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subroutine da_solve_poissoneqn_fst(grid, xbx, del2b, b) 1,12
!--------------------------------------------------------------------------
! Purpose: Solve Del**2 B = A for B with zero field boundary conditions.
!
! Method: 1) Compute spectral del2b using double forward FST.
! 2) Calculate spectral b.
! 3) Reform gridpt. b using inverse double FST.
! Note no mean removed (would make b.ne.0 at boundaries) so
! arbitrary constant still present.
!--------------------------------------------------------------------------
implicit none
type (domain), intent(inout) :: grid
type (xbx_type), intent(in) :: xbx ! Header & non-gridded vars.
real, intent(in) :: del2b(ims:ime,jms:jme,kms:kme) ! Del**2 B.
real, intent(out) :: b(ims:ime,jms:jme,kms:kme) ! B.
integer :: vector_inc ! Increment between FST data.
integer :: vector_jump ! Jump between start of vectors.
integer :: vector_size ! Of form 2**p 3**q 5**r for FSTs.
integer :: num_vectors ! Number of FSTs to perform.
integer :: work_area ! Dimension for FST routine.
integer :: idim ! Size of 1st dimension for FST.
integer :: jdim ! Size of 2nd dimension for FST.
integer :: i, j, k, n, ij ! loop counter
real, allocatable :: work_1d(:) ! FFT work array
if (trace_use) call da_trace_entry
("da_solve_poissoneqn_fst")
!------------------------------------------------------------------------------
! [1.0] Initialise:
!------------------------------------------------------------------------------
! Calculate work space needed.
n = max(xbx%fft_ix*(grid%xp%jtex-grid%xp%jtsx+1), &
xbx%fft_jy*(grid%xp%itey-grid%xp%itsy+1+xbx%pad_num))
! Allocate work arrays.
allocate(work_1d(1:n))
! Copy del2b for transpose.
grid%xp%v1z(its:ite,jts:jte,kts:kte) = del2b(its:ite,jts:jte,kts:kte)
if (ite == ide) grid%xp%v1z(ite,jts:jte,kts:kte) = 0.0
if (jte == jde) grid%xp%v1z(its:ite,jte,kts:kte) = 0.0
!---------------------------------------------------------------------------
! [2.0] Perform forward FFT in x direction:
!---------------------------------------------------------------------------
! [2.1] Apply (i',j',k -> i,j',k') transpose (v1z -> v1x).
call da_transpose_z2x (grid)
! [2.2] Set up FFT parameters:
idim = xbx%fft_ix
jdim = grid%xp%jtex-grid%xp%jtsx+1
vector_inc = 1
vector_jump = idim
vector_size = idim - 1
num_vectors = jdim
work_area = (vector_size+1)*num_vectors
! [2.3] Perform forward FFT:
do k = grid%xp%ktsx, grid%xp%ktex
ij = 0
do j=grid%xp%jtsx, grid%xp%jtex
do i=ids, ide
ij=ij+1
work_1d(ij) = grid%xp%v1x(i,j,k)
end do
do i=1, xbx%fft_pad_i
ij=ij+1
work_1d(ij) = 0.0
end do
end do
call fft661(Forward_FFT, vector_inc, vector_jump, &
num_vectors, vector_size, &
xbx % fft_factors_x, xbx % trig_functs_x, &
work_1d(1), work_area)
ij = 0
do j=grid%xp%jtsx, grid%xp%jtex
do i=ids, ide
ij=ij+1
grid%xp%v1x(i,j,k) = work_1d(ij)
end do
do n=1, xbx%fft_pad_i
i=(n-1)*xbx%pad_inc + 1
ij=ij+1
grid%xp%v2x(i,j,k) = work_1d(ij)
end do
end do
end do
!---------------------------------------------------------------------------
! [3.0] For each k-level, perform forward FFT in y direction, apply spectral
! Poisson equation, and then perform inverse FFT in y direction:
!---------------------------------------------------------------------------
! [3.1] Apply (i,j',k' -> i',j,k') transpose (v1x -> v1y).
call da_transpose_x2y (grid)
call da_transpose_x2y_v2 (grid)
! [3.2] Set up FFT parameters:
idim = grid%xp%itey - grid%xp%itsy + 1 + xbx%pad_num
jdim = xbx%fft_jy
vector_inc = idim
vector_jump = 1
vector_size = jdim - 1
num_vectors = idim
work_area = (vector_size+1)*num_vectors
! [2.3] Perform forward FFT in j:
do k = grid%xp%ktsy, grid%xp%ktey
ij = 0
do j=jds,jde
do i=grid%xp%itsy, grid%xp%itey
ij=ij+1
work_1d(ij) = grid%xp%v1y(i,j,k)
end do
do n=1, xbx%pad_num
i=xbx%pad_loc(n)
ij=ij+1
work_1d(ij) = grid%xp%v2y(i,j,k)
end do
end do
do j=1, xbx%fft_pad_j
do i=grid%xp%itsy, grid%xp%itey+xbx%pad_num
ij=ij+1
work_1d(ij) = 0.0
end do
end do
call fft661(Forward_FFT, vector_inc, vector_jump, &
num_vectors, vector_size, &
xbx % fft_factors_y, xbx % trig_functs_y, &
work_1d(1), work_area)
!------------------------------------------------------------------------
! [4.0] Solve spectral Poisson equation:
!------------------------------------------------------------------------
ij = 0
do j=jds, xbx%fft_jy
do i=grid%xp%itsy, grid%xp%itey
ij=ij+1
work_1d(ij) = xbx%fft_coeffs(i,j)*work_1d(ij)
end do
do n=1, xbx%pad_num
i=xbx%pad_pos(n)
ij=ij+1
work_1d(ij) = xbx%fft_coeffs(i,j)*work_1d(ij)
end do
end do
! [2.3] Reform gridpt. b using inverse double FST in i.
call fft661(Inverse_FFT, vector_inc, vector_jump, &
num_vectors, vector_size, &
xbx % fft_factors_y, xbx % trig_functs_y, &
work_1d(1), work_area)
ij = 0
do j=jds, jde
do i=grid%xp%itsy, grid%xp%itey
ij=ij+1
grid%xp%v1y(i,j,k) = work_1d(ij)
end do
do n=1, xbx%pad_num
i=xbx%pad_loc(n)
ij=ij+1
grid%xp%v2y(i,j,k) = work_1d(ij)
end do
end do
end do
!---------------------------------------------------------------------------
! Perform inverse FFT in x direction:
!---------------------------------------------------------------------------
! Apply (i',j,k' -> i,j',k') transpose (v1y -> v1x).
call da_transpose_y2x (grid)
call da_transpose_y2x_v2 (grid)
! Set up FFT parameters:
idim = xbx%fft_ix
jdim = grid%xp%jtex-grid%xp%jtsx+1
vector_inc = 1
vector_jump = idim
vector_size = idim - 1
num_vectors = jdim
work_area = (vector_size+1)*num_vectors
do k = grid%xp%ktsx, grid%xp%ktex
ij = 0
do j=grid%xp%jtsx, grid%xp%jtex
do i=grid%xp%ids, grid%xp%ide
ij=ij+1
work_1d(ij) = grid%xp%v1x(i,j,k)
end do
do n=1, xbx%fft_pad_i
i=(n-1)*xbx%pad_inc + 1
ij=ij+1
work_1d(ij) = grid%xp%v2x(i,j,k)
end do
end do
call fft661(Inverse_FFT, vector_inc, vector_jump, &
num_vectors, vector_size, &
xbx % fft_factors_x, xbx % trig_functs_x, &
work_1d(1), work_area)
ij = 0
do j=grid%xp%jtsx, grid%xp%jtex
do i=ids, ide
ij=ij+1
grid%xp%v1x(i,j,k) = work_1d(ij)
end do
ij=ij+xbx%fft_pad_i
end do
end do
! Apply (i,j',k') -> i',j',k) transpose to restore v1z.
call da_transpose_x2z (grid)
!---------------------------------------------------------------------------
! [5.0] Tidy up:
!---------------------------------------------------------------------------
if (allocated(work_1d)) deallocate(work_1d)
! [2.5] Write data array into b:
b(its:ite,jts:jte,kts:kte) = grid%xp%v1z(its:ite,jts:jte,kts:kte)
if (trace_use) call da_trace_exit("da_solve_poissoneqn_fst")
end subroutine da_solve_poissoneqn_fst