legendre_rst_finder.f90

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module legendre_rst_finder
  use num_types, only: rp, dp, xp
  use neko_config, only : neko_bcknd_device
  use device, only : host_to_device, device_to_host
  use space, only: space_t
  use utils, only: neko_error, neko_warning
  use vector, only: vector_t
  use matrix, only: matrix_t
  use math, only: neko_eps, matinv39
  use tensor_cpu, only: tnsr3d_cpu, tnsr3d_el_cpu
  use device_local_interpolation, only: device_find_rst_legendre
  use, intrinsic :: iso_c_binding, only: c_ptr, c_null_ptr
  use device, only: device_alloc, device_free, device_memcpy, &
       device_get_ptr, glb_cmd_queue
  use device_math, only: device_vlsc3
  implicit none
  private
 
  type, public :: legendre_rst_finder_t
     type(vector_t) :: x_hat, y_hat, z_hat
     type(space_t), pointer :: xh => null()
     integer :: nelv = 0
     real(kind=rp) :: tol = neko_eps
     integer :: max_iter = 10
   contains
     procedure, pass(this) :: init => legendre_rst_finder_init
     procedure, pass(this) :: free => legendre_rst_finder_free
     procedure, pass(this) :: find => legendre_rst_finder_find
  end type legendre_rst_finder_t
 
contains
 
  subroutine legendre_rst_finder_init(this, x, y, z, nelv, Xh, tol, max_iter)
    class(legendre_rst_finder_t), intent(inout) :: this
    type(space_t), target, intent(in) :: Xh
    integer, intent(in) :: nelv
    real(kind=rp), intent(in), dimension(nelv*Xh%lxyz) :: x, y, z
    real(kind=rp), intent(in), optional :: tol
    integer, intent(in), optional :: max_iter
 
    call this%free()
 
    if (present(tol)) then
       if (tol < neko_eps) then
          call neko_error('Tolerance for the Legendre finder is too small')
       end if
       this%tol = tol
 
    else
       this%tol = neko_eps
    end if
    if (present(max_iter)) then
       if (max_iter < 1) then
          call neko_error('Max iterations for the Legendre finder is too small')
       end if
       this%max_iter = max_iter
    else
       this%max_iter = 10
    end if
 
    this%Xh => xh
    this%nelv = nelv
 
    call this%x_hat%init(nelv*xh%lxyz)
    call this%y_hat%init(nelv*xh%lxyz)
    call this%z_hat%init(nelv*xh%lxyz)
 
    call tnsr3d_cpu(this%x_hat%x, xh%lx, x, &
         xh%lx, xh%vinv, &
         xh%vinvt, xh%vinvt, nelv)
    call tnsr3d_cpu(this%y_hat%x, xh%lx, y, &
         xh%lx, xh%vinv, &
         xh%vinvt, xh%vinvt, nelv)
    call tnsr3d_cpu(this%z_hat%x, xh%lx, z, &
         xh%lx, xh%vinv, &
         xh%vinvt, xh%vinvt, nelv)
 
    call this%x_hat%copy_from(host_to_device, .false.)
    call this%y_hat%copy_from(host_to_device, .false.)
    call this%z_hat%copy_from(host_to_device, .false.)
 
  end subroutine legendre_rst_finder_init
 
  subroutine legendre_rst_finder_free(this)
    class(legendre_rst_finder_t), intent(inout) :: this
 
    call this%x_hat%free()
    call this%y_hat%free()
    call this%z_hat%free()
 
    this%Xh => null()
 
  end subroutine legendre_rst_finder_free
 
  subroutine legendre_rst_finder_find(this, rst_local_cand, x_t, y_t, z_t, &
       el_cands, n_point_cand, resx, resy, resz)
    class(legendre_rst_finder_t), intent(inout) :: this
    type(matrix_t), intent(inout) :: rst_local_cand
    type(vector_t), intent(in) :: x_t, y_t, z_t
    integer, intent(in) :: n_point_cand
    integer, intent(inout) :: el_cands(:)
    type(vector_t), intent(inout) :: resx, resy, resz
    type(c_ptr) :: el_cands_d = c_null_ptr
 
    if (n_point_cand .lt. 1) return
 
    rst_local_cand = 0.0_rp
 
    if (neko_bcknd_device .eq. 1) then
       el_cands_d = device_get_ptr(el_cands)
       call find_rst_legendre_device(this, rst_local_cand%x_d, &
            x_t%x_d, y_t%x_d, z_t%x_d, &
            el_cands_d, n_point_cand, &
            resx%x_d, resy%x_d, resz%x_d)
 
    else
       call find_rst_legendre_cpu(this, rst_local_cand%x, x_t%x, y_t%x, z_t%x, &
            el_cands, n_point_cand, &
            resx%x, resy%x, resz%x)
 
    end if
 
  end subroutine legendre_rst_finder_find
 
  subroutine find_rst_legendre_device(this, rst, pt_x, pt_y, pt_z, &
       el_list, n_pts, resx, resy, resz)
    type(legendre_rst_finder_t), intent(inout) :: this
    type(c_ptr), intent(inout) :: rst
    type(c_ptr), intent(in) :: pt_x, pt_y, pt_z
    type(c_ptr), intent(in) :: el_list
    type(c_ptr), intent(inout) :: resx, resy, resz
    integer, intent(in) :: n_pts
    type(vector_t) :: conv_pts
    integer :: iter
    logical :: converged
    real(kind=rp) :: conv_sum
 
    if (n_pts .eq. 0) return
 
    call conv_pts%init(n_pts)
 
    conv_pts = 1.0_rp
 
    iter = 0
    converged = .false.
    !Iterate until found, not heavily optimized
    do while (.not. converged)
       iter = iter + 1
       call device_find_rst_legendre(rst, pt_x, pt_y, pt_z, &
            this%x_hat%x_d, this%y_hat%x_d, this%z_hat%x_d, &
            resx, resy, resz, &
            this%Xh%lx,el_list, n_pts, this%tol, &
            conv_pts%x_d)
       !This can be made more approriate... avoid memcpy at least
       conv_sum = device_vlsc3(conv_pts%x_d,conv_pts%x_d,conv_pts%x_d,n_pts)
       converged = conv_sum .lt. 0.5
       !print *, conv_sum
       if( iter .ge. this%max_iter) converged = .true.
    end do
 
    call conv_pts%free()
  end subroutine find_rst_legendre_device
 
  subroutine find_rst_legendre_cpu(this, rst, pt_x, pt_y, pt_z, &
       el_list, n_pts, resx, resy, resz)
    type(legendre_rst_finder_t), intent(inout) :: this
    integer, intent(in) :: n_pts
    real(kind=rp), intent(inout) :: rst(3, n_pts)
    real(kind=rp), intent(in) :: pt_x(n_pts)
    real(kind=rp), intent(in) :: pt_y(n_pts)
    real(kind=rp), intent(in) :: pt_z(n_pts)
    real(kind=rp), intent(inout) :: resx(n_pts)
    real(kind=rp), intent(inout) :: resy(n_pts)
    real(kind=rp), intent(inout) :: resz(n_pts)
    integer, intent(in) :: el_list(n_pts)
    real(kind=rp) :: r_legendre(1, this%Xh%lx)
    real(kind=rp) :: s_legendre(this%Xh%lx, 1)
    real(kind=rp) :: t_legendre(this%Xh%lx, 1)
    real(kind=rp) :: dr_legendre(1, this%Xh%lx)
    real(kind=rp) :: ds_legendre(this%Xh%lx, 1)
    real(kind=rp) :: dt_legendre(this%Xh%lx, 1)
    real(kind=rp) :: jac(3,3)
    real(kind=xp) :: rst_d(3), jacinv(3,3)
    integer :: conv_pts
    logical :: converged
    integer :: i, j, e, iter, lx
 
 
 
    lx = this%Xh%lx
    if (n_pts .lt. 1) return
 
    rst = 0.0_rp
    ! If performance critical we should do multiple points at the time
    ! Currently we do one point at the time
    do i = 1, n_pts
       iter = 0
       converged = .false.
       do while (.not. converged)
          iter = iter + 1
          ! Compute legendre polynomials in this rst coordinate
          r_legendre(1, 1) = 1.0
          r_legendre(1, 2) = rst(1,i)
          s_legendre(1, 1) = 1.0
          s_legendre(2, 1) = rst(2,i)
          t_legendre(1, 1) = 1.0
          t_legendre(2, 1) = rst(3,i)
          dr_legendre(1, 1) = 0.0
          dr_legendre(1, 2) = 1.0
          ds_legendre(1, 1) = 0.0
          ds_legendre(2, 1) = 1.0
          dt_legendre(1, 1) = 0.0
          dt_legendre(2, 1) = 1.0
          do j = 2, lx-1
             r_legendre(1, j+1) = ((2.0_xp*(j-1.0_xp)+1.0_xp) * rst(1,i) &
                  * r_legendre(1, j) - (j-1.0_xp) &
                  * r_legendre(1, j-1)) / (real(j,xp))
             s_legendre(j+1, 1) = ((2.0_xp*(j-1.0_xp)+1.0_xp) * rst(2,i) &
                  * s_legendre(j, 1) - (j-1.0_xp) &
                  * s_legendre(j-1, 1))/(real(j,xp))
             t_legendre(j+1, 1) = ((2.0_xp*(j-1.0_xp)+1.0_xp) * rst(3,i) &
                  * t_legendre(j, 1) - (j-1.0_xp) &
                  * t_legendre(j-1, 1))/(real(j,xp))
             dr_legendre(1, j+1) = ((j-1.0_xp)+1.0_xp) * r_legendre(1, j) &
                  + rst(1,i)*dr_legendre(1, j)
             ds_legendre(j+1, 1) = ((j-1.0_xp)+1.0_xp) * s_legendre(j, 1) &
                  + rst(2,i)*ds_legendre(j, 1)
             dt_legendre(j+1, 1) = ((j-1.0_xp)+1.0_xp) * t_legendre(j, 1) &
                  + rst(3,i)*dt_legendre(j, 1)
          end do
          e = (el_list(i))*this%Xh%lxyz + 1
          ! Compute the current xyz value
          call tnsr3d_el_cpu(resx(i), 1, this%x_hat%x(e), lx, &
               r_legendre, s_legendre, t_legendre)
          call tnsr3d_el_cpu(resy(i), 1, this%y_hat%x(e), lx, &
               r_legendre, s_legendre, t_legendre)
          call tnsr3d_el_cpu(resz(i), 1, this%z_hat%x(e), lx, &
               r_legendre, s_legendre, t_legendre)
          ! This should in principle be merged into some larger kernel
          ! Compute the jacobian
          call tnsr3d_el_cpu(jac(1,1), 1, this%x_hat%x(e), lx, &
               dr_legendre, s_legendre, t_legendre)
          call tnsr3d_el_cpu(jac(1,2), 1, this%y_hat%x(e), lx, &
               dr_legendre, s_legendre, t_legendre)
          call tnsr3d_el_cpu(jac(1,3), 1, this%z_hat%x(e), lx, &
               dr_legendre, s_legendre, t_legendre)
          call tnsr3d_el_cpu(jac(2,1), 1, this%x_hat%x(e), lx, &
               r_legendre, ds_legendre, t_legendre)
          call tnsr3d_el_cpu(jac(2,2), 1, this%y_hat%x(e), lx, &
               r_legendre, ds_legendre, t_legendre)
          call tnsr3d_el_cpu(jac(2,3), 1, this%z_hat%x(e), lx, &
               r_legendre, ds_legendre, t_legendre)
          call tnsr3d_el_cpu(jac(3,1), 1, this%x_hat%x(e), lx, &
               r_legendre, s_legendre, dt_legendre)
          call tnsr3d_el_cpu(jac(3,2), 1, this%y_hat%x(e), lx, &
               r_legendre, s_legendre, dt_legendre)
          call tnsr3d_el_cpu(jac(3,3), 1, this%z_hat%x(e), lx, &
               r_legendre, s_legendre, dt_legendre)
          resx(i) = pt_x(i) - resx(i)
          resy(i) = pt_y(i) - resy(i)
          resz(i) = pt_z(i) - resz(i)
          ! Jacobian inverse
          jacinv = matinv39(jac(1,1), jac(1,2), jac(1,3),&
               jac(2,1), jac(2,2), jac(2,3),&
               jac(3,1), jac(3,2), jac(3,3))
          ! Update direction
          rst_d(1) = (resx(i)*jacinv(1,1) &
               + jacinv(2,1)*resy(i) &
               + jacinv(3,1)*resz(i))
          rst_d(2) = (resx(i)*jacinv(1,2) &
               + jacinv(2,2)*resy(i) &
               + jacinv(3,2)*resz(i))
          rst_d(3) = (resx(i)*jacinv(1,3) &
               + jacinv(2,3)*resy(i) &
               + jacinv(3,3)*resz(i))
 
          conv_pts = 0
          if (norm2(real(rst_d,xp)) .le. this%tol) then
             conv_pts = 1
          end if
          if (norm2(real(rst_d,xp)) .gt. 4.0) then
             conv_pts = 1
          end if
          ! Update rst coordinates
          rst(1,i) = rst(1,i) + rst_d(1)
          rst(2,i) = rst(2,i) + rst_d(2)
          rst(3,i) = rst(3,i) + rst_d(3)
 
          converged = conv_pts .eq. 1
          if (iter .ge. this%max_iter) converged = .true.
       end do
    end do
  end subroutine find_rst_legendre_cpu
end module legendre_rst_finder