dofmap.f90

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module dofmap
  use neko_config
  use mesh, only : mesh_t
  use space
  use tuple, only : tuple_i4_t, tuple4_i4_t
  use num_types, only : i4, i8, rp
  use utils, only : neko_error, neko_warning
  use fast3d
  use tensor
  use device
  use math
  use element, only : element_t
  use quad, only : quad_t
  use hex, only : hex_t
  use, intrinsic :: iso_c_binding, only : c_ptr, c_null_ptr
  implicit none
  private
 
  type, public :: dofmap_t
     integer(kind=i8), allocatable :: dof(:,:,:,:)
     logical, allocatable :: shared_dof(:,:,:,:)
     real(kind=rp), allocatable :: x(:,:,:,:)       
     real(kind=rp), allocatable :: y(:,:,:,:)       
     real(kind=rp), allocatable :: z(:,:,:,:)       
     integer, private :: ntot
 
     type(mesh_t), pointer :: msh
     type(space_t), pointer :: xh
 
     !
     ! Device pointers (if present)
     !
     type(c_ptr) :: x_d = c_null_ptr
     type(c_ptr) :: y_d = c_null_ptr
     type(c_ptr) :: z_d = c_null_ptr
 
   contains
     procedure, pass(this) :: size => dofmap_size
!     final :: dofmap_free
  end type dofmap_t
 
  interface dofmap_t
     module procedure dofmap_init
  end interface dofmap_t
 
contains
 
  function dofmap_init(msh, Xh) result(this)
    type(mesh_t), target, intent(inout) :: msh
    type(space_t), target, intent(inout) :: xh
    type(dofmap_t) :: this
 
    if ((msh%gdim .eq. 3 .and. xh%lz .eq. 1) .or. &
         (msh%gdim .eq. 2 .and. xh%lz .gt. 1)) then
       call neko_error("Invalid dimension of function space for the given mesh")
    end if
 
 
    call dofmap_free(this)
 
    this%msh => msh
    this%Xh => xh
 
    this%ntot = xh%lx* xh%ly * xh%lz * msh%nelv
 
    !
    ! Assign a unique id for all dofs
    !
 
    allocate(this%dof(xh%lx, xh%ly, xh%lz, msh%nelv))
    allocate(this%shared_dof(xh%lx, xh%ly, xh%lz, msh%nelv))
 
    this%dof = 0
    this%shared_dof = .false.
 
    if (msh%gdim .eq. 3) then
       call dofmap_number_points(this)
       call dofmap_number_edges(this)
       call dofmap_number_faces(this)
    else
       call dofmap_number_points(this)
       call dofmap_number_edges(this)
    end if
 
    !
    ! Generate x,y,z-coordinates for all dofs
    !
 
    allocate(this%x(xh%lx, xh%ly, xh%lz, msh%nelv))
    allocate(this%y(xh%lx, xh%ly, xh%lz, msh%nelv))
    allocate(this%z(xh%lx, xh%ly, xh%lz, msh%nelv))
 
    this%x = 0d0
    this%y = 0d0
    this%z = 0d0
 
    call dofmap_generate_xyz(this)
 
    if (neko_bcknd_device .eq. 1) then
       call device_map(this%x, this%x_d, this%ntot)
       call device_map(this%y, this%y_d, this%ntot)
       call device_map(this%z, this%z_d, this%ntot)
 
       call device_memcpy(this%x, this%x_d, this%ntot, &
                          host_to_device, sync=.false.)
       call device_memcpy(this%y, this%y_d, this%ntot, &
                          host_to_device, sync=.false.)
       call device_memcpy(this%z, this%z_d, this%ntot, &
                          host_to_device, sync=.false.)
    end if
 
  end function dofmap_init
 
  subroutine dofmap_free(this)
    type(dofmap_t), intent(inout) :: this
 
    if (allocated(this%dof)) then
       deallocate(this%dof)
    end if
 
    if (allocated(this%shared_dof)) then
       deallocate(this%shared_dof)
    end if
 
    if (allocated(this%x)) then
       deallocate(this%x)
    end if
 
    if (allocated(this%y)) then
       deallocate(this%y)
    end if
 
    if (allocated(this%z)) then
       deallocate(this%z)
    end if
 
    nullify(this%msh)
    nullify(this%Xh)
 
    !
    ! Cleanup the device (if present)
    !
    if (c_associated(this%x_d)) then
       call device_free(this%x_d)
    end if
 
    if (c_associated(this%y_d)) then
       call device_free(this%y_d)
    end if
 
    if (c_associated(this%z_d)) then
       call device_free(this%z_d)
    end if
 
  end subroutine dofmap_free
 
  pure function dofmap_size(this) result(res)
    class(dofmap_t), intent(in) :: this
    integer :: res
    res = this%ntot
  end function dofmap_size
 
  subroutine dofmap_number_points(this)
    type(dofmap_t), target :: this
    integer :: il, jl, ix, iy, iz
    type(mesh_t), pointer :: msh
    type(space_t), pointer :: Xh
 
    msh => this%msh
    xh => this%Xh
    do il = 1, msh%nelv
       do jl = 1, msh%npts
          ix = mod(jl - 1, 2)     * (xh%lx - 1) + 1
          iy = (mod(jl - 1, 4)/2) * (xh%ly - 1) + 1
          iz = ((jl - 1)/4)       * (xh%lz - 1) + 1
          this%dof(ix, iy, iz, il) = int(msh%elements(il)%e%pts(jl)%p%id(), i8)
          this%shared_dof(ix, iy, iz, il) = &
               msh%is_shared(msh%elements(il)%e%pts(jl)%p)
       end do
    end do
  end subroutine dofmap_number_points
 
  subroutine dofmap_number_edges(this)
    type(dofmap_t), target :: this
    type(mesh_t), pointer :: msh
    type(space_t), pointer :: Xh
    integer :: i,j,k
    integer :: global_id
    type(tuple_i4_t) :: edge
    integer(kind=i8) :: num_dofs_edges(3) ! #dofs for each dir (r, s, t)
    integer(kind=i8) :: edge_id, edge_offset
    logical :: shared_dof
 
    msh => this%msh
    xh => this%Xh
 
    ! Number of dofs on an edge excluding end-points
    num_dofs_edges(1) =  int(xh%lx - 2, i8)
    num_dofs_edges(2) =  int(xh%ly - 2, i8)
    num_dofs_edges(3) =  int(xh%lz - 2, i8)
    edge_offset = int(msh%glb_mpts, i8) + int(1, 4)
 
    do i = 1, msh%nelv
 
       select type(ep=>msh%elements(i)%e)
       type is (hex_t)
          !
          ! Number edges in r-direction
          !
          call ep%edge_id(edge, 1)
          shared_dof = msh%is_shared(edge)
          global_id = msh%get_global(edge)
          edge_id = edge_offset + int((global_id - 1), i8) * num_dofs_edges(1)
          !Reverse order of tranversal if edge is reversed
          if(int(edge%x(1), i8) .ne. this%dof(1,1,1,i)) then
             do concurrent(j = 2:xh%lx - 1)
                k = xh%lx+1-j
                this%dof(k, 1, 1, i) = edge_id + (j-2)
                this%shared_dof(k, 1, 1, i) = shared_dof
             end do
          else
             do concurrent(j = 2:xh%lx - 1)
                k = j
                this%dof(k, 1, 1, i) = edge_id + (j-2)
                this%shared_dof(k, 1, 1, i) = shared_dof
             end do
          end if
          
          call ep%edge_id(edge, 3)
          shared_dof = msh%is_shared(edge)
          global_id = msh%get_global(edge)
          edge_id = edge_offset + int((global_id - 1), i8) * num_dofs_edges(1)
          if(int(edge%x(1), i8) .ne. this%dof(1,1,xh%lz,i)) then
             do concurrent(j = 2:xh%lx - 1)
                k = xh%lx+1-j
                this%dof(k, 1, xh%lz, i) = edge_id + (j-2)
                this%shared_dof(k, 1, xh%lz, i) = shared_dof
             end do
          else
             do concurrent(j = 2:xh%lx - 1)
                k = j
                this%dof(k, 1, xh%lz, i) = edge_id + (j-2)
                this%shared_dof(k, 1, xh%lz, i) = shared_dof
             end do
          end if
             
          call ep%edge_id(edge, 2)
          shared_dof = msh%is_shared(edge)
          global_id = msh%get_global(edge)
          edge_id = edge_offset + int((global_id - 1), i8) * num_dofs_edges(1)
          if(int(edge%x(1), i8) .ne. this%dof(1,xh%ly,1,i)) then
             do concurrent(j = 2:xh%lx - 1)
                k = xh%lx+1-j
                this%dof(k, xh%ly, 1, i) = edge_id + (j-2)
                this%shared_dof(k, xh%ly, 1, i) = shared_dof
             end do
          else
             do concurrent(j = 2:xh%lx - 1)
                k = j
                this%dof(k, xh%ly, 1, i) = edge_id + (j-2)
                this%shared_dof(k, xh%ly, 1, i) = shared_dof
             end do
          end if
          
          call ep%edge_id(edge, 4)
          shared_dof = msh%is_shared(edge)
          global_id = msh%get_global(edge)
          edge_id = edge_offset + int((global_id - 1), i8) * num_dofs_edges(1)
          if(int(edge%x(1), i8) .ne. this%dof(1,xh%ly,xh%lz,i)) then
             do concurrent(j = 2:xh%lx - 1)
                k = xh%lx+1-j
                this%dof(k, xh%ly, xh%lz, i) = edge_id + (j-2)
                this%shared_dof(k, xh%ly, xh%lz, i) = shared_dof
             end do
          else
             do concurrent(j = 2:xh%lx - 1)
                k = j
                this%dof(k, xh%ly, xh%lz, i) = edge_id + (j-2)
                this%shared_dof(k, xh%ly, xh%lz, i) = shared_dof
             end do
          end if
 
 
          !
          ! Number edges in s-direction
          !
          call ep%edge_id(edge, 5)
          shared_dof = msh%is_shared(edge)
          global_id = msh%get_global(edge)
          edge_id = edge_offset + int((global_id - 1), i8) * num_dofs_edges(2)
          if(int(edge%x(1), i8) .ne. this%dof(1,1,1,i)) then
             do concurrent(j = 2:xh%ly - 1)
                k = xh%ly+1-j
                this%dof(1, k, 1, i) = edge_id + (j-2)
                this%shared_dof(1, k, 1, i) = shared_dof
             end do
          else
             do concurrent(j = 2:xh%ly - 1)
                k = j
                this%dof(1, k, 1, i) = edge_id + (j-2)
                this%shared_dof(1, k, 1, i) = shared_dof
             end do
          end if
          
          call ep%edge_id(edge, 7)
          shared_dof = msh%is_shared(edge)
          global_id = msh%get_global(edge)
          edge_id = edge_offset + int((global_id - 1), i8) * num_dofs_edges(2)
          if(int(edge%x(1), i8) .ne. this%dof(1,1,xh%lz,i)) then
             do concurrent(j = 2:xh%ly - 1)
                k = xh%ly+1-j
                this%dof(1, k, xh%lz, i) = edge_id + (j-2)
                this%shared_dof(1, k, xh%lz, i) = shared_dof
             end do
          else
             do concurrent(j = 2:xh%ly - 1)
                k = j
                this%dof(1, k, xh%lz, i) = edge_id + (j-2)
                this%shared_dof(1, k, xh%lz, i) = shared_dof
             end do
          end if
 
          call ep%edge_id(edge, 6)
          shared_dof = msh%is_shared(edge)
          global_id = msh%get_global(edge)
          edge_id = edge_offset + int((global_id - 1), i8) * num_dofs_edges(2)
          if(int(edge%x(1), i8) .ne. this%dof(xh%lx,1,1,i)) then
             do concurrent(j = 2:xh%ly - 1)
                k = xh%ly+1-j
                this%dof(xh%lx, k, 1, i) = edge_id + (j-2)
                this%shared_dof(xh%lx, k, 1, i) = shared_dof
             end do
          else
             do concurrent(j = 2:xh%ly - 1)
                k = j
                this%dof(xh%lx, k, 1, i) = edge_id + (j-2)
                this%shared_dof(xh%lx, k, 1, i) = shared_dof
             end do
          end if
 
          call ep%edge_id(edge, i8)
          shared_dof = msh%is_shared(edge)
          global_id = msh%get_global(edge)
          edge_id = edge_offset + int((global_id - 1), i8) * num_dofs_edges(2)
          if(int(edge%x(1), i8) .ne. this%dof(xh%lx,1,xh%lz,i)) then
             do concurrent(j = 2:xh%ly - 1)
                k = xh%lz+1-j
                this%dof(xh%lx, k, xh%lz, i) = edge_id + (j-2)
                this%shared_dof(xh%lx, k, xh%lz, i) = shared_dof
             end do
          else
             do concurrent(j = 2:xh%ly - 1)
                k = j
                this%dof(xh%lx, k, xh%lz, i) = edge_id + (j-2)
                this%shared_dof(xh%lx, k, xh%lz, i) = shared_dof
             end do
          end if
 
          !
          ! Number edges in t-direction
          !
          call ep%edge_id(edge, 9)
          shared_dof = msh%is_shared(edge)
          global_id = msh%get_global(edge)
          edge_id = edge_offset + int((global_id - 1), i8) * num_dofs_edges(3)
          if(int(edge%x(1), i8) .ne. this%dof(1,1,1,i)) then
             do concurrent(j = 2:xh%lz - 1)
                k = xh%lz+1-j
                this%dof(1, 1, k, i) = edge_id + (j-2)
                this%shared_dof(1, 1, k, i) = shared_dof
             end do
          else
             do concurrent(j = 2:xh%lz - 1)
                k = j
                this%dof(1, 1, k, i) = edge_id + (j-2)
                this%shared_dof(1, 1, k, i) = shared_dof
             end do
          end if
 
          call ep%edge_id(edge, 10)
          shared_dof = msh%is_shared(edge)
          global_id = msh%get_global(edge)
          edge_id = edge_offset + int((global_id - 1), i8) * num_dofs_edges(3)
          if(int(edge%x(1), i8) .ne. this%dof(xh%lx,1,1,i))  then
             do concurrent(j = 2:xh%lz - 1)
                k = xh%lz+1-j
                this%dof(xh%lx, 1, k, i) = edge_id + (j-2)
                this%shared_dof(xh%lx, 1, k, i) = shared_dof
             end do
          else
             do concurrent(j = 2:xh%lz - 1)
                k = j
                this%dof(xh%lx, 1, k, i) = edge_id + (j-2)
                this%shared_dof(xh%lx, 1, k, i) = shared_dof
             end do
          end if
 
          call ep%edge_id(edge, 11)
          shared_dof = msh%is_shared(edge)
          global_id = msh%get_global(edge)
          edge_id = edge_offset + int((global_id - 1), i8) * num_dofs_edges(3)
          if(int(edge%x(1), i8) .ne. this%dof(1,xh%ly,1,i)) then
             do concurrent(j = 2:xh%lz - 1)
                k = xh%lz+1-j
                this%dof(1, xh%ly, k, i) = edge_id + (j-2)
                this%shared_dof(1, xh%ly, k, i) = shared_dof
             end do
          else
             do concurrent(j = 2:xh%lz - 1)
                k = j
                this%dof(1, xh%ly, k, i) = edge_id + (j-2)
                this%shared_dof(1, xh%ly, k, i) = shared_dof
             end do
          end if
          
          call ep%edge_id(edge, 12)
          shared_dof = msh%is_shared(edge)
          global_id = msh%get_global(edge)
          edge_id = edge_offset + int((global_id - 1), i8) * num_dofs_edges(3)
          if(int(edge%x(1), i8) .ne. this%dof(xh%lx,xh%ly,1,i)) then
             do concurrent(j = 2:xh%lz - 1)
                k = xh%lz+1-j
                this%dof(xh%lx, xh%ly, k, i) = edge_id + (j-2)
                this%shared_dof(xh%lx, xh%ly, k, i) = shared_dof
             end do
          else
             do concurrent(j = 2:xh%lz - 1)
                k = j
                this%dof(xh%lx, xh%ly, k, i) = edge_id + (j-2)
                this%shared_dof(xh%lx, xh%ly, k, i) = shared_dof
             end do
          end if
       type is (quad_t)
          !
          ! Number edges in r-direction
          !
          call ep%facet_id(edge, 3)
          shared_dof = msh%is_shared(edge)
          global_id = msh%get_global(edge)
          edge_id = edge_offset + int((global_id - 1), i8) * num_dofs_edges(1)
          !Reverse order of tranversal if edge is reversed
          if(int(edge%x(1), i8) .ne. this%dof(1,1,1,i)) then
             do concurrent(j = 2:xh%lx - 1)
                k = xh%lx+1-j
                this%dof(k, 1, 1, i) = edge_id + (j-2)
                this%shared_dof(k, 1, 1, i) = shared_dof
             end do
          else
             do concurrent(j = 2:xh%lx - 1)
                k = j
                this%dof(k, 1, 1, i) = edge_id + (j-2)
                this%shared_dof(k, 1, 1, i) = shared_dof
             end do
          end if
 
          call ep%facet_id(edge, 4)
          shared_dof = msh%is_shared(edge)
          global_id = msh%get_global(edge)
          edge_id = edge_offset + int((global_id - 1), i8) * num_dofs_edges(1)
          if(int(edge%x(1), i8) .ne. this%dof(1,xh%ly,1,i)) then
             do concurrent(j = 2:xh%lx - 1)
                k = xh%lx+1-j
                this%dof(k, xh%ly, 1, i) = edge_id + (j-2)
                this%shared_dof(k, xh%ly, 1, i) = shared_dof
             end do
          else
             do concurrent(j = 2:xh%lx - 1)
                k = j
                this%dof(k, xh%ly, 1, i) = edge_id + (j-2)
                this%shared_dof(k, xh%ly, 1, i) = shared_dof
             end do
          end if
 
          !
          ! Number edges in s-direction
          !
          call ep%facet_id(edge, 1)
          shared_dof = msh%is_shared(edge)
          global_id = msh%get_global(edge)
          edge_id = edge_offset + int((global_id - 1), i8) * num_dofs_edges(2)
          if(int(edge%x(1), i8) .ne. this%dof(1,1,1,i)) then
             do concurrent(j = 2:xh%ly - 1)
                k = xh%ly+1-j 
                this%dof(1, k, 1, i) = edge_id + (j-2)
                this%shared_dof(1, k, 1, i) = shared_dof
             end do
          else
             do concurrent(j = 2:xh%ly - 1)
                k = j
                this%dof(1, k, 1, i) = edge_id + (j-2)
                this%shared_dof(1, k, 1, i) = shared_dof
             end do
          end if
          
          call ep%facet_id(edge, 2)
          shared_dof = msh%is_shared(edge)
          global_id = msh%get_global(edge)
          edge_id = edge_offset + int((global_id - 1), i8) * num_dofs_edges(2)
          if(int(edge%x(1), i8) .ne. this%dof(xh%lx,1,1,i)) then
             do concurrent(j = 2:xh%ly - 1)
                k = xh%ly+1-j
                this%dof(xh%lx, k, 1, i) = edge_id + (j-2)
                this%shared_dof(xh%lx, k, 1, i) = shared_dof
             end do
          else
             do concurrent(j = 2:xh%ly - 1)
                k = j
                this%dof(xh%lx, k, 1, i) = edge_id + (j-2)
                this%shared_dof(xh%lx, k, 1, i) = shared_dof
             end do
          end if
       end select
 
    end do
  end subroutine dofmap_number_edges
 
  subroutine dofmap_number_faces(this)
    type(dofmap_t), target :: this
    type(mesh_t), pointer :: msh
    type(space_t), pointer :: Xh
    integer :: i,j,k
    integer :: global_id
    type(tuple4_i4_t) :: face, face_order
    integer(kind=i8) :: num_dofs_faces(3) ! #dofs for each dir (r, s, t)
    integer(kind=i8) :: facet_offset, facet_id
    logical :: shared_dof
 
    msh => this%msh
    xh => this%Xh
 
    facet_offset = int(msh%glb_mpts, i8) + &
         int(msh%glb_meds, i8) * int(xh%lx-2, i8) + int(1, i8)
 
    ! Number of dofs on an face excluding end-points
    num_dofs_faces(1) =  int((xh%ly - 2) * (xh%lz - 2), i8)
    num_dofs_faces(2) =  int((xh%lx - 2) * (xh%lz - 2), i8)
    num_dofs_faces(3) =  int((xh%lx - 2) * (xh%ly - 2), i8)
 
    do i = 1, msh%nelv
 
       !
       ! Number facets in r-direction (s, t)-plane
       !
       call msh%elements(i)%e%facet_id(face, 1)
       call msh%elements(i)%e%facet_order(face_order, 1)
       shared_dof = msh%is_shared(face)
       global_id = msh%get_global(face)
       facet_id = facet_offset + int((global_id - 1), i8) * num_dofs_faces(1)
       do concurrent(j = 2:(xh%ly - 1), k = 2:(xh%lz -1))
          this%dof(1, j, k, i) = &
               dofmap_facetidx(face_order,face,facet_id,j,k,xh%lz,xh%ly)
          this%shared_dof(1, j, k, i) = shared_dof
       end do
 
       call msh%elements(i)%e%facet_id(face, 2)
       call msh%elements(i)%e%facet_order(face_order, 2)
       shared_dof = msh%is_shared(face)
       global_id = msh%get_global(face)
       facet_id = facet_offset + int((global_id - 1), i8) * num_dofs_faces(1)
       do concurrent(j = 2:(xh%ly - 1), k = 2:(xh%lz -1))
          this%dof(xh%lx, j, k, i) = &
                  dofmap_facetidx(face_order,face,facet_id,j,k,xh%lz,xh%ly)
          this%shared_dof(xh%lx, j, k, i) = shared_dof
       end do
 
 
       !
       ! Number facets in s-direction (r, t)-plane
       !
       call msh%elements(i)%e%facet_id(face, 3)
       call msh%elements(i)%e%facet_order(face_order, 3)
       shared_dof = msh%is_shared(face)
       global_id = msh%get_global(face)
       facet_id = facet_offset + int((global_id - 1), i8) * num_dofs_faces(2)
       do concurrent(j = 2:(xh%lx - 1), k = 2:(xh%lz - 1))
          this%dof(j, 1, k, i) = &
               dofmap_facetidx(face_order,face,facet_id,k,j,xh%lz,xh%lx)
          this%shared_dof(j, 1, k, i) = shared_dof
       end do
 
       call msh%elements(i)%e%facet_id(face, 4)
       call msh%elements(i)%e%facet_order(face_order, 4)
       shared_dof = msh%is_shared(face)
       global_id = msh%get_global(face)
       facet_id = facet_offset + int((global_id - 1), i8) * num_dofs_faces(2)
       do concurrent(j = 2:(xh%lx - 1), k = 2:(xh%lz - 1))
          this%dof(j, xh%ly, k, i) = &
               dofmap_facetidx(face_order,face,facet_id,k,j,xh%lz,xh%lx)
          this%shared_dof(j, xh%ly, k, i) = shared_dof
       end do
 
 
       !
       ! Number facets in t-direction (r, s)-plane
       !
       call msh%elements(i)%e%facet_id(face, 5)
       call msh%elements(i)%e%facet_order(face_order, 5)
       shared_dof = msh%is_shared(face)
       global_id = msh%get_global(face)
       facet_id = facet_offset + int((global_id - 1), i8) * num_dofs_faces(3)
       do concurrent(j = 2:(xh%lx - 1), k = 2:(xh%ly - 1))
          this%dof(j, k, 1, i) = &
               dofmap_facetidx(face_order,face,facet_id,k,j,xh%ly,xh%lx)
          this%shared_dof(j, k, 1, i) = shared_dof
       end do
 
       call msh%elements(i)%e%facet_id(face, 6)
       call msh%elements(i)%e%facet_order(face_order, 6)
       shared_dof = msh%is_shared(face)
       global_id = msh%get_global(face)
       facet_id = facet_offset + int((global_id - 1), i8) * num_dofs_faces(3)
       do concurrent(j = 2:(xh%lx - 1), k = 2:(xh%ly - 1))
          this%dof(j, k, xh%lz, i) = &
               dofmap_facetidx(face_order,face,facet_id,k,j,xh%lz,xh%lx)
          this%shared_dof(j, k, xh%lz, i) = shared_dof
       end do
    end do
 
  end subroutine dofmap_number_faces
 
  pure function dofmap_facetidx(face_order, face, facet_id, k1, j1, lk1, lj1) result(facet_idx)
    type(tuple4_i4_t), intent(in) :: face_order, face
    integer(kind=i8), intent(in) :: facet_id
    integer(kind=i8) :: facet_idx
    integer, intent(in) :: k1, j1, lk1, lj1
    integer :: k,j,lk,lj
 
    k = k1 - 2
    j = j1 - 2
    lk = lk1 - 2
    lj = lj1 - 2
 
    ! Given the indexes k,j for a GLL point on the inner part of the
    ! face, we assign a unique number to it that depends on the
    ! corner with the lowest id and its neighbour with the lowest
    ! id. The id is assigned in this way to be consistent regardless
    ! of how the faces are rotated or mirrored.
    !
    !   4 -------- 3
    !     |      |      k
    !     |----->|      ^
    !     |----->|      |
    !     |----->|      |
    !   1 -------- 2    0--->j
 
 
    if(face_order%x(1) .eq. face%x(1)) then
       if(face_order%x(2) .lt. face_order%x(4)) then
          facet_idx = facet_id + j + k*lj
       else
          facet_idx = facet_id + j*lk + k
       end if
    else  if(face_order%x(2) .eq. face%x(1)) then
       if(face_order%x(3) .lt. face_order%x(1)) then
          facet_idx = facet_id + lk*(lj-1-j) + k
       else
          facet_idx = facet_id + (lj-1-j) + k*lj
       end if
    else if(face_order%x(3) .eq. face%x(1)) then
       if(face_order%x(4) .lt. face_order%x(2)) then
          facet_idx = facet_id + (lj-1-j) + lj*(lk-1-k)
       else
          facet_idx = facet_id + lk*(lj-1-j) + (lk-1-k)
       end if
    else if(face_order%x(4) .eq. face%x(1)) then
       if(face_order%x(1) .lt. face_order%x(3)) then
          facet_idx = facet_id + lk*j + (lk-1-k)
       else
          facet_idx = facet_id + j + lj*(lk-1-k)
       end if
    end if
 
  end function dofmap_facetidx
 
  subroutine dofmap_generate_xyz(this)
    type(dofmap_t), target :: this
    integer :: i, j, el_idx
    type(mesh_t), pointer :: msh
    type(space_t), pointer :: Xh
    real(kind=rp) :: rp_curve_data(5), curve_data_tot(5,12)
    logical :: midpoint
    integer :: n_edge, curve_type(12)
 
    msh => this%msh
    xh => this%Xh
 
    if (msh%gdim .eq. 3) then
       n_edge = 12
    else
       n_edge = 4
    end if
 
    do i = 1, msh%nelv
       call dofmap_xyzlin(xh, msh, msh%elements(i)%e, this%x(1,1,1,i), &
                          this%y(1,1,1,i), this%z(1,1,1,i))
    end do
    do i =1, msh%curve%size
       midpoint = .false.
       el_idx = msh%curve%curve_el(i)%el_idx
       curve_type = msh%curve%curve_el(i)%curve_type
       curve_data_tot = msh%curve%curve_el(i)%curve_data
       do j = 1, n_edge
          if (curve_type(j) .eq. 4) then
             midpoint = .true.
          end if
       end do
       if (midpoint .and. xh%lx .gt. 2) then
          call dofmap_xyzquad(xh, msh, msh%elements(el_idx)%e, &
                              this%x(1,1,1,el_idx), this%y(1,1,1,el_idx),&
                              this%z(1,1,1,el_idx),curve_type, curve_data_tot)
       end if
    end do
    do i =1, msh%curve%size
       el_idx = msh%curve%curve_el(i)%el_idx
       do j = 1, 8
          if (msh%curve%curve_el(i)%curve_type(j) .eq. 3) then
             rp_curve_data = msh%curve%curve_el(i)%curve_data(1:5,j)
             call arc_surface(j, rp_curve_data, &
                              this%x(1,1,1,el_idx), &
                              this%y(1,1,1,el_idx), &
                              this%z(1,1,1, el_idx), &
                              xh, msh%elements(el_idx)%e, msh%gdim)
          end if
       end do
    end do
    if (associated(msh%apply_deform)) then
       call msh%apply_deform(this%x, this%y, this%z, xh%lx, xh%ly, xh%lz)
    end if
  end subroutine dofmap_generate_xyz
 
  subroutine dofmap_xyzlin(Xh, msh, element, x, y, z)
    type(mesh_t), pointer, intent(in) :: msh
    type(space_t), intent(in) :: Xh
    class(element_t), intent(in) :: element
    real(kind=rp), intent(inout) :: x(xh%lx, xh%ly, xh%lz), &
                                    y(xh%lx, xh%ly, xh%lz), &
                                    z(xh%lx, xh%ly, xh%lz)
    real(kind=rp) :: xyzb(2,2,2,3), zgml(xh%lx, 3)
    real(kind=rp) :: jx(xh%lx*2)
    real(kind=rp) :: jxt(xh%lx*2), jyt(xh%lx*2), jzt(xh%lx*2)
    real(kind=rp) :: w(4*xh%lx**3), tmp(xh%lx, xh%lx, xh%lx)
    real(kind=rp), dimension(2), parameter :: zlin = (/-1d0, 1d0/)
 
    integer :: j, k
 
    zgml = 0d0
    xyzb = 0d0
 
    w = 0d0
    call copy(zgml(1,1), xh%zg(1,1), xh%lx)
    call copy(zgml(1,2), xh%zg(1,2), xh%ly)
    if (msh%gdim .gt. 2) then
       call copy(zgml(1,3), xh%zg(1,3), xh%lz)
    end if
 
    k = 1
    do j = 1, xh%lx
       call fd_weights_full(zgml(j,1), zlin, 1, 0, jxt(k))
       call fd_weights_full(zgml(j,2), zlin, 1, 0, jyt(k))
       if (msh%gdim .gt. 2) then
          call fd_weights_full(zgml(j,3), zlin, 1, 0, jzt(k))
       end if
       k = k + 2
    end do
    call trsp(jx, xh%lx, jxt, 2)
 
    if (msh%gdim .eq. 2) then
       jzt = 1d0
    end if
 
    if (msh%gdim .gt. 2) then
       do concurrent(j = 1:msh%gdim)
          xyzb(1,1,1,j) = element%pts(1)%p%x(j)
          xyzb(2,1,1,j) = element%pts(2)%p%x(j)
          xyzb(1,2,1,j) = element%pts(3)%p%x(j)
          xyzb(2,2,1,j) = element%pts(4)%p%x(j)
          
          xyzb(1,1,2,j) = element%pts(5)%p%x(j)
          xyzb(2,1,2,j) = element%pts(6)%p%x(j)
          xyzb(1,2,2,j) = element%pts(7)%p%x(j)
          xyzb(2,2,2,j) = element%pts(8)%p%x(j)
       end do
    else
       do concurrent(j = 1:msh%gdim)
          xyzb(1,1,1,j) = element%pts(1)%p%x(j)
          xyzb(2,1,1,j) = element%pts(2)%p%x(j)
          xyzb(1,2,1,j) = element%pts(3)%p%x(j)
          xyzb(2,2,1,j) = element%pts(4)%p%x(j)
       end do
    end if
    if (msh%gdim .eq. 3) then
       call tensr3(tmp, xh%lx, xyzb(1,1,1,1), 2, jx, jyt, jzt, w)
       call copy(x, tmp, xh%lx*xh%ly*xh%lz)
       call tensr3(tmp, xh%ly, xyzb(1,1,1,2), 2, jx, jyt, jzt, w)
       call copy(y, tmp, xh%lx*xh%ly*xh%lz)
       call tensr3(tmp, xh%lz, xyzb(1,1,1,3), 2, jx, jyt, jzt, w)
       call copy(z, tmp, xh%lx*xh%ly*xh%lz)
    else
       call tnsr2d_el(tmp, xh%lx, xyzb(1,1,1,1), 2, jx, jyt)
       call copy(x, tmp, xh%lx*xh%ly*xh%lz)
       call tnsr2d_el(tmp, xh%ly, xyzb(1,1,1,2), 2, jx, jyt)
       call copy(y, tmp, xh%lx*xh%ly*xh%lz)
    end if
  end subroutine dofmap_xyzlin
 
  subroutine dofmap_xyzquad(Xh, msh, element, x, y, z, curve_type, curve_data)
    type(mesh_t), pointer, intent(in) :: msh
    type(space_t), intent(in) :: Xh
    class(element_t), intent(in) :: element
    real(kind=rp), dimension(Xh%lx, Xh%ly, Xh%lz), intent(inout) :: x, y, z
    integer :: curve_type(12), eindx(12)
    real(kind=rp) :: curve_data(5,12), x3(3,3,3), y3(3,3,3), z3(3,3,3)
    type(space_t), target :: xh3
    real(kind=rp), dimension(3), parameter :: zquad = (/-1d0, 0d0,1d0/)
    real(kind=rp) :: zg(3)
    real(kind=rp), dimension(Xh%lx,Xh%lx,Xh%lx) :: tmp
    real(kind=rp) :: jx(xh%lx*3)
    real(kind=rp) :: jxt(xh%lx*3), jyt(xh%lx*3), jzt(xh%lx*3)
    real(kind=rp) :: w(4*xh%lxyz,2)
    integer :: j, k, n_edges
    eindx = (/2 ,  6 ,  8 ,  4, &
              20 , 24 , 26 , 22, &
              10 , 12 , 18 , 16 /)
 
    w = 0d0
    if (msh%gdim .eq. 3) then
       n_edges = 12
       call xh3%init(gll, 3, 3, 3)
    else
       n_edges = 4
       call xh3%init(gll, 3, 3)
    end if
    call dofmap_xyzlin(xh3, msh, element, x3, y3, z3)
 
    do k = 1, n_edges
       if (curve_type(k) .eq. 4) then
          x3(eindx(k),1,1) = curve_data(1,k)
          y3(eindx(k),1,1) = curve_data(2,k)
          z3(eindx(k),1,1) = curve_data(3,k)
       end if
    end do
    zg(1) = -1
    zg(2) =  0
    zg(3) =  1
    if (msh%gdim .eq. 3) then
       call gh_face_extend_3d(x3,zg,3,2,w(1,1),w(1,2)) ! 2 --> edge extend
       call gh_face_extend_3d(y3,zg,3,2,w(1,1),w(1,2))
       call gh_face_extend_3d(z3,zg,3,2,w(1,1),w(1,2))
    else
       call neko_warning(' m deformation not supported for 2d yet')
       call gh_face_extend_2d(x3,zg,3,2,w(1,1),w(1,2)) ! 2 --> edge extend
       call gh_face_extend_2d(y3,zg,3,2,w(1,1),w(1,2))
    end if
    k =1
    do j = 1, xh%lx
       call fd_weights_full(xh%zg(j,1),zquad,2,0,jxt(k))
       call fd_weights_full(xh%zg(j,2),zquad,2,0,jyt(k))
       if (msh%gdim .gt. 2) then
          call fd_weights_full(xh%zg(j,3),zquad,2,0,jzt(k))
       end if
       k = k + 3
    end do
    call trsp(jx, xh%lx, jxt, 3)
    if (msh%gdim .eq. 3) then
       call tensr3(tmp, xh%lx, x3, 3, jx, jyt, jzt, w)
       call copy(x, tmp, xh%lx*xh%ly*xh%lz)
       call tensr3(tmp, xh%ly, y3, 3, jx, jyt, jzt, w)
       call copy(y, tmp, xh%lx*xh%ly*xh%lz)
       call tensr3(tmp, xh%lz, z3, 3, jx, jyt, jzt, w)
       call copy(z, tmp, xh%lx*xh%ly*xh%lz)
    else
       call tnsr2d_el(tmp, xh%lx, x3, 3, jx, jyt)
       call copy(x, tmp, xh%lx*xh%ly*xh%lz)
       call tnsr2d_el(tmp, xh%ly, y3, 3, jx, jyt)
       call copy(y, tmp, xh%lx*xh%ly*xh%lz)
    end if
 
    call xh3%free()
  end subroutine dofmap_xyzquad
 
  subroutine gh_face_extend_3d(x, zg, n, gh_type, e, v)
    integer, intent(in) :: n
    real(kind=rp), intent(inout) ::  x(n, n, n)
    real(kind=rp), intent(in) ::  zg(n)
    real(kind=rp), intent(inout) ::  e(n, n, n)
    real(kind=rp), intent(inout) ::  v(n, n, n)
    integer :: gh_type, ntot, kk, jj, ii, k, j, i
    real(kind=rp) :: si, sj, sk, hi, hj, hk
 
    !
    !  Build vertex interpolant
    !
    ntot = n**3
    do concurrent(i = 1:ntot)
       v(i,1,1) = 0.0_rp
    end do
 
    do concurrent(i = 1:n, j = 1:n, k = 1:n, ii = 1:n, jj = 1:n:n-1, kk = 1:n:n-1)
       si       = 0.5*((n-ii)*(1-zg(i))+(ii-1)*(1+zg(i)))/(n-1)
       sj       = 0.5*((n-jj)*(1-zg(j))+(jj-1)*(1+zg(j)))/(n-1)
       sk       = 0.5*((n-kk)*(1-zg(k))+(kk-1)*(1+zg(k)))/(n-1)
       v(i,j,k) = v(i,j,k) + si*sj*sk*x(ii,jj,kk)
    end do
 
    if (gh_type .eq. 1) then
       do concurrent(i = 1:ntot)
          x(i,1,1) = v(i,1,1)
       end do
       return
    end if
    !
    !
    !  Extend 12 edges
    do concurrent(i = 1:ntot)
       e(i,1,1) = 0.0_rp
    end do
    !
    !  x-edges
    !
    do concurrent(i = 1:n, j = 1:n, k = 1:n, jj=1:n:n-1, kk = 1:n:n-1)
       hj       = 0.5*((n-jj)*(1-zg(j))+(jj-1)*(1+zg(j)))/(n-1)
       hk       = 0.5*((n-kk)*(1-zg(k))+(kk-1)*(1+zg(k)))/(n-1)
       e(i,j,k) = e(i,j,k) + hj*hk*(x(i,jj,kk)-v(i,jj,kk))
    end do
    !
    !  y-edges
    !
    do concurrent(i = 1:n, j = 1:n, k = 1:n, ii = 1:n:n-1, kk = 1:n:n-1)
       hi       = 0.5*((n-ii)*(1-zg(i))+(ii-1)*(1+zg(i)))/(n-1)
       hk       = 0.5*((n-kk)*(1-zg(k))+(kk-1)*(1+zg(k)))/(n-1)
       e(i,j,k) = e(i,j,k) + hi*hk*(x(ii,j,kk)-v(ii,j,kk))
    end do
    !
    !  z-edges
    !
    do concurrent(i = 1:n, j = 1:n, k = 1:n, ii = 1:n:n-1, jj = 1:n:n-1)
       hi       = 0.5*((n-ii)*(1-zg(i))+(ii-1)*(1+zg(i)))/(n-1)
       hj       = 0.5*((n-jj)*(1-zg(j))+(jj-1)*(1+zg(j)))/(n-1)
       e(i,j,k) = e(i,j,k) + hi*hj*(x(ii,jj,k)-v(ii,jj,k))
    end do
 
    do concurrent(i = 1:ntot)
       e(i,1,1) = e(i,1,1) + v(i,1,1)
    end do
 
    if (gh_type .eq. 2) then
       do concurrent(i = 1:ntot)
          x(i,1,1) = e(i,1,1)
       end do
       return
    end if
    !
    !  Extend faces
    !
    do concurrent(i = 1:ntot)
       v(i,1,1) = 0.0_rp
    end do
    !
    !  x-edges
    !
    do concurrent(i = 1:n, j = 1:n, k = 1:n, ii = 1:n:n-1)
       hi       = 0.5*((n-ii)*(1-zg(i))+(ii-1)*(1+zg(i)))/(n-1)
       v(i,j,k) = v(i,j,k) + hi*(x(ii,j,k)-e(ii,j,k))
    end do
 
    !
    ! y-edges
    !
    do concurrent(i = 1:n, j = 1:n, k = 1:n, jj = 1:n:n-1)
       hj       = 0.5*((n-jj)*(1-zg(j))+(jj-1)*(1+zg(j)))/(n-1)
       v(i,j,k) = v(i,j,k) + hj*(x(i,jj,k)-e(i,jj,k))
    end do
 
    !
    !  z-edges
    !
    do concurrent(i = 1:n, j = 1:n, k = 1:n, kk = 1:n:n-1)
       hk       = 0.5*((n-kk)*(1-zg(k))+(kk-1)*(1+zg(k)))/(n-1)
       v(i,j,k) = v(i,j,k) + hk*(x(i,j,kk)-e(i,j,kk))
    end do
 
    do concurrent(i = 1:ntot)
       v(i,1,1) = v(i,1,1) + e(i,1,1)
       x(i,1,1) = v(i,1,1)
    end do
 
  end subroutine gh_face_extend_3d
 
  subroutine gh_face_extend_2d(x, zg, n, gh_type, e, v)
    integer, intent(in) :: n
    real(kind=rp), intent(inout) :: x(n, n)
    real(kind=rp), intent(in) :: zg(n)
    real(kind=rp), intent(inout) :: e(n, n)
    real(kind=rp), intent(inout) :: v(n, n)
    integer, intent(in) :: gh_type
    integer :: i,j , jj, ii, ntot
    real(kind=rp) :: si, sj, hi, hj
 
    !Build vertex interpolant
 
    ntot=n*n
    call rzero(v,ntot)
    do jj = 1, n, n-1
       do ii = 1, n, n-1
          do j = 1, n
             do i = 1, n
                si     = 0.5*((n-ii)*(1-zg(i))+(ii-1)*(1+zg(i)))/(n-1)
                sj     = 0.5*((n-jj)*(1-zg(j))+(jj-1)*(1+zg(j)))/(n-1)
                v(i,j) = v(i,j) + si*sj*x(ii,jj)
             end do
          end do
       end do
    end do
    if (gh_type .eq. 1) then
       call copy(x,v,ntot)
       return
    end if
 
    !Extend 4 edges
    call rzero(e,ntot)
 
    !x-edges
 
    do jj = 1, n, n-1
       do j = 1, n
          do i = 1, n
             hj     = 0.5*((n-jj)*(1-zg(j))+(jj-1)*(1+zg(j)))/(n-1)
             e(i,j) = e(i,j) + hj*(x(i,jj)-v(i,jj))
          end do
       end do
    end do
 
    !y-edges
 
    do ii = 1, n, n-1
       do j = 1, n
          do i = 1, n
             hi     = 0.5*((n-ii)*(1-zg(i))+(ii-1)*(1+zg(i)))/(n-1)
             e(i,j) = e(i,j) + hi*(x(ii,j)-v(ii,j))
          end do
       end do
    end do
 
    call add3(x, e, v, ntot)
 
  end subroutine gh_face_extend_2d
 
 
 
  subroutine arc_surface(isid, curve_data, x, y, z, Xh, element, gdim)
    integer, intent(in) :: isid, gdim
    type(space_t), intent(in) :: Xh
    class(element_t) :: element
    real(kind=rp), dimension(5), intent(in) :: curve_data
    real(kind=rp), dimension(Xh%lx, Xh%ly, Xh%lz), intent(inout) :: x, y, z
    real(kind=rp) :: pt1x, pt1y, pt2x, pt2y, pt12x, pt12y
    real(kind=rp) :: radius, dtheta, r, xys
    real(kind=rp) :: theta0, xcenn, ycenn, h(xh%lx, 3, 2)
    real(kind=rp) :: xcrved(xh%lx), ycrved(xh%lx), xs, ys
    integer :: isid1, ixt, iyt, izt, ix, itmp
    integer(i4),  dimension(6), parameter :: fcyc_to_sym = (/3, 2, 4, 1, 5, 6/) ! cyclic to symmetric face mapping
    integer(i4),  dimension(12), parameter :: ecyc_to_sym = (/1, 6, 2, 5, 3, 8, &
    & 4, 7, 9, 10, 12, 11/) ! cyclic to symmetric edge mapping
    integer, parameter, dimension(2, 12) :: edge_nodes = reshape((/1, 2, 3, 4, 5, 6, &
    & 7, 8, 1, 3, 2, 4, 5, 7, 6, 8, 1, 5, 2, 6, 3, 7, 4, 8/), (/2,12/)) ! symmetric edge to vertex mapping
    ! copy from hex as this has private attribute there
 
    ! this subroutine is a mess of symmetric and cyclic edge/face numberring and
    ! cannot be cleaned without changing an input format (isid seems to be
    ! a cyclic edge number)
    ! following according to cyclic edge numbering and orientation
    itmp = ecyc_to_sym(isid)
    select case(isid)
    case(1:2,5:6)
       pt1x = element%pts(edge_nodes(1,itmp))%p%x(1)
       pt1y = element%pts(edge_nodes(1,itmp))%p%x(2)
       pt2x = element%pts(edge_nodes(2,itmp))%p%x(1)
       pt2y = element%pts(edge_nodes(2,itmp))%p%x(2)
    case(3:4,7:8)
       pt1x = element%pts(edge_nodes(2,itmp))%p%x(1)
       pt1y = element%pts(edge_nodes(2,itmp))%p%x(2)
       pt2x = element%pts(edge_nodes(1,itmp))%p%x(1)
       pt2y = element%pts(edge_nodes(1,itmp))%p%x(2)
    end select
    ! find slope of perpendicular
    radius = curve_data(1)
    xs = pt2y-pt1y
    ys = pt1x-pt2x
    ! make length radius
    xys = sqrt(xs**2 + ys**2)
    ! sanity check
    if (abs(2.0 * radius) <= xys * 1.00001) &
    & call neko_error('Radius to small for arced element surface')
    ! find center
    dtheta = abs(asin(0.5*xys/radius))
    pt12x  = (pt1x + pt2x)/2.0
    pt12y  = (pt1y + pt2y)/2.0
    xcenn  = pt12x - xs/xys * radius*cos(dtheta)
    ycenn  = pt12y - ys/xys * radius*cos(dtheta)
    theta0 = atan2((pt12y-ycenn), (pt12x-xcenn))
!   compute perturbation of geometry
    isid1 = mod(isid+4-1, 4)+1
    call compute_h(h, xh%zg, gdim, xh%lx)
    if (radius < 0.0) dtheta = -dtheta
    do ix=1,xh%lx
       ixt=ix
       if (isid1.gt.2) ixt=xh%lx+1-ix
       r=xh%zg(ix,1)
       xcrved(ixt) = xcenn + abs(radius) * cos(theta0 + r*dtheta) &
                           - ( h(ix,1,1)*pt1x + h(ix,1,2)*pt2x )
       ycrved(ixt) = ycenn + abs(radius) * sin(theta0 + r*dtheta) &
                           - ( h(ix,1,1)*pt1y + h(ix,1,2)*pt2y )
    end do
!   points all set, add perturbation to current mesh.
!   LEGACY WARNING
!   I dont want to dive in this again, Martin Karp 2/3 - 2021
    isid1 = fcyc_to_sym(isid1)
    izt = (isid-1)/4+1
    iyt = isid1-2
    ixt = isid1
    if (isid1 .le. 2) then
       call addtnsr(x, h(1,1,ixt), xcrved, h(1,3,izt) &
                   ,xh%lx, xh%ly, xh%lz)
       call addtnsr(y, h(1,1,ixt), ycrved, h(1,3,izt) &
                   ,xh%lx, xh%ly, xh%lz)
    else
       call addtnsr(x, xcrved, h(1,2,iyt), h(1,3,izt) &
                   ,xh%lx, xh%ly, xh%lz)
       call addtnsr(y, ycrved, h(1,2,iyt), h(1,3,izt) &
                   ,xh%lx, xh%ly, xh%lz)
    end if
  end subroutine arc_surface
 
  subroutine compute_h(h, zgml, gdim, lx)
    integer, intent(in) :: lx, gdim
    real(kind=rp), intent(inout) ::  h(lx, 3, 2)
    real(kind=rp), intent(in) :: zgml(lx, 3)
    integer :: ix, iy, iz
 
    do ix = 1, lx
       h(ix,1,1) = (1.0_rp - zgml(ix, 1)) * 0.5_rp
       h(ix,1,2) = (1.0_rp + zgml(ix, 1)) * 0.5_rp
    end do
 
    do iy = 1, lx
       h(iy,2,1) = (1.0_rp - zgml(iy, 2)) * 0.5_rp
       h(iy,2,2) = (1.0_rp + zgml(iy, 2)) * 0.5_rp
    end do
 
    if (gdim .eq. 3) then
       do iz = 1, lx
          h(iz,3,1) = (1.0_rp - zgml(iz, 3)) * 0.5_rp
          h(iz,3,2) = (1.0_rp + zgml(iz, 3)) * 0.5_rp
       end do
    else
       call rone(h(1,3,1), lx)
       call rone(h(1,3,2), lx)
    end if
 
  end subroutine compute_h
 
end module dofmap