facet(facet)
                   else
                      call neko_error("Invalid shared edge")
                   end if
 
                end if
 
             end do
          type is(htable_i4t4_t)
             do j = 1, n_recv, n_nodes + 2
                neigh_el = recv_buffer(j)
                recv_side = recv_buffer(j+1)
 
                face%x = (/ recv_buffer(j+2), recv_buffer(j+3), &
                     recv_buffer(j+4), recv_buffer(j+5) /)
 
 
                facet_data%x = (/ 0, 0 /)
 
                !Check if the face is present on this PE
                if (fmp%get(face, facet_data) .eq. 0) then
                   ! Determine opposite side and update neighbor
                   element = facet_data%x(1) - this%offset_el
                   do l = 1, 6
                      call this%elements(element)%e%facet_id(face2, l)
                      if(face2 .eq. face) then
                         facet = l
                         exit
                      end if
                   end do
                   this%facet_neigh(facet, element) = -neigh_el
                   facet_data%x(2) = -neigh_el
 
                   ! Update facet map
                   call fmp%set(face, facet_data)
 
                   call this%ddata%set_shared_el_facet(element, facet)
 
                   if (this%htf%get(face, facet) .eq. 0) then
                      call this%ddata%set_shared_facet(facet)
                   else
                      call neko_error("Invalid shared face")
                   end if
 
 
                end if
 
             end do
          end select
       end if
 
       if (this%neigh(dst)) then
          call mpi_wait(send_req, mpi_status_ignore, ierr)
       end if
 
    end do
 
 
    deallocate(recv_buffer)
 
    call buffer%free()
 
  end subroutine mesh_generate_external_facet_conn
 
  subroutine mesh_generate_external_point_conn(this)
    type(mesh_t), intent(inout) :: this
    type(stack_i8_t) :: cr_buf
    integer(i8), allocatable :: buf(:), body(:)
    integer(i8), pointer :: cr_data(:)
    integer, allocatable :: gkey(:), gperm(:), rpos(:)
    integer, contiguous, pointer :: neighs(:)
    integer :: i, j, k, n, p, owner, num_neigh, nrec, rlen
    integer :: pt_glb_idx, pt_loc_idx, src_rank, neigh_el, rk, rp
 
    !
    ! Phase 1: route every local point's element list to its canonical owner.
    !   record payload = [glb_idx, origin, elems...]
    !
    call cr_buf%init(this%mpts * 4)
    allocate(body(8))
    do i = 1, this%mpts
       pt_glb_idx = this%points(i)%id() ! Adhere to standards...
       num_neigh = this%point_neigh(i)%size()
       if (2 + num_neigh .gt. size(body)) then
          deallocate(body)
          allocate(body(2 + num_neigh))
       end if
       body(1) = int(pt_glb_idx, i8) ! glb_idx
       body(2) = int(pe_rank, i8) ! origin
       neighs => this%point_neigh(i)%array()
       do j = 1, num_neigh
          body(2 + j) = int(neighs(j), i8) ! element ids
       end do
       owner = modulo(pt_glb_idx, pe_size)
       call crystal_router_pack(cr_buf, owner, body(1:2 + num_neigh))
    end do
    deallocate(body)
 
    n = cr_buf%size()
    allocate(buf(max(n, 1)))
    if (n .gt. 0) then
       cr_data => cr_buf%array()
       buf(1:n) = cr_data(1:n)
    end if
    call cr_buf%free()
 
    call crystal_router_transfer(buf, n)
 
    !
    ! Phase 2: at the owner, group received records by glb_idx and reflect,
    !   to each holder, the element lists of every *other* holder.
    !   reply = [dest=holder, len=2+num_neigh, glb_idx, src_rank, elems...]
    !
    ! Index the received records and sort their keys (glb_idx) so equal keys
    ! form contiguous runs; per-point holder counts are small, so the
    ! all-pairs reflection within a run is cheap.
    nrec = 0
    p = 1
    do while (p .le. n)
       nrec = nrec + 1
       p = p + 2 + int(buf(p + 1))
    end do
 
    allocate(gkey(max(nrec, 1)), gperm(max(nrec, 1)), rpos(max(nrec, 1)))
    nrec = 0
    p = 1
    do while (p .le. n)
       nrec = nrec + 1
       rpos(nrec) = p ! record start offset in buf
       gkey(nrec) = int(buf(p + 2)) ! glb_idx
       p = p + 2 + int(buf(p + 1))
    end do
    if (nrec .gt. 0) call sort(gkey, gperm, nrec)
 
    call cr_buf%init(max(n, 1))
    i = 1
    do while (i .le. nrec)
       ! [i, j) is the run of records sharing the same glb_idx
       j = i
       do while (j .le. nrec)
          if (gkey(j) .ne. gkey(i)) exit
          j = j + 1
       end do
       ! All-pairs reflection within the run (skip singletons = unshared):
       ! send source holder p's record body (glb_idx, origin, elems) to
       ! recipient holder k, addressed to k's origin rank.
       if (j - i .gt. 1) then
          do k = i, j - 1 ! recipient holder
             rk = rpos(gperm(k))
             do p = i, j - 1 ! source holder
                if (p .eq. k) cycle
                rp = rpos(gperm(p))
                call crystal_router_pack(cr_buf, int(buf(rk + 3)), &
                     buf(rp + 2 : rp + 1 + int(buf(rp + 1))))
             end do
          end do
       end if
       i = j
    end do
    deallocate(gkey, gperm, rpos)
 
    n = cr_buf%size()
    if (allocated(buf)) deallocate(buf)
    allocate(buf(max(n, 1)))
    if (n .gt. 0) then
       cr_data => cr_buf%array()
       buf(1:n) = cr_data(1:n)
    end if
    call cr_buf%free()
 
    call crystal_router_transfer(buf, n)
 
    !
    ! Phase 3: finalise locally. Each reply names a remote holder of one of our
    !   points; mark it as a neighbour and absorb its (remote) element list.
    !
    p = 1
    do while (p .le. n)
       rlen = int(buf(p + 1))
       pt_glb_idx = int(buf(p + 2))
       src_rank = int(buf(p + 3))
       pt_loc_idx = this%have_point_glb_idx(pt_glb_idx)
       if (pt_loc_idx .gt. 0) then
          this%neigh(src_rank) = .true.
          call this%ddata%set_shared_point(pt_loc_idx)
          do k = 1, rlen - 2
             neigh_el = -int(buf(p + 3 + k))
             call this%point_neigh(pt_loc_idx)%push(neigh_el)
          end do
       end if
       p = p + 2 + rlen
    end do
 
    if (allocated(buf)) deallocate(buf)
 
  end subroutine mesh_generate_external_point_conn
 
  subroutine mesh_generate_edge_conn(this)
    type(mesh_t), target, intent(inout) :: this
    type(htable_iter_i4t2_t) :: it
    type(tuple_i4_t), pointer :: edge
    type(uset_i8_t), target :: edge_idx, ghost, owner
    type(stack_i8_t), target :: send_buff
    type(htable_i8_t) :: glb_to_loc
    type(mpi_status) :: status
    type(mpi_request) :: send_req, recv_req
    integer, contiguous, pointer :: p1(:), p2(:), ns_id(:)
    integer :: i, j, id, ierr, num_edge_glb, edge_offset, num_edge_loc
    integer :: k, l , shared_offset, glb_nshared, n_glb_id
    integer(kind=i8) :: C, glb_max, glb_id
    integer(kind=i8), pointer :: glb_ptr
    integer(kind=i8), allocatable :: recv_buff(:)
    logical :: shared_edge
    type(stack_i4_t), target :: non_shared_edges
    integer :: max_recv, src, dst, n_recv
 
 
    allocate(this%ddata%local_to_global_edge(this%meds))
 
    call edge_idx%init(this%hte%num_entries())
    call send_buff%init(this%hte%num_entries())
    call owner%init(this%hte%num_entries())
 
    call glb_to_loc%init(32, i)
 
    !
    ! Determine/ constants used to generate unique global edge numbers
    ! for shared edges
    !
    c = int(this%glb_nelv, i8) * int(neko_hex_neds, i8)
 
    num_edge_glb = 2* this%meds
    call mpi_allreduce(mpi_in_place, num_edge_glb, 1, &
         mpi_integer, mpi_sum, neko_comm, ierr)
 
    glb_max = int(num_edge_glb, i8)
 
    call non_shared_edges%init(this%hte%num_entries())
 
    call it%init(this%hte)
    do while(it%next())
       edge => it%key()
       call it%data(id)
 
       k = this%have_point_glb_idx(edge%x(1))
       l = this%have_point_glb_idx(edge%x(2))
       p1 => this%point_neigh(k)%array()
       p2 => this%point_neigh(l)%array()
 
       shared_edge = .false.
 
       ! Find edge neighbor from point neighbors
       do i = 1, this%point_neigh(k)%size()
          do j = 1, this%point_neigh(l)%size()
             if ((p1(i) .eq. p2(j)) .and. &
                  (p1(i) .lt. 0) .and. (p2(j) .lt. 0)) then
                call this%ddata%set_shared_edge(id)
                shared_edge = .true.
             end if
          end do
       end do
 
       ! Generate a unique id for the shared edge as,
       ! ((e1 * C) + e2 )) + glb_max if e1 > e2
       ! ((e2 * C) + e1 )) + glb_max if e2 > e1
       if (shared_edge) then
          glb_id = ((int(edge%x(1), i8)) + int(edge%x(2), i8)*c) + glb_max
          call glb_to_loc%set(glb_id, id)
          call edge_idx%add(glb_id)
          call owner%add(glb_id) ! Always assume the PE is the owner
          call send_buff%push(glb_id)
       else
          call non_shared_edges%push(id)
       end if
    end do
 
    ! Determine start offset for global numbering of locally owned edges
    edge_offset = 0
    num_edge_loc = non_shared_edges%size()
    call mpi_exscan(num_edge_loc, edge_offset, 1, &
         mpi_integer, mpi_sum, neko_comm, ierr)
    edge_offset = edge_offset + 1
 
    ! Construct global numbering of locally owned edges
    ns_id => non_shared_edges%array()
    do i = 1, non_shared_edges%size()
       call this%ddata%set_local_to_global_edge(ns_id(i), edge_offset)
       edge_offset = edge_offset + 1
    end do
    nullify(ns_id)
 
    !
    ! Renumber shared edges into integer range
    !
 
    call mpi_allreduce(send_buff%size(), max_recv, 1, &
         mpi_integer, mpi_max, neko_comm, ierr)
 
    call ghost%init(send_buff%size())
 
    allocate(recv_buff(max_recv))
 
    do i = 1, size(this%neigh_order)
       src = modulo(pe_rank - this%neigh_order(i) + pe_size, pe_size)
       dst = modulo(pe_rank + this%neigh_order(i), pe_size)
 
       if (this%neigh(src)) then
          call mpi_irecv(recv_buff, max_recv, mpi_integer8, &
               src, 0, neko_comm, recv_req, ierr)
       end if
 
       if (this%neigh(dst)) then
          ! We should use the %array() procedure, which works great for
          ! GNU, Intel and NEC, but it breaks horribly on Cray when using
          ! certain data types
          select type(sbarray=>send_buff%data)
          type is (integer(i8))
             ! Synchronous send to avoid eager-buffering the key list as an
             ! unexpected message (FJMPI buffer-pool exhaustion / SIGBUS under
             ! flat MPI); matching recv is pre-posted by the peer.
             call mpi_issend(sbarray, send_buff%size(), mpi_integer8, &
                  dst, 0, neko_comm, send_req, ierr)
          end select
       end if
 
       if (this%neigh(src)) then
          call mpi_wait(recv_req, status, ierr)
          call mpi_get_count(status, mpi_integer8, n_recv, ierr)
 
          do j = 1, n_recv
             if ((edge_idx%element(recv_buff(j))) .and. (src .lt. pe_rank)) then
                call ghost%add(recv_buff(j))
                call owner%remove(recv_buff(j))
             end if
          end do
       end if
 
       if (this%neigh(dst)) then
          call mpi_wait(send_req, mpi_status_ignore, ierr)
       end if
    end do
 
 
    ! Determine start offset for global numbering of shared edges
    glb_nshared = num_edge_loc
    call mpi_allreduce(mpi_in_place, glb_nshared, 1, &
         mpi_integer, mpi_sum, neko_comm, ierr)
 
    shared_offset = 0
    call mpi_exscan(owner%size(), shared_offset, 1, &
         mpi_integer, mpi_sum, neko_comm, ierr)
    shared_offset = shared_offset + glb_nshared + 1
 
    ! Renumber locally owned set of shared edges
    call send_buff%clear()
    call owner%iter_init()
    do while (owner%iter_next())
       glb_ptr => owner%iter_value()
       if (glb_to_loc%get(glb_ptr, id) .eq. 0) then
          call this%ddata%set_local_to_global_edge(id, shared_offset)
 
          ! Add new number to send data as [old_glb_id new_glb_id] for each edge
          call send_buff%push(glb_ptr) ! Old glb_id integer*8
          glb_id = int(shared_offset, i8) ! Waste some space here...
          call send_buff%push(glb_id) ! New glb_id integer*4
 
          shared_offset = shared_offset + 1
       else
          call neko_error('Invalid edge id')
       end if
    end do
    nullify(glb_ptr)
 
    ! Determine total number of unique edges in the mesh
    ! (This can probably be done in a clever way...)
    this%glb_meds = shared_offset -1
    call mpi_allreduce(mpi_in_place, this%glb_meds, 1, &
         mpi_integer, mpi_max, neko_comm, ierr)
 
    !
    ! Update ghosted edges with new global id
    !
 
    call mpi_allreduce(send_buff%size(), max_recv, 1, &
         mpi_integer, mpi_max, neko_comm, ierr)
 
    deallocate(recv_buff)
    allocate(recv_buff(max_recv))
 
 
    do i = 1, size(this%neigh_order)
       src = modulo(pe_rank - this%neigh_order(i) + pe_size, pe_size)
       dst = modulo(pe_rank + this%neigh_order(i), pe_size)
 
       if (this%neigh(src)) then
          call mpi_irecv(recv_buff, max_recv, mpi_integer8, &
               src, 0, neko_comm, recv_req, ierr)
       end if
 
       if (this%neigh(dst)) then
          ! We should use the %array() procedure, which works great for
          ! GNU, Intel and NEC, but it breaks horribly on Cray when using
          ! certain data types
          select type(sbarray=>send_buff%data)
          type is (integer(i8))
             ! Synchronous send to avoid eager-buffering the key list as an
             ! unexpected message (FJMPI buffer-pool exhaustion / SIGBUS under
             ! flat MPI); matching recv is pre-posted by the peer.
             call mpi_issend(sbarray, send_buff%size(), mpi_integer8, &
                  dst, 0, neko_comm, send_req, ierr)
          end select
       end if
 
       if (this%neigh(src)) then
          call mpi_wait(recv_req, status, ierr)
          call mpi_get_count(status, mpi_integer8, n_recv, ierr)
 
          do j = 1, n_recv, 2
             if (ghost%element(recv_buff(j))) then
                if (glb_to_loc%get(recv_buff(j), id) .eq. 0) then
                   n_glb_id = int(recv_buff(j + 1 ), 4)
                   call this%ddata%set_local_to_global_edge(id, n_glb_id)
                else
                   call neko_error('Invalid edge id')
                end if
             end if
          end do
       end if
 
       if (this%neigh(dst)) then
          call mpi_wait(send_req, mpi_status_ignore, ierr)
       end if
    end do
 
    deallocate(recv_buff)
    call glb_to_loc%free()
    call send_buff%free()
    call edge_idx%free()
    call non_shared_edges%free()
    call ghost%free()
    call owner%free()
 
  end subroutine mesh_generate_edge_conn
 
  subroutine mesh_generate_facet_numbering(this)
    type(mesh_t), target, intent(inout) :: this
    type(htable_iter_i4t4_t), target :: face_it
    type(htable_iter_i4t2_t), target :: edge_it
    type(tuple4_i4_t), pointer :: face, fd(:)
    type(tuple_i4_t), pointer :: edge, ed(:)
    type(tuple_i4_t) :: facet_data
    type(tuple4_i4_t) :: recv_face
    type(tuple_i4_t) :: recv_edge
    type(stack_i4t4_t) :: face_owner
    type(htable_i4t4_t) :: face_ghost
    type(stack_i4t2_t) :: edge_owner
    type(htable_i4t2_t) :: edge_ghost
    type(stack_i4_t) :: send_buff
    type(mpi_status) :: status
    type(mpi_request) :: send_req, recv_req
    integer, allocatable :: recv_buff(:)
    integer :: non_shared_facets, shared_facets, facet_offset
    integer :: id, glb_nshared, shared_offset, owned_facets
    integer :: i, j, ierr, max_recv, src, dst, n_recv
 
    shared_facets = this%ddata%shared_facet%size()
 
    if (this%gdim .eq. 2) then
       allocate(this%ddata%local_to_global_facet(this%meds))
       call edge_owner%init(this%meds)
       call edge_ghost%init(64, i)
       non_shared_facets = this%hte%num_entries() - shared_facets
    else
       allocate(this%ddata%local_to_global_facet(this%mfcs))
       call face_owner%init(this%mfcs)
       call face_ghost%init(64, i)
       non_shared_facets = this%htf%num_entries() - shared_facets
    end if
 
 
    facet_offset = 0
    call mpi_exscan(non_shared_facets, facet_offset, 1, &
         mpi_integer, mpi_sum, neko_comm, ierr)
    facet_offset = facet_offset + 1
 
    ! Determine ownership of shared facets
    if (this%gdim .eq. 2) then
       call edge_it%init(this%hte)
       do while (edge_it%next())
          call edge_it%data(id)
          edge => edge_it%key()
          if (.not. this%ddata%shared_facet%element(id)) then
             call this%ddata%set_local_to_global_facet(id, facet_offset)
             facet_offset = facet_offset + 1
          else
             select type(fmp => this%facet_map)
             type is(htable_i4t2_t)
                if (fmp%get(edge, facet_data) .eq. 0) then
                   if (facet_data%x(2) .lt. 0) then
                      if (abs(facet_data%x(2)) .lt. (this%offset_el + 1)) then
                         call edge_ghost%set(edge, id)
                      else
                         call edge_owner%push(edge)
                      end if
                   else
                      call neko_error("Invalid edge neigh.")
                   end if
                end if
             end select
          end if
       end do
       owned_facets = edge_owner%size()
    else
       call face_it%init(this%htf)
       do while (face_it%next())
          call face_it%data(id)
          face => face_it%key()
          if (.not. this%ddata%shared_facet%element(id)) then
             call this%ddata%set_local_to_global_facet(id, facet_offset)
             facet_offset = facet_offset + 1
          else
             select type(fmp => this%facet_map)
             type is(htable_i4t4_t)
                if (fmp%get(face, facet_data) .eq. 0) then
                   if (facet_data%x(2) .lt. 0) then
                      if (abs(facet_data%x(2)) .lt. (this%offset_el + 1)) then
                         call face_ghost%set(face, id)
                      else
                         call face_owner%push(face)
                      end if
                   else
                      call neko_error("Invalid face neigh.")
                   end if
                end if
             end select
          end if
       end do
       owned_facets = face_owner%size()
    end if
 
    ! Determine start offset for global numbering of shared facets
    glb_nshared = non_shared_facets
    call mpi_allreduce(mpi_in_place, glb_nshared, 1, &
         mpi_integer, mpi_sum, neko_comm, ierr)
 
    shared_offset = 0
    call mpi_exscan(owned_facets, shared_offset, 1, &
         mpi_integer, mpi_sum, neko_comm, ierr)
    shared_offset = shared_offset + glb_nshared + 1
 
    if (this%gdim .eq. 2) then
 
       if (owned_facets .gt. 32) then
          call send_buff%init(owned_facets)
       else
          call send_buff%init()
       end if
 
       ed => edge_owner%array()
       do i = 1, edge_owner%size()
          if (this%hte%get(ed(i), id) .eq. 0) then
             call this%ddata%set_local_to_global_facet(id, shared_offset)
 
             ! Add new number to send buffer
             ! [edge id1 ... edge idn new_glb_id]
             do j = 1, 2
                call send_buff%push(ed(i)%x(j))
             end do
             call send_buff%push(shared_offset)
 
             shared_offset = shared_offset + 1
          end if
       end do
 
    else
 
       if (owned_facets .gt. 32) then
          call send_buff%init(owned_facets)
       else
          call send_buff%init()
       end if
 
       fd => face_owner%array()
       do i = 1, face_owner%size()
          if (this%htf%get(fd(i), id) .eq. 0) then
             call this%ddata%set_local_to_global_facet(id, shared_offset)
 
             ! Add new number to send buffer
             ! [face id1 ... face idn new_glb_id]
             do j = 1, 4
                call send_buff%push(fd(i)%x(j))
             end do
             call send_buff%push(shared_offset)
 
             shared_offset = shared_offset + 1
          end if
       end do
       nullify(fd)
 
    end if
 
    ! Determine total number of unique facets in the mesh
    ! (This can probably be done in a clever way...)
    this%glb_mfcs = shared_offset - 1
    call mpi_allreduce(mpi_in_place, this%glb_mfcs, 1, &
         mpi_integer, mpi_max, neko_comm, ierr)
 
    !
    ! Update ghosted facets with new global id
    !
 
    call mpi_allreduce(send_buff%size(), max_recv, 1, &
         mpi_integer, mpi_max, neko_comm, ierr)
 
    allocate(recv_buff(max_recv))
 
    do i = 1, size(this%neigh_order)
       src = modulo(pe_rank - this%neigh_order(i) + pe_size, pe_size)
       dst = modulo(pe_rank + this%neigh_order(i), pe_size)
 
       if (this%neigh(src)) then
          call mpi_irecv(recv_buff, max_recv, mpi_integer, &
               src, 0, neko_comm, recv_req, ierr)
       end if
 
       if (this%neigh(dst)) then
          ! Synchronous send to avoid eager-buffered unexpected messages
          ! (FJMPI buffer-pool exhaustion / SIGBUS under flat MPI); the
          ! matching recv is pre-posted at the top of the peer's iteration.
          call mpi_issend(send_buff%array(), send_buff%size(), mpi_integer, &
               dst, 0, neko_comm, send_req, ierr)
       end if
 
       if (this%neigh(src)) then
          call mpi_wait(recv_req, status, ierr)
          call mpi_get_count(status, mpi_integer, n_recv, ierr)
 
          if (this%gdim .eq. 2) then
             do j = 1, n_recv, 3
 
                recv_edge = (/recv_buff(j), recv_buff(j+1)/)
 
                ! Check if the PE has the shared edge
                if (edge_ghost%get(recv_edge, id) .eq. 0) then
                   call this%ddata%set_local_to_global_facet(id, recv_buff(j+2))
                end if
             end do
          else
             do j = 1, n_recv, 5
 
                recv_face = (/recv_buff(j), recv_buff(j+1), &
                     recv_buff(j+2), recv_buff(j+3) /)
 
                ! Check if the PE has the shared face
                if (face_ghost%get(recv_face, id) .eq. 0) then
                   call this%ddata%set_local_to_global_facet(id, recv_buff(j+4))
                end if
             end do
          end if
       end if
 
       if (this%neigh(dst)) then
          call mpi_wait(send_req, mpi_status_ignore, ierr)
       end if
 
    end do
 
    if (this%gdim .eq. 2) then
       call edge_owner%free()
       call edge_ghost%free()
    else
       call face_owner%free()
       call face_ghost%free()
    end if
 
    call send_buff%free()
    deallocate(recv_buff)
 
  end subroutine mesh_generate_facet_numbering
 
 
  subroutine mesh_add_quad(this, el, el_glb, p1, p2, p3, p4)
    class(mesh_t), target, intent(inout) :: this
    integer, value :: el, el_glb
    type(point_t), target, intent(inout) :: p1, p2, p3, p4
    integer :: p(4)
    type(tuple_i4_t) :: e
 
    ! Connectivity invalidated if a new element is added
    this%lconn = .false.
 
    ! Numbering invalidated if a new element is added
    this%lnumr = .false.
 
    call this%add_point(p1, p(1))
    call this%add_point(p2, p(2))
    call this%add_point(p3, p(3))
    call this%add_point(p4, p(4))
 
    select type (ep => this%elements(el)%e)
    type is (quad_t)
       call ep%init(el_glb, &
            this%points(p(1)), this%points(p(2)), &
            this%points(p(3)), this%points(p(4)))
 
 
    class default
       call neko_error('Invalid element type')
    end select
 
  end subroutine mesh_add_quad
 
  subroutine mesh_add_hex(this, el, el_glb, p1, p2, p3, p4, p5, p6, p7, p8)
    class(mesh_t), target, intent(inout) :: this
    integer, value :: el, el_glb
    type(point_t), target, intent(inout) :: p1, p2, p3, p4, p5, p6, p7, p8
    integer :: p(8)
    type(tuple4_i4_t) :: f
    type(tuple_i4_t) :: e
 
    ! Connectivity invalidated if a new element is added
    this%lconn = .false.
 
    ! Numbering invalidated if a new element is added
    this%lnumr = .false.
 
    call this%add_point(p1, p(1))
    call this%add_point(p2, p(2))
    call this%add_point(p3, p(3))
    call this%add_point(p4, p(4))
    call this%add_point(p5, p(5))
    call this%add_point(p6, p(6))
    call this%add_point(p7, p(7))
    call this%add_point(p8, p(8))
 
    ! Global to local mapping
    call this%htel%set(el_glb, el)
 
    select type (ep => this%elements(el)%e)
    type is (hex_t)
       call ep%init(el_glb, &
            this%points(p(1)), this%points(p(2)), &
            this%points(p(3)), this%points(p(4)), &
            this%points(p(5)), this%points(p(6)), &
            this%points(p(7)), this%points(p(8)))
    class default
       call neko_error('Invalid element type')
    end select
 
  end subroutine mesh_add_hex
 
  subroutine mesh_add_point(this, p, idx)
    class(mesh_t), intent(inout) :: this
    type(point_t), intent(inout) :: p
    integer, intent(inout) :: idx
    integer :: tmp
 
    tmp = p%id()
 
    this%max_pts_id = max(this%max_pts_id, tmp)
 
    if (tmp .le. 0) then
       call neko_error("Invalid point id")
    end if
 
    if (this%htp%get(tmp, idx) .gt. 0) then
       this%mpts = this%mpts + 1
       call this%htp%set(tmp, this%mpts)
       this%points(this%mpts) = p
       idx = this%mpts
    end if
 
  end subroutine mesh_add_point
 
  subroutine mesh_add_face(this, f)
    class(mesh_t), intent(inout) :: this
    type(tuple4_i4_t), intent(inout) :: f
    integer :: idx
 
    if (this%htf%get(f, idx) .gt. 0) then
       this%mfcs = this%mfcs + 1
       call this%htf%set(f, this%mfcs)
    end if
 
  end subroutine mesh_add_face
 
  subroutine mesh_add_edge(this, e)
    class(mesh_t), intent(inout) :: this
    type(tuple_i4_t), intent(inout) :: e
    integer :: idx
 
    if (this%hte%get(e, idx) .gt. 0) then
       this%meds = this%meds + 1
       call this%hte%set(e, this%meds)
    end if
 
  end subroutine mesh_add_edge
 
  subroutine mesh_mark_curve_element(this, e, curve_data, curve_type)
    class(mesh_t), intent(inout) :: this
    integer, intent(in) :: e
    real(kind=dp), dimension(5,12), intent(in) :: curve_data
    integer, dimension(12), intent(in) :: curve_type
 
    if (e .gt. this%nelv) then
       call neko_error('Invalid element index')
    end if
    if ((this%gdim .eq. 2 .and. sum(curve_type(5:8)) .gt. 0) ) then
       call neko_error('Invalid curve element')
    end if
    call this%curve%add_element(e, curve_data, curve_type)
 
  end subroutine mesh_mark_curve_element
 
  subroutine mesh_mark_labeled_facet(this, f, e, label)
    class(mesh_t), intent(inout) :: this
    integer, intent(in) :: f
    integer, intent(in) :: e
    integer, intent(in) :: label
 
    if (e .gt. this%nelv) then
       call neko_error('Invalid element index')
    end if
 
    if ((this%gdim .eq. 2 .and. f .gt. 4) .or. &
         (this%gdim .eq. 3 .and. f .gt. 6)) then
       call neko_error('Invalid facet index')
    end if
    call this%labeled_zones(label)%add_facet(f, e)
    this%facet_type(f,e) = -label
 
  end subroutine mesh_mark_labeled_facet
 
  subroutine mesh_mark_periodic_facet(this, f, e, pf, pe, pids)
    class(mesh_t), intent(inout) :: this
    integer, intent(in) :: f
    integer, intent(in) :: e
    integer, intent(in) :: pf
    integer, intent(in) :: pe
    integer, intent(inout) :: pids(4)
    integer, dimension(4) :: org_ids
 
    call this%get_facet_ids(f, e, org_ids)
    call this%periodic%add_periodic_facet(f, e, pf, pe, pids, org_ids)
  end subroutine mesh_mark_periodic_facet
 
  subroutine mesh_get_facet_ids(this, f, e, pids)
    class(mesh_t), intent(inout) :: this
    integer, intent(in) :: f
    integer, intent(in) :: e
    integer, intent(inout) :: pids(4)
    type(point_t), pointer :: pi
    type(tuple4_i4_t) :: t
    type(tuple_i4_t) :: t2
 
    select type(ele => this%elements(e)%e)
    type is(hex_t)
       call ele%facet_order(t,f)
       pids = t%x
    type is(quad_t)
       call ele%facet_order(t2,f)
       pids(1) = t2%x(1)
       pids(2) = t2%x(2)
       pids(3) = 0
       pids(4) = 0
    end select
  end subroutine mesh_get_facet_ids
 
  subroutine mesh_reset_periodic_ids(this)
    class(mesh_t), intent(inout) :: this
    integer :: i,j
    integer :: f
    integer :: e
    integer :: pf
    integer :: pe
    integer :: org_ids(4), pids(4)
    type(point_t), pointer :: pi
    integer, dimension(4, 6) :: face_nodes = reshape([ &
         1,5,7,3, &
         2,6,8,4, &
         1,2,6,5, &
         3,4,8,7, &
         1,2,4,3, &
         5,6,8,7],&
         [4,6])
    integer, dimension(2, 4) :: edge_nodes = reshape([ &
         1,3, &
         2,4, &
         1,2, &
         3,4],&
         [2,4])
 
    do i = 1, this%periodic%size
       e = this%periodic%facet_el(i)%x(2)
       f = this%periodic%facet_el(i)%x(1)
       pe = this%periodic%p_facet_el(i)%x(2)
       pf = this%periodic%p_facet_el(i)%x(1)
       pids = this%periodic%p_ids(i)%x
       call this%get_facet_ids(f, e, pids)
       this%periodic%p_ids(i)%x = pids
    end do
    do i = 1, this%periodic%size
       e = this%periodic%facet_el(i)%x(2)
       f = this%periodic%facet_el(i)%x(1)
       org_ids = this%periodic%org_ids(i)%x
       select type(ele => this%elements(e)%e)
       type is(hex_t)
          do j = 1, 4
             pi => ele%pts(face_nodes(j,f))%p
             call pi%set_id(org_ids(j))
          end do
       type is(quad_t)
          do j = 1, 2
             pi => ele%pts(edge_nodes(j,f))%p
             call pi%set_id(org_ids(j))
          end do
       end select
    end do
  end subroutine mesh_reset_periodic_ids
 
  subroutine mesh_create_periodic_ids(this, f, e, pf, pe)
    class(mesh_t), intent(inout) :: this
    integer, intent(in) :: f
    integer, intent(in) :: e
    integer, intent(in) :: pf
    integer, intent(in) :: pe
    type(point_t), pointer :: pi, pj
    real(kind=dp) :: l(3)
    integer :: i, j, id, p_local_idx, match
    type(tuple4_i4_t) :: ft
    type(tuple_i4_t) :: et
    integer :: envvar_len
    character(len=255) :: tol_str
    real(kind=dp) :: tol
    integer, dimension(4, 6) :: face_nodes = reshape([&
         1,5,7,3,&
         2,6,8,4,&
         1,2,6,5,&
         3,4,8,7,&
         1,2,4,3,&
         5,6,8,7],&
         [4,6])
    integer, dimension(2, 4) :: edge_nodes = reshape([&
         1,3,&
         2,4,&
         1,2,&
         3,4 ],&
         [2,4])
 
    call get_environment_variable("NEKO_PERIODIC_TOL", tol_str, envvar_len)
    if (envvar_len .gt. 0) then
       read(tol_str(1:envvar_len), *) tol
    else
       tol = 1d-7
    end if
 
    select type(ele => this%elements(e)%e)
    type is(hex_t)
       select type(elp => this%elements(pe)%e)
       type is(hex_t)
          l = 0d0
          do i = 1, 4
             l = l + ele%pts(face_nodes(i,f))%p%x(1:3) - &
                  elp%pts(face_nodes(i,pf))%p%x(1:3)
          end do
          l = l/4
          do i = 1, 4
             pi => ele%pts(face_nodes(i,f))%p
             match = 0
             do j = 1, 4
                pj => elp%pts(face_nodes(j,pf))%p
                if (norm2(pi%x(1:3) - pj%x(1:3) - l) .lt. tol) then
                   id = min(pi%id(), pj%id())
                   call pi%set_id(id)
                   call pj%set_id(id)
                   p_local_idx = this%get_local(this%points(id))
                   match = match + 1
                end if
             end do
             if ( match .gt. 1) then
                call neko_error('Multiple matches when creating periodic ids')
             else if (match .eq. 0) then
                call neko_error('Cannot find matching periodic point')
             end if
          end do
       end select
    type is(quad_t)
       select type(elp => this%elements(pe)%e)
       type is(quad_t)
          l = 0d0
          do i = 1, 2
             l = l + ele%pts(edge_nodes(i,f))%p%x(1:3) - &
                  elp%pts(edge_nodes(i,pf))%p%x(1:3)
          end do
          l = l/2
          do i = 1, 2
             pi => ele%pts(edge_nodes(i,f))%p
             do j = 1, 2
                pj => elp%pts(edge_nodes(j,pf))%p
                !whatabout thie tolerance?
                if (norm2(pi%x(1:3) - pj%x(1:3) - l) .lt. tol) then
                   id = min(pi%id(), pj%id())
                   call pi%set_id(id)
                   call pj%set_id(id)
                   p_local_idx = this%get_local(this%points(id))
                end if
             end do
          end do
       end select
    end select
  end subroutine mesh_create_periodic_ids
 
  subroutine mesh_apply_periodic_facet(this, f, e, pf, pe, pids)
    class(mesh_t), intent(inout) :: this
    integer, intent(in) :: f
    integer, intent(in) :: e
    integer, intent(in) :: pf
    integer, intent(in) :: pe
    integer, intent(inout) :: pids(4)
    type(point_t), pointer :: pi
    integer :: i, id, p_local_idx
    type(tuple4_i4_t) :: ft
    type(tuple_i4_t) :: et
    integer, dimension(4, 6) :: face_nodes = reshape([&
         1,5,7,3,&
         2,6,8,4,&
         1,2,6,5,&
         3,4,8,7,&
         1,2,4,3,&
         5,6,8,7],&
         [4,6])
    select type(ele => this%elements(e)%e)
    type is(hex_t)
       do i = 1, 4
          pi => ele%pts(face_nodes(i,f))%p
          call pi%set_id(pids(i))
          call this%add_point(pi, id)
          p_local_idx = this%get_local(this%points(id))
       end do
    end select
 
  end subroutine mesh_apply_periodic_facet
 
  function mesh_get_local_point(this, p) result(local_id)
    class(mesh_t), intent(inout) :: this
    type(point_t), intent(inout) :: p
    integer :: local_id
    integer :: tmp
 
    tmp = p%id()
 
    if (this%htp%get(tmp, local_id) .gt. 0) then
       call neko_error('Invalid global id (local point)')
    end if
 
  end function mesh_get_local_point
 
  function mesh_get_local_edge(this, e) result(local_id)
    class(mesh_t), intent(inout) :: this
    type(tuple_i4_t), intent(inout) :: e
    integer :: local_id
 
    if (this%hte%get(e, local_id) .gt. 0) then
       call neko_error('Invalid global id (local edge)')
    end if
 
  end function mesh_get_local_edge
 
  function mesh_get_local_facet(this, f) result(local_id)
    class(mesh_t), intent(inout) :: this
    type(tuple4_i4_t), intent(inout) :: f
    integer :: local_id
 
    if (this%htf%get(f, local_id) .gt. 0) then
       call neko_error('Invalid global id (local facet)')
    end if
 
  end function mesh_get_local_facet
 
  function mesh_get_global_edge(this, e) result(global_id)
    class(mesh_t), intent(inout) :: this
    type(tuple_i4_t), intent(inout) :: e
    integer :: global_id
 
    global_id = this%get_local(e)
 
    if (this%gdim .eq. 2) then
       if (pe_size .gt. 1) then
          global_id = this%ddata%local_to_global_facet(global_id)
       end if
    else
       if (pe_size .gt. 1) then
          global_id = this%ddata%local_to_global_edge(global_id)
       end if
    end if
 
  end function mesh_get_global_edge
 
  function mesh_get_global_facet(this, f) result(global_id)
    class(mesh_t), intent(inout) :: this
    type(tuple4_i4_t), intent(inout) :: f
    integer :: global_id
 
    global_id = this%get_local_facet(f)
 
    if (pe_size .gt. 1) then
       global_id = this%ddata%local_to_global_facet(global_id)
    end if
 
  end function mesh_get_global_facet
 
 
  function mesh_have_point_glb_idx(this, index) result(local_id)
    class(mesh_t), intent(inout) :: this
    integer, intent(inout) :: index
    integer :: local_id
 
    if (this%htp%get(index, local_id) .eq. 1) then
       local_id = -1
    end if
 
  end function mesh_have_point_glb_idx
 
 
  function mesh_is_shared_point(this, p) result(shared)
    class(mesh_t), intent(inout) :: this
    type(point_t), intent(inout) :: p
    integer :: local_index
    logical shared
 
    local_index = this%get_local(p)
    shared = this%ddata%shared_point%element(local_index)
 
  end function mesh_is_shared_point
 
 
  function mesh_is_shared_edge(this, e) result(shared)
    class(mesh_t), intent(inout) :: this
    type(tuple_i4_t), intent(inout) :: e
    integer :: local_index
    logical shared
    local_index = this%get_local(e)
    if (this%gdim .eq. 2) then
       shared = this%ddata%shared_facet%element(local_index)
    else
       shared = this%ddata%shared_edge%element(local_index)
    end if
  end function mesh_is_shared_edge
 
  function mesh_is_shared_facet(this, f) result(shared)
    class(mesh_t), intent(inout) :: this
    type(tuple4_i4_t), intent(inout) :: f
    integer :: local_index
    logical shared
 
    local_index = this%get_local(f)
    shared = this%ddata%shared_facet%element(local_index)
 
  end function mesh_is_shared_facet
 
  subroutine mesh_check_right_handedness(this)
    class(mesh_t), intent(inout) :: this
    integer :: i
    real(kind=rp) :: v(8)
    type(point_t) :: centroid
    logical :: fail
 
    fail = .false.
 
    if (this%gdim .eq. 3) then
       do i = 1, this%nelv
          v(1) = parallelepiped_signed_volume( &
               this%elements(i)%e%pts(2)%p%x, &
               this%elements(i)%e%pts(3)%p%x, &
               this%elements(i)%e%pts(5)%p%x, &
               this%elements(i)%e%pts(1)%p%x &
               )
 
          v(2) = parallelepiped_signed_volume( &
               this%elements(i)%e%pts(4)%p%x, &
               this%elements(i)%e%pts(1)%p%x, &
               this%elements(i)%e%pts(6)%p%x, &
               this%elements(i)%e%pts(2)%p%x &
               )
 
          v(3) = parallelepiped_signed_volume( &
               this%elements(i)%e%pts(1)%p%x, &
               this%elements(i)%e%pts(4)%p%x, &
               this%elements(i)%e%pts(7)%p%x, &
               this%elements(i)%e%pts(3)%p%x &
               )
 
          v(4) = parallelepiped_signed_volume( &
               this%elements(i)%e%pts(3)%p%x, &
               this%elements(i)%e%pts(2)%p%x, &
               this%elements(i)%e%pts(8)%p%x, &
               this%elements(i)%e%pts(4)%p%x &
               )
 
          v(5) = -parallelepiped_signed_volume( &
               this%elements(i)%e%pts(6)%p%x, &
               this%elements(i)%e%pts(7)%p%x, &
               this%elements(i)%e%pts(1)%p%x, &
               this%elements(i)%e%pts(5)%p%x &
               )
 
          v(6) = -parallelepiped_signed_volume( &
               this%elements(i)%e%pts(8)%p%x, &
               this%elements(i)%e%pts(5)%p%x, &
               this%elements(i)%e%pts(2)%p%x, &
               this%elements(i)%e%pts(6)%p%x &
               )
 
          v(7) = -parallelepiped_signed_volume( &
               this%elements(i)%e%pts(5)%p%x, &
               this%elements(i)%e%pts(8)%p%x, &
               this%elements(i)%e%pts(3)%p%x, &
               this%elements(i)%e%pts(7)%p%x &
               )
 
          v(8) = -parallelepiped_signed_volume( &
               this%elements(i)%e%pts(7)%p%x, &
               this%elements(i)%e%pts(6)%p%x, &
               this%elements(i)%e%pts(4)%p%x, &
               this%elements(i)%e%pts(8)%p%x &
               )
 
          if (v(1) .le. 0.0_rp .or. &
               v(2) .le. 0.0_rp .or. &
               v(3) .le. 0.0_rp .or. &
               v(4) .le. 0.0_rp .or. &
               v(5) .le. 0.0_rp .or. &
               v(6) .le. 0.0_rp .or. &
               v(7) .le. 0.0_rp .or. &
               v(8) .le. 0.0_rp ) then
 
             centroid = this%elements(i)%e%centroid()
 
             write(error_unit, '(A, A, I0, A, 3G12.5)') "*** ERROR ***: ", &
                  "Wrong orientation of mesh element ", i, &
                  " with centroid ", centroid%x
 
             fail = .true.
          end if
       end do
    end if
 
    if (fail) then
       call neko_error("Some mesh elements are not right-handed")
    end if
  end subroutine mesh_check_right_handedness
 
  function parallelepiped_signed_volume(p1, p2, p3, origin) result(v)
    real(kind=dp), dimension(3), intent(in) :: p1, p2, p3, origin
    real(kind=dp) :: v
    real(kind=dp) :: vp1(3), vp2(3), vp3(3), cross(3)
 
    vp1 = p1 - origin
    vp2 = p2 - origin
    vp3 = p3 - origin
 
    cross(1) = vp1(2)*vp2(3) - vp2(3)*vp1(2)
    cross(2) = vp1(3)*vp2(1) - vp1(1)*vp2(3)
    cross(3) = vp1(1)*vp2(2) - vp1(2)*vp2(1)
 
    v = cross(1)*vp3(1) + cross(2)*vp3(2) + cross(3)*vp3(3)
 
  end function parallelepiped_signed_volume
 
  subroutine mesh_subset_by_mask(this, other, mask, lx, ly, lz)
    class(mesh_t), intent(in) :: this
    class(mesh_t), intent(inout) :: other
    type(mask_t), intent(in) :: mask
    integer, intent(in) :: lx, ly, lz
    integer :: i, j, k, nelv, lxyz, gdim, e_m, nidx(4), nelv_c, el_c, el, i_m
    type(point_t) :: p(8)
    integer :: p_id = 1
 
    call other%free()
    lxyz = lx * ly * lz
 
    ! Initialize
    nelv = mask%size()/lxyz
    call other%init(this%gdim, nelv)
 
    ! Assign the elements
    if (other%gdim .eq. 2) then
       call neko_error("Subset mesh not implemented for 2d")
    else if (other%gdim .eq. 3) then
       do el = 1, nelv
          i_m = 1 + lxyz * (el - 1)
          nidx = nonlinear_index(mask%get(i_m), lx, ly, lz)
          e_m = nidx(4) ! Actual element from the original mesh
          ! Retrieve the points form the other mesh.
          ! No need to shift points, since original
          ! mesh has done it.
          ! Had to use a new point id to avoid issues at
          ! periodic boundaries
          ! But this means that all points might be incorrectly
          ! marked as unique.
          do j = 1, 8
             call p(j)%init(this%elements(e_m)%e%pts(j)%p%x, p_id)
             p_id = p_id + 1
          end do
 
          call other%add_element(el, el + other%offset_el, &
               p(1), p(2), p(3), p(4), &
               p(5), p(6), p(7), p(8))
       end do
    else
       if (pe_rank .eq. 0) call neko_error('Invalid dimension of mesh')
    end if
 
    ! Skip searching for boundaries.
 
    ! Update the curvature
    nelv_c = this%curve%size
    if (nelv_c .gt. 0) then
       el_c = 1
       el = 1
       ! 2 pointer scan
       do while (el .le. nelv .and. el_c .le. nelv_c)
 
          i_m = 1 + lxyz * (el - 1)
          nidx = nonlinear_index(mask%get(i_m), lx, ly, lz)
          e_m = nidx(4)
 
          if (e_m .lt. this%curve%curve_el(el_c)%el_idx) then
             el = el + 1
 
          else if (e_m .gt. this%curve%curve_el(el_c)%el_idx) then
             el_c = el_c + 1
 
          else
             call other%mark_curve_element(el, &
                  this%curve%curve_el(el_c)%curve_data, &
                  this%curve%curve_el(el_c)%curve_type)
             el = el + 1
             el_c = el_c + 1
          end if
 
       end do
    end if
 
    ! Finalize
    call other%finalize()
 
    other%is_submesh = .true.
 
  end subroutine mesh_subset_by_mask
 
end module mesh