m_cuda_spectral

Uses

- m_common
- cudafor
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Graph Key

Nodes of different colours represent the following:

Solid arrows point from a submodule to the (sub)module which it is descended from. Dashed arrows point from a module or program unit to modules which it uses.
Where possible, edges connecting nodes are given different colours to make them easier to distinguish in large graphs.

Variables

Type	Visibility	Attributes		Name		Initial
real(kind=dp),	public,	parameter	::	eps_wave	=	epsilon(1._dp)

Functions

public function pair_fw(own, partner, i2, a2, b2) result(res)

Forward paired split of one dim2 mode against its mirror. The rule is symmetric, so the partner entry is pair_fw(partner, own, i2_rev).

Arguments

Type	Intent		Name
complex(kind=dp),	intent(in)	::	own
complex(kind=dp),	intent(in)	::	partner
integer,	intent(in)	::	i2
real(kind=dp),	intent(in)	::	a2(*)
real(kind=dp),	intent(in)	::	b2(*)

Return Value complex(kind=dp)

public function pair_bw(own, partner, i2, a2, b2) result(res)

Backward counterpart of pair_fw, symmetric in the same way.

Arguments

Type	Intent		Name
complex(kind=dp),	intent(in)	::	own
complex(kind=dp),	intent(in)	::	partner
integer,	intent(in)	::	i2
real(kind=dp),	intent(in)	::	a2(*)
real(kind=dp),	intent(in)	::	b2(*)

Return Value complex(kind=dp)

Subroutines

public subroutine postprocess_dim13_fw(div_r, div_c, i1, i3, n1, n3, a1, b1, a3, b3)

Forward postprocess of one spectral entry in dim3 then dim1.

Arguments

Type	Intent		Name
real(kind=dp),	intent(inout)	::	div_r
real(kind=dp),	intent(inout)	::	div_c
integer,	intent(in)	::	i1
integer,	intent(in)	::	i3
integer,	intent(in)	::	n1
integer,	intent(in)	::	n3
real(kind=dp),	intent(in)	::	a1(*)
real(kind=dp),	intent(in)	::	b1(*)
real(kind=dp),	intent(in)	::	a3(*)
real(kind=dp),	intent(in)	::	b3(*)

public subroutine postprocess_dim13_bw(div_r, div_c, i1, i3, n1, n3, a1, b1, a3, b3)

Backward counterpart of postprocess_dim13_fw.

Arguments

Type	Intent		Name
real(kind=dp),	intent(inout)	::	div_r
real(kind=dp),	intent(inout)	::	div_c
integer,	intent(in)	::	i1
integer,	intent(in)	::	i3
integer,	intent(in)	::	n1
integer,	intent(in)	::	n3
real(kind=dp),	intent(in)	::	a1(*)
real(kind=dp),	intent(in)	::	b1(*)
real(kind=dp),	intent(in)	::	a3(*)
real(kind=dp),	intent(in)	::	b3(*)

public subroutine poisson_divide(div_r, div_c, wave)

Divide one entry by its spectral equivalence constant, with the eps_wave guard that keeps roundoff noise out of the pressure field.

Arguments

Type	Intent		Name
real(kind=dp),	intent(inout)	::	div_r
real(kind=dp),	intent(inout)	::	div_c
complex(kind=dp),	intent(in)	::	wave

public subroutine memcpy3D(dst, src, nx, ny, nz)

Copy data between x3d2 padded arrays and cuFFTMp descriptors

Arguments

Type	Intent	Attributes		Name
real(kind=dp),	intent(inout),	device, dimension(:, :, :)	::	dst
real(kind=dp),	intent(in),	device, dimension(:, :, :)	::	src
integer,	intent(in),	value	::	nx
integer,	intent(in),	value	::	ny
integer,	intent(in),	value	::	nz

public subroutine memcpy3D_with_transpose(dst, src, nx, ny, nz)

Copy with transpose: src(nx, ny, nz) -> dst(ny, nx, nz) Used for 100 case forward FFT

Arguments

Type	Intent	Attributes		Name
real(kind=dp),	intent(out),	device, dimension(:, :, :)	::	dst
real(kind=dp),	intent(in),	device, dimension(:, :, :)	::	src
integer,	intent(in),	value	::	nx
integer,	intent(in),	value	::	ny
integer,	intent(in),	value	::	nz

public subroutine memcpy3D_with_transpose_back(dst, src, nx, ny, nz)

Copy with transpose back: src(ny, nx, nz) -> dst(nx, ny, nz) Used for 100 case backward FFT

Arguments

Type	Intent	Attributes		Name
real(kind=dp),	intent(out),	device, dimension(:, :, :)	::	dst
real(kind=dp),	intent(in),	device, dimension(:, :, :)	::	src
integer,	intent(in),	value	::	nx
integer,	intent(in),	value	::	ny
integer,	intent(in),	value	::	nz

public subroutine transpose_xyz_to_zxy(dst, src, nx, ny, nz)

Used before R2C FFT for 110 case to put Z (periodic) in fast dim.

Arguments

Type	Intent	Attributes		Name
real(kind=dp),	intent(out),	device, dimension(:, :, :)	::	dst
real(kind=dp),	intent(in),	device, dimension(:, :, :)	::	src
integer,	intent(in),	value	::	nx
integer,	intent(in),	value	::	ny
integer,	intent(in),	value	::	nz

public subroutine transpose_zxy_to_xyz(dst, src, nx, ny, nz)

Transpose back: src(nz, nx, ny) -> dst(nx, ny, nz) Used after C2R FFT for 110 case.

Arguments

Type	Intent	Attributes		Name
real(kind=dp),	intent(out),	device, dimension(:, :, :)	::	dst
real(kind=dp),	intent(in),	device, dimension(:, :, :)	::	src
integer,	intent(in),	value	::	nx
integer,	intent(in),	value	::	ny
integer,	intent(in),	value	::	nz

public subroutine process_spectral_000(div_u, waves, nx_spec, ny_spec, y_sp_st, nx, ny, nz, ax, bx, ay, by, az, bz)

Post-processes the divergence of velocity in spectral space, including scaling w.r.t. grid size.

Arguments

Type	Intent	Attributes		Name
complex(kind=dp),	intent(inout),	device, dimension(:, :, :)	::	div_u	Divergence of velocity in spectral space
complex(kind=dp),	intent(in),	device, dimension(:, :, :)	::	waves	Spectral equivalence constants
integer,	intent(in),	value	::	nx_spec	Grid size in spectral space
integer,	intent(in),	value	::	ny_spec	Grid size in spectral space
integer,	intent(in),	value	::	y_sp_st	Offset in y direction in the permuted slabs in spectral space
integer,	intent(in),	value	::	nx	Grid size
integer,	intent(in),	value	::	ny	Grid size
integer,	intent(in),	value	::	nz	Grid size
real(kind=dp),	intent(in),	device, dimension(:)	::	ax
real(kind=dp),	intent(in),	device, dimension(:)	::	bx
real(kind=dp),	intent(in),	device, dimension(:)	::	ay
real(kind=dp),	intent(in),	device, dimension(:)	::	by
real(kind=dp),	intent(in),	device, dimension(:)	::	az
real(kind=dp),	intent(in),	device, dimension(:)	::	bz

public subroutine process_spectral_010(div_u, waves, nx_spec, ny_spec, y_sp_st, nx, ny, nz, ax, bx, ay, by, az, bz)

Post-processes the divergence of velocity in spectral space, including scaling w.r.t. grid size.

Arguments

Type	Intent	Attributes		Name
complex(kind=dp),	intent(inout),	device, dimension(:, :, :)	::	div_u	Divergence of velocity in spectral space
complex(kind=dp),	intent(in),	device, dimension(:, :, :)	::	waves	Spectral equivalence constants
integer,	intent(in),	value	::	nx_spec	Grid size in spectral space
integer,	intent(in),	value	::	ny_spec	Grid size in spectral space
integer,	intent(in),	value	::	y_sp_st	Offset in y direction in the permuted slabs in spectral space
integer,	intent(in),	value	::	nx	Grid size
integer,	intent(in),	value	::	ny	Grid size
integer,	intent(in),	value	::	nz	Grid size
real(kind=dp),	intent(in),	device, dimension(:)	::	ax
real(kind=dp),	intent(in),	device, dimension(:)	::	bx
real(kind=dp),	intent(in),	device, dimension(:)	::	ay
real(kind=dp),	intent(in),	device, dimension(:)	::	by
real(kind=dp),	intent(in),	device, dimension(:)	::	az
real(kind=dp),	intent(in),	device, dimension(:)	::	bz

public subroutine process_spectral_010_fw(div_u, nx_spec, ny_spec, y_sp_st, nx, ny, nz, ax, bx, ay, by, az, bz)

Post-processes the divergence of velocity in spectral space, including scaling w.r.t. grid size.

Arguments

Type	Intent	Attributes		Name
complex(kind=dp),	intent(inout),	device, dimension(:, :, :)	::	div_u	Divergence of velocity in spectral space
integer,	intent(in),	value	::	nx_spec	Grid size in spectral space
integer,	intent(in),	value	::	ny_spec	Grid size in spectral space
integer,	intent(in),	value	::	y_sp_st	Offset in y direction in the permuted slabs in spectral space
integer,	intent(in),	value	::	nx	Grid size
integer,	intent(in),	value	::	ny	Grid size
integer,	intent(in),	value	::	nz	Grid size
real(kind=dp),	intent(in),	device, dimension(:)	::	ax	Spectral equivalence constants
real(kind=dp),	intent(in),	device, dimension(:)	::	bx	Spectral equivalence constants
real(kind=dp),	intent(in),	device, dimension(:)	::	ay	Spectral equivalence constants
real(kind=dp),	intent(in),	device, dimension(:)	::	by	Spectral equivalence constants
real(kind=dp),	intent(in),	device, dimension(:)	::	az	Spectral equivalence constants
real(kind=dp),	intent(in),	device, dimension(:)	::	bz	Spectral equivalence constants

public subroutine process_spectral_010_poisson(div_u, a_re, a_im, off, inc, nx_spec, n, nx, ny, nz)

Solve the Poisson equation at cell centres with non-perioic BC along y

Arguments

Type	Intent	Attributes		Name
complex(kind=dp),	intent(inout),	device, dimension(:, :, :)	::	div_u	Divergence of velocity in spectral space
real(kind=dp),	intent(inout),	device, dimension(:, :, :, :)	::	a_re	Spectral equivalence constants
real(kind=dp),	intent(inout),	device, dimension(:, :, :, :)	::	a_im	Spectral equivalence constants
integer,	intent(in),	value	::	off	offset and increment. increment is 2 when considering only odd or even
integer,	intent(in),	value	::	inc	offset and increment. increment is 2 when considering only odd or even
integer,	intent(in),	value	::	nx_spec	Grid size in spectral space
integer,	intent(in),	value	::	n	Grid size in spectral space
integer,	intent(in),	value	::	nx	Grid size in spectral space
integer,	intent(in),	value	::	ny	Grid size in spectral space
integer,	intent(in),	value	::	nz	Grid size in spectral space

public subroutine process_spectral_010_bw(div_u, nx_spec, ny_spec, y_sp_st, nx, ny, nz, ax, bx, ay, by, az, bz)

Post-processes the divergence of velocity in spectral space, including scaling w.r.t. grid size.

Arguments

Type	Intent	Attributes		Name
complex(kind=dp),	intent(inout),	device, dimension(:, :, :)	::	div_u	Divergence of velocity in spectral space
integer,	intent(in),	value	::	nx_spec	Grid size in spectral space
integer,	intent(in),	value	::	ny_spec	Grid size in spectral space
integer,	intent(in),	value	::	y_sp_st	Offset in y direction in the permuted slabs in spectral space
integer,	intent(in),	value	::	nx	Grid size
integer,	intent(in),	value	::	ny	Grid size
integer,	intent(in),	value	::	nz	Grid size
real(kind=dp),	intent(in),	device, dimension(:)	::	ax	Spectral equivalence constants
real(kind=dp),	intent(in),	device, dimension(:)	::	bx	Spectral equivalence constants
real(kind=dp),	intent(in),	device, dimension(:)	::	ay	Spectral equivalence constants
real(kind=dp),	intent(in),	device, dimension(:)	::	by	Spectral equivalence constants
real(kind=dp),	intent(in),	device, dimension(:)	::	az	Spectral equivalence constants
real(kind=dp),	intent(in),	device, dimension(:)	::	bz	Spectral equivalence constants

public subroutine process_spectral_100_fw(div_u, nx_spec, ny_spec, nx, ny, nz, ax, bx, az, bz)

Stage 1 (forward): normalisation followed by the dim3 and dim1 postprocess. Every mode is handled on its own here.

Arguments

Type	Intent	Attributes		Name
complex(kind=dp),	intent(inout),	device, dimension(:, :, :)	::	div_u	Divergence of velocity in spectral space
integer,	intent(in),	value	::	nx_spec	Grid size in spectral space
integer,	intent(in),	value	::	ny_spec	Grid size in spectral space
integer,	intent(in),	value	::	nx	Grid size
integer,	intent(in),	value	::	ny	Grid size
integer,	intent(in),	value	::	nz	Grid size
real(kind=dp),	intent(in),	device, dimension(:)	::	ax
real(kind=dp),	intent(in),	device, dimension(:)	::	bx
real(kind=dp),	intent(in),	device, dimension(:)	::	az
real(kind=dp),	intent(in),	device, dimension(:)	::	bz

public subroutine process_spectral_100_pair_fw(div_u, mirror, mirror_plane, waves, nx_spec, ny_spec, y_sp_st, nx, nz, ay, by)

Stage 2 (forward): the dim2 paired split, then the Poisson solve.

Arguments

Type	Intent	Attributes		Name
complex(kind=dp),	intent(inout),	device, dimension(:, :, :)	::	div_u	Divergence of velocity in spectral space
complex(kind=dp),	intent(in),	device, dimension(:, :, :)	::	mirror	dim2 mirror of the local slab, and the single plane below it
complex(kind=dp),	intent(in),	device, dimension(:, :)	::	mirror_plane
complex(kind=dp),	intent(in),	device, dimension(:, :, :)	::	waves	Spectral equivalence constants
integer,	intent(in),	value	::	nx_spec	Grid size in spectral space
integer,	intent(in),	value	::	ny_spec	Grid size in spectral space
integer,	intent(in),	value	::	y_sp_st	Offset in the paired direction in the permuted slabs in spectral space
integer,	intent(in),	value	::	nx	Grid size
integer,	intent(in),	value	::	nz	Grid size
real(kind=dp),	intent(in),	device, dimension(:)	::	ay
real(kind=dp),	intent(in),	device, dimension(:)	::	by

public subroutine process_spectral_100_pair_bw(div_u, mirror, mirror_plane, nx_spec, ny_spec, y_sp_st, nx, nz, ax, bx, ay, by, az, bz)

Stage 3 (backward): the dim2 paired recombination, then the dim3 and dim1 postprocess.

Arguments

Type	Intent	Attributes		Name
complex(kind=dp),	intent(inout),	device, dimension(:, :, :)	::	div_u	Divergence of velocity in spectral space
complex(kind=dp),	intent(in),	device, dimension(:, :, :)	::	mirror	dim2 mirror of the local slab, and the single plane below it
complex(kind=dp),	intent(in),	device, dimension(:, :)	::	mirror_plane
integer,	intent(in),	value	::	nx_spec	Grid size in spectral space
integer,	intent(in),	value	::	ny_spec	Grid size in spectral space
integer,	intent(in),	value	::	y_sp_st	Offset in the paired direction in the permuted slabs in spectral space
integer,	intent(in),	value	::	nx	Grid size
integer,	intent(in),	value	::	nz	Grid size
real(kind=dp),	intent(in),	device, dimension(:)	::	ax
real(kind=dp),	intent(in),	device, dimension(:)	::	bx
real(kind=dp),	intent(in),	device, dimension(:)	::	ay
real(kind=dp),	intent(in),	device, dimension(:)	::	by
real(kind=dp),	intent(in),	device, dimension(:)	::	az
real(kind=dp),	intent(in),	device, dimension(:)	::	bz

public subroutine pack_spectral_plane(plane, div_u, nx_spec, nz_spec)

Copies the first dim2 plane of the local spectral slab into a contiguous buffer so it can be handed to MPI.

Arguments

Type	Intent	Attributes		Name
complex(kind=dp),	intent(out),	device, dimension(:, :)	::	plane
complex(kind=dp),	intent(in),	device, dimension(:, :, :)	::	div_u
integer,	intent(in),	value	::	nx_spec	Grid size in spectral space
integer,	intent(in),	value	::	nz_spec	Grid size in spectral space

public subroutine process_spectral_110_norm_z(div_u, nz_h, nx, ny, nz, az, bz)

Step 1 (forward): normalise + Z periodic post-process Z is dim1 (serial j loop), periodic R2C — no sign flip needed since j only goes to nz/2+1.

Arguments

Type	Intent	Attributes		Name
complex(kind=dp),	intent(inout),	device, dimension(:, :, :)	::	div_u
integer,	intent(in),	value	::	nz_h
integer,	intent(in),	value	::	nx
integer,	intent(in),	value	::	ny
integer,	intent(in),	value	::	nz
real(kind=dp),	intent(in),	device, dimension(:)	::	az
real(kind=dp),	intent(in),	device, dimension(:)	::	bz

public subroutine process_spectral_110_x_pair_fw(div_u, nz_h, nx, ny, x_sp_st, ax, bx)

Step 2 (forward): X paired even/odd split X is dim2 (thread i). Only i in [2, nx/2+1] executes. Writes to i and nx-i+2. Race-free (pair doesn't enter).

Arguments

Type	Intent	Attributes		Name
complex(kind=dp),	intent(inout),	device, dimension(:, :, :)	::	div_u
integer,	intent(in),	value	::	nz_h
integer,	intent(in),	value	::	nx
integer,	intent(in),	value	::	ny
integer,	intent(in),	value	::	x_sp_st
real(kind=dp),	intent(in),	device, dimension(:)	::	ax
real(kind=dp),	intent(in),	device, dimension(:)	::	bx

public subroutine process_spectral_110_y_pair_fw(div_u, nz_h, nx, ny, y_sp_st, ay, by)

Step 3 (forward): Y paired even/odd split Y is dim3 (blockIdx%y = k). Only k in [2, ny/2+1] executes. Writes to k and ny-k+2. Race-free (pair block doesn't enter).

Arguments

Type	Intent	Attributes		Name
complex(kind=dp),	intent(inout),	device, dimension(:, :, :)	::	div_u
integer,	intent(in),	value	::	nz_h
integer,	intent(in),	value	::	nx
integer,	intent(in),	value	::	ny
integer,	intent(in),	value	::	y_sp_st
real(kind=dp),	intent(in),	device, dimension(:)	::	ay
real(kind=dp),	intent(in),	device, dimension(:)	::	by

public subroutine process_spectral_110_poisson(div_u, waves, nz_h, nx, ny, nz, x_sp_st)

Step 4: Poisson solve — divide by waves

Arguments

Type	Intent	Attributes		Name
complex(kind=dp),	intent(inout),	device, dimension(:, :, :)	::	div_u
complex(kind=dp),	intent(in),	device, dimension(:, :, :)	::	waves
integer,	intent(in),	value	::	nz_h
integer,	intent(in),	value	::	nx
integer,	intent(in),	value	::	ny
integer,	intent(in),	value	::	nz
integer,	intent(in),	value	::	x_sp_st

public subroutine process_spectral_110_y_pair_bw(div_u, nz_h, nx, ny, y_sp_st, ay, by)

Step 5 (backward): Y paired even/odd recombine

Arguments

Type	Intent	Attributes		Name
complex(kind=dp),	intent(inout),	device, dimension(:, :, :)	::	div_u
integer,	intent(in),	value	::	nz_h
integer,	intent(in),	value	::	nx
integer,	intent(in),	value	::	ny
integer,	intent(in),	value	::	y_sp_st
real(kind=dp),	intent(in),	device, dimension(:)	::	ay
real(kind=dp),	intent(in),	device, dimension(:)	::	by

public subroutine process_spectral_110_x_pair_bw(div_u, nz_h, nx, ny, x_sp_st, ax, bx)

Step 6 (backward): X paired even/odd recombine

Arguments

Type	Intent	Attributes		Name
complex(kind=dp),	intent(inout),	device, dimension(:, :, :)	::	div_u
integer,	intent(in),	value	::	nz_h
integer,	intent(in),	value	::	nx
integer,	intent(in),	value	::	ny
integer,	intent(in),	value	::	x_sp_st
real(kind=dp),	intent(in),	device, dimension(:)	::	ax
real(kind=dp),	intent(in),	device, dimension(:)	::	bx

public subroutine process_spectral_110_z_bw(div_u, nz_h, nx, ny, az, bz)

Step 7 (backward): Z periodic undo

Arguments

Type	Intent	Attributes		Name
complex(kind=dp),	intent(inout),	device, dimension(:, :, :)	::	div_u
integer,	intent(in),	value	::	nz_h
integer,	intent(in),	value	::	nx
integer,	intent(in),	value	::	ny
real(kind=dp),	intent(in),	device, dimension(:)	::	az
real(kind=dp),	intent(in),	device, dimension(:)	::	bz

public subroutine enforce_periodicity_x(f_out, f_in, nx)

Arguments

Type	Intent	Attributes		Name
real(kind=dp),	intent(out),	device, dimension(:, :, :)	::	f_out
real(kind=dp),	intent(in),	device, dimension(:, :, :)	::	f_in
integer,	intent(in),	value	::	nx

public subroutine undo_periodicity_x(f_out, f_in, nx)

Arguments

Type	Intent	Attributes		Name
real(kind=dp),	intent(out),	device, dimension(:, :, :)	::	f_out
real(kind=dp),	intent(in),	device, dimension(:, :, :)	::	f_in
integer,	intent(in),	value	::	nx

public subroutine enforce_periodicity_y(f_out, f_in, ny)

Arguments

Type	Intent	Attributes		Name
real(kind=dp),	intent(out),	device, dimension(:, :, :)	::	f_out
real(kind=dp),	intent(in),	device, dimension(:, :, :)	::	f_in
integer,	intent(in),	value	::	ny

public subroutine undo_periodicity_y(f_out, f_in, ny)

Arguments

Type	Intent	Attributes		Name
real(kind=dp),	intent(out),	device, dimension(:, :, :)	::	f_out
real(kind=dp),	intent(in),	device, dimension(:, :, :)	::	f_in
integer,	intent(in),	value	::	ny

public subroutine enforce_periodicity_xy(f_out, f_in, nx, ny)

Combined X and Y periodicity enforcement (interleave shuffle).

Arguments

Type	Intent	Attributes		Name
real(kind=dp),	intent(out),	device, dimension(:, :, :)	::	f_out
real(kind=dp),	intent(in),	device, dimension(:, :, :)	::	f_in
integer,	intent(in),	value	::	nx
integer,	intent(in),	value	::	ny

public subroutine undo_periodicity_xy(f_out, f_in, nx, ny)

Combined X and Y periodicity undo (reverse interleave shuffle).

Arguments

Type	Intent	Attributes		Name
real(kind=dp),	intent(out),	device, dimension(:, :, :)	::	f_out
real(kind=dp),	intent(in),	device, dimension(:, :, :)	::	f_in
integer,	intent(in),	value	::	nx
integer,	intent(in),	value	::	ny

m_cuda_spectral Module

Contents

Variables

Functions

Subroutines

Uses

Used by

Variables

Functions

public function pair_fw(own, partner, i2, a2, b2) result(res)

Arguments

Return Value complex(kind=dp)

public function pair_bw(own, partner, i2, a2, b2) result(res)

Arguments

Return Value complex(kind=dp)

Subroutines

public subroutine postprocess_dim13_fw(div_r, div_c, i1, i3, n1, n3, a1, b1, a3, b3)

Arguments

public subroutine postprocess_dim13_bw(div_r, div_c, i1, i3, n1, n3, a1, b1, a3, b3)

Arguments

public subroutine poisson_divide(div_r, div_c, wave)

Arguments

public subroutine memcpy3D(dst, src, nx, ny, nz)

Arguments

public subroutine memcpy3D_with_transpose(dst, src, nx, ny, nz)

Arguments

public subroutine memcpy3D_with_transpose_back(dst, src, nx, ny, nz)

Arguments

public subroutine transpose_xyz_to_zxy(dst, src, nx, ny, nz)

Arguments

public subroutine transpose_zxy_to_xyz(dst, src, nx, ny, nz)

Arguments

public subroutine process_spectral_000(div_u, waves, nx_spec, ny_spec, y_sp_st, nx, ny, nz, ax, bx, ay, by, az, bz)

Arguments

public subroutine process_spectral_010(div_u, waves, nx_spec, ny_spec, y_sp_st, nx, ny, nz, ax, bx, ay, by, az, bz)

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public subroutine process_spectral_010_fw(div_u, nx_spec, ny_spec, y_sp_st, nx, ny, nz, ax, bx, ay, by, az, bz)

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public subroutine process_spectral_010_poisson(div_u, a_re, a_im, off, inc, nx_spec, n, nx, ny, nz)

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public subroutine process_spectral_010_bw(div_u, nx_spec, ny_spec, y_sp_st, nx, ny, nz, ax, bx, ay, by, az, bz)

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public subroutine process_spectral_100_fw(div_u, nx_spec, ny_spec, nx, ny, nz, ax, bx, az, bz)

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public subroutine process_spectral_100_pair_fw(div_u, mirror, mirror_plane, waves, nx_spec, ny_spec, y_sp_st, nx, nz, ay, by)

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public subroutine process_spectral_100_pair_bw(div_u, mirror, mirror_plane, nx_spec, ny_spec, y_sp_st, nx, nz, ax, bx, ay, by, az, bz)

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public subroutine pack_spectral_plane(plane, div_u, nx_spec, nz_spec)

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public subroutine process_spectral_110_norm_z(div_u, nz_h, nx, ny, nz, az, bz)

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public subroutine process_spectral_110_x_pair_fw(div_u, nz_h, nx, ny, x_sp_st, ax, bx)

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public subroutine process_spectral_110_y_pair_fw(div_u, nz_h, nx, ny, y_sp_st, ay, by)

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public subroutine process_spectral_110_poisson(div_u, waves, nz_h, nx, ny, nz, x_sp_st)

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public subroutine process_spectral_110_y_pair_bw(div_u, nz_h, nx, ny, y_sp_st, ay, by)

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public subroutine process_spectral_110_x_pair_bw(div_u, nz_h, nx, ny, x_sp_st, ax, bx)

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public subroutine process_spectral_110_z_bw(div_u, nz_h, nx, ny, az, bz)

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public subroutine enforce_periodicity_x(f_out, f_in, nx)

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public subroutine undo_periodicity_x(f_out, f_in, nx)

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public subroutine enforce_periodicity_y(f_out, f_in, ny)

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public subroutine undo_periodicity_y(f_out, f_in, ny)

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public subroutine enforce_periodicity_xy(f_out, f_in, nx, ny)

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public subroutine undo_periodicity_xy(f_out, f_in, nx, ny)

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