Data Types
type	poisson_fft_t

Functions/Subroutines
subroutine, public	poisson_fft_init (this, namespace, space, cube, kernel, soft_coulb_param, fullcube)

subroutine, public	poisson_fft_get_kernel (namespace, space, cube, coulb, kernel, soft_coulb_param, fullcube)

subroutine	get_cutoff (namespace, default_r_c, r_c)

subroutine	poisson_fft_build_3d_3d (cube, coulb)
	Compute the Coulomb kernel in reciprocal space, for a 3D FFT grid. More...

subroutine	poisson_fft_build_3d_3d_hockney (cube, coulb, fullcube)
	Kernel for Hockneys algorithm that solves the poisson equation in a small box while respecting the periodicity of a larger box A. Damle, L. Lin, L. Ying, JCTC, 2015 DOI: 10.1021/ct500985f, supplementary info. More...

subroutine	poisson_fft_build_3d_2d (namespace, cube, coulb)
	C. A. Rozzi et al., Phys. Rev. B 73, 205119 (2006), Table I. More...

subroutine	poisson_fft_build_3d_1d (namespace, space, cube, coulb)
	C. A. Rozzi et al., Phys. Rev. B 73, 205119 (2006), Table I. More...

subroutine	poisson_fft_build_3d_0d (namespace, cube, kernel, coulb, is_periodic)
	C. A. Rozzi et al., Phys. Rev. B 73, 205119 (2006), Table I. More...

subroutine	poisson_fft_build_2d_0d (namespace, cube, coulb)
	A. Castro et al., Phys. Rev. B 80, 033102 (2009) More...

subroutine	poisson_fft_build_2d_1d (namespace, cube, coulb)
	A. Castro et al., Phys. Rev. B 80, 033102 (2009) More...

subroutine	poisson_fft_build_2d_2d (cube, coulb)
	A. Castro et al., Phys. Rev. B 80, 033102 (2009) More...

subroutine	poisson_fft_build_1d_1d (cube, coulb, poisson_soft_coulomb_param)

subroutine	poisson_fft_build_1d_0d (namespace, cube, coulb, poisson_soft_coulomb_param)

subroutine, public	poisson_fft_end (this)

subroutine, public	dpoisson_fft_solve (this, mesh, cube, pot, rho, mesh_cube_map, average_to_zero, kernel, sm)

subroutine, public	dpoisson_fft_solve_batch (this, mesh, cube, pot, rho, mesh_cube_map, average_to_zero, kernel, sm, pot_buffer, rho_buffer, count)

subroutine, public	zpoisson_fft_solve (this, mesh, cube, pot, rho, mesh_cube_map, average_to_zero, kernel, sm)

subroutine, public	zpoisson_fft_solve_batch (this, mesh, cube, pot, rho, mesh_cube_map, average_to_zero, kernel, sm, pot_buffer, rho_buffer, count)

Variables
integer, parameter, public	poisson_fft_kernel_none = -1

integer, parameter, public	poisson_fft_kernel_sph = 0

integer, parameter, public	poisson_fft_kernel_cyl = 1

integer, parameter, public	poisson_fft_kernel_pla = 2

integer, parameter, public	poisson_fft_kernel_nocut = 3

integer, parameter, public	poisson_fft_kernel_corrected = 4

integer, parameter, public	poisson_fft_kernel_hockney = 5

real(real64), parameter	tol_vanishing_q = 1e-6_real64

Function/Subroutine Documentation

◆ poisson_fft_init()

subroutine, public poisson_fft_oct_m::poisson_fft_init	(	type(poisson_fft_t), intent(out)	this,
		type(namespace_t), intent(in)	namespace,
		class(space_t), intent(in)	space,
		type(cube_t), intent(inout)	cube,
		integer, intent(in)	kernel,
		real(real64), intent(in), optional	soft_coulb_param,
		type(cube_t), intent(in), optional	fullcube
	)

Parameters

[in] fullcube needed for Hockney kernel

Definition at line 172 of file poisson_fft.F90.

◆ poisson_fft_get_kernel()

subroutine, public poisson_fft_oct_m::poisson_fft_get_kernel	(	type(namespace_t), intent(in)	namespace,
		class(space_t), intent(in)	space,
		type(cube_t), intent(in)	cube,
		type(fourier_space_op_t), intent(inout)	coulb,
		integer, intent(in)	kernel,
		real(real64), intent(in), optional	soft_coulb_param,
		type(cube_t), intent(in), optional	fullcube
	)

Parameters

[in] fullcube needed for Hockney kernel

Definition at line 199 of file poisson_fft.F90.

◆ get_cutoff()

subroutine poisson_fft_oct_m::get_cutoff	(	type(namespace_t), intent(in)	namespace,
		real(real64), intent(in)	default_r_c,
		real(real64), intent(out)	r_c
	)

private

Definition at line 285 of file poisson_fft.F90.

◆ poisson_fft_build_3d_3d()

subroutine poisson_fft_oct_m::poisson_fft_build_3d_3d	(	type(cube_t), intent(in)	cube,
		type(fourier_space_op_t), intent(inout)	coulb
	)

private

Compute the Coulomb kernel in reciprocal space, for a 3D FFT grid.

Analytic evaluation of |G + q|^2 follows the logic: Define \( u = G + q \), in integer-mode coordinates. \( |u|^2 = u^T A u = \sum_{ij} u_i A_{ij} u_j\), where \( A \) is the metric tensor of the reciprocal-space grid basis. Expand \( |u|^2 \), and simplify noting that \( a_{ij} = a_{ji}\). Group terms in powers of \( u_x\), forming a quadratic equation:

\[ a_{11} u_x^2 + \beta u_x + g_{yz}, \quad \text{where} \quad \beta = 2(a_{12} u_y + a_{13} u_z), \quad g_{yz} = a_{22} u_y^2 + 2 a_{23} u_y u_z + a_{33} u_z^2. \]

Complete the square to give:

\[ a_{11}(u_x + \frac{\beta}{2 a_{11}})^2 + g_{yz} - \frac{\beta^2}{4 a_{11}}. \]

For any u_x, the squared term must be \( \ge 0 \), therefore:

\[ |u|^2 \ge g_{yz} - \frac{\beta^2}{4 a_{11}} \]

If this lower bound already exceeds the cutoff, no \( u_x \) on the \( (u_y, u_z) \) line can lie within the cutoff sphere, so the inner loop is skipped.

Definition at line 332 of file poisson_fft.F90.

◆ poisson_fft_build_3d_3d_hockney()

subroutine poisson_fft_oct_m::poisson_fft_build_3d_3d_hockney	(	type(cube_t), intent(in)	cube,
		type(fourier_space_op_t), intent(inout)	coulb,
		type(cube_t), intent(in)	fullcube
	)

private

Kernel for Hockneys algorithm that solves the poisson equation in a small box while respecting the periodicity of a larger box A. Damle, L. Lin, L. Ying, JCTC, 2015 DOI: 10.1021/ct500985f, supplementary info.

Definition at line 456 of file poisson_fft.F90.

◆ poisson_fft_build_3d_2d()

subroutine poisson_fft_oct_m::poisson_fft_build_3d_2d	(	type(namespace_t), intent(in)	namespace,
		type(cube_t), intent(in)	cube,
		type(fourier_space_op_t), intent(inout)	coulb
	)

private

C. A. Rozzi et al., Phys. Rev. B 73, 205119 (2006), Table I.

Definition at line 572 of file poisson_fft.F90.

◆ poisson_fft_build_3d_1d()

subroutine poisson_fft_oct_m::poisson_fft_build_3d_1d	(	type(namespace_t), intent(in)	namespace,
		class(space_t), intent(in)	space,
		type(cube_t), intent(in)	cube,
		type(fourier_space_op_t), intent(inout)	coulb
	)

private

C. A. Rozzi et al., Phys. Rev. B 73, 205119 (2006), Table I.

Definition at line 656 of file poisson_fft.F90.

◆ poisson_fft_build_3d_0d()

subroutine poisson_fft_oct_m::poisson_fft_build_3d_0d	(	type(namespace_t), intent(in)	namespace,
		type(cube_t), intent(in)	cube,
		integer, intent(in)	kernel,
		type(fourier_space_op_t), intent(inout)	coulb,
		logical, intent(in)	is_periodic
	)

private

C. A. Rozzi et al., Phys. Rev. B 73, 205119 (2006), Table I.

Definition at line 783 of file poisson_fft.F90.

◆ poisson_fft_build_2d_0d()

subroutine poisson_fft_oct_m::poisson_fft_build_2d_0d	(	type(namespace_t), intent(in)	namespace,
		type(cube_t), intent(in)	cube,
		type(fourier_space_op_t), intent(inout)	coulb
	)

private

A. Castro et al., Phys. Rev. B 80, 033102 (2009)

Definition at line 894 of file poisson_fft.F90.

◆ poisson_fft_build_2d_1d()

subroutine poisson_fft_oct_m::poisson_fft_build_2d_1d	(	type(namespace_t), intent(in)	namespace,
		type(cube_t), intent(in)	cube,
		type(fourier_space_op_t), intent(inout)	coulb
	)

private

A. Castro et al., Phys. Rev. B 80, 033102 (2009)

Definition at line 966 of file poisson_fft.F90.

◆ poisson_fft_build_2d_2d()

subroutine poisson_fft_oct_m::poisson_fft_build_2d_2d	(	type(cube_t), intent(in)	cube,
		type(fourier_space_op_t), intent(inout)	coulb
	)

private

A. Castro et al., Phys. Rev. B 80, 033102 (2009)

Definition at line 1022 of file poisson_fft.F90.

◆ poisson_fft_build_1d_1d()

subroutine poisson_fft_oct_m::poisson_fft_build_1d_1d	(	type(cube_t), intent(in)	cube,
		type(fourier_space_op_t), intent(inout)	coulb,
		real(real64), intent(in)	poisson_soft_coulomb_param
	)

private

Definition at line 1062 of file poisson_fft.F90.

◆ poisson_fft_build_1d_0d()

subroutine poisson_fft_oct_m::poisson_fft_build_1d_0d	(	type(namespace_t), intent(in)	namespace,
		type(cube_t), intent(in)	cube,
		type(fourier_space_op_t), intent(inout)	coulb,
		real(real64), intent(in)	poisson_soft_coulomb_param
	)

private

Definition at line 1101 of file poisson_fft.F90.

◆ poisson_fft_end()

subroutine, public poisson_fft_oct_m::poisson_fft_end ( type(poisson_fft_t), intent(inout) this )

Definition at line 1143 of file poisson_fft.F90.

◆ dpoisson_fft_solve()

subroutine, public poisson_fft_oct_m::dpoisson_fft_solve	(	type(poisson_fft_t), intent(in)	this,
		type(mesh_t), intent(in)	mesh,
		type(cube_t), intent(in)	cube,
		real(real64), dimension(:), intent(out), contiguous	pot,
		real(real64), dimension(:), intent(in), contiguous	rho,
		type(mesh_cube_parallel_map_t), intent(in)	mesh_cube_map,
		logical, intent(in), optional	average_to_zero,
		type(fourier_space_op_t), intent(in), optional	kernel,
		type(submesh_t), intent(in), optional	sm
	)

Parameters

[in] average_to_zero default is false

Definition at line 1220 of file poisson_fft.F90.

◆ dpoisson_fft_solve_batch()

subroutine, public poisson_fft_oct_m::dpoisson_fft_solve_batch	(	type(poisson_fft_t), intent(in)	this,
		type(mesh_t), intent(in)	mesh,
		type(cube_t), intent(in)	cube,
		real(real64), dimension(:, :), intent(out), optional, contiguous	pot,
		real(real64), dimension(:, :), intent(in), optional, contiguous	rho,
		type(mesh_cube_parallel_map_t), intent(in), optional	mesh_cube_map,
		logical, intent(in), optional	average_to_zero,
		type(fourier_space_op_t), intent(in), optional	kernel,
		type(submesh_t), intent(in), optional	sm,
		type(accel_mem_t), intent(inout), optional	pot_buffer,
		type(accel_mem_t), intent(in), optional	rho_buffer,
		integer, intent(in), optional	count
	)

Parameters

[out]	pot	FFT result (host path)
[in]	rho	Quantity to FFT (host path)
[in]	average_to_zero	default is false
[in,out]	pot_buffer	Device-resident buffers for the GPU path. These are mutually exclusive with pot/rho.
[in]	count	number of functions on the device path (default 1)

Definition at line 1292 of file poisson_fft.F90.

◆ zpoisson_fft_solve()

subroutine, public poisson_fft_oct_m::zpoisson_fft_solve	(	type(poisson_fft_t), intent(in)	this,
		type(mesh_t), intent(in)	mesh,
		type(cube_t), intent(in)	cube,
		complex(real64), dimension(:), intent(out), contiguous	pot,
		complex(real64), dimension(:), intent(in), contiguous	rho,
		type(mesh_cube_parallel_map_t), intent(in)	mesh_cube_map,
		logical, intent(in), optional	average_to_zero,
		type(fourier_space_op_t), intent(in), optional	kernel,
		type(submesh_t), intent(in), optional	sm
	)

Parameters

[in] average_to_zero default is false

Definition at line 1477 of file poisson_fft.F90.

◆ zpoisson_fft_solve_batch()

subroutine, public poisson_fft_oct_m::zpoisson_fft_solve_batch	(	type(poisson_fft_t), intent(in)	this,
		type(mesh_t), intent(in)	mesh,
		type(cube_t), intent(in)	cube,
		complex(real64), dimension(:, :), intent(out), optional, contiguous	pot,
		complex(real64), dimension(:, :), intent(in), optional, contiguous	rho,
		type(mesh_cube_parallel_map_t), intent(in), optional	mesh_cube_map,
		logical, intent(in), optional	average_to_zero,
		type(fourier_space_op_t), intent(in), optional	kernel,
		type(submesh_t), intent(in), optional	sm,
		type(accel_mem_t), intent(inout), optional	pot_buffer,
		type(accel_mem_t), intent(in), optional	rho_buffer,
		integer, intent(in), optional	count
	)

Parameters

[out]	pot	FFT result (host path)
[in]	rho	Quantity to FFT (host path)
[in]	average_to_zero	default is false
[in,out]	pot_buffer	Device-resident buffers for the GPU path. These are mutually exclusive with pot/rho.
[in]	count	number of functions on the device path (default 1)

Definition at line 1549 of file poisson_fft.F90.

Variable Documentation

◆ poisson_fft_kernel_none

integer, parameter, public poisson_fft_oct_m::poisson_fft_kernel_none = -1

Definition at line 153 of file poisson_fft.F90.

◆ poisson_fft_kernel_sph

integer, parameter, public poisson_fft_oct_m::poisson_fft_kernel_sph = 0

Definition at line 153 of file poisson_fft.F90.

◆ poisson_fft_kernel_cyl

integer, parameter, public poisson_fft_oct_m::poisson_fft_kernel_cyl = 1

Definition at line 153 of file poisson_fft.F90.

◆ poisson_fft_kernel_pla

integer, parameter, public poisson_fft_oct_m::poisson_fft_kernel_pla = 2

Definition at line 153 of file poisson_fft.F90.

◆ poisson_fft_kernel_nocut

integer, parameter, public poisson_fft_oct_m::poisson_fft_kernel_nocut = 3

Definition at line 153 of file poisson_fft.F90.

◆ poisson_fft_kernel_corrected

integer, parameter, public poisson_fft_oct_m::poisson_fft_kernel_corrected = 4

Definition at line 153 of file poisson_fft.F90.

◆ poisson_fft_kernel_hockney

integer, parameter, public poisson_fft_oct_m::poisson_fft_kernel_hockney = 5

Definition at line 153 of file poisson_fft.F90.

◆ tol_vanishing_q

real(real64), parameter poisson_fft_oct_m::tol_vanishing_q = 1e-6_real64

private

Definition at line 169 of file poisson_fft.F90.

Data Types

Functions/Subroutines

Variables

Function/Subroutine Documentation

◆ poisson_fft_init()

◆ poisson_fft_get_kernel()

◆ get_cutoff()

◆ poisson_fft_build_3d_3d()

◆ poisson_fft_build_3d_3d_hockney()

◆ poisson_fft_build_3d_2d()

◆ poisson_fft_build_3d_1d()

◆ poisson_fft_build_3d_0d()

◆ poisson_fft_build_2d_0d()

◆ poisson_fft_build_2d_1d()

◆ poisson_fft_build_2d_2d()

◆ poisson_fft_build_1d_1d()

◆ poisson_fft_build_1d_0d()

◆ poisson_fft_end()

◆ dpoisson_fft_solve()

◆ dpoisson_fft_solve_batch()

◆ zpoisson_fft_solve()

◆ zpoisson_fft_solve_batch()

Variable Documentation

◆ poisson_fft_kernel_none

◆ poisson_fft_kernel_sph

◆ poisson_fft_kernel_cyl

◆ poisson_fft_kernel_pla

◆ poisson_fft_kernel_nocut

◆ poisson_fft_kernel_corrected

◆ poisson_fft_kernel_hockney

◆ tol_vanishing_q