spongelayer_radial_expon_for_coord Function

  function spongelayer_radial_expon_for_coord(me, coord, nDim, n)  &
    &                           result(res)
    ! --------------------------------------------------------------------------
    !> Spacetime function to evaluate
    type(tem_spongeLayer_radial_type) :: me
    !> Number of arrays to return
    integer, intent(in) :: n
    !> barycentric Ids of an elements.
    !! 1st index goes over number of elements and
    !! 2nd index goes over x,y,z coordinates
    real(kind=rk), intent( in ) :: coord(n,3)
    !> Dimension
    integer, intent(in) :: nDim
    !> return value
    real(kind=rk) :: res(n)
    ! --------------------------------------------------------------------------
    integer :: i
    real(kind=rk) :: sigma, rad, origin(3), outerRadius, vec(3)
    ! --------------------------------------------------------------------------
    origin(:) = me%origin
    outerRadius = me%radius + me%thickness
    vec = 0.0_rk

    do i = 1, n
      vec(1:nDim) = coord(i, 1:nDim) - origin(1:nDim)
      rad = sqrt( vec(1)**2 + vec(2)**2 + vec(3)**2 )

      if ( rad > me%radius .and. rad < outerRadius ) then
        sigma = me%dampFactor                                        &
          &   * ( (rad-me%radius)/me%thickness )**me%dampExponent
      else if (rad > outerRadius) then
        sigma = me%dampFactor
      else
        sigma = 0.0_rk
      end if

      res(i) = sigma

    end do

  end function spongelayer_radial_expon_for_coord